TSTP Solution File: ITP219^3 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP219^3 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n022.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 03:20:53 EDT 2023
% Result : Theorem 11.78s 12.13s
% Output : Proof 11.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 1.34/1.40 % Problem : ITP219^3 : TPTP v8.1.2. Released v8.1.0.
% 1.34/1.41 % Command : do_cvc5 %s %d
% 1.40/1.62 % Computer : n022.cluster.edu
% 1.40/1.62 % Model : x86_64 x86_64
% 1.40/1.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 1.40/1.62 % Memory : 8042.1875MB
% 1.40/1.62 % OS : Linux 3.10.0-693.el7.x86_64
% 1.40/1.62 % CPULimit : 300
% 1.40/1.62 % WCLimit : 300
% 1.40/1.62 % DateTime : Sun Aug 27 11:36:26 EDT 2023
% 1.40/1.62 % CPUTime :
% 2.62/3.00 %----Proving TH0
% 2.62/3.01 %------------------------------------------------------------------------------
% 2.62/3.01 % File : ITP219^3 : TPTP v8.1.2. Released v8.1.0.
% 2.62/3.01 % Domain : Interactive Theorem Proving
% 2.62/3.01 % Problem : Sledgehammer problem VEBT_List_Assn 00252_007651
% 2.62/3.01 % Version : [Des22] axioms.
% 2.62/3.01 % English :
% 2.62/3.01
% 2.62/3.01 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 2.62/3.01 % : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 2.62/3.01 % Source : [Des22]
% 2.62/3.01 % Names : 0062_VEBT_List_Assn_00252_007651 [Des22]
% 2.62/3.01
% 2.62/3.01 % Status : Theorem
% 2.62/3.01 % Rating : 0.31 v8.1.0
% 2.62/3.01 % Syntax : Number of formulae : 7184 (2817 unt;1397 typ; 0 def)
% 2.62/3.01 % Number of atoms : 16077 (6632 equ; 2 cnn)
% 2.62/3.01 % Maximal formula atoms : 13 ( 2 avg)
% 2.62/3.01 % Number of connectives : 55945 (1791 ~; 316 |;1080 &;46232 @)
% 2.62/3.01 % ( 0 <=>;6526 =>; 0 <=; 0 <~>)
% 2.62/3.01 % Maximal formula depth : 29 ( 6 avg)
% 2.62/3.01 % Number of types : 237 ( 236 usr)
% 2.62/3.01 % Number of type conns : 4116 (4116 >; 0 *; 0 +; 0 <<)
% 2.62/3.01 % Number of symbols : 1165 (1161 usr; 89 con; 0-6 aty)
% 2.62/3.01 % Number of variables : 16777 ( 981 ^;15414 !; 382 ?;16777 :)
% 2.62/3.01 % SPC : TH0_THM_EQU_NAR
% 2.62/3.01
% 2.62/3.01 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2.62/3.01 % from the van Emde Boas Trees session in the Archive of Formal
% 2.62/3.01 % proofs -
% 2.62/3.01 % www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 2.62/3.01 % 2022-02-17 17:07:01.933
% 2.62/3.01 %------------------------------------------------------------------------------
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% 2.62/3.01 bNF_Ca8459412986667044542atLess: set_Pr1261947904930325089at_nat ).
% 2.62/3.01
% 2.62/3.01 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,
% 2.62/3.01 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 ).
% 2.62/3.01
% 2.62/3.01 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,
% 2.62/3.01 bNF_re3461391660133120880nt_rat: ( int > int > $o ) > ( ( int > product_prod_int_int ) > ( int > rat ) > $o ) > ( int > int > product_prod_int_int ) > ( int > int > rat ) > $o ).
% 2.62/3.01
% 2.62/3.01 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,
% 2.62/3.01 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 ).
% 2.62/3.01
% 2.62/3.01 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,
% 2.62/3.01 bNF_re2214769303045360666nt_rat: ( int > int > $o ) > ( product_prod_int_int > rat > $o ) > ( int > product_prod_int_int ) > ( int > rat ) > $o ).
% 2.62/3.01
% 2.62/3.01 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,
% 2.62/3.01 bNF_re578469030762574527_nat_o: ( nat > nat > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_Eo_001_Eo,type,
% 2.62/3.01 bNF_re4705727531993890431at_o_o: ( nat > nat > $o ) > ( $o > $o > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
% 2.62/3.01
% 2.62/3.01 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,
% 2.62/3.01 bNF_re6830278522597306478at_int: ( nat > nat > $o ) > ( product_prod_nat_nat > int > $o ) > ( nat > product_prod_nat_nat ) > ( nat > int ) > $o ).
% 2.62/3.01
% 2.62/3.01 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,
% 2.62/3.01 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 ).
% 2.62/3.01
% 2.62/3.01 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,
% 2.62/3.01 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 ).
% 2.62/3.01
% 2.62/3.01 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,
% 2.62/3.01 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 ).
% 2.62/3.01
% 2.62/3.01 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,
% 2.62/3.01 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 ).
% 2.62/3.01
% 2.62/3.01 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,
% 2.62/3.01 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 ).
% 2.62/3.01
% 2.62/3.01 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,
% 2.62/3.01 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 ).
% 2.62/3.01
% 2.62/3.01 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,
% 2.62/3.01 bNF_re6644619430987730960nt_o_o: ( product_prod_nat_nat > int > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ).
% 2.62/3.01
% 2.62/3.01 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,
% 2.62/3.01 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 ).
% 2.62/3.01
% 2.62/3.01 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,
% 2.62/3.01 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 ).
% 2.62/3.01
% 2.62/3.01 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,
% 2.62/3.01 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 ).
% 2.62/3.01
% 2.62/3.01 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,
% 2.62/3.01 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 ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.62/3.01 bNF_re2241393799969408733at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_BNF__Wellorder__Constructions_OordIso_001_Eo_001_Eo,type,
% 2.62/3.01 bNF_We2654380646378065620so_o_o: set_Pr1932065953672099015od_o_o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_BNF__Wellorder__Constructions_OordIso_001t__Nat__Onat_001t__Nat__Onat,type,
% 2.62/3.01 bNF_We5258908940166488438at_nat: set_Pr4329608150637261639at_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_BNF__Wellorder__Constructions_OordLess_001_Eo_001t__Nat__Onat,type,
% 2.62/3.01 bNF_We8182288985678559134_o_nat: set_Pr457366540195662369at_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_BNF__Wellorder__Relation_Owo__rel_001t__Nat__Onat,type,
% 2.62/3.01 bNF_We3818239936649020644el_nat: set_Pr1261947904930325089at_nat > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Binomial_Obinomial,type,
% 2.62/3.01 binomial: nat > nat > nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Bit__Operations_Oand__int__rel,type,
% 2.62/3.01 bit_and_int_rel: product_prod_int_int > product_prod_int_int > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Bit__Operations_Oconcat__bit,type,
% 2.62/3.01 bit_concat_bit: nat > int > int > int ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oand_001t__Int__Oint,type,
% 2.62/3.01 bit_se725231765392027082nd_int: int > int > int ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Omask_001t__Nat__Onat,type,
% 2.62/3.01 bit_se2002935070580805687sk_nat: nat > nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Otake__bit_001t__Int__Oint,type,
% 2.62/3.01 bit_se2923211474154528505it_int: nat > int > int ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Otake__bit_001t__Nat__Onat,type,
% 2.62/3.01 bit_se2925701944663578781it_nat: nat > nat > nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Bit__Operations_Osemiring__bits__class_Obit_001t__Int__Oint,type,
% 2.62/3.01 bit_se1146084159140164899it_int: int > nat > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Code__Numeral_Obit__cut__integer,type,
% 2.62/3.01 code_bit_cut_integer: code_integer > produc6271795597528267376eger_o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Code__Numeral_Odivmod__abs,type,
% 2.62/3.01 code_divmod_abs: code_integer > code_integer > produc8923325533196201883nteger ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Code__Numeral_Odivmod__integer,type,
% 2.62/3.01 code_divmod_integer: code_integer > code_integer > produc8923325533196201883nteger ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Code__Numeral_Onat__of__integer,type,
% 2.62/3.01 code_nat_of_integer: code_integer > nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Code__Numeral_Onatural_Onat__of__natural,type,
% 2.62/3.01 code_nat_of_natural: code_natural > nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Code__Numeral_Onatural_Onatural__of__nat,type,
% 2.62/3.01 code_natural_of_nat: nat > code_natural ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Complete__Lattices_OInf__class_OInf_001t__Nat__Onat,type,
% 2.62/3.01 complete_Inf_Inf_nat: set_nat > nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Complete__Lattices_OInf__class_OInf_001t__Set__Oset_It__Nat__Onat_J,type,
% 2.62/3.01 comple7806235888213564991et_nat: set_set_nat > set_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Nat__Onat,type,
% 2.62/3.01 complete_Sup_Sup_nat: set_nat > nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Divides_Oadjust__div,type,
% 2.62/3.01 adjust_div: product_prod_int_int > int ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Divides_Odivmod__nat,type,
% 2.62/3.01 divmod_nat: nat > nat > product_prod_nat_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Divides_Oeucl__rel__int,type,
% 2.62/3.01 eucl_rel_int: int > int > product_prod_int_int > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux_001t__Code____Numeral__Ointeger,type,
% 2.62/3.01 unique5706413561485394159nteger: produc8923325533196201883nteger > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux_001t__Int__Oint,type,
% 2.62/3.01 unique6319869463603278526ux_int: product_prod_int_int > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux_001t__Nat__Onat,type,
% 2.62/3.01 unique6322359934112328802ux_nat: product_prod_nat_nat > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod_001t__Code____Numeral__Ointeger,type,
% 2.62/3.01 unique3479559517661332726nteger: num > num > produc8923325533196201883nteger ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod_001t__Int__Oint,type,
% 2.62/3.01 unique5052692396658037445od_int: num > num > product_prod_int_int ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod_001t__Nat__Onat,type,
% 2.62/3.01 unique5055182867167087721od_nat: num > num > product_prod_nat_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Code____Numeral__Ointeger,type,
% 2.62/3.01 unique4921790084139445826nteger: num > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Int__Oint,type,
% 2.62/3.01 unique5024387138958732305ep_int: num > product_prod_int_int > product_prod_int_int ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Nat__Onat,type,
% 2.62/3.01 unique5026877609467782581ep_nat: num > product_prod_nat_nat > product_prod_nat_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Nat__Onat,type,
% 2.62/3.01 semiri1408675320244567234ct_nat: nat > nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Rat__Orat,type,
% 2.62/3.01 inverse_inverse_rat: rat > rat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Filter_Oat__top_001t__Nat__Onat,type,
% 2.62/3.01 at_top_nat: filter_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Filter_Ocofinite_001t__Nat__Onat,type,
% 2.62/3.01 cofinite_nat: filter_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Filter_Oeventually_001t__Nat__Onat,type,
% 2.62/3.01 eventually_nat: ( nat > $o ) > filter_nat > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Filter_Oeventually_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.62/3.01 eventu1038000079068216329at_nat: ( product_prod_nat_nat > $o ) > filter1242075044329608583at_nat > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Filter_Ofilterlim_001t__Nat__Onat_001t__Nat__Onat,type,
% 2.62/3.01 filterlim_nat_nat: ( nat > nat ) > filter_nat > filter_nat > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Filter_Ofilterlim_001t__Nat__Onat_001t__Set__Oset_It__Nat__Onat_J,type,
% 2.62/3.01 filter3212408913953519116et_nat: ( nat > set_nat ) > filter_set_nat > filter_nat > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Filter_Ofinite__subsets__at__top_001t__Nat__Onat,type,
% 2.62/3.01 finite3254316476582989077op_nat: set_nat > filter_set_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Filter_Ofrequently_001t__Nat__Onat,type,
% 2.62/3.01 frequently_nat: ( nat > $o ) > filter_nat > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Filter_Oprod__filter_001t__Nat__Onat_001t__Nat__Onat,type,
% 2.62/3.01 prod_filter_nat_nat: filter_nat > filter_nat > filter1242075044329608583at_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Finite__Set_Ocard_001t__Nat__Onat,type,
% 2.62/3.01 finite_card_nat: set_nat > nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Finite__Set_Ofinite_001t__Code____Numeral__Ointeger,type,
% 2.62/3.01 finite6017078050557962740nteger: set_Code_integer > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Finite__Set_Ofinite_001t__Nat__Onat,type,
% 2.62/3.01 finite_finite_nat: set_nat > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.62/3.01 finite6177210948735845034at_nat: set_Pr1261947904930325089at_nat > $o ).
% 2.62/3.01
% 2.62/3.01 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,
% 2.62/3.01 comp_C8797469213163452608nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Fun_Ocomp_001_Eo_001_Eo_001t__Int__Oint,type,
% 2.62/3.01 comp_o_o_int: ( $o > $o ) > ( int > $o ) > int > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Fun_Ocomp_001_Eo_001_Eo_001t__Nat__Onat,type,
% 2.62/3.01 comp_o_o_nat: ( $o > $o ) > ( nat > $o ) > nat > $o ).
% 2.62/3.01
% 2.62/3.01 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,
% 2.62/3.01 comp_C1593894019821074884nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Fun_Oid_001_Eo,type,
% 2.62/3.01 id_o: $o > $o ).
% 2.62/3.01
% 2.62/3.01 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,
% 2.62/3.01 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 ).
% 2.62/3.01
% 2.62/3.01 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,
% 2.62/3.01 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 ).
% 2.62/3.01
% 2.62/3.01 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,
% 2.62/3.01 map_fu4826362097070443709at_o_o: ( int > product_prod_nat_nat ) > ( $o > $o ) > ( product_prod_nat_nat > $o ) > int > $o ).
% 2.62/3.01
% 2.62/3.01 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,
% 2.62/3.01 map_fu3667384564859982768at_int: ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > int ) > ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ).
% 2.62/3.01
% 2.62/3.01 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,
% 2.62/3.01 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 ).
% 2.62/3.01
% 2.62/3.01 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,
% 2.62/3.01 map_fu5673905371560938248nt_rat: ( rat > product_prod_int_int ) > ( product_prod_int_int > rat ) > ( product_prod_int_int > product_prod_int_int ) > rat > rat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Fun_Ostrict__mono__on_001t__Nat__Onat_001t__Nat__Onat,type,
% 2.62/3.01 strict1292158309912662752at_nat: ( nat > nat ) > set_nat > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Fun__Def_Omax__strict,type,
% 2.62/3.01 fun_max_strict: set_Pr4329608150637261639at_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Fun__Def_Omax__weak,type,
% 2.62/3.01 fun_max_weak: set_Pr4329608150637261639at_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Fun__Def_Omin__strict,type,
% 2.62/3.01 fun_min_strict: set_Pr4329608150637261639at_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Fun__Def_Omin__weak,type,
% 2.62/3.01 fun_min_weak: set_Pr4329608150637261639at_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Fun__Def_Opair__leq,type,
% 2.62/3.01 fun_pair_leq: set_Pr8693737435421807431at_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Fun__Def_Opair__less,type,
% 2.62/3.01 fun_pair_less: set_Pr8693737435421807431at_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Fun__Def_Oreduction__pair_001t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.62/3.01 fun_re7357418987779152907at_nat: produc4193628355235574503at_nat > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Fun__Def_Oreduction__pair_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.62/3.01 fun_re2478310338295953701at_nat: produc1319942482725812455at_nat > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_GCD_OGcd__class_OGcd_001t__Int__Oint,type,
% 2.62/3.01 gcd_Gcd_int: set_int > int ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_GCD_OGcd__class_OGcd_001t__Nat__Onat,type,
% 2.62/3.01 gcd_Gcd_nat: set_nat > nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_GCD_OGcd__class_OLcm_001t__Int__Oint,type,
% 2.62/3.01 gcd_Lcm_int: set_int > int ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_GCD_OGcd__class_OLcm_001t__Nat__Onat,type,
% 2.62/3.01 gcd_Lcm_nat: set_nat > nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_GCD_Obezw,type,
% 2.62/3.01 bezw: nat > nat > product_prod_int_int ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_GCD_Obezw__rel,type,
% 2.62/3.01 bezw_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Int__Oint,type,
% 2.62/3.01 gcd_gcd_int: int > int > int ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Nat__Onat,type,
% 2.62/3.01 gcd_gcd_nat: nat > nat > nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_GCD_Ogcd__class_Olcm_001t__Int__Oint,type,
% 2.62/3.01 gcd_lcm_int: int > int > int ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_GCD_Ogcd__class_Olcm_001t__Nat__Onat,type,
% 2.62/3.01 gcd_lcm_nat: nat > nat > nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_GCD_Ogcd__nat__rel,type,
% 2.62/3.01 gcd_nat_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Oabs__class_Oabs_001t__Code____Numeral__Ointeger,type,
% 2.62/3.01 abs_abs_Code_integer: code_integer > code_integer ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Oabs__class_Oabs_001t__Int__Oint,type,
% 2.62/3.01 abs_abs_int: int > int ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Oabs__class_Oabs_001t__Rat__Orat,type,
% 2.62/3.01 abs_abs_rat: rat > rat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Ominus__class_Ominus_001t__Assertions__Oassn,type,
% 2.62/3.01 minus_minus_assn: assn > assn > assn ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Ominus__class_Ominus_001t__Code____Numeral__Ointeger,type,
% 2.62/3.01 minus_8373710615458151222nteger: code_integer > code_integer > code_integer ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Ominus__class_Ominus_001t__Int__Oint,type,
% 2.62/3.01 minus_minus_int: int > int > int ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Ominus__class_Ominus_001t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.62/3.01 minus_4286766774447292334at_nat: multis2468970476368604999at_nat > multis2468970476368604999at_nat > multis2468970476368604999at_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type,
% 2.62/3.01 minus_minus_nat: nat > nat > nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Ominus__class_Ominus_001t__Rat__Orat,type,
% 2.62/3.01 minus_minus_rat: rat > rat > rat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_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_J,type,
% 2.62/3.01 minus_1801376950450012436_nat_o: set_Pr4532377907799695533_nat_o > set_Pr4532377907799695533_nat_o > set_Pr4532377907799695533_nat_o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_I_Eo_J,type,
% 2.62/3.01 minus_minus_set_o: set_o > set_o > set_o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Int__Oint_J,type,
% 2.62/3.01 minus_minus_set_int: set_int > set_int > set_int ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Nat__Onat_J,type,
% 2.62/3.01 minus_minus_set_nat: set_nat > set_nat > set_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J_J,type,
% 2.62/3.01 minus_2301194108115264760n_assn: set_Pr5949110396991348497n_assn > set_Pr5949110396991348497n_assn > set_Pr5949110396991348497n_assn ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.62/3.01 minus_1356011639430497352at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Ominus__class_Ominus_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,
% 2.62/3.01 minus_3314409938677909166at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_Itf__c_J,type,
% 2.62/3.01 minus_minus_set_c: set_c > set_c > set_c ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_Itf__d_J,type,
% 2.62/3.01 minus_minus_set_d: set_d > set_d > set_d ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Oone__class_Oone_001t__Assertions__Oassn,type,
% 2.62/3.01 one_one_assn: assn ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Oone__class_Oone_001t__Code____Numeral__Ointeger,type,
% 2.62/3.01 one_one_Code_integer: code_integer ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Oone__class_Oone_001t__Code____Numeral__Onatural,type,
% 2.62/3.01 one_one_Code_natural: code_natural ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Oone__class_Oone_001t__Int__Oint,type,
% 2.62/3.01 one_one_int: int ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
% 2.62/3.01 one_one_nat: nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Oone__class_Oone_001t__Rat__Orat,type,
% 2.62/3.01 one_one_rat: rat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Oplus__class_Oplus_001t__Code____Numeral__Ointeger,type,
% 2.62/3.01 plus_p5714425477246183910nteger: code_integer > code_integer > code_integer ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Oplus__class_Oplus_001t__Code____Numeral__Onatural,type,
% 2.62/3.01 plus_p4538020629002901425atural: code_natural > code_natural > code_natural ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Oplus__class_Oplus_001t__Int__Oint,type,
% 2.62/3.01 plus_plus_int: int > int > int ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Oplus__class_Oplus_001t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.62/3.01 plus_p7104986032573967614at_nat: multis2468970476368604999at_nat > multis2468970476368604999at_nat > multis2468970476368604999at_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat,type,
% 2.62/3.01 plus_plus_nat: nat > nat > nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Oplus__class_Oplus_001t__Num__Onum,type,
% 2.62/3.01 plus_plus_num: num > num > num ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Oplus__class_Oplus_001t__Rat__Orat,type,
% 2.62/3.01 plus_plus_rat: rat > rat > rat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Osgn__class_Osgn_001t__Code____Numeral__Ointeger,type,
% 2.62/3.01 sgn_sgn_Code_integer: code_integer > code_integer ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Osgn__class_Osgn_001t__Int__Oint,type,
% 2.62/3.01 sgn_sgn_int: int > int ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Osgn__class_Osgn_001t__Rat__Orat,type,
% 2.62/3.01 sgn_sgn_rat: rat > rat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Otimes__class_Otimes_001t__Assertions__Oassn,type,
% 2.62/3.01 times_times_assn: assn > assn > assn ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Otimes__class_Otimes_001t__Code____Numeral__Ointeger,type,
% 2.62/3.01 times_3573771949741848930nteger: code_integer > code_integer > code_integer ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Otimes__class_Otimes_001t__Code____Numeral__Onatural,type,
% 2.62/3.01 times_2397367101498566445atural: code_natural > code_natural > code_natural ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Otimes__class_Otimes_001t__Int__Oint,type,
% 2.62/3.01 times_times_int: int > int > int ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Otimes__class_Otimes_001t__Nat__Onat,type,
% 2.62/3.01 times_times_nat: nat > nat > nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Otimes__class_Otimes_001t__Rat__Orat,type,
% 2.62/3.01 times_times_rat: rat > rat > rat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Assertions__Oassn,type,
% 2.62/3.01 uminus_uminus_assn: assn > assn ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Code____Numeral__Ointeger,type,
% 2.62/3.01 uminus1351360451143612070nteger: code_integer > code_integer ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Int__Oint,type,
% 2.62/3.01 uminus_uminus_int: int > int ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Rat__Orat,type,
% 2.62/3.01 uminus_uminus_rat: rat > rat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Ozero__class_Ozero_001t__Code____Numeral__Ointeger,type,
% 2.62/3.01 zero_z3403309356797280102nteger: code_integer ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Ozero__class_Ozero_001t__Code____Numeral__Onatural,type,
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% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Ozero__class_Ozero_001t__Int__Oint,type,
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% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Ozero__class_Ozero_001t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
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% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 2.62/3.01 zero_zero_nat: nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups_Ozero__class_Ozero_001t__Rat__Orat,type,
% 2.62/3.01 zero_zero_rat: rat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Nat__Onat_001t__Nat__Onat,type,
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% 2.62/3.01
% 2.62/3.01 thf(sy_c_Heap_Oheap_Olim_001t__Product____Type__Ounit,type,
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% 2.62/3.01
% 2.62/3.01 thf(sy_c_Heap__Time__Monad_OHeap_OHeap_001t__Product____Type__Ounit,type,
% 2.62/3.01 heap_T6183433275982383450t_unit: ( heap_e7401611519738050253t_unit > option8956607266484857688it_nat ) > heap_T5738788834812785303t_unit ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Heap__Time__Monad_Oexecute_001t__Product____Type__Ounit,type,
% 2.62/3.01 heap_T875086893843062177t_unit: heap_T5738788834812785303t_unit > heap_e7401611519738050253t_unit > option8956607266484857688it_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Heap__Time__Monad_Owait,type,
% 2.62/3.01 heap_Time_wait: nat > heap_T5738788834812785303t_unit ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Hoare__Triple_Ohoare__triple_001t__Product____Type__Ounit,type,
% 2.62/3.01 hoare_8945653483474564448t_unit: assn > heap_T5738788834812785303t_unit > ( product_unit > assn ) > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Hoare__Triple_Onew__addrs,type,
% 2.62/3.01 hoare_new_addrs: heap_e7401611519738050253t_unit > set_nat > heap_e7401611519738050253t_unit > set_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_If_001t__Assertions__Oassn,type,
% 2.62/3.01 if_assn: $o > assn > assn > assn ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_If_001t__Code____Numeral__Ointeger,type,
% 2.62/3.01 if_Code_integer: $o > code_integer > code_integer > code_integer ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_If_001t__Filter__Ofilter_It__Nat__Onat_J,type,
% 2.62/3.01 if_filter_nat: $o > filter_nat > filter_nat > filter_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_If_001t__Int__Oint,type,
% 2.62/3.01 if_int: $o > int > int > int ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_If_001t__List__Olist_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_J,type,
% 2.62/3.01 if_lis2904118647880296857_nat_o: $o > list_P7985473006766602707_nat_o > list_P7985473006766602707_nat_o > list_P7985473006766602707_nat_o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_If_001t__List__Olist_It__Int__Oint_J,type,
% 2.62/3.01 if_list_int: $o > list_int > list_int > list_int ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_If_001t__List__Olist_It__Nat__Onat_J,type,
% 2.62/3.01 if_list_nat: $o > list_nat > list_nat > list_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_If_001t__List__Olist_It__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J_J,type,
% 2.62/3.01 if_lis7173127979115136509n_assn: $o > list_P8527749157015355191n_assn > list_P8527749157015355191n_assn > list_P8527749157015355191n_assn ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_If_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.62/3.01 if_lis9186351972506106189at_nat: $o > list_P6011104703257516679at_nat > list_P6011104703257516679at_nat > list_P6011104703257516679at_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_If_001t__List__Olist_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,
% 2.62/3.01 if_lis7508161100780771379at_nat: $o > list_P5464809261938338413at_nat > list_P5464809261938338413at_nat > list_P5464809261938338413at_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_If_001t__Nat__Onat,type,
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% 2.62/3.01
% 2.62/3.01 thf(sy_c_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
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% 2.62/3.01
% 2.62/3.01 thf(sy_c_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 2.62/3.01 if_Pro6119634080678213985nteger: $o > produc8923325533196201883nteger > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
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% 2.62/3.01
% 2.62/3.01 thf(sy_c_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 2.62/3.01
% 2.62/3.01 thf(sy_c_If_001t__Set__Oset_It__Int__Oint_J,type,
% 2.62/3.01 if_set_int: $o > set_int > set_int > set_int ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_If_001t__Set__Oset_It__Nat__Onat_J,type,
% 2.62/3.01 if_set_nat: $o > set_nat > set_nat > set_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Infinite__Set_Owellorder__class_Oenumerate_001t__Nat__Onat,type,
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% 2.62/3.01
% 2.62/3.01 thf(sy_c_Int_OAbs__Integ,type,
% 2.62/3.01 abs_Integ: product_prod_nat_nat > int ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Int_ORep__Integ,type,
% 2.62/3.01 rep_Integ: int > product_prod_nat_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Int_Ointrel,type,
% 2.62/3.01 intrel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Int_Onat,type,
% 2.62/3.01 nat2: int > nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Int_Opcr__int,type,
% 2.62/3.01 pcr_int: product_prod_nat_nat > int > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Rat__Orat,type,
% 2.62/3.01 ring_1_of_int_rat: int > rat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Assertions__Oassn,type,
% 2.62/3.01 inf_inf_assn: assn > assn > assn ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Filter__Ofilter_It__Nat__Onat_J,type,
% 2.62/3.01 inf_inf_filter_nat: filter_nat > filter_nat > filter_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Int__Oint,type,
% 2.62/3.01 inf_inf_int: int > int > int ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Nat__Onat,type,
% 2.62/3.01 inf_inf_nat: nat > nat > nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_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_J,type,
% 2.62/3.01 inf_in1906310914598751387_nat_o: set_Pr4532377907799695533_nat_o > set_Pr4532377907799695533_nat_o > set_Pr4532377907799695533_nat_o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_I_Eo_J,type,
% 2.62/3.01 inf_inf_set_o: set_o > set_o > set_o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Int__Oint_J,type,
% 2.62/3.01 inf_inf_set_int: set_int > set_int > set_int ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Nat__Onat_J,type,
% 2.62/3.01 inf_inf_set_nat: set_nat > set_nat > set_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.62/3.01 inf_in2572325071724192079at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 2.62/3.01
% 2.62/3.01 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,
% 2.62/3.01 inf_in7913087082777306421at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Nat__Onat,type,
% 2.62/3.01 semila1623282765462674594er_nat: ( nat > nat > nat ) > nat > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Lattices_Osup__class_Osup_001t__Assertions__Oassn,type,
% 2.62/3.01 sup_sup_assn: assn > assn > assn ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Lattices_Osup__class_Osup_001t__Filter__Ofilter_It__Nat__Onat_J,type,
% 2.62/3.01 sup_sup_filter_nat: filter_nat > filter_nat > filter_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Lattices_Osup__class_Osup_001t__Int__Oint,type,
% 2.62/3.01 sup_sup_int: int > int > int ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Lattices_Osup__class_Osup_001t__Nat__Onat,type,
% 2.62/3.01 sup_sup_nat: nat > nat > nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_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_J,type,
% 2.62/3.01 sup_su5209123915105501825_nat_o: set_Pr4532377907799695533_nat_o > set_Pr4532377907799695533_nat_o > set_Pr4532377907799695533_nat_o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_I_Eo_J,type,
% 2.62/3.01 sup_sup_set_o: set_o > set_o > set_o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Int__Oint_J,type,
% 2.62/3.01 sup_sup_set_int: set_int > set_int > set_int ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Nat__Onat_J,type,
% 2.62/3.01 sup_sup_set_nat: set_nat > set_nat > set_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
% 2.62/3.01 sup_su5769328420594410459od_o_o: set_Product_prod_o_o > set_Product_prod_o_o > set_Product_prod_o_o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J_J,type,
% 2.62/3.01 sup_su1735938885662425829n_assn: set_Pr5949110396991348497n_assn > set_Pr5949110396991348497n_assn > set_Pr5949110396991348497n_assn ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.62/3.01 sup_su6327502436637775413at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_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_Mt__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,
% 2.62/3.01 sup_su6664651903789602459at_nat: set_Pr5564308138774400199at_nat > set_Pr5564308138774400199at_nat > set_Pr5564308138774400199at_nat ).
% 2.62/3.01
% 2.62/3.01 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,
% 2.62/3.01 sup_su5525570899277871387at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 2.62/3.01 sup_su3642409539654194069at_nat: set_se7855581050983116737at_nat > set_se7855581050983116737at_nat > set_se7855581050983116737at_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Nat__Onat,type,
% 2.62/3.01 lattic8265883725875713057ax_nat: set_nat > nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Oall__interval__int,type,
% 2.62/3.01 all_interval_int: ( int > $o ) > int > int > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Oall__interval__nat,type,
% 2.62/3.01 all_interval_nat: ( nat > $o ) > nat > nat > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Oappend_001t__Int__Oint,type,
% 2.62/3.01 append_int: list_int > list_int > list_int ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Oappend_001t__Nat__Onat,type,
% 2.62/3.01 append_nat: list_nat > list_nat > list_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Obutlast_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,
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% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Obutlast_001t__Int__Oint,type,
% 2.62/3.01 butlast_int: list_int > list_int ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Obutlast_001t__Nat__Onat,type,
% 2.62/3.01 butlast_nat: list_nat > list_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Obutlast_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
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% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Obutlast_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Obutlast_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 2.62/3.01 butlas2561766218336428473at_nat: list_P5464809261938338413at_nat > list_P5464809261938338413at_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Obutlast_001tf__c,type,
% 2.62/3.01 butlast_c: list_c > list_c ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Obutlast_001tf__d,type,
% 2.62/3.01 butlast_d: list_d > list_d ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Ocoset_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,
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% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Ocoset_001_Eo,type,
% 2.62/3.01 coset_o: list_o > set_o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Ocoset_001t__Int__Oint,type,
% 2.62/3.01 coset_int: list_int > set_int ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Ocoset_001t__Nat__Onat,type,
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% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Ocoset_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
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% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Ocoset_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Ocoset_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
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% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Ocount__list_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,
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% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Ocount__list_001t__Int__Oint,type,
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% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Ocount__list_001t__Nat__Onat,type,
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% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Ocount__list_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 2.62/3.01 count_2530312006313534765n_assn: list_P8527749157015355191n_assn > produc6575502325842934193n_assn > nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Ocount__list_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.62/3.01 count_4203492906077236349at_nat: list_P6011104703257516679at_nat > product_prod_nat_nat > nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Ocount__list_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 2.62/3.01 count_1483299019173949923at_nat: list_P5464809261938338413at_nat > produc3843707927480180839at_nat > nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Odistinct_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,
% 2.62/3.01 distin299582740263731014_nat_o: list_P7985473006766602707_nat_o > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Odistinct_001_Eo,type,
% 2.62/3.01 distinct_o: list_o > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Odistinct_001t__Code____Numeral__Ointeger,type,
% 2.62/3.01 distin1543349897113766820nteger: list_Code_integer > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Odistinct_001t__Int__Oint,type,
% 2.62/3.01 distinct_int: list_int > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Odistinct_001t__Nat__Onat,type,
% 2.62/3.01 distinct_nat: list_nat > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Odistinct_001t__Num__Onum,type,
% 2.62/3.01 distinct_num: list_num > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Odistinct_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 2.62/3.01 distin4809818325527169450n_assn: list_P8527749157015355191n_assn > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Odistinct_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 2.62/3.01 distin3744728255968310194nt_int: list_P5707943133018811711nt_int > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Odistinct_001t__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J,type,
% 2.62/3.01 distin7922579275477506902nt_nat: list_P8198026277950538467nt_nat > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Odistinct_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
% 2.62/3.01 distin2745374544067255638at_int: list_P3521021558325789923at_int > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Odistinct_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.62/3.01 distin6923225563576452346at_nat: list_P6011104703257516679at_nat > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Odistinct_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 2.62/3.01 distin5355857245021852384at_nat: list_P5464809261938338413at_nat > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Odistinct_001tf__c,type,
% 2.62/3.01 distinct_c: list_c > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Odistinct_001tf__d,type,
% 2.62/3.01 distinct_d: list_d > $o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Odrop_001t__Nat__Onat,type,
% 2.62/3.01 drop_nat: nat > list_nat > list_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Oenumerate_001t__Int__Oint,type,
% 2.62/3.01 enumerate_int: nat > list_int > list_P3521021558325789923at_int ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Oenumerate_001t__Nat__Onat,type,
% 2.62/3.01 enumerate_nat: nat > list_nat > list_P6011104703257516679at_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Oenumerate_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 2.62/3.01 enumer9200277086812776726n_assn: nat > list_P8527749157015355191n_assn > list_P7711101519850957926n_assn ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Oenumerate_001tf__c,type,
% 2.62/3.01 enumerate_c: nat > list_c > list_P2993859830824179253_nat_c ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Oenumerate_001tf__d,type,
% 2.62/3.01 enumerate_d: nat > list_d > list_P3064893870870525238_nat_d ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Ofilter_001t__Nat__Onat,type,
% 2.62/3.01 filter_nat2: ( nat > $o ) > list_nat > list_nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Ofold_001t__Int__Oint_001t__Int__Oint,type,
% 2.62/3.01 fold_int_int: ( int > int > int ) > list_int > int > int ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Ofold_001t__Nat__Onat_001t__Nat__Onat,type,
% 2.62/3.01 fold_nat_nat: ( nat > nat > nat ) > list_nat > nat > nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Ofoldl_001t__Assertions__Oassn_001t__Assertions__Oassn,type,
% 2.62/3.01 foldl_assn_assn: ( assn > assn > assn ) > assn > list_assn > assn ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Ofoldl_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 2.62/3.01 foldl_1542389171486570077nteger: ( code_integer > code_integer > code_integer ) > code_integer > list_Code_integer > code_integer ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Ofoldl_001t__Int__Oint_001t__Int__Oint,type,
% 2.62/3.01 foldl_int_int: ( int > int > int ) > int > list_int > int ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Ofoldl_001t__Nat__Onat_001t__Nat__Onat,type,
% 2.62/3.01 foldl_nat_nat: ( nat > nat > nat ) > nat > list_nat > nat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Ofoldl_001t__Rat__Orat_001t__Rat__Orat,type,
% 2.62/3.01 foldl_rat_rat: ( rat > rat > rat ) > rat > list_rat > rat ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Ofoldl_001t__Set__Oset_I_Eo_J_001t__Set__Oset_I_Eo_J,type,
% 2.62/3.01 foldl_set_o_set_o: ( set_o > set_o > set_o ) > set_o > list_set_o > set_o ).
% 2.62/3.01
% 2.62/3.01 thf(sy_c_List_Ofoldl_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Int__Oint_J,type,
% 2.62/3.01 foldl_6819690284573351271et_int: ( set_int > set_int > set_int ) > set_int > list_set_int > set_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Ofoldl_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J,type,
% 2.62/3.02 foldl_4988731653086973103et_nat: ( set_nat > set_nat > set_nat ) > set_nat > list_set_nat > set_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Ofoldl_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.62/3.02 foldl_5307762784932486881at_nat: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > set_Pr1261947904930325089at_nat > list_s1210847774152347623at_nat > set_Pr1261947904930325089at_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Ofoldl_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_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,
% 2.62/3.02 foldl_4541198706405875041at_nat: ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ) > set_Pr4329608150637261639at_nat > list_s4242580248156217677at_nat > set_Pr4329608150637261639at_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Ofoldr_001t__Assertions__Oassn_001t__Assertions__Oassn,type,
% 2.62/3.02 foldr_assn_assn: ( assn > assn > assn ) > list_assn > assn > assn ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Oinsert_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,
% 2.62/3.02 insert8021100735160035049_nat_o: ( produc3658429121746597890et_nat > $o ) > list_P7985473006766602707_nat_o > list_P7985473006766602707_nat_o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Oinsert_001_Eo,type,
% 2.62/3.02 insert_o: $o > list_o > list_o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Oinsert_001t__Int__Oint,type,
% 2.62/3.02 insert_int: int > list_int > list_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Oinsert_001t__Nat__Onat,type,
% 2.62/3.02 insert_nat: nat > list_nat > list_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Oinsert_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 2.62/3.02 insert3246601298802261197n_assn: produc6575502325842934193n_assn > list_P8527749157015355191n_assn > list_P8527749157015355191n_assn ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Oinsert_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.62/3.02 insert8944034826898310173at_nat: product_prod_nat_nat > list_P6011104703257516679at_nat > list_P6011104703257516679at_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Oinsert_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 2.62/3.02 insert4149901806602606979at_nat: produc3843707927480180839at_nat > list_P5464809261938338413at_nat > list_P5464809261938338413at_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olast_001t__Nat__Onat,type,
% 2.62/3.02 last_nat: list_nat > nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olenlex_001t__Int__Oint,type,
% 2.62/3.02 lenlex_int: set_Pr958786334691620121nt_int > set_Pr765067013931698361st_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olenlex_001t__Nat__Onat,type,
% 2.62/3.02 lenlex_nat: set_Pr1261947904930325089at_nat > set_Pr3451248702717554689st_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olenlex_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 2.62/3.02 lenlex6671093235567761724n_assn: set_Pr8116311503512020807n_assn > set_Pr6863447823992824007n_assn ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olenlex_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.62/3.02 lenlex1357538814655152620at_nat: set_Pr4329608150637261639at_nat > set_Pr4333006031979791559at_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olenlex_001tf__c,type,
% 2.62/3.02 lenlex_c: set_Product_prod_c_c > set_Pr2058341694840537735list_c ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olenlex_001tf__d,type,
% 2.62/3.02 lenlex_d: set_Product_prod_d_d > set_Pr5674772971416283335list_d ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olex_001t__Int__Oint,type,
% 2.62/3.02 lex_int: set_Pr958786334691620121nt_int > set_Pr765067013931698361st_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olex_001t__Nat__Onat,type,
% 2.62/3.02 lex_nat: set_Pr1261947904930325089at_nat > set_Pr3451248702717554689st_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olex_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 2.62/3.02 lex_Pr7559194461235888923n_assn: set_Pr8116311503512020807n_assn > set_Pr6863447823992824007n_assn ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olex_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.62/3.02 lex_se2245640040323279819at_nat: set_Pr4329608150637261639at_nat > set_Pr4333006031979791559at_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olex_001tf__c,type,
% 2.62/3.02 lex_c: set_Product_prod_c_c > set_Pr2058341694840537735list_c ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olex_001tf__d,type,
% 2.62/3.02 lex_d: set_Product_prod_d_d > set_Pr5674772971416283335list_d ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olexn_001t__Int__Oint,type,
% 2.62/3.02 lexn_int: set_Pr958786334691620121nt_int > nat > set_Pr765067013931698361st_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olexn_001t__Nat__Onat,type,
% 2.62/3.02 lexn_nat: set_Pr1261947904930325089at_nat > nat > set_Pr3451248702717554689st_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olexn_001tf__c,type,
% 2.62/3.02 lexn_c: set_Product_prod_c_c > nat > set_Pr2058341694840537735list_c ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olexn_001tf__d,type,
% 2.62/3.02 lexn_d: set_Product_prod_d_d > nat > set_Pr5674772971416283335list_d ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olinorder__class_Osort__key_001t__Int__Oint_001t__Int__Oint,type,
% 2.62/3.02 linord1735203802627413978nt_int: ( int > int ) > list_int > list_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olinorder__class_Osort__key_001t__Nat__Onat_001t__Nat__Onat,type,
% 2.62/3.02 linord738340561235409698at_nat: ( nat > nat ) > list_nat > list_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Nat__Onat,type,
% 2.62/3.02 linord2614967742042102400et_nat: set_nat > list_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist_OCons_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.62/3.02 cons_nat_nat: ( nat > nat ) > list_nat_nat > list_nat_nat ).
% 2.62/3.02
% 2.62/3.02 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,
% 2.62/3.02 cons_P6219271836124797827_nat_o: ( produc3658429121746597890et_nat > $o ) > list_P7985473006766602707_nat_o > list_P7985473006766602707_nat_o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist_OCons_001_062_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Nat__Onat_J,type,
% 2.62/3.02 cons_s2538900923071588440at_nat: ( set_Pr1261947904930325089at_nat > nat ) > list_s9130966667114977576at_nat > list_s9130966667114977576at_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist_OCons_001_Eo,type,
% 2.62/3.02 cons_o: $o > list_o > list_o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist_OCons_001t__Assertions__Oassn,type,
% 2.62/3.02 cons_assn: assn > list_assn > list_assn ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist_OCons_001t__Code____Numeral__Ointeger,type,
% 2.62/3.02 cons_Code_integer: code_integer > list_Code_integer > list_Code_integer ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist_OCons_001t__Int__Oint,type,
% 2.62/3.02 cons_int: int > list_int > list_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Int__Oint_J,type,
% 2.62/3.02 cons_list_int: list_int > list_list_int > list_list_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Nat__Onat_J,type,
% 2.62/3.02 cons_list_nat: list_nat > list_list_nat > list_list_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J_J,type,
% 2.62/3.02 cons_l2423627976422276333n_assn: list_P8527749157015355191n_assn > list_l6351802567095793725n_assn > list_l6351802567095793725n_assn ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 2.62/3.02 cons_nat: nat > list_nat > list_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist_OCons_001t__Num__Onum,type,
% 2.62/3.02 cons_num: num > list_num > list_num ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 2.62/3.02 cons_P2971678138204555879n_assn: produc6575502325842934193n_assn > list_P8527749157015355191n_assn > list_P8527749157015355191n_assn ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 2.62/3.02 cons_P3334398858971670639nt_int: product_prod_int_int > list_P5707943133018811711nt_int > list_P5707943133018811711nt_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J,type,
% 2.62/3.02 cons_P7512249878480867347nt_nat: product_prod_int_nat > list_P8198026277950538467nt_nat > list_P8198026277950538467nt_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Int__Oint_Mt__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J_J,type,
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% 2.62/3.02 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
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% 2.62/3.02 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 2.62/3.02
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% 2.62/3.02
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% 2.62/3.02
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Int__Oint_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Nat__Onat_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
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% 2.62/3.02
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% 2.62/3.02 set_Pr4552580085251402108at_nat: list_P6548900253507351021at_nat > set_Pr5564308138774400199at_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_Itf__c_Mt__Int__Oint_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_Itf__c_Mt__Nat__Onat_J,type,
% 2.62/3.02 set_Pr3395872032415823530_c_nat: list_P5561950507774946575_c_nat > set_Pr6903500605879609269_c_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_Itf__c_Mtf__c_J,type,
% 2.62/3.02 set_Product_prod_c_c2: list_P267710562049004973od_c_c > set_Product_prod_c_c ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_Itf__c_Mtf__d_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_Itf__d_Mt__Int__Oint_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_Itf__d_Mt__Nat__Onat_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_Itf__d_Mtf__c_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_Itf__d_Mtf__d_J,type,
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% 2.62/3.02
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist_Oset_001tf__c,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist_Oset_001tf__d,type,
% 2.62/3.02 set_d2: list_d > set_d ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist_Otl_001t__Nat__Onat,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist__ex_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,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist__ex_001t__Int__Oint,type,
% 2.62/3.02 list_ex_int: ( int > $o ) > list_int > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist__ex_001t__Nat__Onat,type,
% 2.62/3.02 list_ex_nat: ( nat > $o ) > list_nat > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist__ex_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
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% 2.62/3.02
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist__ex_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist__ex_001tf__c,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist__ex_001tf__d,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist__update_001_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist__update_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,
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% 2.62/3.02
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist__update_001_Eo,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist__update_001t__Int__Oint,type,
% 2.62/3.02 list_update_int: list_int > nat > int > list_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist__update_001t__Nat__Onat,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist__update_001t__Product____Type__Oprod_I_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
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% 2.62/3.02
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% 2.62/3.02
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist__update_001t__Product____Type__Oprod_Itf__d_Mtf__c_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist__update_001t__Product____Type__Oprod_Itf__d_Mtf__d_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist__update_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olist__update_001tf__c,type,
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% 2.62/3.02 thf(sy_c_List_Olist__update_001tf__d,type,
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% 2.62/3.02 thf(sy_c_List_Olistrel1_001t__Int__Oint,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olistrel1_001t__Nat__Onat,type,
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% 2.62/3.02 thf(sy_c_List_Olistrel1_001tf__c,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olistrel1_001tf__d,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olistrel_001t__Int__Oint_001t__Int__Oint,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olistrel_001t__Int__Oint_001t__Nat__Onat,type,
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% 2.62/3.02
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olistrel_001t__Nat__Onat_001t__Nat__Onat,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olistrel_001t__Nat__Onat_001tf__c,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olistrel_001t__Nat__Onat_001tf__d,type,
% 2.62/3.02 listrel_nat_d: set_Pr4406443968975187932_nat_d > set_Pr9082979648927643218list_d ).
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% 2.62/3.02 thf(sy_c_List_Olistrel_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J_001t__Int__Oint,type,
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% 2.62/3.02 thf(sy_c_List_Olistrel_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J_001t__Nat__Onat,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olistrel_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olistrel_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olistrel_001tf__c_001t__Int__Oint,type,
% 2.62/3.02 listrel_c_int: set_Pr4413417460947882513_c_int > set_Pr1946635486513090599st_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olistrel_001tf__c_001t__Nat__Onat,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olistrel_001tf__c_001tf__c,type,
% 2.62/3.02 listrel_c_c: set_Product_prod_c_c > set_Pr2058341694840537735list_c ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olistrel_001tf__c_001tf__d,type,
% 2.62/3.02 listrel_c_d: set_Product_prod_c_d > set_Pr8760529213406277896list_d ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olistrel_001tf__d_001t__Int__Oint,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olistrel_001tf__d_001t__Nat__Onat,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olistrel_001tf__d_001tf__c,type,
% 2.62/3.02 listrel_d_c: set_Product_prod_d_c > set_Pr8195957489705318982list_c ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Olistrel_001tf__d_001tf__d,type,
% 2.62/3.02 listrel_d_d: set_Product_prod_d_d > set_Pr5674772971416283335list_d ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Omeasures_001t__Nat__Onat,type,
% 2.62/3.02 measures_nat: list_nat_nat > set_Pr1261947904930325089at_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Omeasures_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
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% 2.62/3.02 thf(sy_c_List_Onth_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,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Onth_001_Eo,type,
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% 2.62/3.02 thf(sy_c_List_Onth_001t__Code____Numeral__Ointeger,type,
% 2.62/3.02 nth_Code_integer: list_Code_integer > nat > code_integer ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Onth_001t__Int__Oint,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 2.62/3.02 nth_nat: list_nat > nat > nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Onth_001t__Num__Onum,type,
% 2.62/3.02 nth_num: list_num > nat > num ).
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% 2.62/3.02 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
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% 2.62/3.02 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mtf__c_J,type,
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% 2.62/3.02 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mtf__d_J,type,
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% 2.62/3.02 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
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% 2.62/3.02 thf(sy_c_List_Onth_001t__Product____Type__Oprod_Itf__c_Mtf__c_J,type,
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% 2.62/3.02 thf(sy_c_List_Onth_001t__Product____Type__Oprod_Itf__c_Mtf__d_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Onth_001t__Product____Type__Oprod_Itf__d_Mtf__d_J,type,
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% 2.62/3.02 thf(sy_c_List_Onth_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Onth_001tf__c,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Onth_001tf__d,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Onull_001t__Int__Oint,type,
% 2.62/3.02 null_int: list_int > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Onull_001t__Nat__Onat,type,
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% 2.62/3.02 thf(sy_c_List_Onull_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
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% 2.62/3.02 thf(sy_c_List_Oproduct_001t__Assertions__Oassn_001t__Assertions__Oassn,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Oproduct_001t__Int__Oint_001t__Int__Oint,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Oproduct_001t__Int__Oint_001t__Nat__Onat,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__Int__Oint,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__Nat__Onat,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Oproduct_001t__Nat__Onat_001tf__c,type,
% 2.62/3.02 product_nat_c: list_nat > list_c > list_P2993859830824179253_nat_c ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Oproduct_001t__Nat__Onat_001tf__d,type,
% 2.62/3.02 product_nat_d: list_nat > list_d > list_P3064893870870525238_nat_d ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Oproduct_001tf__c_001t__Int__Oint,type,
% 2.62/3.02 product_c_int: list_c > list_int > list_P3071867362843219819_c_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Oproduct_001tf__c_001t__Nat__Onat,type,
% 2.62/3.02 product_c_nat: list_c > list_nat > list_P5561950507774946575_c_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Oproduct_001tf__c_001tf__c,type,
% 2.62/3.02 product_c_c: list_c > list_c > list_P267710562049004973od_c_c ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Oproduct_001tf__c_001tf__d,type,
% 2.62/3.02 product_c_d: list_c > list_d > list_P338744602095350958od_c_d ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Oproduct_001tf__d_001t__Int__Oint,type,
% 2.62/3.02 product_d_int: list_d > list_int > list_P8668085978031350508_d_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Oproduct_001tf__d_001t__Nat__Onat,type,
% 2.62/3.02 product_d_nat: list_d > list_nat > list_P1934797086108301456_d_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Oproduct_001tf__d_001tf__c,type,
% 2.62/3.02 product_d_c: list_d > list_c > list_P8855433598298794092od_d_c ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Oproduct_001tf__d_001tf__d,type,
% 2.62/3.02 product_d_d: list_d > list_d > list_P8926467638345140077od_d_d ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Oremdups_001t__Nat__Onat,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Oremove1_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,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Oremove1_001_Eo,type,
% 2.62/3.02 remove1_o: $o > list_o > list_o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Oremove1_001t__Int__Oint,type,
% 2.62/3.02 remove1_int: int > list_int > list_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Oremove1_001t__Nat__Onat,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Oremove1_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Oremove1_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Oremove1_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Oremove1_001tf__c,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Oremove1_001tf__d,type,
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% 2.62/3.02 thf(sy_c_List_OremoveAll_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,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_OremoveAll_001_Eo,type,
% 2.62/3.02 removeAll_o: $o > list_o > list_o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_OremoveAll_001t__Int__Oint,type,
% 2.62/3.02 removeAll_int: int > list_int > list_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_OremoveAll_001t__Nat__Onat,type,
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% 2.62/3.02 thf(sy_c_List_OremoveAll_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_OremoveAll_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_OremoveAll_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_OremoveAll_001tf__c,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_OremoveAll_001tf__d,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Orev_001t__Int__Oint,type,
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% 2.62/3.02 thf(sy_c_List_Orev_001t__Nat__Onat,type,
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% 2.62/3.02 thf(sy_c_List_Orev_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Ozip_001t__Assertions__Oassn_001t__Assertions__Oassn,type,
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% 2.62/3.02
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% 2.62/3.02
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Ozip_001t__Nat__Onat_001t__Int__Oint,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Ozip_001t__Nat__Onat_001t__Nat__Onat,type,
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% 2.62/3.02
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Ozip_001t__Nat__Onat_001tf__c,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Ozip_001t__Nat__Onat_001tf__d,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Ozip_001tf__c_001t__Int__Oint,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Ozip_001tf__c_001t__Nat__Onat,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Ozip_001tf__c_001tf__c,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Ozip_001tf__c_001tf__d,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Ozip_001tf__d_001t__Int__Oint,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Ozip_001tf__d_001t__Nat__Onat,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Ozip_001tf__d_001tf__c,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_List_Ozip_001tf__d_001tf__d,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Misc_Obijective_001_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
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% 2.62/3.02 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,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Misc_Obijective_001t__Nat__Onat_001t__Nat__Onat,type,
% 2.62/3.02 bijective_nat_nat: set_Pr1261947904930325089at_nat > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Misc_Obijective_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
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% 2.62/3.02 thf(sy_c_Misc_Omerge_001t__Code____Numeral__Ointeger,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Misc_Omerge_001t__Int__Oint,type,
% 2.62/3.02 merge_int: list_int > list_int > list_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Misc_Omerge_001t__Nat__Onat,type,
% 2.62/3.02 merge_nat: list_nat > list_nat > list_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Misc_Omerge_001t__Num__Onum,type,
% 2.62/3.02 merge_num: list_num > list_num > list_num ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Misc_Omergesort__remdups_001t__Int__Oint,type,
% 2.62/3.02 merges1654122896337280797ps_int: list_int > list_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Misc_Omergesort__remdups_001t__Nat__Onat,type,
% 2.62/3.02 merges1656613366846331073ps_nat: list_nat > list_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Misc_Oslice_001t__Int__Oint,type,
% 2.62/3.02 slice_int: nat > nat > list_int > list_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Misc_Oslice_001t__Nat__Onat,type,
% 2.62/3.02 slice_nat: nat > nat > list_nat > list_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Misc_Oslice_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 2.62/3.02 slice_7964966981652229398n_assn: nat > nat > list_P8527749157015355191n_assn > list_P8527749157015355191n_assn ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Misc_Oslice_001tf__c,type,
% 2.62/3.02 slice_c: nat > nat > list_c > list_c ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Misc_Oslice_001tf__d,type,
% 2.62/3.02 slice_d: nat > nat > list_d > list_d ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Misc_Ozipf_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 2.62/3.02 zipf_int_int_int: ( int > int > int ) > list_int > list_int > list_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Misc_Ozipf_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat,type,
% 2.62/3.02 zipf_int_int_nat: ( int > int > nat ) > list_int > list_int > list_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Misc_Ozipf_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 2.62/3.02 zipf_i7756021159461276697n_assn: ( int > int > produc6575502325842934193n_assn ) > list_int > list_int > list_P8527749157015355191n_assn ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Misc_Ozipf_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint,type,
% 2.62/3.02 zipf_int_nat_int: ( int > nat > int ) > list_int > list_nat > list_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Misc_Ozipf_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat,type,
% 2.62/3.02 zipf_int_nat_nat: ( int > nat > nat ) > list_int > list_nat > list_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Misc_Ozipf_001t__Int__Oint_001t__Nat__Onat_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 2.62/3.02 zipf_i5995984495708165493n_assn: ( int > nat > produc6575502325842934193n_assn ) > list_int > list_nat > list_P8527749157015355191n_assn ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Misc_Ozipf_001t__Nat__Onat_001t__Int__Oint_001t__Int__Oint,type,
% 2.62/3.02 zipf_nat_int_int: ( nat > int > int ) > list_nat > list_int > list_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Misc_Ozipf_001t__Nat__Onat_001t__Int__Oint_001t__Nat__Onat,type,
% 2.62/3.02 zipf_nat_int_nat: ( nat > int > nat ) > list_nat > list_int > list_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Misc_Ozipf_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint,type,
% 2.62/3.02 zipf_nat_nat_int: ( nat > nat > int ) > list_nat > list_nat > list_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Misc_Ozipf_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 2.62/3.02 zipf_nat_nat_nat: ( nat > nat > nat ) > list_nat > list_nat > list_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Misc_Ozipf_001t__Nat__Onat_001tf__c_001t__Product____Type__Oprod_It__Nat__Onat_Mtf__c_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Misc_Ozipf_001t__Nat__Onat_001tf__d_001t__Product____Type__Oprod_It__Nat__Onat_Mtf__d_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Misc_Ozipf_001tf__c_001t__Int__Oint_001t__Product____Type__Oprod_Itf__c_Mt__Int__Oint_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Misc_Ozipf_001tf__c_001t__Nat__Onat_001t__Product____Type__Oprod_Itf__c_Mt__Nat__Onat_J,type,
% 2.62/3.02 zipf_c7084520048314076179_c_nat: ( c > nat > product_prod_c_nat ) > list_c > list_nat > list_P5561950507774946575_c_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Misc_Ozipf_001tf__c_001tf__c_001t__Product____Type__Oprod_Itf__c_Mtf__c_J,type,
% 2.62/3.02 zipf_c684006316856269033od_c_c: ( c > c > product_prod_c_c ) > list_c > list_c > list_P267710562049004973od_c_c ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Misc_Ozipf_001tf__c_001tf__d_001t__Product____Type__Oprod_Itf__c_Mtf__d_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Misc_Ozipf_001tf__d_001t__Int__Oint_001t__Product____Type__Oprod_Itf__d_Mt__Int__Oint_J,type,
% 2.62/3.02 zipf_d997717096299170253_d_int: ( d > int > product_prod_d_int ) > list_d > list_int > list_P8668085978031350508_d_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Misc_Ozipf_001tf__d_001t__Nat__Onat_001t__Product____Type__Oprod_Itf__d_Mt__Nat__Onat_J,type,
% 2.62/3.02 zipf_d7851395264309270293_d_nat: ( d > nat > product_prod_d_nat ) > list_d > list_nat > list_P1934797086108301456_d_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Misc_Ozipf_001tf__d_001tf__c_001t__Product____Type__Oprod_Itf__d_Mtf__c_J,type,
% 2.62/3.02 zipf_d1836499321508429225od_d_c: ( d > c > product_prod_d_c ) > list_d > list_c > list_P8855433598298794092od_d_c ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Misc_Ozipf_001tf__d_001tf__d_001t__Product____Type__Oprod_Itf__d_Mtf__d_J,type,
% 2.62/3.02 zipf_d1197059025479841897od_d_d: ( d > d > product_prod_d_d ) > list_d > list_d > list_P8926467638345140077od_d_d ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Multiset_Oadd__mset_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Multiset_Oms__strict,type,
% 2.62/3.02 ms_strict: set_Pr8551490117392284871at_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Multiset_Oms__weak,type,
% 2.62/3.02 ms_weak: set_Pr8551490117392284871at_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Multiset_Opw__leq,type,
% 2.62/3.02 pw_leq: multis2468970476368604999at_nat > multis2468970476368604999at_nat > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Multiset_Oset__mset_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Nat_OSuc,type,
% 2.62/3.02 suc: nat > nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Ointeger,type,
% 2.62/3.02 semiri4939895301339042750nteger: nat > code_integer ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 2.62/3.02 semiri1314217659103216013at_int: nat > int ).
% 2.62/3.02
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_I_Eo_J,type,
% 2.62/3.02 size_size_list_o: list_o > nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Assertions__Oassn_J,type,
% 2.62/3.02 size_size_list_assn: list_assn > nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Code____Numeral__Ointeger_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Int__Oint_J,type,
% 2.62/3.02 size_size_list_int: list_int > nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
% 2.62/3.02 size_size_list_nat: list_nat > nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Num__Onum_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mtf__c_J_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mtf__d_J_J,type,
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% 2.62/3.02 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_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,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_Itf__c_Mt__Nat__Onat_J_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_Itf__c_Mtf__c_J_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_Itf__c_Mtf__d_J_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_Itf__d_Mt__Int__Oint_J_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_Itf__d_Mt__Nat__Onat_J_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_Itf__d_Mtf__c_J_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_Itf__d_Mtf__d_J_J,type,
% 2.62/3.02 size_s2191833749160108505od_d_d: list_P8926467638345140077od_d_d > nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_Itf__c_J,type,
% 2.62/3.02 size_size_list_c: list_c > nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_Itf__d_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Nat_Osize__class_Osize_001t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Nat__Bijection_Olist__encode,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Nat__Bijection_Olist__encode__rel,type,
% 2.62/3.02 nat_list_encode_rel: list_nat > list_nat > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Nat__Bijection_Oprod__decode__aux,type,
% 2.62/3.02 nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Nat__Bijection_Oprod__decode__aux__rel,type,
% 2.62/3.02 nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Nat__Bijection_Oprod__encode,type,
% 2.62/3.02 nat_prod_encode: product_prod_nat_nat > nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Nat__Bijection_Oset__decode,type,
% 2.62/3.02 nat_set_decode: nat > set_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Nat__Bijection_Oset__encode,type,
% 2.62/3.02 nat_set_encode: set_nat > nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Num_OBitM,type,
% 2.62/3.02 bitM: num > num ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Num_Oinc,type,
% 2.62/3.02 inc: num > num ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Num_Onat__of__num,type,
% 2.62/3.02 nat_of_num: num > nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Code____Numeral__Ointeger,type,
% 2.62/3.02 neg_nu7757733837767384882nteger: code_integer > code_integer ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Int__Oint,type,
% 2.62/3.02 neg_nu3811975205180677377ec_int: int > int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Rat__Orat,type,
% 2.62/3.02 neg_nu3179335615603231917ec_rat: rat > rat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Num_Onum_OBit0,type,
% 2.62/3.02 bit0: num > num ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Num_Onum_OBit1,type,
% 2.62/3.02 bit1: num > num ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Num_Onum_OOne,type,
% 2.62/3.02 one: num ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Num_Onum__of__nat,type,
% 2.62/3.02 num_of_nat: nat > num ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Code____Numeral__Ointeger,type,
% 2.62/3.02 numera6620942414471956472nteger: num > code_integer ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Code____Numeral__Onatural,type,
% 2.62/3.02 numera5444537566228673987atural: num > code_natural ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Int__Oint,type,
% 2.62/3.02 numeral_numeral_int: num > int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat,type,
% 2.62/3.02 numeral_numeral_nat: num > nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Rat__Orat,type,
% 2.62/3.02 numeral_numeral_rat: num > rat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Num_Opred__numeral,type,
% 2.62/3.02 pred_numeral: num > nat ).
% 2.62/3.02
% 2.62/3.02 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,
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% 2.62/3.02
% 2.62/3.02 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,
% 2.62/3.02 some_P1914260805536162275it_nat: produc8664842809031399944it_nat > option8956607266484857688it_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Order__Relation_OunderS_001t__Nat__Onat,type,
% 2.62/3.02 order_underS_nat: set_Pr1261947904930325089at_nat > nat > set_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Order__Relation_Owell__order__on_001t__Nat__Onat,type,
% 2.62/3.02 order_2888998067076097458on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).
% 2.62/3.02
% 2.62/3.02 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_Eo_J,type,
% 2.62/3.02 bot_bo7963750851167320836at_o_o: ( produc3658429121746597890et_nat > $o ) > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Obot__class_Obot_001_062_I_Eo_M_Eo_J,type,
% 2.62/3.02 bot_bot_o_o: $o > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Int__Oint_M_Eo_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Nat__Onat_M_Eo_J,type,
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% 2.62/3.02
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Obot__class_Obot_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,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Obot__class_Obot_001t__Assertions__Oassn,type,
% 2.62/3.02 bot_bot_assn: assn ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Obot__class_Obot_001t__Filter__Ofilter_It__Nat__Onat_J,type,
% 2.62/3.02 bot_bot_filter_nat: filter_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Obot__class_Obot_001t__Nat__Onat,type,
% 2.62/3.02 bot_bot_nat: nat ).
% 2.62/3.02
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_I_Eo_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Int__Oint_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Nat__Onat_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
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% 2.62/3.02
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% 2.62/3.02
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% 2.62/3.02
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Obot__class_Obot_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,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__c_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__d_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Oless_001t__Assertions__Oassn,type,
% 2.62/3.02 ord_less_assn: assn > assn > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Oless_001t__Code____Numeral__Ointeger,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Oless_001t__Code____Numeral__Onatural,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Oless_001t__Filter__Ofilter_It__Nat__Onat_J,type,
% 2.62/3.02 ord_less_filter_nat: filter_nat > filter_nat > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Oless_001t__Int__Oint,type,
% 2.62/3.02 ord_less_int: int > int > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Oless_001t__Num__Onum,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Oless_001t__Rat__Orat,type,
% 2.62/3.02 ord_less_rat: rat > rat > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_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_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_I_Eo_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Int__Oint_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Nat__Onat_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Oless_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,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Assertions__Oassn,type,
% 2.62/3.02 ord_less_eq_assn: assn > assn > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Code____Numeral__Ointeger,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Filter__Ofilter_It__Nat__Onat_J,type,
% 2.62/3.02 ord_le2510731241096832064er_nat: filter_nat > filter_nat > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Int__Oint,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Num__Onum,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Rat__Orat,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_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_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_I_Eo_J,type,
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% 2.62/3.02
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
% 2.62/3.02 ord_le8725513860283290265nt_int: set_Pr9222295170931077689nt_int > set_Pr9222295170931077689nt_int > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
% 2.62/3.02 ord_le192195778054999463od_o_o: set_Product_prod_o_o > set_Product_prod_o_o > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J_J,type,
% 2.62/3.02 ord_le171416862856029873n_assn: set_Pr5949110396991348497n_assn > set_Pr5949110396991348497n_assn > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.62/3.02 ord_le3146513528884898305at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Oless__eq_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,
% 2.62/3.02 ord_le1268244103169919719at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__c_J,type,
% 2.62/3.02 ord_less_eq_set_c: set_c > set_c > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__d_J,type,
% 2.62/3.02 ord_less_eq_set_d: set_d > set_d > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Omax_001t__Nat__Onat,type,
% 2.62/3.02 ord_max_nat: nat > nat > nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Omin_001t__Assertions__Oassn,type,
% 2.62/3.02 ord_min_assn: assn > assn > assn ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Omin_001t__Code____Numeral__Ointeger,type,
% 2.62/3.02 ord_min_Code_integer: code_integer > code_integer > code_integer ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Omin_001t__Filter__Ofilter_It__Nat__Onat_J,type,
% 2.62/3.02 ord_min_filter_nat: filter_nat > filter_nat > filter_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Omin_001t__Int__Oint,type,
% 2.62/3.02 ord_min_int: int > int > int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Omin_001t__Nat__Onat,type,
% 2.62/3.02 ord_min_nat: nat > nat > nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Omin_001t__Num__Onum,type,
% 2.62/3.02 ord_min_num: num > num > num ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Omin_001t__Rat__Orat,type,
% 2.62/3.02 ord_min_rat: rat > rat > rat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Omin_001t__Set__Oset_I_Eo_J,type,
% 2.62/3.02 ord_min_set_o: set_o > set_o > set_o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Omin_001t__Set__Oset_It__Int__Oint_J,type,
% 2.62/3.02 ord_min_set_int: set_int > set_int > set_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Omin_001t__Set__Oset_It__Nat__Onat_J,type,
% 2.62/3.02 ord_min_set_nat: set_nat > set_nat > set_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Omin_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.62/3.02 ord_mi4194197829855655752at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oord__class_Omin_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,
% 2.62/3.02 ord_mi6693596345299712430at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oorder__class_Omono_001t__Nat__Onat_001t__Nat__Onat,type,
% 2.62/3.02 order_mono_nat_nat: ( nat > nat ) > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Oordering__top_001t__Nat__Onat,type,
% 2.62/3.02 ordering_top_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > nat > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Otop__class_Otop_001t__Assertions__Oassn,type,
% 2.62/3.02 top_top_assn: assn ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_I_Eo_J,type,
% 2.62/3.02 top_top_set_o: set_o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Nat__Onat_J,type,
% 2.62/3.02 top_top_set_nat: set_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Power_Opower__class_Opower_001t__Assertions__Oassn,type,
% 2.62/3.02 power_power_assn: assn > nat > assn ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Power_Opower__class_Opower_001t__Code____Numeral__Ointeger,type,
% 2.62/3.02 power_8256067586552552935nteger: code_integer > nat > code_integer ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Power_Opower__class_Opower_001t__Int__Oint,type,
% 2.62/3.02 power_power_int: int > nat > int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Power_Opower__class_Opower_001t__Nat__Onat,type,
% 2.62/3.02 power_power_nat: nat > nat > nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Power_Opower__class_Opower_001t__Rat__Orat,type,
% 2.62/3.02 power_power_rat: rat > nat > rat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001_062_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 2.62/3.02 produc6137756002093451184nteger: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > produc8763457246119570046nteger ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001_062_It__Code____Numeral__Onatural_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
% 2.62/3.02 produc2252593628808123835atural: ( code_natural > option6357759511663192854e_term ) > produc7822875418678951345atural > produc8731074985263844745atural ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001t__List__Olist_It__Int__Oint_J,type,
% 2.62/3.02 produc8618682346314911123st_int: ( int > int > $o ) > list_int > produc5834231552977413017st_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 2.62/3.02 produc4305682042979456191nt_int: ( int > option6357759511663192854e_term ) > product_prod_int_int > produc7773217078559923341nt_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J_001t__List__Olist_It__Nat__Onat_J,type,
% 2.62/3.02 produc4727192421694094319st_nat: ( nat > nat > $o ) > list_nat > produc254973753779126261st_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J_M_062_It__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J_M_Eo_J_J_001t__List__Olist_It__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J_J,type,
% 2.62/3.02 produc6115016301897879072n_assn: ( produc6575502325842934193n_assn > produc6575502325842934193n_assn > $o ) > list_P8527749157015355191n_assn > produc4530688714081574576n_assn ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 2.62/3.02 produc8603105652947943368nteger: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > produc1908205239877642774nteger ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_It__Code____Numeral__Onatural_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_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_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,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_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,
% 2.62/3.02 produc2245416461498447860et_nat: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > produc2732055786443039994et_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_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,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001_Eo_001_Eo,type,
% 2.62/3.02 product_Pair_o_o: $o > $o > product_prod_o_o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__Assertions__Oassn_001t__Assertions__Oassn,type,
% 2.62/3.02 produc118845697133431529n_assn: assn > assn > produc6575502325842934193n_assn ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__Code____Numeral__Ointeger_001_Eo,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__Code____Numeral__Onatural_001t__Code____Numeral__Onatural,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__Code____Numeral__Onatural_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Nat__Onat,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Set__Oset_It__Nat__Onat_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__Int__Oint_001t__Int__Oint,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__Int__Oint_001t__Nat__Onat,type,
% 2.62/3.02 product_Pair_int_nat: int > nat > product_prod_int_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__Int__Oint_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 2.62/3.02 produc3313821056773121708n_assn: int > produc6575502325842934193n_assn > produc3167338625816234618n_assn ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Int__Oint_J_001t__List__Olist_It__Int__Oint_J,type,
% 2.62/3.02 produc364263696895485585st_int: list_int > list_int > produc1186641810826059865st_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Int__Oint_J_001t__List__Olist_It__Nat__Onat_J,type,
% 2.62/3.02 produc4542114716404682293st_nat: list_int > list_nat > produc3676724955757786621st_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Int__Oint_J_001t__List__Olist_It__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J_J,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Nat__Onat_J_001t__List__Olist_It__Int__Oint_J,type,
% 2.62/3.02 produc7739558402351520821st_int: list_nat > list_int > produc8561936516282095101st_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Nat__Onat_J_001t__List__Olist_It__Nat__Onat_J,type,
% 2.62/3.02 produc2694037385005941721st_nat: list_nat > list_nat > produc1828647624359046049st_nat ).
% 2.62/3.02
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Nat__Onat_J_001t__List__Olist_Itf__c_J,type,
% 2.62/3.02 produc7723716018658481613list_c: list_nat > list_c > produc1655478831073744795list_c ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Nat__Onat_J_001t__List__Olist_Itf__d_J,type,
% 2.62/3.02 produc7723716022961710414list_d: list_nat > list_d > produc1726512871120090780list_d ).
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% 2.62/3.02 produc1996262876970182428st_int: list_P8527749157015355191n_assn > list_int > produc4164172529858598818st_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J_J_001t__List__Olist_It__Nat__Onat_J,type,
% 2.62/3.02 produc6174113896479379136st_nat: list_P8527749157015355191n_assn > list_nat > produc6654255674790325574st_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J_J_001t__List__Olist_It__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J_J,type,
% 2.62/3.02 produc3014731801419794263n_assn: list_P8527749157015355191n_assn > list_P8527749157015355191n_assn > produc337509097454979815n_assn ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__List__Olist_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 2.62/3.02 produc7536900900485677911at_nat: list_s1210847774152347623at_nat > list_s1210847774152347623at_nat > produc424102278133772007at_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__List__Olist_Itf__c_J_001t__List__Olist_It__Int__Oint_J,type,
% 2.62/3.02 produc1948897715771513579st_int: list_c > list_int > produc8499486975545879281st_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__List__Olist_Itf__c_J_001t__List__Olist_It__Nat__Onat_J,type,
% 2.62/3.02 produc6126748735280710287st_nat: list_c > list_nat > produc1766198083622830229st_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__List__Olist_Itf__c_J_001t__List__Olist_Itf__c_J,type,
% 2.62/3.02 produc5515445818230282391list_c: list_c > list_c > produc7985223085803476903list_c ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__List__Olist_Itf__c_J_001t__List__Olist_Itf__d_J,type,
% 2.62/3.02 produc5515445822533511192list_d: list_c > list_d > produc8056257125849822888list_d ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__List__Olist_Itf__d_J_001t__List__Olist_It__Int__Oint_J,type,
% 2.62/3.02 produc2615797191311421932st_int: list_d > list_int > produc9166386451085787634st_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__List__Olist_Itf__d_J_001t__List__Olist_It__Nat__Onat_J,type,
% 2.62/3.02 produc6793648210820618640st_nat: list_d > list_nat > produc2433097559162738582st_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__List__Olist_Itf__d_J_001t__List__Olist_Itf__c_J,type,
% 2.62/3.02 produc242965416994095062list_c: list_d > list_c > produc2712742684567289574list_c ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__List__Olist_Itf__d_J_001t__List__Olist_Itf__d_J,type,
% 2.62/3.02 produc242965421297323863list_d: list_d > list_d > produc2783776724613635559list_d ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_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,
% 2.62/3.02 produc4348348721325984599at_nat: multis2468970476368604999at_nat > multis2468970476368604999at_nat > produc4166570645942440679at_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Int__Oint,type,
% 2.62/3.02 product_Pair_nat_int: nat > int > product_prod_nat_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Nat__Onat,type,
% 2.62/3.02 product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 2.62/3.02 produc1553784393020010504n_assn: nat > produc6575502325842934193n_assn > produc1407301962063123414n_assn ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.62/3.02 produc487386426758144856at_nat: nat > product_prod_nat_nat > produc7248412053542808358at_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001tf__c,type,
% 2.62/3.02 product_Pair_nat_c: nat > c > product_prod_nat_c ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001tf__d,type,
% 2.62/3.02 product_Pair_nat_d: nat > d > product_prod_nat_d ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__Num__Onum_001t__Num__Onum,type,
% 2.62/3.02 product_Pair_num_num: num > num > product_prod_num_num ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_I_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__Product____Type__Oprod_I_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 2.62/3.02 produc8406175334058502835nt_int: produc7773217078559923341nt_int > produc7773217078559923341nt_int > produc2501202720802129403nt_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
% 2.62/3.02 produc7954516348491987909nteger: produc1908205239877642774nteger > produc1908205239877642774nteger > produc824974754969098637nteger ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_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_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,
% 2.62/3.02 produc1940133919992309389et_nat: produc2732055786443039994et_nat > produc2732055786443039994et_nat > produc5657529347773406293et_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
% 2.62/3.02 produc8599840265553166229et_nat: produc3925858234332021118et_nat > produc3925858234332021118et_nat > produc6830853553727218525et_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 2.62/3.02 produc7601053194514725023nt_int: produc2285326912895808259nt_int > produc2285326912895808259nt_int > produc2432570611225516007nt_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J_001t__Int__Oint,type,
% 2.62/3.02 produc6453891449406693510sn_int: produc6575502325842934193n_assn > int > produc8718178513971670540sn_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J_001t__Nat__Onat,type,
% 2.62/3.02 produc6456381919915743786sn_nat: produc6575502325842934193n_assn > nat > produc3672657496626091440sn_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 2.62/3.02 produc6128706242671166167n_assn: produc6575502325842934193n_assn > produc6575502325842934193n_assn > produc9053633027152450663n_assn ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
% 2.62/3.02 produc4480994950612372183atural: produc7822875418678951345atural > produc7822875418678951345atural > produc6756470014200349799atural ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 2.62/3.02 produc6348220600061155286at_int: product_prod_nat_nat > int > produc4196048018000912732at_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
% 2.62/3.02 produc6350711070570205562at_nat: product_prod_nat_nat > nat > produc8373899037510109440at_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.62/3.02 produc6161850002892822231at_nat: product_prod_nat_nat > product_prod_nat_nat > produc859450856879609959at_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 2.62/3.02 produc2335810615602371415at_nat: produc3843707927480180839at_nat > produc3843707927480180839at_nat > produc1906917888121415911at_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__Product____Type__Ounit_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J,type,
% 2.62/3.02 produc7133225469290080770it_nat: product_unit > produc6653097349344004940it_nat > produc8664842809031399944it_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
% 2.62/3.02 produc763777882069021527od_o_o: set_Product_prod_o_o > set_Product_prod_o_o > produc2934264451710624999od_o_o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.62/3.02 produc8517790099723286449at_nat: set_Product_prod_o_o > set_Pr1261947904930325089at_nat > produc732395585841259969at_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_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_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,
% 2.62/3.02 produc5245064249948416855at_nat: set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > produc4193628355235574503at_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.62/3.02 produc2922128104949294807at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > produc3843707927480180839at_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_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_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,
% 2.62/3.02 produc9060074326276436823at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > produc1319942482725812455at_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001tf__c_001t__Int__Oint,type,
% 2.62/3.02 product_Pair_c_int: c > int > product_prod_c_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001tf__c_001t__Nat__Onat,type,
% 2.62/3.02 product_Pair_c_nat: c > nat > product_prod_c_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001tf__c_001tf__c,type,
% 2.62/3.02 product_Pair_c_c: c > c > product_prod_c_c ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001tf__c_001tf__d,type,
% 2.62/3.02 product_Pair_c_d: c > d > product_prod_c_d ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001tf__d_001t__Int__Oint,type,
% 2.62/3.02 product_Pair_d_int: d > int > product_prod_d_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001tf__d_001t__Nat__Onat,type,
% 2.62/3.02 product_Pair_d_nat: d > nat > product_prod_d_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001tf__d_001tf__c,type,
% 2.62/3.02 product_Pair_d_c: d > c > product_prod_d_c ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OPair_001tf__d_001tf__d,type,
% 2.62/3.02 product_Pair_d_d: d > d > product_prod_d_d ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OSigma_001t__Nat__Onat_001t__Nat__Onat,type,
% 2.62/3.02 produc457027306803732586at_nat: set_nat > ( nat > set_nat ) > set_Pr1261947904930325089at_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_OUnity,type,
% 2.62/3.02 product_Unity: product_unit ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_Oapsnd_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 2.62/3.02 produc6499014454317279255nteger: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_Ocurry_001_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_Eo,type,
% 2.62/3.02 produc9098658269643458507_int_o: ( produc7773217078559923341nt_int > $o ) > ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Product__Type_Ocurry_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_Eo,type,
% 2.62/3.02 produc1217013493180205570eger_o: ( produc1908205239877642774nteger > $o ) > ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ).
% 2.62/3.02
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% 2.62/3.02
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% 2.62/3.02 image_4470545334726330049nteger: ( code_integer > code_integer ) > set_Code_integer > set_Code_integer ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Code____Numeral__Ointeger,type,
% 2.62/3.02 image_1215581382706833972nteger: ( nat > code_integer ) > set_nat > set_Code_integer ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Nat__Onat,type,
% 2.62/3.02 image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Set__Oset_It__Nat__Onat_J,type,
% 2.62/3.02 image_nat_set_nat: ( nat > set_nat ) > set_nat > set_set_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Oinsert_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,
% 2.62/3.02 insert5175938949040314269_nat_o: ( produc3658429121746597890et_nat > $o ) > set_Pr4532377907799695533_nat_o > set_Pr4532377907799695533_nat_o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Oinsert_001_Eo,type,
% 2.62/3.02 insert_o2: $o > set_o > set_o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Oinsert_001t__Int__Oint,type,
% 2.62/3.02 insert_int2: int > set_int > set_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Oinsert_001t__Nat__Onat,type,
% 2.62/3.02 insert_nat2: nat > set_nat > set_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
% 2.62/3.02 insert6201435330877294327od_o_o: product_prod_o_o > set_Product_prod_o_o > set_Product_prod_o_o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 2.62/3.02 insert5290817439147925377n_assn: produc6575502325842934193n_assn > set_Pr5949110396991348497n_assn > set_Pr5949110396991348497n_assn ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 2.62/3.02 insert5033312907999012233nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.62/3.02 insert8211810215607154385at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.62/3.02 insert5050368324300391991at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_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_Mt__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,
% 2.62/3.02 insert398606708087465655at_nat: produc1906917888121415911at_nat > set_Pr5564308138774400199at_nat > set_Pr5564308138774400199at_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 2.62/3.02 insert9069300056098147895at_nat: produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Oinsert_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.62/3.02 insert9200635055090092081at_nat: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat > set_se7855581050983116737at_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Oinsert_001tf__c,type,
% 2.62/3.02 insert_c: c > set_c > set_c ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Oinsert_001tf__d,type,
% 2.62/3.02 insert_d: d > set_d > set_d ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Ois__empty_001_Eo,type,
% 2.62/3.02 is_empty_o: set_o > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Ois__empty_001t__Int__Oint,type,
% 2.62/3.02 is_empty_int: set_int > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Ois__empty_001t__Nat__Onat,type,
% 2.62/3.02 is_empty_nat: set_nat > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Ois__empty_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 2.62/3.02 is_emp7749065762491207043n_assn: set_Pr5949110396991348497n_assn > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Ois__empty_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.62/3.02 is_emp1662574758705540307at_nat: set_Pr1261947904930325089at_nat > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Ois__empty_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 2.62/3.02 is_emp7572232645145209145at_nat: set_Pr4329608150637261639at_nat > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Ois__singleton_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,
% 2.62/3.02 is_sin5180296473474724033_nat_o: set_Pr4532377907799695533_nat_o > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Ois__singleton_001_Eo,type,
% 2.62/3.02 is_singleton_o: set_o > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Ois__singleton_001t__Int__Oint,type,
% 2.62/3.02 is_singleton_int: set_int > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Ois__singleton_001t__Nat__Onat,type,
% 2.62/3.02 is_singleton_nat: set_nat > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Ois__singleton_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.62/3.02 is_sin2850979758926227957at_nat: set_Pr1261947904930325089at_nat > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Ois__singleton_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 2.62/3.02 is_sin2937591304547752795at_nat: set_Pr4329608150637261639at_nat > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Opairwise_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,
% 2.62/3.02 pairwi2432143822833250616_nat_o: ( ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > $o ) > set_Pr4532377907799695533_nat_o > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Opairwise_001_Eo,type,
% 2.62/3.02 pairwise_o: ( $o > $o > $o ) > set_o > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Opairwise_001t__Int__Oint,type,
% 2.62/3.02 pairwise_int: ( int > int > $o ) > set_int > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Opairwise_001t__Nat__Onat,type,
% 2.62/3.02 pairwise_nat: ( nat > nat > $o ) > set_nat > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Opairwise_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.62/3.02 pairwi6357175311820755948at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > set_Pr1261947904930325089at_nat > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Opairwise_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 2.62/3.02 pairwi3222497012029234898at_nat: ( produc3843707927480180839at_nat > produc3843707927480180839at_nat > $o ) > set_Pr4329608150637261639at_nat > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Oremove_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,
% 2.62/3.02 remove4651630035290841522_nat_o: ( produc3658429121746597890et_nat > $o ) > set_Pr4532377907799695533_nat_o > set_Pr4532377907799695533_nat_o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Oremove_001_Eo,type,
% 2.62/3.02 remove_o: $o > set_o > set_o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Oremove_001t__Int__Oint,type,
% 2.62/3.02 remove_int: int > set_int > set_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Oremove_001t__Nat__Onat,type,
% 2.62/3.02 remove_nat: nat > set_nat > set_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Oremove_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 2.62/3.02 remove6142905432236673558n_assn: produc6575502325842934193n_assn > set_Pr5949110396991348497n_assn > set_Pr5949110396991348497n_assn ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Oremove_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.62/3.02 remove6466555014256735590at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Oremove_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 2.62/3.02 remove5300788332298244428at_nat: produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Othe__elem_001_Eo,type,
% 2.62/3.02 the_elem_o: set_o > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Othe__elem_001t__Int__Oint,type,
% 2.62/3.02 the_elem_int: set_int > int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Othe__elem_001t__Nat__Onat,type,
% 2.62/3.02 the_elem_nat: set_nat > nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Othe__elem_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.62/3.02 the_el2281957884133575798at_nat: set_Pr1261947904930325089at_nat > product_prod_nat_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Othe__elem_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 2.62/3.02 the_el221668144340439132at_nat: set_Pr4329608150637261639at_nat > produc3843707927480180839at_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set_Ovimage_001t__Nat__Onat_001t__Nat__Onat,type,
% 2.62/3.02 vimage_nat_nat: ( nat > nat ) > set_nat > set_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Nat__Onat,type,
% 2.62/3.02 set_fo2584398358068434914at_nat: ( nat > nat > nat ) > nat > nat > nat > nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Code____Numeral__Ointeger,type,
% 2.62/3.02 set_or189985376899183464nteger: code_integer > code_integer > set_Code_integer ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Int__Oint,type,
% 2.62/3.02 set_or1266510415728281911st_int: int > int > set_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Nat__Onat,type,
% 2.62/3.02 set_or1269000886237332187st_nat: nat > nat > set_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Code____Numeral__Ointeger,type,
% 2.62/3.02 set_or8404916559141939852nteger: code_integer > code_integer > set_Code_integer ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Int__Oint,type,
% 2.62/3.02 set_or4662586982721622107an_int: int > int > set_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Nat__Onat,type,
% 2.62/3.02 set_or4665077453230672383an_nat: nat > nat > set_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Nat__Onat,type,
% 2.62/3.02 set_ord_atLeast_nat: nat > set_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Nat__Onat,type,
% 2.62/3.02 set_ord_atMost_nat: nat > set_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Code____Numeral__Ointeger,type,
% 2.62/3.02 set_or2715278749043346189nteger: code_integer > code_integer > set_Code_integer ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Int__Oint,type,
% 2.62/3.02 set_or6656581121297822940st_int: int > int > set_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Nat__Onat,type,
% 2.62/3.02 set_or6659071591806873216st_nat: nat > nat > set_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Code____Numeral__Ointeger,type,
% 2.62/3.02 set_or4266950643985792945nteger: code_integer > code_integer > set_Code_integer ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Int__Oint,type,
% 2.62/3.02 set_or5832277885323065728an_int: int > int > set_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Nat__Onat,type,
% 2.62/3.02 set_or5834768355832116004an_nat: nat > nat > set_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Nat__Onat,type,
% 2.62/3.02 set_or1210151606488870762an_nat: nat > set_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Nat__Onat,type,
% 2.62/3.02 set_ord_lessThan_nat: nat > set_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Syntax__Match_Osyntax__fo__nomatch_001t__Assertions__Oassn_001t__Assertions__Oassn,type,
% 2.62/3.02 syntax7398250324933576852n_assn: assn > assn > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Transitive__Closure_Ortrancl_001t__Nat__Onat,type,
% 2.62/3.02 transi2905341329935302413cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Transitive__Closure_Otrancl_001t__Int__Oint,type,
% 2.62/3.02 transi6261509568448316235cl_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Transitive__Closure_Otrancl_001t__Nat__Onat,type,
% 2.62/3.02 transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Transitive__Closure_Otrancl_001t__Product____Type__Oprod_I_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 2.62/3.02 transi4533545184864474924nt_int: set_Pr8634505666381077339nt_int > set_Pr8634505666381077339nt_int ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Transitive__Closure_Otrancl_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
% 2.62/3.02 transi6228740973808232501nteger: set_Pr1722956316086891245nteger > set_Pr1722956316086891245nteger ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Transitive__Closure_Otrancl_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,
% 2.62/3.02 transi5221092739591632921et_nat: set_Pr3444600963470892981et_nat > set_Pr3444600963470892981et_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_Transitive__Closure_Otrancl_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,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Transitive__Closure_Otrancl_001tf__c,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Transitive__Closure_Otrancl_001tf__d,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_Transitive__Closure_Otranclp_001t__Nat__Onat,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__Int__Oint_001t__Int__Oint,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__Int__Oint_001t__Nat__Onat,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__Nat__Onat_001t__Int__Oint,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__Nat__Onat_001t__Nat__Onat,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__Nat__Onat_001tf__c,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__Nat__Onat_001tf__d,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_VEBT__List__Assn_OlistI__assn_001tf__c_001t__Int__Oint,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_VEBT__List__Assn_OlistI__assn_001tf__c_001t__Nat__Onat,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_VEBT__List__Assn_OlistI__assn_001tf__c_001tf__c,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_VEBT__List__Assn_OlistI__assn_001tf__c_001tf__d,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_VEBT__List__Assn_OlistI__assn_001tf__d_001t__Int__Oint,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_VEBT__List__Assn_OlistI__assn_001tf__d_001t__Nat__Onat,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_VEBT__List__Assn_OlistI__assn_001tf__d_001tf__c,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_VEBT__List__Assn_OlistI__assn_001tf__d_001tf__d,type,
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% 2.62/3.02
% 2.62/3.02 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Int__Oint_001t__Int__Oint,type,
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% 2.62/3.02
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% 2.62/3.02 member3348759134392003351at_nat: produc8373899037510109440at_nat > set_Pr2539167527615954998at_nat > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.62/3.02 member8206827879206165904at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_member_001t__Product____Type__Oprod_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_Mt__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,
% 2.62/3.02 member6009668390874684176at_nat: produc1906917888121415911at_nat > set_Pr5564308138774400199at_nat > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
% 2.62/3.02 member444158400953824016od_o_o: produc2934264451710624999od_o_o > set_Pr1932065953672099015od_o_o > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 2.62/3.02 member4095101504841534314at_nat: produc732395585841259969at_nat > set_Pr457366540195662369at_nat > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 2.62/3.02 member8757157785044589968at_nat: produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_member_001t__Product____Type__Oprod_Itf__c_Mt__Int__Oint_J,type,
% 2.62/3.02 member4017226226790010994_c_int: product_prod_c_int > set_Pr4413417460947882513_c_int > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_member_001t__Product____Type__Oprod_Itf__c_Mt__Nat__Onat_J,type,
% 2.62/3.02 member8195077246299207702_c_nat: product_prod_c_nat > set_Pr6903500605879609269_c_nat > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_member_001t__Product____Type__Oprod_Itf__c_Mtf__c_J,type,
% 2.62/3.02 member5074992359041316560od_c_c: product_prod_c_c > set_Product_prod_c_c > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_member_001t__Product____Type__Oprod_Itf__c_Mtf__d_J,type,
% 2.62/3.02 member5074992363344545361od_c_d: product_prod_c_d > set_Product_prod_c_d > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_member_001t__Product____Type__Oprod_Itf__d_Mt__Int__Oint_J,type,
% 2.62/3.02 member5252670555746405491_d_int: product_prod_d_int > set_Pr786264039281237394_d_int > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_member_001t__Product____Type__Oprod_Itf__d_Mt__Nat__Onat_J,type,
% 2.62/3.02 member207149538400826391_d_nat: product_prod_d_nat > set_Pr3276347184212964150_d_nat > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_member_001t__Product____Type__Oprod_Itf__d_Mtf__c_J,type,
% 2.62/3.02 member2287536777068640527od_d_c: product_prod_d_c > set_Product_prod_d_c > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_member_001t__Product____Type__Oprod_Itf__d_Mtf__d_J,type,
% 2.62/3.02 member2287536781371869328od_d_d: product_prod_d_d > set_Product_prod_d_d > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_member_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.62/3.02 member2643936169264416010at_nat: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_member_001tf__c,type,
% 2.62/3.02 member_c: c > set_c > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_c_member_001tf__d,type,
% 2.62/3.02 member_d: d > set_d > $o ).
% 2.62/3.02
% 2.62/3.02 thf(sy_v_A,type,
% 2.62/3.02 a: c > d > assn ).
% 2.62/3.02
% 2.62/3.02 thf(sy_v_F,type,
% 2.62/3.02 f: assn ).
% 2.62/3.02
% 2.62/3.02 thf(sy_v_I,type,
% 2.62/3.02 i: set_nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_v_P,type,
% 2.62/3.02 p: assn ).
% 2.62/3.02
% 2.62/3.02 thf(sy_v_Q,type,
% 2.62/3.02 q: assn ).
% 2.62/3.02
% 2.62/3.02 thf(sy_v_i,type,
% 2.62/3.02 i2: nat ).
% 2.62/3.02
% 2.62/3.02 thf(sy_v_x,type,
% 2.62/3.02 x: c ).
% 2.62/3.02
% 2.62/3.02 thf(sy_v_xi,type,
% 2.62/3.02 xi: d ).
% 2.62/3.02
% 2.62/3.02 thf(sy_v_xs,type,
% 2.62/3.02 xs: list_c ).
% 2.62/3.02
% 2.62/3.02 thf(sy_v_xsi,type,
% 2.62/3.02 xsi: list_d ).
% 2.62/3.02
% 2.62/3.02 % Relevant facts (5751)
% 2.62/3.02 thf(fact_0_entailsI,axiom,
% 2.62/3.02 ! [P: assn,Q: assn] :
% 2.62/3.02 ( ! [H: produc3658429121746597890et_nat] :
% 2.62/3.02 ( ( rep_assn @ P @ H )
% 2.62/3.02 => ( rep_assn @ Q @ H ) )
% 2.62/3.02 => ( entails @ P @ Q ) ) ).
% 2.62/3.02
% 2.62/3.02 % entailsI
% 2.62/3.02 thf(fact_1__092_060open_062P_A_092_060Longrightarrow_062_092_060_094sub_062A_Afalse_092_060close_062,axiom,
% 2.62/3.02 entails @ p @ bot_bot_assn ).
% 2.62/3.02
% 2.62/3.02 % \<open>P \<Longrightarrow>\<^sub>A false\<close>
% 2.62/3.02 thf(fact_2_assms_I3_J,axiom,
% 2.62/3.02 member_nat @ i2 @ i ).
% 2.62/3.02
% 2.62/3.02 % assms(3)
% 2.62/3.02 thf(fact_3_ent__iffI,axiom,
% 2.62/3.02 ! [A: assn,B: assn] :
% 2.62/3.02 ( ( entails @ A @ B )
% 2.62/3.02 => ( ( entails @ B @ A )
% 2.62/3.02 => ( A = B ) ) ) ).
% 2.62/3.02
% 2.62/3.02 % ent_iffI
% 2.62/3.02 thf(fact_4_ent__refl,axiom,
% 2.62/3.02 ! [P: assn] : ( entails @ P @ P ) ).
% 2.62/3.02
% 2.62/3.02 % ent_refl
% 2.62/3.02 thf(fact_5_ent__trans,axiom,
% 2.62/3.02 ! [P: assn,Q: assn,R: assn] :
% 2.62/3.02 ( ( entails @ P @ Q )
% 2.62/3.02 => ( ( entails @ Q @ R )
% 2.62/3.02 => ( entails @ P @ R ) ) ) ).
% 2.62/3.02
% 2.62/3.02 % ent_trans
% 2.62/3.02 thf(fact_6_is__entails,axiom,
% 2.62/3.02 ! [P: assn,Q: assn] :
% 2.62/3.02 ( ( entails @ P @ Q )
% 2.62/3.02 => ( entails @ P @ Q ) ) ).
% 2.62/3.02
% 2.62/3.02 % is_entails
% 2.62/3.02 thf(fact_7_ent__false,axiom,
% 2.62/3.02 ! [P: assn] : ( entails @ bot_bot_assn @ P ) ).
% 2.62/3.02
% 2.62/3.02 % ent_false
% 2.62/3.02 thf(fact_8_ent__fwd,axiom,
% 2.62/3.02 ! [P: assn,H2: produc3658429121746597890et_nat,Q: assn] :
% 2.62/3.02 ( ( rep_assn @ P @ H2 )
% 2.62/3.02 => ( ( entails @ P @ Q )
% 2.62/3.02 => ( rep_assn @ Q @ H2 ) ) ) ).
% 2.62/3.02
% 2.62/3.02 % ent_fwd
% 2.62/3.02 thf(fact_9_entailsD,axiom,
% 2.62/3.02 ! [P: assn,Q: assn,H2: produc3658429121746597890et_nat] :
% 2.62/3.02 ( ( entails @ P @ Q )
% 2.62/3.02 => ( ( rep_assn @ P @ H2 )
% 2.62/3.02 => ( rep_assn @ Q @ H2 ) ) ) ).
% 2.62/3.02
% 2.62/3.02 % entailsD
% 2.62/3.02 thf(fact_10_entails__def,axiom,
% 2.62/3.02 ( entails
% 2.62/3.02 = ( ^ [P2: assn,Q2: assn] :
% 2.62/3.02 ! [H3: produc3658429121746597890et_nat] :
% 2.62/3.02 ( ( rep_assn @ P2 @ H3 )
% 2.62/3.02 => ( rep_assn @ Q2 @ H3 ) ) ) ) ).
% 2.62/3.02
% 2.62/3.02 % entails_def
% 2.62/3.02 thf(fact_11_ent__false__iff,axiom,
% 2.62/3.02 ! [P: assn] :
% 2.62/3.02 ( ( entails @ P @ bot_bot_assn )
% 2.62/3.02 = ( ! [H3: produc3658429121746597890et_nat] :
% 2.62/3.02 ~ ( rep_assn @ P @ H3 ) ) ) ).
% 2.62/3.02
% 2.62/3.02 % ent_false_iff
% 2.62/3.02 thf(fact_12_assms_I4_J,axiom,
% 2.62/3.02 entails @ ( times_times_assn @ ( vEBT_L824818263033719201sn_c_d @ i @ a @ ( list_update_c @ xs @ i2 @ x ) @ ( list_update_d @ xsi @ i2 @ xi ) ) @ f ) @ q ).
% 2.62/3.02
% 2.62/3.02 % assms(4)
% 2.62/3.02 thf(fact_13_ent__imp__entt,axiom,
% 2.62/3.02 ! [P: assn,Q: assn] :
% 2.62/3.02 ( ( entails @ P @ Q )
% 2.62/3.02 => ( entailst @ P @ Q ) ) ).
% 2.62/3.03
% 2.62/3.03 % ent_imp_entt
% 2.62/3.03 thf(fact_14_Rep__assn__inject,axiom,
% 2.62/3.03 ! [X: assn,Y: assn] :
% 2.62/3.03 ( ( ( rep_assn @ X )
% 2.62/3.03 = ( rep_assn @ Y ) )
% 2.62/3.03 = ( X = Y ) ) ).
% 2.62/3.03
% 2.62/3.03 % Rep_assn_inject
% 2.62/3.03 thf(fact_15_entt__refl,axiom,
% 2.62/3.03 ! [A: assn] : ( entailst @ A @ A ) ).
% 2.62/3.03
% 2.62/3.03 % entt_refl
% 2.62/3.03 thf(fact_16_star__false__left,axiom,
% 2.62/3.03 ! [P: assn] :
% 2.62/3.03 ( ( times_times_assn @ bot_bot_assn @ P )
% 2.62/3.03 = bot_bot_assn ) ).
% 2.62/3.03
% 2.62/3.03 % star_false_left
% 2.62/3.03 thf(fact_17_star__false__right,axiom,
% 2.62/3.03 ! [P: assn] :
% 2.62/3.03 ( ( times_times_assn @ P @ bot_bot_assn )
% 2.62/3.03 = bot_bot_assn ) ).
% 2.62/3.03
% 2.62/3.03 % star_false_right
% 2.62/3.03 thf(fact_18_assn__aci_I10_J,axiom,
% 2.62/3.03 ! [A2: assn,B2: assn,C: assn] :
% 2.62/3.03 ( ( times_times_assn @ ( times_times_assn @ A2 @ B2 ) @ C )
% 2.62/3.03 = ( times_times_assn @ ( times_times_assn @ A2 @ C ) @ B2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % assn_aci(10)
% 2.62/3.03 thf(fact_19_star__aci_I3_J,axiom,
% 2.62/3.03 ! [A2: assn,B2: assn,C: assn] :
% 2.62/3.03 ( ( times_times_assn @ A2 @ ( times_times_assn @ B2 @ C ) )
% 2.62/3.03 = ( times_times_assn @ B2 @ ( times_times_assn @ A2 @ C ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % star_aci(3)
% 2.62/3.03 thf(fact_20_star__aci_I2_J,axiom,
% 2.62/3.03 ( times_times_assn
% 2.62/3.03 = ( ^ [A3: assn,B3: assn] : ( times_times_assn @ B3 @ A3 ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % star_aci(2)
% 2.62/3.03 thf(fact_21_mod__false,axiom,
% 2.62/3.03 ! [H2: produc3658429121746597890et_nat] :
% 2.62/3.03 ~ ( rep_assn @ bot_bot_assn @ H2 ) ).
% 2.62/3.03
% 2.62/3.03 % mod_false
% 2.62/3.03 thf(fact_22_mod__starD,axiom,
% 2.62/3.03 ! [A: assn,B: assn,H2: produc3658429121746597890et_nat] :
% 2.62/3.03 ( ( rep_assn @ ( times_times_assn @ A @ B ) @ H2 )
% 2.62/3.03 => ? [H1: produc3658429121746597890et_nat,H22: produc3658429121746597890et_nat] :
% 2.62/3.03 ( ( rep_assn @ A @ H1 )
% 2.62/3.03 & ( rep_assn @ B @ H22 ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % mod_starD
% 2.62/3.03 thf(fact_23_mod__starE,axiom,
% 2.62/3.03 ! [A2: assn,B2: assn,H2: produc3658429121746597890et_nat] :
% 2.62/3.03 ( ( rep_assn @ ( times_times_assn @ A2 @ B2 ) @ H2 )
% 2.62/3.03 => ~ ( ? [X_1: produc3658429121746597890et_nat] : ( rep_assn @ A2 @ X_1 )
% 2.62/3.03 => ! [H_2: produc3658429121746597890et_nat] :
% 2.62/3.03 ~ ( rep_assn @ B2 @ H_2 ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % mod_starE
% 2.62/3.03 thf(fact_24_entt__trans,axiom,
% 2.62/3.03 ! [A: assn,B: assn,C2: assn] :
% 2.62/3.03 ( ( entailst @ A @ B )
% 2.62/3.03 => ( ( entailst @ B @ C2 )
% 2.62/3.03 => ( entailst @ A @ C2 ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % entt_trans
% 2.62/3.03 thf(fact_25_star__assoc,axiom,
% 2.62/3.03 ! [A2: assn,B2: assn,C: assn] :
% 2.62/3.03 ( ( times_times_assn @ ( times_times_assn @ A2 @ B2 ) @ C )
% 2.62/3.03 = ( times_times_assn @ A2 @ ( times_times_assn @ B2 @ C ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % star_assoc
% 2.62/3.03 thf(fact_26_entt__fr__drop,axiom,
% 2.62/3.03 ! [F: assn,F2: assn,A: assn] :
% 2.62/3.03 ( ( entailst @ F @ F2 )
% 2.62/3.03 => ( entailst @ ( times_times_assn @ F @ A ) @ F2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % entt_fr_drop
% 2.62/3.03 thf(fact_27_entt__fr__refl,axiom,
% 2.62/3.03 ! [F: assn,F2: assn,A: assn] :
% 2.62/3.03 ( ( entailst @ F @ F2 )
% 2.62/3.03 => ( entailst @ ( times_times_assn @ F @ A ) @ ( times_times_assn @ F2 @ A ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % entt_fr_refl
% 2.62/3.03 thf(fact_28_entt__frame__fwd,axiom,
% 2.62/3.03 ! [P: assn,Q: assn,A: assn,F: assn,B: assn] :
% 2.62/3.03 ( ( entailst @ P @ Q )
% 2.62/3.03 => ( ( entailst @ A @ ( times_times_assn @ P @ F ) )
% 2.62/3.03 => ( ( entailst @ ( times_times_assn @ Q @ F ) @ B )
% 2.62/3.03 => ( entailst @ A @ B ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % entt_frame_fwd
% 2.62/3.03 thf(fact_29_entt__star__mono,axiom,
% 2.62/3.03 ! [A: assn,B: assn,C2: assn,D: assn] :
% 2.62/3.03 ( ( entailst @ A @ B )
% 2.62/3.03 => ( ( entailst @ C2 @ D )
% 2.62/3.03 => ( entailst @ ( times_times_assn @ A @ C2 ) @ ( times_times_assn @ B @ D ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % entt_star_mono
% 2.62/3.03 thf(fact_30_assn__times__comm,axiom,
% 2.62/3.03 ( times_times_assn
% 2.62/3.03 = ( ^ [P2: assn,Q2: assn] : ( times_times_assn @ Q2 @ P2 ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % assn_times_comm
% 2.62/3.03 thf(fact_31_assn__times__assoc,axiom,
% 2.62/3.03 ! [P: assn,Q: assn,R: assn] :
% 2.62/3.03 ( ( times_times_assn @ ( times_times_assn @ P @ Q ) @ R )
% 2.62/3.03 = ( times_times_assn @ P @ ( times_times_assn @ Q @ R ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % assn_times_assoc
% 2.62/3.03 thf(fact_32_mod__frame__fwd,axiom,
% 2.62/3.03 ! [Ps: assn,H2: produc3658429121746597890et_nat,P: assn,R: assn,F: assn] :
% 2.62/3.03 ( ( rep_assn @ Ps @ H2 )
% 2.62/3.03 => ( ( entails @ P @ R )
% 2.62/3.03 => ( ( entails @ Ps @ ( times_times_assn @ P @ F ) )
% 2.62/3.03 => ( rep_assn @ ( times_times_assn @ R @ F ) @ H2 ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % mod_frame_fwd
% 2.62/3.03 thf(fact_33_ent__frame__fwd,axiom,
% 2.62/3.03 ! [P: assn,R: assn,Ps: assn,F: assn,Q: assn] :
% 2.62/3.03 ( ( entails @ P @ R )
% 2.62/3.03 => ( ( entails @ Ps @ ( times_times_assn @ P @ F ) )
% 2.62/3.03 => ( ( entails @ ( times_times_assn @ R @ F ) @ Q )
% 2.62/3.03 => ( entails @ Ps @ Q ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % ent_frame_fwd
% 2.62/3.03 thf(fact_34_ent__star__mono,axiom,
% 2.62/3.03 ! [P: assn,P3: assn,Q: assn,Q3: assn] :
% 2.62/3.03 ( ( entails @ P @ P3 )
% 2.62/3.03 => ( ( entails @ Q @ Q3 )
% 2.62/3.03 => ( entails @ ( times_times_assn @ P @ Q ) @ ( times_times_assn @ P3 @ Q3 ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % ent_star_mono
% 2.62/3.03 thf(fact_35_fr__rot__rhs,axiom,
% 2.62/3.03 ! [A: assn,B: assn,C2: assn] :
% 2.62/3.03 ( ( entails @ A @ ( times_times_assn @ B @ C2 ) )
% 2.62/3.03 => ( entails @ A @ ( times_times_assn @ C2 @ B ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % fr_rot_rhs
% 2.62/3.03 thf(fact_36_fr__refl,axiom,
% 2.62/3.03 ! [A: assn,B: assn,C2: assn] :
% 2.62/3.03 ( ( entails @ A @ B )
% 2.62/3.03 => ( entails @ ( times_times_assn @ A @ C2 ) @ ( times_times_assn @ B @ C2 ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % fr_refl
% 2.62/3.03 thf(fact_37_fr__rot,axiom,
% 2.62/3.03 ! [A: assn,B: assn,C2: assn] :
% 2.62/3.03 ( ( entails @ ( times_times_assn @ A @ B ) @ C2 )
% 2.62/3.03 => ( entails @ ( times_times_assn @ B @ A ) @ C2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % fr_rot
% 2.62/3.03 thf(fact_38_assms_I1_J,axiom,
% 2.62/3.03 entails @ p @ ( times_times_assn @ ( times_times_assn @ ( a @ x @ xi ) @ ( vEBT_L824818263033719201sn_c_d @ ( minus_minus_set_nat @ i @ ( insert_nat2 @ i2 @ bot_bot_set_nat ) ) @ a @ xs @ xsi ) ) @ f ) ).
% 2.62/3.03
% 2.62/3.03 % assms(1)
% 2.62/3.03 thf(fact_39_list__update__overwrite,axiom,
% 2.62/3.03 ! [Xs: list_c,I: nat,X: c,Y: c] :
% 2.62/3.03 ( ( list_update_c @ ( list_update_c @ Xs @ I @ X ) @ I @ Y )
% 2.62/3.03 = ( list_update_c @ Xs @ I @ Y ) ) ).
% 2.62/3.03
% 2.62/3.03 % list_update_overwrite
% 2.62/3.03 thf(fact_40_list__update__overwrite,axiom,
% 2.62/3.03 ! [Xs: list_d,I: nat,X: d,Y: d] :
% 2.62/3.03 ( ( list_update_d @ ( list_update_d @ Xs @ I @ X ) @ I @ Y )
% 2.62/3.03 = ( list_update_d @ Xs @ I @ Y ) ) ).
% 2.62/3.03
% 2.62/3.03 % list_update_overwrite
% 2.62/3.03 thf(fact_41_False,axiom,
% 2.62/3.03 ( ( size_size_list_c @ xs )
% 2.62/3.03 != ( size_size_list_d @ xsi ) ) ).
% 2.62/3.03
% 2.62/3.03 % False
% 2.62/3.03 thf(fact_42_assms_I2_J,axiom,
% 2.62/3.03 ord_less_nat @ i2 @ ( size_size_list_c @ xs ) ).
% 2.62/3.03
% 2.62/3.03 % assms(2)
% 2.62/3.03 thf(fact_43_frame__inference__init,axiom,
% 2.62/3.03 ! [P: assn,Q: assn,F: assn] :
% 2.62/3.03 ( ( fI_QUERY @ P @ Q @ F )
% 2.62/3.03 => ( entails @ P @ ( times_times_assn @ Q @ F ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % frame_inference_init
% 2.62/3.03 thf(fact_44_mem__Collect__eq,axiom,
% 2.62/3.03 ! [A2: produc3843707927480180839at_nat,P: produc3843707927480180839at_nat > $o] :
% 2.62/3.03 ( ( member8757157785044589968at_nat @ A2 @ ( collec6321179662152712658at_nat @ P ) )
% 2.62/3.03 = ( P @ A2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % mem_Collect_eq
% 2.62/3.03 thf(fact_45_mem__Collect__eq,axiom,
% 2.62/3.03 ! [A2: int,P: int > $o] :
% 2.62/3.03 ( ( member_int @ A2 @ ( collect_int @ P ) )
% 2.62/3.03 = ( P @ A2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % mem_Collect_eq
% 2.62/3.03 thf(fact_46_mem__Collect__eq,axiom,
% 2.62/3.03 ! [A2: nat,P: nat > $o] :
% 2.62/3.03 ( ( member_nat @ A2 @ ( collect_nat @ P ) )
% 2.62/3.03 = ( P @ A2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % mem_Collect_eq
% 2.62/3.03 thf(fact_47_mem__Collect__eq,axiom,
% 2.62/3.03 ! [A2: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 2.62/3.03 ( ( member8440522571783428010at_nat @ A2 @ ( collec3392354462482085612at_nat @ P ) )
% 2.62/3.03 = ( P @ A2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % mem_Collect_eq
% 2.62/3.03 thf(fact_48_mem__Collect__eq,axiom,
% 2.62/3.03 ! [A2: produc3658429121746597890et_nat > $o,P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 2.62/3.03 ( ( member6576561426505652726_nat_o @ A2 @ ( collec939566748876313656_nat_o @ P ) )
% 2.62/3.03 = ( P @ A2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % mem_Collect_eq
% 2.62/3.03 thf(fact_49_Collect__mem__eq,axiom,
% 2.62/3.03 ! [A: set_Pr4329608150637261639at_nat] :
% 2.62/3.03 ( ( collec6321179662152712658at_nat
% 2.62/3.03 @ ^ [X2: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X2 @ A ) )
% 2.62/3.03 = A ) ).
% 2.62/3.03
% 2.62/3.03 % Collect_mem_eq
% 2.62/3.03 thf(fact_50_Collect__mem__eq,axiom,
% 2.62/3.03 ! [A: set_int] :
% 2.62/3.03 ( ( collect_int
% 2.62/3.03 @ ^ [X2: int] : ( member_int @ X2 @ A ) )
% 2.62/3.03 = A ) ).
% 2.62/3.03
% 2.62/3.03 % Collect_mem_eq
% 2.62/3.03 thf(fact_51_Collect__mem__eq,axiom,
% 2.62/3.03 ! [A: set_nat] :
% 2.62/3.03 ( ( collect_nat
% 2.62/3.03 @ ^ [X2: nat] : ( member_nat @ X2 @ A ) )
% 2.62/3.03 = A ) ).
% 2.62/3.03
% 2.62/3.03 % Collect_mem_eq
% 2.62/3.03 thf(fact_52_Collect__mem__eq,axiom,
% 2.62/3.03 ! [A: set_Pr1261947904930325089at_nat] :
% 2.62/3.03 ( ( collec3392354462482085612at_nat
% 2.62/3.03 @ ^ [X2: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X2 @ A ) )
% 2.62/3.03 = A ) ).
% 2.62/3.03
% 2.62/3.03 % Collect_mem_eq
% 2.62/3.03 thf(fact_53_Collect__mem__eq,axiom,
% 2.62/3.03 ! [A: set_Pr4532377907799695533_nat_o] :
% 2.62/3.03 ( ( collec939566748876313656_nat_o
% 2.62/3.03 @ ^ [X2: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X2 @ A ) )
% 2.62/3.03 = A ) ).
% 2.62/3.03
% 2.62/3.03 % Collect_mem_eq
% 2.62/3.03 thf(fact_54_Collect__cong,axiom,
% 2.62/3.03 ! [P: nat > $o,Q: nat > $o] :
% 2.62/3.03 ( ! [X3: nat] :
% 2.62/3.03 ( ( P @ X3 )
% 2.62/3.03 = ( Q @ X3 ) )
% 2.62/3.03 => ( ( collect_nat @ P )
% 2.62/3.03 = ( collect_nat @ Q ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % Collect_cong
% 2.62/3.03 thf(fact_55_Collect__cong,axiom,
% 2.62/3.03 ! [P: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
% 2.62/3.03 ( ! [X3: product_prod_nat_nat] :
% 2.62/3.03 ( ( P @ X3 )
% 2.62/3.03 = ( Q @ X3 ) )
% 2.62/3.03 => ( ( collec3392354462482085612at_nat @ P )
% 2.62/3.03 = ( collec3392354462482085612at_nat @ Q ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % Collect_cong
% 2.62/3.03 thf(fact_56_Collect__cong,axiom,
% 2.62/3.03 ! [P: ( produc3658429121746597890et_nat > $o ) > $o,Q: ( produc3658429121746597890et_nat > $o ) > $o] :
% 2.62/3.03 ( ! [X3: produc3658429121746597890et_nat > $o] :
% 2.62/3.03 ( ( P @ X3 )
% 2.62/3.03 = ( Q @ X3 ) )
% 2.62/3.03 => ( ( collec939566748876313656_nat_o @ P )
% 2.62/3.03 = ( collec939566748876313656_nat_o @ Q ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % Collect_cong
% 2.62/3.03 thf(fact_57_FI__QUERY__def,axiom,
% 2.62/3.03 ( fI_QUERY
% 2.62/3.03 = ( ^ [P2: assn,Q2: assn,F3: assn] : ( entails @ P2 @ ( times_times_assn @ Q2 @ F3 ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % FI_QUERY_def
% 2.62/3.03 thf(fact_58_ent__wand__frameI,axiom,
% 2.62/3.03 ! [Q: assn,R: assn,F: assn,S: assn,P: assn,X4: assn] :
% 2.62/3.03 ( ( entails @ ( times_times_assn @ ( wand_assn @ Q @ R ) @ F ) @ S )
% 2.62/3.03 => ( ( entails @ P @ ( times_times_assn @ F @ X4 ) )
% 2.62/3.03 => ( ( entails @ ( times_times_assn @ Q @ X4 ) @ R )
% 2.62/3.03 => ( entails @ P @ S ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % ent_wand_frameI
% 2.62/3.03 thf(fact_59_ent__wandI,axiom,
% 2.62/3.03 ! [Q: assn,P: assn,R: assn] :
% 2.62/3.03 ( ( entails @ ( times_times_assn @ Q @ P ) @ R )
% 2.62/3.03 => ( entails @ P @ ( wand_assn @ Q @ R ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % ent_wandI
% 2.62/3.03 thf(fact_60_ent__mp,axiom,
% 2.62/3.03 ! [P: assn,Q: assn] : ( entails @ ( times_times_assn @ P @ ( wand_assn @ P @ Q ) ) @ Q ) ).
% 2.62/3.03
% 2.62/3.03 % ent_mp
% 2.62/3.03 thf(fact_61_length__list__update,axiom,
% 2.62/3.03 ! [Xs: list_c,I: nat,X: c] :
% 2.62/3.03 ( ( size_size_list_c @ ( list_update_c @ Xs @ I @ X ) )
% 2.62/3.03 = ( size_size_list_c @ Xs ) ) ).
% 2.62/3.03
% 2.62/3.03 % length_list_update
% 2.62/3.03 thf(fact_62_length__list__update,axiom,
% 2.62/3.03 ! [Xs: list_d,I: nat,X: d] :
% 2.62/3.03 ( ( size_size_list_d @ ( list_update_d @ Xs @ I @ X ) )
% 2.62/3.03 = ( size_size_list_d @ Xs ) ) ).
% 2.62/3.03
% 2.62/3.03 % length_list_update
% 2.62/3.03 thf(fact_63_length__list__update,axiom,
% 2.62/3.03 ! [Xs: list_nat,I: nat,X: nat] :
% 2.62/3.03 ( ( size_size_list_nat @ ( list_update_nat @ Xs @ I @ X ) )
% 2.62/3.03 = ( size_size_list_nat @ Xs ) ) ).
% 2.62/3.03
% 2.62/3.03 % length_list_update
% 2.62/3.03 thf(fact_64_length__list__update,axiom,
% 2.62/3.03 ! [Xs: list_int,I: nat,X: int] :
% 2.62/3.03 ( ( size_size_list_int @ ( list_update_int @ Xs @ I @ X ) )
% 2.62/3.03 = ( size_size_list_int @ Xs ) ) ).
% 2.62/3.03
% 2.62/3.03 % length_list_update
% 2.62/3.03 thf(fact_65_order__less__imp__not__less,axiom,
% 2.62/3.03 ! [X: code_integer,Y: code_integer] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ X @ Y )
% 2.62/3.03 => ~ ( ord_le6747313008572928689nteger @ Y @ X ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_imp_not_less
% 2.62/3.03 thf(fact_66_order__less__imp__not__less,axiom,
% 2.62/3.03 ! [X: assn,Y: assn] :
% 2.62/3.03 ( ( ord_less_assn @ X @ Y )
% 2.62/3.03 => ~ ( ord_less_assn @ Y @ X ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_imp_not_less
% 2.62/3.03 thf(fact_67_order__less__imp__not__less,axiom,
% 2.62/3.03 ! [X: num,Y: num] :
% 2.62/3.03 ( ( ord_less_num @ X @ Y )
% 2.62/3.03 => ~ ( ord_less_num @ Y @ X ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_imp_not_less
% 2.62/3.03 thf(fact_68_order__less__imp__not__less,axiom,
% 2.62/3.03 ! [X: nat,Y: nat] :
% 2.62/3.03 ( ( ord_less_nat @ X @ Y )
% 2.62/3.03 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_imp_not_less
% 2.62/3.03 thf(fact_69_order__less__imp__not__less,axiom,
% 2.62/3.03 ! [X: int,Y: int] :
% 2.62/3.03 ( ( ord_less_int @ X @ Y )
% 2.62/3.03 => ~ ( ord_less_int @ Y @ X ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_imp_not_less
% 2.62/3.03 thf(fact_70_order__less__imp__not__eq2,axiom,
% 2.62/3.03 ! [X: code_integer,Y: code_integer] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ X @ Y )
% 2.62/3.03 => ( Y != X ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_imp_not_eq2
% 2.62/3.03 thf(fact_71_order__less__imp__not__eq2,axiom,
% 2.62/3.03 ! [X: assn,Y: assn] :
% 2.62/3.03 ( ( ord_less_assn @ X @ Y )
% 2.62/3.03 => ( Y != X ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_imp_not_eq2
% 2.62/3.03 thf(fact_72_order__less__imp__not__eq2,axiom,
% 2.62/3.03 ! [X: num,Y: num] :
% 2.62/3.03 ( ( ord_less_num @ X @ Y )
% 2.62/3.03 => ( Y != X ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_imp_not_eq2
% 2.62/3.03 thf(fact_73_order__less__imp__not__eq2,axiom,
% 2.62/3.03 ! [X: nat,Y: nat] :
% 2.62/3.03 ( ( ord_less_nat @ X @ Y )
% 2.62/3.03 => ( Y != X ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_imp_not_eq2
% 2.62/3.03 thf(fact_74_order__less__imp__not__eq2,axiom,
% 2.62/3.03 ! [X: int,Y: int] :
% 2.62/3.03 ( ( ord_less_int @ X @ Y )
% 2.62/3.03 => ( Y != X ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_imp_not_eq2
% 2.62/3.03 thf(fact_75_order__less__imp__not__eq,axiom,
% 2.62/3.03 ! [X: code_integer,Y: code_integer] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ X @ Y )
% 2.62/3.03 => ( X != Y ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_imp_not_eq
% 2.62/3.03 thf(fact_76_order__less__imp__not__eq,axiom,
% 2.62/3.03 ! [X: assn,Y: assn] :
% 2.62/3.03 ( ( ord_less_assn @ X @ Y )
% 2.62/3.03 => ( X != Y ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_imp_not_eq
% 2.62/3.03 thf(fact_77_order__less__imp__not__eq,axiom,
% 2.62/3.03 ! [X: num,Y: num] :
% 2.62/3.03 ( ( ord_less_num @ X @ Y )
% 2.62/3.03 => ( X != Y ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_imp_not_eq
% 2.62/3.03 thf(fact_78_order__less__imp__not__eq,axiom,
% 2.62/3.03 ! [X: nat,Y: nat] :
% 2.62/3.03 ( ( ord_less_nat @ X @ Y )
% 2.62/3.03 => ( X != Y ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_imp_not_eq
% 2.62/3.03 thf(fact_79_order__less__imp__not__eq,axiom,
% 2.62/3.03 ! [X: int,Y: int] :
% 2.62/3.03 ( ( ord_less_int @ X @ Y )
% 2.62/3.03 => ( X != Y ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_imp_not_eq
% 2.62/3.03 thf(fact_80_linorder__less__linear,axiom,
% 2.62/3.03 ! [X: code_integer,Y: code_integer] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ X @ Y )
% 2.62/3.03 | ( X = Y )
% 2.62/3.03 | ( ord_le6747313008572928689nteger @ Y @ X ) ) ).
% 2.62/3.03
% 2.62/3.03 % linorder_less_linear
% 2.62/3.03 thf(fact_81_linorder__less__linear,axiom,
% 2.62/3.03 ! [X: num,Y: num] :
% 2.62/3.03 ( ( ord_less_num @ X @ Y )
% 2.62/3.03 | ( X = Y )
% 2.62/3.03 | ( ord_less_num @ Y @ X ) ) ).
% 2.62/3.03
% 2.62/3.03 % linorder_less_linear
% 2.62/3.03 thf(fact_82_linorder__less__linear,axiom,
% 2.62/3.03 ! [X: nat,Y: nat] :
% 2.62/3.03 ( ( ord_less_nat @ X @ Y )
% 2.62/3.03 | ( X = Y )
% 2.62/3.03 | ( ord_less_nat @ Y @ X ) ) ).
% 2.62/3.03
% 2.62/3.03 % linorder_less_linear
% 2.62/3.03 thf(fact_83_linorder__less__linear,axiom,
% 2.62/3.03 ! [X: int,Y: int] :
% 2.62/3.03 ( ( ord_less_int @ X @ Y )
% 2.62/3.03 | ( X = Y )
% 2.62/3.03 | ( ord_less_int @ Y @ X ) ) ).
% 2.62/3.03
% 2.62/3.03 % linorder_less_linear
% 2.62/3.03 thf(fact_84_order__less__imp__triv,axiom,
% 2.62/3.03 ! [X: code_integer,Y: code_integer,P: $o] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ X @ Y )
% 2.62/3.03 => ( ( ord_le6747313008572928689nteger @ Y @ X )
% 2.62/3.03 => P ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_imp_triv
% 2.62/3.03 thf(fact_85_order__less__imp__triv,axiom,
% 2.62/3.03 ! [X: assn,Y: assn,P: $o] :
% 2.62/3.03 ( ( ord_less_assn @ X @ Y )
% 2.62/3.03 => ( ( ord_less_assn @ Y @ X )
% 2.62/3.03 => P ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_imp_triv
% 2.62/3.03 thf(fact_86_order__less__imp__triv,axiom,
% 2.62/3.03 ! [X: num,Y: num,P: $o] :
% 2.62/3.03 ( ( ord_less_num @ X @ Y )
% 2.62/3.03 => ( ( ord_less_num @ Y @ X )
% 2.62/3.03 => P ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_imp_triv
% 2.62/3.03 thf(fact_87_order__less__imp__triv,axiom,
% 2.62/3.03 ! [X: nat,Y: nat,P: $o] :
% 2.62/3.03 ( ( ord_less_nat @ X @ Y )
% 2.62/3.03 => ( ( ord_less_nat @ Y @ X )
% 2.62/3.03 => P ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_imp_triv
% 2.62/3.03 thf(fact_88_order__less__imp__triv,axiom,
% 2.62/3.03 ! [X: int,Y: int,P: $o] :
% 2.62/3.03 ( ( ord_less_int @ X @ Y )
% 2.62/3.03 => ( ( ord_less_int @ Y @ X )
% 2.62/3.03 => P ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_imp_triv
% 2.62/3.03 thf(fact_89_order__less__not__sym,axiom,
% 2.62/3.03 ! [X: code_integer,Y: code_integer] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ X @ Y )
% 2.62/3.03 => ~ ( ord_le6747313008572928689nteger @ Y @ X ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_not_sym
% 2.62/3.03 thf(fact_90_order__less__not__sym,axiom,
% 2.62/3.03 ! [X: assn,Y: assn] :
% 2.62/3.03 ( ( ord_less_assn @ X @ Y )
% 2.62/3.03 => ~ ( ord_less_assn @ Y @ X ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_not_sym
% 2.62/3.03 thf(fact_91_order__less__not__sym,axiom,
% 2.62/3.03 ! [X: num,Y: num] :
% 2.62/3.03 ( ( ord_less_num @ X @ Y )
% 2.62/3.03 => ~ ( ord_less_num @ Y @ X ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_not_sym
% 2.62/3.03 thf(fact_92_order__less__not__sym,axiom,
% 2.62/3.03 ! [X: nat,Y: nat] :
% 2.62/3.03 ( ( ord_less_nat @ X @ Y )
% 2.62/3.03 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_not_sym
% 2.62/3.03 thf(fact_93_order__less__not__sym,axiom,
% 2.62/3.03 ! [X: int,Y: int] :
% 2.62/3.03 ( ( ord_less_int @ X @ Y )
% 2.62/3.03 => ~ ( ord_less_int @ Y @ X ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_not_sym
% 2.62/3.03 thf(fact_94_order__less__subst2,axiom,
% 2.62/3.03 ! [A2: code_integer,B2: code_integer,F4: code_integer > code_integer,C: code_integer] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 2.62/3.03 => ( ( ord_le6747313008572928689nteger @ ( F4 @ B2 ) @ C )
% 2.62/3.03 => ( ! [X3: code_integer,Y2: code_integer] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 2.62/3.03 => ( ord_le6747313008572928689nteger @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.62/3.03 => ( ord_le6747313008572928689nteger @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_subst2
% 2.62/3.03 thf(fact_95_order__less__subst2,axiom,
% 2.62/3.03 ! [A2: code_integer,B2: code_integer,F4: code_integer > assn,C: assn] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 2.62/3.03 => ( ( ord_less_assn @ ( F4 @ B2 ) @ C )
% 2.62/3.03 => ( ! [X3: code_integer,Y2: code_integer] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 2.62/3.03 => ( ord_less_assn @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.62/3.03 => ( ord_less_assn @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_subst2
% 2.62/3.03 thf(fact_96_order__less__subst2,axiom,
% 2.62/3.03 ! [A2: code_integer,B2: code_integer,F4: code_integer > num,C: num] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 2.62/3.03 => ( ( ord_less_num @ ( F4 @ B2 ) @ C )
% 2.62/3.03 => ( ! [X3: code_integer,Y2: code_integer] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 2.62/3.03 => ( ord_less_num @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.62/3.03 => ( ord_less_num @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_subst2
% 2.62/3.03 thf(fact_97_order__less__subst2,axiom,
% 2.62/3.03 ! [A2: code_integer,B2: code_integer,F4: code_integer > nat,C: nat] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 2.62/3.03 => ( ( ord_less_nat @ ( F4 @ B2 ) @ C )
% 2.62/3.03 => ( ! [X3: code_integer,Y2: code_integer] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 2.62/3.03 => ( ord_less_nat @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.62/3.03 => ( ord_less_nat @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_subst2
% 2.62/3.03 thf(fact_98_order__less__subst2,axiom,
% 2.62/3.03 ! [A2: code_integer,B2: code_integer,F4: code_integer > int,C: int] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 2.62/3.03 => ( ( ord_less_int @ ( F4 @ B2 ) @ C )
% 2.62/3.03 => ( ! [X3: code_integer,Y2: code_integer] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 2.62/3.03 => ( ord_less_int @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.62/3.03 => ( ord_less_int @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_subst2
% 2.62/3.03 thf(fact_99_order__less__subst2,axiom,
% 2.62/3.03 ! [A2: assn,B2: assn,F4: assn > code_integer,C: code_integer] :
% 2.62/3.03 ( ( ord_less_assn @ A2 @ B2 )
% 2.62/3.03 => ( ( ord_le6747313008572928689nteger @ ( F4 @ B2 ) @ C )
% 2.62/3.03 => ( ! [X3: assn,Y2: assn] :
% 2.62/3.03 ( ( ord_less_assn @ X3 @ Y2 )
% 2.62/3.03 => ( ord_le6747313008572928689nteger @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.62/3.03 => ( ord_le6747313008572928689nteger @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_subst2
% 2.62/3.03 thf(fact_100_order__less__subst2,axiom,
% 2.62/3.03 ! [A2: assn,B2: assn,F4: assn > assn,C: assn] :
% 2.62/3.03 ( ( ord_less_assn @ A2 @ B2 )
% 2.62/3.03 => ( ( ord_less_assn @ ( F4 @ B2 ) @ C )
% 2.62/3.03 => ( ! [X3: assn,Y2: assn] :
% 2.62/3.03 ( ( ord_less_assn @ X3 @ Y2 )
% 2.62/3.03 => ( ord_less_assn @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.62/3.03 => ( ord_less_assn @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_subst2
% 2.62/3.03 thf(fact_101_order__less__subst2,axiom,
% 2.62/3.03 ! [A2: assn,B2: assn,F4: assn > num,C: num] :
% 2.62/3.03 ( ( ord_less_assn @ A2 @ B2 )
% 2.62/3.03 => ( ( ord_less_num @ ( F4 @ B2 ) @ C )
% 2.62/3.03 => ( ! [X3: assn,Y2: assn] :
% 2.62/3.03 ( ( ord_less_assn @ X3 @ Y2 )
% 2.62/3.03 => ( ord_less_num @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.62/3.03 => ( ord_less_num @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_subst2
% 2.62/3.03 thf(fact_102_order__less__subst2,axiom,
% 2.62/3.03 ! [A2: assn,B2: assn,F4: assn > nat,C: nat] :
% 2.62/3.03 ( ( ord_less_assn @ A2 @ B2 )
% 2.62/3.03 => ( ( ord_less_nat @ ( F4 @ B2 ) @ C )
% 2.62/3.03 => ( ! [X3: assn,Y2: assn] :
% 2.62/3.03 ( ( ord_less_assn @ X3 @ Y2 )
% 2.62/3.03 => ( ord_less_nat @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.62/3.03 => ( ord_less_nat @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_subst2
% 2.62/3.03 thf(fact_103_order__less__subst2,axiom,
% 2.62/3.03 ! [A2: assn,B2: assn,F4: assn > int,C: int] :
% 2.62/3.03 ( ( ord_less_assn @ A2 @ B2 )
% 2.62/3.03 => ( ( ord_less_int @ ( F4 @ B2 ) @ C )
% 2.62/3.03 => ( ! [X3: assn,Y2: assn] :
% 2.62/3.03 ( ( ord_less_assn @ X3 @ Y2 )
% 2.62/3.03 => ( ord_less_int @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.62/3.03 => ( ord_less_int @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_subst2
% 2.62/3.03 thf(fact_104_order__less__subst1,axiom,
% 2.62/3.03 ! [A2: code_integer,F4: code_integer > code_integer,B2: code_integer,C: code_integer] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ A2 @ ( F4 @ B2 ) )
% 2.62/3.03 => ( ( ord_le6747313008572928689nteger @ B2 @ C )
% 2.62/3.03 => ( ! [X3: code_integer,Y2: code_integer] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 2.62/3.03 => ( ord_le6747313008572928689nteger @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.62/3.03 => ( ord_le6747313008572928689nteger @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_subst1
% 2.62/3.03 thf(fact_105_order__less__subst1,axiom,
% 2.62/3.03 ! [A2: code_integer,F4: assn > code_integer,B2: assn,C: assn] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ A2 @ ( F4 @ B2 ) )
% 2.62/3.03 => ( ( ord_less_assn @ B2 @ C )
% 2.62/3.03 => ( ! [X3: assn,Y2: assn] :
% 2.62/3.03 ( ( ord_less_assn @ X3 @ Y2 )
% 2.62/3.03 => ( ord_le6747313008572928689nteger @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.62/3.03 => ( ord_le6747313008572928689nteger @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_subst1
% 2.62/3.03 thf(fact_106_order__less__subst1,axiom,
% 2.62/3.03 ! [A2: code_integer,F4: num > code_integer,B2: num,C: num] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ A2 @ ( F4 @ B2 ) )
% 2.62/3.03 => ( ( ord_less_num @ B2 @ C )
% 2.62/3.03 => ( ! [X3: num,Y2: num] :
% 2.62/3.03 ( ( ord_less_num @ X3 @ Y2 )
% 2.62/3.03 => ( ord_le6747313008572928689nteger @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.62/3.03 => ( ord_le6747313008572928689nteger @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_subst1
% 2.62/3.03 thf(fact_107_order__less__subst1,axiom,
% 2.62/3.03 ! [A2: code_integer,F4: nat > code_integer,B2: nat,C: nat] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ A2 @ ( F4 @ B2 ) )
% 2.62/3.03 => ( ( ord_less_nat @ B2 @ C )
% 2.62/3.03 => ( ! [X3: nat,Y2: nat] :
% 2.62/3.03 ( ( ord_less_nat @ X3 @ Y2 )
% 2.62/3.03 => ( ord_le6747313008572928689nteger @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.62/3.03 => ( ord_le6747313008572928689nteger @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_subst1
% 2.62/3.03 thf(fact_108_order__less__subst1,axiom,
% 2.62/3.03 ! [A2: code_integer,F4: int > code_integer,B2: int,C: int] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ A2 @ ( F4 @ B2 ) )
% 2.62/3.03 => ( ( ord_less_int @ B2 @ C )
% 2.62/3.03 => ( ! [X3: int,Y2: int] :
% 2.62/3.03 ( ( ord_less_int @ X3 @ Y2 )
% 2.62/3.03 => ( ord_le6747313008572928689nteger @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.62/3.03 => ( ord_le6747313008572928689nteger @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_subst1
% 2.62/3.03 thf(fact_109_order__less__subst1,axiom,
% 2.62/3.03 ! [A2: assn,F4: code_integer > assn,B2: code_integer,C: code_integer] :
% 2.62/3.03 ( ( ord_less_assn @ A2 @ ( F4 @ B2 ) )
% 2.62/3.03 => ( ( ord_le6747313008572928689nteger @ B2 @ C )
% 2.62/3.03 => ( ! [X3: code_integer,Y2: code_integer] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 2.62/3.03 => ( ord_less_assn @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.62/3.03 => ( ord_less_assn @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_subst1
% 2.62/3.03 thf(fact_110_order__less__subst1,axiom,
% 2.62/3.03 ! [A2: assn,F4: assn > assn,B2: assn,C: assn] :
% 2.62/3.03 ( ( ord_less_assn @ A2 @ ( F4 @ B2 ) )
% 2.62/3.03 => ( ( ord_less_assn @ B2 @ C )
% 2.62/3.03 => ( ! [X3: assn,Y2: assn] :
% 2.62/3.03 ( ( ord_less_assn @ X3 @ Y2 )
% 2.62/3.03 => ( ord_less_assn @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.62/3.03 => ( ord_less_assn @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_subst1
% 2.62/3.03 thf(fact_111_order__less__subst1,axiom,
% 2.62/3.03 ! [A2: assn,F4: num > assn,B2: num,C: num] :
% 2.62/3.03 ( ( ord_less_assn @ A2 @ ( F4 @ B2 ) )
% 2.62/3.03 => ( ( ord_less_num @ B2 @ C )
% 2.62/3.03 => ( ! [X3: num,Y2: num] :
% 2.62/3.03 ( ( ord_less_num @ X3 @ Y2 )
% 2.62/3.03 => ( ord_less_assn @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.62/3.03 => ( ord_less_assn @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_subst1
% 2.62/3.03 thf(fact_112_order__less__subst1,axiom,
% 2.62/3.03 ! [A2: assn,F4: nat > assn,B2: nat,C: nat] :
% 2.62/3.03 ( ( ord_less_assn @ A2 @ ( F4 @ B2 ) )
% 2.62/3.03 => ( ( ord_less_nat @ B2 @ C )
% 2.62/3.03 => ( ! [X3: nat,Y2: nat] :
% 2.62/3.03 ( ( ord_less_nat @ X3 @ Y2 )
% 2.62/3.03 => ( ord_less_assn @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.62/3.03 => ( ord_less_assn @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_subst1
% 2.62/3.03 thf(fact_113_order__less__subst1,axiom,
% 2.62/3.03 ! [A2: assn,F4: int > assn,B2: int,C: int] :
% 2.62/3.03 ( ( ord_less_assn @ A2 @ ( F4 @ B2 ) )
% 2.62/3.03 => ( ( ord_less_int @ B2 @ C )
% 2.62/3.03 => ( ! [X3: int,Y2: int] :
% 2.62/3.03 ( ( ord_less_int @ X3 @ Y2 )
% 2.62/3.03 => ( ord_less_assn @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.62/3.03 => ( ord_less_assn @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_subst1
% 2.62/3.03 thf(fact_114_order__less__irrefl,axiom,
% 2.62/3.03 ! [X: code_integer] :
% 2.62/3.03 ~ ( ord_le6747313008572928689nteger @ X @ X ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_irrefl
% 2.62/3.03 thf(fact_115_order__less__irrefl,axiom,
% 2.62/3.03 ! [X: assn] :
% 2.62/3.03 ~ ( ord_less_assn @ X @ X ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_irrefl
% 2.62/3.03 thf(fact_116_order__less__irrefl,axiom,
% 2.62/3.03 ! [X: num] :
% 2.62/3.03 ~ ( ord_less_num @ X @ X ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_irrefl
% 2.62/3.03 thf(fact_117_order__less__irrefl,axiom,
% 2.62/3.03 ! [X: nat] :
% 2.62/3.03 ~ ( ord_less_nat @ X @ X ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_irrefl
% 2.62/3.03 thf(fact_118_order__less__irrefl,axiom,
% 2.62/3.03 ! [X: int] :
% 2.62/3.03 ~ ( ord_less_int @ X @ X ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_irrefl
% 2.62/3.03 thf(fact_119_ord__less__eq__subst,axiom,
% 2.62/3.03 ! [A2: code_integer,B2: code_integer,F4: code_integer > code_integer,C: code_integer] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 2.62/3.03 => ( ( ( F4 @ B2 )
% 2.62/3.03 = C )
% 2.62/3.03 => ( ! [X3: code_integer,Y2: code_integer] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 2.62/3.03 => ( ord_le6747313008572928689nteger @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.62/3.03 => ( ord_le6747313008572928689nteger @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % ord_less_eq_subst
% 2.62/3.03 thf(fact_120_ord__less__eq__subst,axiom,
% 2.62/3.03 ! [A2: code_integer,B2: code_integer,F4: code_integer > assn,C: assn] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 2.62/3.03 => ( ( ( F4 @ B2 )
% 2.62/3.03 = C )
% 2.62/3.03 => ( ! [X3: code_integer,Y2: code_integer] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 2.62/3.03 => ( ord_less_assn @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.62/3.03 => ( ord_less_assn @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % ord_less_eq_subst
% 2.62/3.03 thf(fact_121_ord__less__eq__subst,axiom,
% 2.62/3.03 ! [A2: code_integer,B2: code_integer,F4: code_integer > num,C: num] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 2.62/3.03 => ( ( ( F4 @ B2 )
% 2.62/3.03 = C )
% 2.62/3.03 => ( ! [X3: code_integer,Y2: code_integer] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 2.62/3.03 => ( ord_less_num @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.62/3.03 => ( ord_less_num @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % ord_less_eq_subst
% 2.62/3.03 thf(fact_122_ord__less__eq__subst,axiom,
% 2.62/3.03 ! [A2: code_integer,B2: code_integer,F4: code_integer > nat,C: nat] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 2.62/3.03 => ( ( ( F4 @ B2 )
% 2.62/3.03 = C )
% 2.62/3.03 => ( ! [X3: code_integer,Y2: code_integer] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 2.62/3.03 => ( ord_less_nat @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.62/3.03 => ( ord_less_nat @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % ord_less_eq_subst
% 2.62/3.03 thf(fact_123_ord__less__eq__subst,axiom,
% 2.62/3.03 ! [A2: code_integer,B2: code_integer,F4: code_integer > int,C: int] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 2.62/3.03 => ( ( ( F4 @ B2 )
% 2.62/3.03 = C )
% 2.62/3.03 => ( ! [X3: code_integer,Y2: code_integer] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 2.62/3.03 => ( ord_less_int @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.62/3.03 => ( ord_less_int @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % ord_less_eq_subst
% 2.62/3.03 thf(fact_124_ord__less__eq__subst,axiom,
% 2.62/3.03 ! [A2: assn,B2: assn,F4: assn > code_integer,C: code_integer] :
% 2.62/3.03 ( ( ord_less_assn @ A2 @ B2 )
% 2.62/3.03 => ( ( ( F4 @ B2 )
% 2.62/3.03 = C )
% 2.62/3.03 => ( ! [X3: assn,Y2: assn] :
% 2.62/3.03 ( ( ord_less_assn @ X3 @ Y2 )
% 2.62/3.03 => ( ord_le6747313008572928689nteger @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.62/3.03 => ( ord_le6747313008572928689nteger @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % ord_less_eq_subst
% 2.62/3.03 thf(fact_125_ord__less__eq__subst,axiom,
% 2.62/3.03 ! [A2: assn,B2: assn,F4: assn > assn,C: assn] :
% 2.62/3.03 ( ( ord_less_assn @ A2 @ B2 )
% 2.62/3.03 => ( ( ( F4 @ B2 )
% 2.62/3.03 = C )
% 2.62/3.03 => ( ! [X3: assn,Y2: assn] :
% 2.62/3.03 ( ( ord_less_assn @ X3 @ Y2 )
% 2.62/3.03 => ( ord_less_assn @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.62/3.03 => ( ord_less_assn @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % ord_less_eq_subst
% 2.62/3.03 thf(fact_126_ord__less__eq__subst,axiom,
% 2.62/3.03 ! [A2: assn,B2: assn,F4: assn > num,C: num] :
% 2.62/3.03 ( ( ord_less_assn @ A2 @ B2 )
% 2.62/3.03 => ( ( ( F4 @ B2 )
% 2.62/3.03 = C )
% 2.62/3.03 => ( ! [X3: assn,Y2: assn] :
% 2.62/3.03 ( ( ord_less_assn @ X3 @ Y2 )
% 2.62/3.03 => ( ord_less_num @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.62/3.03 => ( ord_less_num @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % ord_less_eq_subst
% 2.62/3.03 thf(fact_127_ord__less__eq__subst,axiom,
% 2.62/3.03 ! [A2: assn,B2: assn,F4: assn > nat,C: nat] :
% 2.62/3.03 ( ( ord_less_assn @ A2 @ B2 )
% 2.62/3.03 => ( ( ( F4 @ B2 )
% 2.62/3.03 = C )
% 2.62/3.03 => ( ! [X3: assn,Y2: assn] :
% 2.62/3.03 ( ( ord_less_assn @ X3 @ Y2 )
% 2.62/3.03 => ( ord_less_nat @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.62/3.03 => ( ord_less_nat @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % ord_less_eq_subst
% 2.62/3.03 thf(fact_128_ord__less__eq__subst,axiom,
% 2.62/3.03 ! [A2: assn,B2: assn,F4: assn > int,C: int] :
% 2.62/3.03 ( ( ord_less_assn @ A2 @ B2 )
% 2.62/3.03 => ( ( ( F4 @ B2 )
% 2.62/3.03 = C )
% 2.62/3.03 => ( ! [X3: assn,Y2: assn] :
% 2.62/3.03 ( ( ord_less_assn @ X3 @ Y2 )
% 2.62/3.03 => ( ord_less_int @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.62/3.03 => ( ord_less_int @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % ord_less_eq_subst
% 2.62/3.03 thf(fact_129_ord__eq__less__subst,axiom,
% 2.62/3.03 ! [A2: code_integer,F4: code_integer > code_integer,B2: code_integer,C: code_integer] :
% 2.62/3.03 ( ( A2
% 2.62/3.03 = ( F4 @ B2 ) )
% 2.62/3.03 => ( ( ord_le6747313008572928689nteger @ B2 @ C )
% 2.62/3.03 => ( ! [X3: code_integer,Y2: code_integer] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 2.62/3.03 => ( ord_le6747313008572928689nteger @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.62/3.03 => ( ord_le6747313008572928689nteger @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % ord_eq_less_subst
% 2.62/3.03 thf(fact_130_ord__eq__less__subst,axiom,
% 2.62/3.03 ! [A2: assn,F4: code_integer > assn,B2: code_integer,C: code_integer] :
% 2.62/3.03 ( ( A2
% 2.62/3.03 = ( F4 @ B2 ) )
% 2.62/3.03 => ( ( ord_le6747313008572928689nteger @ B2 @ C )
% 2.62/3.03 => ( ! [X3: code_integer,Y2: code_integer] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 2.62/3.03 => ( ord_less_assn @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.62/3.03 => ( ord_less_assn @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % ord_eq_less_subst
% 2.62/3.03 thf(fact_131_ord__eq__less__subst,axiom,
% 2.62/3.03 ! [A2: num,F4: code_integer > num,B2: code_integer,C: code_integer] :
% 2.62/3.03 ( ( A2
% 2.62/3.03 = ( F4 @ B2 ) )
% 2.62/3.03 => ( ( ord_le6747313008572928689nteger @ B2 @ C )
% 2.62/3.03 => ( ! [X3: code_integer,Y2: code_integer] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 2.62/3.03 => ( ord_less_num @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.62/3.03 => ( ord_less_num @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % ord_eq_less_subst
% 2.62/3.03 thf(fact_132_ord__eq__less__subst,axiom,
% 2.62/3.03 ! [A2: nat,F4: code_integer > nat,B2: code_integer,C: code_integer] :
% 2.62/3.03 ( ( A2
% 2.62/3.03 = ( F4 @ B2 ) )
% 2.62/3.03 => ( ( ord_le6747313008572928689nteger @ B2 @ C )
% 2.62/3.03 => ( ! [X3: code_integer,Y2: code_integer] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 2.62/3.03 => ( ord_less_nat @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.62/3.03 => ( ord_less_nat @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % ord_eq_less_subst
% 2.62/3.03 thf(fact_133_ord__eq__less__subst,axiom,
% 2.62/3.03 ! [A2: int,F4: code_integer > int,B2: code_integer,C: code_integer] :
% 2.62/3.03 ( ( A2
% 2.62/3.03 = ( F4 @ B2 ) )
% 2.62/3.03 => ( ( ord_le6747313008572928689nteger @ B2 @ C )
% 2.62/3.03 => ( ! [X3: code_integer,Y2: code_integer] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 2.62/3.03 => ( ord_less_int @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.62/3.03 => ( ord_less_int @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % ord_eq_less_subst
% 2.62/3.03 thf(fact_134_ord__eq__less__subst,axiom,
% 2.62/3.03 ! [A2: code_integer,F4: assn > code_integer,B2: assn,C: assn] :
% 2.62/3.03 ( ( A2
% 2.62/3.03 = ( F4 @ B2 ) )
% 2.62/3.03 => ( ( ord_less_assn @ B2 @ C )
% 2.62/3.03 => ( ! [X3: assn,Y2: assn] :
% 2.62/3.03 ( ( ord_less_assn @ X3 @ Y2 )
% 2.62/3.03 => ( ord_le6747313008572928689nteger @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.62/3.03 => ( ord_le6747313008572928689nteger @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % ord_eq_less_subst
% 2.62/3.03 thf(fact_135_ord__eq__less__subst,axiom,
% 2.62/3.03 ! [A2: assn,F4: assn > assn,B2: assn,C: assn] :
% 2.62/3.03 ( ( A2
% 2.62/3.03 = ( F4 @ B2 ) )
% 2.62/3.03 => ( ( ord_less_assn @ B2 @ C )
% 2.62/3.03 => ( ! [X3: assn,Y2: assn] :
% 2.62/3.03 ( ( ord_less_assn @ X3 @ Y2 )
% 2.62/3.03 => ( ord_less_assn @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.62/3.03 => ( ord_less_assn @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % ord_eq_less_subst
% 2.62/3.03 thf(fact_136_ord__eq__less__subst,axiom,
% 2.62/3.03 ! [A2: num,F4: assn > num,B2: assn,C: assn] :
% 2.62/3.03 ( ( A2
% 2.62/3.03 = ( F4 @ B2 ) )
% 2.62/3.03 => ( ( ord_less_assn @ B2 @ C )
% 2.62/3.03 => ( ! [X3: assn,Y2: assn] :
% 2.62/3.03 ( ( ord_less_assn @ X3 @ Y2 )
% 2.62/3.03 => ( ord_less_num @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.62/3.03 => ( ord_less_num @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % ord_eq_less_subst
% 2.62/3.03 thf(fact_137_ord__eq__less__subst,axiom,
% 2.62/3.03 ! [A2: nat,F4: assn > nat,B2: assn,C: assn] :
% 2.62/3.03 ( ( A2
% 2.62/3.03 = ( F4 @ B2 ) )
% 2.62/3.03 => ( ( ord_less_assn @ B2 @ C )
% 2.62/3.03 => ( ! [X3: assn,Y2: assn] :
% 2.62/3.03 ( ( ord_less_assn @ X3 @ Y2 )
% 2.62/3.03 => ( ord_less_nat @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.62/3.03 => ( ord_less_nat @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % ord_eq_less_subst
% 2.62/3.03 thf(fact_138_ord__eq__less__subst,axiom,
% 2.62/3.03 ! [A2: int,F4: assn > int,B2: assn,C: assn] :
% 2.62/3.03 ( ( A2
% 2.62/3.03 = ( F4 @ B2 ) )
% 2.62/3.03 => ( ( ord_less_assn @ B2 @ C )
% 2.62/3.03 => ( ! [X3: assn,Y2: assn] :
% 2.62/3.03 ( ( ord_less_assn @ X3 @ Y2 )
% 2.62/3.03 => ( ord_less_int @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.62/3.03 => ( ord_less_int @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % ord_eq_less_subst
% 2.62/3.03 thf(fact_139_order__less__trans,axiom,
% 2.62/3.03 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ X @ Y )
% 2.62/3.03 => ( ( ord_le6747313008572928689nteger @ Y @ Z )
% 2.62/3.03 => ( ord_le6747313008572928689nteger @ X @ Z ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_trans
% 2.62/3.03 thf(fact_140_order__less__trans,axiom,
% 2.62/3.03 ! [X: assn,Y: assn,Z: assn] :
% 2.62/3.03 ( ( ord_less_assn @ X @ Y )
% 2.62/3.03 => ( ( ord_less_assn @ Y @ Z )
% 2.62/3.03 => ( ord_less_assn @ X @ Z ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_trans
% 2.62/3.03 thf(fact_141_order__less__trans,axiom,
% 2.62/3.03 ! [X: num,Y: num,Z: num] :
% 2.62/3.03 ( ( ord_less_num @ X @ Y )
% 2.62/3.03 => ( ( ord_less_num @ Y @ Z )
% 2.62/3.03 => ( ord_less_num @ X @ Z ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_trans
% 2.62/3.03 thf(fact_142_order__less__trans,axiom,
% 2.62/3.03 ! [X: nat,Y: nat,Z: nat] :
% 2.62/3.03 ( ( ord_less_nat @ X @ Y )
% 2.62/3.03 => ( ( ord_less_nat @ Y @ Z )
% 2.62/3.03 => ( ord_less_nat @ X @ Z ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_trans
% 2.62/3.03 thf(fact_143_order__less__trans,axiom,
% 2.62/3.03 ! [X: int,Y: int,Z: int] :
% 2.62/3.03 ( ( ord_less_int @ X @ Y )
% 2.62/3.03 => ( ( ord_less_int @ Y @ Z )
% 2.62/3.03 => ( ord_less_int @ X @ Z ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_trans
% 2.62/3.03 thf(fact_144_order__less__asym_H,axiom,
% 2.62/3.03 ! [A2: code_integer,B2: code_integer] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 2.62/3.03 => ~ ( ord_le6747313008572928689nteger @ B2 @ A2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_asym'
% 2.62/3.03 thf(fact_145_order__less__asym_H,axiom,
% 2.62/3.03 ! [A2: assn,B2: assn] :
% 2.62/3.03 ( ( ord_less_assn @ A2 @ B2 )
% 2.62/3.03 => ~ ( ord_less_assn @ B2 @ A2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_asym'
% 2.62/3.03 thf(fact_146_order__less__asym_H,axiom,
% 2.62/3.03 ! [A2: num,B2: num] :
% 2.62/3.03 ( ( ord_less_num @ A2 @ B2 )
% 2.62/3.03 => ~ ( ord_less_num @ B2 @ A2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_asym'
% 2.62/3.03 thf(fact_147_order__less__asym_H,axiom,
% 2.62/3.03 ! [A2: nat,B2: nat] :
% 2.62/3.03 ( ( ord_less_nat @ A2 @ B2 )
% 2.62/3.03 => ~ ( ord_less_nat @ B2 @ A2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_asym'
% 2.62/3.03 thf(fact_148_order__less__asym_H,axiom,
% 2.62/3.03 ! [A2: int,B2: int] :
% 2.62/3.03 ( ( ord_less_int @ A2 @ B2 )
% 2.62/3.03 => ~ ( ord_less_int @ B2 @ A2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_asym'
% 2.62/3.03 thf(fact_149_linorder__neq__iff,axiom,
% 2.62/3.03 ! [X: code_integer,Y: code_integer] :
% 2.62/3.03 ( ( X != Y )
% 2.62/3.03 = ( ( ord_le6747313008572928689nteger @ X @ Y )
% 2.62/3.03 | ( ord_le6747313008572928689nteger @ Y @ X ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % linorder_neq_iff
% 2.62/3.03 thf(fact_150_linorder__neq__iff,axiom,
% 2.62/3.03 ! [X: num,Y: num] :
% 2.62/3.03 ( ( X != Y )
% 2.62/3.03 = ( ( ord_less_num @ X @ Y )
% 2.62/3.03 | ( ord_less_num @ Y @ X ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % linorder_neq_iff
% 2.62/3.03 thf(fact_151_linorder__neq__iff,axiom,
% 2.62/3.03 ! [X: nat,Y: nat] :
% 2.62/3.03 ( ( X != Y )
% 2.62/3.03 = ( ( ord_less_nat @ X @ Y )
% 2.62/3.03 | ( ord_less_nat @ Y @ X ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % linorder_neq_iff
% 2.62/3.03 thf(fact_152_linorder__neq__iff,axiom,
% 2.62/3.03 ! [X: int,Y: int] :
% 2.62/3.03 ( ( X != Y )
% 2.62/3.03 = ( ( ord_less_int @ X @ Y )
% 2.62/3.03 | ( ord_less_int @ Y @ X ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % linorder_neq_iff
% 2.62/3.03 thf(fact_153_order__less__asym,axiom,
% 2.62/3.03 ! [X: code_integer,Y: code_integer] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ X @ Y )
% 2.62/3.03 => ~ ( ord_le6747313008572928689nteger @ Y @ X ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_asym
% 2.62/3.03 thf(fact_154_order__less__asym,axiom,
% 2.62/3.03 ! [X: assn,Y: assn] :
% 2.62/3.03 ( ( ord_less_assn @ X @ Y )
% 2.62/3.03 => ~ ( ord_less_assn @ Y @ X ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_asym
% 2.62/3.03 thf(fact_155_order__less__asym,axiom,
% 2.62/3.03 ! [X: num,Y: num] :
% 2.62/3.03 ( ( ord_less_num @ X @ Y )
% 2.62/3.03 => ~ ( ord_less_num @ Y @ X ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_asym
% 2.62/3.03 thf(fact_156_order__less__asym,axiom,
% 2.62/3.03 ! [X: nat,Y: nat] :
% 2.62/3.03 ( ( ord_less_nat @ X @ Y )
% 2.62/3.03 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_asym
% 2.62/3.03 thf(fact_157_order__less__asym,axiom,
% 2.62/3.03 ! [X: int,Y: int] :
% 2.62/3.03 ( ( ord_less_int @ X @ Y )
% 2.62/3.03 => ~ ( ord_less_int @ Y @ X ) ) ).
% 2.62/3.03
% 2.62/3.03 % order_less_asym
% 2.62/3.03 thf(fact_158_linorder__neqE,axiom,
% 2.62/3.03 ! [X: code_integer,Y: code_integer] :
% 2.62/3.03 ( ( X != Y )
% 2.62/3.03 => ( ~ ( ord_le6747313008572928689nteger @ X @ Y )
% 2.62/3.03 => ( ord_le6747313008572928689nteger @ Y @ X ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % linorder_neqE
% 2.62/3.03 thf(fact_159_linorder__neqE,axiom,
% 2.62/3.03 ! [X: num,Y: num] :
% 2.62/3.03 ( ( X != Y )
% 2.62/3.03 => ( ~ ( ord_less_num @ X @ Y )
% 2.62/3.03 => ( ord_less_num @ Y @ X ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % linorder_neqE
% 2.62/3.03 thf(fact_160_linorder__neqE,axiom,
% 2.62/3.03 ! [X: nat,Y: nat] :
% 2.62/3.03 ( ( X != Y )
% 2.62/3.03 => ( ~ ( ord_less_nat @ X @ Y )
% 2.62/3.03 => ( ord_less_nat @ Y @ X ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % linorder_neqE
% 2.62/3.03 thf(fact_161_linorder__neqE,axiom,
% 2.62/3.03 ! [X: int,Y: int] :
% 2.62/3.03 ( ( X != Y )
% 2.62/3.03 => ( ~ ( ord_less_int @ X @ Y )
% 2.62/3.03 => ( ord_less_int @ Y @ X ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % linorder_neqE
% 2.62/3.03 thf(fact_162_neq__if__length__neq,axiom,
% 2.62/3.03 ! [Xs: list_c,Ys: list_c] :
% 2.62/3.03 ( ( ( size_size_list_c @ Xs )
% 2.62/3.03 != ( size_size_list_c @ Ys ) )
% 2.62/3.03 => ( Xs != Ys ) ) ).
% 2.62/3.03
% 2.62/3.03 % neq_if_length_neq
% 2.62/3.03 thf(fact_163_neq__if__length__neq,axiom,
% 2.62/3.03 ! [Xs: list_d,Ys: list_d] :
% 2.62/3.03 ( ( ( size_size_list_d @ Xs )
% 2.62/3.03 != ( size_size_list_d @ Ys ) )
% 2.62/3.03 => ( Xs != Ys ) ) ).
% 2.62/3.03
% 2.62/3.03 % neq_if_length_neq
% 2.62/3.03 thf(fact_164_neq__if__length__neq,axiom,
% 2.62/3.03 ! [Xs: list_nat,Ys: list_nat] :
% 2.62/3.03 ( ( ( size_size_list_nat @ Xs )
% 2.62/3.03 != ( size_size_list_nat @ Ys ) )
% 2.62/3.03 => ( Xs != Ys ) ) ).
% 2.62/3.03
% 2.62/3.03 % neq_if_length_neq
% 2.62/3.03 thf(fact_165_neq__if__length__neq,axiom,
% 2.62/3.03 ! [Xs: list_int,Ys: list_int] :
% 2.62/3.03 ( ( ( size_size_list_int @ Xs )
% 2.62/3.03 != ( size_size_list_int @ Ys ) )
% 2.62/3.03 => ( Xs != Ys ) ) ).
% 2.62/3.03
% 2.62/3.03 % neq_if_length_neq
% 2.62/3.03 thf(fact_166_Ex__list__of__length,axiom,
% 2.62/3.03 ! [N: nat] :
% 2.62/3.03 ? [Xs2: list_c] :
% 2.62/3.03 ( ( size_size_list_c @ Xs2 )
% 2.62/3.03 = N ) ).
% 2.62/3.03
% 2.62/3.03 % Ex_list_of_length
% 2.62/3.03 thf(fact_167_Ex__list__of__length,axiom,
% 2.62/3.03 ! [N: nat] :
% 2.62/3.03 ? [Xs2: list_d] :
% 2.62/3.03 ( ( size_size_list_d @ Xs2 )
% 2.62/3.03 = N ) ).
% 2.62/3.03
% 2.62/3.03 % Ex_list_of_length
% 2.62/3.03 thf(fact_168_Ex__list__of__length,axiom,
% 2.62/3.03 ! [N: nat] :
% 2.62/3.03 ? [Xs2: list_nat] :
% 2.62/3.03 ( ( size_size_list_nat @ Xs2 )
% 2.62/3.03 = N ) ).
% 2.62/3.03
% 2.62/3.03 % Ex_list_of_length
% 2.62/3.03 thf(fact_169_Ex__list__of__length,axiom,
% 2.62/3.03 ! [N: nat] :
% 2.62/3.03 ? [Xs2: list_int] :
% 2.62/3.03 ( ( size_size_list_int @ Xs2 )
% 2.62/3.03 = N ) ).
% 2.62/3.03
% 2.62/3.03 % Ex_list_of_length
% 2.62/3.03 thf(fact_170_length__induct,axiom,
% 2.62/3.03 ! [P: list_c > $o,Xs: list_c] :
% 2.62/3.03 ( ! [Xs2: list_c] :
% 2.62/3.03 ( ! [Ys2: list_c] :
% 2.62/3.03 ( ( ord_less_nat @ ( size_size_list_c @ Ys2 ) @ ( size_size_list_c @ Xs2 ) )
% 2.62/3.03 => ( P @ Ys2 ) )
% 2.62/3.03 => ( P @ Xs2 ) )
% 2.62/3.03 => ( P @ Xs ) ) ).
% 2.62/3.03
% 2.62/3.03 % length_induct
% 2.62/3.03 thf(fact_171_length__induct,axiom,
% 2.62/3.03 ! [P: list_d > $o,Xs: list_d] :
% 2.62/3.03 ( ! [Xs2: list_d] :
% 2.62/3.03 ( ! [Ys2: list_d] :
% 2.62/3.03 ( ( ord_less_nat @ ( size_size_list_d @ Ys2 ) @ ( size_size_list_d @ Xs2 ) )
% 2.62/3.03 => ( P @ Ys2 ) )
% 2.62/3.03 => ( P @ Xs2 ) )
% 2.62/3.03 => ( P @ Xs ) ) ).
% 2.62/3.03
% 2.62/3.03 % length_induct
% 2.62/3.03 thf(fact_172_length__induct,axiom,
% 2.62/3.03 ! [P: list_nat > $o,Xs: list_nat] :
% 2.62/3.03 ( ! [Xs2: list_nat] :
% 2.62/3.03 ( ! [Ys2: list_nat] :
% 2.62/3.03 ( ( ord_less_nat @ ( size_size_list_nat @ Ys2 ) @ ( size_size_list_nat @ Xs2 ) )
% 2.62/3.03 => ( P @ Ys2 ) )
% 2.62/3.03 => ( P @ Xs2 ) )
% 2.62/3.03 => ( P @ Xs ) ) ).
% 2.62/3.03
% 2.62/3.03 % length_induct
% 2.62/3.03 thf(fact_173_length__induct,axiom,
% 2.62/3.03 ! [P: list_int > $o,Xs: list_int] :
% 2.62/3.03 ( ! [Xs2: list_int] :
% 2.62/3.03 ( ! [Ys2: list_int] :
% 2.62/3.03 ( ( ord_less_nat @ ( size_size_list_int @ Ys2 ) @ ( size_size_list_int @ Xs2 ) )
% 2.62/3.03 => ( P @ Ys2 ) )
% 2.62/3.03 => ( P @ Xs2 ) )
% 2.62/3.03 => ( P @ Xs ) ) ).
% 2.62/3.03
% 2.62/3.03 % length_induct
% 2.62/3.03 thf(fact_174_dual__order_Ostrict__implies__not__eq,axiom,
% 2.62/3.03 ! [B2: code_integer,A2: code_integer] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ B2 @ A2 )
% 2.62/3.03 => ( A2 != B2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % dual_order.strict_implies_not_eq
% 2.62/3.03 thf(fact_175_dual__order_Ostrict__implies__not__eq,axiom,
% 2.62/3.03 ! [B2: assn,A2: assn] :
% 2.62/3.03 ( ( ord_less_assn @ B2 @ A2 )
% 2.62/3.03 => ( A2 != B2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % dual_order.strict_implies_not_eq
% 2.62/3.03 thf(fact_176_dual__order_Ostrict__implies__not__eq,axiom,
% 2.62/3.03 ! [B2: num,A2: num] :
% 2.62/3.03 ( ( ord_less_num @ B2 @ A2 )
% 2.62/3.03 => ( A2 != B2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % dual_order.strict_implies_not_eq
% 2.62/3.03 thf(fact_177_dual__order_Ostrict__implies__not__eq,axiom,
% 2.62/3.03 ! [B2: nat,A2: nat] :
% 2.62/3.03 ( ( ord_less_nat @ B2 @ A2 )
% 2.62/3.03 => ( A2 != B2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % dual_order.strict_implies_not_eq
% 2.62/3.03 thf(fact_178_dual__order_Ostrict__implies__not__eq,axiom,
% 2.62/3.03 ! [B2: int,A2: int] :
% 2.62/3.03 ( ( ord_less_int @ B2 @ A2 )
% 2.62/3.03 => ( A2 != B2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % dual_order.strict_implies_not_eq
% 2.62/3.03 thf(fact_179_order_Ostrict__implies__not__eq,axiom,
% 2.62/3.03 ! [A2: code_integer,B2: code_integer] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 2.62/3.03 => ( A2 != B2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % order.strict_implies_not_eq
% 2.62/3.03 thf(fact_180_order_Ostrict__implies__not__eq,axiom,
% 2.62/3.03 ! [A2: assn,B2: assn] :
% 2.62/3.03 ( ( ord_less_assn @ A2 @ B2 )
% 2.62/3.03 => ( A2 != B2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % order.strict_implies_not_eq
% 2.62/3.03 thf(fact_181_order_Ostrict__implies__not__eq,axiom,
% 2.62/3.03 ! [A2: num,B2: num] :
% 2.62/3.03 ( ( ord_less_num @ A2 @ B2 )
% 2.62/3.03 => ( A2 != B2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % order.strict_implies_not_eq
% 2.62/3.03 thf(fact_182_order_Ostrict__implies__not__eq,axiom,
% 2.62/3.03 ! [A2: nat,B2: nat] :
% 2.62/3.03 ( ( ord_less_nat @ A2 @ B2 )
% 2.62/3.03 => ( A2 != B2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % order.strict_implies_not_eq
% 2.62/3.03 thf(fact_183_order_Ostrict__implies__not__eq,axiom,
% 2.62/3.03 ! [A2: int,B2: int] :
% 2.62/3.03 ( ( ord_less_int @ A2 @ B2 )
% 2.62/3.03 => ( A2 != B2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % order.strict_implies_not_eq
% 2.62/3.03 thf(fact_184_dual__order_Ostrict__trans,axiom,
% 2.62/3.03 ! [B2: code_integer,A2: code_integer,C: code_integer] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ B2 @ A2 )
% 2.62/3.03 => ( ( ord_le6747313008572928689nteger @ C @ B2 )
% 2.62/3.03 => ( ord_le6747313008572928689nteger @ C @ A2 ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % dual_order.strict_trans
% 2.62/3.03 thf(fact_185_dual__order_Ostrict__trans,axiom,
% 2.62/3.03 ! [B2: assn,A2: assn,C: assn] :
% 2.62/3.03 ( ( ord_less_assn @ B2 @ A2 )
% 2.62/3.03 => ( ( ord_less_assn @ C @ B2 )
% 2.62/3.03 => ( ord_less_assn @ C @ A2 ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % dual_order.strict_trans
% 2.62/3.03 thf(fact_186_dual__order_Ostrict__trans,axiom,
% 2.62/3.03 ! [B2: num,A2: num,C: num] :
% 2.62/3.03 ( ( ord_less_num @ B2 @ A2 )
% 2.62/3.03 => ( ( ord_less_num @ C @ B2 )
% 2.62/3.03 => ( ord_less_num @ C @ A2 ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % dual_order.strict_trans
% 2.62/3.03 thf(fact_187_dual__order_Ostrict__trans,axiom,
% 2.62/3.03 ! [B2: nat,A2: nat,C: nat] :
% 2.62/3.03 ( ( ord_less_nat @ B2 @ A2 )
% 2.62/3.03 => ( ( ord_less_nat @ C @ B2 )
% 2.62/3.03 => ( ord_less_nat @ C @ A2 ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % dual_order.strict_trans
% 2.62/3.03 thf(fact_188_dual__order_Ostrict__trans,axiom,
% 2.62/3.03 ! [B2: int,A2: int,C: int] :
% 2.62/3.03 ( ( ord_less_int @ B2 @ A2 )
% 2.62/3.03 => ( ( ord_less_int @ C @ B2 )
% 2.62/3.03 => ( ord_less_int @ C @ A2 ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % dual_order.strict_trans
% 2.62/3.03 thf(fact_189_not__less__iff__gr__or__eq,axiom,
% 2.62/3.03 ! [X: code_integer,Y: code_integer] :
% 2.62/3.03 ( ( ~ ( ord_le6747313008572928689nteger @ X @ Y ) )
% 2.62/3.03 = ( ( ord_le6747313008572928689nteger @ Y @ X )
% 2.62/3.03 | ( X = Y ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % not_less_iff_gr_or_eq
% 2.62/3.03 thf(fact_190_not__less__iff__gr__or__eq,axiom,
% 2.62/3.03 ! [X: num,Y: num] :
% 2.62/3.03 ( ( ~ ( ord_less_num @ X @ Y ) )
% 2.62/3.03 = ( ( ord_less_num @ Y @ X )
% 2.62/3.03 | ( X = Y ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % not_less_iff_gr_or_eq
% 2.62/3.03 thf(fact_191_not__less__iff__gr__or__eq,axiom,
% 2.62/3.03 ! [X: nat,Y: nat] :
% 2.62/3.03 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 2.62/3.03 = ( ( ord_less_nat @ Y @ X )
% 2.62/3.03 | ( X = Y ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % not_less_iff_gr_or_eq
% 2.62/3.03 thf(fact_192_not__less__iff__gr__or__eq,axiom,
% 2.62/3.03 ! [X: int,Y: int] :
% 2.62/3.03 ( ( ~ ( ord_less_int @ X @ Y ) )
% 2.62/3.03 = ( ( ord_less_int @ Y @ X )
% 2.62/3.03 | ( X = Y ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % not_less_iff_gr_or_eq
% 2.62/3.03 thf(fact_193_order_Ostrict__trans,axiom,
% 2.62/3.03 ! [A2: code_integer,B2: code_integer,C: code_integer] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 2.62/3.03 => ( ( ord_le6747313008572928689nteger @ B2 @ C )
% 2.62/3.03 => ( ord_le6747313008572928689nteger @ A2 @ C ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % order.strict_trans
% 2.62/3.03 thf(fact_194_order_Ostrict__trans,axiom,
% 2.62/3.03 ! [A2: assn,B2: assn,C: assn] :
% 2.62/3.03 ( ( ord_less_assn @ A2 @ B2 )
% 2.62/3.03 => ( ( ord_less_assn @ B2 @ C )
% 2.62/3.03 => ( ord_less_assn @ A2 @ C ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % order.strict_trans
% 2.62/3.03 thf(fact_195_order_Ostrict__trans,axiom,
% 2.62/3.03 ! [A2: num,B2: num,C: num] :
% 2.62/3.03 ( ( ord_less_num @ A2 @ B2 )
% 2.62/3.03 => ( ( ord_less_num @ B2 @ C )
% 2.62/3.03 => ( ord_less_num @ A2 @ C ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % order.strict_trans
% 2.62/3.03 thf(fact_196_order_Ostrict__trans,axiom,
% 2.62/3.03 ! [A2: nat,B2: nat,C: nat] :
% 2.62/3.03 ( ( ord_less_nat @ A2 @ B2 )
% 2.62/3.03 => ( ( ord_less_nat @ B2 @ C )
% 2.62/3.03 => ( ord_less_nat @ A2 @ C ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % order.strict_trans
% 2.62/3.03 thf(fact_197_order_Ostrict__trans,axiom,
% 2.62/3.03 ! [A2: int,B2: int,C: int] :
% 2.62/3.03 ( ( ord_less_int @ A2 @ B2 )
% 2.62/3.03 => ( ( ord_less_int @ B2 @ C )
% 2.62/3.03 => ( ord_less_int @ A2 @ C ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % order.strict_trans
% 2.62/3.03 thf(fact_198_linorder__less__wlog,axiom,
% 2.62/3.03 ! [P: code_integer > code_integer > $o,A2: code_integer,B2: code_integer] :
% 2.62/3.03 ( ! [A4: code_integer,B4: code_integer] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ A4 @ B4 )
% 2.62/3.03 => ( P @ A4 @ B4 ) )
% 2.62/3.03 => ( ! [A4: code_integer] : ( P @ A4 @ A4 )
% 2.62/3.03 => ( ! [A4: code_integer,B4: code_integer] :
% 2.62/3.03 ( ( P @ B4 @ A4 )
% 2.62/3.03 => ( P @ A4 @ B4 ) )
% 2.62/3.03 => ( P @ A2 @ B2 ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % linorder_less_wlog
% 2.62/3.03 thf(fact_199_linorder__less__wlog,axiom,
% 2.62/3.03 ! [P: num > num > $o,A2: num,B2: num] :
% 2.62/3.03 ( ! [A4: num,B4: num] :
% 2.62/3.03 ( ( ord_less_num @ A4 @ B4 )
% 2.62/3.03 => ( P @ A4 @ B4 ) )
% 2.62/3.03 => ( ! [A4: num] : ( P @ A4 @ A4 )
% 2.62/3.03 => ( ! [A4: num,B4: num] :
% 2.62/3.03 ( ( P @ B4 @ A4 )
% 2.62/3.03 => ( P @ A4 @ B4 ) )
% 2.62/3.03 => ( P @ A2 @ B2 ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % linorder_less_wlog
% 2.62/3.03 thf(fact_200_linorder__less__wlog,axiom,
% 2.62/3.03 ! [P: nat > nat > $o,A2: nat,B2: nat] :
% 2.62/3.03 ( ! [A4: nat,B4: nat] :
% 2.62/3.03 ( ( ord_less_nat @ A4 @ B4 )
% 2.62/3.03 => ( P @ A4 @ B4 ) )
% 2.62/3.03 => ( ! [A4: nat] : ( P @ A4 @ A4 )
% 2.62/3.03 => ( ! [A4: nat,B4: nat] :
% 2.62/3.03 ( ( P @ B4 @ A4 )
% 2.62/3.03 => ( P @ A4 @ B4 ) )
% 2.62/3.03 => ( P @ A2 @ B2 ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % linorder_less_wlog
% 2.62/3.03 thf(fact_201_linorder__less__wlog,axiom,
% 2.62/3.03 ! [P: int > int > $o,A2: int,B2: int] :
% 2.62/3.03 ( ! [A4: int,B4: int] :
% 2.62/3.03 ( ( ord_less_int @ A4 @ B4 )
% 2.62/3.03 => ( P @ A4 @ B4 ) )
% 2.62/3.03 => ( ! [A4: int] : ( P @ A4 @ A4 )
% 2.62/3.03 => ( ! [A4: int,B4: int] :
% 2.62/3.03 ( ( P @ B4 @ A4 )
% 2.62/3.03 => ( P @ A4 @ B4 ) )
% 2.62/3.03 => ( P @ A2 @ B2 ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % linorder_less_wlog
% 2.62/3.03 thf(fact_202_exists__least__iff,axiom,
% 2.62/3.03 ( ( ^ [P4: nat > $o] :
% 2.62/3.03 ? [X5: nat] : ( P4 @ X5 ) )
% 2.62/3.03 = ( ^ [P2: nat > $o] :
% 2.62/3.03 ? [N2: nat] :
% 2.62/3.03 ( ( P2 @ N2 )
% 2.62/3.03 & ! [M: nat] :
% 2.62/3.03 ( ( ord_less_nat @ M @ N2 )
% 2.62/3.03 => ~ ( P2 @ M ) ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % exists_least_iff
% 2.62/3.03 thf(fact_203_dual__order_Oirrefl,axiom,
% 2.62/3.03 ! [A2: code_integer] :
% 2.62/3.03 ~ ( ord_le6747313008572928689nteger @ A2 @ A2 ) ).
% 2.62/3.03
% 2.62/3.03 % dual_order.irrefl
% 2.62/3.03 thf(fact_204_dual__order_Oirrefl,axiom,
% 2.62/3.03 ! [A2: assn] :
% 2.62/3.03 ~ ( ord_less_assn @ A2 @ A2 ) ).
% 2.62/3.03
% 2.62/3.03 % dual_order.irrefl
% 2.62/3.03 thf(fact_205_dual__order_Oirrefl,axiom,
% 2.62/3.03 ! [A2: num] :
% 2.62/3.03 ~ ( ord_less_num @ A2 @ A2 ) ).
% 2.62/3.03
% 2.62/3.03 % dual_order.irrefl
% 2.62/3.03 thf(fact_206_dual__order_Oirrefl,axiom,
% 2.62/3.03 ! [A2: nat] :
% 2.62/3.03 ~ ( ord_less_nat @ A2 @ A2 ) ).
% 2.62/3.03
% 2.62/3.03 % dual_order.irrefl
% 2.62/3.03 thf(fact_207_dual__order_Oirrefl,axiom,
% 2.62/3.03 ! [A2: int] :
% 2.62/3.03 ~ ( ord_less_int @ A2 @ A2 ) ).
% 2.62/3.03
% 2.62/3.03 % dual_order.irrefl
% 2.62/3.03 thf(fact_208_dual__order_Oasym,axiom,
% 2.62/3.03 ! [B2: code_integer,A2: code_integer] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ B2 @ A2 )
% 2.62/3.03 => ~ ( ord_le6747313008572928689nteger @ A2 @ B2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % dual_order.asym
% 2.62/3.03 thf(fact_209_dual__order_Oasym,axiom,
% 2.62/3.03 ! [B2: assn,A2: assn] :
% 2.62/3.03 ( ( ord_less_assn @ B2 @ A2 )
% 2.62/3.03 => ~ ( ord_less_assn @ A2 @ B2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % dual_order.asym
% 2.62/3.03 thf(fact_210_dual__order_Oasym,axiom,
% 2.62/3.03 ! [B2: num,A2: num] :
% 2.62/3.03 ( ( ord_less_num @ B2 @ A2 )
% 2.62/3.03 => ~ ( ord_less_num @ A2 @ B2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % dual_order.asym
% 2.62/3.03 thf(fact_211_dual__order_Oasym,axiom,
% 2.62/3.03 ! [B2: nat,A2: nat] :
% 2.62/3.03 ( ( ord_less_nat @ B2 @ A2 )
% 2.62/3.03 => ~ ( ord_less_nat @ A2 @ B2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % dual_order.asym
% 2.62/3.03 thf(fact_212_dual__order_Oasym,axiom,
% 2.62/3.03 ! [B2: int,A2: int] :
% 2.62/3.03 ( ( ord_less_int @ B2 @ A2 )
% 2.62/3.03 => ~ ( ord_less_int @ A2 @ B2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % dual_order.asym
% 2.62/3.03 thf(fact_213_linorder__cases,axiom,
% 2.62/3.03 ! [X: code_integer,Y: code_integer] :
% 2.62/3.03 ( ~ ( ord_le6747313008572928689nteger @ X @ Y )
% 2.62/3.03 => ( ( X != Y )
% 2.62/3.03 => ( ord_le6747313008572928689nteger @ Y @ X ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % linorder_cases
% 2.62/3.03 thf(fact_214_linorder__cases,axiom,
% 2.62/3.03 ! [X: num,Y: num] :
% 2.62/3.03 ( ~ ( ord_less_num @ X @ Y )
% 2.62/3.03 => ( ( X != Y )
% 2.62/3.03 => ( ord_less_num @ Y @ X ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % linorder_cases
% 2.62/3.03 thf(fact_215_linorder__cases,axiom,
% 2.62/3.03 ! [X: nat,Y: nat] :
% 2.62/3.03 ( ~ ( ord_less_nat @ X @ Y )
% 2.62/3.03 => ( ( X != Y )
% 2.62/3.03 => ( ord_less_nat @ Y @ X ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % linorder_cases
% 2.62/3.03 thf(fact_216_linorder__cases,axiom,
% 2.62/3.03 ! [X: int,Y: int] :
% 2.62/3.03 ( ~ ( ord_less_int @ X @ Y )
% 2.62/3.03 => ( ( X != Y )
% 2.62/3.03 => ( ord_less_int @ Y @ X ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % linorder_cases
% 2.62/3.03 thf(fact_217_antisym__conv3,axiom,
% 2.62/3.03 ! [Y: code_integer,X: code_integer] :
% 2.62/3.03 ( ~ ( ord_le6747313008572928689nteger @ Y @ X )
% 2.62/3.03 => ( ( ~ ( ord_le6747313008572928689nteger @ X @ Y ) )
% 2.62/3.03 = ( X = Y ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % antisym_conv3
% 2.62/3.03 thf(fact_218_antisym__conv3,axiom,
% 2.62/3.03 ! [Y: num,X: num] :
% 2.62/3.03 ( ~ ( ord_less_num @ Y @ X )
% 2.62/3.03 => ( ( ~ ( ord_less_num @ X @ Y ) )
% 2.62/3.03 = ( X = Y ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % antisym_conv3
% 2.62/3.03 thf(fact_219_antisym__conv3,axiom,
% 2.62/3.03 ! [Y: nat,X: nat] :
% 2.62/3.03 ( ~ ( ord_less_nat @ Y @ X )
% 2.62/3.03 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 2.62/3.03 = ( X = Y ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % antisym_conv3
% 2.62/3.03 thf(fact_220_antisym__conv3,axiom,
% 2.62/3.03 ! [Y: int,X: int] :
% 2.62/3.03 ( ~ ( ord_less_int @ Y @ X )
% 2.62/3.03 => ( ( ~ ( ord_less_int @ X @ Y ) )
% 2.62/3.03 = ( X = Y ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % antisym_conv3
% 2.62/3.03 thf(fact_221_less__induct,axiom,
% 2.62/3.03 ! [P: nat > $o,A2: nat] :
% 2.62/3.03 ( ! [X3: nat] :
% 2.62/3.03 ( ! [Y3: nat] :
% 2.62/3.03 ( ( ord_less_nat @ Y3 @ X3 )
% 2.62/3.03 => ( P @ Y3 ) )
% 2.62/3.03 => ( P @ X3 ) )
% 2.62/3.03 => ( P @ A2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % less_induct
% 2.62/3.03 thf(fact_222_ord__less__eq__trans,axiom,
% 2.62/3.03 ! [A2: code_integer,B2: code_integer,C: code_integer] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 2.62/3.03 => ( ( B2 = C )
% 2.62/3.03 => ( ord_le6747313008572928689nteger @ A2 @ C ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % ord_less_eq_trans
% 2.62/3.03 thf(fact_223_ord__less__eq__trans,axiom,
% 2.62/3.03 ! [A2: assn,B2: assn,C: assn] :
% 2.62/3.03 ( ( ord_less_assn @ A2 @ B2 )
% 2.62/3.03 => ( ( B2 = C )
% 2.62/3.03 => ( ord_less_assn @ A2 @ C ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % ord_less_eq_trans
% 2.62/3.03 thf(fact_224_ord__less__eq__trans,axiom,
% 2.62/3.03 ! [A2: num,B2: num,C: num] :
% 2.62/3.03 ( ( ord_less_num @ A2 @ B2 )
% 2.62/3.03 => ( ( B2 = C )
% 2.62/3.03 => ( ord_less_num @ A2 @ C ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % ord_less_eq_trans
% 2.62/3.03 thf(fact_225_ord__less__eq__trans,axiom,
% 2.62/3.03 ! [A2: nat,B2: nat,C: nat] :
% 2.62/3.03 ( ( ord_less_nat @ A2 @ B2 )
% 2.62/3.03 => ( ( B2 = C )
% 2.62/3.03 => ( ord_less_nat @ A2 @ C ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % ord_less_eq_trans
% 2.62/3.03 thf(fact_226_ord__less__eq__trans,axiom,
% 2.62/3.03 ! [A2: int,B2: int,C: int] :
% 2.62/3.03 ( ( ord_less_int @ A2 @ B2 )
% 2.62/3.03 => ( ( B2 = C )
% 2.62/3.03 => ( ord_less_int @ A2 @ C ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % ord_less_eq_trans
% 2.62/3.03 thf(fact_227_ord__eq__less__trans,axiom,
% 2.62/3.03 ! [A2: code_integer,B2: code_integer,C: code_integer] :
% 2.62/3.03 ( ( A2 = B2 )
% 2.62/3.03 => ( ( ord_le6747313008572928689nteger @ B2 @ C )
% 2.62/3.03 => ( ord_le6747313008572928689nteger @ A2 @ C ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % ord_eq_less_trans
% 2.62/3.03 thf(fact_228_ord__eq__less__trans,axiom,
% 2.62/3.03 ! [A2: assn,B2: assn,C: assn] :
% 2.62/3.03 ( ( A2 = B2 )
% 2.62/3.03 => ( ( ord_less_assn @ B2 @ C )
% 2.62/3.03 => ( ord_less_assn @ A2 @ C ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % ord_eq_less_trans
% 2.62/3.03 thf(fact_229_ord__eq__less__trans,axiom,
% 2.62/3.03 ! [A2: num,B2: num,C: num] :
% 2.62/3.03 ( ( A2 = B2 )
% 2.62/3.03 => ( ( ord_less_num @ B2 @ C )
% 2.62/3.03 => ( ord_less_num @ A2 @ C ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % ord_eq_less_trans
% 2.62/3.03 thf(fact_230_ord__eq__less__trans,axiom,
% 2.62/3.03 ! [A2: nat,B2: nat,C: nat] :
% 2.62/3.03 ( ( A2 = B2 )
% 2.62/3.03 => ( ( ord_less_nat @ B2 @ C )
% 2.62/3.03 => ( ord_less_nat @ A2 @ C ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % ord_eq_less_trans
% 2.62/3.03 thf(fact_231_ord__eq__less__trans,axiom,
% 2.62/3.03 ! [A2: int,B2: int,C: int] :
% 2.62/3.03 ( ( A2 = B2 )
% 2.62/3.03 => ( ( ord_less_int @ B2 @ C )
% 2.62/3.03 => ( ord_less_int @ A2 @ C ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % ord_eq_less_trans
% 2.62/3.03 thf(fact_232_order_Oasym,axiom,
% 2.62/3.03 ! [A2: code_integer,B2: code_integer] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 2.62/3.03 => ~ ( ord_le6747313008572928689nteger @ B2 @ A2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % order.asym
% 2.62/3.03 thf(fact_233_order_Oasym,axiom,
% 2.62/3.03 ! [A2: assn,B2: assn] :
% 2.62/3.03 ( ( ord_less_assn @ A2 @ B2 )
% 2.62/3.03 => ~ ( ord_less_assn @ B2 @ A2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % order.asym
% 2.62/3.03 thf(fact_234_order_Oasym,axiom,
% 2.62/3.03 ! [A2: num,B2: num] :
% 2.62/3.03 ( ( ord_less_num @ A2 @ B2 )
% 2.62/3.03 => ~ ( ord_less_num @ B2 @ A2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % order.asym
% 2.62/3.03 thf(fact_235_order_Oasym,axiom,
% 2.62/3.03 ! [A2: nat,B2: nat] :
% 2.62/3.03 ( ( ord_less_nat @ A2 @ B2 )
% 2.62/3.03 => ~ ( ord_less_nat @ B2 @ A2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % order.asym
% 2.62/3.03 thf(fact_236_order_Oasym,axiom,
% 2.62/3.03 ! [A2: int,B2: int] :
% 2.62/3.03 ( ( ord_less_int @ A2 @ B2 )
% 2.62/3.03 => ~ ( ord_less_int @ B2 @ A2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % order.asym
% 2.62/3.03 thf(fact_237_less__imp__neq,axiom,
% 2.62/3.03 ! [X: code_integer,Y: code_integer] :
% 2.62/3.03 ( ( ord_le6747313008572928689nteger @ X @ Y )
% 2.62/3.03 => ( X != Y ) ) ).
% 2.62/3.03
% 2.62/3.03 % less_imp_neq
% 2.62/3.03 thf(fact_238_less__imp__neq,axiom,
% 2.62/3.03 ! [X: assn,Y: assn] :
% 2.62/3.03 ( ( ord_less_assn @ X @ Y )
% 2.62/3.03 => ( X != Y ) ) ).
% 2.62/3.03
% 2.62/3.03 % less_imp_neq
% 2.62/3.03 thf(fact_239_less__imp__neq,axiom,
% 2.62/3.03 ! [X: num,Y: num] :
% 2.62/3.03 ( ( ord_less_num @ X @ Y )
% 2.62/3.03 => ( X != Y ) ) ).
% 2.62/3.03
% 2.62/3.03 % less_imp_neq
% 2.62/3.03 thf(fact_240_less__imp__neq,axiom,
% 2.62/3.03 ! [X: nat,Y: nat] :
% 2.62/3.03 ( ( ord_less_nat @ X @ Y )
% 2.62/3.03 => ( X != Y ) ) ).
% 2.62/3.03
% 2.62/3.03 % less_imp_neq
% 2.62/3.03 thf(fact_241_less__imp__neq,axiom,
% 2.62/3.03 ! [X: int,Y: int] :
% 2.62/3.03 ( ( ord_less_int @ X @ Y )
% 2.62/3.03 => ( X != Y ) ) ).
% 2.62/3.03
% 2.62/3.03 % less_imp_neq
% 2.62/3.03 thf(fact_242_gt__ex,axiom,
% 2.62/3.03 ! [X: nat] :
% 2.62/3.03 ? [X_1: nat] : ( ord_less_nat @ X @ X_1 ) ).
% 2.62/3.03
% 2.62/3.03 % gt_ex
% 2.62/3.03 thf(fact_243_gt__ex,axiom,
% 2.62/3.03 ! [X: int] :
% 2.62/3.03 ? [X_1: int] : ( ord_less_int @ X @ X_1 ) ).
% 2.62/3.03
% 2.62/3.03 % gt_ex
% 2.62/3.03 thf(fact_244_lt__ex,axiom,
% 2.62/3.03 ! [X: int] :
% 2.62/3.03 ? [Y2: int] : ( ord_less_int @ Y2 @ X ) ).
% 2.62/3.03
% 2.62/3.03 % lt_ex
% 2.62/3.03 thf(fact_245_bot_Onot__eq__extremum,axiom,
% 2.62/3.03 ! [A2: set_Pr4329608150637261639at_nat] :
% 2.62/3.03 ( ( A2 != bot_bo228742789529271731at_nat )
% 2.62/3.03 = ( ord_le2604355607129572851at_nat @ bot_bo228742789529271731at_nat @ A2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % bot.not_eq_extremum
% 2.62/3.03 thf(fact_246_bot_Onot__eq__extremum,axiom,
% 2.62/3.03 ! [A2: set_Pr1261947904930325089at_nat] :
% 2.62/3.03 ( ( A2 != bot_bo2099793752762293965at_nat )
% 2.62/3.03 = ( ord_le7866589430770878221at_nat @ bot_bo2099793752762293965at_nat @ A2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % bot.not_eq_extremum
% 2.62/3.03 thf(fact_247_bot_Onot__eq__extremum,axiom,
% 2.62/3.03 ! [A2: set_o] :
% 2.62/3.03 ( ( A2 != bot_bot_set_o )
% 2.62/3.03 = ( ord_less_set_o @ bot_bot_set_o @ A2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % bot.not_eq_extremum
% 2.62/3.03 thf(fact_248_bot_Onot__eq__extremum,axiom,
% 2.62/3.03 ! [A2: set_nat] :
% 2.62/3.03 ( ( A2 != bot_bot_set_nat )
% 2.62/3.03 = ( ord_less_set_nat @ bot_bot_set_nat @ A2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % bot.not_eq_extremum
% 2.62/3.03 thf(fact_249_bot_Onot__eq__extremum,axiom,
% 2.62/3.03 ! [A2: set_int] :
% 2.62/3.03 ( ( A2 != bot_bot_set_int )
% 2.62/3.03 = ( ord_less_set_int @ bot_bot_set_int @ A2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % bot.not_eq_extremum
% 2.62/3.03 thf(fact_250_bot_Onot__eq__extremum,axiom,
% 2.62/3.03 ! [A2: assn] :
% 2.62/3.03 ( ( A2 != bot_bot_assn )
% 2.62/3.03 = ( ord_less_assn @ bot_bot_assn @ A2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % bot.not_eq_extremum
% 2.62/3.03 thf(fact_251_bot_Onot__eq__extremum,axiom,
% 2.62/3.03 ! [A2: nat] :
% 2.62/3.03 ( ( A2 != bot_bot_nat )
% 2.62/3.03 = ( ord_less_nat @ bot_bot_nat @ A2 ) ) ).
% 2.62/3.03
% 2.62/3.03 % bot.not_eq_extremum
% 2.62/3.03 thf(fact_252_bot_Oextremum__strict,axiom,
% 2.62/3.03 ! [A2: set_Pr4329608150637261639at_nat] :
% 2.62/3.03 ~ ( ord_le2604355607129572851at_nat @ A2 @ bot_bo228742789529271731at_nat ) ).
% 2.62/3.03
% 2.62/3.03 % bot.extremum_strict
% 2.62/3.03 thf(fact_253_bot_Oextremum__strict,axiom,
% 2.62/3.03 ! [A2: set_Pr1261947904930325089at_nat] :
% 2.62/3.03 ~ ( ord_le7866589430770878221at_nat @ A2 @ bot_bo2099793752762293965at_nat ) ).
% 2.62/3.03
% 2.62/3.03 % bot.extremum_strict
% 2.62/3.03 thf(fact_254_bot_Oextremum__strict,axiom,
% 2.62/3.03 ! [A2: set_o] :
% 2.62/3.03 ~ ( ord_less_set_o @ A2 @ bot_bot_set_o ) ).
% 2.62/3.03
% 2.62/3.03 % bot.extremum_strict
% 2.62/3.03 thf(fact_255_bot_Oextremum__strict,axiom,
% 2.62/3.03 ! [A2: set_nat] :
% 2.62/3.03 ~ ( ord_less_set_nat @ A2 @ bot_bot_set_nat ) ).
% 2.62/3.03
% 2.62/3.03 % bot.extremum_strict
% 2.62/3.03 thf(fact_256_bot_Oextremum__strict,axiom,
% 2.62/3.03 ! [A2: set_int] :
% 2.62/3.03 ~ ( ord_less_set_int @ A2 @ bot_bot_set_int ) ).
% 2.62/3.03
% 2.62/3.03 % bot.extremum_strict
% 2.62/3.03 thf(fact_257_bot_Oextremum__strict,axiom,
% 2.62/3.03 ! [A2: assn] :
% 2.62/3.03 ~ ( ord_less_assn @ A2 @ bot_bot_assn ) ).
% 2.62/3.03
% 2.62/3.03 % bot.extremum_strict
% 2.62/3.03 thf(fact_258_bot_Oextremum__strict,axiom,
% 2.62/3.03 ! [A2: nat] :
% 2.62/3.03 ~ ( ord_less_nat @ A2 @ bot_bot_nat ) ).
% 2.62/3.03
% 2.62/3.03 % bot.extremum_strict
% 2.62/3.03 thf(fact_259_list__assn__aux__ineq__len,axiom,
% 2.62/3.03 ! [L: list_c,Li: list_c,A: c > c > assn] :
% 2.62/3.03 ( ( ( size_size_list_c @ L )
% 2.62/3.03 != ( size_size_list_c @ Li ) )
% 2.62/3.03 => ( ( vEBT_L7968352277243653187sn_c_c @ A @ L @ Li )
% 2.62/3.03 = bot_bot_assn ) ) ).
% 2.62/3.03
% 2.62/3.03 % list_assn_aux_ineq_len
% 2.62/3.03 thf(fact_260_list__assn__aux__ineq__len,axiom,
% 2.62/3.03 ! [L: list_c,Li: list_d,A: c > d > assn] :
% 2.62/3.03 ( ( ( size_size_list_c @ L )
% 2.62/3.03 != ( size_size_list_d @ Li ) )
% 2.62/3.03 => ( ( vEBT_L7968352277243653188sn_c_d @ A @ L @ Li )
% 2.62/3.03 = bot_bot_assn ) ) ).
% 2.62/3.03
% 2.62/3.03 % list_assn_aux_ineq_len
% 2.62/3.03 thf(fact_261_list__assn__aux__ineq__len,axiom,
% 2.62/3.03 ! [L: list_c,Li: list_nat,A: c > nat > assn] :
% 2.62/3.03 ( ( ( size_size_list_c @ L )
% 2.62/3.03 != ( size_size_list_nat @ Li ) )
% 2.62/3.03 => ( ( vEBT_L4839309063161974733_c_nat @ A @ L @ Li )
% 2.62/3.03 = bot_bot_assn ) ) ).
% 2.62/3.03
% 2.62/3.03 % list_assn_aux_ineq_len
% 2.62/3.03 thf(fact_262_list__assn__aux__ineq__len,axiom,
% 2.62/3.03 ! [L: list_c,Li: list_int,A: c > int > assn] :
% 2.62/3.03 ( ( ( size_size_list_c @ L )
% 2.62/3.03 != ( size_size_list_int @ Li ) )
% 2.62/3.03 => ( ( vEBT_L4836818592652924457_c_int @ A @ L @ Li )
% 2.62/3.03 = bot_bot_assn ) ) ).
% 2.62/3.03
% 2.62/3.03 % list_assn_aux_ineq_len
% 2.62/3.03 thf(fact_263_list__assn__aux__ineq__len,axiom,
% 2.62/3.03 ! [L: list_d,Li: list_c,A: d > c > assn] :
% 2.62/3.03 ( ( ( size_size_list_d @ L )
% 2.62/3.03 != ( size_size_list_c @ Li ) )
% 2.62/3.03 => ( ( vEBT_L5180896695270977154sn_d_c @ A @ L @ Li )
% 2.62/3.03 = bot_bot_assn ) ) ).
% 2.62/3.03
% 2.62/3.03 % list_assn_aux_ineq_len
% 2.62/3.03 thf(fact_264_list__assn__aux__ineq__len,axiom,
% 2.62/3.03 ! [L: list_d,Li: list_d,A: d > d > assn] :
% 2.62/3.03 ( ( ( size_size_list_d @ L )
% 2.62/3.03 != ( size_size_list_d @ Li ) )
% 2.62/3.03 => ( ( vEBT_L5180896695270977155sn_d_d @ A @ L @ Li )
% 2.62/3.03 = bot_bot_assn ) ) ).
% 2.62/3.03
% 2.62/3.03 % list_assn_aux_ineq_len
% 2.62/3.03 thf(fact_265_list__assn__aux__ineq__len,axiom,
% 2.62/3.03 ! [L: list_d,Li: list_nat,A: d > nat > assn] :
% 2.62/3.03 ( ( ( size_size_list_d @ L )
% 2.62/3.03 != ( size_size_list_nat @ Li ) )
% 2.62/3.03 => ( ( vEBT_L6074753392118369230_d_nat @ A @ L @ Li )
% 2.62/3.03 = bot_bot_assn ) ) ).
% 2.62/3.03
% 2.62/3.03 % list_assn_aux_ineq_len
% 2.62/3.03 thf(fact_266_list__assn__aux__ineq__len,axiom,
% 2.62/3.03 ! [L: list_d,Li: list_int,A: d > int > assn] :
% 2.62/3.03 ( ( ( size_size_list_d @ L )
% 2.62/3.03 != ( size_size_list_int @ Li ) )
% 2.62/3.03 => ( ( vEBT_L6072262921609318954_d_int @ A @ L @ Li )
% 2.62/3.03 = bot_bot_assn ) ) ).
% 2.62/3.03
% 2.62/3.03 % list_assn_aux_ineq_len
% 2.62/3.03 thf(fact_267_list__assn__aux__ineq__len,axiom,
% 2.62/3.03 ! [L: list_nat,Li: list_c,A: nat > c > assn] :
% 2.62/3.03 ( ( ( size_size_list_nat @ L )
% 2.62/3.03 != ( size_size_list_c @ Li ) )
% 2.62/3.03 => ( ( vEBT_L6400351906427472171_nat_c @ A @ L @ Li )
% 2.62/3.03 = bot_bot_assn ) ) ).
% 2.62/3.03
% 2.62/3.03 % list_assn_aux_ineq_len
% 2.62/3.03 thf(fact_268_list__assn__aux__ineq__len,axiom,
% 2.62/3.03 ! [L: list_nat,Li: list_d,A: nat > d > assn] :
% 2.62/3.03 ( ( ( size_size_list_nat @ L )
% 2.62/3.03 != ( size_size_list_d @ Li ) )
% 2.62/3.03 => ( ( vEBT_L6400351906427472172_nat_d @ A @ L @ Li )
% 2.62/3.03 = bot_bot_assn ) ) ).
% 2.62/3.03
% 2.62/3.03 % list_assn_aux_ineq_len
% 2.62/3.03 thf(fact_269_list__update__swap,axiom,
% 2.62/3.03 ! [I: nat,I2: nat,Xs: list_c,X: c,X6: c] :
% 2.62/3.03 ( ( I != I2 )
% 2.62/3.03 => ( ( list_update_c @ ( list_update_c @ Xs @ I @ X ) @ I2 @ X6 )
% 2.62/3.03 = ( list_update_c @ ( list_update_c @ Xs @ I2 @ X6 ) @ I @ X ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % list_update_swap
% 2.62/3.03 thf(fact_270_list__update__swap,axiom,
% 2.62/3.03 ! [I: nat,I2: nat,Xs: list_d,X: d,X6: d] :
% 2.62/3.03 ( ( I != I2 )
% 2.62/3.03 => ( ( list_update_d @ ( list_update_d @ Xs @ I @ X ) @ I2 @ X6 )
% 2.62/3.03 = ( list_update_d @ ( list_update_d @ Xs @ I2 @ X6 ) @ I @ X ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % list_update_swap
% 2.62/3.03 thf(fact_271_insert__Diff__single,axiom,
% 2.62/3.03 ! [A2: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat] :
% 2.62/3.03 ( ( insert9069300056098147895at_nat @ A2 @ ( minus_3314409938677909166at_nat @ A @ ( insert9069300056098147895at_nat @ A2 @ bot_bo228742789529271731at_nat ) ) )
% 2.62/3.03 = ( insert9069300056098147895at_nat @ A2 @ A ) ) ).
% 2.62/3.03
% 2.62/3.03 % insert_Diff_single
% 2.62/3.03 thf(fact_272_insert__Diff__single,axiom,
% 2.62/3.03 ! [A2: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat] :
% 2.62/3.03 ( ( insert8211810215607154385at_nat @ A2 @ ( minus_1356011639430497352at_nat @ A @ ( insert8211810215607154385at_nat @ A2 @ bot_bo2099793752762293965at_nat ) ) )
% 2.62/3.03 = ( insert8211810215607154385at_nat @ A2 @ A ) ) ).
% 2.62/3.03
% 2.62/3.03 % insert_Diff_single
% 2.62/3.03 thf(fact_273_insert__Diff__single,axiom,
% 2.62/3.03 ! [A2: $o,A: set_o] :
% 2.62/3.03 ( ( insert_o2 @ A2 @ ( minus_minus_set_o @ A @ ( insert_o2 @ A2 @ bot_bot_set_o ) ) )
% 2.62/3.03 = ( insert_o2 @ A2 @ A ) ) ).
% 2.62/3.03
% 2.62/3.03 % insert_Diff_single
% 2.62/3.03 thf(fact_274_insert__Diff__single,axiom,
% 2.62/3.03 ! [A2: int,A: set_int] :
% 2.62/3.03 ( ( insert_int2 @ A2 @ ( minus_minus_set_int @ A @ ( insert_int2 @ A2 @ bot_bot_set_int ) ) )
% 2.62/3.03 = ( insert_int2 @ A2 @ A ) ) ).
% 2.62/3.03
% 2.62/3.03 % insert_Diff_single
% 2.62/3.03 thf(fact_275_insert__Diff__single,axiom,
% 2.62/3.03 ! [A2: nat,A: set_nat] :
% 2.62/3.03 ( ( insert_nat2 @ A2 @ ( minus_minus_set_nat @ A @ ( insert_nat2 @ A2 @ bot_bot_set_nat ) ) )
% 2.62/3.03 = ( insert_nat2 @ A2 @ A ) ) ).
% 2.62/3.03
% 2.62/3.03 % insert_Diff_single
% 2.62/3.03 thf(fact_276_insert__Diff1,axiom,
% 2.62/3.03 ! [X: $o,B: set_o,A: set_o] :
% 2.62/3.03 ( ( member_o @ X @ B )
% 2.62/3.03 => ( ( minus_minus_set_o @ ( insert_o2 @ X @ A ) @ B )
% 2.62/3.03 = ( minus_minus_set_o @ A @ B ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % insert_Diff1
% 2.62/3.03 thf(fact_277_insert__Diff1,axiom,
% 2.62/3.03 ! [X: produc3843707927480180839at_nat,B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 2.62/3.03 ( ( member8757157785044589968at_nat @ X @ B )
% 2.62/3.03 => ( ( minus_3314409938677909166at_nat @ ( insert9069300056098147895at_nat @ X @ A ) @ B )
% 2.62/3.03 = ( minus_3314409938677909166at_nat @ A @ B ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % insert_Diff1
% 2.62/3.03 thf(fact_278_insert__Diff1,axiom,
% 2.62/3.03 ! [X: product_prod_nat_nat,B: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 2.62/3.03 ( ( member8440522571783428010at_nat @ X @ B )
% 2.62/3.03 => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X @ A ) @ B )
% 2.62/3.03 = ( minus_1356011639430497352at_nat @ A @ B ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % insert_Diff1
% 2.62/3.03 thf(fact_279_insert__Diff1,axiom,
% 2.62/3.03 ! [X: int,B: set_int,A: set_int] :
% 2.62/3.03 ( ( member_int @ X @ B )
% 2.62/3.03 => ( ( minus_minus_set_int @ ( insert_int2 @ X @ A ) @ B )
% 2.62/3.03 = ( minus_minus_set_int @ A @ B ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % insert_Diff1
% 2.62/3.03 thf(fact_280_insert__Diff1,axiom,
% 2.62/3.03 ! [X: produc3658429121746597890et_nat > $o,B: set_Pr4532377907799695533_nat_o,A: set_Pr4532377907799695533_nat_o] :
% 2.62/3.03 ( ( member6576561426505652726_nat_o @ X @ B )
% 2.62/3.03 => ( ( minus_1801376950450012436_nat_o @ ( insert5175938949040314269_nat_o @ X @ A ) @ B )
% 2.62/3.03 = ( minus_1801376950450012436_nat_o @ A @ B ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % insert_Diff1
% 2.62/3.03 thf(fact_281_insert__Diff1,axiom,
% 2.62/3.03 ! [X: nat,B: set_nat,A: set_nat] :
% 2.62/3.03 ( ( member_nat @ X @ B )
% 2.62/3.03 => ( ( minus_minus_set_nat @ ( insert_nat2 @ X @ A ) @ B )
% 2.62/3.03 = ( minus_minus_set_nat @ A @ B ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % insert_Diff1
% 2.62/3.03 thf(fact_282_Diff__insert0,axiom,
% 2.62/3.03 ! [X: $o,A: set_o,B: set_o] :
% 2.62/3.03 ( ~ ( member_o @ X @ A )
% 2.62/3.03 => ( ( minus_minus_set_o @ A @ ( insert_o2 @ X @ B ) )
% 2.62/3.03 = ( minus_minus_set_o @ A @ B ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % Diff_insert0
% 2.62/3.03 thf(fact_283_Diff__insert0,axiom,
% 2.62/3.03 ! [X: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.62/3.03 ( ~ ( member8757157785044589968at_nat @ X @ A )
% 2.62/3.03 => ( ( minus_3314409938677909166at_nat @ A @ ( insert9069300056098147895at_nat @ X @ B ) )
% 2.62/3.03 = ( minus_3314409938677909166at_nat @ A @ B ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % Diff_insert0
% 2.62/3.03 thf(fact_284_Diff__insert0,axiom,
% 2.62/3.03 ! [X: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.62/3.03 ( ~ ( member8440522571783428010at_nat @ X @ A )
% 2.62/3.03 => ( ( minus_1356011639430497352at_nat @ A @ ( insert8211810215607154385at_nat @ X @ B ) )
% 2.62/3.03 = ( minus_1356011639430497352at_nat @ A @ B ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % Diff_insert0
% 2.62/3.03 thf(fact_285_Diff__insert0,axiom,
% 2.62/3.03 ! [X: int,A: set_int,B: set_int] :
% 2.62/3.03 ( ~ ( member_int @ X @ A )
% 2.62/3.03 => ( ( minus_minus_set_int @ A @ ( insert_int2 @ X @ B ) )
% 2.62/3.03 = ( minus_minus_set_int @ A @ B ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % Diff_insert0
% 2.62/3.03 thf(fact_286_Diff__insert0,axiom,
% 2.62/3.03 ! [X: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o] :
% 2.62/3.03 ( ~ ( member6576561426505652726_nat_o @ X @ A )
% 2.62/3.03 => ( ( minus_1801376950450012436_nat_o @ A @ ( insert5175938949040314269_nat_o @ X @ B ) )
% 2.62/3.03 = ( minus_1801376950450012436_nat_o @ A @ B ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % Diff_insert0
% 2.62/3.03 thf(fact_287_Diff__insert0,axiom,
% 2.62/3.03 ! [X: nat,A: set_nat,B: set_nat] :
% 2.62/3.03 ( ~ ( member_nat @ X @ A )
% 2.62/3.03 => ( ( minus_minus_set_nat @ A @ ( insert_nat2 @ X @ B ) )
% 2.62/3.03 = ( minus_minus_set_nat @ A @ B ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % Diff_insert0
% 2.62/3.03 thf(fact_288_Diff__empty,axiom,
% 2.62/3.03 ! [A: set_Pr4329608150637261639at_nat] :
% 2.62/3.03 ( ( minus_3314409938677909166at_nat @ A @ bot_bo228742789529271731at_nat )
% 2.62/3.03 = A ) ).
% 2.62/3.03
% 2.62/3.03 % Diff_empty
% 2.62/3.03 thf(fact_289_Diff__empty,axiom,
% 2.62/3.03 ! [A: set_Pr1261947904930325089at_nat] :
% 2.62/3.03 ( ( minus_1356011639430497352at_nat @ A @ bot_bo2099793752762293965at_nat )
% 2.62/3.03 = A ) ).
% 2.62/3.03
% 2.62/3.03 % Diff_empty
% 2.62/3.03 thf(fact_290_Diff__empty,axiom,
% 2.62/3.03 ! [A: set_o] :
% 2.62/3.03 ( ( minus_minus_set_o @ A @ bot_bot_set_o )
% 2.62/3.03 = A ) ).
% 2.62/3.03
% 2.62/3.03 % Diff_empty
% 2.62/3.03 thf(fact_291_Diff__empty,axiom,
% 2.62/3.03 ! [A: set_int] :
% 2.62/3.03 ( ( minus_minus_set_int @ A @ bot_bot_set_int )
% 2.62/3.03 = A ) ).
% 2.62/3.03
% 2.62/3.03 % Diff_empty
% 2.62/3.03 thf(fact_292_Diff__empty,axiom,
% 2.62/3.03 ! [A: set_nat] :
% 2.62/3.03 ( ( minus_minus_set_nat @ A @ bot_bot_set_nat )
% 2.62/3.03 = A ) ).
% 2.62/3.03
% 2.62/3.03 % Diff_empty
% 2.62/3.03 thf(fact_293_empty__Diff,axiom,
% 2.62/3.03 ! [A: set_Pr4329608150637261639at_nat] :
% 2.62/3.03 ( ( minus_3314409938677909166at_nat @ bot_bo228742789529271731at_nat @ A )
% 2.62/3.03 = bot_bo228742789529271731at_nat ) ).
% 2.62/3.03
% 2.62/3.03 % empty_Diff
% 2.62/3.03 thf(fact_294_empty__Diff,axiom,
% 2.62/3.03 ! [A: set_Pr1261947904930325089at_nat] :
% 2.62/3.03 ( ( minus_1356011639430497352at_nat @ bot_bo2099793752762293965at_nat @ A )
% 2.62/3.03 = bot_bo2099793752762293965at_nat ) ).
% 2.62/3.03
% 2.62/3.03 % empty_Diff
% 2.62/3.03 thf(fact_295_empty__Diff,axiom,
% 2.62/3.03 ! [A: set_o] :
% 2.62/3.03 ( ( minus_minus_set_o @ bot_bot_set_o @ A )
% 2.62/3.03 = bot_bot_set_o ) ).
% 2.62/3.03
% 2.62/3.03 % empty_Diff
% 2.62/3.03 thf(fact_296_empty__Diff,axiom,
% 2.62/3.03 ! [A: set_int] :
% 2.62/3.03 ( ( minus_minus_set_int @ bot_bot_set_int @ A )
% 2.62/3.03 = bot_bot_set_int ) ).
% 2.62/3.03
% 2.62/3.03 % empty_Diff
% 2.62/3.03 thf(fact_297_empty__Diff,axiom,
% 2.62/3.03 ! [A: set_nat] :
% 2.62/3.03 ( ( minus_minus_set_nat @ bot_bot_set_nat @ A )
% 2.62/3.03 = bot_bot_set_nat ) ).
% 2.62/3.03
% 2.62/3.03 % empty_Diff
% 2.62/3.03 thf(fact_298_Diff__cancel,axiom,
% 2.62/3.03 ! [A: set_Pr4329608150637261639at_nat] :
% 2.62/3.03 ( ( minus_3314409938677909166at_nat @ A @ A )
% 2.62/3.03 = bot_bo228742789529271731at_nat ) ).
% 2.62/3.03
% 2.62/3.03 % Diff_cancel
% 2.62/3.03 thf(fact_299_Diff__cancel,axiom,
% 2.62/3.03 ! [A: set_Pr1261947904930325089at_nat] :
% 2.62/3.03 ( ( minus_1356011639430497352at_nat @ A @ A )
% 2.62/3.03 = bot_bo2099793752762293965at_nat ) ).
% 2.62/3.03
% 2.62/3.03 % Diff_cancel
% 2.62/3.03 thf(fact_300_Diff__cancel,axiom,
% 2.62/3.03 ! [A: set_o] :
% 2.62/3.03 ( ( minus_minus_set_o @ A @ A )
% 2.62/3.03 = bot_bot_set_o ) ).
% 2.62/3.03
% 2.62/3.03 % Diff_cancel
% 2.62/3.03 thf(fact_301_Diff__cancel,axiom,
% 2.62/3.03 ! [A: set_int] :
% 2.62/3.03 ( ( minus_minus_set_int @ A @ A )
% 2.62/3.03 = bot_bot_set_int ) ).
% 2.62/3.03
% 2.62/3.03 % Diff_cancel
% 2.62/3.03 thf(fact_302_Diff__cancel,axiom,
% 2.62/3.03 ! [A: set_nat] :
% 2.62/3.03 ( ( minus_minus_set_nat @ A @ A )
% 2.62/3.03 = bot_bot_set_nat ) ).
% 2.62/3.03
% 2.62/3.03 % Diff_cancel
% 2.62/3.03 thf(fact_303_singletonI,axiom,
% 2.62/3.03 ! [A2: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ A2 @ bot_bo7824918357723582233_nat_o ) ) ).
% 2.62/3.03
% 2.62/3.03 % singletonI
% 2.62/3.03 thf(fact_304_singletonI,axiom,
% 2.62/3.03 ! [A2: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ A2 @ ( insert9069300056098147895at_nat @ A2 @ bot_bo228742789529271731at_nat ) ) ).
% 2.62/3.03
% 2.62/3.03 % singletonI
% 2.62/3.03 thf(fact_305_singletonI,axiom,
% 2.62/3.03 ! [A2: product_prod_nat_nat] : ( member8440522571783428010at_nat @ A2 @ ( insert8211810215607154385at_nat @ A2 @ bot_bo2099793752762293965at_nat ) ) ).
% 2.62/3.03
% 2.62/3.03 % singletonI
% 2.62/3.03 thf(fact_306_singletonI,axiom,
% 2.62/3.03 ! [A2: $o] : ( member_o @ A2 @ ( insert_o2 @ A2 @ bot_bot_set_o ) ) ).
% 2.62/3.03
% 2.62/3.03 % singletonI
% 2.62/3.03 thf(fact_307_singletonI,axiom,
% 2.62/3.03 ! [A2: nat] : ( member_nat @ A2 @ ( insert_nat2 @ A2 @ bot_bot_set_nat ) ) ).
% 2.62/3.03
% 2.62/3.03 % singletonI
% 2.62/3.03 thf(fact_308_singletonI,axiom,
% 2.62/3.03 ! [A2: int] : ( member_int @ A2 @ ( insert_int2 @ A2 @ bot_bot_set_int ) ) ).
% 2.62/3.03
% 2.62/3.03 % singletonI
% 2.62/3.03 thf(fact_309_Diff__insert,axiom,
% 2.62/3.03 ! [A: set_Pr4329608150637261639at_nat,A2: produc3843707927480180839at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.62/3.03 ( ( minus_3314409938677909166at_nat @ A @ ( insert9069300056098147895at_nat @ A2 @ B ) )
% 2.62/3.03 = ( minus_3314409938677909166at_nat @ ( minus_3314409938677909166at_nat @ A @ B ) @ ( insert9069300056098147895at_nat @ A2 @ bot_bo228742789529271731at_nat ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % Diff_insert
% 2.62/3.03 thf(fact_310_Diff__insert,axiom,
% 2.62/3.03 ! [A: set_Pr1261947904930325089at_nat,A2: product_prod_nat_nat,B: set_Pr1261947904930325089at_nat] :
% 2.62/3.03 ( ( minus_1356011639430497352at_nat @ A @ ( insert8211810215607154385at_nat @ A2 @ B ) )
% 2.62/3.03 = ( minus_1356011639430497352at_nat @ ( minus_1356011639430497352at_nat @ A @ B ) @ ( insert8211810215607154385at_nat @ A2 @ bot_bo2099793752762293965at_nat ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % Diff_insert
% 2.62/3.03 thf(fact_311_Diff__insert,axiom,
% 2.62/3.03 ! [A: set_o,A2: $o,B: set_o] :
% 2.62/3.03 ( ( minus_minus_set_o @ A @ ( insert_o2 @ A2 @ B ) )
% 2.62/3.03 = ( minus_minus_set_o @ ( minus_minus_set_o @ A @ B ) @ ( insert_o2 @ A2 @ bot_bot_set_o ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % Diff_insert
% 2.62/3.03 thf(fact_312_Diff__insert,axiom,
% 2.62/3.03 ! [A: set_int,A2: int,B: set_int] :
% 2.62/3.03 ( ( minus_minus_set_int @ A @ ( insert_int2 @ A2 @ B ) )
% 2.62/3.03 = ( minus_minus_set_int @ ( minus_minus_set_int @ A @ B ) @ ( insert_int2 @ A2 @ bot_bot_set_int ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % Diff_insert
% 2.62/3.03 thf(fact_313_Diff__insert,axiom,
% 2.62/3.03 ! [A: set_nat,A2: nat,B: set_nat] :
% 2.62/3.03 ( ( minus_minus_set_nat @ A @ ( insert_nat2 @ A2 @ B ) )
% 2.62/3.03 = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A @ B ) @ ( insert_nat2 @ A2 @ bot_bot_set_nat ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % Diff_insert
% 2.62/3.03 thf(fact_314_insert__Diff,axiom,
% 2.62/3.03 ! [A2: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o] :
% 2.62/3.03 ( ( member6576561426505652726_nat_o @ A2 @ A )
% 2.62/3.03 => ( ( insert5175938949040314269_nat_o @ A2 @ ( minus_1801376950450012436_nat_o @ A @ ( insert5175938949040314269_nat_o @ A2 @ bot_bo7824918357723582233_nat_o ) ) )
% 2.62/3.03 = A ) ) ).
% 2.62/3.03
% 2.62/3.03 % insert_Diff
% 2.62/3.03 thf(fact_315_insert__Diff,axiom,
% 2.62/3.03 ! [A2: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat] :
% 2.62/3.03 ( ( member8757157785044589968at_nat @ A2 @ A )
% 2.62/3.03 => ( ( insert9069300056098147895at_nat @ A2 @ ( minus_3314409938677909166at_nat @ A @ ( insert9069300056098147895at_nat @ A2 @ bot_bo228742789529271731at_nat ) ) )
% 2.62/3.03 = A ) ) ).
% 2.62/3.03
% 2.62/3.03 % insert_Diff
% 2.62/3.03 thf(fact_316_insert__Diff,axiom,
% 2.62/3.03 ! [A2: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat] :
% 2.62/3.03 ( ( member8440522571783428010at_nat @ A2 @ A )
% 2.62/3.03 => ( ( insert8211810215607154385at_nat @ A2 @ ( minus_1356011639430497352at_nat @ A @ ( insert8211810215607154385at_nat @ A2 @ bot_bo2099793752762293965at_nat ) ) )
% 2.62/3.03 = A ) ) ).
% 2.62/3.03
% 2.62/3.03 % insert_Diff
% 2.62/3.03 thf(fact_317_insert__Diff,axiom,
% 2.62/3.03 ! [A2: $o,A: set_o] :
% 2.62/3.03 ( ( member_o @ A2 @ A )
% 2.62/3.03 => ( ( insert_o2 @ A2 @ ( minus_minus_set_o @ A @ ( insert_o2 @ A2 @ bot_bot_set_o ) ) )
% 2.62/3.03 = A ) ) ).
% 2.62/3.03
% 2.62/3.03 % insert_Diff
% 2.62/3.03 thf(fact_318_insert__Diff,axiom,
% 2.62/3.03 ! [A2: int,A: set_int] :
% 2.62/3.03 ( ( member_int @ A2 @ A )
% 2.62/3.03 => ( ( insert_int2 @ A2 @ ( minus_minus_set_int @ A @ ( insert_int2 @ A2 @ bot_bot_set_int ) ) )
% 2.62/3.03 = A ) ) ).
% 2.62/3.03
% 2.62/3.03 % insert_Diff
% 2.62/3.03 thf(fact_319_insert__Diff,axiom,
% 2.62/3.03 ! [A2: nat,A: set_nat] :
% 2.62/3.03 ( ( member_nat @ A2 @ A )
% 2.62/3.03 => ( ( insert_nat2 @ A2 @ ( minus_minus_set_nat @ A @ ( insert_nat2 @ A2 @ bot_bot_set_nat ) ) )
% 2.62/3.03 = A ) ) ).
% 2.62/3.03
% 2.62/3.03 % insert_Diff
% 2.62/3.03 thf(fact_320_Diff__insert2,axiom,
% 2.62/3.03 ! [A: set_Pr4329608150637261639at_nat,A2: produc3843707927480180839at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.62/3.03 ( ( minus_3314409938677909166at_nat @ A @ ( insert9069300056098147895at_nat @ A2 @ B ) )
% 2.62/3.03 = ( minus_3314409938677909166at_nat @ ( minus_3314409938677909166at_nat @ A @ ( insert9069300056098147895at_nat @ A2 @ bot_bo228742789529271731at_nat ) ) @ B ) ) ).
% 2.62/3.03
% 2.62/3.03 % Diff_insert2
% 2.62/3.03 thf(fact_321_Diff__insert2,axiom,
% 2.62/3.03 ! [A: set_Pr1261947904930325089at_nat,A2: product_prod_nat_nat,B: set_Pr1261947904930325089at_nat] :
% 2.62/3.03 ( ( minus_1356011639430497352at_nat @ A @ ( insert8211810215607154385at_nat @ A2 @ B ) )
% 2.62/3.03 = ( minus_1356011639430497352at_nat @ ( minus_1356011639430497352at_nat @ A @ ( insert8211810215607154385at_nat @ A2 @ bot_bo2099793752762293965at_nat ) ) @ B ) ) ).
% 2.62/3.03
% 2.62/3.03 % Diff_insert2
% 2.62/3.03 thf(fact_322_Diff__insert2,axiom,
% 2.62/3.03 ! [A: set_o,A2: $o,B: set_o] :
% 2.62/3.03 ( ( minus_minus_set_o @ A @ ( insert_o2 @ A2 @ B ) )
% 2.62/3.03 = ( minus_minus_set_o @ ( minus_minus_set_o @ A @ ( insert_o2 @ A2 @ bot_bot_set_o ) ) @ B ) ) ).
% 2.62/3.03
% 2.62/3.03 % Diff_insert2
% 2.62/3.03 thf(fact_323_Diff__insert2,axiom,
% 2.62/3.03 ! [A: set_int,A2: int,B: set_int] :
% 2.62/3.03 ( ( minus_minus_set_int @ A @ ( insert_int2 @ A2 @ B ) )
% 2.62/3.03 = ( minus_minus_set_int @ ( minus_minus_set_int @ A @ ( insert_int2 @ A2 @ bot_bot_set_int ) ) @ B ) ) ).
% 2.62/3.03
% 2.62/3.03 % Diff_insert2
% 2.62/3.03 thf(fact_324_Diff__insert2,axiom,
% 2.62/3.03 ! [A: set_nat,A2: nat,B: set_nat] :
% 2.62/3.03 ( ( minus_minus_set_nat @ A @ ( insert_nat2 @ A2 @ B ) )
% 2.62/3.03 = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A @ ( insert_nat2 @ A2 @ bot_bot_set_nat ) ) @ B ) ) ).
% 2.62/3.03
% 2.62/3.03 % Diff_insert2
% 2.62/3.03 thf(fact_325_insert__minus__eq,axiom,
% 2.62/3.03 ! [X: produc3843707927480180839at_nat,Y: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat] :
% 2.62/3.03 ( ( X != Y )
% 2.62/3.03 => ( ( minus_3314409938677909166at_nat @ ( insert9069300056098147895at_nat @ X @ A ) @ ( insert9069300056098147895at_nat @ Y @ bot_bo228742789529271731at_nat ) )
% 2.62/3.03 = ( insert9069300056098147895at_nat @ X @ ( minus_3314409938677909166at_nat @ A @ ( insert9069300056098147895at_nat @ Y @ bot_bo228742789529271731at_nat ) ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % insert_minus_eq
% 2.62/3.03 thf(fact_326_insert__minus__eq,axiom,
% 2.62/3.03 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat] :
% 2.62/3.03 ( ( X != Y )
% 2.62/3.03 => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X @ A ) @ ( insert8211810215607154385at_nat @ Y @ bot_bo2099793752762293965at_nat ) )
% 2.62/3.03 = ( insert8211810215607154385at_nat @ X @ ( minus_1356011639430497352at_nat @ A @ ( insert8211810215607154385at_nat @ Y @ bot_bo2099793752762293965at_nat ) ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % insert_minus_eq
% 2.62/3.03 thf(fact_327_insert__minus__eq,axiom,
% 2.62/3.03 ! [X: $o,Y: $o,A: set_o] :
% 2.62/3.03 ( ( X != Y )
% 2.62/3.03 => ( ( minus_minus_set_o @ ( insert_o2 @ X @ A ) @ ( insert_o2 @ Y @ bot_bot_set_o ) )
% 2.62/3.03 = ( insert_o2 @ X @ ( minus_minus_set_o @ A @ ( insert_o2 @ Y @ bot_bot_set_o ) ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % insert_minus_eq
% 2.62/3.03 thf(fact_328_insert__minus__eq,axiom,
% 2.62/3.03 ! [X: int,Y: int,A: set_int] :
% 2.62/3.03 ( ( X != Y )
% 2.62/3.03 => ( ( minus_minus_set_int @ ( insert_int2 @ X @ A ) @ ( insert_int2 @ Y @ bot_bot_set_int ) )
% 2.62/3.03 = ( insert_int2 @ X @ ( minus_minus_set_int @ A @ ( insert_int2 @ Y @ bot_bot_set_int ) ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % insert_minus_eq
% 2.62/3.03 thf(fact_329_insert__minus__eq,axiom,
% 2.62/3.03 ! [X: nat,Y: nat,A: set_nat] :
% 2.62/3.03 ( ( X != Y )
% 2.62/3.03 => ( ( minus_minus_set_nat @ ( insert_nat2 @ X @ A ) @ ( insert_nat2 @ Y @ bot_bot_set_nat ) )
% 2.62/3.03 = ( insert_nat2 @ X @ ( minus_minus_set_nat @ A @ ( insert_nat2 @ Y @ bot_bot_set_nat ) ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % insert_minus_eq
% 2.62/3.03 thf(fact_330_Diff__insert__absorb,axiom,
% 2.62/3.03 ! [X: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o] :
% 2.62/3.03 ( ~ ( member6576561426505652726_nat_o @ X @ A )
% 2.62/3.03 => ( ( minus_1801376950450012436_nat_o @ ( insert5175938949040314269_nat_o @ X @ A ) @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) )
% 2.62/3.03 = A ) ) ).
% 2.62/3.03
% 2.62/3.03 % Diff_insert_absorb
% 2.62/3.03 thf(fact_331_Diff__insert__absorb,axiom,
% 2.62/3.03 ! [X: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat] :
% 2.62/3.03 ( ~ ( member8757157785044589968at_nat @ X @ A )
% 2.62/3.03 => ( ( minus_3314409938677909166at_nat @ ( insert9069300056098147895at_nat @ X @ A ) @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 2.62/3.03 = A ) ) ).
% 2.62/3.03
% 2.62/3.03 % Diff_insert_absorb
% 2.62/3.03 thf(fact_332_Diff__insert__absorb,axiom,
% 2.62/3.03 ! [X: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat] :
% 2.62/3.03 ( ~ ( member8440522571783428010at_nat @ X @ A )
% 2.62/3.03 => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X @ A ) @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 2.62/3.03 = A ) ) ).
% 2.62/3.03
% 2.62/3.03 % Diff_insert_absorb
% 2.62/3.03 thf(fact_333_Diff__insert__absorb,axiom,
% 2.62/3.03 ! [X: $o,A: set_o] :
% 2.62/3.03 ( ~ ( member_o @ X @ A )
% 2.62/3.03 => ( ( minus_minus_set_o @ ( insert_o2 @ X @ A ) @ ( insert_o2 @ X @ bot_bot_set_o ) )
% 2.62/3.03 = A ) ) ).
% 2.62/3.03
% 2.62/3.03 % Diff_insert_absorb
% 2.62/3.03 thf(fact_334_Diff__insert__absorb,axiom,
% 2.62/3.03 ! [X: int,A: set_int] :
% 2.62/3.03 ( ~ ( member_int @ X @ A )
% 2.62/3.03 => ( ( minus_minus_set_int @ ( insert_int2 @ X @ A ) @ ( insert_int2 @ X @ bot_bot_set_int ) )
% 2.62/3.03 = A ) ) ).
% 2.62/3.03
% 2.62/3.03 % Diff_insert_absorb
% 2.62/3.03 thf(fact_335_Diff__insert__absorb,axiom,
% 2.62/3.03 ! [X: nat,A: set_nat] :
% 2.62/3.03 ( ~ ( member_nat @ X @ A )
% 2.62/3.03 => ( ( minus_minus_set_nat @ ( insert_nat2 @ X @ A ) @ ( insert_nat2 @ X @ bot_bot_set_nat ) )
% 2.62/3.03 = A ) ) ).
% 2.62/3.03
% 2.62/3.03 % Diff_insert_absorb
% 2.62/3.03 thf(fact_336_empty__Collect__eq,axiom,
% 2.62/3.03 ! [P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 2.62/3.03 ( ( bot_bo7824918357723582233_nat_o
% 2.62/3.03 = ( collec939566748876313656_nat_o @ P ) )
% 2.62/3.03 = ( ! [X2: produc3658429121746597890et_nat > $o] :
% 2.62/3.03 ~ ( P @ X2 ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % empty_Collect_eq
% 2.62/3.03 thf(fact_337_empty__Collect__eq,axiom,
% 2.62/3.03 ! [P: produc3843707927480180839at_nat > $o] :
% 2.62/3.03 ( ( bot_bo228742789529271731at_nat
% 2.62/3.03 = ( collec6321179662152712658at_nat @ P ) )
% 2.62/3.03 = ( ! [X2: produc3843707927480180839at_nat] :
% 2.62/3.03 ~ ( P @ X2 ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % empty_Collect_eq
% 2.62/3.03 thf(fact_338_empty__Collect__eq,axiom,
% 2.62/3.03 ! [P: product_prod_nat_nat > $o] :
% 2.62/3.03 ( ( bot_bo2099793752762293965at_nat
% 2.62/3.03 = ( collec3392354462482085612at_nat @ P ) )
% 2.62/3.03 = ( ! [X2: product_prod_nat_nat] :
% 2.62/3.03 ~ ( P @ X2 ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % empty_Collect_eq
% 2.62/3.03 thf(fact_339_empty__Collect__eq,axiom,
% 2.62/3.03 ! [P: $o > $o] :
% 2.62/3.03 ( ( bot_bot_set_o
% 2.62/3.03 = ( collect_o @ P ) )
% 2.62/3.03 = ( ! [X2: $o] :
% 2.62/3.03 ~ ( P @ X2 ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % empty_Collect_eq
% 2.62/3.03 thf(fact_340_empty__Collect__eq,axiom,
% 2.62/3.03 ! [P: nat > $o] :
% 2.62/3.03 ( ( bot_bot_set_nat
% 2.62/3.03 = ( collect_nat @ P ) )
% 2.62/3.03 = ( ! [X2: nat] :
% 2.62/3.03 ~ ( P @ X2 ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % empty_Collect_eq
% 2.62/3.03 thf(fact_341_empty__Collect__eq,axiom,
% 2.62/3.03 ! [P: int > $o] :
% 2.62/3.03 ( ( bot_bot_set_int
% 2.62/3.03 = ( collect_int @ P ) )
% 2.62/3.03 = ( ! [X2: int] :
% 2.62/3.03 ~ ( P @ X2 ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % empty_Collect_eq
% 2.62/3.03 thf(fact_342_Collect__empty__eq,axiom,
% 2.62/3.03 ! [P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 2.62/3.03 ( ( ( collec939566748876313656_nat_o @ P )
% 2.62/3.03 = bot_bo7824918357723582233_nat_o )
% 2.62/3.03 = ( ! [X2: produc3658429121746597890et_nat > $o] :
% 2.62/3.03 ~ ( P @ X2 ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % Collect_empty_eq
% 2.62/3.03 thf(fact_343_Collect__empty__eq,axiom,
% 2.62/3.03 ! [P: produc3843707927480180839at_nat > $o] :
% 2.62/3.03 ( ( ( collec6321179662152712658at_nat @ P )
% 2.62/3.03 = bot_bo228742789529271731at_nat )
% 2.62/3.03 = ( ! [X2: produc3843707927480180839at_nat] :
% 2.62/3.03 ~ ( P @ X2 ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % Collect_empty_eq
% 2.62/3.03 thf(fact_344_Collect__empty__eq,axiom,
% 2.62/3.03 ! [P: product_prod_nat_nat > $o] :
% 2.62/3.03 ( ( ( collec3392354462482085612at_nat @ P )
% 2.62/3.03 = bot_bo2099793752762293965at_nat )
% 2.62/3.03 = ( ! [X2: product_prod_nat_nat] :
% 2.62/3.03 ~ ( P @ X2 ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % Collect_empty_eq
% 2.62/3.03 thf(fact_345_Collect__empty__eq,axiom,
% 2.62/3.03 ! [P: $o > $o] :
% 2.62/3.03 ( ( ( collect_o @ P )
% 2.62/3.03 = bot_bot_set_o )
% 2.62/3.03 = ( ! [X2: $o] :
% 2.62/3.03 ~ ( P @ X2 ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % Collect_empty_eq
% 2.62/3.03 thf(fact_346_Collect__empty__eq,axiom,
% 2.62/3.03 ! [P: nat > $o] :
% 2.62/3.03 ( ( ( collect_nat @ P )
% 2.62/3.03 = bot_bot_set_nat )
% 2.62/3.03 = ( ! [X2: nat] :
% 2.62/3.03 ~ ( P @ X2 ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % Collect_empty_eq
% 2.62/3.03 thf(fact_347_Collect__empty__eq,axiom,
% 2.62/3.03 ! [P: int > $o] :
% 2.62/3.03 ( ( ( collect_int @ P )
% 2.62/3.03 = bot_bot_set_int )
% 2.62/3.03 = ( ! [X2: int] :
% 2.62/3.03 ~ ( P @ X2 ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % Collect_empty_eq
% 2.62/3.03 thf(fact_348_all__not__in__conv,axiom,
% 2.62/3.03 ! [A: set_Pr4532377907799695533_nat_o] :
% 2.62/3.03 ( ( ! [X2: produc3658429121746597890et_nat > $o] :
% 2.62/3.03 ~ ( member6576561426505652726_nat_o @ X2 @ A ) )
% 2.62/3.03 = ( A = bot_bo7824918357723582233_nat_o ) ) ).
% 2.62/3.03
% 2.62/3.03 % all_not_in_conv
% 2.62/3.03 thf(fact_349_all__not__in__conv,axiom,
% 2.62/3.03 ! [A: set_Pr4329608150637261639at_nat] :
% 2.62/3.03 ( ( ! [X2: produc3843707927480180839at_nat] :
% 2.62/3.03 ~ ( member8757157785044589968at_nat @ X2 @ A ) )
% 2.62/3.03 = ( A = bot_bo228742789529271731at_nat ) ) ).
% 2.62/3.03
% 2.62/3.03 % all_not_in_conv
% 2.62/3.03 thf(fact_350_all__not__in__conv,axiom,
% 2.62/3.03 ! [A: set_Pr1261947904930325089at_nat] :
% 2.62/3.03 ( ( ! [X2: product_prod_nat_nat] :
% 2.62/3.03 ~ ( member8440522571783428010at_nat @ X2 @ A ) )
% 2.62/3.03 = ( A = bot_bo2099793752762293965at_nat ) ) ).
% 2.62/3.03
% 2.62/3.03 % all_not_in_conv
% 2.62/3.03 thf(fact_351_all__not__in__conv,axiom,
% 2.62/3.03 ! [A: set_o] :
% 2.62/3.03 ( ( ! [X2: $o] :
% 2.62/3.03 ~ ( member_o @ X2 @ A ) )
% 2.62/3.03 = ( A = bot_bot_set_o ) ) ).
% 2.62/3.03
% 2.62/3.03 % all_not_in_conv
% 2.62/3.03 thf(fact_352_all__not__in__conv,axiom,
% 2.62/3.03 ! [A: set_nat] :
% 2.62/3.03 ( ( ! [X2: nat] :
% 2.62/3.03 ~ ( member_nat @ X2 @ A ) )
% 2.62/3.03 = ( A = bot_bot_set_nat ) ) ).
% 2.62/3.03
% 2.62/3.03 % all_not_in_conv
% 2.62/3.03 thf(fact_353_all__not__in__conv,axiom,
% 2.62/3.03 ! [A: set_int] :
% 2.62/3.03 ( ( ! [X2: int] :
% 2.62/3.03 ~ ( member_int @ X2 @ A ) )
% 2.62/3.03 = ( A = bot_bot_set_int ) ) ).
% 2.62/3.03
% 2.62/3.03 % all_not_in_conv
% 2.62/3.03 thf(fact_354_empty__iff,axiom,
% 2.62/3.03 ! [C: produc3658429121746597890et_nat > $o] :
% 2.62/3.03 ~ ( member6576561426505652726_nat_o @ C @ bot_bo7824918357723582233_nat_o ) ).
% 2.62/3.03
% 2.62/3.03 % empty_iff
% 2.62/3.03 thf(fact_355_empty__iff,axiom,
% 2.62/3.03 ! [C: produc3843707927480180839at_nat] :
% 2.62/3.03 ~ ( member8757157785044589968at_nat @ C @ bot_bo228742789529271731at_nat ) ).
% 2.62/3.03
% 2.62/3.03 % empty_iff
% 2.62/3.03 thf(fact_356_empty__iff,axiom,
% 2.62/3.03 ! [C: product_prod_nat_nat] :
% 2.62/3.03 ~ ( member8440522571783428010at_nat @ C @ bot_bo2099793752762293965at_nat ) ).
% 2.62/3.03
% 2.62/3.03 % empty_iff
% 2.62/3.03 thf(fact_357_empty__iff,axiom,
% 2.62/3.03 ! [C: $o] :
% 2.62/3.03 ~ ( member_o @ C @ bot_bot_set_o ) ).
% 2.62/3.03
% 2.62/3.03 % empty_iff
% 2.62/3.03 thf(fact_358_empty__iff,axiom,
% 2.62/3.03 ! [C: nat] :
% 2.62/3.03 ~ ( member_nat @ C @ bot_bot_set_nat ) ).
% 2.62/3.03
% 2.62/3.03 % empty_iff
% 2.62/3.03 thf(fact_359_empty__iff,axiom,
% 2.62/3.03 ! [C: int] :
% 2.62/3.03 ~ ( member_int @ C @ bot_bot_set_int ) ).
% 2.62/3.03
% 2.62/3.03 % empty_iff
% 2.62/3.03 thf(fact_360_insertCI,axiom,
% 2.62/3.03 ! [A2: $o,B: set_o,B2: $o] :
% 2.62/3.03 ( ( ~ ( member_o @ A2 @ B )
% 2.62/3.03 => ( A2 = B2 ) )
% 2.62/3.03 => ( member_o @ A2 @ ( insert_o2 @ B2 @ B ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % insertCI
% 2.62/3.03 thf(fact_361_insertCI,axiom,
% 2.62/3.03 ! [A2: produc3843707927480180839at_nat,B: set_Pr4329608150637261639at_nat,B2: produc3843707927480180839at_nat] :
% 2.62/3.03 ( ( ~ ( member8757157785044589968at_nat @ A2 @ B )
% 2.62/3.03 => ( A2 = B2 ) )
% 2.62/3.03 => ( member8757157785044589968at_nat @ A2 @ ( insert9069300056098147895at_nat @ B2 @ B ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % insertCI
% 2.62/3.03 thf(fact_362_insertCI,axiom,
% 2.62/3.03 ! [A2: product_prod_nat_nat,B: set_Pr1261947904930325089at_nat,B2: product_prod_nat_nat] :
% 2.62/3.03 ( ( ~ ( member8440522571783428010at_nat @ A2 @ B )
% 2.62/3.03 => ( A2 = B2 ) )
% 2.62/3.03 => ( member8440522571783428010at_nat @ A2 @ ( insert8211810215607154385at_nat @ B2 @ B ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % insertCI
% 2.62/3.03 thf(fact_363_insertCI,axiom,
% 2.62/3.03 ! [A2: nat,B: set_nat,B2: nat] :
% 2.62/3.03 ( ( ~ ( member_nat @ A2 @ B )
% 2.62/3.03 => ( A2 = B2 ) )
% 2.62/3.03 => ( member_nat @ A2 @ ( insert_nat2 @ B2 @ B ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % insertCI
% 2.62/3.03 thf(fact_364_insertCI,axiom,
% 2.62/3.03 ! [A2: int,B: set_int,B2: int] :
% 2.62/3.03 ( ( ~ ( member_int @ A2 @ B )
% 2.62/3.03 => ( A2 = B2 ) )
% 2.62/3.03 => ( member_int @ A2 @ ( insert_int2 @ B2 @ B ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % insertCI
% 2.62/3.03 thf(fact_365_insertCI,axiom,
% 2.62/3.03 ! [A2: produc3658429121746597890et_nat > $o,B: set_Pr4532377907799695533_nat_o,B2: produc3658429121746597890et_nat > $o] :
% 2.62/3.03 ( ( ~ ( member6576561426505652726_nat_o @ A2 @ B )
% 2.62/3.03 => ( A2 = B2 ) )
% 2.62/3.03 => ( member6576561426505652726_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ B2 @ B ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % insertCI
% 2.62/3.03 thf(fact_366_insert__iff,axiom,
% 2.62/3.03 ! [A2: $o,B2: $o,A: set_o] :
% 2.62/3.03 ( ( member_o @ A2 @ ( insert_o2 @ B2 @ A ) )
% 2.62/3.03 = ( ( A2 = B2 )
% 2.62/3.03 | ( member_o @ A2 @ A ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % insert_iff
% 2.62/3.03 thf(fact_367_insert__iff,axiom,
% 2.62/3.03 ! [A2: produc3843707927480180839at_nat,B2: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat] :
% 2.62/3.03 ( ( member8757157785044589968at_nat @ A2 @ ( insert9069300056098147895at_nat @ B2 @ A ) )
% 2.62/3.03 = ( ( A2 = B2 )
% 2.62/3.03 | ( member8757157785044589968at_nat @ A2 @ A ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % insert_iff
% 2.62/3.03 thf(fact_368_insert__iff,axiom,
% 2.62/3.03 ! [A2: product_prod_nat_nat,B2: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat] :
% 2.62/3.03 ( ( member8440522571783428010at_nat @ A2 @ ( insert8211810215607154385at_nat @ B2 @ A ) )
% 2.62/3.03 = ( ( A2 = B2 )
% 2.62/3.03 | ( member8440522571783428010at_nat @ A2 @ A ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % insert_iff
% 2.62/3.03 thf(fact_369_insert__iff,axiom,
% 2.62/3.03 ! [A2: nat,B2: nat,A: set_nat] :
% 2.62/3.03 ( ( member_nat @ A2 @ ( insert_nat2 @ B2 @ A ) )
% 2.62/3.03 = ( ( A2 = B2 )
% 2.62/3.03 | ( member_nat @ A2 @ A ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % insert_iff
% 2.62/3.03 thf(fact_370_insert__iff,axiom,
% 2.62/3.03 ! [A2: int,B2: int,A: set_int] :
% 2.62/3.03 ( ( member_int @ A2 @ ( insert_int2 @ B2 @ A ) )
% 2.62/3.03 = ( ( A2 = B2 )
% 2.62/3.03 | ( member_int @ A2 @ A ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % insert_iff
% 2.62/3.03 thf(fact_371_insert__iff,axiom,
% 2.62/3.03 ! [A2: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o] :
% 2.62/3.03 ( ( member6576561426505652726_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ B2 @ A ) )
% 2.62/3.03 = ( ( A2 = B2 )
% 2.62/3.03 | ( member6576561426505652726_nat_o @ A2 @ A ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % insert_iff
% 2.62/3.03 thf(fact_372_insert__absorb2,axiom,
% 2.62/3.03 ! [X: nat,A: set_nat] :
% 2.62/3.03 ( ( insert_nat2 @ X @ ( insert_nat2 @ X @ A ) )
% 2.62/3.03 = ( insert_nat2 @ X @ A ) ) ).
% 2.62/3.03
% 2.62/3.03 % insert_absorb2
% 2.62/3.03 thf(fact_373_insert__absorb2,axiom,
% 2.62/3.03 ! [X: int,A: set_int] :
% 2.62/3.03 ( ( insert_int2 @ X @ ( insert_int2 @ X @ A ) )
% 2.62/3.03 = ( insert_int2 @ X @ A ) ) ).
% 2.62/3.03
% 2.62/3.03 % insert_absorb2
% 2.62/3.03 thf(fact_374_insert__absorb2,axiom,
% 2.62/3.03 ! [X: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat] :
% 2.62/3.03 ( ( insert8211810215607154385at_nat @ X @ ( insert8211810215607154385at_nat @ X @ A ) )
% 2.62/3.03 = ( insert8211810215607154385at_nat @ X @ A ) ) ).
% 2.62/3.03
% 2.62/3.03 % insert_absorb2
% 2.62/3.03 thf(fact_375_insert__absorb2,axiom,
% 2.62/3.03 ! [X: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat] :
% 2.62/3.03 ( ( insert9069300056098147895at_nat @ X @ ( insert9069300056098147895at_nat @ X @ A ) )
% 2.62/3.03 = ( insert9069300056098147895at_nat @ X @ A ) ) ).
% 2.62/3.03
% 2.62/3.03 % insert_absorb2
% 2.62/3.03 thf(fact_376_insert__absorb2,axiom,
% 2.62/3.03 ! [X: $o,A: set_o] :
% 2.62/3.03 ( ( insert_o2 @ X @ ( insert_o2 @ X @ A ) )
% 2.62/3.03 = ( insert_o2 @ X @ A ) ) ).
% 2.62/3.03
% 2.62/3.03 % insert_absorb2
% 2.62/3.03 thf(fact_377_DiffI,axiom,
% 2.62/3.03 ! [C: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.62/3.03 ( ( member8757157785044589968at_nat @ C @ A )
% 2.62/3.03 => ( ~ ( member8757157785044589968at_nat @ C @ B )
% 2.62/3.03 => ( member8757157785044589968at_nat @ C @ ( minus_3314409938677909166at_nat @ A @ B ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % DiffI
% 2.62/3.03 thf(fact_378_DiffI,axiom,
% 2.62/3.03 ! [C: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.62/3.03 ( ( member8440522571783428010at_nat @ C @ A )
% 2.62/3.03 => ( ~ ( member8440522571783428010at_nat @ C @ B )
% 2.62/3.03 => ( member8440522571783428010at_nat @ C @ ( minus_1356011639430497352at_nat @ A @ B ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % DiffI
% 2.62/3.03 thf(fact_379_DiffI,axiom,
% 2.62/3.03 ! [C: int,A: set_int,B: set_int] :
% 2.62/3.03 ( ( member_int @ C @ A )
% 2.62/3.03 => ( ~ ( member_int @ C @ B )
% 2.62/3.03 => ( member_int @ C @ ( minus_minus_set_int @ A @ B ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % DiffI
% 2.62/3.03 thf(fact_380_DiffI,axiom,
% 2.62/3.03 ! [C: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o] :
% 2.62/3.03 ( ( member6576561426505652726_nat_o @ C @ A )
% 2.62/3.03 => ( ~ ( member6576561426505652726_nat_o @ C @ B )
% 2.62/3.03 => ( member6576561426505652726_nat_o @ C @ ( minus_1801376950450012436_nat_o @ A @ B ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % DiffI
% 2.62/3.03 thf(fact_381_DiffI,axiom,
% 2.62/3.03 ! [C: nat,A: set_nat,B: set_nat] :
% 2.62/3.03 ( ( member_nat @ C @ A )
% 2.62/3.03 => ( ~ ( member_nat @ C @ B )
% 2.62/3.03 => ( member_nat @ C @ ( minus_minus_set_nat @ A @ B ) ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % DiffI
% 2.62/3.03 thf(fact_382_Diff__iff,axiom,
% 2.62/3.03 ! [C: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.62/3.03 ( ( member8757157785044589968at_nat @ C @ ( minus_3314409938677909166at_nat @ A @ B ) )
% 2.62/3.03 = ( ( member8757157785044589968at_nat @ C @ A )
% 2.62/3.03 & ~ ( member8757157785044589968at_nat @ C @ B ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % Diff_iff
% 2.62/3.03 thf(fact_383_Diff__iff,axiom,
% 2.62/3.03 ! [C: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.62/3.03 ( ( member8440522571783428010at_nat @ C @ ( minus_1356011639430497352at_nat @ A @ B ) )
% 2.62/3.03 = ( ( member8440522571783428010at_nat @ C @ A )
% 2.62/3.03 & ~ ( member8440522571783428010at_nat @ C @ B ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % Diff_iff
% 2.62/3.03 thf(fact_384_Diff__iff,axiom,
% 2.62/3.03 ! [C: int,A: set_int,B: set_int] :
% 2.62/3.03 ( ( member_int @ C @ ( minus_minus_set_int @ A @ B ) )
% 2.62/3.03 = ( ( member_int @ C @ A )
% 2.62/3.03 & ~ ( member_int @ C @ B ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % Diff_iff
% 2.62/3.03 thf(fact_385_Diff__iff,axiom,
% 2.62/3.03 ! [C: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o] :
% 2.62/3.03 ( ( member6576561426505652726_nat_o @ C @ ( minus_1801376950450012436_nat_o @ A @ B ) )
% 2.62/3.03 = ( ( member6576561426505652726_nat_o @ C @ A )
% 2.62/3.03 & ~ ( member6576561426505652726_nat_o @ C @ B ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % Diff_iff
% 2.62/3.03 thf(fact_386_Diff__iff,axiom,
% 2.62/3.03 ! [C: nat,A: set_nat,B: set_nat] :
% 2.62/3.03 ( ( member_nat @ C @ ( minus_minus_set_nat @ A @ B ) )
% 2.62/3.03 = ( ( member_nat @ C @ A )
% 2.62/3.03 & ~ ( member_nat @ C @ B ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % Diff_iff
% 2.62/3.03 thf(fact_387_Diff__idemp,axiom,
% 2.62/3.03 ! [A: set_nat,B: set_nat] :
% 2.62/3.03 ( ( minus_minus_set_nat @ ( minus_minus_set_nat @ A @ B ) @ B )
% 2.62/3.03 = ( minus_minus_set_nat @ A @ B ) ) ).
% 2.62/3.03
% 2.62/3.03 % Diff_idemp
% 2.62/3.03 thf(fact_388_not__psubset__empty,axiom,
% 2.62/3.03 ! [A: set_Pr4329608150637261639at_nat] :
% 2.62/3.03 ~ ( ord_le2604355607129572851at_nat @ A @ bot_bo228742789529271731at_nat ) ).
% 2.62/3.03
% 2.62/3.03 % not_psubset_empty
% 2.62/3.03 thf(fact_389_not__psubset__empty,axiom,
% 2.62/3.03 ! [A: set_Pr1261947904930325089at_nat] :
% 2.62/3.03 ~ ( ord_le7866589430770878221at_nat @ A @ bot_bo2099793752762293965at_nat ) ).
% 2.62/3.03
% 2.62/3.03 % not_psubset_empty
% 2.62/3.03 thf(fact_390_not__psubset__empty,axiom,
% 2.62/3.03 ! [A: set_o] :
% 2.62/3.03 ~ ( ord_less_set_o @ A @ bot_bot_set_o ) ).
% 2.62/3.03
% 2.62/3.03 % not_psubset_empty
% 2.62/3.03 thf(fact_391_not__psubset__empty,axiom,
% 2.62/3.03 ! [A: set_nat] :
% 2.62/3.03 ~ ( ord_less_set_nat @ A @ bot_bot_set_nat ) ).
% 2.62/3.03
% 2.62/3.03 % not_psubset_empty
% 2.62/3.03 thf(fact_392_not__psubset__empty,axiom,
% 2.62/3.03 ! [A: set_int] :
% 2.62/3.03 ~ ( ord_less_set_int @ A @ bot_bot_set_int ) ).
% 2.62/3.03
% 2.62/3.03 % not_psubset_empty
% 2.62/3.03 thf(fact_393_psubset__imp__ex__mem,axiom,
% 2.62/3.03 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.62/3.03 ( ( ord_le2604355607129572851at_nat @ A @ B )
% 2.62/3.03 => ? [B4: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ B4 @ ( minus_3314409938677909166at_nat @ B @ A ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % psubset_imp_ex_mem
% 2.62/3.03 thf(fact_394_psubset__imp__ex__mem,axiom,
% 2.62/3.03 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.62/3.03 ( ( ord_le7866589430770878221at_nat @ A @ B )
% 2.62/3.03 => ? [B4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ B4 @ ( minus_1356011639430497352at_nat @ B @ A ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % psubset_imp_ex_mem
% 2.62/3.03 thf(fact_395_psubset__imp__ex__mem,axiom,
% 2.62/3.03 ! [A: set_int,B: set_int] :
% 2.62/3.03 ( ( ord_less_set_int @ A @ B )
% 2.62/3.03 => ? [B4: int] : ( member_int @ B4 @ ( minus_minus_set_int @ B @ A ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % psubset_imp_ex_mem
% 2.62/3.03 thf(fact_396_psubset__imp__ex__mem,axiom,
% 2.62/3.03 ! [A: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o] :
% 2.62/3.03 ( ( ord_le2453136405763929_nat_o @ A @ B )
% 2.62/3.03 => ? [B4: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ B4 @ ( minus_1801376950450012436_nat_o @ B @ A ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % psubset_imp_ex_mem
% 2.62/3.03 thf(fact_397_psubset__imp__ex__mem,axiom,
% 2.62/3.03 ! [A: set_nat,B: set_nat] :
% 2.62/3.03 ( ( ord_less_set_nat @ A @ B )
% 2.62/3.03 => ? [B4: nat] : ( member_nat @ B4 @ ( minus_minus_set_nat @ B @ A ) ) ) ).
% 2.62/3.03
% 2.62/3.03 % psubset_imp_ex_mem
% 2.62/3.03 thf(fact_398_remove__subset,axiom,
% 2.62/3.03 ! [X: produc3658429121746597890et_nat > $o,S: set_Pr4532377907799695533_nat_o] :
% 2.62/3.03 ( ( member6576561426505652726_nat_o @ X @ S )
% 2.62/3.03 => ( ord_le2453136405763929_nat_o @ ( minus_1801376950450012436_nat_o @ S @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) @ S ) ) ).
% 2.62/3.03
% 2.62/3.03 % remove_subset
% 2.62/3.03 thf(fact_399_remove__subset,axiom,
% 2.62/3.03 ! [X: produc3843707927480180839at_nat,S: set_Pr4329608150637261639at_nat] :
% 2.62/3.03 ( ( member8757157785044589968at_nat @ X @ S )
% 2.62/3.03 => ( ord_le2604355607129572851at_nat @ ( minus_3314409938677909166at_nat @ S @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) @ S ) ) ).
% 2.62/3.03
% 2.62/3.03 % remove_subset
% 2.62/3.03 thf(fact_400_remove__subset,axiom,
% 2.62/3.03 ! [X: product_prod_nat_nat,S: set_Pr1261947904930325089at_nat] :
% 2.62/3.03 ( ( member8440522571783428010at_nat @ X @ S )
% 2.62/3.03 => ( ord_le7866589430770878221at_nat @ ( minus_1356011639430497352at_nat @ S @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) @ S ) ) ).
% 2.62/3.03
% 2.62/3.03 % remove_subset
% 2.62/3.03 thf(fact_401_remove__subset,axiom,
% 2.62/3.03 ! [X: $o,S: set_o] :
% 2.62/3.03 ( ( member_o @ X @ S )
% 2.62/3.03 => ( ord_less_set_o @ ( minus_minus_set_o @ S @ ( insert_o2 @ X @ bot_bot_set_o ) ) @ S ) ) ).
% 2.62/3.03
% 2.62/3.03 % remove_subset
% 2.62/3.03 thf(fact_402_remove__subset,axiom,
% 2.62/3.03 ! [X: int,S: set_int] :
% 2.62/3.03 ( ( member_int @ X @ S )
% 2.62/3.03 => ( ord_less_set_int @ ( minus_minus_set_int @ S @ ( insert_int2 @ X @ bot_bot_set_int ) ) @ S ) ) ).
% 2.62/3.03
% 2.62/3.03 % remove_subset
% 2.62/3.03 thf(fact_403_remove__subset,axiom,
% 2.62/3.03 ! [X: nat,S: set_nat] :
% 2.62/3.03 ( ( member_nat @ X @ S )
% 2.62/3.03 => ( ord_less_set_nat @ ( minus_minus_set_nat @ S @ ( insert_nat2 @ X @ bot_bot_set_nat ) ) @ S ) ) ).
% 2.62/3.03
% 2.62/3.03 % remove_subset
% 2.62/3.03 thf(fact_404_memb__imp__not__empty,axiom,
% 2.62/3.03 ! [X: produc3658429121746597890et_nat > $o,S: set_Pr4532377907799695533_nat_o] :
% 2.62/3.03 ( ( member6576561426505652726_nat_o @ X @ S )
% 2.62/3.03 => ( S != bot_bo7824918357723582233_nat_o ) ) ).
% 2.62/3.03
% 2.62/3.03 % memb_imp_not_empty
% 2.62/3.03 thf(fact_405_memb__imp__not__empty,axiom,
% 2.62/3.03 ! [X: produc3843707927480180839at_nat,S: set_Pr4329608150637261639at_nat] :
% 2.62/3.03 ( ( member8757157785044589968at_nat @ X @ S )
% 2.62/3.03 => ( S != bot_bo228742789529271731at_nat ) ) ).
% 2.62/3.03
% 2.62/3.03 % memb_imp_not_empty
% 2.62/3.03 thf(fact_406_memb__imp__not__empty,axiom,
% 2.62/3.03 ! [X: product_prod_nat_nat,S: set_Pr1261947904930325089at_nat] :
% 2.62/3.03 ( ( member8440522571783428010at_nat @ X @ S )
% 2.62/3.03 => ( S != bot_bo2099793752762293965at_nat ) ) ).
% 2.62/3.03
% 2.62/3.03 % memb_imp_not_empty
% 2.62/3.03 thf(fact_407_memb__imp__not__empty,axiom,
% 2.62/3.03 ! [X: $o,S: set_o] :
% 2.62/3.03 ( ( member_o @ X @ S )
% 2.62/3.03 => ( S != bot_bot_set_o ) ) ).
% 2.62/3.03
% 2.62/3.03 % memb_imp_not_empty
% 2.62/3.03 thf(fact_408_memb__imp__not__empty,axiom,
% 2.62/3.03 ! [X: nat,S: set_nat] :
% 2.62/3.03 ( ( member_nat @ X @ S )
% 2.62/3.03 => ( S != bot_bot_set_nat ) ) ).
% 2.62/3.03
% 2.62/3.03 % memb_imp_not_empty
% 2.62/3.03 thf(fact_409_memb__imp__not__empty,axiom,
% 2.62/3.03 ! [X: int,S: set_int] :
% 2.62/3.03 ( ( member_int @ X @ S )
% 2.62/3.03 => ( S != bot_bot_set_int ) ) ).
% 2.62/3.03
% 2.62/3.03 % memb_imp_not_empty
% 2.62/3.03 thf(fact_410_set__notEmptyE,axiom,
% 2.62/3.03 ! [S: set_Pr4532377907799695533_nat_o] :
% 2.62/3.03 ( ( S != bot_bo7824918357723582233_nat_o )
% 2.62/3.03 => ~ ! [X3: produc3658429121746597890et_nat > $o] :
% 2.62/3.03 ~ ( member6576561426505652726_nat_o @ X3 @ S ) ) ).
% 2.62/3.03
% 2.62/3.03 % set_notEmptyE
% 2.62/3.03 thf(fact_411_set__notEmptyE,axiom,
% 2.62/3.03 ! [S: set_Pr4329608150637261639at_nat] :
% 2.62/3.03 ( ( S != bot_bo228742789529271731at_nat )
% 2.62/3.03 => ~ ! [X3: produc3843707927480180839at_nat] :
% 2.62/3.03 ~ ( member8757157785044589968at_nat @ X3 @ S ) ) ).
% 2.62/3.03
% 2.62/3.03 % set_notEmptyE
% 2.62/3.03 thf(fact_412_set__notEmptyE,axiom,
% 2.62/3.03 ! [S: set_Pr1261947904930325089at_nat] :
% 2.62/3.03 ( ( S != bot_bo2099793752762293965at_nat )
% 2.62/3.03 => ~ ! [X3: product_prod_nat_nat] :
% 2.62/3.03 ~ ( member8440522571783428010at_nat @ X3 @ S ) ) ).
% 2.62/3.03
% 2.62/3.03 % set_notEmptyE
% 2.62/3.03 thf(fact_413_set__notEmptyE,axiom,
% 2.62/3.03 ! [S: set_o] :
% 2.62/3.03 ( ( S != bot_bot_set_o )
% 2.62/3.03 => ~ ! [X3: $o] :
% 2.62/3.03 ~ ( member_o @ X3 @ S ) ) ).
% 2.62/3.03
% 2.62/3.03 % set_notEmptyE
% 2.62/3.03 thf(fact_414_set__notEmptyE,axiom,
% 2.62/3.03 ! [S: set_nat] :
% 2.62/3.03 ( ( S != bot_bot_set_nat )
% 2.62/3.03 => ~ ! [X3: nat] :
% 2.62/3.03 ~ ( member_nat @ X3 @ S ) ) ).
% 2.62/3.03
% 2.62/3.03 % set_notEmptyE
% 2.62/3.03 thf(fact_415_set__notEmptyE,axiom,
% 2.62/3.03 ! [S: set_int] :
% 2.62/3.03 ( ( S != bot_bot_set_int )
% 2.62/3.03 => ~ ! [X3: int] :
% 2.62/3.03 ~ ( member_int @ X3 @ S ) ) ).
% 2.62/3.03
% 2.62/3.03 % set_notEmptyE
% 2.62/3.03 thf(fact_416_bot__set__def,axiom,
% 2.62/3.03 ( bot_bo7824918357723582233_nat_o
% 2.62/3.03 = ( collec939566748876313656_nat_o @ bot_bo7963750851167320836at_o_o ) ) ).
% 2.62/3.03
% 2.62/3.03 % bot_set_def
% 2.62/3.03 thf(fact_417_bot__set__def,axiom,
% 2.62/3.03 ( bot_bo228742789529271731at_nat
% 2.62/3.03 = ( collec6321179662152712658at_nat @ bot_bo6829958733157050602_nat_o ) ) ).
% 2.62/3.03
% 2.62/3.03 % bot_set_def
% 2.62/3.03 thf(fact_418_bot__set__def,axiom,
% 2.62/3.03 ( bot_bo2099793752762293965at_nat
% 2.62/3.03 = ( collec3392354462482085612at_nat @ bot_bo482883023278783056_nat_o ) ) ).
% 2.62/3.03
% 2.62/3.03 % bot_set_def
% 2.62/3.03 thf(fact_419_bot__set__def,axiom,
% 2.62/3.03 ( bot_bot_set_o
% 2.62/3.03 = ( collect_o @ bot_bot_o_o ) ) ).
% 2.62/3.03
% 2.62/3.03 % bot_set_def
% 2.62/3.03 thf(fact_420_bot__set__def,axiom,
% 2.62/3.03 ( bot_bot_set_nat
% 2.62/3.03 = ( collect_nat @ bot_bot_nat_o ) ) ).
% 2.62/3.03
% 2.62/3.03 % bot_set_def
% 2.62/3.03 thf(fact_421_bot__set__def,axiom,
% 2.62/3.03 ( bot_bot_set_int
% 2.62/3.03 = ( collect_int @ bot_bot_int_o ) ) ).
% 2.62/3.03
% 2.62/3.03 % bot_set_def
% 2.62/3.03 thf(fact_422_ex__in__conv,axiom,
% 2.62/3.03 ! [A: set_Pr4532377907799695533_nat_o] :
% 2.62/3.03 ( ( ? [X2: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X2 @ A ) )
% 2.75/3.03 = ( A != bot_bo7824918357723582233_nat_o ) ) ).
% 2.75/3.03
% 2.75/3.03 % ex_in_conv
% 2.75/3.03 thf(fact_423_ex__in__conv,axiom,
% 2.75/3.03 ! [A: set_Pr4329608150637261639at_nat] :
% 2.75/3.03 ( ( ? [X2: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X2 @ A ) )
% 2.75/3.03 = ( A != bot_bo228742789529271731at_nat ) ) ).
% 2.75/3.03
% 2.75/3.03 % ex_in_conv
% 2.75/3.03 thf(fact_424_ex__in__conv,axiom,
% 2.75/3.03 ! [A: set_Pr1261947904930325089at_nat] :
% 2.75/3.03 ( ( ? [X2: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X2 @ A ) )
% 2.75/3.03 = ( A != bot_bo2099793752762293965at_nat ) ) ).
% 2.75/3.03
% 2.75/3.03 % ex_in_conv
% 2.75/3.03 thf(fact_425_ex__in__conv,axiom,
% 2.75/3.03 ! [A: set_o] :
% 2.75/3.03 ( ( ? [X2: $o] : ( member_o @ X2 @ A ) )
% 2.75/3.03 = ( A != bot_bot_set_o ) ) ).
% 2.75/3.03
% 2.75/3.03 % ex_in_conv
% 2.75/3.03 thf(fact_426_ex__in__conv,axiom,
% 2.75/3.03 ! [A: set_nat] :
% 2.75/3.03 ( ( ? [X2: nat] : ( member_nat @ X2 @ A ) )
% 2.75/3.03 = ( A != bot_bot_set_nat ) ) ).
% 2.75/3.03
% 2.75/3.03 % ex_in_conv
% 2.75/3.03 thf(fact_427_ex__in__conv,axiom,
% 2.75/3.03 ! [A: set_int] :
% 2.75/3.03 ( ( ? [X2: int] : ( member_int @ X2 @ A ) )
% 2.75/3.04 = ( A != bot_bot_set_int ) ) ).
% 2.75/3.04
% 2.75/3.04 % ex_in_conv
% 2.75/3.04 thf(fact_428_equals0I,axiom,
% 2.75/3.04 ! [A: set_Pr4532377907799695533_nat_o] :
% 2.75/3.04 ( ! [Y2: produc3658429121746597890et_nat > $o] :
% 2.75/3.04 ~ ( member6576561426505652726_nat_o @ Y2 @ A )
% 2.75/3.04 => ( A = bot_bo7824918357723582233_nat_o ) ) ).
% 2.75/3.04
% 2.75/3.04 % equals0I
% 2.75/3.04 thf(fact_429_equals0I,axiom,
% 2.75/3.04 ! [A: set_Pr4329608150637261639at_nat] :
% 2.75/3.04 ( ! [Y2: produc3843707927480180839at_nat] :
% 2.75/3.04 ~ ( member8757157785044589968at_nat @ Y2 @ A )
% 2.75/3.04 => ( A = bot_bo228742789529271731at_nat ) ) ).
% 2.75/3.04
% 2.75/3.04 % equals0I
% 2.75/3.04 thf(fact_430_equals0I,axiom,
% 2.75/3.04 ! [A: set_Pr1261947904930325089at_nat] :
% 2.75/3.04 ( ! [Y2: product_prod_nat_nat] :
% 2.75/3.04 ~ ( member8440522571783428010at_nat @ Y2 @ A )
% 2.75/3.04 => ( A = bot_bo2099793752762293965at_nat ) ) ).
% 2.75/3.04
% 2.75/3.04 % equals0I
% 2.75/3.04 thf(fact_431_equals0I,axiom,
% 2.75/3.04 ! [A: set_o] :
% 2.75/3.04 ( ! [Y2: $o] :
% 2.75/3.04 ~ ( member_o @ Y2 @ A )
% 2.75/3.04 => ( A = bot_bot_set_o ) ) ).
% 2.75/3.04
% 2.75/3.04 % equals0I
% 2.75/3.04 thf(fact_432_equals0I,axiom,
% 2.75/3.04 ! [A: set_nat] :
% 2.75/3.04 ( ! [Y2: nat] :
% 2.75/3.04 ~ ( member_nat @ Y2 @ A )
% 2.75/3.04 => ( A = bot_bot_set_nat ) ) ).
% 2.75/3.04
% 2.75/3.04 % equals0I
% 2.75/3.04 thf(fact_433_equals0I,axiom,
% 2.75/3.04 ! [A: set_int] :
% 2.75/3.04 ( ! [Y2: int] :
% 2.75/3.04 ~ ( member_int @ Y2 @ A )
% 2.75/3.04 => ( A = bot_bot_set_int ) ) ).
% 2.75/3.04
% 2.75/3.04 % equals0I
% 2.75/3.04 thf(fact_434_equals0D,axiom,
% 2.75/3.04 ! [A: set_Pr4532377907799695533_nat_o,A2: produc3658429121746597890et_nat > $o] :
% 2.75/3.04 ( ( A = bot_bo7824918357723582233_nat_o )
% 2.75/3.04 => ~ ( member6576561426505652726_nat_o @ A2 @ A ) ) ).
% 2.75/3.04
% 2.75/3.04 % equals0D
% 2.75/3.04 thf(fact_435_equals0D,axiom,
% 2.75/3.04 ! [A: set_Pr4329608150637261639at_nat,A2: produc3843707927480180839at_nat] :
% 2.75/3.04 ( ( A = bot_bo228742789529271731at_nat )
% 2.75/3.04 => ~ ( member8757157785044589968at_nat @ A2 @ A ) ) ).
% 2.75/3.04
% 2.75/3.04 % equals0D
% 2.75/3.04 thf(fact_436_equals0D,axiom,
% 2.75/3.04 ! [A: set_Pr1261947904930325089at_nat,A2: product_prod_nat_nat] :
% 2.75/3.04 ( ( A = bot_bo2099793752762293965at_nat )
% 2.75/3.04 => ~ ( member8440522571783428010at_nat @ A2 @ A ) ) ).
% 2.75/3.04
% 2.75/3.04 % equals0D
% 2.75/3.04 thf(fact_437_equals0D,axiom,
% 2.75/3.04 ! [A: set_o,A2: $o] :
% 2.75/3.04 ( ( A = bot_bot_set_o )
% 2.75/3.04 => ~ ( member_o @ A2 @ A ) ) ).
% 2.75/3.04
% 2.75/3.04 % equals0D
% 2.75/3.04 thf(fact_438_equals0D,axiom,
% 2.75/3.04 ! [A: set_nat,A2: nat] :
% 2.75/3.04 ( ( A = bot_bot_set_nat )
% 2.75/3.04 => ~ ( member_nat @ A2 @ A ) ) ).
% 2.75/3.04
% 2.75/3.04 % equals0D
% 2.75/3.04 thf(fact_439_equals0D,axiom,
% 2.75/3.04 ! [A: set_int,A2: int] :
% 2.75/3.04 ( ( A = bot_bot_set_int )
% 2.75/3.04 => ~ ( member_int @ A2 @ A ) ) ).
% 2.75/3.04
% 2.75/3.04 % equals0D
% 2.75/3.04 thf(fact_440_emptyE,axiom,
% 2.75/3.04 ! [A2: produc3658429121746597890et_nat > $o] :
% 2.75/3.04 ~ ( member6576561426505652726_nat_o @ A2 @ bot_bo7824918357723582233_nat_o ) ).
% 2.75/3.04
% 2.75/3.04 % emptyE
% 2.75/3.04 thf(fact_441_emptyE,axiom,
% 2.75/3.04 ! [A2: produc3843707927480180839at_nat] :
% 2.75/3.04 ~ ( member8757157785044589968at_nat @ A2 @ bot_bo228742789529271731at_nat ) ).
% 2.75/3.04
% 2.75/3.04 % emptyE
% 2.75/3.04 thf(fact_442_emptyE,axiom,
% 2.75/3.04 ! [A2: product_prod_nat_nat] :
% 2.75/3.04 ~ ( member8440522571783428010at_nat @ A2 @ bot_bo2099793752762293965at_nat ) ).
% 2.75/3.04
% 2.75/3.04 % emptyE
% 2.75/3.04 thf(fact_443_emptyE,axiom,
% 2.75/3.04 ! [A2: $o] :
% 2.75/3.04 ~ ( member_o @ A2 @ bot_bot_set_o ) ).
% 2.75/3.04
% 2.75/3.04 % emptyE
% 2.75/3.04 thf(fact_444_emptyE,axiom,
% 2.75/3.04 ! [A2: nat] :
% 2.75/3.04 ~ ( member_nat @ A2 @ bot_bot_set_nat ) ).
% 2.75/3.04
% 2.75/3.04 % emptyE
% 2.75/3.04 thf(fact_445_emptyE,axiom,
% 2.75/3.04 ! [A2: int] :
% 2.75/3.04 ~ ( member_int @ A2 @ bot_bot_set_int ) ).
% 2.75/3.04
% 2.75/3.04 % emptyE
% 2.75/3.04 thf(fact_446_insertE,axiom,
% 2.75/3.04 ! [A2: $o,B2: $o,A: set_o] :
% 2.75/3.04 ( ( member_o @ A2 @ ( insert_o2 @ B2 @ A ) )
% 2.75/3.04 => ( ( A2 = ~ B2 )
% 2.75/3.04 => ( member_o @ A2 @ A ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % insertE
% 2.75/3.04 thf(fact_447_insertE,axiom,
% 2.75/3.04 ! [A2: produc3843707927480180839at_nat,B2: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat] :
% 2.75/3.04 ( ( member8757157785044589968at_nat @ A2 @ ( insert9069300056098147895at_nat @ B2 @ A ) )
% 2.75/3.04 => ( ( A2 != B2 )
% 2.75/3.04 => ( member8757157785044589968at_nat @ A2 @ A ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % insertE
% 2.75/3.04 thf(fact_448_insertE,axiom,
% 2.75/3.04 ! [A2: product_prod_nat_nat,B2: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat] :
% 2.75/3.04 ( ( member8440522571783428010at_nat @ A2 @ ( insert8211810215607154385at_nat @ B2 @ A ) )
% 2.75/3.04 => ( ( A2 != B2 )
% 2.75/3.04 => ( member8440522571783428010at_nat @ A2 @ A ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % insertE
% 2.75/3.04 thf(fact_449_insertE,axiom,
% 2.75/3.04 ! [A2: nat,B2: nat,A: set_nat] :
% 2.75/3.04 ( ( member_nat @ A2 @ ( insert_nat2 @ B2 @ A ) )
% 2.75/3.04 => ( ( A2 != B2 )
% 2.75/3.04 => ( member_nat @ A2 @ A ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % insertE
% 2.75/3.04 thf(fact_450_insertE,axiom,
% 2.75/3.04 ! [A2: int,B2: int,A: set_int] :
% 2.75/3.04 ( ( member_int @ A2 @ ( insert_int2 @ B2 @ A ) )
% 2.75/3.04 => ( ( A2 != B2 )
% 2.75/3.04 => ( member_int @ A2 @ A ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % insertE
% 2.75/3.04 thf(fact_451_insertE,axiom,
% 2.75/3.04 ! [A2: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o] :
% 2.75/3.04 ( ( member6576561426505652726_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ B2 @ A ) )
% 2.75/3.04 => ( ( A2 != B2 )
% 2.75/3.04 => ( member6576561426505652726_nat_o @ A2 @ A ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % insertE
% 2.75/3.04 thf(fact_452_insertI1,axiom,
% 2.75/3.04 ! [A2: $o,B: set_o] : ( member_o @ A2 @ ( insert_o2 @ A2 @ B ) ) ).
% 2.75/3.04
% 2.75/3.04 % insertI1
% 2.75/3.04 thf(fact_453_insertI1,axiom,
% 2.75/3.04 ! [A2: produc3843707927480180839at_nat,B: set_Pr4329608150637261639at_nat] : ( member8757157785044589968at_nat @ A2 @ ( insert9069300056098147895at_nat @ A2 @ B ) ) ).
% 2.75/3.04
% 2.75/3.04 % insertI1
% 2.75/3.04 thf(fact_454_insertI1,axiom,
% 2.75/3.04 ! [A2: product_prod_nat_nat,B: set_Pr1261947904930325089at_nat] : ( member8440522571783428010at_nat @ A2 @ ( insert8211810215607154385at_nat @ A2 @ B ) ) ).
% 2.75/3.04
% 2.75/3.04 % insertI1
% 2.75/3.04 thf(fact_455_insertI1,axiom,
% 2.75/3.04 ! [A2: nat,B: set_nat] : ( member_nat @ A2 @ ( insert_nat2 @ A2 @ B ) ) ).
% 2.75/3.04
% 2.75/3.04 % insertI1
% 2.75/3.04 thf(fact_456_insertI1,axiom,
% 2.75/3.04 ! [A2: int,B: set_int] : ( member_int @ A2 @ ( insert_int2 @ A2 @ B ) ) ).
% 2.75/3.04
% 2.75/3.04 % insertI1
% 2.75/3.04 thf(fact_457_insertI1,axiom,
% 2.75/3.04 ! [A2: produc3658429121746597890et_nat > $o,B: set_Pr4532377907799695533_nat_o] : ( member6576561426505652726_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ A2 @ B ) ) ).
% 2.75/3.04
% 2.75/3.04 % insertI1
% 2.75/3.04 thf(fact_458_insertI2,axiom,
% 2.75/3.04 ! [A2: $o,B: set_o,B2: $o] :
% 2.75/3.04 ( ( member_o @ A2 @ B )
% 2.75/3.04 => ( member_o @ A2 @ ( insert_o2 @ B2 @ B ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % insertI2
% 2.75/3.04 thf(fact_459_insertI2,axiom,
% 2.75/3.04 ! [A2: produc3843707927480180839at_nat,B: set_Pr4329608150637261639at_nat,B2: produc3843707927480180839at_nat] :
% 2.75/3.04 ( ( member8757157785044589968at_nat @ A2 @ B )
% 2.75/3.04 => ( member8757157785044589968at_nat @ A2 @ ( insert9069300056098147895at_nat @ B2 @ B ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % insertI2
% 2.75/3.04 thf(fact_460_insertI2,axiom,
% 2.75/3.04 ! [A2: product_prod_nat_nat,B: set_Pr1261947904930325089at_nat,B2: product_prod_nat_nat] :
% 2.75/3.04 ( ( member8440522571783428010at_nat @ A2 @ B )
% 2.75/3.04 => ( member8440522571783428010at_nat @ A2 @ ( insert8211810215607154385at_nat @ B2 @ B ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % insertI2
% 2.75/3.04 thf(fact_461_insertI2,axiom,
% 2.75/3.04 ! [A2: nat,B: set_nat,B2: nat] :
% 2.75/3.04 ( ( member_nat @ A2 @ B )
% 2.75/3.04 => ( member_nat @ A2 @ ( insert_nat2 @ B2 @ B ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % insertI2
% 2.75/3.04 thf(fact_462_insertI2,axiom,
% 2.75/3.04 ! [A2: int,B: set_int,B2: int] :
% 2.75/3.04 ( ( member_int @ A2 @ B )
% 2.75/3.04 => ( member_int @ A2 @ ( insert_int2 @ B2 @ B ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % insertI2
% 2.75/3.04 thf(fact_463_insertI2,axiom,
% 2.75/3.04 ! [A2: produc3658429121746597890et_nat > $o,B: set_Pr4532377907799695533_nat_o,B2: produc3658429121746597890et_nat > $o] :
% 2.75/3.04 ( ( member6576561426505652726_nat_o @ A2 @ B )
% 2.75/3.04 => ( member6576561426505652726_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ B2 @ B ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % insertI2
% 2.75/3.04 thf(fact_464_Set_Oset__insert,axiom,
% 2.75/3.04 ! [X: $o,A: set_o] :
% 2.75/3.04 ( ( member_o @ X @ A )
% 2.75/3.04 => ~ ! [B5: set_o] :
% 2.75/3.04 ( ( A
% 2.75/3.04 = ( insert_o2 @ X @ B5 ) )
% 2.75/3.04 => ( member_o @ X @ B5 ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % Set.set_insert
% 2.75/3.04 thf(fact_465_Set_Oset__insert,axiom,
% 2.75/3.04 ! [X: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat] :
% 2.75/3.04 ( ( member8757157785044589968at_nat @ X @ A )
% 2.75/3.04 => ~ ! [B5: set_Pr4329608150637261639at_nat] :
% 2.75/3.04 ( ( A
% 2.75/3.04 = ( insert9069300056098147895at_nat @ X @ B5 ) )
% 2.75/3.04 => ( member8757157785044589968at_nat @ X @ B5 ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % Set.set_insert
% 2.75/3.04 thf(fact_466_Set_Oset__insert,axiom,
% 2.75/3.04 ! [X: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat] :
% 2.75/3.04 ( ( member8440522571783428010at_nat @ X @ A )
% 2.75/3.04 => ~ ! [B5: set_Pr1261947904930325089at_nat] :
% 2.75/3.04 ( ( A
% 2.75/3.04 = ( insert8211810215607154385at_nat @ X @ B5 ) )
% 2.75/3.04 => ( member8440522571783428010at_nat @ X @ B5 ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % Set.set_insert
% 2.75/3.04 thf(fact_467_Set_Oset__insert,axiom,
% 2.75/3.04 ! [X: nat,A: set_nat] :
% 2.75/3.04 ( ( member_nat @ X @ A )
% 2.75/3.04 => ~ ! [B5: set_nat] :
% 2.75/3.04 ( ( A
% 2.75/3.04 = ( insert_nat2 @ X @ B5 ) )
% 2.75/3.04 => ( member_nat @ X @ B5 ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % Set.set_insert
% 2.75/3.04 thf(fact_468_Set_Oset__insert,axiom,
% 2.75/3.04 ! [X: int,A: set_int] :
% 2.75/3.04 ( ( member_int @ X @ A )
% 2.75/3.04 => ~ ! [B5: set_int] :
% 2.75/3.04 ( ( A
% 2.75/3.04 = ( insert_int2 @ X @ B5 ) )
% 2.75/3.04 => ( member_int @ X @ B5 ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % Set.set_insert
% 2.75/3.04 thf(fact_469_Set_Oset__insert,axiom,
% 2.75/3.04 ! [X: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o] :
% 2.75/3.04 ( ( member6576561426505652726_nat_o @ X @ A )
% 2.75/3.04 => ~ ! [B5: set_Pr4532377907799695533_nat_o] :
% 2.75/3.04 ( ( A
% 2.75/3.04 = ( insert5175938949040314269_nat_o @ X @ B5 ) )
% 2.75/3.04 => ( member6576561426505652726_nat_o @ X @ B5 ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % Set.set_insert
% 2.75/3.04 thf(fact_470_insert__ident,axiom,
% 2.75/3.04 ! [X: $o,A: set_o,B: set_o] :
% 2.75/3.04 ( ~ ( member_o @ X @ A )
% 2.75/3.04 => ( ~ ( member_o @ X @ B )
% 2.75/3.04 => ( ( ( insert_o2 @ X @ A )
% 2.75/3.04 = ( insert_o2 @ X @ B ) )
% 2.75/3.04 = ( A = B ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % insert_ident
% 2.75/3.04 thf(fact_471_insert__ident,axiom,
% 2.75/3.04 ! [X: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.75/3.04 ( ~ ( member8757157785044589968at_nat @ X @ A )
% 2.75/3.04 => ( ~ ( member8757157785044589968at_nat @ X @ B )
% 2.75/3.04 => ( ( ( insert9069300056098147895at_nat @ X @ A )
% 2.75/3.04 = ( insert9069300056098147895at_nat @ X @ B ) )
% 2.75/3.04 = ( A = B ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % insert_ident
% 2.75/3.04 thf(fact_472_insert__ident,axiom,
% 2.75/3.04 ! [X: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.75/3.04 ( ~ ( member8440522571783428010at_nat @ X @ A )
% 2.75/3.04 => ( ~ ( member8440522571783428010at_nat @ X @ B )
% 2.75/3.04 => ( ( ( insert8211810215607154385at_nat @ X @ A )
% 2.75/3.04 = ( insert8211810215607154385at_nat @ X @ B ) )
% 2.75/3.04 = ( A = B ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % insert_ident
% 2.75/3.04 thf(fact_473_insert__ident,axiom,
% 2.75/3.04 ! [X: nat,A: set_nat,B: set_nat] :
% 2.75/3.04 ( ~ ( member_nat @ X @ A )
% 2.75/3.04 => ( ~ ( member_nat @ X @ B )
% 2.75/3.04 => ( ( ( insert_nat2 @ X @ A )
% 2.75/3.04 = ( insert_nat2 @ X @ B ) )
% 2.75/3.04 = ( A = B ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % insert_ident
% 2.75/3.04 thf(fact_474_insert__ident,axiom,
% 2.75/3.04 ! [X: int,A: set_int,B: set_int] :
% 2.75/3.04 ( ~ ( member_int @ X @ A )
% 2.75/3.04 => ( ~ ( member_int @ X @ B )
% 2.75/3.04 => ( ( ( insert_int2 @ X @ A )
% 2.75/3.04 = ( insert_int2 @ X @ B ) )
% 2.75/3.04 = ( A = B ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % insert_ident
% 2.75/3.04 thf(fact_475_insert__ident,axiom,
% 2.75/3.04 ! [X: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o] :
% 2.75/3.04 ( ~ ( member6576561426505652726_nat_o @ X @ A )
% 2.75/3.04 => ( ~ ( member6576561426505652726_nat_o @ X @ B )
% 2.75/3.04 => ( ( ( insert5175938949040314269_nat_o @ X @ A )
% 2.75/3.04 = ( insert5175938949040314269_nat_o @ X @ B ) )
% 2.75/3.04 = ( A = B ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % insert_ident
% 2.75/3.04 thf(fact_476_insert__absorb,axiom,
% 2.75/3.04 ! [A2: $o,A: set_o] :
% 2.75/3.04 ( ( member_o @ A2 @ A )
% 2.75/3.04 => ( ( insert_o2 @ A2 @ A )
% 2.75/3.04 = A ) ) ).
% 2.75/3.04
% 2.75/3.04 % insert_absorb
% 2.75/3.04 thf(fact_477_insert__absorb,axiom,
% 2.75/3.04 ! [A2: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat] :
% 2.75/3.04 ( ( member8757157785044589968at_nat @ A2 @ A )
% 2.75/3.04 => ( ( insert9069300056098147895at_nat @ A2 @ A )
% 2.75/3.04 = A ) ) ).
% 2.75/3.04
% 2.75/3.04 % insert_absorb
% 2.75/3.04 thf(fact_478_insert__absorb,axiom,
% 2.75/3.04 ! [A2: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat] :
% 2.75/3.04 ( ( member8440522571783428010at_nat @ A2 @ A )
% 2.75/3.04 => ( ( insert8211810215607154385at_nat @ A2 @ A )
% 2.75/3.04 = A ) ) ).
% 2.75/3.04
% 2.75/3.04 % insert_absorb
% 2.75/3.04 thf(fact_479_insert__absorb,axiom,
% 2.75/3.04 ! [A2: nat,A: set_nat] :
% 2.75/3.04 ( ( member_nat @ A2 @ A )
% 2.75/3.04 => ( ( insert_nat2 @ A2 @ A )
% 2.75/3.04 = A ) ) ).
% 2.75/3.04
% 2.75/3.04 % insert_absorb
% 2.75/3.04 thf(fact_480_insert__absorb,axiom,
% 2.75/3.04 ! [A2: int,A: set_int] :
% 2.75/3.04 ( ( member_int @ A2 @ A )
% 2.75/3.04 => ( ( insert_int2 @ A2 @ A )
% 2.75/3.04 = A ) ) ).
% 2.75/3.04
% 2.75/3.04 % insert_absorb
% 2.75/3.04 thf(fact_481_insert__absorb,axiom,
% 2.75/3.04 ! [A2: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o] :
% 2.75/3.04 ( ( member6576561426505652726_nat_o @ A2 @ A )
% 2.75/3.04 => ( ( insert5175938949040314269_nat_o @ A2 @ A )
% 2.75/3.04 = A ) ) ).
% 2.75/3.04
% 2.75/3.04 % insert_absorb
% 2.75/3.04 thf(fact_482_insert__eq__iff,axiom,
% 2.75/3.04 ! [A2: $o,A: set_o,B2: $o,B: set_o] :
% 2.75/3.04 ( ~ ( member_o @ A2 @ A )
% 2.75/3.04 => ( ~ ( member_o @ B2 @ B )
% 2.75/3.04 => ( ( ( insert_o2 @ A2 @ A )
% 2.75/3.04 = ( insert_o2 @ B2 @ B ) )
% 2.75/3.04 = ( ( ( A2 = B2 )
% 2.75/3.04 => ( A = B ) )
% 2.75/3.04 & ( ( A2 = ~ B2 )
% 2.75/3.04 => ? [C3: set_o] :
% 2.75/3.04 ( ( A
% 2.75/3.04 = ( insert_o2 @ B2 @ C3 ) )
% 2.75/3.04 & ~ ( member_o @ B2 @ C3 )
% 2.75/3.04 & ( B
% 2.75/3.04 = ( insert_o2 @ A2 @ C3 ) )
% 2.75/3.04 & ~ ( member_o @ A2 @ C3 ) ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % insert_eq_iff
% 2.75/3.04 thf(fact_483_insert__eq__iff,axiom,
% 2.75/3.04 ! [A2: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat,B2: produc3843707927480180839at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.75/3.04 ( ~ ( member8757157785044589968at_nat @ A2 @ A )
% 2.75/3.04 => ( ~ ( member8757157785044589968at_nat @ B2 @ B )
% 2.75/3.04 => ( ( ( insert9069300056098147895at_nat @ A2 @ A )
% 2.75/3.04 = ( insert9069300056098147895at_nat @ B2 @ B ) )
% 2.75/3.04 = ( ( ( A2 = B2 )
% 2.75/3.04 => ( A = B ) )
% 2.75/3.04 & ( ( A2 != B2 )
% 2.75/3.04 => ? [C3: set_Pr4329608150637261639at_nat] :
% 2.75/3.04 ( ( A
% 2.75/3.04 = ( insert9069300056098147895at_nat @ B2 @ C3 ) )
% 2.75/3.04 & ~ ( member8757157785044589968at_nat @ B2 @ C3 )
% 2.75/3.04 & ( B
% 2.75/3.04 = ( insert9069300056098147895at_nat @ A2 @ C3 ) )
% 2.75/3.04 & ~ ( member8757157785044589968at_nat @ A2 @ C3 ) ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % insert_eq_iff
% 2.75/3.04 thf(fact_484_insert__eq__iff,axiom,
% 2.75/3.04 ! [A2: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat,B2: product_prod_nat_nat,B: set_Pr1261947904930325089at_nat] :
% 2.75/3.04 ( ~ ( member8440522571783428010at_nat @ A2 @ A )
% 2.75/3.04 => ( ~ ( member8440522571783428010at_nat @ B2 @ B )
% 2.75/3.04 => ( ( ( insert8211810215607154385at_nat @ A2 @ A )
% 2.75/3.04 = ( insert8211810215607154385at_nat @ B2 @ B ) )
% 2.75/3.04 = ( ( ( A2 = B2 )
% 2.75/3.04 => ( A = B ) )
% 2.75/3.04 & ( ( A2 != B2 )
% 2.75/3.04 => ? [C3: set_Pr1261947904930325089at_nat] :
% 2.75/3.04 ( ( A
% 2.75/3.04 = ( insert8211810215607154385at_nat @ B2 @ C3 ) )
% 2.75/3.04 & ~ ( member8440522571783428010at_nat @ B2 @ C3 )
% 2.75/3.04 & ( B
% 2.75/3.04 = ( insert8211810215607154385at_nat @ A2 @ C3 ) )
% 2.75/3.04 & ~ ( member8440522571783428010at_nat @ A2 @ C3 ) ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % insert_eq_iff
% 2.75/3.04 thf(fact_485_insert__eq__iff,axiom,
% 2.75/3.04 ! [A2: nat,A: set_nat,B2: nat,B: set_nat] :
% 2.75/3.04 ( ~ ( member_nat @ A2 @ A )
% 2.75/3.04 => ( ~ ( member_nat @ B2 @ B )
% 2.75/3.04 => ( ( ( insert_nat2 @ A2 @ A )
% 2.75/3.04 = ( insert_nat2 @ B2 @ B ) )
% 2.75/3.04 = ( ( ( A2 = B2 )
% 2.75/3.04 => ( A = B ) )
% 2.75/3.04 & ( ( A2 != B2 )
% 2.75/3.04 => ? [C3: set_nat] :
% 2.75/3.04 ( ( A
% 2.75/3.04 = ( insert_nat2 @ B2 @ C3 ) )
% 2.75/3.04 & ~ ( member_nat @ B2 @ C3 )
% 2.75/3.04 & ( B
% 2.75/3.04 = ( insert_nat2 @ A2 @ C3 ) )
% 2.75/3.04 & ~ ( member_nat @ A2 @ C3 ) ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % insert_eq_iff
% 2.75/3.04 thf(fact_486_insert__eq__iff,axiom,
% 2.75/3.04 ! [A2: int,A: set_int,B2: int,B: set_int] :
% 2.75/3.04 ( ~ ( member_int @ A2 @ A )
% 2.75/3.04 => ( ~ ( member_int @ B2 @ B )
% 2.75/3.04 => ( ( ( insert_int2 @ A2 @ A )
% 2.75/3.04 = ( insert_int2 @ B2 @ B ) )
% 2.75/3.04 = ( ( ( A2 = B2 )
% 2.75/3.04 => ( A = B ) )
% 2.75/3.04 & ( ( A2 != B2 )
% 2.75/3.04 => ? [C3: set_int] :
% 2.75/3.04 ( ( A
% 2.75/3.04 = ( insert_int2 @ B2 @ C3 ) )
% 2.75/3.04 & ~ ( member_int @ B2 @ C3 )
% 2.75/3.04 & ( B
% 2.75/3.04 = ( insert_int2 @ A2 @ C3 ) )
% 2.75/3.04 & ~ ( member_int @ A2 @ C3 ) ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % insert_eq_iff
% 2.75/3.04 thf(fact_487_insert__eq__iff,axiom,
% 2.75/3.04 ! [A2: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B2: produc3658429121746597890et_nat > $o,B: set_Pr4532377907799695533_nat_o] :
% 2.75/3.04 ( ~ ( member6576561426505652726_nat_o @ A2 @ A )
% 2.75/3.04 => ( ~ ( member6576561426505652726_nat_o @ B2 @ B )
% 2.75/3.04 => ( ( ( insert5175938949040314269_nat_o @ A2 @ A )
% 2.75/3.04 = ( insert5175938949040314269_nat_o @ B2 @ B ) )
% 2.75/3.04 = ( ( ( A2 = B2 )
% 2.75/3.04 => ( A = B ) )
% 2.75/3.04 & ( ( A2 != B2 )
% 2.75/3.04 => ? [C3: set_Pr4532377907799695533_nat_o] :
% 2.75/3.04 ( ( A
% 2.75/3.04 = ( insert5175938949040314269_nat_o @ B2 @ C3 ) )
% 2.75/3.04 & ~ ( member6576561426505652726_nat_o @ B2 @ C3 )
% 2.75/3.04 & ( B
% 2.75/3.04 = ( insert5175938949040314269_nat_o @ A2 @ C3 ) )
% 2.75/3.04 & ~ ( member6576561426505652726_nat_o @ A2 @ C3 ) ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % insert_eq_iff
% 2.75/3.04 thf(fact_488_insert__commute,axiom,
% 2.75/3.04 ! [X: nat,Y: nat,A: set_nat] :
% 2.75/3.04 ( ( insert_nat2 @ X @ ( insert_nat2 @ Y @ A ) )
% 2.75/3.04 = ( insert_nat2 @ Y @ ( insert_nat2 @ X @ A ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % insert_commute
% 2.75/3.04 thf(fact_489_insert__commute,axiom,
% 2.75/3.04 ! [X: int,Y: int,A: set_int] :
% 2.75/3.04 ( ( insert_int2 @ X @ ( insert_int2 @ Y @ A ) )
% 2.75/3.04 = ( insert_int2 @ Y @ ( insert_int2 @ X @ A ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % insert_commute
% 2.75/3.04 thf(fact_490_insert__commute,axiom,
% 2.75/3.04 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat] :
% 2.75/3.04 ( ( insert8211810215607154385at_nat @ X @ ( insert8211810215607154385at_nat @ Y @ A ) )
% 2.75/3.04 = ( insert8211810215607154385at_nat @ Y @ ( insert8211810215607154385at_nat @ X @ A ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % insert_commute
% 2.75/3.04 thf(fact_491_insert__commute,axiom,
% 2.75/3.04 ! [X: produc3843707927480180839at_nat,Y: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat] :
% 2.75/3.04 ( ( insert9069300056098147895at_nat @ X @ ( insert9069300056098147895at_nat @ Y @ A ) )
% 2.75/3.04 = ( insert9069300056098147895at_nat @ Y @ ( insert9069300056098147895at_nat @ X @ A ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % insert_commute
% 2.75/3.04 thf(fact_492_insert__commute,axiom,
% 2.75/3.04 ! [X: $o,Y: $o,A: set_o] :
% 2.75/3.04 ( ( insert_o2 @ X @ ( insert_o2 @ Y @ A ) )
% 2.75/3.04 = ( insert_o2 @ Y @ ( insert_o2 @ X @ A ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % insert_commute
% 2.75/3.04 thf(fact_493_mk__disjoint__insert,axiom,
% 2.75/3.04 ! [A2: $o,A: set_o] :
% 2.75/3.04 ( ( member_o @ A2 @ A )
% 2.75/3.04 => ? [B5: set_o] :
% 2.75/3.04 ( ( A
% 2.75/3.04 = ( insert_o2 @ A2 @ B5 ) )
% 2.75/3.04 & ~ ( member_o @ A2 @ B5 ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % mk_disjoint_insert
% 2.75/3.04 thf(fact_494_mk__disjoint__insert,axiom,
% 2.75/3.04 ! [A2: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat] :
% 2.75/3.04 ( ( member8757157785044589968at_nat @ A2 @ A )
% 2.75/3.04 => ? [B5: set_Pr4329608150637261639at_nat] :
% 2.75/3.04 ( ( A
% 2.75/3.04 = ( insert9069300056098147895at_nat @ A2 @ B5 ) )
% 2.75/3.04 & ~ ( member8757157785044589968at_nat @ A2 @ B5 ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % mk_disjoint_insert
% 2.75/3.04 thf(fact_495_mk__disjoint__insert,axiom,
% 2.75/3.04 ! [A2: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat] :
% 2.75/3.04 ( ( member8440522571783428010at_nat @ A2 @ A )
% 2.75/3.04 => ? [B5: set_Pr1261947904930325089at_nat] :
% 2.75/3.04 ( ( A
% 2.75/3.04 = ( insert8211810215607154385at_nat @ A2 @ B5 ) )
% 2.75/3.04 & ~ ( member8440522571783428010at_nat @ A2 @ B5 ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % mk_disjoint_insert
% 2.75/3.04 thf(fact_496_mk__disjoint__insert,axiom,
% 2.75/3.04 ! [A2: nat,A: set_nat] :
% 2.75/3.04 ( ( member_nat @ A2 @ A )
% 2.75/3.04 => ? [B5: set_nat] :
% 2.75/3.04 ( ( A
% 2.75/3.04 = ( insert_nat2 @ A2 @ B5 ) )
% 2.75/3.04 & ~ ( member_nat @ A2 @ B5 ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % mk_disjoint_insert
% 2.75/3.04 thf(fact_497_mk__disjoint__insert,axiom,
% 2.75/3.04 ! [A2: int,A: set_int] :
% 2.75/3.04 ( ( member_int @ A2 @ A )
% 2.75/3.04 => ? [B5: set_int] :
% 2.75/3.04 ( ( A
% 2.75/3.04 = ( insert_int2 @ A2 @ B5 ) )
% 2.75/3.04 & ~ ( member_int @ A2 @ B5 ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % mk_disjoint_insert
% 2.75/3.04 thf(fact_498_mk__disjoint__insert,axiom,
% 2.75/3.04 ! [A2: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o] :
% 2.75/3.04 ( ( member6576561426505652726_nat_o @ A2 @ A )
% 2.75/3.04 => ? [B5: set_Pr4532377907799695533_nat_o] :
% 2.75/3.04 ( ( A
% 2.75/3.04 = ( insert5175938949040314269_nat_o @ A2 @ B5 ) )
% 2.75/3.04 & ~ ( member6576561426505652726_nat_o @ A2 @ B5 ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % mk_disjoint_insert
% 2.75/3.04 thf(fact_499_DiffE,axiom,
% 2.75/3.04 ! [C: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.75/3.04 ( ( member8757157785044589968at_nat @ C @ ( minus_3314409938677909166at_nat @ A @ B ) )
% 2.75/3.04 => ~ ( ( member8757157785044589968at_nat @ C @ A )
% 2.75/3.04 => ( member8757157785044589968at_nat @ C @ B ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % DiffE
% 2.75/3.04 thf(fact_500_DiffE,axiom,
% 2.75/3.04 ! [C: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.75/3.04 ( ( member8440522571783428010at_nat @ C @ ( minus_1356011639430497352at_nat @ A @ B ) )
% 2.75/3.04 => ~ ( ( member8440522571783428010at_nat @ C @ A )
% 2.75/3.04 => ( member8440522571783428010at_nat @ C @ B ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % DiffE
% 2.75/3.04 thf(fact_501_DiffE,axiom,
% 2.75/3.04 ! [C: int,A: set_int,B: set_int] :
% 2.75/3.04 ( ( member_int @ C @ ( minus_minus_set_int @ A @ B ) )
% 2.75/3.04 => ~ ( ( member_int @ C @ A )
% 2.75/3.04 => ( member_int @ C @ B ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % DiffE
% 2.75/3.04 thf(fact_502_DiffE,axiom,
% 2.75/3.04 ! [C: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o] :
% 2.75/3.04 ( ( member6576561426505652726_nat_o @ C @ ( minus_1801376950450012436_nat_o @ A @ B ) )
% 2.75/3.04 => ~ ( ( member6576561426505652726_nat_o @ C @ A )
% 2.75/3.04 => ( member6576561426505652726_nat_o @ C @ B ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % DiffE
% 2.75/3.04 thf(fact_503_DiffE,axiom,
% 2.75/3.04 ! [C: nat,A: set_nat,B: set_nat] :
% 2.75/3.04 ( ( member_nat @ C @ ( minus_minus_set_nat @ A @ B ) )
% 2.75/3.04 => ~ ( ( member_nat @ C @ A )
% 2.75/3.04 => ( member_nat @ C @ B ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % DiffE
% 2.75/3.04 thf(fact_504_DiffD1,axiom,
% 2.75/3.04 ! [C: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.75/3.04 ( ( member8757157785044589968at_nat @ C @ ( minus_3314409938677909166at_nat @ A @ B ) )
% 2.75/3.04 => ( member8757157785044589968at_nat @ C @ A ) ) ).
% 2.75/3.04
% 2.75/3.04 % DiffD1
% 2.75/3.04 thf(fact_505_DiffD1,axiom,
% 2.75/3.04 ! [C: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.75/3.04 ( ( member8440522571783428010at_nat @ C @ ( minus_1356011639430497352at_nat @ A @ B ) )
% 2.75/3.04 => ( member8440522571783428010at_nat @ C @ A ) ) ).
% 2.75/3.04
% 2.75/3.04 % DiffD1
% 2.75/3.04 thf(fact_506_DiffD1,axiom,
% 2.75/3.04 ! [C: int,A: set_int,B: set_int] :
% 2.75/3.04 ( ( member_int @ C @ ( minus_minus_set_int @ A @ B ) )
% 2.75/3.04 => ( member_int @ C @ A ) ) ).
% 2.75/3.04
% 2.75/3.04 % DiffD1
% 2.75/3.04 thf(fact_507_DiffD1,axiom,
% 2.75/3.04 ! [C: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o] :
% 2.75/3.04 ( ( member6576561426505652726_nat_o @ C @ ( minus_1801376950450012436_nat_o @ A @ B ) )
% 2.75/3.04 => ( member6576561426505652726_nat_o @ C @ A ) ) ).
% 2.75/3.04
% 2.75/3.04 % DiffD1
% 2.75/3.04 thf(fact_508_DiffD1,axiom,
% 2.75/3.04 ! [C: nat,A: set_nat,B: set_nat] :
% 2.75/3.04 ( ( member_nat @ C @ ( minus_minus_set_nat @ A @ B ) )
% 2.75/3.04 => ( member_nat @ C @ A ) ) ).
% 2.75/3.04
% 2.75/3.04 % DiffD1
% 2.75/3.04 thf(fact_509_DiffD2,axiom,
% 2.75/3.04 ! [C: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.75/3.04 ( ( member8757157785044589968at_nat @ C @ ( minus_3314409938677909166at_nat @ A @ B ) )
% 2.75/3.04 => ~ ( member8757157785044589968at_nat @ C @ B ) ) ).
% 2.75/3.04
% 2.75/3.04 % DiffD2
% 2.75/3.04 thf(fact_510_DiffD2,axiom,
% 2.75/3.04 ! [C: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.75/3.04 ( ( member8440522571783428010at_nat @ C @ ( minus_1356011639430497352at_nat @ A @ B ) )
% 2.75/3.04 => ~ ( member8440522571783428010at_nat @ C @ B ) ) ).
% 2.75/3.04
% 2.75/3.04 % DiffD2
% 2.75/3.04 thf(fact_511_DiffD2,axiom,
% 2.75/3.04 ! [C: int,A: set_int,B: set_int] :
% 2.75/3.04 ( ( member_int @ C @ ( minus_minus_set_int @ A @ B ) )
% 2.75/3.04 => ~ ( member_int @ C @ B ) ) ).
% 2.75/3.04
% 2.75/3.04 % DiffD2
% 2.75/3.04 thf(fact_512_DiffD2,axiom,
% 2.75/3.04 ! [C: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o] :
% 2.75/3.04 ( ( member6576561426505652726_nat_o @ C @ ( minus_1801376950450012436_nat_o @ A @ B ) )
% 2.75/3.04 => ~ ( member6576561426505652726_nat_o @ C @ B ) ) ).
% 2.75/3.04
% 2.75/3.04 % DiffD2
% 2.75/3.04 thf(fact_513_DiffD2,axiom,
% 2.75/3.04 ! [C: nat,A: set_nat,B: set_nat] :
% 2.75/3.04 ( ( member_nat @ C @ ( minus_minus_set_nat @ A @ B ) )
% 2.75/3.04 => ~ ( member_nat @ C @ B ) ) ).
% 2.75/3.04
% 2.75/3.04 % DiffD2
% 2.75/3.04 thf(fact_514_singleton__inject,axiom,
% 2.75/3.04 ! [A2: produc3843707927480180839at_nat,B2: produc3843707927480180839at_nat] :
% 2.75/3.04 ( ( ( insert9069300056098147895at_nat @ A2 @ bot_bo228742789529271731at_nat )
% 2.75/3.04 = ( insert9069300056098147895at_nat @ B2 @ bot_bo228742789529271731at_nat ) )
% 2.75/3.04 => ( A2 = B2 ) ) ).
% 2.75/3.04
% 2.75/3.04 % singleton_inject
% 2.75/3.04 thf(fact_515_singleton__inject,axiom,
% 2.75/3.04 ! [A2: product_prod_nat_nat,B2: product_prod_nat_nat] :
% 2.75/3.04 ( ( ( insert8211810215607154385at_nat @ A2 @ bot_bo2099793752762293965at_nat )
% 2.75/3.04 = ( insert8211810215607154385at_nat @ B2 @ bot_bo2099793752762293965at_nat ) )
% 2.75/3.04 => ( A2 = B2 ) ) ).
% 2.75/3.04
% 2.75/3.04 % singleton_inject
% 2.75/3.04 thf(fact_516_singleton__inject,axiom,
% 2.75/3.04 ! [A2: $o,B2: $o] :
% 2.75/3.04 ( ( ( insert_o2 @ A2 @ bot_bot_set_o )
% 2.75/3.04 = ( insert_o2 @ B2 @ bot_bot_set_o ) )
% 2.75/3.04 => ( A2 = B2 ) ) ).
% 2.75/3.04
% 2.75/3.04 % singleton_inject
% 2.75/3.04 thf(fact_517_singleton__inject,axiom,
% 2.75/3.04 ! [A2: nat,B2: nat] :
% 2.75/3.04 ( ( ( insert_nat2 @ A2 @ bot_bot_set_nat )
% 2.75/3.04 = ( insert_nat2 @ B2 @ bot_bot_set_nat ) )
% 2.75/3.04 => ( A2 = B2 ) ) ).
% 2.75/3.04
% 2.75/3.04 % singleton_inject
% 2.75/3.04 thf(fact_518_singleton__inject,axiom,
% 2.75/3.04 ! [A2: int,B2: int] :
% 2.75/3.04 ( ( ( insert_int2 @ A2 @ bot_bot_set_int )
% 2.75/3.04 = ( insert_int2 @ B2 @ bot_bot_set_int ) )
% 2.75/3.04 => ( A2 = B2 ) ) ).
% 2.75/3.04
% 2.75/3.04 % singleton_inject
% 2.75/3.04 thf(fact_519_insert__not__empty,axiom,
% 2.75/3.04 ! [A2: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat] :
% 2.75/3.04 ( ( insert9069300056098147895at_nat @ A2 @ A )
% 2.75/3.04 != bot_bo228742789529271731at_nat ) ).
% 2.75/3.04
% 2.75/3.04 % insert_not_empty
% 2.75/3.04 thf(fact_520_insert__not__empty,axiom,
% 2.75/3.04 ! [A2: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat] :
% 2.75/3.04 ( ( insert8211810215607154385at_nat @ A2 @ A )
% 2.75/3.04 != bot_bo2099793752762293965at_nat ) ).
% 2.75/3.04
% 2.75/3.04 % insert_not_empty
% 2.75/3.04 thf(fact_521_insert__not__empty,axiom,
% 2.75/3.04 ! [A2: $o,A: set_o] :
% 2.75/3.04 ( ( insert_o2 @ A2 @ A )
% 2.75/3.04 != bot_bot_set_o ) ).
% 2.75/3.04
% 2.75/3.04 % insert_not_empty
% 2.75/3.04 thf(fact_522_insert__not__empty,axiom,
% 2.75/3.04 ! [A2: nat,A: set_nat] :
% 2.75/3.04 ( ( insert_nat2 @ A2 @ A )
% 2.75/3.04 != bot_bot_set_nat ) ).
% 2.75/3.04
% 2.75/3.04 % insert_not_empty
% 2.75/3.04 thf(fact_523_insert__not__empty,axiom,
% 2.75/3.04 ! [A2: int,A: set_int] :
% 2.75/3.04 ( ( insert_int2 @ A2 @ A )
% 2.75/3.04 != bot_bot_set_int ) ).
% 2.75/3.04
% 2.75/3.04 % insert_not_empty
% 2.75/3.04 thf(fact_524_doubleton__eq__iff,axiom,
% 2.75/3.04 ! [A2: produc3843707927480180839at_nat,B2: produc3843707927480180839at_nat,C: produc3843707927480180839at_nat,D2: produc3843707927480180839at_nat] :
% 2.75/3.04 ( ( ( insert9069300056098147895at_nat @ A2 @ ( insert9069300056098147895at_nat @ B2 @ bot_bo228742789529271731at_nat ) )
% 2.75/3.04 = ( insert9069300056098147895at_nat @ C @ ( insert9069300056098147895at_nat @ D2 @ bot_bo228742789529271731at_nat ) ) )
% 2.75/3.04 = ( ( ( A2 = C )
% 2.75/3.04 & ( B2 = D2 ) )
% 2.75/3.04 | ( ( A2 = D2 )
% 2.75/3.04 & ( B2 = C ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % doubleton_eq_iff
% 2.75/3.04 thf(fact_525_doubleton__eq__iff,axiom,
% 2.75/3.04 ! [A2: product_prod_nat_nat,B2: product_prod_nat_nat,C: product_prod_nat_nat,D2: product_prod_nat_nat] :
% 2.75/3.04 ( ( ( insert8211810215607154385at_nat @ A2 @ ( insert8211810215607154385at_nat @ B2 @ bot_bo2099793752762293965at_nat ) )
% 2.75/3.04 = ( insert8211810215607154385at_nat @ C @ ( insert8211810215607154385at_nat @ D2 @ bot_bo2099793752762293965at_nat ) ) )
% 2.75/3.04 = ( ( ( A2 = C )
% 2.75/3.04 & ( B2 = D2 ) )
% 2.75/3.04 | ( ( A2 = D2 )
% 2.75/3.04 & ( B2 = C ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % doubleton_eq_iff
% 2.75/3.04 thf(fact_526_doubleton__eq__iff,axiom,
% 2.75/3.04 ! [A2: $o,B2: $o,C: $o,D2: $o] :
% 2.75/3.04 ( ( ( insert_o2 @ A2 @ ( insert_o2 @ B2 @ bot_bot_set_o ) )
% 2.75/3.04 = ( insert_o2 @ C @ ( insert_o2 @ D2 @ bot_bot_set_o ) ) )
% 2.75/3.04 = ( ( ( A2 = C )
% 2.75/3.04 & ( B2 = D2 ) )
% 2.75/3.04 | ( ( A2 = D2 )
% 2.75/3.04 & ( B2 = C ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % doubleton_eq_iff
% 2.75/3.04 thf(fact_527_doubleton__eq__iff,axiom,
% 2.75/3.04 ! [A2: nat,B2: nat,C: nat,D2: nat] :
% 2.75/3.04 ( ( ( insert_nat2 @ A2 @ ( insert_nat2 @ B2 @ bot_bot_set_nat ) )
% 2.75/3.04 = ( insert_nat2 @ C @ ( insert_nat2 @ D2 @ bot_bot_set_nat ) ) )
% 2.75/3.04 = ( ( ( A2 = C )
% 2.75/3.04 & ( B2 = D2 ) )
% 2.75/3.04 | ( ( A2 = D2 )
% 2.75/3.04 & ( B2 = C ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % doubleton_eq_iff
% 2.75/3.04 thf(fact_528_doubleton__eq__iff,axiom,
% 2.75/3.04 ! [A2: int,B2: int,C: int,D2: int] :
% 2.75/3.04 ( ( ( insert_int2 @ A2 @ ( insert_int2 @ B2 @ bot_bot_set_int ) )
% 2.75/3.04 = ( insert_int2 @ C @ ( insert_int2 @ D2 @ bot_bot_set_int ) ) )
% 2.75/3.04 = ( ( ( A2 = C )
% 2.75/3.04 & ( B2 = D2 ) )
% 2.75/3.04 | ( ( A2 = D2 )
% 2.75/3.04 & ( B2 = C ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % doubleton_eq_iff
% 2.75/3.04 thf(fact_529_singleton__iff,axiom,
% 2.75/3.04 ! [B2: produc3658429121746597890et_nat > $o,A2: produc3658429121746597890et_nat > $o] :
% 2.75/3.04 ( ( member6576561426505652726_nat_o @ B2 @ ( insert5175938949040314269_nat_o @ A2 @ bot_bo7824918357723582233_nat_o ) )
% 2.75/3.04 = ( B2 = A2 ) ) ).
% 2.75/3.04
% 2.75/3.04 % singleton_iff
% 2.75/3.04 thf(fact_530_singleton__iff,axiom,
% 2.75/3.04 ! [B2: produc3843707927480180839at_nat,A2: produc3843707927480180839at_nat] :
% 2.75/3.04 ( ( member8757157785044589968at_nat @ B2 @ ( insert9069300056098147895at_nat @ A2 @ bot_bo228742789529271731at_nat ) )
% 2.75/3.04 = ( B2 = A2 ) ) ).
% 2.75/3.04
% 2.75/3.04 % singleton_iff
% 2.75/3.04 thf(fact_531_singleton__iff,axiom,
% 2.75/3.04 ! [B2: product_prod_nat_nat,A2: product_prod_nat_nat] :
% 2.75/3.04 ( ( member8440522571783428010at_nat @ B2 @ ( insert8211810215607154385at_nat @ A2 @ bot_bo2099793752762293965at_nat ) )
% 2.75/3.04 = ( B2 = A2 ) ) ).
% 2.75/3.04
% 2.75/3.04 % singleton_iff
% 2.75/3.04 thf(fact_532_singleton__iff,axiom,
% 2.75/3.04 ! [B2: $o,A2: $o] :
% 2.75/3.04 ( ( member_o @ B2 @ ( insert_o2 @ A2 @ bot_bot_set_o ) )
% 2.75/3.04 = ( B2 = A2 ) ) ).
% 2.75/3.04
% 2.75/3.04 % singleton_iff
% 2.75/3.04 thf(fact_533_singleton__iff,axiom,
% 2.75/3.04 ! [B2: nat,A2: nat] :
% 2.75/3.04 ( ( member_nat @ B2 @ ( insert_nat2 @ A2 @ bot_bot_set_nat ) )
% 2.75/3.04 = ( B2 = A2 ) ) ).
% 2.75/3.04
% 2.75/3.04 % singleton_iff
% 2.75/3.04 thf(fact_534_singleton__iff,axiom,
% 2.75/3.04 ! [B2: int,A2: int] :
% 2.75/3.04 ( ( member_int @ B2 @ ( insert_int2 @ A2 @ bot_bot_set_int ) )
% 2.75/3.04 = ( B2 = A2 ) ) ).
% 2.75/3.04
% 2.75/3.04 % singleton_iff
% 2.75/3.04 thf(fact_535_singletonD,axiom,
% 2.75/3.04 ! [B2: produc3658429121746597890et_nat > $o,A2: produc3658429121746597890et_nat > $o] :
% 2.75/3.04 ( ( member6576561426505652726_nat_o @ B2 @ ( insert5175938949040314269_nat_o @ A2 @ bot_bo7824918357723582233_nat_o ) )
% 2.75/3.04 => ( B2 = A2 ) ) ).
% 2.75/3.04
% 2.75/3.04 % singletonD
% 2.75/3.04 thf(fact_536_singletonD,axiom,
% 2.75/3.04 ! [B2: produc3843707927480180839at_nat,A2: produc3843707927480180839at_nat] :
% 2.75/3.04 ( ( member8757157785044589968at_nat @ B2 @ ( insert9069300056098147895at_nat @ A2 @ bot_bo228742789529271731at_nat ) )
% 2.75/3.04 => ( B2 = A2 ) ) ).
% 2.75/3.04
% 2.75/3.04 % singletonD
% 2.75/3.04 thf(fact_537_singletonD,axiom,
% 2.75/3.04 ! [B2: product_prod_nat_nat,A2: product_prod_nat_nat] :
% 2.75/3.04 ( ( member8440522571783428010at_nat @ B2 @ ( insert8211810215607154385at_nat @ A2 @ bot_bo2099793752762293965at_nat ) )
% 2.75/3.04 => ( B2 = A2 ) ) ).
% 2.75/3.04
% 2.75/3.04 % singletonD
% 2.75/3.04 thf(fact_538_singletonD,axiom,
% 2.75/3.04 ! [B2: $o,A2: $o] :
% 2.75/3.04 ( ( member_o @ B2 @ ( insert_o2 @ A2 @ bot_bot_set_o ) )
% 2.75/3.04 => ( B2 = A2 ) ) ).
% 2.75/3.04
% 2.75/3.04 % singletonD
% 2.75/3.04 thf(fact_539_singletonD,axiom,
% 2.75/3.04 ! [B2: nat,A2: nat] :
% 2.75/3.04 ( ( member_nat @ B2 @ ( insert_nat2 @ A2 @ bot_bot_set_nat ) )
% 2.75/3.04 => ( B2 = A2 ) ) ).
% 2.75/3.04
% 2.75/3.04 % singletonD
% 2.75/3.04 thf(fact_540_singletonD,axiom,
% 2.75/3.04 ! [B2: int,A2: int] :
% 2.75/3.04 ( ( member_int @ B2 @ ( insert_int2 @ A2 @ bot_bot_set_int ) )
% 2.75/3.04 => ( B2 = A2 ) ) ).
% 2.75/3.04
% 2.75/3.04 % singletonD
% 2.75/3.04 thf(fact_541_insert__Diff__if,axiom,
% 2.75/3.04 ! [X: $o,B: set_o,A: set_o] :
% 2.75/3.04 ( ( ( member_o @ X @ B )
% 2.75/3.04 => ( ( minus_minus_set_o @ ( insert_o2 @ X @ A ) @ B )
% 2.75/3.04 = ( minus_minus_set_o @ A @ B ) ) )
% 2.75/3.04 & ( ~ ( member_o @ X @ B )
% 2.75/3.04 => ( ( minus_minus_set_o @ ( insert_o2 @ X @ A ) @ B )
% 2.75/3.04 = ( insert_o2 @ X @ ( minus_minus_set_o @ A @ B ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % insert_Diff_if
% 2.75/3.04 thf(fact_542_insert__Diff__if,axiom,
% 2.75/3.04 ! [X: produc3843707927480180839at_nat,B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 2.75/3.04 ( ( ( member8757157785044589968at_nat @ X @ B )
% 2.75/3.04 => ( ( minus_3314409938677909166at_nat @ ( insert9069300056098147895at_nat @ X @ A ) @ B )
% 2.75/3.04 = ( minus_3314409938677909166at_nat @ A @ B ) ) )
% 2.75/3.04 & ( ~ ( member8757157785044589968at_nat @ X @ B )
% 2.75/3.04 => ( ( minus_3314409938677909166at_nat @ ( insert9069300056098147895at_nat @ X @ A ) @ B )
% 2.75/3.04 = ( insert9069300056098147895at_nat @ X @ ( minus_3314409938677909166at_nat @ A @ B ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % insert_Diff_if
% 2.75/3.04 thf(fact_543_insert__Diff__if,axiom,
% 2.75/3.04 ! [X: product_prod_nat_nat,B: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 2.75/3.04 ( ( ( member8440522571783428010at_nat @ X @ B )
% 2.75/3.04 => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X @ A ) @ B )
% 2.75/3.04 = ( minus_1356011639430497352at_nat @ A @ B ) ) )
% 2.75/3.04 & ( ~ ( member8440522571783428010at_nat @ X @ B )
% 2.75/3.04 => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X @ A ) @ B )
% 2.75/3.04 = ( insert8211810215607154385at_nat @ X @ ( minus_1356011639430497352at_nat @ A @ B ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % insert_Diff_if
% 2.75/3.04 thf(fact_544_insert__Diff__if,axiom,
% 2.75/3.04 ! [X: int,B: set_int,A: set_int] :
% 2.75/3.04 ( ( ( member_int @ X @ B )
% 2.75/3.04 => ( ( minus_minus_set_int @ ( insert_int2 @ X @ A ) @ B )
% 2.75/3.04 = ( minus_minus_set_int @ A @ B ) ) )
% 2.75/3.04 & ( ~ ( member_int @ X @ B )
% 2.75/3.04 => ( ( minus_minus_set_int @ ( insert_int2 @ X @ A ) @ B )
% 2.75/3.04 = ( insert_int2 @ X @ ( minus_minus_set_int @ A @ B ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % insert_Diff_if
% 2.75/3.04 thf(fact_545_insert__Diff__if,axiom,
% 2.75/3.04 ! [X: produc3658429121746597890et_nat > $o,B: set_Pr4532377907799695533_nat_o,A: set_Pr4532377907799695533_nat_o] :
% 2.75/3.04 ( ( ( member6576561426505652726_nat_o @ X @ B )
% 2.75/3.04 => ( ( minus_1801376950450012436_nat_o @ ( insert5175938949040314269_nat_o @ X @ A ) @ B )
% 2.75/3.04 = ( minus_1801376950450012436_nat_o @ A @ B ) ) )
% 2.75/3.04 & ( ~ ( member6576561426505652726_nat_o @ X @ B )
% 2.75/3.04 => ( ( minus_1801376950450012436_nat_o @ ( insert5175938949040314269_nat_o @ X @ A ) @ B )
% 2.75/3.04 = ( insert5175938949040314269_nat_o @ X @ ( minus_1801376950450012436_nat_o @ A @ B ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % insert_Diff_if
% 2.75/3.04 thf(fact_546_insert__Diff__if,axiom,
% 2.75/3.04 ! [X: nat,B: set_nat,A: set_nat] :
% 2.75/3.04 ( ( ( member_nat @ X @ B )
% 2.75/3.04 => ( ( minus_minus_set_nat @ ( insert_nat2 @ X @ A ) @ B )
% 2.75/3.04 = ( minus_minus_set_nat @ A @ B ) ) )
% 2.75/3.04 & ( ~ ( member_nat @ X @ B )
% 2.75/3.04 => ( ( minus_minus_set_nat @ ( insert_nat2 @ X @ A ) @ B )
% 2.75/3.04 = ( insert_nat2 @ X @ ( minus_minus_set_nat @ A @ B ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % insert_Diff_if
% 2.75/3.04 thf(fact_547_set__minus__singleton__eq,axiom,
% 2.75/3.04 ! [X: produc3658429121746597890et_nat > $o,X4: set_Pr4532377907799695533_nat_o] :
% 2.75/3.04 ( ~ ( member6576561426505652726_nat_o @ X @ X4 )
% 2.75/3.04 => ( ( minus_1801376950450012436_nat_o @ X4 @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) )
% 2.75/3.04 = X4 ) ) ).
% 2.75/3.04
% 2.75/3.04 % set_minus_singleton_eq
% 2.75/3.04 thf(fact_548_set__minus__singleton__eq,axiom,
% 2.75/3.04 ! [X: produc3843707927480180839at_nat,X4: set_Pr4329608150637261639at_nat] :
% 2.75/3.04 ( ~ ( member8757157785044589968at_nat @ X @ X4 )
% 2.75/3.04 => ( ( minus_3314409938677909166at_nat @ X4 @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 2.75/3.04 = X4 ) ) ).
% 2.75/3.04
% 2.75/3.04 % set_minus_singleton_eq
% 2.75/3.04 thf(fact_549_set__minus__singleton__eq,axiom,
% 2.75/3.04 ! [X: product_prod_nat_nat,X4: set_Pr1261947904930325089at_nat] :
% 2.75/3.04 ( ~ ( member8440522571783428010at_nat @ X @ X4 )
% 2.75/3.04 => ( ( minus_1356011639430497352at_nat @ X4 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 2.75/3.04 = X4 ) ) ).
% 2.75/3.04
% 2.75/3.04 % set_minus_singleton_eq
% 2.75/3.04 thf(fact_550_set__minus__singleton__eq,axiom,
% 2.75/3.04 ! [X: $o,X4: set_o] :
% 2.75/3.04 ( ~ ( member_o @ X @ X4 )
% 2.75/3.04 => ( ( minus_minus_set_o @ X4 @ ( insert_o2 @ X @ bot_bot_set_o ) )
% 2.75/3.04 = X4 ) ) ).
% 2.75/3.04
% 2.75/3.04 % set_minus_singleton_eq
% 2.75/3.04 thf(fact_551_set__minus__singleton__eq,axiom,
% 2.75/3.04 ! [X: int,X4: set_int] :
% 2.75/3.04 ( ~ ( member_int @ X @ X4 )
% 2.75/3.04 => ( ( minus_minus_set_int @ X4 @ ( insert_int2 @ X @ bot_bot_set_int ) )
% 2.75/3.04 = X4 ) ) ).
% 2.75/3.04
% 2.75/3.04 % set_minus_singleton_eq
% 2.75/3.04 thf(fact_552_set__minus__singleton__eq,axiom,
% 2.75/3.04 ! [X: nat,X4: set_nat] :
% 2.75/3.04 ( ~ ( member_nat @ X @ X4 )
% 2.75/3.04 => ( ( minus_minus_set_nat @ X4 @ ( insert_nat2 @ X @ bot_bot_set_nat ) )
% 2.75/3.04 = X4 ) ) ).
% 2.75/3.04
% 2.75/3.04 % set_minus_singleton_eq
% 2.75/3.04 thf(fact_553_listI__assn__reinsert,axiom,
% 2.75/3.04 ! [P: assn,A: c > nat > assn,Xs: list_c,I: nat,Xsi: list_nat,I3: set_nat,F: assn,Q: assn] :
% 2.75/3.04 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_c @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L6585172037124793648_c_nat @ ( minus_minus_set_nat @ I3 @ ( insert_nat2 @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F ) )
% 2.75/3.04 => ( ( ord_less_nat @ I @ ( size_size_list_c @ Xs ) )
% 2.75/3.04 => ( ( member_nat @ I @ I3 )
% 2.75/3.04 => ( ( entails @ ( times_times_assn @ ( vEBT_L6585172037124793648_c_nat @ I3 @ A @ Xs @ Xsi ) @ F ) @ Q )
% 2.75/3.04 => ( entails @ P @ Q ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % listI_assn_reinsert
% 2.75/3.04 thf(fact_554_listI__assn__reinsert,axiom,
% 2.75/3.04 ! [P: assn,A: c > int > assn,Xs: list_c,I: nat,Xsi: list_int,I3: set_nat,F: assn,Q: assn] :
% 2.75/3.04 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_c @ Xs @ I ) @ ( nth_int @ Xsi @ I ) ) @ ( vEBT_L6582681566615743372_c_int @ ( minus_minus_set_nat @ I3 @ ( insert_nat2 @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F ) )
% 2.75/3.04 => ( ( ord_less_nat @ I @ ( size_size_list_c @ Xs ) )
% 2.75/3.04 => ( ( member_nat @ I @ I3 )
% 2.75/3.04 => ( ( entails @ ( times_times_assn @ ( vEBT_L6582681566615743372_c_int @ I3 @ A @ Xs @ Xsi ) @ F ) @ Q )
% 2.75/3.04 => ( entails @ P @ Q ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % listI_assn_reinsert
% 2.75/3.04 thf(fact_555_listI__assn__reinsert,axiom,
% 2.75/3.04 ! [P: assn,A: d > nat > assn,Xs: list_d,I: nat,Xsi: list_nat,I3: set_nat,F: assn,Q: assn] :
% 2.75/3.04 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_d @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L7820616366081188145_d_nat @ ( minus_minus_set_nat @ I3 @ ( insert_nat2 @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F ) )
% 2.75/3.04 => ( ( ord_less_nat @ I @ ( size_size_list_d @ Xs ) )
% 2.75/3.04 => ( ( member_nat @ I @ I3 )
% 2.75/3.04 => ( ( entails @ ( times_times_assn @ ( vEBT_L7820616366081188145_d_nat @ I3 @ A @ Xs @ Xsi ) @ F ) @ Q )
% 2.75/3.04 => ( entails @ P @ Q ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % listI_assn_reinsert
% 2.75/3.04 thf(fact_556_listI__assn__reinsert,axiom,
% 2.75/3.04 ! [P: assn,A: d > int > assn,Xs: list_d,I: nat,Xsi: list_int,I3: set_nat,F: assn,Q: assn] :
% 2.75/3.04 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_d @ Xs @ I ) @ ( nth_int @ Xsi @ I ) ) @ ( vEBT_L7818125895572137869_d_int @ ( minus_minus_set_nat @ I3 @ ( insert_nat2 @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F ) )
% 2.75/3.04 => ( ( ord_less_nat @ I @ ( size_size_list_d @ Xs ) )
% 2.75/3.04 => ( ( member_nat @ I @ I3 )
% 2.75/3.04 => ( ( entails @ ( times_times_assn @ ( vEBT_L7818125895572137869_d_int @ I3 @ A @ Xs @ Xsi ) @ F ) @ Q )
% 2.75/3.04 => ( entails @ P @ Q ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % listI_assn_reinsert
% 2.75/3.04 thf(fact_557_listI__assn__reinsert,axiom,
% 2.75/3.04 ! [P: assn,A: nat > nat > assn,Xs: list_nat,I: nat,Xsi: list_nat,I3: set_nat,F: assn,Q: assn] :
% 2.75/3.04 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_nat @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L7892069108621897922at_nat @ ( minus_minus_set_nat @ I3 @ ( insert_nat2 @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F ) )
% 2.75/3.04 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 2.75/3.04 => ( ( member_nat @ I @ I3 )
% 2.75/3.04 => ( ( entails @ ( times_times_assn @ ( vEBT_L7892069108621897922at_nat @ I3 @ A @ Xs @ Xsi ) @ F ) @ Q )
% 2.75/3.04 => ( entails @ P @ Q ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % listI_assn_reinsert
% 2.75/3.04 thf(fact_558_listI__assn__reinsert,axiom,
% 2.75/3.04 ! [P: assn,A: nat > int > assn,Xs: list_nat,I: nat,Xsi: list_int,I3: set_nat,F: assn,Q: assn] :
% 2.75/3.04 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_nat @ Xs @ I ) @ ( nth_int @ Xsi @ I ) ) @ ( vEBT_L7889578638112847646at_int @ ( minus_minus_set_nat @ I3 @ ( insert_nat2 @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F ) )
% 2.75/3.04 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 2.75/3.04 => ( ( member_nat @ I @ I3 )
% 2.75/3.04 => ( ( entails @ ( times_times_assn @ ( vEBT_L7889578638112847646at_int @ I3 @ A @ Xs @ Xsi ) @ F ) @ Q )
% 2.75/3.04 => ( entails @ P @ Q ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % listI_assn_reinsert
% 2.75/3.04 thf(fact_559_listI__assn__reinsert,axiom,
% 2.75/3.04 ! [P: assn,A: int > nat > assn,Xs: list_int,I: nat,Xsi: list_nat,I3: set_nat,F: assn,Q: assn] :
% 2.75/3.04 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_int @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L8891422820522952478nt_nat @ ( minus_minus_set_nat @ I3 @ ( insert_nat2 @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F ) )
% 2.75/3.04 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 2.75/3.04 => ( ( member_nat @ I @ I3 )
% 2.75/3.04 => ( ( entails @ ( times_times_assn @ ( vEBT_L8891422820522952478nt_nat @ I3 @ A @ Xs @ Xsi ) @ F ) @ Q )
% 2.75/3.04 => ( entails @ P @ Q ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % listI_assn_reinsert
% 2.75/3.04 thf(fact_560_listI__assn__reinsert,axiom,
% 2.75/3.04 ! [P: assn,A: int > int > assn,Xs: list_int,I: nat,Xsi: list_int,I3: set_nat,F: assn,Q: assn] :
% 2.75/3.04 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_int @ Xs @ I ) @ ( nth_int @ Xsi @ I ) ) @ ( vEBT_L8888932350013902202nt_int @ ( minus_minus_set_nat @ I3 @ ( insert_nat2 @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F ) )
% 2.75/3.04 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 2.75/3.04 => ( ( member_nat @ I @ I3 )
% 2.75/3.04 => ( ( entails @ ( times_times_assn @ ( vEBT_L8888932350013902202nt_int @ I3 @ A @ Xs @ Xsi ) @ F ) @ Q )
% 2.75/3.04 => ( entails @ P @ Q ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % listI_assn_reinsert
% 2.75/3.04 thf(fact_561_listI__assn__reinsert,axiom,
% 2.75/3.04 ! [P: assn,A: c > d > assn,Xs: list_c,I: nat,Xsi: list_d,I3: set_nat,F: assn,Q: assn] :
% 2.75/3.04 ( ( entails @ P @ ( times_times_assn @ ( times_times_assn @ ( A @ ( nth_c @ Xs @ I ) @ ( nth_d @ Xsi @ I ) ) @ ( vEBT_L824818263033719201sn_c_d @ ( minus_minus_set_nat @ I3 @ ( insert_nat2 @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) @ F ) )
% 2.75/3.04 => ( ( ord_less_nat @ I @ ( size_size_list_c @ Xs ) )
% 2.75/3.04 => ( ( member_nat @ I @ I3 )
% 2.75/3.04 => ( ( entails @ ( times_times_assn @ ( vEBT_L824818263033719201sn_c_d @ I3 @ A @ Xs @ Xsi ) @ F ) @ Q )
% 2.75/3.04 => ( entails @ P @ Q ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % listI_assn_reinsert
% 2.75/3.04 thf(fact_562_the__elem__eq,axiom,
% 2.75/3.04 ! [X: produc3843707927480180839at_nat] :
% 2.75/3.04 ( ( the_el221668144340439132at_nat @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 2.75/3.04 = X ) ).
% 2.75/3.04
% 2.75/3.04 % the_elem_eq
% 2.75/3.04 thf(fact_563_the__elem__eq,axiom,
% 2.75/3.04 ! [X: product_prod_nat_nat] :
% 2.75/3.04 ( ( the_el2281957884133575798at_nat @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 2.75/3.04 = X ) ).
% 2.75/3.04
% 2.75/3.04 % the_elem_eq
% 2.75/3.04 thf(fact_564_the__elem__eq,axiom,
% 2.75/3.04 ! [X: $o] :
% 2.75/3.04 ( ( the_elem_o @ ( insert_o2 @ X @ bot_bot_set_o ) )
% 2.75/3.04 = X ) ).
% 2.75/3.04
% 2.75/3.04 % the_elem_eq
% 2.75/3.04 thf(fact_565_the__elem__eq,axiom,
% 2.75/3.04 ! [X: nat] :
% 2.75/3.04 ( ( the_elem_nat @ ( insert_nat2 @ X @ bot_bot_set_nat ) )
% 2.75/3.04 = X ) ).
% 2.75/3.04
% 2.75/3.04 % the_elem_eq
% 2.75/3.04 thf(fact_566_the__elem__eq,axiom,
% 2.75/3.04 ! [X: int] :
% 2.75/3.04 ( ( the_elem_int @ ( insert_int2 @ X @ bot_bot_set_int ) )
% 2.75/3.04 = X ) ).
% 2.75/3.04
% 2.75/3.04 % the_elem_eq
% 2.75/3.04 thf(fact_567_listI__assn__extract,axiom,
% 2.75/3.04 ! [I: nat,I3: set_nat,Xs: list_c,A: c > nat > assn,Xsi: list_nat] :
% 2.75/3.04 ( ( member_nat @ I @ I3 )
% 2.75/3.04 => ( ( ord_less_nat @ I @ ( size_size_list_c @ Xs ) )
% 2.75/3.04 => ( ( vEBT_L6585172037124793648_c_nat @ I3 @ A @ Xs @ Xsi )
% 2.75/3.04 = ( times_times_assn @ ( A @ ( nth_c @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L6585172037124793648_c_nat @ ( minus_minus_set_nat @ I3 @ ( insert_nat2 @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % listI_assn_extract
% 2.75/3.04 thf(fact_568_listI__assn__extract,axiom,
% 2.75/3.04 ! [I: nat,I3: set_nat,Xs: list_c,A: c > int > assn,Xsi: list_int] :
% 2.75/3.04 ( ( member_nat @ I @ I3 )
% 2.75/3.04 => ( ( ord_less_nat @ I @ ( size_size_list_c @ Xs ) )
% 2.75/3.04 => ( ( vEBT_L6582681566615743372_c_int @ I3 @ A @ Xs @ Xsi )
% 2.75/3.04 = ( times_times_assn @ ( A @ ( nth_c @ Xs @ I ) @ ( nth_int @ Xsi @ I ) ) @ ( vEBT_L6582681566615743372_c_int @ ( minus_minus_set_nat @ I3 @ ( insert_nat2 @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % listI_assn_extract
% 2.75/3.04 thf(fact_569_listI__assn__extract,axiom,
% 2.75/3.04 ! [I: nat,I3: set_nat,Xs: list_d,A: d > nat > assn,Xsi: list_nat] :
% 2.75/3.04 ( ( member_nat @ I @ I3 )
% 2.75/3.04 => ( ( ord_less_nat @ I @ ( size_size_list_d @ Xs ) )
% 2.75/3.04 => ( ( vEBT_L7820616366081188145_d_nat @ I3 @ A @ Xs @ Xsi )
% 2.75/3.04 = ( times_times_assn @ ( A @ ( nth_d @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L7820616366081188145_d_nat @ ( minus_minus_set_nat @ I3 @ ( insert_nat2 @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % listI_assn_extract
% 2.75/3.04 thf(fact_570_listI__assn__extract,axiom,
% 2.75/3.04 ! [I: nat,I3: set_nat,Xs: list_d,A: d > int > assn,Xsi: list_int] :
% 2.75/3.04 ( ( member_nat @ I @ I3 )
% 2.75/3.04 => ( ( ord_less_nat @ I @ ( size_size_list_d @ Xs ) )
% 2.75/3.04 => ( ( vEBT_L7818125895572137869_d_int @ I3 @ A @ Xs @ Xsi )
% 2.75/3.04 = ( times_times_assn @ ( A @ ( nth_d @ Xs @ I ) @ ( nth_int @ Xsi @ I ) ) @ ( vEBT_L7818125895572137869_d_int @ ( minus_minus_set_nat @ I3 @ ( insert_nat2 @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % listI_assn_extract
% 2.75/3.04 thf(fact_571_listI__assn__extract,axiom,
% 2.75/3.04 ! [I: nat,I3: set_nat,Xs: list_nat,A: nat > nat > assn,Xsi: list_nat] :
% 2.75/3.04 ( ( member_nat @ I @ I3 )
% 2.75/3.04 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 2.75/3.04 => ( ( vEBT_L7892069108621897922at_nat @ I3 @ A @ Xs @ Xsi )
% 2.75/3.04 = ( times_times_assn @ ( A @ ( nth_nat @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L7892069108621897922at_nat @ ( minus_minus_set_nat @ I3 @ ( insert_nat2 @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % listI_assn_extract
% 2.75/3.04 thf(fact_572_listI__assn__extract,axiom,
% 2.75/3.04 ! [I: nat,I3: set_nat,Xs: list_nat,A: nat > int > assn,Xsi: list_int] :
% 2.75/3.04 ( ( member_nat @ I @ I3 )
% 2.75/3.04 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 2.75/3.04 => ( ( vEBT_L7889578638112847646at_int @ I3 @ A @ Xs @ Xsi )
% 2.75/3.04 = ( times_times_assn @ ( A @ ( nth_nat @ Xs @ I ) @ ( nth_int @ Xsi @ I ) ) @ ( vEBT_L7889578638112847646at_int @ ( minus_minus_set_nat @ I3 @ ( insert_nat2 @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % listI_assn_extract
% 2.75/3.04 thf(fact_573_listI__assn__extract,axiom,
% 2.75/3.04 ! [I: nat,I3: set_nat,Xs: list_int,A: int > nat > assn,Xsi: list_nat] :
% 2.75/3.04 ( ( member_nat @ I @ I3 )
% 2.75/3.04 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 2.75/3.04 => ( ( vEBT_L8891422820522952478nt_nat @ I3 @ A @ Xs @ Xsi )
% 2.75/3.04 = ( times_times_assn @ ( A @ ( nth_int @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L8891422820522952478nt_nat @ ( minus_minus_set_nat @ I3 @ ( insert_nat2 @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % listI_assn_extract
% 2.75/3.04 thf(fact_574_listI__assn__extract,axiom,
% 2.75/3.04 ! [I: nat,I3: set_nat,Xs: list_int,A: int > int > assn,Xsi: list_int] :
% 2.75/3.04 ( ( member_nat @ I @ I3 )
% 2.75/3.04 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 2.75/3.04 => ( ( vEBT_L8888932350013902202nt_int @ I3 @ A @ Xs @ Xsi )
% 2.75/3.04 = ( times_times_assn @ ( A @ ( nth_int @ Xs @ I ) @ ( nth_int @ Xsi @ I ) ) @ ( vEBT_L8888932350013902202nt_int @ ( minus_minus_set_nat @ I3 @ ( insert_nat2 @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % listI_assn_extract
% 2.75/3.04 thf(fact_575_listI__assn__extract,axiom,
% 2.75/3.04 ! [I: nat,I3: set_nat,Xs: list_c,A: c > d > assn,Xsi: list_d] :
% 2.75/3.04 ( ( member_nat @ I @ I3 )
% 2.75/3.04 => ( ( ord_less_nat @ I @ ( size_size_list_c @ Xs ) )
% 2.75/3.04 => ( ( vEBT_L824818263033719201sn_c_d @ I3 @ A @ Xs @ Xsi )
% 2.75/3.04 = ( times_times_assn @ ( A @ ( nth_c @ Xs @ I ) @ ( nth_d @ Xsi @ I ) ) @ ( vEBT_L824818263033719201sn_c_d @ ( minus_minus_set_nat @ I3 @ ( insert_nat2 @ I @ bot_bot_set_nat ) ) @ A @ Xs @ Xsi ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % listI_assn_extract
% 2.75/3.04 thf(fact_576_is__singletonI,axiom,
% 2.75/3.04 ! [X: produc3843707927480180839at_nat] : ( is_sin2937591304547752795at_nat @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) ).
% 2.75/3.04
% 2.75/3.04 % is_singletonI
% 2.75/3.04 thf(fact_577_is__singletonI,axiom,
% 2.75/3.04 ! [X: product_prod_nat_nat] : ( is_sin2850979758926227957at_nat @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ).
% 2.75/3.04
% 2.75/3.04 % is_singletonI
% 2.75/3.04 thf(fact_578_is__singletonI,axiom,
% 2.75/3.04 ! [X: $o] : ( is_singleton_o @ ( insert_o2 @ X @ bot_bot_set_o ) ) ).
% 2.75/3.04
% 2.75/3.04 % is_singletonI
% 2.75/3.04 thf(fact_579_is__singletonI,axiom,
% 2.75/3.04 ! [X: nat] : ( is_singleton_nat @ ( insert_nat2 @ X @ bot_bot_set_nat ) ) ).
% 2.75/3.04
% 2.75/3.04 % is_singletonI
% 2.75/3.04 thf(fact_580_is__singletonI,axiom,
% 2.75/3.04 ! [X: int] : ( is_singleton_int @ ( insert_int2 @ X @ bot_bot_set_int ) ) ).
% 2.75/3.04
% 2.75/3.04 % is_singletonI
% 2.75/3.04 thf(fact_581_inf__period_I2_J,axiom,
% 2.75/3.04 ! [P: code_integer > $o,D: code_integer,Q: code_integer > $o] :
% 2.75/3.04 ( ! [X3: code_integer,K: code_integer] :
% 2.75/3.04 ( ( P @ X3 )
% 2.75/3.04 = ( P @ ( minus_8373710615458151222nteger @ X3 @ ( times_3573771949741848930nteger @ K @ D ) ) ) )
% 2.75/3.04 => ( ! [X3: code_integer,K: code_integer] :
% 2.75/3.04 ( ( Q @ X3 )
% 2.75/3.04 = ( Q @ ( minus_8373710615458151222nteger @ X3 @ ( times_3573771949741848930nteger @ K @ D ) ) ) )
% 2.75/3.04 => ! [X7: code_integer,K2: code_integer] :
% 2.75/3.04 ( ( ( P @ X7 )
% 2.75/3.04 | ( Q @ X7 ) )
% 2.75/3.04 = ( ( P @ ( minus_8373710615458151222nteger @ X7 @ ( times_3573771949741848930nteger @ K2 @ D ) ) )
% 2.75/3.04 | ( Q @ ( minus_8373710615458151222nteger @ X7 @ ( times_3573771949741848930nteger @ K2 @ D ) ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % inf_period(2)
% 2.75/3.04 thf(fact_582_inf__period_I2_J,axiom,
% 2.75/3.04 ! [P: rat > $o,D: rat,Q: rat > $o] :
% 2.75/3.04 ( ! [X3: rat,K: rat] :
% 2.75/3.04 ( ( P @ X3 )
% 2.75/3.04 = ( P @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K @ D ) ) ) )
% 2.75/3.04 => ( ! [X3: rat,K: rat] :
% 2.75/3.04 ( ( Q @ X3 )
% 2.75/3.04 = ( Q @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K @ D ) ) ) )
% 2.75/3.04 => ! [X7: rat,K2: rat] :
% 2.75/3.04 ( ( ( P @ X7 )
% 2.75/3.04 | ( Q @ X7 ) )
% 2.75/3.04 = ( ( P @ ( minus_minus_rat @ X7 @ ( times_times_rat @ K2 @ D ) ) )
% 2.75/3.04 | ( Q @ ( minus_minus_rat @ X7 @ ( times_times_rat @ K2 @ D ) ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % inf_period(2)
% 2.75/3.04 thf(fact_583_inf__period_I2_J,axiom,
% 2.75/3.04 ! [P: int > $o,D: int,Q: int > $o] :
% 2.75/3.04 ( ! [X3: int,K: int] :
% 2.75/3.04 ( ( P @ X3 )
% 2.75/3.04 = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D ) ) ) )
% 2.75/3.04 => ( ! [X3: int,K: int] :
% 2.75/3.04 ( ( Q @ X3 )
% 2.75/3.04 = ( Q @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D ) ) ) )
% 2.75/3.04 => ! [X7: int,K2: int] :
% 2.75/3.04 ( ( ( P @ X7 )
% 2.75/3.04 | ( Q @ X7 ) )
% 2.75/3.04 = ( ( P @ ( minus_minus_int @ X7 @ ( times_times_int @ K2 @ D ) ) )
% 2.75/3.04 | ( Q @ ( minus_minus_int @ X7 @ ( times_times_int @ K2 @ D ) ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % inf_period(2)
% 2.75/3.04 thf(fact_584_inf__period_I1_J,axiom,
% 2.75/3.04 ! [P: code_integer > $o,D: code_integer,Q: code_integer > $o] :
% 2.75/3.04 ( ! [X3: code_integer,K: code_integer] :
% 2.75/3.04 ( ( P @ X3 )
% 2.75/3.04 = ( P @ ( minus_8373710615458151222nteger @ X3 @ ( times_3573771949741848930nteger @ K @ D ) ) ) )
% 2.75/3.04 => ( ! [X3: code_integer,K: code_integer] :
% 2.75/3.04 ( ( Q @ X3 )
% 2.75/3.04 = ( Q @ ( minus_8373710615458151222nteger @ X3 @ ( times_3573771949741848930nteger @ K @ D ) ) ) )
% 2.75/3.04 => ! [X7: code_integer,K2: code_integer] :
% 2.75/3.04 ( ( ( P @ X7 )
% 2.75/3.04 & ( Q @ X7 ) )
% 2.75/3.04 = ( ( P @ ( minus_8373710615458151222nteger @ X7 @ ( times_3573771949741848930nteger @ K2 @ D ) ) )
% 2.75/3.04 & ( Q @ ( minus_8373710615458151222nteger @ X7 @ ( times_3573771949741848930nteger @ K2 @ D ) ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % inf_period(1)
% 2.75/3.04 thf(fact_585_inf__period_I1_J,axiom,
% 2.75/3.04 ! [P: rat > $o,D: rat,Q: rat > $o] :
% 2.75/3.04 ( ! [X3: rat,K: rat] :
% 2.75/3.04 ( ( P @ X3 )
% 2.75/3.04 = ( P @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K @ D ) ) ) )
% 2.75/3.04 => ( ! [X3: rat,K: rat] :
% 2.75/3.04 ( ( Q @ X3 )
% 2.75/3.04 = ( Q @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K @ D ) ) ) )
% 2.75/3.04 => ! [X7: rat,K2: rat] :
% 2.75/3.04 ( ( ( P @ X7 )
% 2.75/3.04 & ( Q @ X7 ) )
% 2.75/3.04 = ( ( P @ ( minus_minus_rat @ X7 @ ( times_times_rat @ K2 @ D ) ) )
% 2.75/3.04 & ( Q @ ( minus_minus_rat @ X7 @ ( times_times_rat @ K2 @ D ) ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % inf_period(1)
% 2.75/3.04 thf(fact_586_inf__period_I1_J,axiom,
% 2.75/3.04 ! [P: int > $o,D: int,Q: int > $o] :
% 2.75/3.04 ( ! [X3: int,K: int] :
% 2.75/3.04 ( ( P @ X3 )
% 2.75/3.04 = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D ) ) ) )
% 2.75/3.04 => ( ! [X3: int,K: int] :
% 2.75/3.04 ( ( Q @ X3 )
% 2.75/3.04 = ( Q @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D ) ) ) )
% 2.75/3.04 => ! [X7: int,K2: int] :
% 2.75/3.04 ( ( ( P @ X7 )
% 2.75/3.04 & ( Q @ X7 ) )
% 2.75/3.04 = ( ( P @ ( minus_minus_int @ X7 @ ( times_times_int @ K2 @ D ) ) )
% 2.75/3.04 & ( Q @ ( minus_minus_int @ X7 @ ( times_times_int @ K2 @ D ) ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % inf_period(1)
% 2.75/3.04 thf(fact_587_left__diff__distrib,axiom,
% 2.75/3.04 ! [A2: code_integer,B2: code_integer,C: code_integer] :
% 2.75/3.04 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A2 @ B2 ) @ C )
% 2.75/3.04 = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ ( times_3573771949741848930nteger @ B2 @ C ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % left_diff_distrib
% 2.75/3.04 thf(fact_588_left__diff__distrib,axiom,
% 2.75/3.04 ! [A2: rat,B2: rat,C: rat] :
% 2.75/3.04 ( ( times_times_rat @ ( minus_minus_rat @ A2 @ B2 ) @ C )
% 2.75/3.04 = ( minus_minus_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B2 @ C ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % left_diff_distrib
% 2.75/3.04 thf(fact_589_left__diff__distrib,axiom,
% 2.75/3.04 ! [A2: int,B2: int,C: int] :
% 2.75/3.04 ( ( times_times_int @ ( minus_minus_int @ A2 @ B2 ) @ C )
% 2.75/3.04 = ( minus_minus_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B2 @ C ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % left_diff_distrib
% 2.75/3.04 thf(fact_590_right__diff__distrib,axiom,
% 2.75/3.04 ! [A2: code_integer,B2: code_integer,C: code_integer] :
% 2.75/3.04 ( ( times_3573771949741848930nteger @ A2 @ ( minus_8373710615458151222nteger @ B2 @ C ) )
% 2.75/3.04 = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A2 @ B2 ) @ ( times_3573771949741848930nteger @ A2 @ C ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % right_diff_distrib
% 2.75/3.04 thf(fact_591_right__diff__distrib,axiom,
% 2.75/3.04 ! [A2: rat,B2: rat,C: rat] :
% 2.75/3.04 ( ( times_times_rat @ A2 @ ( minus_minus_rat @ B2 @ C ) )
% 2.75/3.04 = ( minus_minus_rat @ ( times_times_rat @ A2 @ B2 ) @ ( times_times_rat @ A2 @ C ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % right_diff_distrib
% 2.75/3.04 thf(fact_592_right__diff__distrib,axiom,
% 2.75/3.04 ! [A2: int,B2: int,C: int] :
% 2.75/3.04 ( ( times_times_int @ A2 @ ( minus_minus_int @ B2 @ C ) )
% 2.75/3.04 = ( minus_minus_int @ ( times_times_int @ A2 @ B2 ) @ ( times_times_int @ A2 @ C ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % right_diff_distrib
% 2.75/3.04 thf(fact_593_left__diff__distrib_H,axiom,
% 2.75/3.04 ! [B2: code_integer,C: code_integer,A2: code_integer] :
% 2.75/3.04 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ B2 @ C ) @ A2 )
% 2.75/3.04 = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ B2 @ A2 ) @ ( times_3573771949741848930nteger @ C @ A2 ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % left_diff_distrib'
% 2.75/3.04 thf(fact_594_left__diff__distrib_H,axiom,
% 2.75/3.04 ! [B2: rat,C: rat,A2: rat] :
% 2.75/3.04 ( ( times_times_rat @ ( minus_minus_rat @ B2 @ C ) @ A2 )
% 2.75/3.04 = ( minus_minus_rat @ ( times_times_rat @ B2 @ A2 ) @ ( times_times_rat @ C @ A2 ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % left_diff_distrib'
% 2.75/3.04 thf(fact_595_left__diff__distrib_H,axiom,
% 2.75/3.04 ! [B2: nat,C: nat,A2: nat] :
% 2.75/3.04 ( ( times_times_nat @ ( minus_minus_nat @ B2 @ C ) @ A2 )
% 2.75/3.04 = ( minus_minus_nat @ ( times_times_nat @ B2 @ A2 ) @ ( times_times_nat @ C @ A2 ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % left_diff_distrib'
% 2.75/3.04 thf(fact_596_left__diff__distrib_H,axiom,
% 2.75/3.04 ! [B2: int,C: int,A2: int] :
% 2.75/3.04 ( ( times_times_int @ ( minus_minus_int @ B2 @ C ) @ A2 )
% 2.75/3.04 = ( minus_minus_int @ ( times_times_int @ B2 @ A2 ) @ ( times_times_int @ C @ A2 ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % left_diff_distrib'
% 2.75/3.04 thf(fact_597_right__diff__distrib_H,axiom,
% 2.75/3.04 ! [A2: code_integer,B2: code_integer,C: code_integer] :
% 2.75/3.04 ( ( times_3573771949741848930nteger @ A2 @ ( minus_8373710615458151222nteger @ B2 @ C ) )
% 2.75/3.04 = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A2 @ B2 ) @ ( times_3573771949741848930nteger @ A2 @ C ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % right_diff_distrib'
% 2.75/3.04 thf(fact_598_right__diff__distrib_H,axiom,
% 2.75/3.04 ! [A2: rat,B2: rat,C: rat] :
% 2.75/3.04 ( ( times_times_rat @ A2 @ ( minus_minus_rat @ B2 @ C ) )
% 2.75/3.04 = ( minus_minus_rat @ ( times_times_rat @ A2 @ B2 ) @ ( times_times_rat @ A2 @ C ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % right_diff_distrib'
% 2.75/3.04 thf(fact_599_right__diff__distrib_H,axiom,
% 2.75/3.04 ! [A2: nat,B2: nat,C: nat] :
% 2.75/3.04 ( ( times_times_nat @ A2 @ ( minus_minus_nat @ B2 @ C ) )
% 2.75/3.04 = ( minus_minus_nat @ ( times_times_nat @ A2 @ B2 ) @ ( times_times_nat @ A2 @ C ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % right_diff_distrib'
% 2.75/3.04 thf(fact_600_right__diff__distrib_H,axiom,
% 2.75/3.04 ! [A2: int,B2: int,C: int] :
% 2.75/3.04 ( ( times_times_int @ A2 @ ( minus_minus_int @ B2 @ C ) )
% 2.75/3.04 = ( minus_minus_int @ ( times_times_int @ A2 @ B2 ) @ ( times_times_int @ A2 @ C ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % right_diff_distrib'
% 2.75/3.04 thf(fact_601_diff__strict__mono,axiom,
% 2.75/3.04 ! [A2: rat,B2: rat,D2: rat,C: rat] :
% 2.75/3.04 ( ( ord_less_rat @ A2 @ B2 )
% 2.75/3.04 => ( ( ord_less_rat @ D2 @ C )
% 2.75/3.04 => ( ord_less_rat @ ( minus_minus_rat @ A2 @ C ) @ ( minus_minus_rat @ B2 @ D2 ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % diff_strict_mono
% 2.75/3.04 thf(fact_602_diff__strict__mono,axiom,
% 2.75/3.04 ! [A2: code_integer,B2: code_integer,D2: code_integer,C: code_integer] :
% 2.75/3.04 ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 2.75/3.04 => ( ( ord_le6747313008572928689nteger @ D2 @ C )
% 2.75/3.04 => ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A2 @ C ) @ ( minus_8373710615458151222nteger @ B2 @ D2 ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % diff_strict_mono
% 2.75/3.04 thf(fact_603_diff__strict__mono,axiom,
% 2.75/3.04 ! [A2: int,B2: int,D2: int,C: int] :
% 2.75/3.04 ( ( ord_less_int @ A2 @ B2 )
% 2.75/3.04 => ( ( ord_less_int @ D2 @ C )
% 2.75/3.04 => ( ord_less_int @ ( minus_minus_int @ A2 @ C ) @ ( minus_minus_int @ B2 @ D2 ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % diff_strict_mono
% 2.75/3.04 thf(fact_604_nth__list__update__neq,axiom,
% 2.75/3.04 ! [I: nat,J: nat,Xs: list_nat,X: nat] :
% 2.75/3.04 ( ( I != J )
% 2.75/3.04 => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X ) @ J )
% 2.75/3.04 = ( nth_nat @ Xs @ J ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % nth_list_update_neq
% 2.75/3.04 thf(fact_605_nth__list__update__neq,axiom,
% 2.75/3.04 ! [I: nat,J: nat,Xs: list_int,X: int] :
% 2.75/3.04 ( ( I != J )
% 2.75/3.04 => ( ( nth_int @ ( list_update_int @ Xs @ I @ X ) @ J )
% 2.75/3.04 = ( nth_int @ Xs @ J ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % nth_list_update_neq
% 2.75/3.04 thf(fact_606_nth__list__update__neq,axiom,
% 2.75/3.04 ! [I: nat,J: nat,Xs: list_c,X: c] :
% 2.75/3.04 ( ( I != J )
% 2.75/3.04 => ( ( nth_c @ ( list_update_c @ Xs @ I @ X ) @ J )
% 2.75/3.04 = ( nth_c @ Xs @ J ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % nth_list_update_neq
% 2.75/3.04 thf(fact_607_nth__list__update__neq,axiom,
% 2.75/3.04 ! [I: nat,J: nat,Xs: list_d,X: d] :
% 2.75/3.04 ( ( I != J )
% 2.75/3.04 => ( ( nth_d @ ( list_update_d @ Xs @ I @ X ) @ J )
% 2.75/3.04 = ( nth_d @ Xs @ J ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % nth_list_update_neq
% 2.75/3.04 thf(fact_608_list__update__id,axiom,
% 2.75/3.04 ! [Xs: list_nat,I: nat] :
% 2.75/3.04 ( ( list_update_nat @ Xs @ I @ ( nth_nat @ Xs @ I ) )
% 2.75/3.04 = Xs ) ).
% 2.75/3.04
% 2.75/3.04 % list_update_id
% 2.75/3.04 thf(fact_609_list__update__id,axiom,
% 2.75/3.04 ! [Xs: list_int,I: nat] :
% 2.75/3.04 ( ( list_update_int @ Xs @ I @ ( nth_int @ Xs @ I ) )
% 2.75/3.04 = Xs ) ).
% 2.75/3.04
% 2.75/3.04 % list_update_id
% 2.75/3.04 thf(fact_610_list__update__id,axiom,
% 2.75/3.04 ! [Xs: list_c,I: nat] :
% 2.75/3.04 ( ( list_update_c @ Xs @ I @ ( nth_c @ Xs @ I ) )
% 2.75/3.04 = Xs ) ).
% 2.75/3.04
% 2.75/3.04 % list_update_id
% 2.75/3.04 thf(fact_611_list__update__id,axiom,
% 2.75/3.04 ! [Xs: list_d,I: nat] :
% 2.75/3.04 ( ( list_update_d @ Xs @ I @ ( nth_d @ Xs @ I ) )
% 2.75/3.04 = Xs ) ).
% 2.75/3.04
% 2.75/3.04 % list_update_id
% 2.75/3.04 thf(fact_612_nth__list__update__eq,axiom,
% 2.75/3.04 ! [I: nat,Xs: list_c,X: c] :
% 2.75/3.04 ( ( ord_less_nat @ I @ ( size_size_list_c @ Xs ) )
% 2.75/3.04 => ( ( nth_c @ ( list_update_c @ Xs @ I @ X ) @ I )
% 2.75/3.04 = X ) ) ).
% 2.75/3.04
% 2.75/3.04 % nth_list_update_eq
% 2.75/3.04 thf(fact_613_nth__list__update__eq,axiom,
% 2.75/3.04 ! [I: nat,Xs: list_d,X: d] :
% 2.75/3.04 ( ( ord_less_nat @ I @ ( size_size_list_d @ Xs ) )
% 2.75/3.04 => ( ( nth_d @ ( list_update_d @ Xs @ I @ X ) @ I )
% 2.75/3.04 = X ) ) ).
% 2.75/3.04
% 2.75/3.04 % nth_list_update_eq
% 2.75/3.04 thf(fact_614_nth__list__update__eq,axiom,
% 2.75/3.04 ! [I: nat,Xs: list_nat,X: nat] :
% 2.75/3.04 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 2.75/3.04 => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X ) @ I )
% 2.75/3.04 = X ) ) ).
% 2.75/3.04
% 2.75/3.04 % nth_list_update_eq
% 2.75/3.04 thf(fact_615_nth__list__update__eq,axiom,
% 2.75/3.04 ! [I: nat,Xs: list_int,X: int] :
% 2.75/3.04 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 2.75/3.04 => ( ( nth_int @ ( list_update_int @ Xs @ I @ X ) @ I )
% 2.75/3.04 = X ) ) ).
% 2.75/3.04
% 2.75/3.04 % nth_list_update_eq
% 2.75/3.04 thf(fact_616_nth__update__invalid,axiom,
% 2.75/3.04 ! [I: nat,L: list_c,J: nat,X: c] :
% 2.75/3.04 ( ~ ( ord_less_nat @ I @ ( size_size_list_c @ L ) )
% 2.75/3.04 => ( ( nth_c @ ( list_update_c @ L @ J @ X ) @ I )
% 2.75/3.04 = ( nth_c @ L @ I ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % nth_update_invalid
% 2.75/3.04 thf(fact_617_nth__update__invalid,axiom,
% 2.75/3.04 ! [I: nat,L: list_d,J: nat,X: d] :
% 2.75/3.04 ( ~ ( ord_less_nat @ I @ ( size_size_list_d @ L ) )
% 2.75/3.04 => ( ( nth_d @ ( list_update_d @ L @ J @ X ) @ I )
% 2.75/3.04 = ( nth_d @ L @ I ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % nth_update_invalid
% 2.75/3.04 thf(fact_618_nth__update__invalid,axiom,
% 2.75/3.04 ! [I: nat,L: list_nat,J: nat,X: nat] :
% 2.75/3.04 ( ~ ( ord_less_nat @ I @ ( size_size_list_nat @ L ) )
% 2.75/3.04 => ( ( nth_nat @ ( list_update_nat @ L @ J @ X ) @ I )
% 2.75/3.04 = ( nth_nat @ L @ I ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % nth_update_invalid
% 2.75/3.04 thf(fact_619_nth__update__invalid,axiom,
% 2.75/3.04 ! [I: nat,L: list_int,J: nat,X: int] :
% 2.75/3.04 ( ~ ( ord_less_nat @ I @ ( size_size_list_int @ L ) )
% 2.75/3.04 => ( ( nth_int @ ( list_update_int @ L @ J @ X ) @ I )
% 2.75/3.04 = ( nth_int @ L @ I ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % nth_update_invalid
% 2.75/3.04 thf(fact_620_psubsetD,axiom,
% 2.75/3.04 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,C: produc3843707927480180839at_nat] :
% 2.75/3.04 ( ( ord_le2604355607129572851at_nat @ A @ B )
% 2.75/3.04 => ( ( member8757157785044589968at_nat @ C @ A )
% 2.75/3.04 => ( member8757157785044589968at_nat @ C @ B ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % psubsetD
% 2.75/3.04 thf(fact_621_psubsetD,axiom,
% 2.75/3.04 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C: product_prod_nat_nat] :
% 2.75/3.04 ( ( ord_le7866589430770878221at_nat @ A @ B )
% 2.75/3.04 => ( ( member8440522571783428010at_nat @ C @ A )
% 2.75/3.04 => ( member8440522571783428010at_nat @ C @ B ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % psubsetD
% 2.75/3.04 thf(fact_622_psubsetD,axiom,
% 2.75/3.04 ! [A: set_nat,B: set_nat,C: nat] :
% 2.75/3.04 ( ( ord_less_set_nat @ A @ B )
% 2.75/3.04 => ( ( member_nat @ C @ A )
% 2.75/3.04 => ( member_nat @ C @ B ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % psubsetD
% 2.75/3.04 thf(fact_623_psubsetD,axiom,
% 2.75/3.04 ! [A: set_int,B: set_int,C: int] :
% 2.75/3.04 ( ( ord_less_set_int @ A @ B )
% 2.75/3.04 => ( ( member_int @ C @ A )
% 2.75/3.04 => ( member_int @ C @ B ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % psubsetD
% 2.75/3.04 thf(fact_624_psubsetD,axiom,
% 2.75/3.04 ! [A: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o,C: produc3658429121746597890et_nat > $o] :
% 2.75/3.04 ( ( ord_le2453136405763929_nat_o @ A @ B )
% 2.75/3.04 => ( ( member6576561426505652726_nat_o @ C @ A )
% 2.75/3.04 => ( member6576561426505652726_nat_o @ C @ B ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % psubsetD
% 2.75/3.04 thf(fact_625_list__eq__iff__nth__eq,axiom,
% 2.75/3.04 ( ( ^ [Y4: list_c,Z2: list_c] : ( Y4 = Z2 ) )
% 2.75/3.04 = ( ^ [Xs3: list_c,Ys3: list_c] :
% 2.75/3.04 ( ( ( size_size_list_c @ Xs3 )
% 2.75/3.04 = ( size_size_list_c @ Ys3 ) )
% 2.75/3.04 & ! [I4: nat] :
% 2.75/3.04 ( ( ord_less_nat @ I4 @ ( size_size_list_c @ Xs3 ) )
% 2.75/3.04 => ( ( nth_c @ Xs3 @ I4 )
% 2.75/3.04 = ( nth_c @ Ys3 @ I4 ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % list_eq_iff_nth_eq
% 2.75/3.04 thf(fact_626_list__eq__iff__nth__eq,axiom,
% 2.75/3.04 ( ( ^ [Y4: list_d,Z2: list_d] : ( Y4 = Z2 ) )
% 2.75/3.04 = ( ^ [Xs3: list_d,Ys3: list_d] :
% 2.75/3.04 ( ( ( size_size_list_d @ Xs3 )
% 2.75/3.04 = ( size_size_list_d @ Ys3 ) )
% 2.75/3.04 & ! [I4: nat] :
% 2.75/3.04 ( ( ord_less_nat @ I4 @ ( size_size_list_d @ Xs3 ) )
% 2.75/3.04 => ( ( nth_d @ Xs3 @ I4 )
% 2.75/3.04 = ( nth_d @ Ys3 @ I4 ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % list_eq_iff_nth_eq
% 2.75/3.04 thf(fact_627_list__eq__iff__nth__eq,axiom,
% 2.75/3.04 ( ( ^ [Y4: list_nat,Z2: list_nat] : ( Y4 = Z2 ) )
% 2.75/3.04 = ( ^ [Xs3: list_nat,Ys3: list_nat] :
% 2.75/3.04 ( ( ( size_size_list_nat @ Xs3 )
% 2.75/3.04 = ( size_size_list_nat @ Ys3 ) )
% 2.75/3.04 & ! [I4: nat] :
% 2.75/3.04 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs3 ) )
% 2.75/3.04 => ( ( nth_nat @ Xs3 @ I4 )
% 2.75/3.04 = ( nth_nat @ Ys3 @ I4 ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % list_eq_iff_nth_eq
% 2.75/3.04 thf(fact_628_list__eq__iff__nth__eq,axiom,
% 2.75/3.04 ( ( ^ [Y4: list_int,Z2: list_int] : ( Y4 = Z2 ) )
% 2.75/3.04 = ( ^ [Xs3: list_int,Ys3: list_int] :
% 2.75/3.04 ( ( ( size_size_list_int @ Xs3 )
% 2.75/3.04 = ( size_size_list_int @ Ys3 ) )
% 2.75/3.04 & ! [I4: nat] :
% 2.75/3.04 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs3 ) )
% 2.75/3.04 => ( ( nth_int @ Xs3 @ I4 )
% 2.75/3.04 = ( nth_int @ Ys3 @ I4 ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % list_eq_iff_nth_eq
% 2.75/3.04 thf(fact_629_Skolem__list__nth,axiom,
% 2.75/3.04 ! [K3: nat,P: nat > c > $o] :
% 2.75/3.04 ( ( ! [I4: nat] :
% 2.75/3.04 ( ( ord_less_nat @ I4 @ K3 )
% 2.75/3.04 => ? [X8: c] : ( P @ I4 @ X8 ) ) )
% 2.75/3.04 = ( ? [Xs3: list_c] :
% 2.75/3.04 ( ( ( size_size_list_c @ Xs3 )
% 2.75/3.04 = K3 )
% 2.75/3.04 & ! [I4: nat] :
% 2.75/3.04 ( ( ord_less_nat @ I4 @ K3 )
% 2.75/3.04 => ( P @ I4 @ ( nth_c @ Xs3 @ I4 ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % Skolem_list_nth
% 2.75/3.04 thf(fact_630_Skolem__list__nth,axiom,
% 2.75/3.04 ! [K3: nat,P: nat > d > $o] :
% 2.75/3.04 ( ( ! [I4: nat] :
% 2.75/3.04 ( ( ord_less_nat @ I4 @ K3 )
% 2.75/3.04 => ? [X8: d] : ( P @ I4 @ X8 ) ) )
% 2.75/3.04 = ( ? [Xs3: list_d] :
% 2.75/3.04 ( ( ( size_size_list_d @ Xs3 )
% 2.75/3.04 = K3 )
% 2.75/3.04 & ! [I4: nat] :
% 2.75/3.04 ( ( ord_less_nat @ I4 @ K3 )
% 2.75/3.04 => ( P @ I4 @ ( nth_d @ Xs3 @ I4 ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % Skolem_list_nth
% 2.75/3.04 thf(fact_631_Skolem__list__nth,axiom,
% 2.75/3.04 ! [K3: nat,P: nat > nat > $o] :
% 2.75/3.04 ( ( ! [I4: nat] :
% 2.75/3.04 ( ( ord_less_nat @ I4 @ K3 )
% 2.75/3.04 => ? [X8: nat] : ( P @ I4 @ X8 ) ) )
% 2.75/3.04 = ( ? [Xs3: list_nat] :
% 2.75/3.04 ( ( ( size_size_list_nat @ Xs3 )
% 2.75/3.04 = K3 )
% 2.75/3.04 & ! [I4: nat] :
% 2.75/3.04 ( ( ord_less_nat @ I4 @ K3 )
% 2.75/3.04 => ( P @ I4 @ ( nth_nat @ Xs3 @ I4 ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % Skolem_list_nth
% 2.75/3.04 thf(fact_632_Skolem__list__nth,axiom,
% 2.75/3.04 ! [K3: nat,P: nat > int > $o] :
% 2.75/3.04 ( ( ! [I4: nat] :
% 2.75/3.04 ( ( ord_less_nat @ I4 @ K3 )
% 2.75/3.04 => ? [X8: int] : ( P @ I4 @ X8 ) ) )
% 2.75/3.04 = ( ? [Xs3: list_int] :
% 2.75/3.04 ( ( ( size_size_list_int @ Xs3 )
% 2.75/3.04 = K3 )
% 2.75/3.04 & ! [I4: nat] :
% 2.75/3.04 ( ( ord_less_nat @ I4 @ K3 )
% 2.75/3.04 => ( P @ I4 @ ( nth_int @ Xs3 @ I4 ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % Skolem_list_nth
% 2.75/3.04 thf(fact_633_nth__equalityI,axiom,
% 2.75/3.04 ! [Xs: list_c,Ys: list_c] :
% 2.75/3.04 ( ( ( size_size_list_c @ Xs )
% 2.75/3.04 = ( size_size_list_c @ Ys ) )
% 2.75/3.04 => ( ! [I5: nat] :
% 2.75/3.04 ( ( ord_less_nat @ I5 @ ( size_size_list_c @ Xs ) )
% 2.75/3.04 => ( ( nth_c @ Xs @ I5 )
% 2.75/3.04 = ( nth_c @ Ys @ I5 ) ) )
% 2.75/3.04 => ( Xs = Ys ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % nth_equalityI
% 2.75/3.04 thf(fact_634_nth__equalityI,axiom,
% 2.75/3.04 ! [Xs: list_d,Ys: list_d] :
% 2.75/3.04 ( ( ( size_size_list_d @ Xs )
% 2.75/3.04 = ( size_size_list_d @ Ys ) )
% 2.75/3.04 => ( ! [I5: nat] :
% 2.75/3.04 ( ( ord_less_nat @ I5 @ ( size_size_list_d @ Xs ) )
% 2.75/3.04 => ( ( nth_d @ Xs @ I5 )
% 2.75/3.04 = ( nth_d @ Ys @ I5 ) ) )
% 2.75/3.04 => ( Xs = Ys ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % nth_equalityI
% 2.75/3.04 thf(fact_635_nth__equalityI,axiom,
% 2.75/3.04 ! [Xs: list_nat,Ys: list_nat] :
% 2.75/3.04 ( ( ( size_size_list_nat @ Xs )
% 2.75/3.04 = ( size_size_list_nat @ Ys ) )
% 2.75/3.04 => ( ! [I5: nat] :
% 2.75/3.04 ( ( ord_less_nat @ I5 @ ( size_size_list_nat @ Xs ) )
% 2.75/3.04 => ( ( nth_nat @ Xs @ I5 )
% 2.75/3.04 = ( nth_nat @ Ys @ I5 ) ) )
% 2.75/3.04 => ( Xs = Ys ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % nth_equalityI
% 2.75/3.04 thf(fact_636_nth__equalityI,axiom,
% 2.75/3.04 ! [Xs: list_int,Ys: list_int] :
% 2.75/3.04 ( ( ( size_size_list_int @ Xs )
% 2.75/3.04 = ( size_size_list_int @ Ys ) )
% 2.75/3.04 => ( ! [I5: nat] :
% 2.75/3.04 ( ( ord_less_nat @ I5 @ ( size_size_list_int @ Xs ) )
% 2.75/3.04 => ( ( nth_int @ Xs @ I5 )
% 2.75/3.04 = ( nth_int @ Ys @ I5 ) ) )
% 2.75/3.04 => ( Xs = Ys ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % nth_equalityI
% 2.75/3.04 thf(fact_637_obtain__list__from__elements,axiom,
% 2.75/3.04 ! [N: nat,P: c > nat > $o] :
% 2.75/3.04 ( ! [I5: nat] :
% 2.75/3.04 ( ( ord_less_nat @ I5 @ N )
% 2.75/3.04 => ? [Li2: c] : ( P @ Li2 @ I5 ) )
% 2.75/3.04 => ~ ! [L2: list_c] :
% 2.75/3.04 ( ( ( size_size_list_c @ L2 )
% 2.75/3.04 = N )
% 2.75/3.04 => ~ ! [I6: nat] :
% 2.75/3.04 ( ( ord_less_nat @ I6 @ N )
% 2.75/3.04 => ( P @ ( nth_c @ L2 @ I6 ) @ I6 ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % obtain_list_from_elements
% 2.75/3.04 thf(fact_638_obtain__list__from__elements,axiom,
% 2.75/3.04 ! [N: nat,P: d > nat > $o] :
% 2.75/3.04 ( ! [I5: nat] :
% 2.75/3.04 ( ( ord_less_nat @ I5 @ N )
% 2.75/3.04 => ? [Li2: d] : ( P @ Li2 @ I5 ) )
% 2.75/3.04 => ~ ! [L2: list_d] :
% 2.75/3.04 ( ( ( size_size_list_d @ L2 )
% 2.75/3.04 = N )
% 2.75/3.04 => ~ ! [I6: nat] :
% 2.75/3.04 ( ( ord_less_nat @ I6 @ N )
% 2.75/3.04 => ( P @ ( nth_d @ L2 @ I6 ) @ I6 ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % obtain_list_from_elements
% 2.75/3.04 thf(fact_639_obtain__list__from__elements,axiom,
% 2.75/3.04 ! [N: nat,P: nat > nat > $o] :
% 2.75/3.04 ( ! [I5: nat] :
% 2.75/3.04 ( ( ord_less_nat @ I5 @ N )
% 2.75/3.04 => ? [Li2: nat] : ( P @ Li2 @ I5 ) )
% 2.75/3.04 => ~ ! [L2: list_nat] :
% 2.75/3.04 ( ( ( size_size_list_nat @ L2 )
% 2.75/3.04 = N )
% 2.75/3.04 => ~ ! [I6: nat] :
% 2.75/3.04 ( ( ord_less_nat @ I6 @ N )
% 2.75/3.04 => ( P @ ( nth_nat @ L2 @ I6 ) @ I6 ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % obtain_list_from_elements
% 2.75/3.04 thf(fact_640_obtain__list__from__elements,axiom,
% 2.75/3.04 ! [N: nat,P: int > nat > $o] :
% 2.75/3.04 ( ! [I5: nat] :
% 2.75/3.04 ( ( ord_less_nat @ I5 @ N )
% 2.75/3.04 => ? [Li2: int] : ( P @ Li2 @ I5 ) )
% 2.75/3.04 => ~ ! [L2: list_int] :
% 2.75/3.04 ( ( ( size_size_list_int @ L2 )
% 2.75/3.04 = N )
% 2.75/3.04 => ~ ! [I6: nat] :
% 2.75/3.04 ( ( ord_less_nat @ I6 @ N )
% 2.75/3.04 => ( P @ ( nth_int @ L2 @ I6 ) @ I6 ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % obtain_list_from_elements
% 2.75/3.04 thf(fact_641_is__singleton__the__elem,axiom,
% 2.75/3.04 ( is_sin2937591304547752795at_nat
% 2.75/3.04 = ( ^ [A5: set_Pr4329608150637261639at_nat] :
% 2.75/3.04 ( A5
% 2.75/3.04 = ( insert9069300056098147895at_nat @ ( the_el221668144340439132at_nat @ A5 ) @ bot_bo228742789529271731at_nat ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % is_singleton_the_elem
% 2.75/3.04 thf(fact_642_is__singleton__the__elem,axiom,
% 2.75/3.04 ( is_sin2850979758926227957at_nat
% 2.75/3.04 = ( ^ [A5: set_Pr1261947904930325089at_nat] :
% 2.75/3.04 ( A5
% 2.75/3.04 = ( insert8211810215607154385at_nat @ ( the_el2281957884133575798at_nat @ A5 ) @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % is_singleton_the_elem
% 2.75/3.04 thf(fact_643_is__singleton__the__elem,axiom,
% 2.75/3.04 ( is_singleton_o
% 2.75/3.04 = ( ^ [A5: set_o] :
% 2.75/3.04 ( A5
% 2.75/3.04 = ( insert_o2 @ ( the_elem_o @ A5 ) @ bot_bot_set_o ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % is_singleton_the_elem
% 2.75/3.04 thf(fact_644_is__singleton__the__elem,axiom,
% 2.75/3.04 ( is_singleton_nat
% 2.75/3.04 = ( ^ [A5: set_nat] :
% 2.75/3.04 ( A5
% 2.75/3.04 = ( insert_nat2 @ ( the_elem_nat @ A5 ) @ bot_bot_set_nat ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % is_singleton_the_elem
% 2.75/3.04 thf(fact_645_is__singleton__the__elem,axiom,
% 2.75/3.04 ( is_singleton_int
% 2.75/3.04 = ( ^ [A5: set_int] :
% 2.75/3.04 ( A5
% 2.75/3.04 = ( insert_int2 @ ( the_elem_int @ A5 ) @ bot_bot_set_int ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % is_singleton_the_elem
% 2.75/3.04 thf(fact_646_is__singletonI_H,axiom,
% 2.75/3.04 ! [A: set_Pr4532377907799695533_nat_o] :
% 2.75/3.04 ( ( A != bot_bo7824918357723582233_nat_o )
% 2.75/3.04 => ( ! [X3: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat > $o] :
% 2.75/3.04 ( ( member6576561426505652726_nat_o @ X3 @ A )
% 2.75/3.04 => ( ( member6576561426505652726_nat_o @ Y2 @ A )
% 2.75/3.04 => ( X3 = Y2 ) ) )
% 2.75/3.04 => ( is_sin5180296473474724033_nat_o @ A ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % is_singletonI'
% 2.75/3.04 thf(fact_647_is__singletonI_H,axiom,
% 2.75/3.04 ! [A: set_Pr4329608150637261639at_nat] :
% 2.75/3.04 ( ( A != bot_bo228742789529271731at_nat )
% 2.75/3.04 => ( ! [X3: produc3843707927480180839at_nat,Y2: produc3843707927480180839at_nat] :
% 2.75/3.04 ( ( member8757157785044589968at_nat @ X3 @ A )
% 2.75/3.04 => ( ( member8757157785044589968at_nat @ Y2 @ A )
% 2.75/3.04 => ( X3 = Y2 ) ) )
% 2.75/3.04 => ( is_sin2937591304547752795at_nat @ A ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % is_singletonI'
% 2.75/3.04 thf(fact_648_is__singletonI_H,axiom,
% 2.75/3.04 ! [A: set_Pr1261947904930325089at_nat] :
% 2.75/3.04 ( ( A != bot_bo2099793752762293965at_nat )
% 2.75/3.04 => ( ! [X3: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 2.75/3.04 ( ( member8440522571783428010at_nat @ X3 @ A )
% 2.75/3.04 => ( ( member8440522571783428010at_nat @ Y2 @ A )
% 2.75/3.04 => ( X3 = Y2 ) ) )
% 2.75/3.04 => ( is_sin2850979758926227957at_nat @ A ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % is_singletonI'
% 2.75/3.04 thf(fact_649_is__singletonI_H,axiom,
% 2.75/3.04 ! [A: set_o] :
% 2.75/3.04 ( ( A != bot_bot_set_o )
% 2.75/3.04 => ( ! [X3: $o,Y2: $o] :
% 2.75/3.04 ( ( member_o @ X3 @ A )
% 2.75/3.04 => ( ( member_o @ Y2 @ A )
% 2.75/3.04 => ( X3 = Y2 ) ) )
% 2.75/3.04 => ( is_singleton_o @ A ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % is_singletonI'
% 2.75/3.04 thf(fact_650_is__singletonI_H,axiom,
% 2.75/3.04 ! [A: set_nat] :
% 2.75/3.04 ( ( A != bot_bot_set_nat )
% 2.75/3.04 => ( ! [X3: nat,Y2: nat] :
% 2.75/3.04 ( ( member_nat @ X3 @ A )
% 2.75/3.04 => ( ( member_nat @ Y2 @ A )
% 2.75/3.04 => ( X3 = Y2 ) ) )
% 2.75/3.04 => ( is_singleton_nat @ A ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % is_singletonI'
% 2.75/3.04 thf(fact_651_is__singletonI_H,axiom,
% 2.75/3.04 ! [A: set_int] :
% 2.75/3.04 ( ( A != bot_bot_set_int )
% 2.75/3.04 => ( ! [X3: int,Y2: int] :
% 2.75/3.04 ( ( member_int @ X3 @ A )
% 2.75/3.04 => ( ( member_int @ Y2 @ A )
% 2.75/3.04 => ( X3 = Y2 ) ) )
% 2.75/3.04 => ( is_singleton_int @ A ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % is_singletonI'
% 2.75/3.04 thf(fact_652_nth__list__update,axiom,
% 2.75/3.04 ! [I: nat,Xs: list_c,J: nat,X: c] :
% 2.75/3.04 ( ( ord_less_nat @ I @ ( size_size_list_c @ Xs ) )
% 2.75/3.04 => ( ( ( I = J )
% 2.75/3.04 => ( ( nth_c @ ( list_update_c @ Xs @ I @ X ) @ J )
% 2.75/3.04 = X ) )
% 2.75/3.04 & ( ( I != J )
% 2.75/3.04 => ( ( nth_c @ ( list_update_c @ Xs @ I @ X ) @ J )
% 2.75/3.04 = ( nth_c @ Xs @ J ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % nth_list_update
% 2.75/3.04 thf(fact_653_nth__list__update,axiom,
% 2.75/3.04 ! [I: nat,Xs: list_d,J: nat,X: d] :
% 2.75/3.04 ( ( ord_less_nat @ I @ ( size_size_list_d @ Xs ) )
% 2.75/3.04 => ( ( ( I = J )
% 2.75/3.04 => ( ( nth_d @ ( list_update_d @ Xs @ I @ X ) @ J )
% 2.75/3.04 = X ) )
% 2.75/3.04 & ( ( I != J )
% 2.75/3.04 => ( ( nth_d @ ( list_update_d @ Xs @ I @ X ) @ J )
% 2.75/3.04 = ( nth_d @ Xs @ J ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % nth_list_update
% 2.75/3.04 thf(fact_654_nth__list__update,axiom,
% 2.75/3.04 ! [I: nat,Xs: list_nat,J: nat,X: nat] :
% 2.75/3.04 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 2.75/3.04 => ( ( ( I = J )
% 2.75/3.04 => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X ) @ J )
% 2.75/3.04 = X ) )
% 2.75/3.04 & ( ( I != J )
% 2.75/3.04 => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X ) @ J )
% 2.75/3.04 = ( nth_nat @ Xs @ J ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % nth_list_update
% 2.75/3.04 thf(fact_655_nth__list__update,axiom,
% 2.75/3.04 ! [I: nat,Xs: list_int,J: nat,X: int] :
% 2.75/3.04 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 2.75/3.04 => ( ( ( I = J )
% 2.75/3.04 => ( ( nth_int @ ( list_update_int @ Xs @ I @ X ) @ J )
% 2.75/3.04 = X ) )
% 2.75/3.04 & ( ( I != J )
% 2.75/3.04 => ( ( nth_int @ ( list_update_int @ Xs @ I @ X ) @ J )
% 2.75/3.04 = ( nth_int @ Xs @ J ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % nth_list_update
% 2.75/3.04 thf(fact_656_list__update__same__conv,axiom,
% 2.75/3.04 ! [I: nat,Xs: list_c,X: c] :
% 2.75/3.04 ( ( ord_less_nat @ I @ ( size_size_list_c @ Xs ) )
% 2.75/3.04 => ( ( ( list_update_c @ Xs @ I @ X )
% 2.75/3.04 = Xs )
% 2.75/3.04 = ( ( nth_c @ Xs @ I )
% 2.75/3.04 = X ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % list_update_same_conv
% 2.75/3.04 thf(fact_657_list__update__same__conv,axiom,
% 2.75/3.04 ! [I: nat,Xs: list_d,X: d] :
% 2.75/3.04 ( ( ord_less_nat @ I @ ( size_size_list_d @ Xs ) )
% 2.75/3.04 => ( ( ( list_update_d @ Xs @ I @ X )
% 2.75/3.04 = Xs )
% 2.75/3.04 = ( ( nth_d @ Xs @ I )
% 2.75/3.04 = X ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % list_update_same_conv
% 2.75/3.04 thf(fact_658_list__update__same__conv,axiom,
% 2.75/3.04 ! [I: nat,Xs: list_nat,X: nat] :
% 2.75/3.04 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 2.75/3.04 => ( ( ( list_update_nat @ Xs @ I @ X )
% 2.75/3.04 = Xs )
% 2.75/3.04 = ( ( nth_nat @ Xs @ I )
% 2.75/3.04 = X ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % list_update_same_conv
% 2.75/3.04 thf(fact_659_list__update__same__conv,axiom,
% 2.75/3.04 ! [I: nat,Xs: list_int,X: int] :
% 2.75/3.04 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 2.75/3.04 => ( ( ( list_update_int @ Xs @ I @ X )
% 2.75/3.04 = Xs )
% 2.75/3.04 = ( ( nth_int @ Xs @ I )
% 2.75/3.04 = X ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % list_update_same_conv
% 2.75/3.04 thf(fact_660_nth__list__update_H,axiom,
% 2.75/3.04 ! [I: nat,J: nat,L: list_c,X: c] :
% 2.75/3.04 ( ( ( ( I = J )
% 2.75/3.04 & ( ord_less_nat @ I @ ( size_size_list_c @ L ) ) )
% 2.75/3.04 => ( ( nth_c @ ( list_update_c @ L @ I @ X ) @ J )
% 2.75/3.04 = X ) )
% 2.75/3.04 & ( ~ ( ( I = J )
% 2.75/3.04 & ( ord_less_nat @ I @ ( size_size_list_c @ L ) ) )
% 2.75/3.04 => ( ( nth_c @ ( list_update_c @ L @ I @ X ) @ J )
% 2.75/3.04 = ( nth_c @ L @ J ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % nth_list_update'
% 2.75/3.04 thf(fact_661_nth__list__update_H,axiom,
% 2.75/3.04 ! [I: nat,J: nat,L: list_d,X: d] :
% 2.75/3.04 ( ( ( ( I = J )
% 2.75/3.04 & ( ord_less_nat @ I @ ( size_size_list_d @ L ) ) )
% 2.75/3.04 => ( ( nth_d @ ( list_update_d @ L @ I @ X ) @ J )
% 2.75/3.04 = X ) )
% 2.75/3.04 & ( ~ ( ( I = J )
% 2.75/3.04 & ( ord_less_nat @ I @ ( size_size_list_d @ L ) ) )
% 2.75/3.04 => ( ( nth_d @ ( list_update_d @ L @ I @ X ) @ J )
% 2.75/3.04 = ( nth_d @ L @ J ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % nth_list_update'
% 2.75/3.04 thf(fact_662_nth__list__update_H,axiom,
% 2.75/3.04 ! [I: nat,J: nat,L: list_nat,X: nat] :
% 2.75/3.04 ( ( ( ( I = J )
% 2.75/3.04 & ( ord_less_nat @ I @ ( size_size_list_nat @ L ) ) )
% 2.75/3.04 => ( ( nth_nat @ ( list_update_nat @ L @ I @ X ) @ J )
% 2.75/3.04 = X ) )
% 2.75/3.04 & ( ~ ( ( I = J )
% 2.75/3.04 & ( ord_less_nat @ I @ ( size_size_list_nat @ L ) ) )
% 2.75/3.04 => ( ( nth_nat @ ( list_update_nat @ L @ I @ X ) @ J )
% 2.75/3.04 = ( nth_nat @ L @ J ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % nth_list_update'
% 2.75/3.04 thf(fact_663_nth__list__update_H,axiom,
% 2.75/3.04 ! [I: nat,J: nat,L: list_int,X: int] :
% 2.75/3.04 ( ( ( ( I = J )
% 2.75/3.04 & ( ord_less_nat @ I @ ( size_size_list_int @ L ) ) )
% 2.75/3.04 => ( ( nth_int @ ( list_update_int @ L @ I @ X ) @ J )
% 2.75/3.04 = X ) )
% 2.75/3.04 & ( ~ ( ( I = J )
% 2.75/3.04 & ( ord_less_nat @ I @ ( size_size_list_int @ L ) ) )
% 2.75/3.04 => ( ( nth_int @ ( list_update_int @ L @ I @ X ) @ J )
% 2.75/3.04 = ( nth_int @ L @ J ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % nth_list_update'
% 2.75/3.04 thf(fact_664_linorder__neqE__linordered__idom,axiom,
% 2.75/3.04 ! [X: code_integer,Y: code_integer] :
% 2.75/3.04 ( ( X != Y )
% 2.75/3.04 => ( ~ ( ord_le6747313008572928689nteger @ X @ Y )
% 2.75/3.04 => ( ord_le6747313008572928689nteger @ Y @ X ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % linorder_neqE_linordered_idom
% 2.75/3.04 thf(fact_665_linorder__neqE__linordered__idom,axiom,
% 2.75/3.04 ! [X: int,Y: int] :
% 2.75/3.04 ( ( X != Y )
% 2.75/3.04 => ( ~ ( ord_less_int @ X @ Y )
% 2.75/3.04 => ( ord_less_int @ Y @ X ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % linorder_neqE_linordered_idom
% 2.75/3.04 thf(fact_666_pinf_I1_J,axiom,
% 2.75/3.04 ! [P: code_integer > $o,P3: code_integer > $o,Q: code_integer > $o,Q3: code_integer > $o] :
% 2.75/3.04 ( ? [Z3: code_integer] :
% 2.75/3.04 ! [X3: code_integer] :
% 2.75/3.04 ( ( ord_le6747313008572928689nteger @ Z3 @ X3 )
% 2.75/3.04 => ( ( P @ X3 )
% 2.75/3.04 = ( P3 @ X3 ) ) )
% 2.75/3.04 => ( ? [Z3: code_integer] :
% 2.75/3.04 ! [X3: code_integer] :
% 2.75/3.04 ( ( ord_le6747313008572928689nteger @ Z3 @ X3 )
% 2.75/3.04 => ( ( Q @ X3 )
% 2.75/3.04 = ( Q3 @ X3 ) ) )
% 2.75/3.04 => ? [Z4: code_integer] :
% 2.75/3.04 ! [X7: code_integer] :
% 2.75/3.04 ( ( ord_le6747313008572928689nteger @ Z4 @ X7 )
% 2.75/3.04 => ( ( ( P @ X7 )
% 2.75/3.04 & ( Q @ X7 ) )
% 2.75/3.04 = ( ( P3 @ X7 )
% 2.75/3.04 & ( Q3 @ X7 ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % pinf(1)
% 2.75/3.04 thf(fact_667_pinf_I1_J,axiom,
% 2.75/3.04 ! [P: num > $o,P3: num > $o,Q: num > $o,Q3: num > $o] :
% 2.75/3.04 ( ? [Z3: num] :
% 2.75/3.04 ! [X3: num] :
% 2.75/3.04 ( ( ord_less_num @ Z3 @ X3 )
% 2.75/3.04 => ( ( P @ X3 )
% 2.75/3.04 = ( P3 @ X3 ) ) )
% 2.75/3.04 => ( ? [Z3: num] :
% 2.75/3.04 ! [X3: num] :
% 2.75/3.04 ( ( ord_less_num @ Z3 @ X3 )
% 2.75/3.04 => ( ( Q @ X3 )
% 2.75/3.04 = ( Q3 @ X3 ) ) )
% 2.75/3.04 => ? [Z4: num] :
% 2.75/3.04 ! [X7: num] :
% 2.75/3.04 ( ( ord_less_num @ Z4 @ X7 )
% 2.75/3.04 => ( ( ( P @ X7 )
% 2.75/3.04 & ( Q @ X7 ) )
% 2.75/3.04 = ( ( P3 @ X7 )
% 2.75/3.04 & ( Q3 @ X7 ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % pinf(1)
% 2.75/3.04 thf(fact_668_pinf_I1_J,axiom,
% 2.75/3.04 ! [P: nat > $o,P3: nat > $o,Q: nat > $o,Q3: nat > $o] :
% 2.75/3.04 ( ? [Z3: nat] :
% 2.75/3.04 ! [X3: nat] :
% 2.75/3.04 ( ( ord_less_nat @ Z3 @ X3 )
% 2.75/3.04 => ( ( P @ X3 )
% 2.75/3.04 = ( P3 @ X3 ) ) )
% 2.75/3.04 => ( ? [Z3: nat] :
% 2.75/3.04 ! [X3: nat] :
% 2.75/3.04 ( ( ord_less_nat @ Z3 @ X3 )
% 2.75/3.04 => ( ( Q @ X3 )
% 2.75/3.04 = ( Q3 @ X3 ) ) )
% 2.75/3.04 => ? [Z4: nat] :
% 2.75/3.04 ! [X7: nat] :
% 2.75/3.04 ( ( ord_less_nat @ Z4 @ X7 )
% 2.75/3.04 => ( ( ( P @ X7 )
% 2.75/3.04 & ( Q @ X7 ) )
% 2.75/3.04 = ( ( P3 @ X7 )
% 2.75/3.04 & ( Q3 @ X7 ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % pinf(1)
% 2.75/3.04 thf(fact_669_pinf_I1_J,axiom,
% 2.75/3.04 ! [P: int > $o,P3: int > $o,Q: int > $o,Q3: int > $o] :
% 2.75/3.04 ( ? [Z3: int] :
% 2.75/3.04 ! [X3: int] :
% 2.75/3.04 ( ( ord_less_int @ Z3 @ X3 )
% 2.75/3.04 => ( ( P @ X3 )
% 2.75/3.04 = ( P3 @ X3 ) ) )
% 2.75/3.04 => ( ? [Z3: int] :
% 2.75/3.04 ! [X3: int] :
% 2.75/3.04 ( ( ord_less_int @ Z3 @ X3 )
% 2.75/3.04 => ( ( Q @ X3 )
% 2.75/3.04 = ( Q3 @ X3 ) ) )
% 2.75/3.04 => ? [Z4: int] :
% 2.75/3.04 ! [X7: int] :
% 2.75/3.04 ( ( ord_less_int @ Z4 @ X7 )
% 2.75/3.04 => ( ( ( P @ X7 )
% 2.75/3.04 & ( Q @ X7 ) )
% 2.75/3.04 = ( ( P3 @ X7 )
% 2.75/3.04 & ( Q3 @ X7 ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % pinf(1)
% 2.75/3.04 thf(fact_670_pinf_I2_J,axiom,
% 2.75/3.04 ! [P: code_integer > $o,P3: code_integer > $o,Q: code_integer > $o,Q3: code_integer > $o] :
% 2.75/3.04 ( ? [Z3: code_integer] :
% 2.75/3.04 ! [X3: code_integer] :
% 2.75/3.04 ( ( ord_le6747313008572928689nteger @ Z3 @ X3 )
% 2.75/3.04 => ( ( P @ X3 )
% 2.75/3.04 = ( P3 @ X3 ) ) )
% 2.75/3.04 => ( ? [Z3: code_integer] :
% 2.75/3.04 ! [X3: code_integer] :
% 2.75/3.04 ( ( ord_le6747313008572928689nteger @ Z3 @ X3 )
% 2.75/3.04 => ( ( Q @ X3 )
% 2.75/3.04 = ( Q3 @ X3 ) ) )
% 2.75/3.04 => ? [Z4: code_integer] :
% 2.75/3.04 ! [X7: code_integer] :
% 2.75/3.04 ( ( ord_le6747313008572928689nteger @ Z4 @ X7 )
% 2.75/3.04 => ( ( ( P @ X7 )
% 2.75/3.04 | ( Q @ X7 ) )
% 2.75/3.04 = ( ( P3 @ X7 )
% 2.75/3.04 | ( Q3 @ X7 ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % pinf(2)
% 2.75/3.04 thf(fact_671_pinf_I2_J,axiom,
% 2.75/3.04 ! [P: num > $o,P3: num > $o,Q: num > $o,Q3: num > $o] :
% 2.75/3.04 ( ? [Z3: num] :
% 2.75/3.04 ! [X3: num] :
% 2.75/3.04 ( ( ord_less_num @ Z3 @ X3 )
% 2.75/3.04 => ( ( P @ X3 )
% 2.75/3.04 = ( P3 @ X3 ) ) )
% 2.75/3.04 => ( ? [Z3: num] :
% 2.75/3.04 ! [X3: num] :
% 2.75/3.04 ( ( ord_less_num @ Z3 @ X3 )
% 2.75/3.04 => ( ( Q @ X3 )
% 2.75/3.04 = ( Q3 @ X3 ) ) )
% 2.75/3.04 => ? [Z4: num] :
% 2.75/3.04 ! [X7: num] :
% 2.75/3.04 ( ( ord_less_num @ Z4 @ X7 )
% 2.75/3.04 => ( ( ( P @ X7 )
% 2.75/3.04 | ( Q @ X7 ) )
% 2.75/3.04 = ( ( P3 @ X7 )
% 2.75/3.04 | ( Q3 @ X7 ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % pinf(2)
% 2.75/3.04 thf(fact_672_pinf_I2_J,axiom,
% 2.75/3.04 ! [P: nat > $o,P3: nat > $o,Q: nat > $o,Q3: nat > $o] :
% 2.75/3.04 ( ? [Z3: nat] :
% 2.75/3.04 ! [X3: nat] :
% 2.75/3.04 ( ( ord_less_nat @ Z3 @ X3 )
% 2.75/3.04 => ( ( P @ X3 )
% 2.75/3.04 = ( P3 @ X3 ) ) )
% 2.75/3.04 => ( ? [Z3: nat] :
% 2.75/3.04 ! [X3: nat] :
% 2.75/3.04 ( ( ord_less_nat @ Z3 @ X3 )
% 2.75/3.04 => ( ( Q @ X3 )
% 2.75/3.04 = ( Q3 @ X3 ) ) )
% 2.75/3.04 => ? [Z4: nat] :
% 2.75/3.04 ! [X7: nat] :
% 2.75/3.04 ( ( ord_less_nat @ Z4 @ X7 )
% 2.75/3.04 => ( ( ( P @ X7 )
% 2.75/3.04 | ( Q @ X7 ) )
% 2.75/3.04 = ( ( P3 @ X7 )
% 2.75/3.04 | ( Q3 @ X7 ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % pinf(2)
% 2.75/3.04 thf(fact_673_pinf_I2_J,axiom,
% 2.75/3.04 ! [P: int > $o,P3: int > $o,Q: int > $o,Q3: int > $o] :
% 2.75/3.04 ( ? [Z3: int] :
% 2.75/3.04 ! [X3: int] :
% 2.75/3.04 ( ( ord_less_int @ Z3 @ X3 )
% 2.75/3.04 => ( ( P @ X3 )
% 2.75/3.04 = ( P3 @ X3 ) ) )
% 2.75/3.04 => ( ? [Z3: int] :
% 2.75/3.04 ! [X3: int] :
% 2.75/3.04 ( ( ord_less_int @ Z3 @ X3 )
% 2.75/3.04 => ( ( Q @ X3 )
% 2.75/3.04 = ( Q3 @ X3 ) ) )
% 2.75/3.04 => ? [Z4: int] :
% 2.75/3.04 ! [X7: int] :
% 2.75/3.04 ( ( ord_less_int @ Z4 @ X7 )
% 2.75/3.04 => ( ( ( P @ X7 )
% 2.75/3.04 | ( Q @ X7 ) )
% 2.75/3.04 = ( ( P3 @ X7 )
% 2.75/3.04 | ( Q3 @ X7 ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % pinf(2)
% 2.75/3.04 thf(fact_674_pinf_I3_J,axiom,
% 2.75/3.04 ! [T: code_integer] :
% 2.75/3.04 ? [Z4: code_integer] :
% 2.75/3.04 ! [X7: code_integer] :
% 2.75/3.04 ( ( ord_le6747313008572928689nteger @ Z4 @ X7 )
% 2.75/3.04 => ( X7 != T ) ) ).
% 2.75/3.04
% 2.75/3.04 % pinf(3)
% 2.75/3.04 thf(fact_675_pinf_I3_J,axiom,
% 2.75/3.04 ! [T: num] :
% 2.75/3.04 ? [Z4: num] :
% 2.75/3.04 ! [X7: num] :
% 2.75/3.04 ( ( ord_less_num @ Z4 @ X7 )
% 2.75/3.04 => ( X7 != T ) ) ).
% 2.75/3.04
% 2.75/3.04 % pinf(3)
% 2.75/3.04 thf(fact_676_pinf_I3_J,axiom,
% 2.75/3.04 ! [T: nat] :
% 2.75/3.04 ? [Z4: nat] :
% 2.75/3.04 ! [X7: nat] :
% 2.75/3.04 ( ( ord_less_nat @ Z4 @ X7 )
% 2.75/3.04 => ( X7 != T ) ) ).
% 2.75/3.04
% 2.75/3.04 % pinf(3)
% 2.75/3.04 thf(fact_677_pinf_I3_J,axiom,
% 2.75/3.04 ! [T: int] :
% 2.75/3.04 ? [Z4: int] :
% 2.75/3.04 ! [X7: int] :
% 2.75/3.04 ( ( ord_less_int @ Z4 @ X7 )
% 2.75/3.04 => ( X7 != T ) ) ).
% 2.75/3.04
% 2.75/3.04 % pinf(3)
% 2.75/3.04 thf(fact_678_pinf_I4_J,axiom,
% 2.75/3.04 ! [T: code_integer] :
% 2.75/3.04 ? [Z4: code_integer] :
% 2.75/3.04 ! [X7: code_integer] :
% 2.75/3.04 ( ( ord_le6747313008572928689nteger @ Z4 @ X7 )
% 2.75/3.04 => ( X7 != T ) ) ).
% 2.75/3.04
% 2.75/3.04 % pinf(4)
% 2.75/3.04 thf(fact_679_pinf_I4_J,axiom,
% 2.75/3.04 ! [T: num] :
% 2.75/3.04 ? [Z4: num] :
% 2.75/3.04 ! [X7: num] :
% 2.75/3.04 ( ( ord_less_num @ Z4 @ X7 )
% 2.75/3.04 => ( X7 != T ) ) ).
% 2.75/3.04
% 2.75/3.04 % pinf(4)
% 2.75/3.04 thf(fact_680_pinf_I4_J,axiom,
% 2.75/3.04 ! [T: nat] :
% 2.75/3.04 ? [Z4: nat] :
% 2.75/3.04 ! [X7: nat] :
% 2.75/3.04 ( ( ord_less_nat @ Z4 @ X7 )
% 2.75/3.04 => ( X7 != T ) ) ).
% 2.75/3.04
% 2.75/3.04 % pinf(4)
% 2.75/3.04 thf(fact_681_pinf_I4_J,axiom,
% 2.75/3.04 ! [T: int] :
% 2.75/3.04 ? [Z4: int] :
% 2.75/3.04 ! [X7: int] :
% 2.75/3.04 ( ( ord_less_int @ Z4 @ X7 )
% 2.75/3.04 => ( X7 != T ) ) ).
% 2.75/3.04
% 2.75/3.04 % pinf(4)
% 2.75/3.04 thf(fact_682_pinf_I5_J,axiom,
% 2.75/3.04 ! [T: code_integer] :
% 2.75/3.04 ? [Z4: code_integer] :
% 2.75/3.04 ! [X7: code_integer] :
% 2.75/3.04 ( ( ord_le6747313008572928689nteger @ Z4 @ X7 )
% 2.75/3.04 => ~ ( ord_le6747313008572928689nteger @ X7 @ T ) ) ).
% 2.75/3.04
% 2.75/3.04 % pinf(5)
% 2.75/3.04 thf(fact_683_pinf_I5_J,axiom,
% 2.75/3.04 ! [T: num] :
% 2.75/3.04 ? [Z4: num] :
% 2.75/3.04 ! [X7: num] :
% 2.75/3.04 ( ( ord_less_num @ Z4 @ X7 )
% 2.75/3.04 => ~ ( ord_less_num @ X7 @ T ) ) ).
% 2.75/3.04
% 2.75/3.04 % pinf(5)
% 2.75/3.04 thf(fact_684_pinf_I5_J,axiom,
% 2.75/3.04 ! [T: nat] :
% 2.75/3.04 ? [Z4: nat] :
% 2.75/3.04 ! [X7: nat] :
% 2.75/3.04 ( ( ord_less_nat @ Z4 @ X7 )
% 2.75/3.04 => ~ ( ord_less_nat @ X7 @ T ) ) ).
% 2.75/3.04
% 2.75/3.04 % pinf(5)
% 2.75/3.04 thf(fact_685_pinf_I5_J,axiom,
% 2.75/3.04 ! [T: int] :
% 2.75/3.04 ? [Z4: int] :
% 2.75/3.04 ! [X7: int] :
% 2.75/3.04 ( ( ord_less_int @ Z4 @ X7 )
% 2.75/3.04 => ~ ( ord_less_int @ X7 @ T ) ) ).
% 2.75/3.04
% 2.75/3.04 % pinf(5)
% 2.75/3.04 thf(fact_686_pinf_I7_J,axiom,
% 2.75/3.04 ! [T: code_integer] :
% 2.75/3.04 ? [Z4: code_integer] :
% 2.75/3.04 ! [X7: code_integer] :
% 2.75/3.04 ( ( ord_le6747313008572928689nteger @ Z4 @ X7 )
% 2.75/3.04 => ( ord_le6747313008572928689nteger @ T @ X7 ) ) ).
% 2.75/3.04
% 2.75/3.04 % pinf(7)
% 2.75/3.04 thf(fact_687_pinf_I7_J,axiom,
% 2.75/3.04 ! [T: num] :
% 2.75/3.04 ? [Z4: num] :
% 2.75/3.04 ! [X7: num] :
% 2.75/3.04 ( ( ord_less_num @ Z4 @ X7 )
% 2.75/3.04 => ( ord_less_num @ T @ X7 ) ) ).
% 2.75/3.04
% 2.75/3.04 % pinf(7)
% 2.75/3.04 thf(fact_688_pinf_I7_J,axiom,
% 2.75/3.04 ! [T: nat] :
% 2.75/3.04 ? [Z4: nat] :
% 2.75/3.04 ! [X7: nat] :
% 2.75/3.04 ( ( ord_less_nat @ Z4 @ X7 )
% 2.75/3.04 => ( ord_less_nat @ T @ X7 ) ) ).
% 2.75/3.04
% 2.75/3.04 % pinf(7)
% 2.75/3.04 thf(fact_689_pinf_I7_J,axiom,
% 2.75/3.04 ! [T: int] :
% 2.75/3.04 ? [Z4: int] :
% 2.75/3.04 ! [X7: int] :
% 2.75/3.04 ( ( ord_less_int @ Z4 @ X7 )
% 2.75/3.04 => ( ord_less_int @ T @ X7 ) ) ).
% 2.75/3.04
% 2.75/3.04 % pinf(7)
% 2.75/3.04 thf(fact_690_minf_I1_J,axiom,
% 2.75/3.04 ! [P: code_integer > $o,P3: code_integer > $o,Q: code_integer > $o,Q3: code_integer > $o] :
% 2.75/3.04 ( ? [Z3: code_integer] :
% 2.75/3.04 ! [X3: code_integer] :
% 2.75/3.04 ( ( ord_le6747313008572928689nteger @ X3 @ Z3 )
% 2.75/3.04 => ( ( P @ X3 )
% 2.75/3.04 = ( P3 @ X3 ) ) )
% 2.75/3.04 => ( ? [Z3: code_integer] :
% 2.75/3.04 ! [X3: code_integer] :
% 2.75/3.04 ( ( ord_le6747313008572928689nteger @ X3 @ Z3 )
% 2.75/3.04 => ( ( Q @ X3 )
% 2.75/3.04 = ( Q3 @ X3 ) ) )
% 2.75/3.04 => ? [Z4: code_integer] :
% 2.75/3.04 ! [X7: code_integer] :
% 2.75/3.04 ( ( ord_le6747313008572928689nteger @ X7 @ Z4 )
% 2.75/3.04 => ( ( ( P @ X7 )
% 2.75/3.04 & ( Q @ X7 ) )
% 2.75/3.04 = ( ( P3 @ X7 )
% 2.75/3.04 & ( Q3 @ X7 ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % minf(1)
% 2.75/3.04 thf(fact_691_minf_I1_J,axiom,
% 2.75/3.04 ! [P: num > $o,P3: num > $o,Q: num > $o,Q3: num > $o] :
% 2.75/3.04 ( ? [Z3: num] :
% 2.75/3.04 ! [X3: num] :
% 2.75/3.04 ( ( ord_less_num @ X3 @ Z3 )
% 2.75/3.04 => ( ( P @ X3 )
% 2.75/3.04 = ( P3 @ X3 ) ) )
% 2.75/3.04 => ( ? [Z3: num] :
% 2.75/3.04 ! [X3: num] :
% 2.75/3.04 ( ( ord_less_num @ X3 @ Z3 )
% 2.75/3.04 => ( ( Q @ X3 )
% 2.75/3.04 = ( Q3 @ X3 ) ) )
% 2.75/3.04 => ? [Z4: num] :
% 2.75/3.04 ! [X7: num] :
% 2.75/3.04 ( ( ord_less_num @ X7 @ Z4 )
% 2.75/3.04 => ( ( ( P @ X7 )
% 2.75/3.04 & ( Q @ X7 ) )
% 2.75/3.04 = ( ( P3 @ X7 )
% 2.75/3.04 & ( Q3 @ X7 ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % minf(1)
% 2.75/3.04 thf(fact_692_minf_I1_J,axiom,
% 2.75/3.04 ! [P: nat > $o,P3: nat > $o,Q: nat > $o,Q3: nat > $o] :
% 2.75/3.04 ( ? [Z3: nat] :
% 2.75/3.04 ! [X3: nat] :
% 2.75/3.04 ( ( ord_less_nat @ X3 @ Z3 )
% 2.75/3.04 => ( ( P @ X3 )
% 2.75/3.04 = ( P3 @ X3 ) ) )
% 2.75/3.04 => ( ? [Z3: nat] :
% 2.75/3.04 ! [X3: nat] :
% 2.75/3.04 ( ( ord_less_nat @ X3 @ Z3 )
% 2.75/3.04 => ( ( Q @ X3 )
% 2.75/3.04 = ( Q3 @ X3 ) ) )
% 2.75/3.04 => ? [Z4: nat] :
% 2.75/3.04 ! [X7: nat] :
% 2.75/3.04 ( ( ord_less_nat @ X7 @ Z4 )
% 2.75/3.04 => ( ( ( P @ X7 )
% 2.75/3.04 & ( Q @ X7 ) )
% 2.75/3.04 = ( ( P3 @ X7 )
% 2.75/3.04 & ( Q3 @ X7 ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % minf(1)
% 2.75/3.04 thf(fact_693_minf_I1_J,axiom,
% 2.75/3.04 ! [P: int > $o,P3: int > $o,Q: int > $o,Q3: int > $o] :
% 2.75/3.04 ( ? [Z3: int] :
% 2.75/3.04 ! [X3: int] :
% 2.75/3.04 ( ( ord_less_int @ X3 @ Z3 )
% 2.75/3.04 => ( ( P @ X3 )
% 2.75/3.04 = ( P3 @ X3 ) ) )
% 2.75/3.04 => ( ? [Z3: int] :
% 2.75/3.04 ! [X3: int] :
% 2.75/3.04 ( ( ord_less_int @ X3 @ Z3 )
% 2.75/3.04 => ( ( Q @ X3 )
% 2.75/3.04 = ( Q3 @ X3 ) ) )
% 2.75/3.04 => ? [Z4: int] :
% 2.75/3.04 ! [X7: int] :
% 2.75/3.04 ( ( ord_less_int @ X7 @ Z4 )
% 2.75/3.04 => ( ( ( P @ X7 )
% 2.75/3.04 & ( Q @ X7 ) )
% 2.75/3.04 = ( ( P3 @ X7 )
% 2.75/3.04 & ( Q3 @ X7 ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % minf(1)
% 2.75/3.04 thf(fact_694_minf_I2_J,axiom,
% 2.75/3.04 ! [P: code_integer > $o,P3: code_integer > $o,Q: code_integer > $o,Q3: code_integer > $o] :
% 2.75/3.04 ( ? [Z3: code_integer] :
% 2.75/3.04 ! [X3: code_integer] :
% 2.75/3.04 ( ( ord_le6747313008572928689nteger @ X3 @ Z3 )
% 2.75/3.04 => ( ( P @ X3 )
% 2.75/3.04 = ( P3 @ X3 ) ) )
% 2.75/3.04 => ( ? [Z3: code_integer] :
% 2.75/3.04 ! [X3: code_integer] :
% 2.75/3.04 ( ( ord_le6747313008572928689nteger @ X3 @ Z3 )
% 2.75/3.04 => ( ( Q @ X3 )
% 2.75/3.04 = ( Q3 @ X3 ) ) )
% 2.75/3.04 => ? [Z4: code_integer] :
% 2.75/3.04 ! [X7: code_integer] :
% 2.75/3.04 ( ( ord_le6747313008572928689nteger @ X7 @ Z4 )
% 2.75/3.04 => ( ( ( P @ X7 )
% 2.75/3.04 | ( Q @ X7 ) )
% 2.75/3.04 = ( ( P3 @ X7 )
% 2.75/3.04 | ( Q3 @ X7 ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % minf(2)
% 2.75/3.04 thf(fact_695_minf_I2_J,axiom,
% 2.75/3.04 ! [P: num > $o,P3: num > $o,Q: num > $o,Q3: num > $o] :
% 2.75/3.04 ( ? [Z3: num] :
% 2.75/3.04 ! [X3: num] :
% 2.75/3.04 ( ( ord_less_num @ X3 @ Z3 )
% 2.75/3.04 => ( ( P @ X3 )
% 2.75/3.04 = ( P3 @ X3 ) ) )
% 2.75/3.04 => ( ? [Z3: num] :
% 2.75/3.04 ! [X3: num] :
% 2.75/3.04 ( ( ord_less_num @ X3 @ Z3 )
% 2.75/3.04 => ( ( Q @ X3 )
% 2.75/3.04 = ( Q3 @ X3 ) ) )
% 2.75/3.04 => ? [Z4: num] :
% 2.75/3.04 ! [X7: num] :
% 2.75/3.04 ( ( ord_less_num @ X7 @ Z4 )
% 2.75/3.04 => ( ( ( P @ X7 )
% 2.75/3.04 | ( Q @ X7 ) )
% 2.75/3.04 = ( ( P3 @ X7 )
% 2.75/3.04 | ( Q3 @ X7 ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % minf(2)
% 2.75/3.04 thf(fact_696_minf_I2_J,axiom,
% 2.75/3.04 ! [P: nat > $o,P3: nat > $o,Q: nat > $o,Q3: nat > $o] :
% 2.75/3.04 ( ? [Z3: nat] :
% 2.75/3.04 ! [X3: nat] :
% 2.75/3.04 ( ( ord_less_nat @ X3 @ Z3 )
% 2.75/3.04 => ( ( P @ X3 )
% 2.75/3.04 = ( P3 @ X3 ) ) )
% 2.75/3.04 => ( ? [Z3: nat] :
% 2.75/3.04 ! [X3: nat] :
% 2.75/3.04 ( ( ord_less_nat @ X3 @ Z3 )
% 2.75/3.04 => ( ( Q @ X3 )
% 2.75/3.04 = ( Q3 @ X3 ) ) )
% 2.75/3.04 => ? [Z4: nat] :
% 2.75/3.04 ! [X7: nat] :
% 2.75/3.04 ( ( ord_less_nat @ X7 @ Z4 )
% 2.75/3.04 => ( ( ( P @ X7 )
% 2.75/3.04 | ( Q @ X7 ) )
% 2.75/3.04 = ( ( P3 @ X7 )
% 2.75/3.04 | ( Q3 @ X7 ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % minf(2)
% 2.75/3.04 thf(fact_697_minf_I2_J,axiom,
% 2.75/3.04 ! [P: int > $o,P3: int > $o,Q: int > $o,Q3: int > $o] :
% 2.75/3.04 ( ? [Z3: int] :
% 2.75/3.04 ! [X3: int] :
% 2.75/3.04 ( ( ord_less_int @ X3 @ Z3 )
% 2.75/3.04 => ( ( P @ X3 )
% 2.75/3.04 = ( P3 @ X3 ) ) )
% 2.75/3.04 => ( ? [Z3: int] :
% 2.75/3.04 ! [X3: int] :
% 2.75/3.04 ( ( ord_less_int @ X3 @ Z3 )
% 2.75/3.04 => ( ( Q @ X3 )
% 2.75/3.04 = ( Q3 @ X3 ) ) )
% 2.75/3.04 => ? [Z4: int] :
% 2.75/3.04 ! [X7: int] :
% 2.75/3.04 ( ( ord_less_int @ X7 @ Z4 )
% 2.75/3.04 => ( ( ( P @ X7 )
% 2.75/3.04 | ( Q @ X7 ) )
% 2.75/3.04 = ( ( P3 @ X7 )
% 2.75/3.04 | ( Q3 @ X7 ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % minf(2)
% 2.75/3.04 thf(fact_698_minf_I3_J,axiom,
% 2.75/3.04 ! [T: code_integer] :
% 2.75/3.04 ? [Z4: code_integer] :
% 2.75/3.04 ! [X7: code_integer] :
% 2.75/3.04 ( ( ord_le6747313008572928689nteger @ X7 @ Z4 )
% 2.75/3.04 => ( X7 != T ) ) ).
% 2.75/3.04
% 2.75/3.04 % minf(3)
% 2.75/3.04 thf(fact_699_minf_I3_J,axiom,
% 2.75/3.04 ! [T: num] :
% 2.75/3.04 ? [Z4: num] :
% 2.75/3.04 ! [X7: num] :
% 2.75/3.04 ( ( ord_less_num @ X7 @ Z4 )
% 2.75/3.04 => ( X7 != T ) ) ).
% 2.75/3.04
% 2.75/3.04 % minf(3)
% 2.75/3.04 thf(fact_700_minf_I3_J,axiom,
% 2.75/3.04 ! [T: nat] :
% 2.75/3.04 ? [Z4: nat] :
% 2.75/3.04 ! [X7: nat] :
% 2.75/3.04 ( ( ord_less_nat @ X7 @ Z4 )
% 2.75/3.04 => ( X7 != T ) ) ).
% 2.75/3.04
% 2.75/3.04 % minf(3)
% 2.75/3.04 thf(fact_701_minf_I3_J,axiom,
% 2.75/3.04 ! [T: int] :
% 2.75/3.04 ? [Z4: int] :
% 2.75/3.04 ! [X7: int] :
% 2.75/3.04 ( ( ord_less_int @ X7 @ Z4 )
% 2.75/3.04 => ( X7 != T ) ) ).
% 2.75/3.04
% 2.75/3.04 % minf(3)
% 2.75/3.04 thf(fact_702_minf_I4_J,axiom,
% 2.75/3.04 ! [T: code_integer] :
% 2.75/3.04 ? [Z4: code_integer] :
% 2.75/3.04 ! [X7: code_integer] :
% 2.75/3.04 ( ( ord_le6747313008572928689nteger @ X7 @ Z4 )
% 2.75/3.04 => ( X7 != T ) ) ).
% 2.75/3.04
% 2.75/3.04 % minf(4)
% 2.75/3.04 thf(fact_703_minf_I4_J,axiom,
% 2.75/3.04 ! [T: num] :
% 2.75/3.04 ? [Z4: num] :
% 2.75/3.04 ! [X7: num] :
% 2.75/3.04 ( ( ord_less_num @ X7 @ Z4 )
% 2.75/3.04 => ( X7 != T ) ) ).
% 2.75/3.04
% 2.75/3.04 % minf(4)
% 2.75/3.04 thf(fact_704_minf_I4_J,axiom,
% 2.75/3.04 ! [T: nat] :
% 2.75/3.04 ? [Z4: nat] :
% 2.75/3.04 ! [X7: nat] :
% 2.75/3.04 ( ( ord_less_nat @ X7 @ Z4 )
% 2.75/3.04 => ( X7 != T ) ) ).
% 2.75/3.04
% 2.75/3.04 % minf(4)
% 2.75/3.04 thf(fact_705_minf_I4_J,axiom,
% 2.75/3.04 ! [T: int] :
% 2.75/3.04 ? [Z4: int] :
% 2.75/3.04 ! [X7: int] :
% 2.75/3.04 ( ( ord_less_int @ X7 @ Z4 )
% 2.75/3.04 => ( X7 != T ) ) ).
% 2.75/3.04
% 2.75/3.04 % minf(4)
% 2.75/3.04 thf(fact_706_minf_I5_J,axiom,
% 2.75/3.04 ! [T: code_integer] :
% 2.75/3.04 ? [Z4: code_integer] :
% 2.75/3.04 ! [X7: code_integer] :
% 2.75/3.04 ( ( ord_le6747313008572928689nteger @ X7 @ Z4 )
% 2.75/3.04 => ( ord_le6747313008572928689nteger @ X7 @ T ) ) ).
% 2.75/3.04
% 2.75/3.04 % minf(5)
% 2.75/3.04 thf(fact_707_minf_I5_J,axiom,
% 2.75/3.04 ! [T: num] :
% 2.75/3.04 ? [Z4: num] :
% 2.75/3.04 ! [X7: num] :
% 2.75/3.04 ( ( ord_less_num @ X7 @ Z4 )
% 2.75/3.04 => ( ord_less_num @ X7 @ T ) ) ).
% 2.75/3.04
% 2.75/3.04 % minf(5)
% 2.75/3.04 thf(fact_708_minf_I5_J,axiom,
% 2.75/3.04 ! [T: nat] :
% 2.75/3.04 ? [Z4: nat] :
% 2.75/3.04 ! [X7: nat] :
% 2.75/3.04 ( ( ord_less_nat @ X7 @ Z4 )
% 2.75/3.04 => ( ord_less_nat @ X7 @ T ) ) ).
% 2.75/3.04
% 2.75/3.04 % minf(5)
% 2.75/3.04 thf(fact_709_minf_I5_J,axiom,
% 2.75/3.04 ! [T: int] :
% 2.75/3.04 ? [Z4: int] :
% 2.75/3.04 ! [X7: int] :
% 2.75/3.04 ( ( ord_less_int @ X7 @ Z4 )
% 2.75/3.04 => ( ord_less_int @ X7 @ T ) ) ).
% 2.75/3.04
% 2.75/3.04 % minf(5)
% 2.75/3.04 thf(fact_710_minf_I7_J,axiom,
% 2.75/3.04 ! [T: code_integer] :
% 2.75/3.04 ? [Z4: code_integer] :
% 2.75/3.04 ! [X7: code_integer] :
% 2.75/3.04 ( ( ord_le6747313008572928689nteger @ X7 @ Z4 )
% 2.75/3.04 => ~ ( ord_le6747313008572928689nteger @ T @ X7 ) ) ).
% 2.75/3.04
% 2.75/3.04 % minf(7)
% 2.75/3.04 thf(fact_711_minf_I7_J,axiom,
% 2.75/3.04 ! [T: num] :
% 2.75/3.04 ? [Z4: num] :
% 2.75/3.04 ! [X7: num] :
% 2.75/3.04 ( ( ord_less_num @ X7 @ Z4 )
% 2.75/3.04 => ~ ( ord_less_num @ T @ X7 ) ) ).
% 2.75/3.04
% 2.75/3.04 % minf(7)
% 2.75/3.04 thf(fact_712_minf_I7_J,axiom,
% 2.75/3.04 ! [T: nat] :
% 2.75/3.04 ? [Z4: nat] :
% 2.75/3.04 ! [X7: nat] :
% 2.75/3.04 ( ( ord_less_nat @ X7 @ Z4 )
% 2.75/3.04 => ~ ( ord_less_nat @ T @ X7 ) ) ).
% 2.75/3.04
% 2.75/3.04 % minf(7)
% 2.75/3.04 thf(fact_713_minf_I7_J,axiom,
% 2.75/3.04 ! [T: int] :
% 2.75/3.04 ? [Z4: int] :
% 2.75/3.04 ! [X7: int] :
% 2.75/3.04 ( ( ord_less_int @ X7 @ Z4 )
% 2.75/3.04 => ~ ( ord_less_int @ T @ X7 ) ) ).
% 2.75/3.04
% 2.75/3.04 % minf(7)
% 2.75/3.04 thf(fact_714_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 2.75/3.04 ! [B2: code_integer,A2: code_integer,C: code_integer] :
% 2.75/3.04 ( ( times_3573771949741848930nteger @ B2 @ ( times_3573771949741848930nteger @ A2 @ C ) )
% 2.75/3.04 = ( times_3573771949741848930nteger @ A2 @ ( times_3573771949741848930nteger @ B2 @ C ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % ab_semigroup_mult_class.mult.left_commute
% 2.75/3.04 thf(fact_715_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 2.75/3.04 ! [B2: assn,A2: assn,C: assn] :
% 2.75/3.04 ( ( times_times_assn @ B2 @ ( times_times_assn @ A2 @ C ) )
% 2.75/3.04 = ( times_times_assn @ A2 @ ( times_times_assn @ B2 @ C ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % ab_semigroup_mult_class.mult.left_commute
% 2.75/3.04 thf(fact_716_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 2.75/3.04 ! [B2: rat,A2: rat,C: rat] :
% 2.75/3.04 ( ( times_times_rat @ B2 @ ( times_times_rat @ A2 @ C ) )
% 2.75/3.04 = ( times_times_rat @ A2 @ ( times_times_rat @ B2 @ C ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % ab_semigroup_mult_class.mult.left_commute
% 2.75/3.04 thf(fact_717_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 2.75/3.04 ! [B2: nat,A2: nat,C: nat] :
% 2.75/3.04 ( ( times_times_nat @ B2 @ ( times_times_nat @ A2 @ C ) )
% 2.75/3.04 = ( times_times_nat @ A2 @ ( times_times_nat @ B2 @ C ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % ab_semigroup_mult_class.mult.left_commute
% 2.75/3.04 thf(fact_718_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 2.75/3.04 ! [B2: int,A2: int,C: int] :
% 2.75/3.04 ( ( times_times_int @ B2 @ ( times_times_int @ A2 @ C ) )
% 2.75/3.04 = ( times_times_int @ A2 @ ( times_times_int @ B2 @ C ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % ab_semigroup_mult_class.mult.left_commute
% 2.75/3.04 thf(fact_719_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 2.75/3.04 ( times_3573771949741848930nteger
% 2.75/3.04 = ( ^ [A3: code_integer,B3: code_integer] : ( times_3573771949741848930nteger @ B3 @ A3 ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % ab_semigroup_mult_class.mult.commute
% 2.75/3.04 thf(fact_720_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 2.75/3.04 ( times_times_assn
% 2.75/3.04 = ( ^ [A3: assn,B3: assn] : ( times_times_assn @ B3 @ A3 ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % ab_semigroup_mult_class.mult.commute
% 2.75/3.04 thf(fact_721_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 2.75/3.04 ( times_times_rat
% 2.75/3.04 = ( ^ [A3: rat,B3: rat] : ( times_times_rat @ B3 @ A3 ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % ab_semigroup_mult_class.mult.commute
% 2.75/3.04 thf(fact_722_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 2.75/3.04 ( times_times_nat
% 2.75/3.04 = ( ^ [A3: nat,B3: nat] : ( times_times_nat @ B3 @ A3 ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % ab_semigroup_mult_class.mult.commute
% 2.75/3.04 thf(fact_723_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 2.75/3.04 ( times_times_int
% 2.75/3.04 = ( ^ [A3: int,B3: int] : ( times_times_int @ B3 @ A3 ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % ab_semigroup_mult_class.mult.commute
% 2.75/3.04 thf(fact_724_mult_Oassoc,axiom,
% 2.75/3.04 ! [A2: code_integer,B2: code_integer,C: code_integer] :
% 2.75/3.04 ( ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ A2 @ B2 ) @ C )
% 2.75/3.04 = ( times_3573771949741848930nteger @ A2 @ ( times_3573771949741848930nteger @ B2 @ C ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % mult.assoc
% 2.75/3.04 thf(fact_725_mult_Oassoc,axiom,
% 2.75/3.04 ! [A2: assn,B2: assn,C: assn] :
% 2.75/3.04 ( ( times_times_assn @ ( times_times_assn @ A2 @ B2 ) @ C )
% 2.75/3.04 = ( times_times_assn @ A2 @ ( times_times_assn @ B2 @ C ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % mult.assoc
% 2.75/3.04 thf(fact_726_mult_Oassoc,axiom,
% 2.75/3.04 ! [A2: rat,B2: rat,C: rat] :
% 2.75/3.04 ( ( times_times_rat @ ( times_times_rat @ A2 @ B2 ) @ C )
% 2.75/3.04 = ( times_times_rat @ A2 @ ( times_times_rat @ B2 @ C ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % mult.assoc
% 2.75/3.04 thf(fact_727_mult_Oassoc,axiom,
% 2.75/3.04 ! [A2: nat,B2: nat,C: nat] :
% 2.75/3.04 ( ( times_times_nat @ ( times_times_nat @ A2 @ B2 ) @ C )
% 2.75/3.04 = ( times_times_nat @ A2 @ ( times_times_nat @ B2 @ C ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % mult.assoc
% 2.75/3.04 thf(fact_728_mult_Oassoc,axiom,
% 2.75/3.04 ! [A2: int,B2: int,C: int] :
% 2.75/3.04 ( ( times_times_int @ ( times_times_int @ A2 @ B2 ) @ C )
% 2.75/3.04 = ( times_times_int @ A2 @ ( times_times_int @ B2 @ C ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % mult.assoc
% 2.75/3.04 thf(fact_729_listI__assn__cong,axiom,
% 2.75/3.04 ! [I3: set_nat,I7: set_nat,Xs: list_c,Xs4: list_c,Xsi: list_c,Xsi2: list_c,A: c > c > assn,A6: c > c > assn] :
% 2.75/3.04 ( ( I3 = I7 )
% 2.75/3.04 => ( ( ( size_size_list_c @ Xs )
% 2.75/3.04 = ( size_size_list_c @ Xs4 ) )
% 2.75/3.04 => ( ( ( size_size_list_c @ Xsi )
% 2.75/3.04 = ( size_size_list_c @ Xsi2 ) )
% 2.75/3.04 => ( ! [I5: nat] :
% 2.75/3.04 ( ( member_nat @ I5 @ I3 )
% 2.75/3.04 => ( ( ord_less_nat @ I5 @ ( size_size_list_c @ Xs ) )
% 2.75/3.04 => ( ( ( size_size_list_c @ Xs )
% 2.75/3.04 = ( size_size_list_c @ Xsi ) )
% 2.75/3.04 => ( ( ( nth_c @ Xs @ I5 )
% 2.75/3.04 = ( nth_c @ Xs4 @ I5 ) )
% 2.75/3.04 & ( ( nth_c @ Xsi @ I5 )
% 2.75/3.04 = ( nth_c @ Xsi2 @ I5 ) )
% 2.75/3.04 & ( ( A @ ( nth_c @ Xs @ I5 ) @ ( nth_c @ Xsi @ I5 ) )
% 2.75/3.04 = ( A6 @ ( nth_c @ Xs4 @ I5 ) @ ( nth_c @ Xsi2 @ I5 ) ) ) ) ) ) )
% 2.75/3.04 => ( ( vEBT_L824818263033719200sn_c_c @ I3 @ A @ Xs @ Xsi )
% 2.75/3.04 = ( vEBT_L824818263033719200sn_c_c @ I7 @ A6 @ Xs4 @ Xsi2 ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % listI_assn_cong
% 2.75/3.04 thf(fact_730_listI__assn__cong,axiom,
% 2.75/3.04 ! [I3: set_nat,I7: set_nat,Xs: list_c,Xs4: list_c,Xsi: list_nat,Xsi2: list_nat,A: c > nat > assn,A6: c > nat > assn] :
% 2.75/3.04 ( ( I3 = I7 )
% 2.75/3.04 => ( ( ( size_size_list_c @ Xs )
% 2.75/3.04 = ( size_size_list_c @ Xs4 ) )
% 2.75/3.04 => ( ( ( size_size_list_nat @ Xsi )
% 2.75/3.04 = ( size_size_list_nat @ Xsi2 ) )
% 2.75/3.04 => ( ! [I5: nat] :
% 2.75/3.04 ( ( member_nat @ I5 @ I3 )
% 2.75/3.04 => ( ( ord_less_nat @ I5 @ ( size_size_list_c @ Xs ) )
% 2.75/3.04 => ( ( ( size_size_list_c @ Xs )
% 2.75/3.04 = ( size_size_list_nat @ Xsi ) )
% 2.75/3.04 => ( ( ( nth_c @ Xs @ I5 )
% 2.75/3.04 = ( nth_c @ Xs4 @ I5 ) )
% 2.75/3.04 & ( ( nth_nat @ Xsi @ I5 )
% 2.75/3.04 = ( nth_nat @ Xsi2 @ I5 ) )
% 2.75/3.04 & ( ( A @ ( nth_c @ Xs @ I5 ) @ ( nth_nat @ Xsi @ I5 ) )
% 2.75/3.04 = ( A6 @ ( nth_c @ Xs4 @ I5 ) @ ( nth_nat @ Xsi2 @ I5 ) ) ) ) ) ) )
% 2.75/3.04 => ( ( vEBT_L6585172037124793648_c_nat @ I3 @ A @ Xs @ Xsi )
% 2.75/3.04 = ( vEBT_L6585172037124793648_c_nat @ I7 @ A6 @ Xs4 @ Xsi2 ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % listI_assn_cong
% 2.75/3.04 thf(fact_731_listI__assn__cong,axiom,
% 2.75/3.04 ! [I3: set_nat,I7: set_nat,Xs: list_c,Xs4: list_c,Xsi: list_int,Xsi2: list_int,A: c > int > assn,A6: c > int > assn] :
% 2.75/3.04 ( ( I3 = I7 )
% 2.75/3.04 => ( ( ( size_size_list_c @ Xs )
% 2.75/3.04 = ( size_size_list_c @ Xs4 ) )
% 2.75/3.04 => ( ( ( size_size_list_int @ Xsi )
% 2.75/3.04 = ( size_size_list_int @ Xsi2 ) )
% 2.75/3.04 => ( ! [I5: nat] :
% 2.75/3.04 ( ( member_nat @ I5 @ I3 )
% 2.75/3.04 => ( ( ord_less_nat @ I5 @ ( size_size_list_c @ Xs ) )
% 2.75/3.04 => ( ( ( size_size_list_c @ Xs )
% 2.75/3.04 = ( size_size_list_int @ Xsi ) )
% 2.75/3.04 => ( ( ( nth_c @ Xs @ I5 )
% 2.75/3.04 = ( nth_c @ Xs4 @ I5 ) )
% 2.75/3.04 & ( ( nth_int @ Xsi @ I5 )
% 2.75/3.04 = ( nth_int @ Xsi2 @ I5 ) )
% 2.75/3.04 & ( ( A @ ( nth_c @ Xs @ I5 ) @ ( nth_int @ Xsi @ I5 ) )
% 2.75/3.04 = ( A6 @ ( nth_c @ Xs4 @ I5 ) @ ( nth_int @ Xsi2 @ I5 ) ) ) ) ) ) )
% 2.75/3.04 => ( ( vEBT_L6582681566615743372_c_int @ I3 @ A @ Xs @ Xsi )
% 2.75/3.04 = ( vEBT_L6582681566615743372_c_int @ I7 @ A6 @ Xs4 @ Xsi2 ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % listI_assn_cong
% 2.75/3.04 thf(fact_732_listI__assn__cong,axiom,
% 2.75/3.04 ! [I3: set_nat,I7: set_nat,Xs: list_d,Xs4: list_d,Xsi: list_c,Xsi2: list_c,A: d > c > assn,A6: d > c > assn] :
% 2.75/3.04 ( ( I3 = I7 )
% 2.75/3.04 => ( ( ( size_size_list_d @ Xs )
% 2.75/3.04 = ( size_size_list_d @ Xs4 ) )
% 2.75/3.04 => ( ( ( size_size_list_c @ Xsi )
% 2.75/3.04 = ( size_size_list_c @ Xsi2 ) )
% 2.75/3.04 => ( ! [I5: nat] :
% 2.75/3.04 ( ( member_nat @ I5 @ I3 )
% 2.75/3.04 => ( ( ord_less_nat @ I5 @ ( size_size_list_d @ Xs ) )
% 2.75/3.04 => ( ( ( size_size_list_d @ Xs )
% 2.75/3.04 = ( size_size_list_c @ Xsi ) )
% 2.75/3.04 => ( ( ( nth_d @ Xs @ I5 )
% 2.75/3.04 = ( nth_d @ Xs4 @ I5 ) )
% 2.75/3.04 & ( ( nth_c @ Xsi @ I5 )
% 2.75/3.04 = ( nth_c @ Xsi2 @ I5 ) )
% 2.75/3.04 & ( ( A @ ( nth_d @ Xs @ I5 ) @ ( nth_c @ Xsi @ I5 ) )
% 2.75/3.04 = ( A6 @ ( nth_d @ Xs4 @ I5 ) @ ( nth_c @ Xsi2 @ I5 ) ) ) ) ) ) )
% 2.75/3.04 => ( ( vEBT_L7260734717915818975sn_d_c @ I3 @ A @ Xs @ Xsi )
% 2.75/3.04 = ( vEBT_L7260734717915818975sn_d_c @ I7 @ A6 @ Xs4 @ Xsi2 ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % listI_assn_cong
% 2.75/3.04 thf(fact_733_listI__assn__cong,axiom,
% 2.75/3.04 ! [I3: set_nat,I7: set_nat,Xs: list_d,Xs4: list_d,Xsi: list_d,Xsi2: list_d,A: d > d > assn,A6: d > d > assn] :
% 2.75/3.04 ( ( I3 = I7 )
% 2.75/3.04 => ( ( ( size_size_list_d @ Xs )
% 2.75/3.04 = ( size_size_list_d @ Xs4 ) )
% 2.75/3.04 => ( ( ( size_size_list_d @ Xsi )
% 2.75/3.04 = ( size_size_list_d @ Xsi2 ) )
% 2.75/3.04 => ( ! [I5: nat] :
% 2.75/3.04 ( ( member_nat @ I5 @ I3 )
% 2.75/3.04 => ( ( ord_less_nat @ I5 @ ( size_size_list_d @ Xs ) )
% 2.75/3.04 => ( ( ( size_size_list_d @ Xs )
% 2.75/3.04 = ( size_size_list_d @ Xsi ) )
% 2.75/3.04 => ( ( ( nth_d @ Xs @ I5 )
% 2.75/3.04 = ( nth_d @ Xs4 @ I5 ) )
% 2.75/3.04 & ( ( nth_d @ Xsi @ I5 )
% 2.75/3.04 = ( nth_d @ Xsi2 @ I5 ) )
% 2.75/3.04 & ( ( A @ ( nth_d @ Xs @ I5 ) @ ( nth_d @ Xsi @ I5 ) )
% 2.75/3.04 = ( A6 @ ( nth_d @ Xs4 @ I5 ) @ ( nth_d @ Xsi2 @ I5 ) ) ) ) ) ) )
% 2.75/3.04 => ( ( vEBT_L7260734717915818976sn_d_d @ I3 @ A @ Xs @ Xsi )
% 2.75/3.04 = ( vEBT_L7260734717915818976sn_d_d @ I7 @ A6 @ Xs4 @ Xsi2 ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % listI_assn_cong
% 2.75/3.04 thf(fact_734_listI__assn__cong,axiom,
% 2.75/3.04 ! [I3: set_nat,I7: set_nat,Xs: list_d,Xs4: list_d,Xsi: list_nat,Xsi2: list_nat,A: d > nat > assn,A6: d > nat > assn] :
% 2.75/3.04 ( ( I3 = I7 )
% 2.75/3.04 => ( ( ( size_size_list_d @ Xs )
% 2.75/3.04 = ( size_size_list_d @ Xs4 ) )
% 2.75/3.04 => ( ( ( size_size_list_nat @ Xsi )
% 2.75/3.04 = ( size_size_list_nat @ Xsi2 ) )
% 2.75/3.04 => ( ! [I5: nat] :
% 2.75/3.04 ( ( member_nat @ I5 @ I3 )
% 2.75/3.04 => ( ( ord_less_nat @ I5 @ ( size_size_list_d @ Xs ) )
% 2.75/3.04 => ( ( ( size_size_list_d @ Xs )
% 2.75/3.04 = ( size_size_list_nat @ Xsi ) )
% 2.75/3.04 => ( ( ( nth_d @ Xs @ I5 )
% 2.75/3.04 = ( nth_d @ Xs4 @ I5 ) )
% 2.75/3.04 & ( ( nth_nat @ Xsi @ I5 )
% 2.75/3.04 = ( nth_nat @ Xsi2 @ I5 ) )
% 2.75/3.04 & ( ( A @ ( nth_d @ Xs @ I5 ) @ ( nth_nat @ Xsi @ I5 ) )
% 2.75/3.04 = ( A6 @ ( nth_d @ Xs4 @ I5 ) @ ( nth_nat @ Xsi2 @ I5 ) ) ) ) ) ) )
% 2.75/3.04 => ( ( vEBT_L7820616366081188145_d_nat @ I3 @ A @ Xs @ Xsi )
% 2.75/3.04 = ( vEBT_L7820616366081188145_d_nat @ I7 @ A6 @ Xs4 @ Xsi2 ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % listI_assn_cong
% 2.75/3.04 thf(fact_735_listI__assn__cong,axiom,
% 2.75/3.04 ! [I3: set_nat,I7: set_nat,Xs: list_d,Xs4: list_d,Xsi: list_int,Xsi2: list_int,A: d > int > assn,A6: d > int > assn] :
% 2.75/3.04 ( ( I3 = I7 )
% 2.75/3.04 => ( ( ( size_size_list_d @ Xs )
% 2.75/3.04 = ( size_size_list_d @ Xs4 ) )
% 2.75/3.04 => ( ( ( size_size_list_int @ Xsi )
% 2.75/3.04 = ( size_size_list_int @ Xsi2 ) )
% 2.75/3.04 => ( ! [I5: nat] :
% 2.75/3.04 ( ( member_nat @ I5 @ I3 )
% 2.75/3.04 => ( ( ord_less_nat @ I5 @ ( size_size_list_d @ Xs ) )
% 2.75/3.04 => ( ( ( size_size_list_d @ Xs )
% 2.75/3.04 = ( size_size_list_int @ Xsi ) )
% 2.75/3.04 => ( ( ( nth_d @ Xs @ I5 )
% 2.75/3.04 = ( nth_d @ Xs4 @ I5 ) )
% 2.75/3.04 & ( ( nth_int @ Xsi @ I5 )
% 2.75/3.04 = ( nth_int @ Xsi2 @ I5 ) )
% 2.75/3.04 & ( ( A @ ( nth_d @ Xs @ I5 ) @ ( nth_int @ Xsi @ I5 ) )
% 2.75/3.04 = ( A6 @ ( nth_d @ Xs4 @ I5 ) @ ( nth_int @ Xsi2 @ I5 ) ) ) ) ) ) )
% 2.75/3.04 => ( ( vEBT_L7818125895572137869_d_int @ I3 @ A @ Xs @ Xsi )
% 2.75/3.04 = ( vEBT_L7818125895572137869_d_int @ I7 @ A6 @ Xs4 @ Xsi2 ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % listI_assn_cong
% 2.75/3.04 thf(fact_736_listI__assn__cong,axiom,
% 2.75/3.04 ! [I3: set_nat,I7: set_nat,Xs: list_nat,Xs4: list_nat,Xsi: list_c,Xsi2: list_c,A: nat > c > assn,A6: nat > c > assn] :
% 2.75/3.04 ( ( I3 = I7 )
% 2.75/3.04 => ( ( ( size_size_list_nat @ Xs )
% 2.75/3.04 = ( size_size_list_nat @ Xs4 ) )
% 2.75/3.04 => ( ( ( size_size_list_c @ Xsi )
% 2.75/3.04 = ( size_size_list_c @ Xsi2 ) )
% 2.75/3.04 => ( ! [I5: nat] :
% 2.75/3.04 ( ( member_nat @ I5 @ I3 )
% 2.75/3.04 => ( ( ord_less_nat @ I5 @ ( size_size_list_nat @ Xs ) )
% 2.75/3.04 => ( ( ( size_size_list_nat @ Xs )
% 2.75/3.04 = ( size_size_list_c @ Xsi ) )
% 2.75/3.04 => ( ( ( nth_nat @ Xs @ I5 )
% 2.75/3.04 = ( nth_nat @ Xs4 @ I5 ) )
% 2.75/3.04 & ( ( nth_c @ Xsi @ I5 )
% 2.75/3.04 = ( nth_c @ Xsi2 @ I5 ) )
% 2.75/3.04 & ( ( A @ ( nth_nat @ Xs @ I5 ) @ ( nth_c @ Xsi @ I5 ) )
% 2.75/3.04 = ( A6 @ ( nth_nat @ Xs4 @ I5 ) @ ( nth_c @ Xsi2 @ I5 ) ) ) ) ) ) )
% 2.75/3.04 => ( ( vEBT_L8146214880390291086_nat_c @ I3 @ A @ Xs @ Xsi )
% 2.75/3.04 = ( vEBT_L8146214880390291086_nat_c @ I7 @ A6 @ Xs4 @ Xsi2 ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % listI_assn_cong
% 2.75/3.04 thf(fact_737_listI__assn__cong,axiom,
% 2.75/3.04 ! [I3: set_nat,I7: set_nat,Xs: list_nat,Xs4: list_nat,Xsi: list_d,Xsi2: list_d,A: nat > d > assn,A6: nat > d > assn] :
% 2.75/3.04 ( ( I3 = I7 )
% 2.75/3.04 => ( ( ( size_size_list_nat @ Xs )
% 2.75/3.04 = ( size_size_list_nat @ Xs4 ) )
% 2.75/3.04 => ( ( ( size_size_list_d @ Xsi )
% 2.75/3.04 = ( size_size_list_d @ Xsi2 ) )
% 2.75/3.04 => ( ! [I5: nat] :
% 2.75/3.04 ( ( member_nat @ I5 @ I3 )
% 2.75/3.04 => ( ( ord_less_nat @ I5 @ ( size_size_list_nat @ Xs ) )
% 2.75/3.04 => ( ( ( size_size_list_nat @ Xs )
% 2.75/3.04 = ( size_size_list_d @ Xsi ) )
% 2.75/3.04 => ( ( ( nth_nat @ Xs @ I5 )
% 2.75/3.04 = ( nth_nat @ Xs4 @ I5 ) )
% 2.75/3.04 & ( ( nth_d @ Xsi @ I5 )
% 2.75/3.04 = ( nth_d @ Xsi2 @ I5 ) )
% 2.75/3.04 & ( ( A @ ( nth_nat @ Xs @ I5 ) @ ( nth_d @ Xsi @ I5 ) )
% 2.75/3.04 = ( A6 @ ( nth_nat @ Xs4 @ I5 ) @ ( nth_d @ Xsi2 @ I5 ) ) ) ) ) ) )
% 2.75/3.04 => ( ( vEBT_L8146214880390291087_nat_d @ I3 @ A @ Xs @ Xsi )
% 2.75/3.04 = ( vEBT_L8146214880390291087_nat_d @ I7 @ A6 @ Xs4 @ Xsi2 ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % listI_assn_cong
% 2.75/3.04 thf(fact_738_listI__assn__cong,axiom,
% 2.75/3.04 ! [I3: set_nat,I7: set_nat,Xs: list_nat,Xs4: list_nat,Xsi: list_nat,Xsi2: list_nat,A: nat > nat > assn,A6: nat > nat > assn] :
% 2.75/3.04 ( ( I3 = I7 )
% 2.75/3.04 => ( ( ( size_size_list_nat @ Xs )
% 2.75/3.04 = ( size_size_list_nat @ Xs4 ) )
% 2.75/3.04 => ( ( ( size_size_list_nat @ Xsi )
% 2.75/3.04 = ( size_size_list_nat @ Xsi2 ) )
% 2.75/3.04 => ( ! [I5: nat] :
% 2.75/3.04 ( ( member_nat @ I5 @ I3 )
% 2.75/3.04 => ( ( ord_less_nat @ I5 @ ( size_size_list_nat @ Xs ) )
% 2.75/3.04 => ( ( ( size_size_list_nat @ Xs )
% 2.75/3.04 = ( size_size_list_nat @ Xsi ) )
% 2.75/3.04 => ( ( ( nth_nat @ Xs @ I5 )
% 2.75/3.04 = ( nth_nat @ Xs4 @ I5 ) )
% 2.75/3.04 & ( ( nth_nat @ Xsi @ I5 )
% 2.75/3.04 = ( nth_nat @ Xsi2 @ I5 ) )
% 2.75/3.04 & ( ( A @ ( nth_nat @ Xs @ I5 ) @ ( nth_nat @ Xsi @ I5 ) )
% 2.75/3.04 = ( A6 @ ( nth_nat @ Xs4 @ I5 ) @ ( nth_nat @ Xsi2 @ I5 ) ) ) ) ) ) )
% 2.75/3.04 => ( ( vEBT_L7892069108621897922at_nat @ I3 @ A @ Xs @ Xsi )
% 2.75/3.04 = ( vEBT_L7892069108621897922at_nat @ I7 @ A6 @ Xs4 @ Xsi2 ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % listI_assn_cong
% 2.75/3.04 thf(fact_739_listI__assn__weak__cong,axiom,
% 2.75/3.04 ! [I3: set_nat,I7: set_nat,A: c > c > assn,A6: c > c > assn,Xs: list_c,Xs4: list_c,Xsi: list_c,Xsi2: list_c] :
% 2.75/3.04 ( ( I3 = I7 )
% 2.75/3.04 => ( ( A = A6 )
% 2.75/3.04 => ( ( ( size_size_list_c @ Xs )
% 2.75/3.04 = ( size_size_list_c @ Xs4 ) )
% 2.75/3.04 => ( ( ( size_size_list_c @ Xsi )
% 2.75/3.04 = ( size_size_list_c @ Xsi2 ) )
% 2.75/3.04 => ( ! [I5: nat] :
% 2.75/3.04 ( ( member_nat @ I5 @ I3 )
% 2.75/3.04 => ( ( ord_less_nat @ I5 @ ( size_size_list_c @ Xs ) )
% 2.75/3.04 => ( ( ( size_size_list_c @ Xs )
% 2.75/3.04 = ( size_size_list_c @ Xsi ) )
% 2.75/3.04 => ( ( ( nth_c @ Xs @ I5 )
% 2.75/3.04 = ( nth_c @ Xs4 @ I5 ) )
% 2.75/3.04 & ( ( nth_c @ Xsi @ I5 )
% 2.75/3.04 = ( nth_c @ Xsi2 @ I5 ) ) ) ) ) )
% 2.75/3.04 => ( ( vEBT_L824818263033719200sn_c_c @ I3 @ A @ Xs @ Xsi )
% 2.75/3.04 = ( vEBT_L824818263033719200sn_c_c @ I7 @ A6 @ Xs4 @ Xsi2 ) ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % listI_assn_weak_cong
% 2.75/3.04 thf(fact_740_listI__assn__weak__cong,axiom,
% 2.75/3.04 ! [I3: set_nat,I7: set_nat,A: c > nat > assn,A6: c > nat > assn,Xs: list_c,Xs4: list_c,Xsi: list_nat,Xsi2: list_nat] :
% 2.75/3.04 ( ( I3 = I7 )
% 2.75/3.04 => ( ( A = A6 )
% 2.75/3.04 => ( ( ( size_size_list_c @ Xs )
% 2.75/3.04 = ( size_size_list_c @ Xs4 ) )
% 2.75/3.04 => ( ( ( size_size_list_nat @ Xsi )
% 2.75/3.04 = ( size_size_list_nat @ Xsi2 ) )
% 2.75/3.04 => ( ! [I5: nat] :
% 2.75/3.04 ( ( member_nat @ I5 @ I3 )
% 2.75/3.04 => ( ( ord_less_nat @ I5 @ ( size_size_list_c @ Xs ) )
% 2.75/3.04 => ( ( ( size_size_list_c @ Xs )
% 2.75/3.04 = ( size_size_list_nat @ Xsi ) )
% 2.75/3.04 => ( ( ( nth_c @ Xs @ I5 )
% 2.75/3.04 = ( nth_c @ Xs4 @ I5 ) )
% 2.75/3.04 & ( ( nth_nat @ Xsi @ I5 )
% 2.75/3.04 = ( nth_nat @ Xsi2 @ I5 ) ) ) ) ) )
% 2.75/3.04 => ( ( vEBT_L6585172037124793648_c_nat @ I3 @ A @ Xs @ Xsi )
% 2.75/3.04 = ( vEBT_L6585172037124793648_c_nat @ I7 @ A6 @ Xs4 @ Xsi2 ) ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % listI_assn_weak_cong
% 2.75/3.04 thf(fact_741_listI__assn__weak__cong,axiom,
% 2.75/3.04 ! [I3: set_nat,I7: set_nat,A: c > int > assn,A6: c > int > assn,Xs: list_c,Xs4: list_c,Xsi: list_int,Xsi2: list_int] :
% 2.75/3.04 ( ( I3 = I7 )
% 2.75/3.04 => ( ( A = A6 )
% 2.75/3.04 => ( ( ( size_size_list_c @ Xs )
% 2.75/3.04 = ( size_size_list_c @ Xs4 ) )
% 2.75/3.04 => ( ( ( size_size_list_int @ Xsi )
% 2.75/3.04 = ( size_size_list_int @ Xsi2 ) )
% 2.75/3.04 => ( ! [I5: nat] :
% 2.75/3.04 ( ( member_nat @ I5 @ I3 )
% 2.75/3.04 => ( ( ord_less_nat @ I5 @ ( size_size_list_c @ Xs ) )
% 2.75/3.04 => ( ( ( size_size_list_c @ Xs )
% 2.75/3.04 = ( size_size_list_int @ Xsi ) )
% 2.75/3.04 => ( ( ( nth_c @ Xs @ I5 )
% 2.75/3.04 = ( nth_c @ Xs4 @ I5 ) )
% 2.75/3.04 & ( ( nth_int @ Xsi @ I5 )
% 2.75/3.04 = ( nth_int @ Xsi2 @ I5 ) ) ) ) ) )
% 2.75/3.04 => ( ( vEBT_L6582681566615743372_c_int @ I3 @ A @ Xs @ Xsi )
% 2.75/3.04 = ( vEBT_L6582681566615743372_c_int @ I7 @ A6 @ Xs4 @ Xsi2 ) ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % listI_assn_weak_cong
% 2.75/3.04 thf(fact_742_listI__assn__weak__cong,axiom,
% 2.75/3.04 ! [I3: set_nat,I7: set_nat,A: d > c > assn,A6: d > c > assn,Xs: list_d,Xs4: list_d,Xsi: list_c,Xsi2: list_c] :
% 2.75/3.04 ( ( I3 = I7 )
% 2.75/3.04 => ( ( A = A6 )
% 2.75/3.04 => ( ( ( size_size_list_d @ Xs )
% 2.75/3.04 = ( size_size_list_d @ Xs4 ) )
% 2.75/3.04 => ( ( ( size_size_list_c @ Xsi )
% 2.75/3.04 = ( size_size_list_c @ Xsi2 ) )
% 2.75/3.04 => ( ! [I5: nat] :
% 2.75/3.04 ( ( member_nat @ I5 @ I3 )
% 2.75/3.04 => ( ( ord_less_nat @ I5 @ ( size_size_list_d @ Xs ) )
% 2.75/3.04 => ( ( ( size_size_list_d @ Xs )
% 2.75/3.04 = ( size_size_list_c @ Xsi ) )
% 2.75/3.04 => ( ( ( nth_d @ Xs @ I5 )
% 2.75/3.04 = ( nth_d @ Xs4 @ I5 ) )
% 2.75/3.04 & ( ( nth_c @ Xsi @ I5 )
% 2.75/3.04 = ( nth_c @ Xsi2 @ I5 ) ) ) ) ) )
% 2.75/3.04 => ( ( vEBT_L7260734717915818975sn_d_c @ I3 @ A @ Xs @ Xsi )
% 2.75/3.04 = ( vEBT_L7260734717915818975sn_d_c @ I7 @ A6 @ Xs4 @ Xsi2 ) ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % listI_assn_weak_cong
% 2.75/3.04 thf(fact_743_listI__assn__weak__cong,axiom,
% 2.75/3.04 ! [I3: set_nat,I7: set_nat,A: d > d > assn,A6: d > d > assn,Xs: list_d,Xs4: list_d,Xsi: list_d,Xsi2: list_d] :
% 2.75/3.04 ( ( I3 = I7 )
% 2.75/3.04 => ( ( A = A6 )
% 2.75/3.04 => ( ( ( size_size_list_d @ Xs )
% 2.75/3.04 = ( size_size_list_d @ Xs4 ) )
% 2.75/3.04 => ( ( ( size_size_list_d @ Xsi )
% 2.75/3.04 = ( size_size_list_d @ Xsi2 ) )
% 2.75/3.04 => ( ! [I5: nat] :
% 2.75/3.04 ( ( member_nat @ I5 @ I3 )
% 2.75/3.04 => ( ( ord_less_nat @ I5 @ ( size_size_list_d @ Xs ) )
% 2.75/3.04 => ( ( ( size_size_list_d @ Xs )
% 2.75/3.04 = ( size_size_list_d @ Xsi ) )
% 2.75/3.04 => ( ( ( nth_d @ Xs @ I5 )
% 2.75/3.04 = ( nth_d @ Xs4 @ I5 ) )
% 2.75/3.04 & ( ( nth_d @ Xsi @ I5 )
% 2.75/3.04 = ( nth_d @ Xsi2 @ I5 ) ) ) ) ) )
% 2.75/3.04 => ( ( vEBT_L7260734717915818976sn_d_d @ I3 @ A @ Xs @ Xsi )
% 2.75/3.04 = ( vEBT_L7260734717915818976sn_d_d @ I7 @ A6 @ Xs4 @ Xsi2 ) ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % listI_assn_weak_cong
% 2.75/3.04 thf(fact_744_listI__assn__weak__cong,axiom,
% 2.75/3.04 ! [I3: set_nat,I7: set_nat,A: d > nat > assn,A6: d > nat > assn,Xs: list_d,Xs4: list_d,Xsi: list_nat,Xsi2: list_nat] :
% 2.75/3.04 ( ( I3 = I7 )
% 2.75/3.04 => ( ( A = A6 )
% 2.75/3.04 => ( ( ( size_size_list_d @ Xs )
% 2.75/3.04 = ( size_size_list_d @ Xs4 ) )
% 2.75/3.04 => ( ( ( size_size_list_nat @ Xsi )
% 2.75/3.04 = ( size_size_list_nat @ Xsi2 ) )
% 2.75/3.04 => ( ! [I5: nat] :
% 2.75/3.04 ( ( member_nat @ I5 @ I3 )
% 2.75/3.04 => ( ( ord_less_nat @ I5 @ ( size_size_list_d @ Xs ) )
% 2.75/3.04 => ( ( ( size_size_list_d @ Xs )
% 2.75/3.04 = ( size_size_list_nat @ Xsi ) )
% 2.75/3.04 => ( ( ( nth_d @ Xs @ I5 )
% 2.75/3.04 = ( nth_d @ Xs4 @ I5 ) )
% 2.75/3.04 & ( ( nth_nat @ Xsi @ I5 )
% 2.75/3.04 = ( nth_nat @ Xsi2 @ I5 ) ) ) ) ) )
% 2.75/3.04 => ( ( vEBT_L7820616366081188145_d_nat @ I3 @ A @ Xs @ Xsi )
% 2.75/3.04 = ( vEBT_L7820616366081188145_d_nat @ I7 @ A6 @ Xs4 @ Xsi2 ) ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % listI_assn_weak_cong
% 2.75/3.04 thf(fact_745_listI__assn__weak__cong,axiom,
% 2.75/3.04 ! [I3: set_nat,I7: set_nat,A: d > int > assn,A6: d > int > assn,Xs: list_d,Xs4: list_d,Xsi: list_int,Xsi2: list_int] :
% 2.75/3.04 ( ( I3 = I7 )
% 2.75/3.04 => ( ( A = A6 )
% 2.75/3.04 => ( ( ( size_size_list_d @ Xs )
% 2.75/3.04 = ( size_size_list_d @ Xs4 ) )
% 2.75/3.04 => ( ( ( size_size_list_int @ Xsi )
% 2.75/3.04 = ( size_size_list_int @ Xsi2 ) )
% 2.75/3.04 => ( ! [I5: nat] :
% 2.75/3.04 ( ( member_nat @ I5 @ I3 )
% 2.75/3.04 => ( ( ord_less_nat @ I5 @ ( size_size_list_d @ Xs ) )
% 2.75/3.04 => ( ( ( size_size_list_d @ Xs )
% 2.75/3.04 = ( size_size_list_int @ Xsi ) )
% 2.75/3.04 => ( ( ( nth_d @ Xs @ I5 )
% 2.75/3.04 = ( nth_d @ Xs4 @ I5 ) )
% 2.75/3.04 & ( ( nth_int @ Xsi @ I5 )
% 2.75/3.04 = ( nth_int @ Xsi2 @ I5 ) ) ) ) ) )
% 2.75/3.04 => ( ( vEBT_L7818125895572137869_d_int @ I3 @ A @ Xs @ Xsi )
% 2.75/3.04 = ( vEBT_L7818125895572137869_d_int @ I7 @ A6 @ Xs4 @ Xsi2 ) ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % listI_assn_weak_cong
% 2.75/3.04 thf(fact_746_listI__assn__weak__cong,axiom,
% 2.75/3.04 ! [I3: set_nat,I7: set_nat,A: nat > c > assn,A6: nat > c > assn,Xs: list_nat,Xs4: list_nat,Xsi: list_c,Xsi2: list_c] :
% 2.75/3.04 ( ( I3 = I7 )
% 2.75/3.04 => ( ( A = A6 )
% 2.75/3.04 => ( ( ( size_size_list_nat @ Xs )
% 2.75/3.04 = ( size_size_list_nat @ Xs4 ) )
% 2.75/3.04 => ( ( ( size_size_list_c @ Xsi )
% 2.75/3.04 = ( size_size_list_c @ Xsi2 ) )
% 2.75/3.04 => ( ! [I5: nat] :
% 2.75/3.04 ( ( member_nat @ I5 @ I3 )
% 2.75/3.04 => ( ( ord_less_nat @ I5 @ ( size_size_list_nat @ Xs ) )
% 2.75/3.04 => ( ( ( size_size_list_nat @ Xs )
% 2.75/3.04 = ( size_size_list_c @ Xsi ) )
% 2.75/3.04 => ( ( ( nth_nat @ Xs @ I5 )
% 2.75/3.04 = ( nth_nat @ Xs4 @ I5 ) )
% 2.75/3.04 & ( ( nth_c @ Xsi @ I5 )
% 2.75/3.04 = ( nth_c @ Xsi2 @ I5 ) ) ) ) ) )
% 2.75/3.04 => ( ( vEBT_L8146214880390291086_nat_c @ I3 @ A @ Xs @ Xsi )
% 2.75/3.04 = ( vEBT_L8146214880390291086_nat_c @ I7 @ A6 @ Xs4 @ Xsi2 ) ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % listI_assn_weak_cong
% 2.75/3.04 thf(fact_747_listI__assn__weak__cong,axiom,
% 2.75/3.04 ! [I3: set_nat,I7: set_nat,A: nat > d > assn,A6: nat > d > assn,Xs: list_nat,Xs4: list_nat,Xsi: list_d,Xsi2: list_d] :
% 2.75/3.04 ( ( I3 = I7 )
% 2.75/3.04 => ( ( A = A6 )
% 2.75/3.04 => ( ( ( size_size_list_nat @ Xs )
% 2.75/3.04 = ( size_size_list_nat @ Xs4 ) )
% 2.75/3.04 => ( ( ( size_size_list_d @ Xsi )
% 2.75/3.04 = ( size_size_list_d @ Xsi2 ) )
% 2.75/3.04 => ( ! [I5: nat] :
% 2.75/3.04 ( ( member_nat @ I5 @ I3 )
% 2.75/3.04 => ( ( ord_less_nat @ I5 @ ( size_size_list_nat @ Xs ) )
% 2.75/3.04 => ( ( ( size_size_list_nat @ Xs )
% 2.75/3.04 = ( size_size_list_d @ Xsi ) )
% 2.75/3.04 => ( ( ( nth_nat @ Xs @ I5 )
% 2.75/3.04 = ( nth_nat @ Xs4 @ I5 ) )
% 2.75/3.04 & ( ( nth_d @ Xsi @ I5 )
% 2.75/3.04 = ( nth_d @ Xsi2 @ I5 ) ) ) ) ) )
% 2.75/3.04 => ( ( vEBT_L8146214880390291087_nat_d @ I3 @ A @ Xs @ Xsi )
% 2.75/3.04 = ( vEBT_L8146214880390291087_nat_d @ I7 @ A6 @ Xs4 @ Xsi2 ) ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % listI_assn_weak_cong
% 2.75/3.04 thf(fact_748_listI__assn__weak__cong,axiom,
% 2.75/3.04 ! [I3: set_nat,I7: set_nat,A: nat > nat > assn,A6: nat > nat > assn,Xs: list_nat,Xs4: list_nat,Xsi: list_nat,Xsi2: list_nat] :
% 2.75/3.04 ( ( I3 = I7 )
% 2.75/3.04 => ( ( A = A6 )
% 2.75/3.04 => ( ( ( size_size_list_nat @ Xs )
% 2.75/3.04 = ( size_size_list_nat @ Xs4 ) )
% 2.75/3.04 => ( ( ( size_size_list_nat @ Xsi )
% 2.75/3.04 = ( size_size_list_nat @ Xsi2 ) )
% 2.75/3.04 => ( ! [I5: nat] :
% 2.75/3.04 ( ( member_nat @ I5 @ I3 )
% 2.75/3.04 => ( ( ord_less_nat @ I5 @ ( size_size_list_nat @ Xs ) )
% 2.75/3.04 => ( ( ( size_size_list_nat @ Xs )
% 2.75/3.04 = ( size_size_list_nat @ Xsi ) )
% 2.75/3.04 => ( ( ( nth_nat @ Xs @ I5 )
% 2.75/3.04 = ( nth_nat @ Xs4 @ I5 ) )
% 2.75/3.04 & ( ( nth_nat @ Xsi @ I5 )
% 2.75/3.04 = ( nth_nat @ Xsi2 @ I5 ) ) ) ) ) )
% 2.75/3.04 => ( ( vEBT_L7892069108621897922at_nat @ I3 @ A @ Xs @ Xsi )
% 2.75/3.04 = ( vEBT_L7892069108621897922at_nat @ I7 @ A6 @ Xs4 @ Xsi2 ) ) ) ) ) ) ) ).
% 2.75/3.04
% 2.75/3.04 % listI_assn_weak_cong
% 2.75/3.04 thf(fact_749_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 2.75/3.05 ! [A2: rat,C: rat,B2: rat] :
% 2.75/3.05 ( ( minus_minus_rat @ ( minus_minus_rat @ A2 @ C ) @ B2 )
% 2.75/3.05 = ( minus_minus_rat @ ( minus_minus_rat @ A2 @ B2 ) @ C ) ) ).
% 2.75/3.05
% 2.75/3.05 % cancel_ab_semigroup_add_class.diff_right_commute
% 2.75/3.05 thf(fact_750_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 2.75/3.05 ! [A2: nat,C: nat,B2: nat] :
% 2.75/3.05 ( ( minus_minus_nat @ ( minus_minus_nat @ A2 @ C ) @ B2 )
% 2.75/3.05 = ( minus_minus_nat @ ( minus_minus_nat @ A2 @ B2 ) @ C ) ) ).
% 2.75/3.05
% 2.75/3.05 % cancel_ab_semigroup_add_class.diff_right_commute
% 2.75/3.05 thf(fact_751_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 2.75/3.05 ! [A2: int,C: int,B2: int] :
% 2.75/3.05 ( ( minus_minus_int @ ( minus_minus_int @ A2 @ C ) @ B2 )
% 2.75/3.05 = ( minus_minus_int @ ( minus_minus_int @ A2 @ B2 ) @ C ) ) ).
% 2.75/3.05
% 2.75/3.05 % cancel_ab_semigroup_add_class.diff_right_commute
% 2.75/3.05 thf(fact_752_diff__eq__diff__eq,axiom,
% 2.75/3.05 ! [A2: rat,B2: rat,C: rat,D2: rat] :
% 2.75/3.05 ( ( ( minus_minus_rat @ A2 @ B2 )
% 2.75/3.05 = ( minus_minus_rat @ C @ D2 ) )
% 2.75/3.05 => ( ( A2 = B2 )
% 2.75/3.05 = ( C = D2 ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % diff_eq_diff_eq
% 2.75/3.05 thf(fact_753_diff__eq__diff__eq,axiom,
% 2.75/3.05 ! [A2: int,B2: int,C: int,D2: int] :
% 2.75/3.05 ( ( ( minus_minus_int @ A2 @ B2 )
% 2.75/3.05 = ( minus_minus_int @ C @ D2 ) )
% 2.75/3.05 => ( ( A2 = B2 )
% 2.75/3.05 = ( C = D2 ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % diff_eq_diff_eq
% 2.75/3.05 thf(fact_754_is__singletonE,axiom,
% 2.75/3.05 ! [A: set_Pr4329608150637261639at_nat] :
% 2.75/3.05 ( ( is_sin2937591304547752795at_nat @ A )
% 2.75/3.05 => ~ ! [X3: produc3843707927480180839at_nat] :
% 2.75/3.05 ( A
% 2.75/3.05 != ( insert9069300056098147895at_nat @ X3 @ bot_bo228742789529271731at_nat ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % is_singletonE
% 2.75/3.05 thf(fact_755_is__singletonE,axiom,
% 2.75/3.05 ! [A: set_Pr1261947904930325089at_nat] :
% 2.75/3.05 ( ( is_sin2850979758926227957at_nat @ A )
% 2.75/3.05 => ~ ! [X3: product_prod_nat_nat] :
% 2.75/3.05 ( A
% 2.75/3.05 != ( insert8211810215607154385at_nat @ X3 @ bot_bo2099793752762293965at_nat ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % is_singletonE
% 2.75/3.05 thf(fact_756_is__singletonE,axiom,
% 2.75/3.05 ! [A: set_o] :
% 2.75/3.05 ( ( is_singleton_o @ A )
% 2.75/3.05 => ~ ! [X3: $o] :
% 2.75/3.05 ( A
% 2.75/3.05 != ( insert_o2 @ X3 @ bot_bot_set_o ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % is_singletonE
% 2.75/3.05 thf(fact_757_is__singletonE,axiom,
% 2.75/3.05 ! [A: set_nat] :
% 2.75/3.05 ( ( is_singleton_nat @ A )
% 2.75/3.05 => ~ ! [X3: nat] :
% 2.75/3.05 ( A
% 2.75/3.05 != ( insert_nat2 @ X3 @ bot_bot_set_nat ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % is_singletonE
% 2.75/3.05 thf(fact_758_is__singletonE,axiom,
% 2.75/3.05 ! [A: set_int] :
% 2.75/3.05 ( ( is_singleton_int @ A )
% 2.75/3.05 => ~ ! [X3: int] :
% 2.75/3.05 ( A
% 2.75/3.05 != ( insert_int2 @ X3 @ bot_bot_set_int ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % is_singletonE
% 2.75/3.05 thf(fact_759_is__singleton__def,axiom,
% 2.75/3.05 ( is_sin2937591304547752795at_nat
% 2.75/3.05 = ( ^ [A5: set_Pr4329608150637261639at_nat] :
% 2.75/3.05 ? [X2: produc3843707927480180839at_nat] :
% 2.75/3.05 ( A5
% 2.75/3.05 = ( insert9069300056098147895at_nat @ X2 @ bot_bo228742789529271731at_nat ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % is_singleton_def
% 2.75/3.05 thf(fact_760_is__singleton__def,axiom,
% 2.75/3.05 ( is_sin2850979758926227957at_nat
% 2.75/3.05 = ( ^ [A5: set_Pr1261947904930325089at_nat] :
% 2.75/3.05 ? [X2: product_prod_nat_nat] :
% 2.75/3.05 ( A5
% 2.75/3.05 = ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % is_singleton_def
% 2.75/3.05 thf(fact_761_is__singleton__def,axiom,
% 2.75/3.05 ( is_singleton_o
% 2.75/3.05 = ( ^ [A5: set_o] :
% 2.75/3.05 ? [X2: $o] :
% 2.75/3.05 ( A5
% 2.75/3.05 = ( insert_o2 @ X2 @ bot_bot_set_o ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % is_singleton_def
% 2.75/3.05 thf(fact_762_is__singleton__def,axiom,
% 2.75/3.05 ( is_singleton_nat
% 2.75/3.05 = ( ^ [A5: set_nat] :
% 2.75/3.05 ? [X2: nat] :
% 2.75/3.05 ( A5
% 2.75/3.05 = ( insert_nat2 @ X2 @ bot_bot_set_nat ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % is_singleton_def
% 2.75/3.05 thf(fact_763_is__singleton__def,axiom,
% 2.75/3.05 ( is_singleton_int
% 2.75/3.05 = ( ^ [A5: set_int] :
% 2.75/3.05 ? [X2: int] :
% 2.75/3.05 ( A5
% 2.75/3.05 = ( insert_int2 @ X2 @ bot_bot_set_int ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % is_singleton_def
% 2.75/3.05 thf(fact_764_listI__assn__insert,axiom,
% 2.75/3.05 ! [I: nat,I3: set_nat,Xs: list_c,A: c > nat > assn,Xsi: list_nat] :
% 2.75/3.05 ( ~ ( member_nat @ I @ I3 )
% 2.75/3.05 => ( ( ord_less_nat @ I @ ( size_size_list_c @ Xs ) )
% 2.75/3.05 => ( ( vEBT_L6585172037124793648_c_nat @ ( insert_nat2 @ I @ I3 ) @ A @ Xs @ Xsi )
% 2.75/3.05 = ( times_times_assn @ ( A @ ( nth_c @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L6585172037124793648_c_nat @ I3 @ A @ Xs @ Xsi ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % listI_assn_insert
% 2.75/3.05 thf(fact_765_listI__assn__insert,axiom,
% 2.75/3.05 ! [I: nat,I3: set_nat,Xs: list_c,A: c > int > assn,Xsi: list_int] :
% 2.75/3.05 ( ~ ( member_nat @ I @ I3 )
% 2.75/3.05 => ( ( ord_less_nat @ I @ ( size_size_list_c @ Xs ) )
% 2.75/3.05 => ( ( vEBT_L6582681566615743372_c_int @ ( insert_nat2 @ I @ I3 ) @ A @ Xs @ Xsi )
% 2.75/3.05 = ( times_times_assn @ ( A @ ( nth_c @ Xs @ I ) @ ( nth_int @ Xsi @ I ) ) @ ( vEBT_L6582681566615743372_c_int @ I3 @ A @ Xs @ Xsi ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % listI_assn_insert
% 2.75/3.05 thf(fact_766_listI__assn__insert,axiom,
% 2.75/3.05 ! [I: nat,I3: set_nat,Xs: list_d,A: d > nat > assn,Xsi: list_nat] :
% 2.75/3.05 ( ~ ( member_nat @ I @ I3 )
% 2.75/3.05 => ( ( ord_less_nat @ I @ ( size_size_list_d @ Xs ) )
% 2.75/3.05 => ( ( vEBT_L7820616366081188145_d_nat @ ( insert_nat2 @ I @ I3 ) @ A @ Xs @ Xsi )
% 2.75/3.05 = ( times_times_assn @ ( A @ ( nth_d @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L7820616366081188145_d_nat @ I3 @ A @ Xs @ Xsi ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % listI_assn_insert
% 2.75/3.05 thf(fact_767_listI__assn__insert,axiom,
% 2.75/3.05 ! [I: nat,I3: set_nat,Xs: list_d,A: d > int > assn,Xsi: list_int] :
% 2.75/3.05 ( ~ ( member_nat @ I @ I3 )
% 2.75/3.05 => ( ( ord_less_nat @ I @ ( size_size_list_d @ Xs ) )
% 2.75/3.05 => ( ( vEBT_L7818125895572137869_d_int @ ( insert_nat2 @ I @ I3 ) @ A @ Xs @ Xsi )
% 2.75/3.05 = ( times_times_assn @ ( A @ ( nth_d @ Xs @ I ) @ ( nth_int @ Xsi @ I ) ) @ ( vEBT_L7818125895572137869_d_int @ I3 @ A @ Xs @ Xsi ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % listI_assn_insert
% 2.75/3.05 thf(fact_768_listI__assn__insert,axiom,
% 2.75/3.05 ! [I: nat,I3: set_nat,Xs: list_nat,A: nat > nat > assn,Xsi: list_nat] :
% 2.75/3.05 ( ~ ( member_nat @ I @ I3 )
% 2.75/3.05 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 2.75/3.05 => ( ( vEBT_L7892069108621897922at_nat @ ( insert_nat2 @ I @ I3 ) @ A @ Xs @ Xsi )
% 2.75/3.05 = ( times_times_assn @ ( A @ ( nth_nat @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L7892069108621897922at_nat @ I3 @ A @ Xs @ Xsi ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % listI_assn_insert
% 2.75/3.05 thf(fact_769_listI__assn__insert,axiom,
% 2.75/3.05 ! [I: nat,I3: set_nat,Xs: list_nat,A: nat > int > assn,Xsi: list_int] :
% 2.75/3.05 ( ~ ( member_nat @ I @ I3 )
% 2.75/3.05 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 2.75/3.05 => ( ( vEBT_L7889578638112847646at_int @ ( insert_nat2 @ I @ I3 ) @ A @ Xs @ Xsi )
% 2.75/3.05 = ( times_times_assn @ ( A @ ( nth_nat @ Xs @ I ) @ ( nth_int @ Xsi @ I ) ) @ ( vEBT_L7889578638112847646at_int @ I3 @ A @ Xs @ Xsi ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % listI_assn_insert
% 2.75/3.05 thf(fact_770_listI__assn__insert,axiom,
% 2.75/3.05 ! [I: nat,I3: set_nat,Xs: list_int,A: int > nat > assn,Xsi: list_nat] :
% 2.75/3.05 ( ~ ( member_nat @ I @ I3 )
% 2.75/3.05 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 2.75/3.05 => ( ( vEBT_L8891422820522952478nt_nat @ ( insert_nat2 @ I @ I3 ) @ A @ Xs @ Xsi )
% 2.75/3.05 = ( times_times_assn @ ( A @ ( nth_int @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L8891422820522952478nt_nat @ I3 @ A @ Xs @ Xsi ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % listI_assn_insert
% 2.75/3.05 thf(fact_771_listI__assn__insert,axiom,
% 2.75/3.05 ! [I: nat,I3: set_nat,Xs: list_int,A: int > int > assn,Xsi: list_int] :
% 2.75/3.05 ( ~ ( member_nat @ I @ I3 )
% 2.75/3.05 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 2.75/3.05 => ( ( vEBT_L8888932350013902202nt_int @ ( insert_nat2 @ I @ I3 ) @ A @ Xs @ Xsi )
% 2.75/3.05 = ( times_times_assn @ ( A @ ( nth_int @ Xs @ I ) @ ( nth_int @ Xsi @ I ) ) @ ( vEBT_L8888932350013902202nt_int @ I3 @ A @ Xs @ Xsi ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % listI_assn_insert
% 2.75/3.05 thf(fact_772_listI__assn__insert,axiom,
% 2.75/3.05 ! [I: nat,I3: set_nat,Xs: list_c,A: c > d > assn,Xsi: list_d] :
% 2.75/3.05 ( ~ ( member_nat @ I @ I3 )
% 2.75/3.05 => ( ( ord_less_nat @ I @ ( size_size_list_c @ Xs ) )
% 2.75/3.05 => ( ( vEBT_L824818263033719201sn_c_d @ ( insert_nat2 @ I @ I3 ) @ A @ Xs @ Xsi )
% 2.75/3.05 = ( times_times_assn @ ( A @ ( nth_c @ Xs @ I ) @ ( nth_d @ Xsi @ I ) ) @ ( vEBT_L824818263033719201sn_c_d @ I3 @ A @ Xs @ Xsi ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % listI_assn_insert
% 2.75/3.05 thf(fact_773_diff__strict__right__mono,axiom,
% 2.75/3.05 ! [A2: rat,B2: rat,C: rat] :
% 2.75/3.05 ( ( ord_less_rat @ A2 @ B2 )
% 2.75/3.05 => ( ord_less_rat @ ( minus_minus_rat @ A2 @ C ) @ ( minus_minus_rat @ B2 @ C ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % diff_strict_right_mono
% 2.75/3.05 thf(fact_774_diff__strict__right__mono,axiom,
% 2.75/3.05 ! [A2: code_integer,B2: code_integer,C: code_integer] :
% 2.75/3.05 ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 2.75/3.05 => ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A2 @ C ) @ ( minus_8373710615458151222nteger @ B2 @ C ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % diff_strict_right_mono
% 2.75/3.05 thf(fact_775_diff__strict__right__mono,axiom,
% 2.75/3.05 ! [A2: int,B2: int,C: int] :
% 2.75/3.05 ( ( ord_less_int @ A2 @ B2 )
% 2.75/3.05 => ( ord_less_int @ ( minus_minus_int @ A2 @ C ) @ ( minus_minus_int @ B2 @ C ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % diff_strict_right_mono
% 2.75/3.05 thf(fact_776_diff__strict__left__mono,axiom,
% 2.75/3.05 ! [B2: rat,A2: rat,C: rat] :
% 2.75/3.05 ( ( ord_less_rat @ B2 @ A2 )
% 2.75/3.05 => ( ord_less_rat @ ( minus_minus_rat @ C @ A2 ) @ ( minus_minus_rat @ C @ B2 ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % diff_strict_left_mono
% 2.75/3.05 thf(fact_777_diff__strict__left__mono,axiom,
% 2.75/3.05 ! [B2: code_integer,A2: code_integer,C: code_integer] :
% 2.75/3.05 ( ( ord_le6747313008572928689nteger @ B2 @ A2 )
% 2.75/3.05 => ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ C @ A2 ) @ ( minus_8373710615458151222nteger @ C @ B2 ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % diff_strict_left_mono
% 2.75/3.05 thf(fact_778_diff__strict__left__mono,axiom,
% 2.75/3.05 ! [B2: int,A2: int,C: int] :
% 2.75/3.05 ( ( ord_less_int @ B2 @ A2 )
% 2.75/3.05 => ( ord_less_int @ ( minus_minus_int @ C @ A2 ) @ ( minus_minus_int @ C @ B2 ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % diff_strict_left_mono
% 2.75/3.05 thf(fact_779_diff__eq__diff__less,axiom,
% 2.75/3.05 ! [A2: rat,B2: rat,C: rat,D2: rat] :
% 2.75/3.05 ( ( ( minus_minus_rat @ A2 @ B2 )
% 2.75/3.05 = ( minus_minus_rat @ C @ D2 ) )
% 2.75/3.05 => ( ( ord_less_rat @ A2 @ B2 )
% 2.75/3.05 = ( ord_less_rat @ C @ D2 ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % diff_eq_diff_less
% 2.75/3.05 thf(fact_780_diff__eq__diff__less,axiom,
% 2.75/3.05 ! [A2: code_integer,B2: code_integer,C: code_integer,D2: code_integer] :
% 2.75/3.05 ( ( ( minus_8373710615458151222nteger @ A2 @ B2 )
% 2.75/3.05 = ( minus_8373710615458151222nteger @ C @ D2 ) )
% 2.75/3.05 => ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 2.75/3.05 = ( ord_le6747313008572928689nteger @ C @ D2 ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % diff_eq_diff_less
% 2.75/3.05 thf(fact_781_diff__eq__diff__less,axiom,
% 2.75/3.05 ! [A2: int,B2: int,C: int,D2: int] :
% 2.75/3.05 ( ( ( minus_minus_int @ A2 @ B2 )
% 2.75/3.05 = ( minus_minus_int @ C @ D2 ) )
% 2.75/3.05 => ( ( ord_less_int @ A2 @ B2 )
% 2.75/3.05 = ( ord_less_int @ C @ D2 ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % diff_eq_diff_less
% 2.75/3.05 thf(fact_782_bot__empty__eq,axiom,
% 2.75/3.05 ( bot_bo7963750851167320836at_o_o
% 2.75/3.05 = ( ^ [X2: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X2 @ bot_bo7824918357723582233_nat_o ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % bot_empty_eq
% 2.75/3.05 thf(fact_783_bot__empty__eq,axiom,
% 2.75/3.05 ( bot_bo6829958733157050602_nat_o
% 2.75/3.05 = ( ^ [X2: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X2 @ bot_bo228742789529271731at_nat ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % bot_empty_eq
% 2.75/3.05 thf(fact_784_bot__empty__eq,axiom,
% 2.75/3.05 ( bot_bo482883023278783056_nat_o
% 2.75/3.05 = ( ^ [X2: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X2 @ bot_bo2099793752762293965at_nat ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % bot_empty_eq
% 2.75/3.05 thf(fact_785_bot__empty__eq,axiom,
% 2.75/3.05 ( bot_bot_o_o
% 2.75/3.05 = ( ^ [X2: $o] : ( member_o @ X2 @ bot_bot_set_o ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % bot_empty_eq
% 2.75/3.05 thf(fact_786_bot__empty__eq,axiom,
% 2.75/3.05 ( bot_bot_nat_o
% 2.75/3.05 = ( ^ [X2: nat] : ( member_nat @ X2 @ bot_bot_set_nat ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % bot_empty_eq
% 2.75/3.05 thf(fact_787_bot__empty__eq,axiom,
% 2.75/3.05 ( bot_bot_int_o
% 2.75/3.05 = ( ^ [X2: int] : ( member_int @ X2 @ bot_bot_set_int ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % bot_empty_eq
% 2.75/3.05 thf(fact_788_Collect__empty__eq__bot,axiom,
% 2.75/3.05 ! [P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 2.75/3.05 ( ( ( collec939566748876313656_nat_o @ P )
% 2.75/3.05 = bot_bo7824918357723582233_nat_o )
% 2.75/3.05 = ( P = bot_bo7963750851167320836at_o_o ) ) ).
% 2.75/3.05
% 2.75/3.05 % Collect_empty_eq_bot
% 2.75/3.05 thf(fact_789_Collect__empty__eq__bot,axiom,
% 2.75/3.05 ! [P: produc3843707927480180839at_nat > $o] :
% 2.75/3.05 ( ( ( collec6321179662152712658at_nat @ P )
% 2.75/3.05 = bot_bo228742789529271731at_nat )
% 2.75/3.05 = ( P = bot_bo6829958733157050602_nat_o ) ) ).
% 2.75/3.05
% 2.75/3.05 % Collect_empty_eq_bot
% 2.75/3.05 thf(fact_790_Collect__empty__eq__bot,axiom,
% 2.75/3.05 ! [P: product_prod_nat_nat > $o] :
% 2.75/3.05 ( ( ( collec3392354462482085612at_nat @ P )
% 2.75/3.05 = bot_bo2099793752762293965at_nat )
% 2.75/3.05 = ( P = bot_bo482883023278783056_nat_o ) ) ).
% 2.75/3.05
% 2.75/3.05 % Collect_empty_eq_bot
% 2.75/3.05 thf(fact_791_Collect__empty__eq__bot,axiom,
% 2.75/3.05 ! [P: $o > $o] :
% 2.75/3.05 ( ( ( collect_o @ P )
% 2.75/3.05 = bot_bot_set_o )
% 2.75/3.05 = ( P = bot_bot_o_o ) ) ).
% 2.75/3.05
% 2.75/3.05 % Collect_empty_eq_bot
% 2.75/3.05 thf(fact_792_Collect__empty__eq__bot,axiom,
% 2.75/3.05 ! [P: nat > $o] :
% 2.75/3.05 ( ( ( collect_nat @ P )
% 2.75/3.05 = bot_bot_set_nat )
% 2.75/3.05 = ( P = bot_bot_nat_o ) ) ).
% 2.75/3.05
% 2.75/3.05 % Collect_empty_eq_bot
% 2.75/3.05 thf(fact_793_Collect__empty__eq__bot,axiom,
% 2.75/3.05 ! [P: int > $o] :
% 2.75/3.05 ( ( ( collect_int @ P )
% 2.75/3.05 = bot_bot_set_int )
% 2.75/3.05 = ( P = bot_bot_int_o ) ) ).
% 2.75/3.05
% 2.75/3.05 % Collect_empty_eq_bot
% 2.75/3.05 thf(fact_794_remove__def,axiom,
% 2.75/3.05 ( remove5300788332298244428at_nat
% 2.75/3.05 = ( ^ [X2: produc3843707927480180839at_nat,A5: set_Pr4329608150637261639at_nat] : ( minus_3314409938677909166at_nat @ A5 @ ( insert9069300056098147895at_nat @ X2 @ bot_bo228742789529271731at_nat ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % remove_def
% 2.75/3.05 thf(fact_795_remove__def,axiom,
% 2.75/3.05 ( remove6466555014256735590at_nat
% 2.75/3.05 = ( ^ [X2: product_prod_nat_nat,A5: set_Pr1261947904930325089at_nat] : ( minus_1356011639430497352at_nat @ A5 @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % remove_def
% 2.75/3.05 thf(fact_796_remove__def,axiom,
% 2.75/3.05 ( remove_o
% 2.75/3.05 = ( ^ [X2: $o,A5: set_o] : ( minus_minus_set_o @ A5 @ ( insert_o2 @ X2 @ bot_bot_set_o ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % remove_def
% 2.75/3.05 thf(fact_797_remove__def,axiom,
% 2.75/3.05 ( remove_int
% 2.75/3.05 = ( ^ [X2: int,A5: set_int] : ( minus_minus_set_int @ A5 @ ( insert_int2 @ X2 @ bot_bot_set_int ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % remove_def
% 2.75/3.05 thf(fact_798_remove__def,axiom,
% 2.75/3.05 ( remove_nat
% 2.75/3.05 = ( ^ [X2: nat,A5: set_nat] : ( minus_minus_set_nat @ A5 @ ( insert_nat2 @ X2 @ bot_bot_set_nat ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % remove_def
% 2.75/3.05 thf(fact_799_insert__swap__set__eq,axiom,
% 2.75/3.05 ! [I: nat,L: list_P6011104703257516679at_nat,X: product_prod_nat_nat] :
% 2.75/3.05 ( ( ord_less_nat @ I @ ( size_s5460976970255530739at_nat @ L ) )
% 2.75/3.05 => ( ( insert8211810215607154385at_nat @ ( nth_Pr7617993195940197384at_nat @ L @ I ) @ ( set_Pr5648618587558075414at_nat @ ( list_u6180841689913720943at_nat @ L @ I @ X ) ) )
% 2.75/3.05 = ( insert8211810215607154385at_nat @ X @ ( set_Pr5648618587558075414at_nat @ L ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % insert_swap_set_eq
% 2.75/3.05 thf(fact_800_insert__swap__set__eq,axiom,
% 2.75/3.05 ! [I: nat,L: list_P5464809261938338413at_nat,X: produc3843707927480180839at_nat] :
% 2.75/3.05 ( ( ord_less_nat @ I @ ( size_s1588839187904960729at_nat @ L ) )
% 2.75/3.05 => ( ( insert9069300056098147895at_nat @ ( nth_Pr1239524528086697198at_nat @ L @ I ) @ ( set_Pr3765526544606949372at_nat @ ( list_u4696772448584712917at_nat @ L @ I @ X ) ) )
% 2.75/3.05 = ( insert9069300056098147895at_nat @ X @ ( set_Pr3765526544606949372at_nat @ L ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % insert_swap_set_eq
% 2.75/3.05 thf(fact_801_insert__swap__set__eq,axiom,
% 2.75/3.05 ! [I: nat,L: list_o,X: $o] :
% 2.75/3.05 ( ( ord_less_nat @ I @ ( size_size_list_o @ L ) )
% 2.75/3.05 => ( ( insert_o2 @ ( nth_o @ L @ I ) @ ( set_o2 @ ( list_update_o @ L @ I @ X ) ) )
% 2.75/3.05 = ( insert_o2 @ X @ ( set_o2 @ L ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % insert_swap_set_eq
% 2.75/3.05 thf(fact_802_insert__swap__set__eq,axiom,
% 2.75/3.05 ! [I: nat,L: list_P8527749157015355191n_assn,X: produc6575502325842934193n_assn] :
% 2.75/3.05 ( ( ord_less_nat @ I @ ( size_s6829681357464350627n_assn @ L ) )
% 2.75/3.05 => ( ( insert5290817439147925377n_assn @ ( nth_Pr1769885009046257848n_assn @ L @ I ) @ ( set_Pr1139785259514867910n_assn @ ( list_u4534839942911652127n_assn @ L @ I @ X ) ) )
% 2.75/3.05 = ( insert5290817439147925377n_assn @ X @ ( set_Pr1139785259514867910n_assn @ L ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % insert_swap_set_eq
% 2.75/3.05 thf(fact_803_insert__swap__set__eq,axiom,
% 2.75/3.05 ! [I: nat,L: list_c,X: c] :
% 2.75/3.05 ( ( ord_less_nat @ I @ ( size_size_list_c @ L ) )
% 2.75/3.05 => ( ( insert_c @ ( nth_c @ L @ I ) @ ( set_c2 @ ( list_update_c @ L @ I @ X ) ) )
% 2.75/3.05 = ( insert_c @ X @ ( set_c2 @ L ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % insert_swap_set_eq
% 2.75/3.05 thf(fact_804_insert__swap__set__eq,axiom,
% 2.75/3.05 ! [I: nat,L: list_d,X: d] :
% 2.75/3.05 ( ( ord_less_nat @ I @ ( size_size_list_d @ L ) )
% 2.75/3.05 => ( ( insert_d @ ( nth_d @ L @ I ) @ ( set_d2 @ ( list_update_d @ L @ I @ X ) ) )
% 2.75/3.05 = ( insert_d @ X @ ( set_d2 @ L ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % insert_swap_set_eq
% 2.75/3.05 thf(fact_805_insert__swap__set__eq,axiom,
% 2.75/3.05 ! [I: nat,L: list_nat,X: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I @ ( size_size_list_nat @ L ) )
% 2.75/3.05 => ( ( insert_nat2 @ ( nth_nat @ L @ I ) @ ( set_nat2 @ ( list_update_nat @ L @ I @ X ) ) )
% 2.75/3.05 = ( insert_nat2 @ X @ ( set_nat2 @ L ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % insert_swap_set_eq
% 2.75/3.05 thf(fact_806_insert__swap__set__eq,axiom,
% 2.75/3.05 ! [I: nat,L: list_int,X: int] :
% 2.75/3.05 ( ( ord_less_nat @ I @ ( size_size_list_int @ L ) )
% 2.75/3.05 => ( ( insert_int2 @ ( nth_int @ L @ I ) @ ( set_int2 @ ( list_update_int @ L @ I @ X ) ) )
% 2.75/3.05 = ( insert_int2 @ X @ ( set_int2 @ L ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % insert_swap_set_eq
% 2.75/3.05 thf(fact_807_set__swap,axiom,
% 2.75/3.05 ! [I: nat,Xs: list_P8527749157015355191n_assn,J: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I @ ( size_s6829681357464350627n_assn @ Xs ) )
% 2.75/3.05 => ( ( ord_less_nat @ J @ ( size_s6829681357464350627n_assn @ Xs ) )
% 2.75/3.05 => ( ( set_Pr1139785259514867910n_assn @ ( list_u4534839942911652127n_assn @ ( list_u4534839942911652127n_assn @ Xs @ I @ ( nth_Pr1769885009046257848n_assn @ Xs @ J ) ) @ J @ ( nth_Pr1769885009046257848n_assn @ Xs @ I ) ) )
% 2.75/3.05 = ( set_Pr1139785259514867910n_assn @ Xs ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % set_swap
% 2.75/3.05 thf(fact_808_set__swap,axiom,
% 2.75/3.05 ! [I: nat,Xs: list_c,J: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I @ ( size_size_list_c @ Xs ) )
% 2.75/3.05 => ( ( ord_less_nat @ J @ ( size_size_list_c @ Xs ) )
% 2.75/3.05 => ( ( set_c2 @ ( list_update_c @ ( list_update_c @ Xs @ I @ ( nth_c @ Xs @ J ) ) @ J @ ( nth_c @ Xs @ I ) ) )
% 2.75/3.05 = ( set_c2 @ Xs ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % set_swap
% 2.75/3.05 thf(fact_809_set__swap,axiom,
% 2.75/3.05 ! [I: nat,Xs: list_d,J: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I @ ( size_size_list_d @ Xs ) )
% 2.75/3.05 => ( ( ord_less_nat @ J @ ( size_size_list_d @ Xs ) )
% 2.75/3.05 => ( ( set_d2 @ ( list_update_d @ ( list_update_d @ Xs @ I @ ( nth_d @ Xs @ J ) ) @ J @ ( nth_d @ Xs @ I ) ) )
% 2.75/3.05 = ( set_d2 @ Xs ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % set_swap
% 2.75/3.05 thf(fact_810_set__swap,axiom,
% 2.75/3.05 ! [I: nat,Xs: list_nat,J: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 2.75/3.05 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs ) )
% 2.75/3.05 => ( ( set_nat2 @ ( list_update_nat @ ( list_update_nat @ Xs @ I @ ( nth_nat @ Xs @ J ) ) @ J @ ( nth_nat @ Xs @ I ) ) )
% 2.75/3.05 = ( set_nat2 @ Xs ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % set_swap
% 2.75/3.05 thf(fact_811_set__swap,axiom,
% 2.75/3.05 ! [I: nat,Xs: list_int,J: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 2.75/3.05 => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs ) )
% 2.75/3.05 => ( ( set_int2 @ ( list_update_int @ ( list_update_int @ Xs @ I @ ( nth_int @ Xs @ J ) ) @ J @ ( nth_int @ Xs @ I ) ) )
% 2.75/3.05 = ( set_int2 @ Xs ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % set_swap
% 2.75/3.05 thf(fact_812_Set_Ois__empty__def,axiom,
% 2.75/3.05 ( is_emp7572232645145209145at_nat
% 2.75/3.05 = ( ^ [A5: set_Pr4329608150637261639at_nat] : ( A5 = bot_bo228742789529271731at_nat ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % Set.is_empty_def
% 2.75/3.05 thf(fact_813_Set_Ois__empty__def,axiom,
% 2.75/3.05 ( is_emp1662574758705540307at_nat
% 2.75/3.05 = ( ^ [A5: set_Pr1261947904930325089at_nat] : ( A5 = bot_bo2099793752762293965at_nat ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % Set.is_empty_def
% 2.75/3.05 thf(fact_814_Set_Ois__empty__def,axiom,
% 2.75/3.05 ( is_empty_o
% 2.75/3.05 = ( ^ [A5: set_o] : ( A5 = bot_bot_set_o ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % Set.is_empty_def
% 2.75/3.05 thf(fact_815_Set_Ois__empty__def,axiom,
% 2.75/3.05 ( is_empty_nat
% 2.75/3.05 = ( ^ [A5: set_nat] : ( A5 = bot_bot_set_nat ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % Set.is_empty_def
% 2.75/3.05 thf(fact_816_Set_Ois__empty__def,axiom,
% 2.75/3.05 ( is_empty_int
% 2.75/3.05 = ( ^ [A5: set_int] : ( A5 = bot_bot_set_int ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % Set.is_empty_def
% 2.75/3.05 thf(fact_817_distinct__swap,axiom,
% 2.75/3.05 ! [I: nat,Xs: list_c,J: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I @ ( size_size_list_c @ Xs ) )
% 2.75/3.05 => ( ( ord_less_nat @ J @ ( size_size_list_c @ Xs ) )
% 2.75/3.05 => ( ( distinct_c @ ( list_update_c @ ( list_update_c @ Xs @ I @ ( nth_c @ Xs @ J ) ) @ J @ ( nth_c @ Xs @ I ) ) )
% 2.75/3.05 = ( distinct_c @ Xs ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % distinct_swap
% 2.75/3.05 thf(fact_818_distinct__swap,axiom,
% 2.75/3.05 ! [I: nat,Xs: list_d,J: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I @ ( size_size_list_d @ Xs ) )
% 2.75/3.05 => ( ( ord_less_nat @ J @ ( size_size_list_d @ Xs ) )
% 2.75/3.05 => ( ( distinct_d @ ( list_update_d @ ( list_update_d @ Xs @ I @ ( nth_d @ Xs @ J ) ) @ J @ ( nth_d @ Xs @ I ) ) )
% 2.75/3.05 = ( distinct_d @ Xs ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % distinct_swap
% 2.75/3.05 thf(fact_819_distinct__swap,axiom,
% 2.75/3.05 ! [I: nat,Xs: list_nat,J: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 2.75/3.05 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs ) )
% 2.75/3.05 => ( ( distinct_nat @ ( list_update_nat @ ( list_update_nat @ Xs @ I @ ( nth_nat @ Xs @ J ) ) @ J @ ( nth_nat @ Xs @ I ) ) )
% 2.75/3.05 = ( distinct_nat @ Xs ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % distinct_swap
% 2.75/3.05 thf(fact_820_distinct__swap,axiom,
% 2.75/3.05 ! [I: nat,Xs: list_int,J: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 2.75/3.05 => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs ) )
% 2.75/3.05 => ( ( distinct_int @ ( list_update_int @ ( list_update_int @ Xs @ I @ ( nth_int @ Xs @ J ) ) @ J @ ( nth_int @ Xs @ I ) ) )
% 2.75/3.05 = ( distinct_int @ Xs ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % distinct_swap
% 2.75/3.05 thf(fact_821_list__ex__length,axiom,
% 2.75/3.05 ( list_ex_c
% 2.75/3.05 = ( ^ [P2: c > $o,Xs3: list_c] :
% 2.75/3.05 ? [N2: nat] :
% 2.75/3.05 ( ( ord_less_nat @ N2 @ ( size_size_list_c @ Xs3 ) )
% 2.75/3.05 & ( P2 @ ( nth_c @ Xs3 @ N2 ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % list_ex_length
% 2.75/3.05 thf(fact_822_list__ex__length,axiom,
% 2.75/3.05 ( list_ex_d
% 2.75/3.05 = ( ^ [P2: d > $o,Xs3: list_d] :
% 2.75/3.05 ? [N2: nat] :
% 2.75/3.05 ( ( ord_less_nat @ N2 @ ( size_size_list_d @ Xs3 ) )
% 2.75/3.05 & ( P2 @ ( nth_d @ Xs3 @ N2 ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % list_ex_length
% 2.75/3.05 thf(fact_823_list__ex__length,axiom,
% 2.75/3.05 ( list_ex_nat
% 2.75/3.05 = ( ^ [P2: nat > $o,Xs3: list_nat] :
% 2.75/3.05 ? [N2: nat] :
% 2.75/3.05 ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs3 ) )
% 2.75/3.05 & ( P2 @ ( nth_nat @ Xs3 @ N2 ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % list_ex_length
% 2.75/3.05 thf(fact_824_list__ex__length,axiom,
% 2.75/3.05 ( list_ex_int
% 2.75/3.05 = ( ^ [P2: int > $o,Xs3: list_int] :
% 2.75/3.05 ? [N2: nat] :
% 2.75/3.05 ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs3 ) )
% 2.75/3.05 & ( P2 @ ( nth_int @ Xs3 @ N2 ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % list_ex_length
% 2.75/3.05 thf(fact_825_ent__pure__post__iff,axiom,
% 2.75/3.05 ! [P: assn,Q: assn,B2: $o] :
% 2.75/3.05 ( ( entails @ P @ ( times_times_assn @ Q @ ( pure_assn @ B2 ) ) )
% 2.75/3.05 = ( ! [H3: produc3658429121746597890et_nat] :
% 2.75/3.05 ( ( rep_assn @ P @ H3 )
% 2.75/3.05 => B2 )
% 2.75/3.05 & ( entails @ P @ Q ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % ent_pure_post_iff
% 2.75/3.05 thf(fact_826_pure__assn__eq__conv,axiom,
% 2.75/3.05 ! [P: $o,Q: $o] :
% 2.75/3.05 ( ( ( pure_assn @ P )
% 2.75/3.05 = ( pure_assn @ Q ) )
% 2.75/3.05 = ( P = Q ) ) ).
% 2.75/3.05
% 2.75/3.05 % pure_assn_eq_conv
% 2.75/3.05 thf(fact_827_member__remove,axiom,
% 2.75/3.05 ! [X: produc3843707927480180839at_nat,Y: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat] :
% 2.75/3.05 ( ( member8757157785044589968at_nat @ X @ ( remove5300788332298244428at_nat @ Y @ A ) )
% 2.75/3.05 = ( ( member8757157785044589968at_nat @ X @ A )
% 2.75/3.05 & ( X != Y ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % member_remove
% 2.75/3.05 thf(fact_828_member__remove,axiom,
% 2.75/3.05 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat] :
% 2.75/3.05 ( ( member8440522571783428010at_nat @ X @ ( remove6466555014256735590at_nat @ Y @ A ) )
% 2.75/3.05 = ( ( member8440522571783428010at_nat @ X @ A )
% 2.75/3.05 & ( X != Y ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % member_remove
% 2.75/3.05 thf(fact_829_member__remove,axiom,
% 2.75/3.05 ! [X: nat,Y: nat,A: set_nat] :
% 2.75/3.05 ( ( member_nat @ X @ ( remove_nat @ Y @ A ) )
% 2.75/3.05 = ( ( member_nat @ X @ A )
% 2.75/3.05 & ( X != Y ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % member_remove
% 2.75/3.05 thf(fact_830_member__remove,axiom,
% 2.75/3.05 ! [X: int,Y: int,A: set_int] :
% 2.75/3.05 ( ( member_int @ X @ ( remove_int @ Y @ A ) )
% 2.75/3.05 = ( ( member_int @ X @ A )
% 2.75/3.05 & ( X != Y ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % member_remove
% 2.75/3.05 thf(fact_831_member__remove,axiom,
% 2.75/3.05 ! [X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o] :
% 2.75/3.05 ( ( member6576561426505652726_nat_o @ X @ ( remove4651630035290841522_nat_o @ Y @ A ) )
% 2.75/3.05 = ( ( member6576561426505652726_nat_o @ X @ A )
% 2.75/3.05 & ( X != Y ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % member_remove
% 2.75/3.05 thf(fact_832_merge__pure__star,axiom,
% 2.75/3.05 ! [A2: $o,B2: $o] :
% 2.75/3.05 ( ( times_times_assn @ ( pure_assn @ A2 ) @ ( pure_assn @ B2 ) )
% 2.75/3.05 = ( pure_assn
% 2.75/3.05 @ ( A2
% 2.75/3.05 & B2 ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % merge_pure_star
% 2.75/3.05 thf(fact_833_pure__false,axiom,
% 2.75/3.05 ( ( pure_assn @ $false )
% 2.75/3.05 = bot_bot_assn ) ).
% 2.75/3.05
% 2.75/3.05 % pure_false
% 2.75/3.05 thf(fact_834_pure__assn__eq__false__iff,axiom,
% 2.75/3.05 ! [P: $o] :
% 2.75/3.05 ( ( ( pure_assn @ P )
% 2.75/3.05 = bot_bot_assn )
% 2.75/3.05 = ~ P ) ).
% 2.75/3.05
% 2.75/3.05 % pure_assn_eq_false_iff
% 2.75/3.05 thf(fact_835_mod__pure__star__dist,axiom,
% 2.75/3.05 ! [P: assn,B2: $o,H2: produc3658429121746597890et_nat] :
% 2.75/3.05 ( ( rep_assn @ ( times_times_assn @ P @ ( pure_assn @ B2 ) ) @ H2 )
% 2.75/3.05 = ( ( rep_assn @ P @ H2 )
% 2.75/3.05 & B2 ) ) ).
% 2.75/3.05
% 2.75/3.05 % mod_pure_star_dist
% 2.75/3.05 thf(fact_836_ent__pure__pre__iff,axiom,
% 2.75/3.05 ! [P: assn,B2: $o,Q: assn] :
% 2.75/3.05 ( ( entails @ ( times_times_assn @ P @ ( pure_assn @ B2 ) ) @ Q )
% 2.75/3.05 = ( B2
% 2.75/3.05 => ( entails @ P @ Q ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % ent_pure_pre_iff
% 2.75/3.05 thf(fact_837_mod__h__bot__iff_I5_J,axiom,
% 2.75/3.05 ! [P: assn,Q: assn,H2: heap_e7401611519738050253t_unit] :
% 2.75/3.05 ( ( rep_assn @ ( times_times_assn @ P @ Q ) @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) )
% 2.75/3.05 = ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) )
% 2.75/3.05 & ( rep_assn @ Q @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % mod_h_bot_iff(5)
% 2.75/3.05 thf(fact_838_mod__h__bot__iff_I1_J,axiom,
% 2.75/3.05 ! [B2: $o,H2: heap_e7401611519738050253t_unit] :
% 2.75/3.05 ( ( rep_assn @ ( pure_assn @ B2 ) @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) )
% 2.75/3.05 = B2 ) ).
% 2.75/3.05
% 2.75/3.05 % mod_h_bot_iff(1)
% 2.75/3.05 thf(fact_839_list__ex__cong,axiom,
% 2.75/3.05 ! [Xs: list_P5464809261938338413at_nat,Ys: list_P5464809261938338413at_nat,F4: produc3843707927480180839at_nat > $o,G: produc3843707927480180839at_nat > $o] :
% 2.75/3.05 ( ( Xs = Ys )
% 2.75/3.05 => ( ! [X3: produc3843707927480180839at_nat] :
% 2.75/3.05 ( ( member8757157785044589968at_nat @ X3 @ ( set_Pr3765526544606949372at_nat @ Ys ) )
% 2.75/3.05 => ( ( F4 @ X3 )
% 2.75/3.05 = ( G @ X3 ) ) )
% 2.75/3.05 => ( ( list_e5181628221095382443at_nat @ F4 @ Xs )
% 2.75/3.05 = ( list_e5181628221095382443at_nat @ G @ Ys ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % list_ex_cong
% 2.75/3.05 thf(fact_840_list__ex__cong,axiom,
% 2.75/3.05 ! [Xs: list_P6011104703257516679at_nat,Ys: list_P6011104703257516679at_nat,F4: product_prod_nat_nat > $o,G: product_prod_nat_nat > $o] :
% 2.75/3.05 ( ( Xs = Ys )
% 2.75/3.05 => ( ! [X3: product_prod_nat_nat] :
% 2.75/3.05 ( ( member8440522571783428010at_nat @ X3 @ ( set_Pr5648618587558075414at_nat @ Ys ) )
% 2.75/3.05 => ( ( F4 @ X3 )
% 2.75/3.05 = ( G @ X3 ) ) )
% 2.75/3.05 => ( ( list_e7689525607045846085at_nat @ F4 @ Xs )
% 2.75/3.05 = ( list_e7689525607045846085at_nat @ G @ Ys ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % list_ex_cong
% 2.75/3.05 thf(fact_841_list__ex__cong,axiom,
% 2.75/3.05 ! [Xs: list_P7985473006766602707_nat_o,Ys: list_P7985473006766602707_nat_o,F4: ( produc3658429121746597890et_nat > $o ) > $o,G: ( produc3658429121746597890et_nat > $o ) > $o] :
% 2.75/3.05 ( ( Xs = Ys )
% 2.75/3.05 => ( ! [X3: produc3658429121746597890et_nat > $o] :
% 2.75/3.05 ( ( member6576561426505652726_nat_o @ X3 @ ( set_Pr400311997697478754_nat_o @ Ys ) )
% 2.75/3.05 => ( ( F4 @ X3 )
% 2.75/3.05 = ( G @ X3 ) ) )
% 2.75/3.05 => ( ( list_e4587384546317177617_nat_o @ F4 @ Xs )
% 2.75/3.05 = ( list_e4587384546317177617_nat_o @ G @ Ys ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % list_ex_cong
% 2.75/3.05 thf(fact_842_list__ex__cong,axiom,
% 2.75/3.05 ! [Xs: list_int,Ys: list_int,F4: int > $o,G: int > $o] :
% 2.75/3.05 ( ( Xs = Ys )
% 2.75/3.05 => ( ! [X3: int] :
% 2.75/3.05 ( ( member_int @ X3 @ ( set_int2 @ Ys ) )
% 2.75/3.05 => ( ( F4 @ X3 )
% 2.75/3.05 = ( G @ X3 ) ) )
% 2.75/3.05 => ( ( list_ex_int @ F4 @ Xs )
% 2.75/3.05 = ( list_ex_int @ G @ Ys ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % list_ex_cong
% 2.75/3.05 thf(fact_843_list__ex__cong,axiom,
% 2.75/3.05 ! [Xs: list_nat,Ys: list_nat,F4: nat > $o,G: nat > $o] :
% 2.75/3.05 ( ( Xs = Ys )
% 2.75/3.05 => ( ! [X3: nat] :
% 2.75/3.05 ( ( member_nat @ X3 @ ( set_nat2 @ Ys ) )
% 2.75/3.05 => ( ( F4 @ X3 )
% 2.75/3.05 = ( G @ X3 ) ) )
% 2.75/3.05 => ( ( list_ex_nat @ F4 @ Xs )
% 2.75/3.05 = ( list_ex_nat @ G @ Ys ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % list_ex_cong
% 2.75/3.05 thf(fact_844_list__ex__cong,axiom,
% 2.75/3.05 ! [Xs: list_P8527749157015355191n_assn,Ys: list_P8527749157015355191n_assn,F4: produc6575502325842934193n_assn > $o,G: produc6575502325842934193n_assn > $o] :
% 2.75/3.05 ( ( Xs = Ys )
% 2.75/3.05 => ( ! [X3: produc6575502325842934193n_assn] :
% 2.75/3.05 ( ( member7957490590177025114n_assn @ X3 @ ( set_Pr1139785259514867910n_assn @ Ys ) )
% 2.75/3.05 => ( ( F4 @ X3 )
% 2.75/3.05 = ( G @ X3 ) ) )
% 2.75/3.05 => ( ( list_e1087220904399170805n_assn @ F4 @ Xs )
% 2.75/3.05 = ( list_e1087220904399170805n_assn @ G @ Ys ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % list_ex_cong
% 2.75/3.05 thf(fact_845_sorted__list__of__set_Odistinct__if__distinct__map,axiom,
% 2.75/3.05 ! [Xs: list_int] :
% 2.75/3.05 ( ( distinct_int @ Xs )
% 2.75/3.05 => ( distinct_int @ Xs ) ) ).
% 2.75/3.05
% 2.75/3.05 % sorted_list_of_set.distinct_if_distinct_map
% 2.75/3.05 thf(fact_846_sorted__list__of__set_Odistinct__if__distinct__map,axiom,
% 2.75/3.05 ! [Xs: list_nat] :
% 2.75/3.05 ( ( distinct_nat @ Xs )
% 2.75/3.05 => ( distinct_nat @ Xs ) ) ).
% 2.75/3.05
% 2.75/3.05 % sorted_list_of_set.distinct_if_distinct_map
% 2.75/3.05 thf(fact_847_one__assn__raw_Ocases,axiom,
% 2.75/3.05 ! [X: produc3658429121746597890et_nat] :
% 2.75/3.05 ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.75/3.05 ( X
% 2.75/3.05 != ( produc7507926704131184380et_nat @ H @ As ) ) ).
% 2.75/3.05
% 2.75/3.05 % one_assn_raw.cases
% 2.75/3.05 thf(fact_848_bex2I,axiom,
% 2.75/3.05 ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,S: set_Pr4329608150637261639at_nat,P: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o] :
% 2.75/3.05 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A2 @ B2 ) @ S )
% 2.75/3.05 => ( ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A2 @ B2 ) @ S )
% 2.75/3.05 => ( P @ A2 @ B2 ) )
% 2.75/3.05 => ? [A4: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat] :
% 2.75/3.05 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A4 @ B4 ) @ S )
% 2.75/3.05 & ( P @ A4 @ B4 ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % bex2I
% 2.75/3.05 thf(fact_849_bex2I,axiom,
% 2.75/3.05 ! [A2: nat,B2: nat,S: set_Pr1261947904930325089at_nat,P: nat > nat > $o] :
% 2.75/3.05 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B2 ) @ S )
% 2.75/3.05 => ( ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B2 ) @ S )
% 2.75/3.05 => ( P @ A2 @ B2 ) )
% 2.75/3.05 => ? [A4: nat,B4: nat] :
% 2.75/3.05 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A4 @ B4 ) @ S )
% 2.75/3.05 & ( P @ A4 @ B4 ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % bex2I
% 2.75/3.05 thf(fact_850_bex2I,axiom,
% 2.75/3.05 ! [A2: produc6241069584506657477e_term > option6357759511663192854e_term,B2: produc8923325533196201883nteger,S: set_Pr1281608226676607948nteger,P: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o] :
% 2.75/3.05 ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ A2 @ B2 ) @ S )
% 2.75/3.05 => ( ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ A2 @ B2 ) @ S )
% 2.75/3.05 => ( P @ A2 @ B2 ) )
% 2.75/3.05 => ? [A4: produc6241069584506657477e_term > option6357759511663192854e_term,B4: produc8923325533196201883nteger] :
% 2.75/3.05 ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ A4 @ B4 ) @ S )
% 2.75/3.05 & ( P @ A4 @ B4 ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % bex2I
% 2.75/3.05 thf(fact_851_bex2I,axiom,
% 2.75/3.05 ! [A2: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat,S: set_Pr3286484037609594932et_nat,P: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o] :
% 2.75/3.05 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A2 @ B2 ) @ S )
% 2.75/3.05 => ( ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A2 @ B2 ) @ S )
% 2.75/3.05 => ( P @ A2 @ B2 ) )
% 2.75/3.05 => ? [A4: produc3658429121746597890et_nat > $o,B4: produc3658429121746597890et_nat] :
% 2.75/3.05 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A4 @ B4 ) @ S )
% 2.75/3.05 & ( P @ A4 @ B4 ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % bex2I
% 2.75/3.05 thf(fact_852_bex2I,axiom,
% 2.75/3.05 ! [A2: produc3658429121746597890et_nat > $o,B2: produc3925858234332021118et_nat,S: set_Pr8536935166611901872et_nat,P: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o] :
% 2.75/3.05 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A2 @ B2 ) @ S )
% 2.75/3.05 => ( ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A2 @ B2 ) @ S )
% 2.75/3.05 => ( P @ A2 @ B2 ) )
% 2.75/3.05 => ? [A4: produc3658429121746597890et_nat > $o,B4: produc3925858234332021118et_nat] :
% 2.75/3.05 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A4 @ B4 ) @ S )
% 2.75/3.05 & ( P @ A4 @ B4 ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % bex2I
% 2.75/3.05 thf(fact_853_bex2I,axiom,
% 2.75/3.05 ! [A2: produc8551481072490612790e_term > option6357759511663192854e_term,B2: product_prod_int_int,S: set_Pr9222295170931077689nt_int,P: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o] :
% 2.75/3.05 ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ A2 @ B2 ) @ S )
% 2.75/3.05 => ( ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ A2 @ B2 ) @ S )
% 2.75/3.05 => ( P @ A2 @ B2 ) )
% 2.75/3.05 => ? [A4: produc8551481072490612790e_term > option6357759511663192854e_term,B4: product_prod_int_int] :
% 2.75/3.05 ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ A4 @ B4 ) @ S )
% 2.75/3.05 & ( P @ A4 @ B4 ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % bex2I
% 2.75/3.05 thf(fact_854_bex2I,axiom,
% 2.75/3.05 ! [A2: int > option6357759511663192854e_term,B2: product_prod_int_int,S: set_Pr1872883991513573699nt_int,P: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o] :
% 2.75/3.05 ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ A2 @ B2 ) @ S )
% 2.75/3.05 => ( ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ A2 @ B2 ) @ S )
% 2.75/3.05 => ( P @ A2 @ B2 ) )
% 2.75/3.05 => ? [A4: int > option6357759511663192854e_term,B4: product_prod_int_int] :
% 2.75/3.05 ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ A4 @ B4 ) @ S )
% 2.75/3.05 & ( P @ A4 @ B4 ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % bex2I
% 2.75/3.05 thf(fact_855_pairself_Ocases,axiom,
% 2.75/3.05 ! [X: produc7773217078559923341nt_int] :
% 2.75/3.05 ~ ! [F5: int > option6357759511663192854e_term,A4: int,B4: int] :
% 2.75/3.05 ( X
% 2.75/3.05 != ( produc4305682042979456191nt_int @ F5 @ ( product_Pair_int_int @ A4 @ B4 ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % pairself.cases
% 2.75/3.05 thf(fact_856_list__assn__cong,axiom,
% 2.75/3.05 ! [Xs: list_int,Xs4: list_int,Xsi: list_int,Xsi2: list_int,A: int > int > assn,A6: int > int > assn] :
% 2.75/3.05 ( ( Xs = Xs4 )
% 2.75/3.05 => ( ( Xsi = Xsi2 )
% 2.75/3.05 => ( ! [X3: int,Xi: int] :
% 2.75/3.05 ( ( member_int @ X3 @ ( set_int2 @ Xs4 ) )
% 2.75/3.05 => ( ( member_int @ Xi @ ( set_int2 @ Xsi2 ) )
% 2.75/3.05 => ( ( A @ X3 @ Xi )
% 2.75/3.05 = ( A6 @ X3 @ Xi ) ) ) )
% 2.75/3.05 => ( ( vEBT_L74593716426352029nt_int @ A @ Xs @ Xsi )
% 2.75/3.05 = ( vEBT_L74593716426352029nt_int @ A6 @ Xs4 @ Xsi2 ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % list_assn_cong
% 2.75/3.05 thf(fact_857_list__assn__cong,axiom,
% 2.75/3.05 ! [Xs: list_int,Xs4: list_int,Xsi: list_nat,Xsi2: list_nat,A: int > nat > assn,A6: int > nat > assn] :
% 2.75/3.05 ( ( Xs = Xs4 )
% 2.75/3.05 => ( ( Xsi = Xsi2 )
% 2.75/3.05 => ( ! [X3: int,Xi: nat] :
% 2.75/3.05 ( ( member_int @ X3 @ ( set_int2 @ Xs4 ) )
% 2.75/3.05 => ( ( member_nat @ Xi @ ( set_nat2 @ Xsi2 ) )
% 2.75/3.05 => ( ( A @ X3 @ Xi )
% 2.75/3.05 = ( A6 @ X3 @ Xi ) ) ) )
% 2.75/3.05 => ( ( vEBT_L77084186935402305nt_nat @ A @ Xs @ Xsi )
% 2.75/3.05 = ( vEBT_L77084186935402305nt_nat @ A6 @ Xs4 @ Xsi2 ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % list_assn_cong
% 2.75/3.05 thf(fact_858_list__assn__cong,axiom,
% 2.75/3.05 ! [Xs: list_nat,Xs4: list_nat,Xsi: list_int,Xsi2: list_int,A: nat > int > assn,A6: nat > int > assn] :
% 2.75/3.05 ( ( Xs = Xs4 )
% 2.75/3.05 => ( ( Xsi = Xsi2 )
% 2.75/3.05 => ( ! [X3: nat,Xi: int] :
% 2.75/3.05 ( ( member_nat @ X3 @ ( set_nat2 @ Xs4 ) )
% 2.75/3.05 => ( ( member_int @ Xi @ ( set_int2 @ Xsi2 ) )
% 2.75/3.05 => ( ( A @ X3 @ Xi )
% 2.75/3.05 = ( A6 @ X3 @ Xi ) ) ) )
% 2.75/3.05 => ( ( vEBT_L8298612041380073281at_int @ A @ Xs @ Xsi )
% 2.75/3.05 = ( vEBT_L8298612041380073281at_int @ A6 @ Xs4 @ Xsi2 ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % list_assn_cong
% 2.75/3.05 thf(fact_859_list__assn__cong,axiom,
% 2.75/3.05 ! [Xs: list_nat,Xs4: list_nat,Xsi: list_nat,Xsi2: list_nat,A: nat > nat > assn,A6: nat > nat > assn] :
% 2.75/3.05 ( ( Xs = Xs4 )
% 2.75/3.05 => ( ( Xsi = Xsi2 )
% 2.75/3.05 => ( ! [X3: nat,Xi: nat] :
% 2.75/3.05 ( ( member_nat @ X3 @ ( set_nat2 @ Xs4 ) )
% 2.75/3.05 => ( ( member_nat @ Xi @ ( set_nat2 @ Xsi2 ) )
% 2.75/3.05 => ( ( A @ X3 @ Xi )
% 2.75/3.05 = ( A6 @ X3 @ Xi ) ) ) )
% 2.75/3.05 => ( ( vEBT_L8301102511889123557at_nat @ A @ Xs @ Xsi )
% 2.75/3.05 = ( vEBT_L8301102511889123557at_nat @ A6 @ Xs4 @ Xsi2 ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % list_assn_cong
% 2.75/3.05 thf(fact_860_list__assn__cong,axiom,
% 2.75/3.05 ! [Xs: list_P6011104703257516679at_nat,Xs4: list_P6011104703257516679at_nat,Xsi: list_int,Xsi2: list_int,A: product_prod_nat_nat > int > assn,A6: product_prod_nat_nat > int > assn] :
% 2.75/3.05 ( ( Xs = Xs4 )
% 2.75/3.05 => ( ( Xsi = Xsi2 )
% 2.75/3.05 => ( ! [X3: product_prod_nat_nat,Xi: int] :
% 2.75/3.05 ( ( member8440522571783428010at_nat @ X3 @ ( set_Pr5648618587558075414at_nat @ Xs4 ) )
% 2.75/3.05 => ( ( member_int @ Xi @ ( set_int2 @ Xsi2 ) )
% 2.75/3.05 => ( ( A @ X3 @ Xi )
% 2.75/3.05 = ( A6 @ X3 @ Xi ) ) ) )
% 2.75/3.05 => ( ( vEBT_L6295016686126367274at_int @ A @ Xs @ Xsi )
% 2.75/3.05 = ( vEBT_L6295016686126367274at_int @ A6 @ Xs4 @ Xsi2 ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % list_assn_cong
% 2.75/3.05 thf(fact_861_list__assn__cong,axiom,
% 2.75/3.05 ! [Xs: list_P6011104703257516679at_nat,Xs4: list_P6011104703257516679at_nat,Xsi: list_nat,Xsi2: list_nat,A: product_prod_nat_nat > nat > assn,A6: product_prod_nat_nat > nat > assn] :
% 2.75/3.05 ( ( Xs = Xs4 )
% 2.75/3.05 => ( ( Xsi = Xsi2 )
% 2.75/3.05 => ( ! [X3: product_prod_nat_nat,Xi: nat] :
% 2.75/3.05 ( ( member8440522571783428010at_nat @ X3 @ ( set_Pr5648618587558075414at_nat @ Xs4 ) )
% 2.75/3.05 => ( ( member_nat @ Xi @ ( set_nat2 @ Xsi2 ) )
% 2.75/3.05 => ( ( A @ X3 @ Xi )
% 2.75/3.05 = ( A6 @ X3 @ Xi ) ) ) )
% 2.75/3.05 => ( ( vEBT_L6297507156635417550at_nat @ A @ Xs @ Xsi )
% 2.75/3.05 = ( vEBT_L6297507156635417550at_nat @ A6 @ Xs4 @ Xsi2 ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % list_assn_cong
% 2.75/3.05 thf(fact_862_list__assn__cong,axiom,
% 2.75/3.05 ! [Xs: list_int,Xs4: list_int,Xsi: list_P6011104703257516679at_nat,Xsi2: list_P6011104703257516679at_nat,A: int > product_prod_nat_nat > assn,A6: int > product_prod_nat_nat > assn] :
% 2.75/3.05 ( ( Xs = Xs4 )
% 2.75/3.05 => ( ( Xsi = Xsi2 )
% 2.75/3.05 => ( ! [X3: int,Xi: product_prod_nat_nat] :
% 2.75/3.05 ( ( member_int @ X3 @ ( set_int2 @ Xs4 ) )
% 2.75/3.05 => ( ( member8440522571783428010at_nat @ Xi @ ( set_Pr5648618587558075414at_nat @ Xsi2 ) )
% 2.75/3.05 => ( ( A @ X3 @ Xi )
% 2.75/3.05 = ( A6 @ X3 @ Xi ) ) ) )
% 2.75/3.05 => ( ( vEBT_L3472024597287490640at_nat @ A @ Xs @ Xsi )
% 2.75/3.05 = ( vEBT_L3472024597287490640at_nat @ A6 @ Xs4 @ Xsi2 ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % list_assn_cong
% 2.75/3.05 thf(fact_863_list__assn__cong,axiom,
% 2.75/3.05 ! [Xs: list_int,Xs4: list_int,Xsi: list_P8527749157015355191n_assn,Xsi2: list_P8527749157015355191n_assn,A: int > produc6575502325842934193n_assn > assn,A6: int > produc6575502325842934193n_assn > assn] :
% 2.75/3.05 ( ( Xs = Xs4 )
% 2.75/3.05 => ( ( Xsi = Xsi2 )
% 2.75/3.05 => ( ! [X3: int,Xi: produc6575502325842934193n_assn] :
% 2.75/3.05 ( ( member_int @ X3 @ ( set_int2 @ Xs4 ) )
% 2.75/3.05 => ( ( member7957490590177025114n_assn @ Xi @ ( set_Pr1139785259514867910n_assn @ Xsi2 ) )
% 2.75/3.05 => ( ( A @ X3 @ Xi )
% 2.75/3.05 = ( A6 @ X3 @ Xi ) ) ) )
% 2.75/3.05 => ( ( vEBT_L1620274777744359680n_assn @ A @ Xs @ Xsi )
% 2.75/3.05 = ( vEBT_L1620274777744359680n_assn @ A6 @ Xs4 @ Xsi2 ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % list_assn_cong
% 2.75/3.05 thf(fact_864_list__assn__cong,axiom,
% 2.75/3.05 ! [Xs: list_nat,Xs4: list_nat,Xsi: list_P6011104703257516679at_nat,Xsi2: list_P6011104703257516679at_nat,A: nat > product_prod_nat_nat > assn,A6: nat > product_prod_nat_nat > assn] :
% 2.75/3.05 ( ( Xs = Xs4 )
% 2.75/3.05 => ( ( Xsi = Xsi2 )
% 2.75/3.05 => ( ! [X3: nat,Xi: product_prod_nat_nat] :
% 2.75/3.05 ( ( member_nat @ X3 @ ( set_nat2 @ Xs4 ) )
% 2.75/3.05 => ( ( member8440522571783428010at_nat @ Xi @ ( set_Pr5648618587558075414at_nat @ Xsi2 ) )
% 2.75/3.05 => ( ( A @ X3 @ Xi )
% 2.75/3.05 = ( A6 @ X3 @ Xi ) ) ) )
% 2.75/3.05 => ( ( vEBT_L434182512823356844at_nat @ A @ Xs @ Xsi )
% 2.75/3.05 = ( vEBT_L434182512823356844at_nat @ A6 @ Xs4 @ Xsi2 ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % list_assn_cong
% 2.75/3.05 thf(fact_865_list__assn__cong,axiom,
% 2.75/3.05 ! [Xs: list_nat,Xs4: list_nat,Xsi: list_P8527749157015355191n_assn,Xsi2: list_P8527749157015355191n_assn,A: nat > produc6575502325842934193n_assn > assn,A6: nat > produc6575502325842934193n_assn > assn] :
% 2.75/3.05 ( ( Xs = Xs4 )
% 2.75/3.05 => ( ( Xsi = Xsi2 )
% 2.75/3.05 => ( ! [X3: nat,Xi: produc6575502325842934193n_assn] :
% 2.75/3.05 ( ( member_nat @ X3 @ ( set_nat2 @ Xs4 ) )
% 2.75/3.05 => ( ( member7957490590177025114n_assn @ Xi @ ( set_Pr1139785259514867910n_assn @ Xsi2 ) )
% 2.75/3.05 => ( ( A @ X3 @ Xi )
% 2.75/3.05 = ( A6 @ X3 @ Xi ) ) ) )
% 2.75/3.05 => ( ( vEBT_L9083610150846024284n_assn @ A @ Xs @ Xsi )
% 2.75/3.05 = ( vEBT_L9083610150846024284n_assn @ A6 @ Xs4 @ Xsi2 ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % list_assn_cong
% 2.75/3.05 thf(fact_866_distinct__Ex1,axiom,
% 2.75/3.05 ! [Xs: list_P5464809261938338413at_nat,X: produc3843707927480180839at_nat] :
% 2.75/3.05 ( ( distin5355857245021852384at_nat @ Xs )
% 2.75/3.05 => ( ( member8757157785044589968at_nat @ X @ ( set_Pr3765526544606949372at_nat @ Xs ) )
% 2.75/3.05 => ? [X3: nat] :
% 2.75/3.05 ( ( ord_less_nat @ X3 @ ( size_s1588839187904960729at_nat @ Xs ) )
% 2.75/3.05 & ( ( nth_Pr1239524528086697198at_nat @ Xs @ X3 )
% 2.75/3.05 = X )
% 2.75/3.05 & ! [Y3: nat] :
% 2.75/3.05 ( ( ( ord_less_nat @ Y3 @ ( size_s1588839187904960729at_nat @ Xs ) )
% 2.75/3.05 & ( ( nth_Pr1239524528086697198at_nat @ Xs @ Y3 )
% 2.75/3.05 = X ) )
% 2.75/3.05 => ( Y3 = X3 ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % distinct_Ex1
% 2.75/3.05 thf(fact_867_distinct__Ex1,axiom,
% 2.75/3.05 ! [Xs: list_P6011104703257516679at_nat,X: product_prod_nat_nat] :
% 2.75/3.05 ( ( distin6923225563576452346at_nat @ Xs )
% 2.75/3.05 => ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 2.75/3.05 => ? [X3: nat] :
% 2.75/3.05 ( ( ord_less_nat @ X3 @ ( size_s5460976970255530739at_nat @ Xs ) )
% 2.75/3.05 & ( ( nth_Pr7617993195940197384at_nat @ Xs @ X3 )
% 2.75/3.05 = X )
% 2.75/3.05 & ! [Y3: nat] :
% 2.75/3.05 ( ( ( ord_less_nat @ Y3 @ ( size_s5460976970255530739at_nat @ Xs ) )
% 2.75/3.05 & ( ( nth_Pr7617993195940197384at_nat @ Xs @ Y3 )
% 2.75/3.05 = X ) )
% 2.75/3.05 => ( Y3 = X3 ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % distinct_Ex1
% 2.75/3.05 thf(fact_868_distinct__Ex1,axiom,
% 2.75/3.05 ! [Xs: list_P7985473006766602707_nat_o,X: produc3658429121746597890et_nat > $o] :
% 2.75/3.05 ( ( distin299582740263731014_nat_o @ Xs )
% 2.75/3.05 => ( ( member6576561426505652726_nat_o @ X @ ( set_Pr400311997697478754_nat_o @ Xs ) )
% 2.75/3.05 => ? [X3: nat] :
% 2.75/3.05 ( ( ord_less_nat @ X3 @ ( size_s8908918004648414271_nat_o @ Xs ) )
% 2.75/3.05 & ( ( nth_Pr6840583978799713108_nat_o @ Xs @ X3 )
% 2.75/3.05 = X )
% 2.75/3.05 & ! [Y3: nat] :
% 2.75/3.05 ( ( ( ord_less_nat @ Y3 @ ( size_s8908918004648414271_nat_o @ Xs ) )
% 2.75/3.05 & ( ( nth_Pr6840583978799713108_nat_o @ Xs @ Y3 )
% 2.75/3.05 = X ) )
% 2.75/3.05 => ( Y3 = X3 ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % distinct_Ex1
% 2.75/3.05 thf(fact_869_distinct__Ex1,axiom,
% 2.75/3.05 ! [Xs: list_P8527749157015355191n_assn,X: produc6575502325842934193n_assn] :
% 2.75/3.05 ( ( distin4809818325527169450n_assn @ Xs )
% 2.75/3.05 => ( ( member7957490590177025114n_assn @ X @ ( set_Pr1139785259514867910n_assn @ Xs ) )
% 2.75/3.05 => ? [X3: nat] :
% 2.75/3.05 ( ( ord_less_nat @ X3 @ ( size_s6829681357464350627n_assn @ Xs ) )
% 2.75/3.05 & ( ( nth_Pr1769885009046257848n_assn @ Xs @ X3 )
% 2.75/3.05 = X )
% 2.75/3.05 & ! [Y3: nat] :
% 2.75/3.05 ( ( ( ord_less_nat @ Y3 @ ( size_s6829681357464350627n_assn @ Xs ) )
% 2.75/3.05 & ( ( nth_Pr1769885009046257848n_assn @ Xs @ Y3 )
% 2.75/3.05 = X ) )
% 2.75/3.05 => ( Y3 = X3 ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % distinct_Ex1
% 2.75/3.05 thf(fact_870_distinct__Ex1,axiom,
% 2.75/3.05 ! [Xs: list_c,X: c] :
% 2.75/3.05 ( ( distinct_c @ Xs )
% 2.75/3.05 => ( ( member_c @ X @ ( set_c2 @ Xs ) )
% 2.75/3.05 => ? [X3: nat] :
% 2.75/3.05 ( ( ord_less_nat @ X3 @ ( size_size_list_c @ Xs ) )
% 2.75/3.05 & ( ( nth_c @ Xs @ X3 )
% 2.75/3.05 = X )
% 2.75/3.05 & ! [Y3: nat] :
% 2.75/3.05 ( ( ( ord_less_nat @ Y3 @ ( size_size_list_c @ Xs ) )
% 2.75/3.05 & ( ( nth_c @ Xs @ Y3 )
% 2.75/3.05 = X ) )
% 2.75/3.05 => ( Y3 = X3 ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % distinct_Ex1
% 2.75/3.05 thf(fact_871_distinct__Ex1,axiom,
% 2.75/3.05 ! [Xs: list_d,X: d] :
% 2.75/3.05 ( ( distinct_d @ Xs )
% 2.75/3.05 => ( ( member_d @ X @ ( set_d2 @ Xs ) )
% 2.75/3.05 => ? [X3: nat] :
% 2.75/3.05 ( ( ord_less_nat @ X3 @ ( size_size_list_d @ Xs ) )
% 2.75/3.05 & ( ( nth_d @ Xs @ X3 )
% 2.75/3.05 = X )
% 2.75/3.05 & ! [Y3: nat] :
% 2.75/3.05 ( ( ( ord_less_nat @ Y3 @ ( size_size_list_d @ Xs ) )
% 2.75/3.05 & ( ( nth_d @ Xs @ Y3 )
% 2.75/3.05 = X ) )
% 2.75/3.05 => ( Y3 = X3 ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % distinct_Ex1
% 2.75/3.05 thf(fact_872_distinct__Ex1,axiom,
% 2.75/3.05 ! [Xs: list_nat,X: nat] :
% 2.75/3.05 ( ( distinct_nat @ Xs )
% 2.75/3.05 => ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 2.75/3.05 => ? [X3: nat] :
% 2.75/3.05 ( ( ord_less_nat @ X3 @ ( size_size_list_nat @ Xs ) )
% 2.75/3.05 & ( ( nth_nat @ Xs @ X3 )
% 2.75/3.05 = X )
% 2.75/3.05 & ! [Y3: nat] :
% 2.75/3.05 ( ( ( ord_less_nat @ Y3 @ ( size_size_list_nat @ Xs ) )
% 2.75/3.05 & ( ( nth_nat @ Xs @ Y3 )
% 2.75/3.05 = X ) )
% 2.75/3.05 => ( Y3 = X3 ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % distinct_Ex1
% 2.75/3.05 thf(fact_873_distinct__Ex1,axiom,
% 2.75/3.05 ! [Xs: list_int,X: int] :
% 2.75/3.05 ( ( distinct_int @ Xs )
% 2.75/3.05 => ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 2.75/3.05 => ? [X3: nat] :
% 2.75/3.05 ( ( ord_less_nat @ X3 @ ( size_size_list_int @ Xs ) )
% 2.75/3.05 & ( ( nth_int @ Xs @ X3 )
% 2.75/3.05 = X )
% 2.75/3.05 & ! [Y3: nat] :
% 2.75/3.05 ( ( ( ord_less_nat @ Y3 @ ( size_size_list_int @ Xs ) )
% 2.75/3.05 & ( ( nth_int @ Xs @ Y3 )
% 2.75/3.05 = X ) )
% 2.75/3.05 => ( Y3 = X3 ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % distinct_Ex1
% 2.75/3.05 thf(fact_874_mod__h__bot__indep,axiom,
% 2.75/3.05 ! [P: assn,H2: heap_e7401611519738050253t_unit,H4: heap_e7401611519738050253t_unit] :
% 2.75/3.05 ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) )
% 2.75/3.05 = ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H4 @ bot_bot_set_nat ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % mod_h_bot_indep
% 2.75/3.05 thf(fact_875_distinct__list__update,axiom,
% 2.75/3.05 ! [Xs: list_P7985473006766602707_nat_o,A2: produc3658429121746597890et_nat > $o,I: nat] :
% 2.75/3.05 ( ( distin299582740263731014_nat_o @ Xs )
% 2.75/3.05 => ( ~ ( member6576561426505652726_nat_o @ A2 @ ( minus_1801376950450012436_nat_o @ ( set_Pr400311997697478754_nat_o @ Xs ) @ ( insert5175938949040314269_nat_o @ ( nth_Pr6840583978799713108_nat_o @ Xs @ I ) @ bot_bo7824918357723582233_nat_o ) ) )
% 2.75/3.05 => ( distin299582740263731014_nat_o @ ( list_u6943956310655620667_nat_o @ Xs @ I @ A2 ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % distinct_list_update
% 2.75/3.05 thf(fact_876_distinct__list__update,axiom,
% 2.75/3.05 ! [Xs: list_P8527749157015355191n_assn,A2: produc6575502325842934193n_assn,I: nat] :
% 2.75/3.05 ( ( distin4809818325527169450n_assn @ Xs )
% 2.75/3.05 => ( ~ ( member7957490590177025114n_assn @ A2 @ ( minus_2301194108115264760n_assn @ ( set_Pr1139785259514867910n_assn @ Xs ) @ ( insert5290817439147925377n_assn @ ( nth_Pr1769885009046257848n_assn @ Xs @ I ) @ bot_bo1176836662018730877n_assn ) ) )
% 2.75/3.05 => ( distin4809818325527169450n_assn @ ( list_u4534839942911652127n_assn @ Xs @ I @ A2 ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % distinct_list_update
% 2.75/3.05 thf(fact_877_distinct__list__update,axiom,
% 2.75/3.05 ! [Xs: list_c,A2: c,I: nat] :
% 2.75/3.05 ( ( distinct_c @ Xs )
% 2.75/3.05 => ( ~ ( member_c @ A2 @ ( minus_minus_set_c @ ( set_c2 @ Xs ) @ ( insert_c @ ( nth_c @ Xs @ I ) @ bot_bot_set_c ) ) )
% 2.75/3.05 => ( distinct_c @ ( list_update_c @ Xs @ I @ A2 ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % distinct_list_update
% 2.75/3.05 thf(fact_878_distinct__list__update,axiom,
% 2.75/3.05 ! [Xs: list_d,A2: d,I: nat] :
% 2.75/3.05 ( ( distinct_d @ Xs )
% 2.75/3.05 => ( ~ ( member_d @ A2 @ ( minus_minus_set_d @ ( set_d2 @ Xs ) @ ( insert_d @ ( nth_d @ Xs @ I ) @ bot_bot_set_d ) ) )
% 2.75/3.05 => ( distinct_d @ ( list_update_d @ Xs @ I @ A2 ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % distinct_list_update
% 2.75/3.05 thf(fact_879_distinct__list__update,axiom,
% 2.75/3.05 ! [Xs: list_P5464809261938338413at_nat,A2: produc3843707927480180839at_nat,I: nat] :
% 2.75/3.05 ( ( distin5355857245021852384at_nat @ Xs )
% 2.75/3.05 => ( ~ ( member8757157785044589968at_nat @ A2 @ ( minus_3314409938677909166at_nat @ ( set_Pr3765526544606949372at_nat @ Xs ) @ ( insert9069300056098147895at_nat @ ( nth_Pr1239524528086697198at_nat @ Xs @ I ) @ bot_bo228742789529271731at_nat ) ) )
% 2.75/3.05 => ( distin5355857245021852384at_nat @ ( list_u4696772448584712917at_nat @ Xs @ I @ A2 ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % distinct_list_update
% 2.75/3.05 thf(fact_880_distinct__list__update,axiom,
% 2.75/3.05 ! [Xs: list_P6011104703257516679at_nat,A2: product_prod_nat_nat,I: nat] :
% 2.75/3.05 ( ( distin6923225563576452346at_nat @ Xs )
% 2.75/3.05 => ( ~ ( member8440522571783428010at_nat @ A2 @ ( minus_1356011639430497352at_nat @ ( set_Pr5648618587558075414at_nat @ Xs ) @ ( insert8211810215607154385at_nat @ ( nth_Pr7617993195940197384at_nat @ Xs @ I ) @ bot_bo2099793752762293965at_nat ) ) )
% 2.75/3.05 => ( distin6923225563576452346at_nat @ ( list_u6180841689913720943at_nat @ Xs @ I @ A2 ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % distinct_list_update
% 2.75/3.05 thf(fact_881_distinct__list__update,axiom,
% 2.75/3.05 ! [Xs: list_o,A2: $o,I: nat] :
% 2.75/3.05 ( ( distinct_o @ Xs )
% 2.75/3.05 => ( ~ ( member_o @ A2 @ ( minus_minus_set_o @ ( set_o2 @ Xs ) @ ( insert_o2 @ ( nth_o @ Xs @ I ) @ bot_bot_set_o ) ) )
% 2.75/3.05 => ( distinct_o @ ( list_update_o @ Xs @ I @ A2 ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % distinct_list_update
% 2.75/3.05 thf(fact_882_distinct__list__update,axiom,
% 2.75/3.05 ! [Xs: list_int,A2: int,I: nat] :
% 2.75/3.05 ( ( distinct_int @ Xs )
% 2.75/3.05 => ( ~ ( member_int @ A2 @ ( minus_minus_set_int @ ( set_int2 @ Xs ) @ ( insert_int2 @ ( nth_int @ Xs @ I ) @ bot_bot_set_int ) ) )
% 2.75/3.05 => ( distinct_int @ ( list_update_int @ Xs @ I @ A2 ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % distinct_list_update
% 2.75/3.05 thf(fact_883_distinct__list__update,axiom,
% 2.75/3.05 ! [Xs: list_nat,A2: nat,I: nat] :
% 2.75/3.05 ( ( distinct_nat @ Xs )
% 2.75/3.05 => ( ~ ( member_nat @ A2 @ ( minus_minus_set_nat @ ( set_nat2 @ Xs ) @ ( insert_nat2 @ ( nth_nat @ Xs @ I ) @ bot_bot_set_nat ) ) )
% 2.75/3.05 => ( distinct_nat @ ( list_update_nat @ Xs @ I @ A2 ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % distinct_list_update
% 2.75/3.05 thf(fact_884_distinct__conv__nth,axiom,
% 2.75/3.05 ( distinct_c
% 2.75/3.05 = ( ^ [Xs3: list_c] :
% 2.75/3.05 ! [I4: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I4 @ ( size_size_list_c @ Xs3 ) )
% 2.75/3.05 => ! [J2: nat] :
% 2.75/3.05 ( ( ord_less_nat @ J2 @ ( size_size_list_c @ Xs3 ) )
% 2.75/3.05 => ( ( I4 != J2 )
% 2.75/3.05 => ( ( nth_c @ Xs3 @ I4 )
% 2.75/3.05 != ( nth_c @ Xs3 @ J2 ) ) ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % distinct_conv_nth
% 2.75/3.05 thf(fact_885_distinct__conv__nth,axiom,
% 2.75/3.05 ( distinct_d
% 2.75/3.05 = ( ^ [Xs3: list_d] :
% 2.75/3.05 ! [I4: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I4 @ ( size_size_list_d @ Xs3 ) )
% 2.75/3.05 => ! [J2: nat] :
% 2.75/3.05 ( ( ord_less_nat @ J2 @ ( size_size_list_d @ Xs3 ) )
% 2.75/3.05 => ( ( I4 != J2 )
% 2.75/3.05 => ( ( nth_d @ Xs3 @ I4 )
% 2.75/3.05 != ( nth_d @ Xs3 @ J2 ) ) ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % distinct_conv_nth
% 2.75/3.05 thf(fact_886_distinct__conv__nth,axiom,
% 2.75/3.05 ( distinct_nat
% 2.75/3.05 = ( ^ [Xs3: list_nat] :
% 2.75/3.05 ! [I4: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs3 ) )
% 2.75/3.05 => ! [J2: nat] :
% 2.75/3.05 ( ( ord_less_nat @ J2 @ ( size_size_list_nat @ Xs3 ) )
% 2.75/3.05 => ( ( I4 != J2 )
% 2.75/3.05 => ( ( nth_nat @ Xs3 @ I4 )
% 2.75/3.05 != ( nth_nat @ Xs3 @ J2 ) ) ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % distinct_conv_nth
% 2.75/3.05 thf(fact_887_distinct__conv__nth,axiom,
% 2.75/3.05 ( distinct_int
% 2.75/3.05 = ( ^ [Xs3: list_int] :
% 2.75/3.05 ! [I4: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs3 ) )
% 2.75/3.05 => ! [J2: nat] :
% 2.75/3.05 ( ( ord_less_nat @ J2 @ ( size_size_list_int @ Xs3 ) )
% 2.75/3.05 => ( ( I4 != J2 )
% 2.75/3.05 => ( ( nth_int @ Xs3 @ I4 )
% 2.75/3.05 != ( nth_int @ Xs3 @ J2 ) ) ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % distinct_conv_nth
% 2.75/3.05 thf(fact_888_nth__eq__iff__index__eq,axiom,
% 2.75/3.05 ! [Xs: list_c,I: nat,J: nat] :
% 2.75/3.05 ( ( distinct_c @ Xs )
% 2.75/3.05 => ( ( ord_less_nat @ I @ ( size_size_list_c @ Xs ) )
% 2.75/3.05 => ( ( ord_less_nat @ J @ ( size_size_list_c @ Xs ) )
% 2.75/3.05 => ( ( ( nth_c @ Xs @ I )
% 2.75/3.05 = ( nth_c @ Xs @ J ) )
% 2.75/3.05 = ( I = J ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % nth_eq_iff_index_eq
% 2.75/3.05 thf(fact_889_nth__eq__iff__index__eq,axiom,
% 2.75/3.05 ! [Xs: list_d,I: nat,J: nat] :
% 2.75/3.05 ( ( distinct_d @ Xs )
% 2.75/3.05 => ( ( ord_less_nat @ I @ ( size_size_list_d @ Xs ) )
% 2.75/3.05 => ( ( ord_less_nat @ J @ ( size_size_list_d @ Xs ) )
% 2.75/3.05 => ( ( ( nth_d @ Xs @ I )
% 2.75/3.05 = ( nth_d @ Xs @ J ) )
% 2.75/3.05 = ( I = J ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % nth_eq_iff_index_eq
% 2.75/3.05 thf(fact_890_nth__eq__iff__index__eq,axiom,
% 2.75/3.05 ! [Xs: list_nat,I: nat,J: nat] :
% 2.75/3.05 ( ( distinct_nat @ Xs )
% 2.75/3.05 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 2.75/3.05 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs ) )
% 2.75/3.05 => ( ( ( nth_nat @ Xs @ I )
% 2.75/3.05 = ( nth_nat @ Xs @ J ) )
% 2.75/3.05 = ( I = J ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % nth_eq_iff_index_eq
% 2.75/3.05 thf(fact_891_nth__eq__iff__index__eq,axiom,
% 2.75/3.05 ! [Xs: list_int,I: nat,J: nat] :
% 2.75/3.05 ( ( distinct_int @ Xs )
% 2.75/3.05 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 2.75/3.05 => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs ) )
% 2.75/3.05 => ( ( ( nth_int @ Xs @ I )
% 2.75/3.05 = ( nth_int @ Xs @ J ) )
% 2.75/3.05 = ( I = J ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % nth_eq_iff_index_eq
% 2.75/3.05 thf(fact_892_all__set__conv__nth,axiom,
% 2.75/3.05 ! [L: list_P8527749157015355191n_assn,P: produc6575502325842934193n_assn > $o] :
% 2.75/3.05 ( ( ! [X2: produc6575502325842934193n_assn] :
% 2.75/3.05 ( ( member7957490590177025114n_assn @ X2 @ ( set_Pr1139785259514867910n_assn @ L ) )
% 2.75/3.05 => ( P @ X2 ) ) )
% 2.75/3.05 = ( ! [I4: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I4 @ ( size_s6829681357464350627n_assn @ L ) )
% 2.75/3.05 => ( P @ ( nth_Pr1769885009046257848n_assn @ L @ I4 ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % all_set_conv_nth
% 2.75/3.05 thf(fact_893_all__set__conv__nth,axiom,
% 2.75/3.05 ! [L: list_c,P: c > $o] :
% 2.75/3.05 ( ( ! [X2: c] :
% 2.75/3.05 ( ( member_c @ X2 @ ( set_c2 @ L ) )
% 2.75/3.05 => ( P @ X2 ) ) )
% 2.75/3.05 = ( ! [I4: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I4 @ ( size_size_list_c @ L ) )
% 2.75/3.05 => ( P @ ( nth_c @ L @ I4 ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % all_set_conv_nth
% 2.75/3.05 thf(fact_894_all__set__conv__nth,axiom,
% 2.75/3.05 ! [L: list_d,P: d > $o] :
% 2.75/3.05 ( ( ! [X2: d] :
% 2.75/3.05 ( ( member_d @ X2 @ ( set_d2 @ L ) )
% 2.75/3.05 => ( P @ X2 ) ) )
% 2.75/3.05 = ( ! [I4: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I4 @ ( size_size_list_d @ L ) )
% 2.75/3.05 => ( P @ ( nth_d @ L @ I4 ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % all_set_conv_nth
% 2.75/3.05 thf(fact_895_all__set__conv__nth,axiom,
% 2.75/3.05 ! [L: list_nat,P: nat > $o] :
% 2.75/3.05 ( ( ! [X2: nat] :
% 2.75/3.05 ( ( member_nat @ X2 @ ( set_nat2 @ L ) )
% 2.75/3.05 => ( P @ X2 ) ) )
% 2.75/3.05 = ( ! [I4: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ L ) )
% 2.75/3.05 => ( P @ ( nth_nat @ L @ I4 ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % all_set_conv_nth
% 2.75/3.05 thf(fact_896_all__set__conv__nth,axiom,
% 2.75/3.05 ! [L: list_int,P: int > $o] :
% 2.75/3.05 ( ( ! [X2: int] :
% 2.75/3.05 ( ( member_int @ X2 @ ( set_int2 @ L ) )
% 2.75/3.05 => ( P @ X2 ) ) )
% 2.75/3.05 = ( ! [I4: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ L ) )
% 2.75/3.05 => ( P @ ( nth_int @ L @ I4 ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % all_set_conv_nth
% 2.75/3.05 thf(fact_897_nth__mem,axiom,
% 2.75/3.05 ! [N: nat,Xs: list_P5464809261938338413at_nat] :
% 2.75/3.05 ( ( ord_less_nat @ N @ ( size_s1588839187904960729at_nat @ Xs ) )
% 2.75/3.05 => ( member8757157785044589968at_nat @ ( nth_Pr1239524528086697198at_nat @ Xs @ N ) @ ( set_Pr3765526544606949372at_nat @ Xs ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % nth_mem
% 2.75/3.05 thf(fact_898_nth__mem,axiom,
% 2.75/3.05 ! [N: nat,Xs: list_P6011104703257516679at_nat] :
% 2.75/3.05 ( ( ord_less_nat @ N @ ( size_s5460976970255530739at_nat @ Xs ) )
% 2.75/3.05 => ( member8440522571783428010at_nat @ ( nth_Pr7617993195940197384at_nat @ Xs @ N ) @ ( set_Pr5648618587558075414at_nat @ Xs ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % nth_mem
% 2.75/3.05 thf(fact_899_nth__mem,axiom,
% 2.75/3.05 ! [N: nat,Xs: list_P7985473006766602707_nat_o] :
% 2.75/3.05 ( ( ord_less_nat @ N @ ( size_s8908918004648414271_nat_o @ Xs ) )
% 2.75/3.05 => ( member6576561426505652726_nat_o @ ( nth_Pr6840583978799713108_nat_o @ Xs @ N ) @ ( set_Pr400311997697478754_nat_o @ Xs ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % nth_mem
% 2.75/3.05 thf(fact_900_nth__mem,axiom,
% 2.75/3.05 ! [N: nat,Xs: list_P8527749157015355191n_assn] :
% 2.75/3.05 ( ( ord_less_nat @ N @ ( size_s6829681357464350627n_assn @ Xs ) )
% 2.75/3.05 => ( member7957490590177025114n_assn @ ( nth_Pr1769885009046257848n_assn @ Xs @ N ) @ ( set_Pr1139785259514867910n_assn @ Xs ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % nth_mem
% 2.75/3.05 thf(fact_901_nth__mem,axiom,
% 2.75/3.05 ! [N: nat,Xs: list_c] :
% 2.75/3.05 ( ( ord_less_nat @ N @ ( size_size_list_c @ Xs ) )
% 2.75/3.05 => ( member_c @ ( nth_c @ Xs @ N ) @ ( set_c2 @ Xs ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % nth_mem
% 2.75/3.05 thf(fact_902_nth__mem,axiom,
% 2.75/3.05 ! [N: nat,Xs: list_d] :
% 2.75/3.05 ( ( ord_less_nat @ N @ ( size_size_list_d @ Xs ) )
% 2.75/3.05 => ( member_d @ ( nth_d @ Xs @ N ) @ ( set_d2 @ Xs ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % nth_mem
% 2.75/3.05 thf(fact_903_nth__mem,axiom,
% 2.75/3.05 ! [N: nat,Xs: list_nat] :
% 2.75/3.05 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 2.75/3.05 => ( member_nat @ ( nth_nat @ Xs @ N ) @ ( set_nat2 @ Xs ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % nth_mem
% 2.75/3.05 thf(fact_904_nth__mem,axiom,
% 2.75/3.05 ! [N: nat,Xs: list_int] :
% 2.75/3.05 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 2.75/3.05 => ( member_int @ ( nth_int @ Xs @ N ) @ ( set_int2 @ Xs ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % nth_mem
% 2.75/3.05 thf(fact_905_list__ball__nth,axiom,
% 2.75/3.05 ! [N: nat,Xs: list_P8527749157015355191n_assn,P: produc6575502325842934193n_assn > $o] :
% 2.75/3.05 ( ( ord_less_nat @ N @ ( size_s6829681357464350627n_assn @ Xs ) )
% 2.75/3.05 => ( ! [X3: produc6575502325842934193n_assn] :
% 2.75/3.05 ( ( member7957490590177025114n_assn @ X3 @ ( set_Pr1139785259514867910n_assn @ Xs ) )
% 2.75/3.05 => ( P @ X3 ) )
% 2.75/3.05 => ( P @ ( nth_Pr1769885009046257848n_assn @ Xs @ N ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % list_ball_nth
% 2.75/3.05 thf(fact_906_list__ball__nth,axiom,
% 2.75/3.05 ! [N: nat,Xs: list_c,P: c > $o] :
% 2.75/3.05 ( ( ord_less_nat @ N @ ( size_size_list_c @ Xs ) )
% 2.75/3.05 => ( ! [X3: c] :
% 2.75/3.05 ( ( member_c @ X3 @ ( set_c2 @ Xs ) )
% 2.75/3.05 => ( P @ X3 ) )
% 2.75/3.05 => ( P @ ( nth_c @ Xs @ N ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % list_ball_nth
% 2.75/3.05 thf(fact_907_list__ball__nth,axiom,
% 2.75/3.05 ! [N: nat,Xs: list_d,P: d > $o] :
% 2.75/3.05 ( ( ord_less_nat @ N @ ( size_size_list_d @ Xs ) )
% 2.75/3.05 => ( ! [X3: d] :
% 2.75/3.05 ( ( member_d @ X3 @ ( set_d2 @ Xs ) )
% 2.75/3.05 => ( P @ X3 ) )
% 2.75/3.05 => ( P @ ( nth_d @ Xs @ N ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % list_ball_nth
% 2.75/3.05 thf(fact_908_list__ball__nth,axiom,
% 2.75/3.05 ! [N: nat,Xs: list_nat,P: nat > $o] :
% 2.75/3.05 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 2.75/3.05 => ( ! [X3: nat] :
% 2.75/3.05 ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 2.75/3.05 => ( P @ X3 ) )
% 2.75/3.05 => ( P @ ( nth_nat @ Xs @ N ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % list_ball_nth
% 2.75/3.05 thf(fact_909_list__ball__nth,axiom,
% 2.75/3.05 ! [N: nat,Xs: list_int,P: int > $o] :
% 2.75/3.05 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 2.75/3.05 => ( ! [X3: int] :
% 2.75/3.05 ( ( member_int @ X3 @ ( set_int2 @ Xs ) )
% 2.75/3.05 => ( P @ X3 ) )
% 2.75/3.05 => ( P @ ( nth_int @ Xs @ N ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % list_ball_nth
% 2.75/3.05 thf(fact_910_in__set__conv__nth,axiom,
% 2.75/3.05 ! [X: produc3843707927480180839at_nat,Xs: list_P5464809261938338413at_nat] :
% 2.75/3.05 ( ( member8757157785044589968at_nat @ X @ ( set_Pr3765526544606949372at_nat @ Xs ) )
% 2.75/3.05 = ( ? [I4: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I4 @ ( size_s1588839187904960729at_nat @ Xs ) )
% 2.75/3.05 & ( ( nth_Pr1239524528086697198at_nat @ Xs @ I4 )
% 2.75/3.05 = X ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_conv_nth
% 2.75/3.05 thf(fact_911_in__set__conv__nth,axiom,
% 2.75/3.05 ! [X: product_prod_nat_nat,Xs: list_P6011104703257516679at_nat] :
% 2.75/3.05 ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 2.75/3.05 = ( ? [I4: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I4 @ ( size_s5460976970255530739at_nat @ Xs ) )
% 2.75/3.05 & ( ( nth_Pr7617993195940197384at_nat @ Xs @ I4 )
% 2.75/3.05 = X ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_conv_nth
% 2.75/3.05 thf(fact_912_in__set__conv__nth,axiom,
% 2.75/3.05 ! [X: produc3658429121746597890et_nat > $o,Xs: list_P7985473006766602707_nat_o] :
% 2.75/3.05 ( ( member6576561426505652726_nat_o @ X @ ( set_Pr400311997697478754_nat_o @ Xs ) )
% 2.75/3.05 = ( ? [I4: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I4 @ ( size_s8908918004648414271_nat_o @ Xs ) )
% 2.75/3.05 & ( ( nth_Pr6840583978799713108_nat_o @ Xs @ I4 )
% 2.75/3.05 = X ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_conv_nth
% 2.75/3.05 thf(fact_913_in__set__conv__nth,axiom,
% 2.75/3.05 ! [X: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn] :
% 2.75/3.05 ( ( member7957490590177025114n_assn @ X @ ( set_Pr1139785259514867910n_assn @ Xs ) )
% 2.75/3.05 = ( ? [I4: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I4 @ ( size_s6829681357464350627n_assn @ Xs ) )
% 2.75/3.05 & ( ( nth_Pr1769885009046257848n_assn @ Xs @ I4 )
% 2.75/3.05 = X ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_conv_nth
% 2.75/3.05 thf(fact_914_in__set__conv__nth,axiom,
% 2.75/3.05 ! [X: c,Xs: list_c] :
% 2.75/3.05 ( ( member_c @ X @ ( set_c2 @ Xs ) )
% 2.75/3.05 = ( ? [I4: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I4 @ ( size_size_list_c @ Xs ) )
% 2.75/3.05 & ( ( nth_c @ Xs @ I4 )
% 2.75/3.05 = X ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_conv_nth
% 2.75/3.05 thf(fact_915_in__set__conv__nth,axiom,
% 2.75/3.05 ! [X: d,Xs: list_d] :
% 2.75/3.05 ( ( member_d @ X @ ( set_d2 @ Xs ) )
% 2.75/3.05 = ( ? [I4: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I4 @ ( size_size_list_d @ Xs ) )
% 2.75/3.05 & ( ( nth_d @ Xs @ I4 )
% 2.75/3.05 = X ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_conv_nth
% 2.75/3.05 thf(fact_916_in__set__conv__nth,axiom,
% 2.75/3.05 ! [X: nat,Xs: list_nat] :
% 2.75/3.05 ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 2.75/3.05 = ( ? [I4: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs ) )
% 2.75/3.05 & ( ( nth_nat @ Xs @ I4 )
% 2.75/3.05 = X ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_conv_nth
% 2.75/3.05 thf(fact_917_in__set__conv__nth,axiom,
% 2.75/3.05 ! [X: int,Xs: list_int] :
% 2.75/3.05 ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 2.75/3.05 = ( ? [I4: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs ) )
% 2.75/3.05 & ( ( nth_int @ Xs @ I4 )
% 2.75/3.05 = X ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_conv_nth
% 2.75/3.05 thf(fact_918_all__nth__imp__all__set,axiom,
% 2.75/3.05 ! [Xs: list_P5464809261938338413at_nat,P: produc3843707927480180839at_nat > $o,X: produc3843707927480180839at_nat] :
% 2.75/3.05 ( ! [I5: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I5 @ ( size_s1588839187904960729at_nat @ Xs ) )
% 2.75/3.05 => ( P @ ( nth_Pr1239524528086697198at_nat @ Xs @ I5 ) ) )
% 2.75/3.05 => ( ( member8757157785044589968at_nat @ X @ ( set_Pr3765526544606949372at_nat @ Xs ) )
% 2.75/3.05 => ( P @ X ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % all_nth_imp_all_set
% 2.75/3.05 thf(fact_919_all__nth__imp__all__set,axiom,
% 2.75/3.05 ! [Xs: list_P6011104703257516679at_nat,P: product_prod_nat_nat > $o,X: product_prod_nat_nat] :
% 2.75/3.05 ( ! [I5: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I5 @ ( size_s5460976970255530739at_nat @ Xs ) )
% 2.75/3.05 => ( P @ ( nth_Pr7617993195940197384at_nat @ Xs @ I5 ) ) )
% 2.75/3.05 => ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 2.75/3.05 => ( P @ X ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % all_nth_imp_all_set
% 2.75/3.05 thf(fact_920_all__nth__imp__all__set,axiom,
% 2.75/3.05 ! [Xs: list_P7985473006766602707_nat_o,P: ( produc3658429121746597890et_nat > $o ) > $o,X: produc3658429121746597890et_nat > $o] :
% 2.75/3.05 ( ! [I5: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I5 @ ( size_s8908918004648414271_nat_o @ Xs ) )
% 2.75/3.05 => ( P @ ( nth_Pr6840583978799713108_nat_o @ Xs @ I5 ) ) )
% 2.75/3.05 => ( ( member6576561426505652726_nat_o @ X @ ( set_Pr400311997697478754_nat_o @ Xs ) )
% 2.75/3.05 => ( P @ X ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % all_nth_imp_all_set
% 2.75/3.05 thf(fact_921_all__nth__imp__all__set,axiom,
% 2.75/3.05 ! [Xs: list_P8527749157015355191n_assn,P: produc6575502325842934193n_assn > $o,X: produc6575502325842934193n_assn] :
% 2.75/3.05 ( ! [I5: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I5 @ ( size_s6829681357464350627n_assn @ Xs ) )
% 2.75/3.05 => ( P @ ( nth_Pr1769885009046257848n_assn @ Xs @ I5 ) ) )
% 2.75/3.05 => ( ( member7957490590177025114n_assn @ X @ ( set_Pr1139785259514867910n_assn @ Xs ) )
% 2.75/3.05 => ( P @ X ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % all_nth_imp_all_set
% 2.75/3.05 thf(fact_922_all__nth__imp__all__set,axiom,
% 2.75/3.05 ! [Xs: list_c,P: c > $o,X: c] :
% 2.75/3.05 ( ! [I5: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I5 @ ( size_size_list_c @ Xs ) )
% 2.75/3.05 => ( P @ ( nth_c @ Xs @ I5 ) ) )
% 2.75/3.05 => ( ( member_c @ X @ ( set_c2 @ Xs ) )
% 2.75/3.05 => ( P @ X ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % all_nth_imp_all_set
% 2.75/3.05 thf(fact_923_all__nth__imp__all__set,axiom,
% 2.75/3.05 ! [Xs: list_d,P: d > $o,X: d] :
% 2.75/3.05 ( ! [I5: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I5 @ ( size_size_list_d @ Xs ) )
% 2.75/3.05 => ( P @ ( nth_d @ Xs @ I5 ) ) )
% 2.75/3.05 => ( ( member_d @ X @ ( set_d2 @ Xs ) )
% 2.75/3.05 => ( P @ X ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % all_nth_imp_all_set
% 2.75/3.05 thf(fact_924_all__nth__imp__all__set,axiom,
% 2.75/3.05 ! [Xs: list_nat,P: nat > $o,X: nat] :
% 2.75/3.05 ( ! [I5: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I5 @ ( size_size_list_nat @ Xs ) )
% 2.75/3.05 => ( P @ ( nth_nat @ Xs @ I5 ) ) )
% 2.75/3.05 => ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 2.75/3.05 => ( P @ X ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % all_nth_imp_all_set
% 2.75/3.05 thf(fact_925_all__nth__imp__all__set,axiom,
% 2.75/3.05 ! [Xs: list_int,P: int > $o,X: int] :
% 2.75/3.05 ( ! [I5: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I5 @ ( size_size_list_int @ Xs ) )
% 2.75/3.05 => ( P @ ( nth_int @ Xs @ I5 ) ) )
% 2.75/3.05 => ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 2.75/3.05 => ( P @ X ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % all_nth_imp_all_set
% 2.75/3.05 thf(fact_926_all__set__conv__all__nth,axiom,
% 2.75/3.05 ! [Xs: list_P8527749157015355191n_assn,P: produc6575502325842934193n_assn > $o] :
% 2.75/3.05 ( ( ! [X2: produc6575502325842934193n_assn] :
% 2.75/3.05 ( ( member7957490590177025114n_assn @ X2 @ ( set_Pr1139785259514867910n_assn @ Xs ) )
% 2.75/3.05 => ( P @ X2 ) ) )
% 2.75/3.05 = ( ! [I4: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I4 @ ( size_s6829681357464350627n_assn @ Xs ) )
% 2.75/3.05 => ( P @ ( nth_Pr1769885009046257848n_assn @ Xs @ I4 ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % all_set_conv_all_nth
% 2.75/3.05 thf(fact_927_all__set__conv__all__nth,axiom,
% 2.75/3.05 ! [Xs: list_c,P: c > $o] :
% 2.75/3.05 ( ( ! [X2: c] :
% 2.75/3.05 ( ( member_c @ X2 @ ( set_c2 @ Xs ) )
% 2.75/3.05 => ( P @ X2 ) ) )
% 2.75/3.05 = ( ! [I4: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I4 @ ( size_size_list_c @ Xs ) )
% 2.75/3.05 => ( P @ ( nth_c @ Xs @ I4 ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % all_set_conv_all_nth
% 2.75/3.05 thf(fact_928_all__set__conv__all__nth,axiom,
% 2.75/3.05 ! [Xs: list_d,P: d > $o] :
% 2.75/3.05 ( ( ! [X2: d] :
% 2.75/3.05 ( ( member_d @ X2 @ ( set_d2 @ Xs ) )
% 2.75/3.05 => ( P @ X2 ) ) )
% 2.75/3.05 = ( ! [I4: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I4 @ ( size_size_list_d @ Xs ) )
% 2.75/3.05 => ( P @ ( nth_d @ Xs @ I4 ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % all_set_conv_all_nth
% 2.75/3.05 thf(fact_929_all__set__conv__all__nth,axiom,
% 2.75/3.05 ! [Xs: list_nat,P: nat > $o] :
% 2.75/3.05 ( ( ! [X2: nat] :
% 2.75/3.05 ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 2.75/3.05 => ( P @ X2 ) ) )
% 2.75/3.05 = ( ! [I4: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs ) )
% 2.75/3.05 => ( P @ ( nth_nat @ Xs @ I4 ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % all_set_conv_all_nth
% 2.75/3.05 thf(fact_930_all__set__conv__all__nth,axiom,
% 2.75/3.05 ! [Xs: list_int,P: int > $o] :
% 2.75/3.05 ( ( ! [X2: int] :
% 2.75/3.05 ( ( member_int @ X2 @ ( set_int2 @ Xs ) )
% 2.75/3.05 => ( P @ X2 ) ) )
% 2.75/3.05 = ( ! [I4: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs ) )
% 2.75/3.05 => ( P @ ( nth_int @ Xs @ I4 ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % all_set_conv_all_nth
% 2.75/3.05 thf(fact_931_in__set__upd__eq__aux,axiom,
% 2.75/3.05 ! [I: nat,L: list_P5464809261938338413at_nat,X: produc3843707927480180839at_nat,Y: produc3843707927480180839at_nat] :
% 2.75/3.05 ( ( ord_less_nat @ I @ ( size_s1588839187904960729at_nat @ L ) )
% 2.75/3.05 => ( ( member8757157785044589968at_nat @ X @ ( set_Pr3765526544606949372at_nat @ ( list_u4696772448584712917at_nat @ L @ I @ Y ) ) )
% 2.75/3.05 = ( ( X = Y )
% 2.75/3.05 | ! [Y5: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X @ ( set_Pr3765526544606949372at_nat @ ( list_u4696772448584712917at_nat @ L @ I @ Y5 ) ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_upd_eq_aux
% 2.75/3.05 thf(fact_932_in__set__upd__eq__aux,axiom,
% 2.75/3.05 ! [I: nat,L: list_P6011104703257516679at_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 2.75/3.05 ( ( ord_less_nat @ I @ ( size_s5460976970255530739at_nat @ L ) )
% 2.75/3.05 => ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ ( list_u6180841689913720943at_nat @ L @ I @ Y ) ) )
% 2.75/3.05 = ( ( X = Y )
% 2.75/3.05 | ! [Y5: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ ( list_u6180841689913720943at_nat @ L @ I @ Y5 ) ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_upd_eq_aux
% 2.75/3.05 thf(fact_933_in__set__upd__eq__aux,axiom,
% 2.75/3.05 ! [I: nat,L: list_P7985473006766602707_nat_o,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat > $o] :
% 2.75/3.05 ( ( ord_less_nat @ I @ ( size_s8908918004648414271_nat_o @ L ) )
% 2.75/3.05 => ( ( member6576561426505652726_nat_o @ X @ ( set_Pr400311997697478754_nat_o @ ( list_u6943956310655620667_nat_o @ L @ I @ Y ) ) )
% 2.75/3.05 = ( ( X = Y )
% 2.75/3.05 | ! [Y5: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X @ ( set_Pr400311997697478754_nat_o @ ( list_u6943956310655620667_nat_o @ L @ I @ Y5 ) ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_upd_eq_aux
% 2.75/3.05 thf(fact_934_in__set__upd__eq__aux,axiom,
% 2.75/3.05 ! [I: nat,L: list_P8527749157015355191n_assn,X: produc6575502325842934193n_assn,Y: produc6575502325842934193n_assn] :
% 2.75/3.05 ( ( ord_less_nat @ I @ ( size_s6829681357464350627n_assn @ L ) )
% 2.75/3.05 => ( ( member7957490590177025114n_assn @ X @ ( set_Pr1139785259514867910n_assn @ ( list_u4534839942911652127n_assn @ L @ I @ Y ) ) )
% 2.75/3.05 = ( ( X = Y )
% 2.75/3.05 | ! [Y5: produc6575502325842934193n_assn] : ( member7957490590177025114n_assn @ X @ ( set_Pr1139785259514867910n_assn @ ( list_u4534839942911652127n_assn @ L @ I @ Y5 ) ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_upd_eq_aux
% 2.75/3.05 thf(fact_935_in__set__upd__eq__aux,axiom,
% 2.75/3.05 ! [I: nat,L: list_c,X: c,Y: c] :
% 2.75/3.05 ( ( ord_less_nat @ I @ ( size_size_list_c @ L ) )
% 2.75/3.05 => ( ( member_c @ X @ ( set_c2 @ ( list_update_c @ L @ I @ Y ) ) )
% 2.75/3.05 = ( ( X = Y )
% 2.75/3.05 | ! [Y5: c] : ( member_c @ X @ ( set_c2 @ ( list_update_c @ L @ I @ Y5 ) ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_upd_eq_aux
% 2.75/3.05 thf(fact_936_in__set__upd__eq__aux,axiom,
% 2.75/3.05 ! [I: nat,L: list_d,X: d,Y: d] :
% 2.75/3.05 ( ( ord_less_nat @ I @ ( size_size_list_d @ L ) )
% 2.75/3.05 => ( ( member_d @ X @ ( set_d2 @ ( list_update_d @ L @ I @ Y ) ) )
% 2.75/3.05 = ( ( X = Y )
% 2.75/3.05 | ! [Y5: d] : ( member_d @ X @ ( set_d2 @ ( list_update_d @ L @ I @ Y5 ) ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_upd_eq_aux
% 2.75/3.05 thf(fact_937_in__set__upd__eq__aux,axiom,
% 2.75/3.05 ! [I: nat,L: list_nat,X: nat,Y: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I @ ( size_size_list_nat @ L ) )
% 2.75/3.05 => ( ( member_nat @ X @ ( set_nat2 @ ( list_update_nat @ L @ I @ Y ) ) )
% 2.75/3.05 = ( ( X = Y )
% 2.75/3.05 | ! [Y5: nat] : ( member_nat @ X @ ( set_nat2 @ ( list_update_nat @ L @ I @ Y5 ) ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_upd_eq_aux
% 2.75/3.05 thf(fact_938_in__set__upd__eq__aux,axiom,
% 2.75/3.05 ! [I: nat,L: list_int,X: int,Y: int] :
% 2.75/3.05 ( ( ord_less_nat @ I @ ( size_size_list_int @ L ) )
% 2.75/3.05 => ( ( member_int @ X @ ( set_int2 @ ( list_update_int @ L @ I @ Y ) ) )
% 2.75/3.05 = ( ( X = Y )
% 2.75/3.05 | ! [Y5: int] : ( member_int @ X @ ( set_int2 @ ( list_update_int @ L @ I @ Y5 ) ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_upd_eq_aux
% 2.75/3.05 thf(fact_939_in__set__upd__cases,axiom,
% 2.75/3.05 ! [X: produc3843707927480180839at_nat,L: list_P5464809261938338413at_nat,I: nat,Y: produc3843707927480180839at_nat] :
% 2.75/3.05 ( ( member8757157785044589968at_nat @ X @ ( set_Pr3765526544606949372at_nat @ ( list_u4696772448584712917at_nat @ L @ I @ Y ) ) )
% 2.75/3.05 => ( ( ( ord_less_nat @ I @ ( size_s1588839187904960729at_nat @ L ) )
% 2.75/3.05 => ( X != Y ) )
% 2.75/3.05 => ( member8757157785044589968at_nat @ X @ ( set_Pr3765526544606949372at_nat @ L ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_upd_cases
% 2.75/3.05 thf(fact_940_in__set__upd__cases,axiom,
% 2.75/3.05 ! [X: product_prod_nat_nat,L: list_P6011104703257516679at_nat,I: nat,Y: product_prod_nat_nat] :
% 2.75/3.05 ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ ( list_u6180841689913720943at_nat @ L @ I @ Y ) ) )
% 2.75/3.05 => ( ( ( ord_less_nat @ I @ ( size_s5460976970255530739at_nat @ L ) )
% 2.75/3.05 => ( X != Y ) )
% 2.75/3.05 => ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ L ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_upd_cases
% 2.75/3.05 thf(fact_941_in__set__upd__cases,axiom,
% 2.75/3.05 ! [X: produc3658429121746597890et_nat > $o,L: list_P7985473006766602707_nat_o,I: nat,Y: produc3658429121746597890et_nat > $o] :
% 2.75/3.05 ( ( member6576561426505652726_nat_o @ X @ ( set_Pr400311997697478754_nat_o @ ( list_u6943956310655620667_nat_o @ L @ I @ Y ) ) )
% 2.75/3.05 => ( ( ( ord_less_nat @ I @ ( size_s8908918004648414271_nat_o @ L ) )
% 2.75/3.05 => ( X != Y ) )
% 2.75/3.05 => ( member6576561426505652726_nat_o @ X @ ( set_Pr400311997697478754_nat_o @ L ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_upd_cases
% 2.75/3.05 thf(fact_942_in__set__upd__cases,axiom,
% 2.75/3.05 ! [X: produc6575502325842934193n_assn,L: list_P8527749157015355191n_assn,I: nat,Y: produc6575502325842934193n_assn] :
% 2.75/3.05 ( ( member7957490590177025114n_assn @ X @ ( set_Pr1139785259514867910n_assn @ ( list_u4534839942911652127n_assn @ L @ I @ Y ) ) )
% 2.75/3.05 => ( ( ( ord_less_nat @ I @ ( size_s6829681357464350627n_assn @ L ) )
% 2.75/3.05 => ( X != Y ) )
% 2.75/3.05 => ( member7957490590177025114n_assn @ X @ ( set_Pr1139785259514867910n_assn @ L ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_upd_cases
% 2.75/3.05 thf(fact_943_in__set__upd__cases,axiom,
% 2.75/3.05 ! [X: c,L: list_c,I: nat,Y: c] :
% 2.75/3.05 ( ( member_c @ X @ ( set_c2 @ ( list_update_c @ L @ I @ Y ) ) )
% 2.75/3.05 => ( ( ( ord_less_nat @ I @ ( size_size_list_c @ L ) )
% 2.75/3.05 => ( X != Y ) )
% 2.75/3.05 => ( member_c @ X @ ( set_c2 @ L ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_upd_cases
% 2.75/3.05 thf(fact_944_in__set__upd__cases,axiom,
% 2.75/3.05 ! [X: d,L: list_d,I: nat,Y: d] :
% 2.75/3.05 ( ( member_d @ X @ ( set_d2 @ ( list_update_d @ L @ I @ Y ) ) )
% 2.75/3.05 => ( ( ( ord_less_nat @ I @ ( size_size_list_d @ L ) )
% 2.75/3.05 => ( X != Y ) )
% 2.75/3.05 => ( member_d @ X @ ( set_d2 @ L ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_upd_cases
% 2.75/3.05 thf(fact_945_in__set__upd__cases,axiom,
% 2.75/3.05 ! [X: nat,L: list_nat,I: nat,Y: nat] :
% 2.75/3.05 ( ( member_nat @ X @ ( set_nat2 @ ( list_update_nat @ L @ I @ Y ) ) )
% 2.75/3.05 => ( ( ( ord_less_nat @ I @ ( size_size_list_nat @ L ) )
% 2.75/3.05 => ( X != Y ) )
% 2.75/3.05 => ( member_nat @ X @ ( set_nat2 @ L ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_upd_cases
% 2.75/3.05 thf(fact_946_in__set__upd__cases,axiom,
% 2.75/3.05 ! [X: int,L: list_int,I: nat,Y: int] :
% 2.75/3.05 ( ( member_int @ X @ ( set_int2 @ ( list_update_int @ L @ I @ Y ) ) )
% 2.75/3.05 => ( ( ( ord_less_nat @ I @ ( size_size_list_int @ L ) )
% 2.75/3.05 => ( X != Y ) )
% 2.75/3.05 => ( member_int @ X @ ( set_int2 @ L ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_upd_cases
% 2.75/3.05 thf(fact_947_in__set__upd__eq,axiom,
% 2.75/3.05 ! [I: nat,L: list_P5464809261938338413at_nat,X: produc3843707927480180839at_nat,Y: produc3843707927480180839at_nat] :
% 2.75/3.05 ( ( ord_less_nat @ I @ ( size_s1588839187904960729at_nat @ L ) )
% 2.75/3.05 => ( ( member8757157785044589968at_nat @ X @ ( set_Pr3765526544606949372at_nat @ ( list_u4696772448584712917at_nat @ L @ I @ Y ) ) )
% 2.75/3.05 = ( ( X = Y )
% 2.75/3.05 | ( ( member8757157785044589968at_nat @ X @ ( set_Pr3765526544606949372at_nat @ L ) )
% 2.75/3.05 & ! [Y5: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X @ ( set_Pr3765526544606949372at_nat @ ( list_u4696772448584712917at_nat @ L @ I @ Y5 ) ) ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_upd_eq
% 2.75/3.05 thf(fact_948_in__set__upd__eq,axiom,
% 2.75/3.05 ! [I: nat,L: list_P6011104703257516679at_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 2.75/3.05 ( ( ord_less_nat @ I @ ( size_s5460976970255530739at_nat @ L ) )
% 2.75/3.05 => ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ ( list_u6180841689913720943at_nat @ L @ I @ Y ) ) )
% 2.75/3.05 = ( ( X = Y )
% 2.75/3.05 | ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ L ) )
% 2.75/3.05 & ! [Y5: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ ( list_u6180841689913720943at_nat @ L @ I @ Y5 ) ) ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_upd_eq
% 2.75/3.05 thf(fact_949_in__set__upd__eq,axiom,
% 2.75/3.05 ! [I: nat,L: list_P7985473006766602707_nat_o,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat > $o] :
% 2.75/3.05 ( ( ord_less_nat @ I @ ( size_s8908918004648414271_nat_o @ L ) )
% 2.75/3.05 => ( ( member6576561426505652726_nat_o @ X @ ( set_Pr400311997697478754_nat_o @ ( list_u6943956310655620667_nat_o @ L @ I @ Y ) ) )
% 2.75/3.05 = ( ( X = Y )
% 2.75/3.05 | ( ( member6576561426505652726_nat_o @ X @ ( set_Pr400311997697478754_nat_o @ L ) )
% 2.75/3.05 & ! [Y5: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X @ ( set_Pr400311997697478754_nat_o @ ( list_u6943956310655620667_nat_o @ L @ I @ Y5 ) ) ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_upd_eq
% 2.75/3.05 thf(fact_950_in__set__upd__eq,axiom,
% 2.75/3.05 ! [I: nat,L: list_P8527749157015355191n_assn,X: produc6575502325842934193n_assn,Y: produc6575502325842934193n_assn] :
% 2.75/3.05 ( ( ord_less_nat @ I @ ( size_s6829681357464350627n_assn @ L ) )
% 2.75/3.05 => ( ( member7957490590177025114n_assn @ X @ ( set_Pr1139785259514867910n_assn @ ( list_u4534839942911652127n_assn @ L @ I @ Y ) ) )
% 2.75/3.05 = ( ( X = Y )
% 2.75/3.05 | ( ( member7957490590177025114n_assn @ X @ ( set_Pr1139785259514867910n_assn @ L ) )
% 2.75/3.05 & ! [Y5: produc6575502325842934193n_assn] : ( member7957490590177025114n_assn @ X @ ( set_Pr1139785259514867910n_assn @ ( list_u4534839942911652127n_assn @ L @ I @ Y5 ) ) ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_upd_eq
% 2.75/3.05 thf(fact_951_in__set__upd__eq,axiom,
% 2.75/3.05 ! [I: nat,L: list_c,X: c,Y: c] :
% 2.75/3.05 ( ( ord_less_nat @ I @ ( size_size_list_c @ L ) )
% 2.75/3.05 => ( ( member_c @ X @ ( set_c2 @ ( list_update_c @ L @ I @ Y ) ) )
% 2.75/3.05 = ( ( X = Y )
% 2.75/3.05 | ( ( member_c @ X @ ( set_c2 @ L ) )
% 2.75/3.05 & ! [Y5: c] : ( member_c @ X @ ( set_c2 @ ( list_update_c @ L @ I @ Y5 ) ) ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_upd_eq
% 2.75/3.05 thf(fact_952_in__set__upd__eq,axiom,
% 2.75/3.05 ! [I: nat,L: list_d,X: d,Y: d] :
% 2.75/3.05 ( ( ord_less_nat @ I @ ( size_size_list_d @ L ) )
% 2.75/3.05 => ( ( member_d @ X @ ( set_d2 @ ( list_update_d @ L @ I @ Y ) ) )
% 2.75/3.05 = ( ( X = Y )
% 2.75/3.05 | ( ( member_d @ X @ ( set_d2 @ L ) )
% 2.75/3.05 & ! [Y5: d] : ( member_d @ X @ ( set_d2 @ ( list_update_d @ L @ I @ Y5 ) ) ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_upd_eq
% 2.75/3.05 thf(fact_953_in__set__upd__eq,axiom,
% 2.75/3.05 ! [I: nat,L: list_nat,X: nat,Y: nat] :
% 2.75/3.05 ( ( ord_less_nat @ I @ ( size_size_list_nat @ L ) )
% 2.75/3.05 => ( ( member_nat @ X @ ( set_nat2 @ ( list_update_nat @ L @ I @ Y ) ) )
% 2.75/3.05 = ( ( X = Y )
% 2.75/3.05 | ( ( member_nat @ X @ ( set_nat2 @ L ) )
% 2.75/3.05 & ! [Y5: nat] : ( member_nat @ X @ ( set_nat2 @ ( list_update_nat @ L @ I @ Y5 ) ) ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_upd_eq
% 2.75/3.05 thf(fact_954_in__set__upd__eq,axiom,
% 2.75/3.05 ! [I: nat,L: list_int,X: int,Y: int] :
% 2.75/3.05 ( ( ord_less_nat @ I @ ( size_size_list_int @ L ) )
% 2.75/3.05 => ( ( member_int @ X @ ( set_int2 @ ( list_update_int @ L @ I @ Y ) ) )
% 2.75/3.05 = ( ( X = Y )
% 2.75/3.05 | ( ( member_int @ X @ ( set_int2 @ L ) )
% 2.75/3.05 & ! [Y5: int] : ( member_int @ X @ ( set_int2 @ ( list_update_int @ L @ I @ Y5 ) ) ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_upd_eq
% 2.75/3.05 thf(fact_955_set__update__memI,axiom,
% 2.75/3.05 ! [N: nat,Xs: list_P5464809261938338413at_nat,X: produc3843707927480180839at_nat] :
% 2.75/3.05 ( ( ord_less_nat @ N @ ( size_s1588839187904960729at_nat @ Xs ) )
% 2.75/3.05 => ( member8757157785044589968at_nat @ X @ ( set_Pr3765526544606949372at_nat @ ( list_u4696772448584712917at_nat @ Xs @ N @ X ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % set_update_memI
% 2.75/3.05 thf(fact_956_set__update__memI,axiom,
% 2.75/3.05 ! [N: nat,Xs: list_P6011104703257516679at_nat,X: product_prod_nat_nat] :
% 2.75/3.05 ( ( ord_less_nat @ N @ ( size_s5460976970255530739at_nat @ Xs ) )
% 2.75/3.05 => ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ ( list_u6180841689913720943at_nat @ Xs @ N @ X ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % set_update_memI
% 2.75/3.05 thf(fact_957_set__update__memI,axiom,
% 2.75/3.05 ! [N: nat,Xs: list_P7985473006766602707_nat_o,X: produc3658429121746597890et_nat > $o] :
% 2.75/3.05 ( ( ord_less_nat @ N @ ( size_s8908918004648414271_nat_o @ Xs ) )
% 2.75/3.05 => ( member6576561426505652726_nat_o @ X @ ( set_Pr400311997697478754_nat_o @ ( list_u6943956310655620667_nat_o @ Xs @ N @ X ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % set_update_memI
% 2.75/3.05 thf(fact_958_set__update__memI,axiom,
% 2.75/3.05 ! [N: nat,Xs: list_P8527749157015355191n_assn,X: produc6575502325842934193n_assn] :
% 2.75/3.05 ( ( ord_less_nat @ N @ ( size_s6829681357464350627n_assn @ Xs ) )
% 2.75/3.05 => ( member7957490590177025114n_assn @ X @ ( set_Pr1139785259514867910n_assn @ ( list_u4534839942911652127n_assn @ Xs @ N @ X ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % set_update_memI
% 2.75/3.05 thf(fact_959_set__update__memI,axiom,
% 2.75/3.05 ! [N: nat,Xs: list_c,X: c] :
% 2.75/3.05 ( ( ord_less_nat @ N @ ( size_size_list_c @ Xs ) )
% 2.75/3.05 => ( member_c @ X @ ( set_c2 @ ( list_update_c @ Xs @ N @ X ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % set_update_memI
% 2.75/3.05 thf(fact_960_set__update__memI,axiom,
% 2.75/3.05 ! [N: nat,Xs: list_d,X: d] :
% 2.75/3.05 ( ( ord_less_nat @ N @ ( size_size_list_d @ Xs ) )
% 2.75/3.05 => ( member_d @ X @ ( set_d2 @ ( list_update_d @ Xs @ N @ X ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % set_update_memI
% 2.75/3.05 thf(fact_961_set__update__memI,axiom,
% 2.75/3.05 ! [N: nat,Xs: list_nat,X: nat] :
% 2.75/3.05 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 2.75/3.05 => ( member_nat @ X @ ( set_nat2 @ ( list_update_nat @ Xs @ N @ X ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % set_update_memI
% 2.75/3.05 thf(fact_962_set__update__memI,axiom,
% 2.75/3.05 ! [N: nat,Xs: list_int,X: int] :
% 2.75/3.05 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 2.75/3.05 => ( member_int @ X @ ( set_int2 @ ( list_update_int @ Xs @ N @ X ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % set_update_memI
% 2.75/3.05 thf(fact_963_set__update__distinct,axiom,
% 2.75/3.05 ! [Xs: list_P8527749157015355191n_assn,N: nat,X: produc6575502325842934193n_assn] :
% 2.75/3.05 ( ( distin4809818325527169450n_assn @ Xs )
% 2.75/3.05 => ( ( ord_less_nat @ N @ ( size_s6829681357464350627n_assn @ Xs ) )
% 2.75/3.05 => ( ( set_Pr1139785259514867910n_assn @ ( list_u4534839942911652127n_assn @ Xs @ N @ X ) )
% 2.75/3.05 = ( insert5290817439147925377n_assn @ X @ ( minus_2301194108115264760n_assn @ ( set_Pr1139785259514867910n_assn @ Xs ) @ ( insert5290817439147925377n_assn @ ( nth_Pr1769885009046257848n_assn @ Xs @ N ) @ bot_bo1176836662018730877n_assn ) ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % set_update_distinct
% 2.75/3.05 thf(fact_964_set__update__distinct,axiom,
% 2.75/3.05 ! [Xs: list_c,N: nat,X: c] :
% 2.75/3.05 ( ( distinct_c @ Xs )
% 2.75/3.05 => ( ( ord_less_nat @ N @ ( size_size_list_c @ Xs ) )
% 2.75/3.05 => ( ( set_c2 @ ( list_update_c @ Xs @ N @ X ) )
% 2.75/3.05 = ( insert_c @ X @ ( minus_minus_set_c @ ( set_c2 @ Xs ) @ ( insert_c @ ( nth_c @ Xs @ N ) @ bot_bot_set_c ) ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % set_update_distinct
% 2.75/3.05 thf(fact_965_set__update__distinct,axiom,
% 2.75/3.05 ! [Xs: list_d,N: nat,X: d] :
% 2.75/3.05 ( ( distinct_d @ Xs )
% 2.75/3.05 => ( ( ord_less_nat @ N @ ( size_size_list_d @ Xs ) )
% 2.75/3.05 => ( ( set_d2 @ ( list_update_d @ Xs @ N @ X ) )
% 2.75/3.05 = ( insert_d @ X @ ( minus_minus_set_d @ ( set_d2 @ Xs ) @ ( insert_d @ ( nth_d @ Xs @ N ) @ bot_bot_set_d ) ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % set_update_distinct
% 2.75/3.05 thf(fact_966_set__update__distinct,axiom,
% 2.75/3.05 ! [Xs: list_P5464809261938338413at_nat,N: nat,X: produc3843707927480180839at_nat] :
% 2.75/3.05 ( ( distin5355857245021852384at_nat @ Xs )
% 2.75/3.05 => ( ( ord_less_nat @ N @ ( size_s1588839187904960729at_nat @ Xs ) )
% 2.75/3.05 => ( ( set_Pr3765526544606949372at_nat @ ( list_u4696772448584712917at_nat @ Xs @ N @ X ) )
% 2.75/3.05 = ( insert9069300056098147895at_nat @ X @ ( minus_3314409938677909166at_nat @ ( set_Pr3765526544606949372at_nat @ Xs ) @ ( insert9069300056098147895at_nat @ ( nth_Pr1239524528086697198at_nat @ Xs @ N ) @ bot_bo228742789529271731at_nat ) ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % set_update_distinct
% 2.75/3.05 thf(fact_967_set__update__distinct,axiom,
% 2.75/3.05 ! [Xs: list_P6011104703257516679at_nat,N: nat,X: product_prod_nat_nat] :
% 2.75/3.05 ( ( distin6923225563576452346at_nat @ Xs )
% 2.75/3.05 => ( ( ord_less_nat @ N @ ( size_s5460976970255530739at_nat @ Xs ) )
% 2.75/3.05 => ( ( set_Pr5648618587558075414at_nat @ ( list_u6180841689913720943at_nat @ Xs @ N @ X ) )
% 2.75/3.05 = ( insert8211810215607154385at_nat @ X @ ( minus_1356011639430497352at_nat @ ( set_Pr5648618587558075414at_nat @ Xs ) @ ( insert8211810215607154385at_nat @ ( nth_Pr7617993195940197384at_nat @ Xs @ N ) @ bot_bo2099793752762293965at_nat ) ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % set_update_distinct
% 2.75/3.05 thf(fact_968_set__update__distinct,axiom,
% 2.75/3.05 ! [Xs: list_o,N: nat,X: $o] :
% 2.75/3.05 ( ( distinct_o @ Xs )
% 2.75/3.05 => ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 2.75/3.05 => ( ( set_o2 @ ( list_update_o @ Xs @ N @ X ) )
% 2.75/3.05 = ( insert_o2 @ X @ ( minus_minus_set_o @ ( set_o2 @ Xs ) @ ( insert_o2 @ ( nth_o @ Xs @ N ) @ bot_bot_set_o ) ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % set_update_distinct
% 2.75/3.05 thf(fact_969_set__update__distinct,axiom,
% 2.75/3.05 ! [Xs: list_int,N: nat,X: int] :
% 2.75/3.05 ( ( distinct_int @ Xs )
% 2.75/3.05 => ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 2.75/3.05 => ( ( set_int2 @ ( list_update_int @ Xs @ N @ X ) )
% 2.75/3.05 = ( insert_int2 @ X @ ( minus_minus_set_int @ ( set_int2 @ Xs ) @ ( insert_int2 @ ( nth_int @ Xs @ N ) @ bot_bot_set_int ) ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % set_update_distinct
% 2.75/3.05 thf(fact_970_set__update__distinct,axiom,
% 2.75/3.05 ! [Xs: list_nat,N: nat,X: nat] :
% 2.75/3.05 ( ( distinct_nat @ Xs )
% 2.75/3.05 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 2.75/3.05 => ( ( set_nat2 @ ( list_update_nat @ Xs @ N @ X ) )
% 2.75/3.05 = ( insert_nat2 @ X @ ( minus_minus_set_nat @ ( set_nat2 @ Xs ) @ ( insert_nat2 @ ( nth_nat @ Xs @ N ) @ bot_bot_set_nat ) ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % set_update_distinct
% 2.75/3.05 thf(fact_971_prod_Oinject,axiom,
% 2.75/3.05 ! [X1: produc6241069584506657477e_term > option6357759511663192854e_term,X22: produc8923325533196201883nteger,Y1: produc6241069584506657477e_term > option6357759511663192854e_term,Y22: produc8923325533196201883nteger] :
% 2.75/3.05 ( ( ( produc8603105652947943368nteger @ X1 @ X22 )
% 2.75/3.05 = ( produc8603105652947943368nteger @ Y1 @ Y22 ) )
% 2.75/3.05 = ( ( X1 = Y1 )
% 2.75/3.05 & ( X22 = Y22 ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % prod.inject
% 2.75/3.05 thf(fact_972_prod_Oinject,axiom,
% 2.75/3.05 ! [X1: produc3658429121746597890et_nat > $o,X22: produc3658429121746597890et_nat,Y1: produc3658429121746597890et_nat > $o,Y22: produc3658429121746597890et_nat] :
% 2.75/3.05 ( ( ( produc5001842942810119800et_nat @ X1 @ X22 )
% 2.75/3.05 = ( produc5001842942810119800et_nat @ Y1 @ Y22 ) )
% 2.75/3.05 = ( ( X1 = Y1 )
% 2.75/3.05 & ( X22 = Y22 ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % prod.inject
% 2.75/3.05 thf(fact_973_prod_Oinject,axiom,
% 2.75/3.05 ! [X1: produc3658429121746597890et_nat > $o,X22: produc3925858234332021118et_nat,Y1: produc3658429121746597890et_nat > $o,Y22: produc3925858234332021118et_nat] :
% 2.75/3.05 ( ( ( produc2245416461498447860et_nat @ X1 @ X22 )
% 2.75/3.05 = ( produc2245416461498447860et_nat @ Y1 @ Y22 ) )
% 2.75/3.05 = ( ( X1 = Y1 )
% 2.75/3.05 & ( X22 = Y22 ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % prod.inject
% 2.75/3.05 thf(fact_974_prod_Oinject,axiom,
% 2.75/3.05 ! [X1: produc8551481072490612790e_term > option6357759511663192854e_term,X22: product_prod_int_int,Y1: produc8551481072490612790e_term > option6357759511663192854e_term,Y22: product_prod_int_int] :
% 2.75/3.05 ( ( ( produc5700946648718959541nt_int @ X1 @ X22 )
% 2.75/3.05 = ( produc5700946648718959541nt_int @ Y1 @ Y22 ) )
% 2.75/3.05 = ( ( X1 = Y1 )
% 2.75/3.05 & ( X22 = Y22 ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % prod.inject
% 2.75/3.05 thf(fact_975_prod_Oinject,axiom,
% 2.75/3.05 ! [X1: int > option6357759511663192854e_term,X22: product_prod_int_int,Y1: int > option6357759511663192854e_term,Y22: product_prod_int_int] :
% 2.75/3.05 ( ( ( produc4305682042979456191nt_int @ X1 @ X22 )
% 2.75/3.05 = ( produc4305682042979456191nt_int @ Y1 @ Y22 ) )
% 2.75/3.05 = ( ( X1 = Y1 )
% 2.75/3.05 & ( X22 = Y22 ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % prod.inject
% 2.75/3.05 thf(fact_976_old_Oprod_Oinject,axiom,
% 2.75/3.05 ! [A2: produc6241069584506657477e_term > option6357759511663192854e_term,B2: produc8923325533196201883nteger,A7: produc6241069584506657477e_term > option6357759511663192854e_term,B6: produc8923325533196201883nteger] :
% 2.75/3.05 ( ( ( produc8603105652947943368nteger @ A2 @ B2 )
% 2.75/3.05 = ( produc8603105652947943368nteger @ A7 @ B6 ) )
% 2.75/3.05 = ( ( A2 = A7 )
% 2.75/3.05 & ( B2 = B6 ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % old.prod.inject
% 2.75/3.05 thf(fact_977_old_Oprod_Oinject,axiom,
% 2.75/3.05 ! [A2: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat,A7: produc3658429121746597890et_nat > $o,B6: produc3658429121746597890et_nat] :
% 2.75/3.05 ( ( ( produc5001842942810119800et_nat @ A2 @ B2 )
% 2.75/3.05 = ( produc5001842942810119800et_nat @ A7 @ B6 ) )
% 2.75/3.05 = ( ( A2 = A7 )
% 2.75/3.05 & ( B2 = B6 ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % old.prod.inject
% 2.75/3.05 thf(fact_978_old_Oprod_Oinject,axiom,
% 2.75/3.05 ! [A2: produc3658429121746597890et_nat > $o,B2: produc3925858234332021118et_nat,A7: produc3658429121746597890et_nat > $o,B6: produc3925858234332021118et_nat] :
% 2.75/3.05 ( ( ( produc2245416461498447860et_nat @ A2 @ B2 )
% 2.75/3.05 = ( produc2245416461498447860et_nat @ A7 @ B6 ) )
% 2.75/3.05 = ( ( A2 = A7 )
% 2.75/3.05 & ( B2 = B6 ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % old.prod.inject
% 2.75/3.05 thf(fact_979_old_Oprod_Oinject,axiom,
% 2.75/3.05 ! [A2: produc8551481072490612790e_term > option6357759511663192854e_term,B2: product_prod_int_int,A7: produc8551481072490612790e_term > option6357759511663192854e_term,B6: product_prod_int_int] :
% 2.75/3.05 ( ( ( produc5700946648718959541nt_int @ A2 @ B2 )
% 2.75/3.05 = ( produc5700946648718959541nt_int @ A7 @ B6 ) )
% 2.75/3.05 = ( ( A2 = A7 )
% 2.75/3.05 & ( B2 = B6 ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % old.prod.inject
% 2.75/3.05 thf(fact_980_old_Oprod_Oinject,axiom,
% 2.75/3.05 ! [A2: int > option6357759511663192854e_term,B2: product_prod_int_int,A7: int > option6357759511663192854e_term,B6: product_prod_int_int] :
% 2.75/3.05 ( ( ( produc4305682042979456191nt_int @ A2 @ B2 )
% 2.75/3.05 = ( produc4305682042979456191nt_int @ A7 @ B6 ) )
% 2.75/3.05 = ( ( A2 = A7 )
% 2.75/3.05 & ( B2 = B6 ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % old.prod.inject
% 2.75/3.05 thf(fact_981_distinct__union,axiom,
% 2.75/3.05 ! [Xs: list_int,Ys: list_int] :
% 2.75/3.05 ( ( distinct_int @ ( union_int @ Xs @ Ys ) )
% 2.75/3.05 = ( distinct_int @ Ys ) ) ).
% 2.75/3.05
% 2.75/3.05 % distinct_union
% 2.75/3.05 thf(fact_982_distinct__union,axiom,
% 2.75/3.05 ! [Xs: list_nat,Ys: list_nat] :
% 2.75/3.05 ( ( distinct_nat @ ( union_nat @ Xs @ Ys ) )
% 2.75/3.05 = ( distinct_nat @ Ys ) ) ).
% 2.75/3.05
% 2.75/3.05 % distinct_union
% 2.75/3.05 thf(fact_983_set__remove1__eq,axiom,
% 2.75/3.05 ! [Xs: list_P8527749157015355191n_assn,X: produc6575502325842934193n_assn] :
% 2.75/3.05 ( ( distin4809818325527169450n_assn @ Xs )
% 2.75/3.05 => ( ( set_Pr1139785259514867910n_assn @ ( remove1670527618125605709n_assn @ X @ Xs ) )
% 2.75/3.05 = ( minus_2301194108115264760n_assn @ ( set_Pr1139785259514867910n_assn @ Xs ) @ ( insert5290817439147925377n_assn @ X @ bot_bo1176836662018730877n_assn ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % set_remove1_eq
% 2.75/3.05 thf(fact_984_set__remove1__eq,axiom,
% 2.75/3.05 ! [Xs: list_P5464809261938338413at_nat,X: produc3843707927480180839at_nat] :
% 2.75/3.05 ( ( distin5355857245021852384at_nat @ Xs )
% 2.75/3.05 => ( ( set_Pr3765526544606949372at_nat @ ( remove8895909992688781315at_nat @ X @ Xs ) )
% 2.75/3.05 = ( minus_3314409938677909166at_nat @ ( set_Pr3765526544606949372at_nat @ Xs ) @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % set_remove1_eq
% 2.75/3.05 thf(fact_985_set__remove1__eq,axiom,
% 2.75/3.05 ! [Xs: list_P6011104703257516679at_nat,X: product_prod_nat_nat] :
% 2.75/3.05 ( ( distin6923225563576452346at_nat @ Xs )
% 2.75/3.05 => ( ( set_Pr5648618587558075414at_nat @ ( remove5766854097993331357at_nat @ X @ Xs ) )
% 2.75/3.05 = ( minus_1356011639430497352at_nat @ ( set_Pr5648618587558075414at_nat @ Xs ) @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % set_remove1_eq
% 2.75/3.05 thf(fact_986_set__remove1__eq,axiom,
% 2.75/3.05 ! [Xs: list_o,X: $o] :
% 2.75/3.05 ( ( distinct_o @ Xs )
% 2.75/3.05 => ( ( set_o2 @ ( remove1_o @ X @ Xs ) )
% 2.75/3.05 = ( minus_minus_set_o @ ( set_o2 @ Xs ) @ ( insert_o2 @ X @ bot_bot_set_o ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % set_remove1_eq
% 2.75/3.05 thf(fact_987_set__remove1__eq,axiom,
% 2.75/3.05 ! [Xs: list_int,X: int] :
% 2.75/3.05 ( ( distinct_int @ Xs )
% 2.75/3.05 => ( ( set_int2 @ ( remove1_int @ X @ Xs ) )
% 2.75/3.05 = ( minus_minus_set_int @ ( set_int2 @ Xs ) @ ( insert_int2 @ X @ bot_bot_set_int ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % set_remove1_eq
% 2.75/3.05 thf(fact_988_set__remove1__eq,axiom,
% 2.75/3.05 ! [Xs: list_nat,X: nat] :
% 2.75/3.05 ( ( distinct_nat @ Xs )
% 2.75/3.05 => ( ( set_nat2 @ ( remove1_nat @ X @ Xs ) )
% 2.75/3.05 = ( minus_minus_set_nat @ ( set_nat2 @ Xs ) @ ( insert_nat2 @ X @ bot_bot_set_nat ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % set_remove1_eq
% 2.75/3.05 thf(fact_989_is__empty__set,axiom,
% 2.75/3.05 ! [Xs: list_int] :
% 2.75/3.05 ( ( is_empty_int @ ( set_int2 @ Xs ) )
% 2.75/3.05 = ( null_int @ Xs ) ) ).
% 2.75/3.05
% 2.75/3.05 % is_empty_set
% 2.75/3.05 thf(fact_990_is__empty__set,axiom,
% 2.75/3.05 ! [Xs: list_nat] :
% 2.75/3.05 ( ( is_empty_nat @ ( set_nat2 @ Xs ) )
% 2.75/3.05 = ( null_nat @ Xs ) ) ).
% 2.75/3.05
% 2.75/3.05 % is_empty_set
% 2.75/3.05 thf(fact_991_is__empty__set,axiom,
% 2.75/3.05 ! [Xs: list_P8527749157015355191n_assn] :
% 2.75/3.05 ( ( is_emp7749065762491207043n_assn @ ( set_Pr1139785259514867910n_assn @ Xs ) )
% 2.75/3.05 = ( null_P7596217980778516671n_assn @ Xs ) ) ).
% 2.75/3.05
% 2.75/3.05 % is_empty_set
% 2.75/3.05 thf(fact_992_set__removeAll,axiom,
% 2.75/3.05 ! [X: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn] :
% 2.75/3.05 ( ( set_Pr1139785259514867910n_assn @ ( remove1763081955827946941n_assn @ X @ Xs ) )
% 2.75/3.05 = ( minus_2301194108115264760n_assn @ ( set_Pr1139785259514867910n_assn @ Xs ) @ ( insert5290817439147925377n_assn @ X @ bot_bo1176836662018730877n_assn ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % set_removeAll
% 2.75/3.05 thf(fact_993_set__removeAll,axiom,
% 2.75/3.05 ! [X: produc3843707927480180839at_nat,Xs: list_P5464809261938338413at_nat] :
% 2.75/3.05 ( ( set_Pr3765526544606949372at_nat @ ( remove4908499291543849587at_nat @ X @ Xs ) )
% 2.75/3.05 = ( minus_3314409938677909166at_nat @ ( set_Pr3765526544606949372at_nat @ Xs ) @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % set_removeAll
% 2.75/3.05 thf(fact_994_set__removeAll,axiom,
% 2.75/3.05 ! [X: product_prod_nat_nat,Xs: list_P6011104703257516679at_nat] :
% 2.75/3.05 ( ( set_Pr5648618587558075414at_nat @ ( remove3673390508374433037at_nat @ X @ Xs ) )
% 2.75/3.05 = ( minus_1356011639430497352at_nat @ ( set_Pr5648618587558075414at_nat @ Xs ) @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % set_removeAll
% 2.75/3.05 thf(fact_995_set__removeAll,axiom,
% 2.75/3.05 ! [X: $o,Xs: list_o] :
% 2.75/3.05 ( ( set_o2 @ ( removeAll_o @ X @ Xs ) )
% 2.75/3.05 = ( minus_minus_set_o @ ( set_o2 @ Xs ) @ ( insert_o2 @ X @ bot_bot_set_o ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % set_removeAll
% 2.75/3.05 thf(fact_996_set__removeAll,axiom,
% 2.75/3.05 ! [X: int,Xs: list_int] :
% 2.75/3.05 ( ( set_int2 @ ( removeAll_int @ X @ Xs ) )
% 2.75/3.05 = ( minus_minus_set_int @ ( set_int2 @ Xs ) @ ( insert_int2 @ X @ bot_bot_set_int ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % set_removeAll
% 2.75/3.05 thf(fact_997_set__removeAll,axiom,
% 2.75/3.05 ! [X: nat,Xs: list_nat] :
% 2.75/3.05 ( ( set_nat2 @ ( removeAll_nat @ X @ Xs ) )
% 2.75/3.05 = ( minus_minus_set_nat @ ( set_nat2 @ Xs ) @ ( insert_nat2 @ X @ bot_bot_set_nat ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % set_removeAll
% 2.75/3.05 thf(fact_998_listrel1__iff__update,axiom,
% 2.75/3.05 ! [Xs: list_s1210847774152347623at_nat,Ys: list_s1210847774152347623at_nat,R2: set_Pr4329608150637261639at_nat] :
% 2.75/3.05 ( ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ Xs @ Ys ) @ ( listre8180072825634266816at_nat @ R2 ) )
% 2.75/3.05 = ( ? [Y5: set_Pr1261947904930325089at_nat,N2: nat] :
% 2.75/3.05 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( nth_se5679702624988424552at_nat @ Xs @ N2 ) @ Y5 ) @ R2 )
% 2.75/3.05 & ( ord_less_nat @ N2 @ ( size_s8736152011456118867at_nat @ Xs ) )
% 2.75/3.05 & ( Ys
% 2.75/3.05 = ( list_u8444657558853818831at_nat @ Xs @ N2 @ Y5 ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % listrel1_iff_update
% 2.75/3.05 thf(fact_999_listrel1__iff__update,axiom,
% 2.75/3.05 ! [Xs: list_c,Ys: list_c,R2: set_Product_prod_c_c] :
% 2.75/3.05 ( ( member7012247553653173456list_c @ ( produc5515445818230282391list_c @ Xs @ Ys ) @ ( listrel1_c @ R2 ) )
% 2.75/3.05 = ( ? [Y5: c,N2: nat] :
% 2.75/3.05 ( ( member5074992359041316560od_c_c @ ( product_Pair_c_c @ ( nth_c @ Xs @ N2 ) @ Y5 ) @ R2 )
% 2.75/3.05 & ( ord_less_nat @ N2 @ ( size_size_list_c @ Xs ) )
% 2.75/3.05 & ( Ys
% 2.75/3.05 = ( list_update_c @ Xs @ N2 @ Y5 ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % listrel1_iff_update
% 2.75/3.05 thf(fact_1000_listrel1__iff__update,axiom,
% 2.75/3.05 ! [Xs: list_d,Ys: list_d,R2: set_Product_prod_d_d] :
% 2.75/3.05 ( ( member1810801192463332112list_d @ ( produc242965421297323863list_d @ Xs @ Ys ) @ ( listrel1_d @ R2 ) )
% 2.75/3.05 = ( ? [Y5: d,N2: nat] :
% 2.75/3.05 ( ( member2287536781371869328od_d_d @ ( product_Pair_d_d @ ( nth_d @ Xs @ N2 ) @ Y5 ) @ R2 )
% 2.75/3.05 & ( ord_less_nat @ N2 @ ( size_size_list_d @ Xs ) )
% 2.75/3.05 & ( Ys
% 2.75/3.05 = ( list_update_d @ Xs @ N2 @ Y5 ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % listrel1_iff_update
% 2.75/3.05 thf(fact_1001_listrel1__iff__update,axiom,
% 2.75/3.05 ! [Xs: list_nat,Ys: list_nat,R2: set_Pr1261947904930325089at_nat] :
% 2.75/3.05 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs @ Ys ) @ ( listrel1_nat @ R2 ) )
% 2.75/3.05 = ( ? [Y5: nat,N2: nat] :
% 2.75/3.05 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( nth_nat @ Xs @ N2 ) @ Y5 ) @ R2 )
% 2.75/3.05 & ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) )
% 2.75/3.05 & ( Ys
% 2.75/3.05 = ( list_update_nat @ Xs @ N2 @ Y5 ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % listrel1_iff_update
% 2.75/3.05 thf(fact_1002_listrel1__iff__update,axiom,
% 2.75/3.05 ! [Xs: list_int,Ys: list_int,R2: set_Pr958786334691620121nt_int] :
% 2.75/3.05 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs @ Ys ) @ ( listrel1_int @ R2 ) )
% 2.75/3.05 = ( ? [Y5: int,N2: nat] :
% 2.75/3.05 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( nth_int @ Xs @ N2 ) @ Y5 ) @ R2 )
% 2.75/3.05 & ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs ) )
% 2.75/3.05 & ( Ys
% 2.75/3.05 = ( list_update_int @ Xs @ N2 @ Y5 ) ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % listrel1_iff_update
% 2.75/3.05 thf(fact_1003_List_Oset__insert,axiom,
% 2.75/3.05 ! [X: product_prod_nat_nat,Xs: list_P6011104703257516679at_nat] :
% 2.75/3.05 ( ( set_Pr5648618587558075414at_nat @ ( insert8944034826898310173at_nat @ X @ Xs ) )
% 2.75/3.05 = ( insert8211810215607154385at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % List.set_insert
% 2.75/3.05 thf(fact_1004_List_Oset__insert,axiom,
% 2.75/3.05 ! [X: produc3843707927480180839at_nat,Xs: list_P5464809261938338413at_nat] :
% 2.75/3.05 ( ( set_Pr3765526544606949372at_nat @ ( insert4149901806602606979at_nat @ X @ Xs ) )
% 2.75/3.05 = ( insert9069300056098147895at_nat @ X @ ( set_Pr3765526544606949372at_nat @ Xs ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % List.set_insert
% 2.75/3.05 thf(fact_1005_List_Oset__insert,axiom,
% 2.75/3.05 ! [X: $o,Xs: list_o] :
% 2.75/3.05 ( ( set_o2 @ ( insert_o @ X @ Xs ) )
% 2.75/3.05 = ( insert_o2 @ X @ ( set_o2 @ Xs ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % List.set_insert
% 2.75/3.05 thf(fact_1006_List_Oset__insert,axiom,
% 2.75/3.05 ! [X: int,Xs: list_int] :
% 2.75/3.05 ( ( set_int2 @ ( insert_int @ X @ Xs ) )
% 2.75/3.05 = ( insert_int2 @ X @ ( set_int2 @ Xs ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % List.set_insert
% 2.75/3.05 thf(fact_1007_List_Oset__insert,axiom,
% 2.75/3.05 ! [X: nat,Xs: list_nat] :
% 2.75/3.05 ( ( set_nat2 @ ( insert_nat @ X @ Xs ) )
% 2.75/3.05 = ( insert_nat2 @ X @ ( set_nat2 @ Xs ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % List.set_insert
% 2.75/3.05 thf(fact_1008_List_Oset__insert,axiom,
% 2.75/3.05 ! [X: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn] :
% 2.75/3.05 ( ( set_Pr1139785259514867910n_assn @ ( insert3246601298802261197n_assn @ X @ Xs ) )
% 2.75/3.05 = ( insert5290817439147925377n_assn @ X @ ( set_Pr1139785259514867910n_assn @ Xs ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % List.set_insert
% 2.75/3.05 thf(fact_1009_listrel__iff__nth,axiom,
% 2.75/3.05 ! [Xs: list_c,Ys: list_c,R2: set_Product_prod_c_c] :
% 2.75/3.05 ( ( member7012247553653173456list_c @ ( produc5515445818230282391list_c @ Xs @ Ys ) @ ( listrel_c_c @ R2 ) )
% 2.75/3.05 = ( ( ( size_size_list_c @ Xs )
% 2.75/3.05 = ( size_size_list_c @ Ys ) )
% 2.75/3.05 & ! [N2: nat] :
% 2.75/3.05 ( ( ord_less_nat @ N2 @ ( size_size_list_c @ Xs ) )
% 2.75/3.05 => ( member5074992359041316560od_c_c @ ( product_Pair_c_c @ ( nth_c @ Xs @ N2 ) @ ( nth_c @ Ys @ N2 ) ) @ R2 ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % listrel_iff_nth
% 2.75/3.05 thf(fact_1010_listrel__iff__nth,axiom,
% 2.75/3.05 ! [Xs: list_c,Ys: list_d,R2: set_Product_prod_c_d] :
% 2.75/3.05 ( ( member7083281593699519441list_d @ ( produc5515445822533511192list_d @ Xs @ Ys ) @ ( listrel_c_d @ R2 ) )
% 2.75/3.05 = ( ( ( size_size_list_c @ Xs )
% 2.75/3.05 = ( size_size_list_d @ Ys ) )
% 2.75/3.05 & ! [N2: nat] :
% 2.75/3.05 ( ( ord_less_nat @ N2 @ ( size_size_list_c @ Xs ) )
% 2.75/3.05 => ( member5074992363344545361od_c_d @ ( product_Pair_c_d @ ( nth_c @ Xs @ N2 ) @ ( nth_d @ Ys @ N2 ) ) @ R2 ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % listrel_iff_nth
% 2.75/3.05 thf(fact_1011_listrel__iff__nth,axiom,
% 2.75/3.05 ! [Xs: list_c,Ys: list_nat,R2: set_Pr6903500605879609269_c_nat] :
% 2.75/3.05 ( ( member6184937725913850668st_nat @ ( produc6126748735280710287st_nat @ Xs @ Ys ) @ ( listrel_c_nat @ R2 ) )
% 2.75/3.05 = ( ( ( size_size_list_c @ Xs )
% 2.75/3.05 = ( size_size_list_nat @ Ys ) )
% 2.75/3.05 & ! [N2: nat] :
% 2.75/3.05 ( ( ord_less_nat @ N2 @ ( size_size_list_c @ Xs ) )
% 2.75/3.05 => ( member8195077246299207702_c_nat @ ( product_Pair_c_nat @ ( nth_c @ Xs @ N2 ) @ ( nth_nat @ Ys @ N2 ) ) @ R2 ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % listrel_iff_nth
% 2.75/3.05 thf(fact_1012_listrel__iff__nth,axiom,
% 2.75/3.05 ! [Xs: list_c,Ys: list_int,R2: set_Pr4413417460947882513_c_int] :
% 2.75/3.05 ( ( member3694854580982123912st_int @ ( produc1948897715771513579st_int @ Xs @ Ys ) @ ( listrel_c_int @ R2 ) )
% 2.75/3.05 = ( ( ( size_size_list_c @ Xs )
% 2.75/3.05 = ( size_size_list_int @ Ys ) )
% 2.75/3.05 & ! [N2: nat] :
% 2.75/3.05 ( ( ord_less_nat @ N2 @ ( size_size_list_c @ Xs ) )
% 2.75/3.05 => ( member4017226226790010994_c_int @ ( product_Pair_c_int @ ( nth_c @ Xs @ N2 ) @ ( nth_int @ Ys @ N2 ) ) @ R2 ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % listrel_iff_nth
% 2.75/3.05 thf(fact_1013_listrel__iff__nth,axiom,
% 2.75/3.05 ! [Xs: list_d,Ys: list_c,R2: set_Product_prod_d_c] :
% 2.75/3.05 ( ( member1739767152416986127list_c @ ( produc242965416994095062list_c @ Xs @ Ys ) @ ( listrel_d_c @ R2 ) )
% 2.75/3.05 = ( ( ( size_size_list_d @ Xs )
% 2.75/3.05 = ( size_size_list_c @ Ys ) )
% 2.75/3.05 & ! [N2: nat] :
% 2.75/3.05 ( ( ord_less_nat @ N2 @ ( size_size_list_d @ Xs ) )
% 2.75/3.05 => ( member2287536777068640527od_d_c @ ( product_Pair_d_c @ ( nth_d @ Xs @ N2 ) @ ( nth_c @ Ys @ N2 ) ) @ R2 ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % listrel_iff_nth
% 2.75/3.05 thf(fact_1014_listrel__iff__nth,axiom,
% 2.75/3.05 ! [Xs: list_d,Ys: list_d,R2: set_Product_prod_d_d] :
% 2.75/3.05 ( ( member1810801192463332112list_d @ ( produc242965421297323863list_d @ Xs @ Ys ) @ ( listrel_d_d @ R2 ) )
% 2.75/3.05 = ( ( ( size_size_list_d @ Xs )
% 2.75/3.05 = ( size_size_list_d @ Ys ) )
% 2.75/3.05 & ! [N2: nat] :
% 2.75/3.05 ( ( ord_less_nat @ N2 @ ( size_size_list_d @ Xs ) )
% 2.75/3.05 => ( member2287536781371869328od_d_d @ ( product_Pair_d_d @ ( nth_d @ Xs @ N2 ) @ ( nth_d @ Ys @ N2 ) ) @ R2 ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % listrel_iff_nth
% 2.75/3.05 thf(fact_1015_listrel__iff__nth,axiom,
% 2.75/3.05 ! [Xs: list_d,Ys: list_nat,R2: set_Pr3276347184212964150_d_nat] :
% 2.75/3.05 ( ( member6851837201453759021st_nat @ ( produc6793648210820618640st_nat @ Xs @ Ys ) @ ( listrel_d_nat @ R2 ) )
% 2.75/3.05 = ( ( ( size_size_list_d @ Xs )
% 2.75/3.05 = ( size_size_list_nat @ Ys ) )
% 2.75/3.05 & ! [N2: nat] :
% 2.75/3.05 ( ( ord_less_nat @ N2 @ ( size_size_list_d @ Xs ) )
% 2.75/3.05 => ( member207149538400826391_d_nat @ ( product_Pair_d_nat @ ( nth_d @ Xs @ N2 ) @ ( nth_nat @ Ys @ N2 ) ) @ R2 ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % listrel_iff_nth
% 2.75/3.05 thf(fact_1016_listrel__iff__nth,axiom,
% 2.75/3.05 ! [Xs: list_d,Ys: list_int,R2: set_Pr786264039281237394_d_int] :
% 2.75/3.05 ( ( member4361754056522032265st_int @ ( produc2615797191311421932st_int @ Xs @ Ys ) @ ( listrel_d_int @ R2 ) )
% 2.75/3.05 = ( ( ( size_size_list_d @ Xs )
% 2.75/3.05 = ( size_size_list_int @ Ys ) )
% 2.75/3.05 & ! [N2: nat] :
% 2.75/3.05 ( ( ord_less_nat @ N2 @ ( size_size_list_d @ Xs ) )
% 2.75/3.05 => ( member5252670555746405491_d_int @ ( product_Pair_d_int @ ( nth_d @ Xs @ N2 ) @ ( nth_int @ Ys @ N2 ) ) @ R2 ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % listrel_iff_nth
% 2.75/3.05 thf(fact_1017_listrel__iff__nth,axiom,
% 2.75/3.05 ! [Xs: list_nat,Ys: list_c,R2: set_Pr4335409928928841947_nat_c] :
% 2.75/3.05 ( ( member6074218473364765234list_c @ ( produc7723716018658481613list_c @ Xs @ Ys ) @ ( listrel_nat_c @ R2 ) )
% 2.75/3.05 = ( ( ( size_size_list_nat @ Xs )
% 2.75/3.05 = ( size_size_list_c @ Ys ) )
% 2.75/3.05 & ! [N2: nat] :
% 2.75/3.05 ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) )
% 2.75/3.05 => ( member8962352060716553276_nat_c @ ( product_Pair_nat_c @ ( nth_nat @ Xs @ N2 ) @ ( nth_c @ Ys @ N2 ) ) @ R2 ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % listrel_iff_nth
% 2.75/3.05 thf(fact_1018_listrel__iff__nth,axiom,
% 2.75/3.05 ! [Xs: list_nat,Ys: list_d,R2: set_Pr4406443968975187932_nat_d] :
% 2.75/3.05 ( ( member6145252513411111219list_d @ ( produc7723716022961710414list_d @ Xs @ Ys ) @ ( listrel_nat_d @ R2 ) )
% 2.75/3.05 = ( ( ( size_size_list_nat @ Xs )
% 2.75/3.05 = ( size_size_list_d @ Ys ) )
% 2.75/3.05 & ! [N2: nat] :
% 2.75/3.05 ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) )
% 2.75/3.05 => ( member8962352065019782077_nat_d @ ( product_Pair_nat_d @ ( nth_nat @ Xs @ N2 ) @ ( nth_d @ Ys @ N2 ) ) @ R2 ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % listrel_iff_nth
% 2.75/3.05 thf(fact_1019_ent__pure__post__iff__sng,axiom,
% 2.75/3.05 ! [P: assn,B2: $o] :
% 2.75/3.05 ( ( entails @ P @ ( pure_assn @ B2 ) )
% 2.75/3.05 = ( ! [H3: produc3658429121746597890et_nat] :
% 2.75/3.05 ( ( rep_assn @ P @ H3 )
% 2.75/3.05 => B2 )
% 2.75/3.05 & ( entails @ P @ one_one_assn ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % ent_pure_post_iff_sng
% 2.75/3.05 thf(fact_1020_mult__1,axiom,
% 2.75/3.05 ! [A2: code_integer] :
% 2.75/3.05 ( ( times_3573771949741848930nteger @ one_one_Code_integer @ A2 )
% 2.75/3.05 = A2 ) ).
% 2.75/3.05
% 2.75/3.05 % mult_1
% 2.75/3.05 thf(fact_1021_mult__1,axiom,
% 2.75/3.05 ! [A2: assn] :
% 2.75/3.05 ( ( times_times_assn @ one_one_assn @ A2 )
% 2.75/3.05 = A2 ) ).
% 2.75/3.05
% 2.75/3.05 % mult_1
% 2.75/3.05 thf(fact_1022_mult__1,axiom,
% 2.75/3.05 ! [A2: rat] :
% 2.75/3.05 ( ( times_times_rat @ one_one_rat @ A2 )
% 2.75/3.05 = A2 ) ).
% 2.75/3.05
% 2.75/3.05 % mult_1
% 2.75/3.05 thf(fact_1023_mult__1,axiom,
% 2.75/3.05 ! [A2: nat] :
% 2.75/3.05 ( ( times_times_nat @ one_one_nat @ A2 )
% 2.75/3.05 = A2 ) ).
% 2.75/3.05
% 2.75/3.05 % mult_1
% 2.75/3.05 thf(fact_1024_mult__1,axiom,
% 2.75/3.05 ! [A2: int] :
% 2.75/3.05 ( ( times_times_int @ one_one_int @ A2 )
% 2.75/3.05 = A2 ) ).
% 2.75/3.05
% 2.75/3.05 % mult_1
% 2.75/3.05 thf(fact_1025_mult_Oright__neutral,axiom,
% 2.75/3.05 ! [A2: code_integer] :
% 2.75/3.05 ( ( times_3573771949741848930nteger @ A2 @ one_one_Code_integer )
% 2.75/3.05 = A2 ) ).
% 2.75/3.05
% 2.75/3.05 % mult.right_neutral
% 2.75/3.05 thf(fact_1026_mult_Oright__neutral,axiom,
% 2.75/3.05 ! [A2: assn] :
% 2.75/3.05 ( ( times_times_assn @ A2 @ one_one_assn )
% 2.75/3.05 = A2 ) ).
% 2.75/3.05
% 2.75/3.05 % mult.right_neutral
% 2.75/3.05 thf(fact_1027_mult_Oright__neutral,axiom,
% 2.75/3.05 ! [A2: rat] :
% 2.75/3.05 ( ( times_times_rat @ A2 @ one_one_rat )
% 2.75/3.05 = A2 ) ).
% 2.75/3.05
% 2.75/3.05 % mult.right_neutral
% 2.75/3.05 thf(fact_1028_mult_Oright__neutral,axiom,
% 2.75/3.05 ! [A2: nat] :
% 2.75/3.05 ( ( times_times_nat @ A2 @ one_one_nat )
% 2.75/3.05 = A2 ) ).
% 2.75/3.05
% 2.75/3.05 % mult.right_neutral
% 2.75/3.05 thf(fact_1029_mult_Oright__neutral,axiom,
% 2.75/3.05 ! [A2: int] :
% 2.75/3.05 ( ( times_times_int @ A2 @ one_one_int )
% 2.75/3.05 = A2 ) ).
% 2.75/3.05
% 2.75/3.05 % mult.right_neutral
% 2.75/3.05 thf(fact_1030_in__set__remove1,axiom,
% 2.75/3.05 ! [A2: produc3843707927480180839at_nat,B2: produc3843707927480180839at_nat,Xs: list_P5464809261938338413at_nat] :
% 2.75/3.05 ( ( A2 != B2 )
% 2.75/3.05 => ( ( member8757157785044589968at_nat @ A2 @ ( set_Pr3765526544606949372at_nat @ ( remove8895909992688781315at_nat @ B2 @ Xs ) ) )
% 2.75/3.05 = ( member8757157785044589968at_nat @ A2 @ ( set_Pr3765526544606949372at_nat @ Xs ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_remove1
% 2.75/3.05 thf(fact_1031_in__set__remove1,axiom,
% 2.75/3.05 ! [A2: product_prod_nat_nat,B2: product_prod_nat_nat,Xs: list_P6011104703257516679at_nat] :
% 2.75/3.05 ( ( A2 != B2 )
% 2.75/3.05 => ( ( member8440522571783428010at_nat @ A2 @ ( set_Pr5648618587558075414at_nat @ ( remove5766854097993331357at_nat @ B2 @ Xs ) ) )
% 2.75/3.05 = ( member8440522571783428010at_nat @ A2 @ ( set_Pr5648618587558075414at_nat @ Xs ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_remove1
% 2.75/3.05 thf(fact_1032_in__set__remove1,axiom,
% 2.75/3.05 ! [A2: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat > $o,Xs: list_P7985473006766602707_nat_o] :
% 2.75/3.05 ( ( A2 != B2 )
% 2.75/3.05 => ( ( member6576561426505652726_nat_o @ A2 @ ( set_Pr400311997697478754_nat_o @ ( remove4235003712227595625_nat_o @ B2 @ Xs ) ) )
% 2.75/3.05 = ( member6576561426505652726_nat_o @ A2 @ ( set_Pr400311997697478754_nat_o @ Xs ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_remove1
% 2.75/3.05 thf(fact_1033_in__set__remove1,axiom,
% 2.75/3.05 ! [A2: int,B2: int,Xs: list_int] :
% 2.75/3.05 ( ( A2 != B2 )
% 2.75/3.05 => ( ( member_int @ A2 @ ( set_int2 @ ( remove1_int @ B2 @ Xs ) ) )
% 2.75/3.05 = ( member_int @ A2 @ ( set_int2 @ Xs ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_remove1
% 2.75/3.05 thf(fact_1034_in__set__remove1,axiom,
% 2.75/3.05 ! [A2: nat,B2: nat,Xs: list_nat] :
% 2.75/3.05 ( ( A2 != B2 )
% 2.75/3.05 => ( ( member_nat @ A2 @ ( set_nat2 @ ( remove1_nat @ B2 @ Xs ) ) )
% 2.75/3.05 = ( member_nat @ A2 @ ( set_nat2 @ Xs ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_remove1
% 2.75/3.05 thf(fact_1035_in__set__remove1,axiom,
% 2.75/3.05 ! [A2: produc6575502325842934193n_assn,B2: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn] :
% 2.75/3.05 ( ( A2 != B2 )
% 2.75/3.05 => ( ( member7957490590177025114n_assn @ A2 @ ( set_Pr1139785259514867910n_assn @ ( remove1670527618125605709n_assn @ B2 @ Xs ) ) )
% 2.75/3.05 = ( member7957490590177025114n_assn @ A2 @ ( set_Pr1139785259514867910n_assn @ Xs ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_remove1
% 2.75/3.05 thf(fact_1036_removeAll__id,axiom,
% 2.75/3.05 ! [X: produc3843707927480180839at_nat,Xs: list_P5464809261938338413at_nat] :
% 2.75/3.05 ( ~ ( member8757157785044589968at_nat @ X @ ( set_Pr3765526544606949372at_nat @ Xs ) )
% 2.75/3.05 => ( ( remove4908499291543849587at_nat @ X @ Xs )
% 2.75/3.05 = Xs ) ) ).
% 2.75/3.05
% 2.75/3.05 % removeAll_id
% 2.75/3.05 thf(fact_1037_removeAll__id,axiom,
% 2.75/3.05 ! [X: product_prod_nat_nat,Xs: list_P6011104703257516679at_nat] :
% 2.75/3.05 ( ~ ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 2.75/3.05 => ( ( remove3673390508374433037at_nat @ X @ Xs )
% 2.75/3.05 = Xs ) ) ).
% 2.75/3.05
% 2.75/3.05 % removeAll_id
% 2.75/3.05 thf(fact_1038_removeAll__id,axiom,
% 2.75/3.05 ! [X: produc3658429121746597890et_nat > $o,Xs: list_P7985473006766602707_nat_o] :
% 2.75/3.05 ( ~ ( member6576561426505652726_nat_o @ X @ ( set_Pr400311997697478754_nat_o @ Xs ) )
% 2.75/3.05 => ( ( remove7604696131425036249_nat_o @ X @ Xs )
% 2.75/3.05 = Xs ) ) ).
% 2.75/3.05
% 2.75/3.05 % removeAll_id
% 2.75/3.05 thf(fact_1039_removeAll__id,axiom,
% 2.75/3.05 ! [X: int,Xs: list_int] :
% 2.75/3.05 ( ~ ( member_int @ X @ ( set_int2 @ Xs ) )
% 2.75/3.05 => ( ( removeAll_int @ X @ Xs )
% 2.75/3.05 = Xs ) ) ).
% 2.75/3.05
% 2.75/3.05 % removeAll_id
% 2.75/3.05 thf(fact_1040_removeAll__id,axiom,
% 2.75/3.05 ! [X: nat,Xs: list_nat] :
% 2.75/3.05 ( ~ ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 2.75/3.05 => ( ( removeAll_nat @ X @ Xs )
% 2.75/3.05 = Xs ) ) ).
% 2.75/3.05
% 2.75/3.05 % removeAll_id
% 2.75/3.05 thf(fact_1041_removeAll__id,axiom,
% 2.75/3.05 ! [X: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn] :
% 2.75/3.05 ( ~ ( member7957490590177025114n_assn @ X @ ( set_Pr1139785259514867910n_assn @ Xs ) )
% 2.75/3.05 => ( ( remove1763081955827946941n_assn @ X @ Xs )
% 2.75/3.05 = Xs ) ) ).
% 2.75/3.05
% 2.75/3.05 % removeAll_id
% 2.75/3.05 thf(fact_1042_pure__true,axiom,
% 2.75/3.05 ( ( pure_assn @ $true )
% 2.75/3.05 = one_one_assn ) ).
% 2.75/3.05
% 2.75/3.05 % pure_true
% 2.75/3.05 thf(fact_1043_pure__assn__eq__emp__iff,axiom,
% 2.75/3.05 ! [P: $o] :
% 2.75/3.05 ( ( ( pure_assn @ P )
% 2.75/3.05 = one_one_assn )
% 2.75/3.05 = P ) ).
% 2.75/3.05
% 2.75/3.05 % pure_assn_eq_emp_iff
% 2.75/3.05 thf(fact_1044_entt__emp,axiom,
% 2.75/3.05 ! [A: assn] : ( entailst @ A @ one_one_assn ) ).
% 2.75/3.05
% 2.75/3.05 % entt_emp
% 2.75/3.05 thf(fact_1045_in__set__insert,axiom,
% 2.75/3.05 ! [X: produc3843707927480180839at_nat,Xs: list_P5464809261938338413at_nat] :
% 2.75/3.05 ( ( member8757157785044589968at_nat @ X @ ( set_Pr3765526544606949372at_nat @ Xs ) )
% 2.75/3.05 => ( ( insert4149901806602606979at_nat @ X @ Xs )
% 2.75/3.05 = Xs ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_insert
% 2.75/3.05 thf(fact_1046_in__set__insert,axiom,
% 2.75/3.05 ! [X: product_prod_nat_nat,Xs: list_P6011104703257516679at_nat] :
% 2.75/3.05 ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 2.75/3.05 => ( ( insert8944034826898310173at_nat @ X @ Xs )
% 2.75/3.05 = Xs ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_insert
% 2.75/3.05 thf(fact_1047_in__set__insert,axiom,
% 2.75/3.05 ! [X: produc3658429121746597890et_nat > $o,Xs: list_P7985473006766602707_nat_o] :
% 2.75/3.05 ( ( member6576561426505652726_nat_o @ X @ ( set_Pr400311997697478754_nat_o @ Xs ) )
% 2.75/3.05 => ( ( insert8021100735160035049_nat_o @ X @ Xs )
% 2.75/3.05 = Xs ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_insert
% 2.75/3.05 thf(fact_1048_in__set__insert,axiom,
% 2.75/3.05 ! [X: int,Xs: list_int] :
% 2.75/3.05 ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 2.75/3.05 => ( ( insert_int @ X @ Xs )
% 2.75/3.05 = Xs ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_insert
% 2.75/3.05 thf(fact_1049_in__set__insert,axiom,
% 2.75/3.05 ! [X: nat,Xs: list_nat] :
% 2.75/3.05 ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 2.75/3.05 => ( ( insert_nat @ X @ Xs )
% 2.75/3.05 = Xs ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_insert
% 2.75/3.05 thf(fact_1050_in__set__insert,axiom,
% 2.75/3.05 ! [X: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn] :
% 2.75/3.05 ( ( member7957490590177025114n_assn @ X @ ( set_Pr1139785259514867910n_assn @ Xs ) )
% 2.75/3.05 => ( ( insert3246601298802261197n_assn @ X @ Xs )
% 2.75/3.05 = Xs ) ) ).
% 2.75/3.05
% 2.75/3.05 % in_set_insert
% 2.75/3.05 thf(fact_1051_assn__basic__inequalities_I3_J,axiom,
% 2.75/3.05 bot_bot_assn != one_one_assn ).
% 2.75/3.05
% 2.75/3.05 % assn_basic_inequalities(3)
% 2.75/3.05 thf(fact_1052_distinct__insert,axiom,
% 2.75/3.05 ! [X: int,Xs: list_int] :
% 2.75/3.05 ( ( distinct_int @ ( insert_int @ X @ Xs ) )
% 2.75/3.05 = ( distinct_int @ Xs ) ) ).
% 2.75/3.05
% 2.75/3.05 % distinct_insert
% 2.75/3.05 thf(fact_1053_distinct__insert,axiom,
% 2.75/3.05 ! [X: nat,Xs: list_nat] :
% 2.75/3.05 ( ( distinct_nat @ ( insert_nat @ X @ Xs ) )
% 2.75/3.05 = ( distinct_nat @ Xs ) ) ).
% 2.75/3.05
% 2.75/3.05 % distinct_insert
% 2.75/3.05 thf(fact_1054_ent__pure__pre__iff__sng,axiom,
% 2.75/3.05 ! [B2: $o,Q: assn] :
% 2.75/3.05 ( ( entails @ ( pure_assn @ B2 ) @ Q )
% 2.75/3.05 = ( B2
% 2.75/3.05 => ( entails @ one_one_assn @ Q ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % ent_pure_pre_iff_sng
% 2.75/3.05 thf(fact_1055_one__reorient,axiom,
% 2.75/3.05 ! [X: code_integer] :
% 2.75/3.05 ( ( one_one_Code_integer = X )
% 2.75/3.05 = ( X = one_one_Code_integer ) ) ).
% 2.75/3.05
% 2.75/3.05 % one_reorient
% 2.75/3.05 thf(fact_1056_one__reorient,axiom,
% 2.75/3.05 ! [X: assn] :
% 2.75/3.05 ( ( one_one_assn = X )
% 2.75/3.05 = ( X = one_one_assn ) ) ).
% 2.75/3.05
% 2.75/3.05 % one_reorient
% 2.75/3.05 thf(fact_1057_one__reorient,axiom,
% 2.75/3.05 ! [X: rat] :
% 2.75/3.05 ( ( one_one_rat = X )
% 2.75/3.05 = ( X = one_one_rat ) ) ).
% 2.75/3.05
% 2.75/3.05 % one_reorient
% 2.75/3.05 thf(fact_1058_one__reorient,axiom,
% 2.75/3.05 ! [X: nat] :
% 2.75/3.05 ( ( one_one_nat = X )
% 2.75/3.05 = ( X = one_one_nat ) ) ).
% 2.75/3.05
% 2.75/3.05 % one_reorient
% 2.75/3.05 thf(fact_1059_one__reorient,axiom,
% 2.75/3.05 ! [X: int] :
% 2.75/3.05 ( ( one_one_int = X )
% 2.75/3.05 = ( X = one_one_int ) ) ).
% 2.75/3.05
% 2.75/3.05 % one_reorient
% 2.75/3.05 thf(fact_1060_times__assn__raw_Ocases,axiom,
% 2.75/3.05 ! [X: produc2732055786443039994et_nat] :
% 2.75/3.05 ~ ! [P5: produc3658429121746597890et_nat > $o,Q4: produc3658429121746597890et_nat > $o,H: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.75/3.05 ( X
% 2.75/3.05 != ( produc2245416461498447860et_nat @ P5 @ ( produc5001842942810119800et_nat @ Q4 @ ( produc7507926704131184380et_nat @ H @ As ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % times_assn_raw.cases
% 2.75/3.05 thf(fact_1061_listrel1__eq__len,axiom,
% 2.75/3.05 ! [Xs: list_c,Ys: list_c,R2: set_Product_prod_c_c] :
% 2.75/3.05 ( ( member7012247553653173456list_c @ ( produc5515445818230282391list_c @ Xs @ Ys ) @ ( listrel1_c @ R2 ) )
% 2.75/3.05 => ( ( size_size_list_c @ Xs )
% 2.75/3.05 = ( size_size_list_c @ Ys ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % listrel1_eq_len
% 2.75/3.05 thf(fact_1062_listrel1__eq__len,axiom,
% 2.75/3.05 ! [Xs: list_d,Ys: list_d,R2: set_Product_prod_d_d] :
% 2.75/3.05 ( ( member1810801192463332112list_d @ ( produc242965421297323863list_d @ Xs @ Ys ) @ ( listrel1_d @ R2 ) )
% 2.75/3.05 => ( ( size_size_list_d @ Xs )
% 2.75/3.05 = ( size_size_list_d @ Ys ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % listrel1_eq_len
% 2.75/3.05 thf(fact_1063_listrel1__eq__len,axiom,
% 2.75/3.05 ! [Xs: list_nat,Ys: list_nat,R2: set_Pr1261947904930325089at_nat] :
% 2.75/3.05 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs @ Ys ) @ ( listrel1_nat @ R2 ) )
% 2.75/3.05 => ( ( size_size_list_nat @ Xs )
% 2.75/3.05 = ( size_size_list_nat @ Ys ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % listrel1_eq_len
% 2.75/3.05 thf(fact_1064_listrel1__eq__len,axiom,
% 2.75/3.05 ! [Xs: list_int,Ys: list_int,R2: set_Pr958786334691620121nt_int] :
% 2.75/3.05 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs @ Ys ) @ ( listrel1_int @ R2 ) )
% 2.75/3.05 => ( ( size_size_list_int @ Xs )
% 2.75/3.05 = ( size_size_list_int @ Ys ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % listrel1_eq_len
% 2.75/3.05 thf(fact_1065_listrel__eq__len,axiom,
% 2.75/3.05 ! [Xs: list_c,Ys: list_c,R2: set_Product_prod_c_c] :
% 2.75/3.05 ( ( member7012247553653173456list_c @ ( produc5515445818230282391list_c @ Xs @ Ys ) @ ( listrel_c_c @ R2 ) )
% 2.75/3.05 => ( ( size_size_list_c @ Xs )
% 2.75/3.05 = ( size_size_list_c @ Ys ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % listrel_eq_len
% 2.75/3.05 thf(fact_1066_listrel__eq__len,axiom,
% 2.75/3.05 ! [Xs: list_c,Ys: list_d,R2: set_Product_prod_c_d] :
% 2.75/3.05 ( ( member7083281593699519441list_d @ ( produc5515445822533511192list_d @ Xs @ Ys ) @ ( listrel_c_d @ R2 ) )
% 2.75/3.05 => ( ( size_size_list_c @ Xs )
% 2.75/3.05 = ( size_size_list_d @ Ys ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % listrel_eq_len
% 2.75/3.05 thf(fact_1067_listrel__eq__len,axiom,
% 2.75/3.05 ! [Xs: list_c,Ys: list_nat,R2: set_Pr6903500605879609269_c_nat] :
% 2.75/3.05 ( ( member6184937725913850668st_nat @ ( produc6126748735280710287st_nat @ Xs @ Ys ) @ ( listrel_c_nat @ R2 ) )
% 2.75/3.05 => ( ( size_size_list_c @ Xs )
% 2.75/3.05 = ( size_size_list_nat @ Ys ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % listrel_eq_len
% 2.75/3.05 thf(fact_1068_listrel__eq__len,axiom,
% 2.75/3.05 ! [Xs: list_c,Ys: list_int,R2: set_Pr4413417460947882513_c_int] :
% 2.75/3.05 ( ( member3694854580982123912st_int @ ( produc1948897715771513579st_int @ Xs @ Ys ) @ ( listrel_c_int @ R2 ) )
% 2.75/3.05 => ( ( size_size_list_c @ Xs )
% 2.75/3.05 = ( size_size_list_int @ Ys ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % listrel_eq_len
% 2.75/3.05 thf(fact_1069_listrel__eq__len,axiom,
% 2.75/3.05 ! [Xs: list_d,Ys: list_c,R2: set_Product_prod_d_c] :
% 2.75/3.05 ( ( member1739767152416986127list_c @ ( produc242965416994095062list_c @ Xs @ Ys ) @ ( listrel_d_c @ R2 ) )
% 2.75/3.05 => ( ( size_size_list_d @ Xs )
% 2.75/3.05 = ( size_size_list_c @ Ys ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % listrel_eq_len
% 2.75/3.05 thf(fact_1070_listrel__eq__len,axiom,
% 2.75/3.05 ! [Xs: list_d,Ys: list_d,R2: set_Product_prod_d_d] :
% 2.75/3.05 ( ( member1810801192463332112list_d @ ( produc242965421297323863list_d @ Xs @ Ys ) @ ( listrel_d_d @ R2 ) )
% 2.75/3.05 => ( ( size_size_list_d @ Xs )
% 2.75/3.05 = ( size_size_list_d @ Ys ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % listrel_eq_len
% 2.75/3.05 thf(fact_1071_listrel__eq__len,axiom,
% 2.75/3.05 ! [Xs: list_d,Ys: list_nat,R2: set_Pr3276347184212964150_d_nat] :
% 2.75/3.05 ( ( member6851837201453759021st_nat @ ( produc6793648210820618640st_nat @ Xs @ Ys ) @ ( listrel_d_nat @ R2 ) )
% 2.75/3.05 => ( ( size_size_list_d @ Xs )
% 2.75/3.05 = ( size_size_list_nat @ Ys ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % listrel_eq_len
% 2.75/3.05 thf(fact_1072_listrel__eq__len,axiom,
% 2.75/3.05 ! [Xs: list_d,Ys: list_int,R2: set_Pr786264039281237394_d_int] :
% 2.75/3.05 ( ( member4361754056522032265st_int @ ( produc2615797191311421932st_int @ Xs @ Ys ) @ ( listrel_d_int @ R2 ) )
% 2.75/3.05 => ( ( size_size_list_d @ Xs )
% 2.75/3.05 = ( size_size_list_int @ Ys ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % listrel_eq_len
% 2.75/3.05 thf(fact_1073_listrel__eq__len,axiom,
% 2.75/3.05 ! [Xs: list_nat,Ys: list_c,R2: set_Pr4335409928928841947_nat_c] :
% 2.75/3.05 ( ( member6074218473364765234list_c @ ( produc7723716018658481613list_c @ Xs @ Ys ) @ ( listrel_nat_c @ R2 ) )
% 2.75/3.05 => ( ( size_size_list_nat @ Xs )
% 2.75/3.05 = ( size_size_list_c @ Ys ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % listrel_eq_len
% 2.75/3.05 thf(fact_1074_listrel__eq__len,axiom,
% 2.75/3.05 ! [Xs: list_nat,Ys: list_d,R2: set_Pr4406443968975187932_nat_d] :
% 2.75/3.05 ( ( member6145252513411111219list_d @ ( produc7723716022961710414list_d @ Xs @ Ys ) @ ( listrel_nat_d @ R2 ) )
% 2.75/3.05 => ( ( size_size_list_nat @ Xs )
% 2.75/3.05 = ( size_size_list_d @ Ys ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % listrel_eq_len
% 2.75/3.05 thf(fact_1075_distinct__remove1__removeAll,axiom,
% 2.75/3.05 ! [Xs: list_int,X: int] :
% 2.75/3.05 ( ( distinct_int @ Xs )
% 2.75/3.05 => ( ( remove1_int @ X @ Xs )
% 2.75/3.05 = ( removeAll_int @ X @ Xs ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % distinct_remove1_removeAll
% 2.75/3.05 thf(fact_1076_distinct__remove1__removeAll,axiom,
% 2.75/3.05 ! [Xs: list_nat,X: nat] :
% 2.75/3.05 ( ( distinct_nat @ Xs )
% 2.75/3.05 => ( ( remove1_nat @ X @ Xs )
% 2.75/3.05 = ( removeAll_nat @ X @ Xs ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % distinct_remove1_removeAll
% 2.75/3.05 thf(fact_1077_mult_Ocomm__neutral,axiom,
% 2.75/3.05 ! [A2: code_integer] :
% 2.75/3.05 ( ( times_3573771949741848930nteger @ A2 @ one_one_Code_integer )
% 2.75/3.05 = A2 ) ).
% 2.75/3.05
% 2.75/3.05 % mult.comm_neutral
% 2.75/3.05 thf(fact_1078_mult_Ocomm__neutral,axiom,
% 2.75/3.05 ! [A2: assn] :
% 2.75/3.05 ( ( times_times_assn @ A2 @ one_one_assn )
% 2.75/3.05 = A2 ) ).
% 2.75/3.05
% 2.75/3.05 % mult.comm_neutral
% 2.75/3.05 thf(fact_1079_mult_Ocomm__neutral,axiom,
% 2.75/3.05 ! [A2: rat] :
% 2.75/3.05 ( ( times_times_rat @ A2 @ one_one_rat )
% 2.75/3.05 = A2 ) ).
% 2.75/3.05
% 2.75/3.05 % mult.comm_neutral
% 2.75/3.05 thf(fact_1080_mult_Ocomm__neutral,axiom,
% 2.75/3.05 ! [A2: nat] :
% 2.75/3.05 ( ( times_times_nat @ A2 @ one_one_nat )
% 2.75/3.05 = A2 ) ).
% 2.75/3.05
% 2.75/3.05 % mult.comm_neutral
% 2.75/3.05 thf(fact_1081_mult_Ocomm__neutral,axiom,
% 2.75/3.05 ! [A2: int] :
% 2.75/3.05 ( ( times_times_int @ A2 @ one_one_int )
% 2.75/3.05 = A2 ) ).
% 2.75/3.05
% 2.75/3.05 % mult.comm_neutral
% 2.75/3.05 thf(fact_1082_comm__monoid__mult__class_Omult__1,axiom,
% 2.75/3.05 ! [A2: code_integer] :
% 2.75/3.05 ( ( times_3573771949741848930nteger @ one_one_Code_integer @ A2 )
% 2.75/3.05 = A2 ) ).
% 2.75/3.05
% 2.75/3.05 % comm_monoid_mult_class.mult_1
% 2.75/3.05 thf(fact_1083_comm__monoid__mult__class_Omult__1,axiom,
% 2.75/3.05 ! [A2: assn] :
% 2.75/3.05 ( ( times_times_assn @ one_one_assn @ A2 )
% 2.75/3.05 = A2 ) ).
% 2.75/3.05
% 2.75/3.05 % comm_monoid_mult_class.mult_1
% 2.75/3.05 thf(fact_1084_comm__monoid__mult__class_Omult__1,axiom,
% 2.75/3.05 ! [A2: rat] :
% 2.75/3.05 ( ( times_times_rat @ one_one_rat @ A2 )
% 2.75/3.05 = A2 ) ).
% 2.75/3.05
% 2.75/3.05 % comm_monoid_mult_class.mult_1
% 2.75/3.05 thf(fact_1085_comm__monoid__mult__class_Omult__1,axiom,
% 2.75/3.05 ! [A2: nat] :
% 2.75/3.05 ( ( times_times_nat @ one_one_nat @ A2 )
% 2.75/3.05 = A2 ) ).
% 2.75/3.05
% 2.75/3.05 % comm_monoid_mult_class.mult_1
% 2.75/3.05 thf(fact_1086_comm__monoid__mult__class_Omult__1,axiom,
% 2.75/3.05 ! [A2: int] :
% 2.75/3.05 ( ( times_times_int @ one_one_int @ A2 )
% 2.75/3.05 = A2 ) ).
% 2.75/3.05
% 2.75/3.05 % comm_monoid_mult_class.mult_1
% 2.75/3.05 thf(fact_1087_assn__one__left,axiom,
% 2.75/3.05 ! [P: assn] :
% 2.75/3.05 ( ( times_times_assn @ one_one_assn @ P )
% 2.75/3.05 = P ) ).
% 2.75/3.05
% 2.75/3.05 % assn_one_left
% 2.75/3.05 thf(fact_1088_norm__assertion__simps_I1_J,axiom,
% 2.75/3.05 ! [A2: assn] :
% 2.75/3.05 ( ( times_times_assn @ one_one_assn @ A2 )
% 2.75/3.05 = A2 ) ).
% 2.75/3.05
% 2.75/3.05 % norm_assertion_simps(1)
% 2.75/3.05 thf(fact_1089_norm__assertion__simps_I2_J,axiom,
% 2.75/3.05 ! [A2: assn] :
% 2.75/3.05 ( ( times_times_assn @ A2 @ one_one_assn )
% 2.75/3.05 = A2 ) ).
% 2.75/3.05
% 2.75/3.05 % norm_assertion_simps(2)
% 2.75/3.05 thf(fact_1090_remove1__idem,axiom,
% 2.75/3.05 ! [X: produc3843707927480180839at_nat,Xs: list_P5464809261938338413at_nat] :
% 2.75/3.05 ( ~ ( member8757157785044589968at_nat @ X @ ( set_Pr3765526544606949372at_nat @ Xs ) )
% 2.75/3.05 => ( ( remove8895909992688781315at_nat @ X @ Xs )
% 2.75/3.05 = Xs ) ) ).
% 2.75/3.05
% 2.75/3.05 % remove1_idem
% 2.75/3.05 thf(fact_1091_remove1__idem,axiom,
% 2.75/3.05 ! [X: product_prod_nat_nat,Xs: list_P6011104703257516679at_nat] :
% 2.75/3.05 ( ~ ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 2.75/3.05 => ( ( remove5766854097993331357at_nat @ X @ Xs )
% 2.75/3.05 = Xs ) ) ).
% 2.75/3.05
% 2.75/3.05 % remove1_idem
% 2.75/3.05 thf(fact_1092_remove1__idem,axiom,
% 2.75/3.05 ! [X: produc3658429121746597890et_nat > $o,Xs: list_P7985473006766602707_nat_o] :
% 2.75/3.05 ( ~ ( member6576561426505652726_nat_o @ X @ ( set_Pr400311997697478754_nat_o @ Xs ) )
% 2.75/3.05 => ( ( remove4235003712227595625_nat_o @ X @ Xs )
% 2.75/3.05 = Xs ) ) ).
% 2.75/3.05
% 2.75/3.05 % remove1_idem
% 2.75/3.05 thf(fact_1093_remove1__idem,axiom,
% 2.75/3.05 ! [X: int,Xs: list_int] :
% 2.75/3.05 ( ~ ( member_int @ X @ ( set_int2 @ Xs ) )
% 2.75/3.05 => ( ( remove1_int @ X @ Xs )
% 2.75/3.05 = Xs ) ) ).
% 2.75/3.05
% 2.75/3.05 % remove1_idem
% 2.75/3.05 thf(fact_1094_remove1__idem,axiom,
% 2.75/3.05 ! [X: nat,Xs: list_nat] :
% 2.75/3.05 ( ~ ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 2.75/3.05 => ( ( remove1_nat @ X @ Xs )
% 2.75/3.05 = Xs ) ) ).
% 2.75/3.05
% 2.75/3.05 % remove1_idem
% 2.75/3.05 thf(fact_1095_remove1__idem,axiom,
% 2.75/3.05 ! [X: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn] :
% 2.75/3.05 ( ~ ( member7957490590177025114n_assn @ X @ ( set_Pr1139785259514867910n_assn @ Xs ) )
% 2.75/3.05 => ( ( remove1670527618125605709n_assn @ X @ Xs )
% 2.75/3.05 = Xs ) ) ).
% 2.75/3.05
% 2.75/3.05 % remove1_idem
% 2.75/3.05 thf(fact_1096_notin__set__remove1,axiom,
% 2.75/3.05 ! [X: produc3843707927480180839at_nat,Xs: list_P5464809261938338413at_nat,Y: produc3843707927480180839at_nat] :
% 2.75/3.05 ( ~ ( member8757157785044589968at_nat @ X @ ( set_Pr3765526544606949372at_nat @ Xs ) )
% 2.75/3.05 => ~ ( member8757157785044589968at_nat @ X @ ( set_Pr3765526544606949372at_nat @ ( remove8895909992688781315at_nat @ Y @ Xs ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % notin_set_remove1
% 2.75/3.05 thf(fact_1097_notin__set__remove1,axiom,
% 2.75/3.05 ! [X: product_prod_nat_nat,Xs: list_P6011104703257516679at_nat,Y: product_prod_nat_nat] :
% 2.75/3.05 ( ~ ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 2.75/3.05 => ~ ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ ( remove5766854097993331357at_nat @ Y @ Xs ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % notin_set_remove1
% 2.75/3.05 thf(fact_1098_notin__set__remove1,axiom,
% 2.75/3.05 ! [X: produc3658429121746597890et_nat > $o,Xs: list_P7985473006766602707_nat_o,Y: produc3658429121746597890et_nat > $o] :
% 2.75/3.05 ( ~ ( member6576561426505652726_nat_o @ X @ ( set_Pr400311997697478754_nat_o @ Xs ) )
% 2.75/3.05 => ~ ( member6576561426505652726_nat_o @ X @ ( set_Pr400311997697478754_nat_o @ ( remove4235003712227595625_nat_o @ Y @ Xs ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % notin_set_remove1
% 2.75/3.05 thf(fact_1099_notin__set__remove1,axiom,
% 2.75/3.05 ! [X: int,Xs: list_int,Y: int] :
% 2.75/3.05 ( ~ ( member_int @ X @ ( set_int2 @ Xs ) )
% 2.75/3.05 => ~ ( member_int @ X @ ( set_int2 @ ( remove1_int @ Y @ Xs ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % notin_set_remove1
% 2.75/3.05 thf(fact_1100_notin__set__remove1,axiom,
% 2.75/3.05 ! [X: nat,Xs: list_nat,Y: nat] :
% 2.75/3.05 ( ~ ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 2.75/3.05 => ~ ( member_nat @ X @ ( set_nat2 @ ( remove1_nat @ Y @ Xs ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % notin_set_remove1
% 2.75/3.05 thf(fact_1101_notin__set__remove1,axiom,
% 2.75/3.05 ! [X: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn,Y: produc6575502325842934193n_assn] :
% 2.75/3.05 ( ~ ( member7957490590177025114n_assn @ X @ ( set_Pr1139785259514867910n_assn @ Xs ) )
% 2.75/3.05 => ~ ( member7957490590177025114n_assn @ X @ ( set_Pr1139785259514867910n_assn @ ( remove1670527618125605709n_assn @ Y @ Xs ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % notin_set_remove1
% 2.75/3.05 thf(fact_1102_distinct__remove1,axiom,
% 2.75/3.05 ! [Xs: list_int,X: int] :
% 2.75/3.05 ( ( distinct_int @ Xs )
% 2.75/3.05 => ( distinct_int @ ( remove1_int @ X @ Xs ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % distinct_remove1
% 2.75/3.05 thf(fact_1103_distinct__remove1,axiom,
% 2.75/3.05 ! [Xs: list_nat,X: nat] :
% 2.75/3.05 ( ( distinct_nat @ Xs )
% 2.75/3.05 => ( distinct_nat @ ( remove1_nat @ X @ Xs ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % distinct_remove1
% 2.75/3.05 thf(fact_1104_distinct__removeAll,axiom,
% 2.75/3.05 ! [Xs: list_int,X: int] :
% 2.75/3.05 ( ( distinct_int @ Xs )
% 2.75/3.05 => ( distinct_int @ ( removeAll_int @ X @ Xs ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % distinct_removeAll
% 2.75/3.05 thf(fact_1105_distinct__removeAll,axiom,
% 2.75/3.05 ! [Xs: list_nat,X: nat] :
% 2.75/3.05 ( ( distinct_nat @ Xs )
% 2.75/3.05 => ( distinct_nat @ ( removeAll_nat @ X @ Xs ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % distinct_removeAll
% 2.75/3.05 thf(fact_1106_less__1__mult,axiom,
% 2.75/3.05 ! [M2: rat,N: rat] :
% 2.75/3.05 ( ( ord_less_rat @ one_one_rat @ M2 )
% 2.75/3.05 => ( ( ord_less_rat @ one_one_rat @ N )
% 2.75/3.05 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M2 @ N ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % less_1_mult
% 2.75/3.05 thf(fact_1107_less__1__mult,axiom,
% 2.75/3.05 ! [M2: code_integer,N: code_integer] :
% 2.75/3.05 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ M2 )
% 2.75/3.05 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ N )
% 2.75/3.05 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ M2 @ N ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % less_1_mult
% 2.75/3.05 thf(fact_1108_less__1__mult,axiom,
% 2.75/3.05 ! [M2: nat,N: nat] :
% 2.75/3.05 ( ( ord_less_nat @ one_one_nat @ M2 )
% 2.75/3.05 => ( ( ord_less_nat @ one_one_nat @ N )
% 2.75/3.05 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M2 @ N ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % less_1_mult
% 2.75/3.05 thf(fact_1109_less__1__mult,axiom,
% 2.75/3.05 ! [M2: int,N: int] :
% 2.75/3.05 ( ( ord_less_int @ one_one_int @ M2 )
% 2.75/3.05 => ( ( ord_less_int @ one_one_int @ N )
% 2.75/3.05 => ( ord_less_int @ one_one_int @ ( times_times_int @ M2 @ N ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % less_1_mult
% 2.75/3.05 thf(fact_1110_entails__solve__init_I2_J,axiom,
% 2.75/3.05 ! [P: assn,Q: assn] :
% 2.75/3.05 ( ( fI_QUERY @ P @ Q @ one_one_assn )
% 2.75/3.05 => ( entails @ P @ Q ) ) ).
% 2.75/3.05
% 2.75/3.05 % entails_solve_init(2)
% 2.75/3.05 thf(fact_1111_prod__induct4,axiom,
% 2.75/3.05 ! [P: produc2732055786443039994et_nat > $o,X: produc2732055786443039994et_nat] :
% 2.75/3.05 ( ! [A4: produc3658429121746597890et_nat > $o,B4: produc3658429121746597890et_nat > $o,C4: heap_e7401611519738050253t_unit,D3: set_nat] : ( P @ ( produc2245416461498447860et_nat @ A4 @ ( produc5001842942810119800et_nat @ B4 @ ( produc7507926704131184380et_nat @ C4 @ D3 ) ) ) )
% 2.75/3.05 => ( P @ X ) ) ).
% 2.75/3.05
% 2.75/3.05 % prod_induct4
% 2.75/3.05 thf(fact_1112_prod__induct3,axiom,
% 2.75/3.05 ! [P: produc1908205239877642774nteger > $o,X: produc1908205239877642774nteger] :
% 2.75/3.05 ( ! [A4: produc6241069584506657477e_term > option6357759511663192854e_term,B4: code_integer,C4: code_integer] : ( P @ ( produc8603105652947943368nteger @ A4 @ ( produc1086072967326762835nteger @ B4 @ C4 ) ) )
% 2.75/3.05 => ( P @ X ) ) ).
% 2.75/3.05
% 2.75/3.05 % prod_induct3
% 2.75/3.05 thf(fact_1113_prod__induct3,axiom,
% 2.75/3.05 ! [P: produc3925858234332021118et_nat > $o,X: produc3925858234332021118et_nat] :
% 2.75/3.05 ( ! [A4: produc3658429121746597890et_nat > $o,B4: heap_e7401611519738050253t_unit,C4: set_nat] : ( P @ ( produc5001842942810119800et_nat @ A4 @ ( produc7507926704131184380et_nat @ B4 @ C4 ) ) )
% 2.75/3.05 => ( P @ X ) ) ).
% 2.75/3.05
% 2.75/3.05 % prod_induct3
% 2.75/3.05 thf(fact_1114_prod__induct3,axiom,
% 2.75/3.05 ! [P: produc2732055786443039994et_nat > $o,X: produc2732055786443039994et_nat] :
% 2.75/3.05 ( ! [A4: produc3658429121746597890et_nat > $o,B4: produc3658429121746597890et_nat > $o,C4: produc3658429121746597890et_nat] : ( P @ ( produc2245416461498447860et_nat @ A4 @ ( produc5001842942810119800et_nat @ B4 @ C4 ) ) )
% 2.75/3.05 => ( P @ X ) ) ).
% 2.75/3.05
% 2.75/3.05 % prod_induct3
% 2.75/3.05 thf(fact_1115_prod__induct3,axiom,
% 2.75/3.05 ! [P: produc2285326912895808259nt_int > $o,X: produc2285326912895808259nt_int] :
% 2.75/3.05 ( ! [A4: produc8551481072490612790e_term > option6357759511663192854e_term,B4: int,C4: int] : ( P @ ( produc5700946648718959541nt_int @ A4 @ ( product_Pair_int_int @ B4 @ C4 ) ) )
% 2.75/3.05 => ( P @ X ) ) ).
% 2.75/3.05
% 2.75/3.05 % prod_induct3
% 2.75/3.05 thf(fact_1116_prod__induct3,axiom,
% 2.75/3.05 ! [P: produc7773217078559923341nt_int > $o,X: produc7773217078559923341nt_int] :
% 2.75/3.05 ( ! [A4: int > option6357759511663192854e_term,B4: int,C4: int] : ( P @ ( produc4305682042979456191nt_int @ A4 @ ( product_Pair_int_int @ B4 @ C4 ) ) )
% 2.75/3.05 => ( P @ X ) ) ).
% 2.75/3.05
% 2.75/3.05 % prod_induct3
% 2.75/3.05 thf(fact_1117_prod__cases4,axiom,
% 2.75/3.05 ! [Y: produc2732055786443039994et_nat] :
% 2.75/3.05 ~ ! [A4: produc3658429121746597890et_nat > $o,B4: produc3658429121746597890et_nat > $o,C4: heap_e7401611519738050253t_unit,D3: set_nat] :
% 2.75/3.05 ( Y
% 2.75/3.05 != ( produc2245416461498447860et_nat @ A4 @ ( produc5001842942810119800et_nat @ B4 @ ( produc7507926704131184380et_nat @ C4 @ D3 ) ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % prod_cases4
% 2.75/3.05 thf(fact_1118_prod__cases3,axiom,
% 2.75/3.05 ! [Y: produc1908205239877642774nteger] :
% 2.75/3.05 ~ ! [A4: produc6241069584506657477e_term > option6357759511663192854e_term,B4: code_integer,C4: code_integer] :
% 2.75/3.05 ( Y
% 2.75/3.05 != ( produc8603105652947943368nteger @ A4 @ ( produc1086072967326762835nteger @ B4 @ C4 ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % prod_cases3
% 2.75/3.05 thf(fact_1119_prod__cases3,axiom,
% 2.75/3.05 ! [Y: produc3925858234332021118et_nat] :
% 2.75/3.05 ~ ! [A4: produc3658429121746597890et_nat > $o,B4: heap_e7401611519738050253t_unit,C4: set_nat] :
% 2.75/3.05 ( Y
% 2.75/3.05 != ( produc5001842942810119800et_nat @ A4 @ ( produc7507926704131184380et_nat @ B4 @ C4 ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % prod_cases3
% 2.75/3.05 thf(fact_1120_prod__cases3,axiom,
% 2.75/3.05 ! [Y: produc2732055786443039994et_nat] :
% 2.75/3.05 ~ ! [A4: produc3658429121746597890et_nat > $o,B4: produc3658429121746597890et_nat > $o,C4: produc3658429121746597890et_nat] :
% 2.75/3.05 ( Y
% 2.75/3.05 != ( produc2245416461498447860et_nat @ A4 @ ( produc5001842942810119800et_nat @ B4 @ C4 ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % prod_cases3
% 2.75/3.05 thf(fact_1121_prod__cases3,axiom,
% 2.75/3.05 ! [Y: produc2285326912895808259nt_int] :
% 2.75/3.05 ~ ! [A4: produc8551481072490612790e_term > option6357759511663192854e_term,B4: int,C4: int] :
% 2.75/3.05 ( Y
% 2.75/3.05 != ( produc5700946648718959541nt_int @ A4 @ ( product_Pair_int_int @ B4 @ C4 ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % prod_cases3
% 2.75/3.05 thf(fact_1122_prod__cases3,axiom,
% 2.75/3.05 ! [Y: produc7773217078559923341nt_int] :
% 2.75/3.05 ~ ! [A4: int > option6357759511663192854e_term,B4: int,C4: int] :
% 2.75/3.05 ( Y
% 2.75/3.05 != ( produc4305682042979456191nt_int @ A4 @ ( product_Pair_int_int @ B4 @ C4 ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % prod_cases3
% 2.75/3.05 thf(fact_1123_Pair__inject,axiom,
% 2.75/3.05 ! [A2: produc6241069584506657477e_term > option6357759511663192854e_term,B2: produc8923325533196201883nteger,A7: produc6241069584506657477e_term > option6357759511663192854e_term,B6: produc8923325533196201883nteger] :
% 2.75/3.05 ( ( ( produc8603105652947943368nteger @ A2 @ B2 )
% 2.75/3.05 = ( produc8603105652947943368nteger @ A7 @ B6 ) )
% 2.75/3.05 => ~ ( ( A2 = A7 )
% 2.75/3.05 => ( B2 != B6 ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % Pair_inject
% 2.75/3.05 thf(fact_1124_Pair__inject,axiom,
% 2.75/3.05 ! [A2: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat,A7: produc3658429121746597890et_nat > $o,B6: produc3658429121746597890et_nat] :
% 2.75/3.05 ( ( ( produc5001842942810119800et_nat @ A2 @ B2 )
% 2.75/3.05 = ( produc5001842942810119800et_nat @ A7 @ B6 ) )
% 2.75/3.05 => ~ ( ( A2 = A7 )
% 2.75/3.05 => ( B2 != B6 ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % Pair_inject
% 2.75/3.05 thf(fact_1125_Pair__inject,axiom,
% 2.75/3.05 ! [A2: produc3658429121746597890et_nat > $o,B2: produc3925858234332021118et_nat,A7: produc3658429121746597890et_nat > $o,B6: produc3925858234332021118et_nat] :
% 2.75/3.05 ( ( ( produc2245416461498447860et_nat @ A2 @ B2 )
% 2.75/3.05 = ( produc2245416461498447860et_nat @ A7 @ B6 ) )
% 2.75/3.05 => ~ ( ( A2 = A7 )
% 2.75/3.05 => ( B2 != B6 ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % Pair_inject
% 2.75/3.05 thf(fact_1126_Pair__inject,axiom,
% 2.75/3.05 ! [A2: produc8551481072490612790e_term > option6357759511663192854e_term,B2: product_prod_int_int,A7: produc8551481072490612790e_term > option6357759511663192854e_term,B6: product_prod_int_int] :
% 2.75/3.05 ( ( ( produc5700946648718959541nt_int @ A2 @ B2 )
% 2.75/3.05 = ( produc5700946648718959541nt_int @ A7 @ B6 ) )
% 2.75/3.05 => ~ ( ( A2 = A7 )
% 2.75/3.05 => ( B2 != B6 ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % Pair_inject
% 2.75/3.05 thf(fact_1127_Pair__inject,axiom,
% 2.75/3.05 ! [A2: int > option6357759511663192854e_term,B2: product_prod_int_int,A7: int > option6357759511663192854e_term,B6: product_prod_int_int] :
% 2.75/3.05 ( ( ( produc4305682042979456191nt_int @ A2 @ B2 )
% 2.75/3.05 = ( produc4305682042979456191nt_int @ A7 @ B6 ) )
% 2.75/3.05 => ~ ( ( A2 = A7 )
% 2.75/3.05 => ( B2 != B6 ) ) ) ).
% 2.75/3.05
% 2.75/3.05 % Pair_inject
% 2.75/3.05 thf(fact_1128_prod__cases,axiom,
% 2.75/3.05 ! [P: produc1908205239877642774nteger > $o,P6: produc1908205239877642774nteger] :
% 2.75/3.05 ( ! [A4: produc6241069584506657477e_term > option6357759511663192854e_term,B4: produc8923325533196201883nteger] : ( P @ ( produc8603105652947943368nteger @ A4 @ B4 ) )
% 2.75/3.05 => ( P @ P6 ) ) ).
% 2.75/3.05
% 2.75/3.05 % prod_cases
% 2.75/3.05 thf(fact_1129_prod__cases,axiom,
% 2.75/3.05 ! [P: produc3925858234332021118et_nat > $o,P6: produc3925858234332021118et_nat] :
% 2.75/3.05 ( ! [A4: produc3658429121746597890et_nat > $o,B4: produc3658429121746597890et_nat] : ( P @ ( produc5001842942810119800et_nat @ A4 @ B4 ) )
% 2.75/3.05 => ( P @ P6 ) ) ).
% 2.75/3.05
% 2.75/3.05 % prod_cases
% 2.75/3.05 thf(fact_1130_prod__cases,axiom,
% 2.75/3.05 ! [P: produc2732055786443039994et_nat > $o,P6: produc2732055786443039994et_nat] :
% 2.75/3.05 ( ! [A4: produc3658429121746597890et_nat > $o,B4: produc3925858234332021118et_nat] : ( P @ ( produc2245416461498447860et_nat @ A4 @ B4 ) )
% 2.75/3.05 => ( P @ P6 ) ) ).
% 2.75/3.05
% 2.75/3.05 % prod_cases
% 2.75/3.05 thf(fact_1131_prod__cases,axiom,
% 2.75/3.05 ! [P: produc2285326912895808259nt_int > $o,P6: produc2285326912895808259nt_int] :
% 2.75/3.05 ( ! [A4: produc8551481072490612790e_term > option6357759511663192854e_term,B4: product_prod_int_int] : ( P @ ( produc5700946648718959541nt_int @ A4 @ B4 ) )
% 2.75/3.05 => ( P @ P6 ) ) ).
% 2.75/3.05
% 2.75/3.05 % prod_cases
% 2.75/3.05 thf(fact_1132_prod__cases,axiom,
% 2.75/3.05 ! [P: produc7773217078559923341nt_int > $o,P6: produc7773217078559923341nt_int] :
% 2.75/3.05 ( ! [A4: int > option6357759511663192854e_term,B4: product_prod_int_int] : ( P @ ( produc4305682042979456191nt_int @ A4 @ B4 ) )
% 2.75/3.05 => ( P @ P6 ) ) ).
% 2.75/3.05
% 2.75/3.05 % prod_cases
% 2.75/3.05 thf(fact_1133_surj__pair,axiom,
% 2.75/3.05 ! [P6: produc1908205239877642774nteger] :
% 2.75/3.05 ? [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y2: produc8923325533196201883nteger] :
% 2.75/3.05 ( P6
% 2.75/3.05 = ( produc8603105652947943368nteger @ X3 @ Y2 ) ) ).
% 2.75/3.05
% 2.75/3.05 % surj_pair
% 2.75/3.05 thf(fact_1134_surj__pair,axiom,
% 2.75/3.05 ! [P6: produc3925858234332021118et_nat] :
% 2.75/3.05 ? [X3: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat] :
% 2.75/3.05 ( P6
% 2.75/3.05 = ( produc5001842942810119800et_nat @ X3 @ Y2 ) ) ).
% 2.75/3.05
% 2.75/3.05 % surj_pair
% 2.75/3.05 thf(fact_1135_surj__pair,axiom,
% 2.75/3.05 ! [P6: produc2732055786443039994et_nat] :
% 2.75/3.05 ? [X3: produc3658429121746597890et_nat > $o,Y2: produc3925858234332021118et_nat] :
% 2.75/3.05 ( P6
% 2.75/3.05 = ( produc2245416461498447860et_nat @ X3 @ Y2 ) ) ).
% 2.75/3.05
% 2.75/3.05 % surj_pair
% 2.75/3.05 thf(fact_1136_surj__pair,axiom,
% 2.75/3.05 ! [P6: produc2285326912895808259nt_int] :
% 2.75/3.05 ? [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y2: product_prod_int_int] :
% 2.75/3.05 ( P6
% 2.75/3.05 = ( produc5700946648718959541nt_int @ X3 @ Y2 ) ) ).
% 2.75/3.05
% 2.75/3.05 % surj_pair
% 2.75/3.05 thf(fact_1137_surj__pair,axiom,
% 2.75/3.05 ! [P6: produc7773217078559923341nt_int] :
% 2.75/3.05 ? [X3: int > option6357759511663192854e_term,Y2: product_prod_int_int] :
% 2.75/3.05 ( P6
% 2.75/3.05 = ( produc4305682042979456191nt_int @ X3 @ Y2 ) ) ).
% 2.75/3.05
% 2.75/3.05 % surj_pair
% 2.75/3.05 thf(fact_1138_old_Oprod_Oexhaust,axiom,
% 2.75/3.05 ! [Y: produc1908205239877642774nteger] :
% 2.75/3.05 ~ ! [A4: produc6241069584506657477e_term > option6357759511663192854e_term,B4: produc8923325533196201883nteger] :
% 2.75/3.05 ( Y
% 2.75/3.05 != ( produc8603105652947943368nteger @ A4 @ B4 ) ) ).
% 2.75/3.05
% 2.75/3.05 % old.prod.exhaust
% 2.75/3.05 thf(fact_1139_old_Oprod_Oexhaust,axiom,
% 2.75/3.05 ! [Y: produc3925858234332021118et_nat] :
% 2.75/3.05 ~ ! [A4: produc3658429121746597890et_nat > $o,B4: produc3658429121746597890et_nat] :
% 2.75/3.05 ( Y
% 2.75/3.05 != ( produc5001842942810119800et_nat @ A4 @ B4 ) ) ).
% 2.75/3.05
% 2.75/3.05 % old.prod.exhaust
% 2.75/3.05 thf(fact_1140_old_Oprod_Oexhaust,axiom,
% 2.75/3.05 ! [Y: produc2732055786443039994et_nat] :
% 2.75/3.05 ~ ! [A4: produc3658429121746597890et_nat > $o,B4: produc3925858234332021118et_nat] :
% 2.75/3.05 ( Y
% 2.75/3.05 != ( produc2245416461498447860et_nat @ A4 @ B4 ) ) ).
% 2.75/3.05
% 2.75/3.05 % old.prod.exhaust
% 2.75/3.05 thf(fact_1141_old_Oprod_Oexhaust,axiom,
% 2.75/3.05 ! [Y: produc2285326912895808259nt_int] :
% 2.75/3.05 ~ ! [A4: produc8551481072490612790e_term > option6357759511663192854e_term,B4: product_prod_int_int] :
% 2.75/3.05 ( Y
% 2.75/3.05 != ( produc5700946648718959541nt_int @ A4 @ B4 ) ) ).
% 2.75/3.05
% 2.75/3.05 % old.prod.exhaust
% 2.75/3.05 thf(fact_1142_old_Oprod_Oexhaust,axiom,
% 2.75/3.05 ! [Y: produc7773217078559923341nt_int] :
% 2.75/3.05 ~ ! [A4: int > option6357759511663192854e_term,B4: product_prod_int_int] :
% 2.75/3.05 ( Y
% 2.75/3.05 != ( produc4305682042979456191nt_int @ A4 @ B4 ) ) ).
% 2.75/3.05
% 2.75/3.05 % old.prod.exhaust
% 2.75/3.05 thf(fact_1143_remove__code_I1_J,axiom,
% 2.75/3.05 ! [X: int,Xs: list_int] :
% 2.75/3.05 ( ( remove_int @ X @ ( set_int2 @ Xs ) )
% 2.75/3.05 = ( set_int2 @ ( removeAll_int @ X @ Xs ) ) ) ).
% 2.75/3.06
% 2.75/3.06 % remove_code(1)
% 2.75/3.06 thf(fact_1144_remove__code_I1_J,axiom,
% 2.75/3.06 ! [X: nat,Xs: list_nat] :
% 2.75/3.06 ( ( remove_nat @ X @ ( set_nat2 @ Xs ) )
% 2.75/3.06 = ( set_nat2 @ ( removeAll_nat @ X @ Xs ) ) ) ).
% 2.75/3.06
% 2.75/3.06 % remove_code(1)
% 2.75/3.06 thf(fact_1145_remove__code_I1_J,axiom,
% 2.75/3.06 ! [X: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn] :
% 2.75/3.06 ( ( remove6142905432236673558n_assn @ X @ ( set_Pr1139785259514867910n_assn @ Xs ) )
% 2.75/3.06 = ( set_Pr1139785259514867910n_assn @ ( remove1763081955827946941n_assn @ X @ Xs ) ) ) ).
% 2.75/3.06
% 2.75/3.06 % remove_code(1)
% 2.75/3.06 thf(fact_1146_mod__emp__simp,axiom,
% 2.75/3.06 ! [H2: heap_e7401611519738050253t_unit] : ( rep_assn @ one_one_assn @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) ) ).
% 2.75/3.06
% 2.75/3.06 % mod_emp_simp
% 2.75/3.06 thf(fact_1147_length__removeAll__less,axiom,
% 2.75/3.06 ! [X: produc3843707927480180839at_nat,Xs: list_P5464809261938338413at_nat] :
% 2.75/3.06 ( ( member8757157785044589968at_nat @ X @ ( set_Pr3765526544606949372at_nat @ Xs ) )
% 2.75/3.06 => ( ord_less_nat @ ( size_s1588839187904960729at_nat @ ( remove4908499291543849587at_nat @ X @ Xs ) ) @ ( size_s1588839187904960729at_nat @ Xs ) ) ) ).
% 2.75/3.06
% 2.75/3.06 % length_removeAll_less
% 2.75/3.06 thf(fact_1148_length__removeAll__less,axiom,
% 2.75/3.06 ! [X: product_prod_nat_nat,Xs: list_P6011104703257516679at_nat] :
% 2.75/3.06 ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 2.75/3.06 => ( ord_less_nat @ ( size_s5460976970255530739at_nat @ ( remove3673390508374433037at_nat @ X @ Xs ) ) @ ( size_s5460976970255530739at_nat @ Xs ) ) ) ).
% 2.75/3.06
% 2.75/3.06 % length_removeAll_less
% 2.75/3.06 thf(fact_1149_length__removeAll__less,axiom,
% 2.75/3.06 ! [X: produc3658429121746597890et_nat > $o,Xs: list_P7985473006766602707_nat_o] :
% 2.75/3.06 ( ( member6576561426505652726_nat_o @ X @ ( set_Pr400311997697478754_nat_o @ Xs ) )
% 2.75/3.06 => ( ord_less_nat @ ( size_s8908918004648414271_nat_o @ ( remove7604696131425036249_nat_o @ X @ Xs ) ) @ ( size_s8908918004648414271_nat_o @ Xs ) ) ) ).
% 2.75/3.06
% 2.75/3.06 % length_removeAll_less
% 2.75/3.06 thf(fact_1150_length__removeAll__less,axiom,
% 2.75/3.06 ! [X: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn] :
% 2.86/3.06 ( ( member7957490590177025114n_assn @ X @ ( set_Pr1139785259514867910n_assn @ Xs ) )
% 2.86/3.06 => ( ord_less_nat @ ( size_s6829681357464350627n_assn @ ( remove1763081955827946941n_assn @ X @ Xs ) ) @ ( size_s6829681357464350627n_assn @ Xs ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % length_removeAll_less
% 2.86/3.06 thf(fact_1151_length__removeAll__less,axiom,
% 2.86/3.06 ! [X: c,Xs: list_c] :
% 2.86/3.06 ( ( member_c @ X @ ( set_c2 @ Xs ) )
% 2.86/3.06 => ( ord_less_nat @ ( size_size_list_c @ ( removeAll_c @ X @ Xs ) ) @ ( size_size_list_c @ Xs ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % length_removeAll_less
% 2.86/3.06 thf(fact_1152_length__removeAll__less,axiom,
% 2.86/3.06 ! [X: d,Xs: list_d] :
% 2.86/3.06 ( ( member_d @ X @ ( set_d2 @ Xs ) )
% 2.86/3.06 => ( ord_less_nat @ ( size_size_list_d @ ( removeAll_d @ X @ Xs ) ) @ ( size_size_list_d @ Xs ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % length_removeAll_less
% 2.86/3.06 thf(fact_1153_length__removeAll__less,axiom,
% 2.86/3.06 ! [X: nat,Xs: list_nat] :
% 2.86/3.06 ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 2.86/3.06 => ( ord_less_nat @ ( size_size_list_nat @ ( removeAll_nat @ X @ Xs ) ) @ ( size_size_list_nat @ Xs ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % length_removeAll_less
% 2.86/3.06 thf(fact_1154_length__removeAll__less,axiom,
% 2.86/3.06 ! [X: int,Xs: list_int] :
% 2.86/3.06 ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 2.86/3.06 => ( ord_less_nat @ ( size_size_list_int @ ( removeAll_int @ X @ Xs ) ) @ ( size_size_list_int @ Xs ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % length_removeAll_less
% 2.86/3.06 thf(fact_1155_less__numeral__extra_I4_J,axiom,
% 2.86/3.06 ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 2.86/3.06
% 2.86/3.06 % less_numeral_extra(4)
% 2.86/3.06 thf(fact_1156_less__numeral__extra_I4_J,axiom,
% 2.86/3.06 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ one_one_Code_integer ) ).
% 2.86/3.06
% 2.86/3.06 % less_numeral_extra(4)
% 2.86/3.06 thf(fact_1157_less__numeral__extra_I4_J,axiom,
% 2.86/3.06 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 2.86/3.06
% 2.86/3.06 % less_numeral_extra(4)
% 2.86/3.06 thf(fact_1158_less__numeral__extra_I4_J,axiom,
% 2.86/3.06 ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 2.86/3.06
% 2.86/3.06 % less_numeral_extra(4)
% 2.86/3.06 thf(fact_1159_pure__assn__raw_Oelims_I3_J,axiom,
% 2.86/3.06 ! [X: $o,Xa: produc3658429121746597890et_nat] :
% 2.86/3.06 ( ~ ( pure_a825153325127701367it_nat @ X @ Xa )
% 2.86/3.06 => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.86/3.06 ( ( Xa
% 2.86/3.06 = ( produc7507926704131184380et_nat @ H @ As ) )
% 2.86/3.06 => ( ( As = bot_bot_set_nat )
% 2.86/3.06 & X ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % pure_assn_raw.elims(3)
% 2.86/3.06 thf(fact_1160_pure__assn__raw_Oelims_I2_J,axiom,
% 2.86/3.06 ! [X: $o,Xa: produc3658429121746597890et_nat] :
% 2.86/3.06 ( ( pure_a825153325127701367it_nat @ X @ Xa )
% 2.86/3.06 => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.86/3.06 ( ( Xa
% 2.86/3.06 = ( produc7507926704131184380et_nat @ H @ As ) )
% 2.86/3.06 => ~ ( ( As = bot_bot_set_nat )
% 2.86/3.06 & X ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % pure_assn_raw.elims(2)
% 2.86/3.06 thf(fact_1161_pure__assn__raw_Oelims_I1_J,axiom,
% 2.86/3.06 ! [X: $o,Xa: produc3658429121746597890et_nat,Y: $o] :
% 2.86/3.06 ( ( ( pure_a825153325127701367it_nat @ X @ Xa )
% 2.86/3.06 = Y )
% 2.86/3.06 => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.86/3.06 ( ( Xa
% 2.86/3.06 = ( produc7507926704131184380et_nat @ H @ As ) )
% 2.86/3.06 => ( Y
% 2.86/3.06 = ( ~ ( ( As = bot_bot_set_nat )
% 2.86/3.06 & X ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % pure_assn_raw.elims(1)
% 2.86/3.06 thf(fact_1162_pure__assn__raw_Osimps,axiom,
% 2.86/3.06 ! [B2: $o,H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 2.86/3.06 ( ( pure_a825153325127701367it_nat @ B2 @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 2.86/3.06 = ( ( As2 = bot_bot_set_nat )
% 2.86/3.06 & B2 ) ) ).
% 2.86/3.06
% 2.86/3.06 % pure_assn_raw.simps
% 2.86/3.06 thf(fact_1163_nth__zip,axiom,
% 2.86/3.06 ! [I: nat,Xs: list_c,Ys: list_c] :
% 2.86/3.06 ( ( ord_less_nat @ I @ ( size_size_list_c @ Xs ) )
% 2.86/3.06 => ( ( ord_less_nat @ I @ ( size_size_list_c @ Ys ) )
% 2.86/3.06 => ( ( nth_Product_prod_c_c @ ( zip_c_c @ Xs @ Ys ) @ I )
% 2.86/3.06 = ( product_Pair_c_c @ ( nth_c @ Xs @ I ) @ ( nth_c @ Ys @ I ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % nth_zip
% 2.86/3.06 thf(fact_1164_nth__zip,axiom,
% 2.86/3.06 ! [I: nat,Xs: list_c,Ys: list_d] :
% 2.86/3.06 ( ( ord_less_nat @ I @ ( size_size_list_c @ Xs ) )
% 2.86/3.06 => ( ( ord_less_nat @ I @ ( size_size_list_d @ Ys ) )
% 2.86/3.06 => ( ( nth_Product_prod_c_d @ ( zip_c_d @ Xs @ Ys ) @ I )
% 2.86/3.06 = ( product_Pair_c_d @ ( nth_c @ Xs @ I ) @ ( nth_d @ Ys @ I ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % nth_zip
% 2.86/3.06 thf(fact_1165_nth__zip,axiom,
% 2.86/3.06 ! [I: nat,Xs: list_c,Ys: list_nat] :
% 2.86/3.06 ( ( ord_less_nat @ I @ ( size_size_list_c @ Xs ) )
% 2.86/3.06 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Ys ) )
% 2.86/3.06 => ( ( nth_Pr1708982275578427192_c_nat @ ( zip_c_nat @ Xs @ Ys ) @ I )
% 2.86/3.06 = ( product_Pair_c_nat @ ( nth_c @ Xs @ I ) @ ( nth_nat @ Ys @ I ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % nth_zip
% 2.86/3.06 thf(fact_1166_nth__zip,axiom,
% 2.86/3.06 ! [I: nat,Xs: list_c,Ys: list_int] :
% 2.86/3.06 ( ( ord_less_nat @ I @ ( size_size_list_c @ Xs ) )
% 2.86/3.06 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Ys ) )
% 2.86/3.06 => ( ( nth_Pr6754503292924006292_c_int @ ( zip_c_int @ Xs @ Ys ) @ I )
% 2.86/3.06 = ( product_Pair_c_int @ ( nth_c @ Xs @ I ) @ ( nth_int @ Ys @ I ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % nth_zip
% 2.86/3.06 thf(fact_1167_nth__zip,axiom,
% 2.86/3.06 ! [I: nat,Xs: list_d,Ys: list_c] :
% 2.86/3.06 ( ( ord_less_nat @ I @ ( size_size_list_d @ Xs ) )
% 2.86/3.06 => ( ( ord_less_nat @ I @ ( size_size_list_c @ Ys ) )
% 2.86/3.06 => ( ( nth_Product_prod_d_c @ ( zip_d_c @ Xs @ Ys ) @ I )
% 2.86/3.06 = ( product_Pair_d_c @ ( nth_d @ Xs @ I ) @ ( nth_c @ Ys @ I ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % nth_zip
% 2.86/3.06 thf(fact_1168_nth__zip,axiom,
% 2.86/3.06 ! [I: nat,Xs: list_d,Ys: list_d] :
% 2.86/3.06 ( ( ord_less_nat @ I @ ( size_size_list_d @ Xs ) )
% 2.86/3.06 => ( ( ord_less_nat @ I @ ( size_size_list_d @ Ys ) )
% 2.86/3.06 => ( ( nth_Product_prod_d_d @ ( zip_d_d @ Xs @ Ys ) @ I )
% 2.86/3.06 = ( product_Pair_d_d @ ( nth_d @ Xs @ I ) @ ( nth_d @ Ys @ I ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % nth_zip
% 2.86/3.06 thf(fact_1169_nth__zip,axiom,
% 2.86/3.06 ! [I: nat,Xs: list_d,Ys: list_nat] :
% 2.86/3.06 ( ( ord_less_nat @ I @ ( size_size_list_d @ Xs ) )
% 2.86/3.06 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Ys ) )
% 2.86/3.06 => ( ( nth_Pr2944426604534821689_d_nat @ ( zip_d_nat @ Xs @ Ys ) @ I )
% 2.86/3.06 = ( product_Pair_d_nat @ ( nth_d @ Xs @ I ) @ ( nth_nat @ Ys @ I ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % nth_zip
% 2.86/3.06 thf(fact_1170_nth__zip,axiom,
% 2.86/3.06 ! [I: nat,Xs: list_d,Ys: list_int] :
% 2.86/3.06 ( ( ord_less_nat @ I @ ( size_size_list_d @ Xs ) )
% 2.86/3.06 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Ys ) )
% 2.86/3.06 => ( ( nth_Pr7989947621880400789_d_int @ ( zip_d_int @ Xs @ Ys ) @ I )
% 2.86/3.06 = ( product_Pair_d_int @ ( nth_d @ Xs @ I ) @ ( nth_int @ Ys @ I ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % nth_zip
% 2.86/3.06 thf(fact_1171_nth__zip,axiom,
% 2.86/3.06 ! [I: nat,Xs: list_nat,Ys: list_c] :
% 2.86/3.06 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 2.86/3.06 => ( ( ord_less_nat @ I @ ( size_size_list_c @ Ys ) )
% 2.86/3.06 => ( ( nth_Pr2476257089995772766_nat_c @ ( zip_nat_c @ Xs @ Ys ) @ I )
% 2.86/3.06 = ( product_Pair_nat_c @ ( nth_nat @ Xs @ I ) @ ( nth_c @ Ys @ I ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % nth_zip
% 2.86/3.06 thf(fact_1172_nth__zip,axiom,
% 2.86/3.06 ! [I: nat,Xs: list_nat,Ys: list_d] :
% 2.86/3.06 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 2.86/3.06 => ( ( ord_less_nat @ I @ ( size_size_list_d @ Ys ) )
% 2.86/3.06 => ( ( nth_Pr2476257094299001567_nat_d @ ( zip_nat_d @ Xs @ Ys ) @ I )
% 2.86/3.06 = ( product_Pair_nat_d @ ( nth_nat @ Xs @ I ) @ ( nth_d @ Ys @ I ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % nth_zip
% 2.86/3.06 thf(fact_1173_curryI,axiom,
% 2.86/3.06 ! [F4: produc1908205239877642774nteger > $o,A2: produc6241069584506657477e_term > option6357759511663192854e_term,B2: produc8923325533196201883nteger] :
% 2.86/3.06 ( ( F4 @ ( produc8603105652947943368nteger @ A2 @ B2 ) )
% 2.86/3.06 => ( produc1217013493180205570eger_o @ F4 @ A2 @ B2 ) ) ).
% 2.86/3.06
% 2.86/3.06 % curryI
% 2.86/3.06 thf(fact_1174_curryI,axiom,
% 2.86/3.06 ! [F4: produc3925858234332021118et_nat > $o,A2: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat] :
% 2.86/3.06 ( ( F4 @ ( produc5001842942810119800et_nat @ A2 @ B2 ) )
% 2.86/3.06 => ( produc6216949301066131538_nat_o @ F4 @ A2 @ B2 ) ) ).
% 2.86/3.06
% 2.86/3.06 % curryI
% 2.86/3.06 thf(fact_1175_curryI,axiom,
% 2.86/3.06 ! [F4: produc2732055786443039994et_nat > $o,A2: produc3658429121746597890et_nat > $o,B2: produc3925858234332021118et_nat] :
% 2.86/3.06 ( ( F4 @ ( produc2245416461498447860et_nat @ A2 @ B2 ) )
% 2.86/3.06 => ( produc5101573711933517782_nat_o @ F4 @ A2 @ B2 ) ) ).
% 2.86/3.06
% 2.86/3.06 % curryI
% 2.86/3.06 thf(fact_1176_curryI,axiom,
% 2.86/3.06 ! [F4: produc2285326912895808259nt_int > $o,A2: produc8551481072490612790e_term > option6357759511663192854e_term,B2: product_prod_int_int] :
% 2.86/3.06 ( ( F4 @ ( produc5700946648718959541nt_int @ A2 @ B2 ) )
% 2.86/3.06 => ( produc730925184835016917_int_o @ F4 @ A2 @ B2 ) ) ).
% 2.86/3.06
% 2.86/3.06 % curryI
% 2.86/3.06 thf(fact_1177_curryI,axiom,
% 2.86/3.06 ! [F4: produc7773217078559923341nt_int > $o,A2: int > option6357759511663192854e_term,B2: product_prod_int_int] :
% 2.86/3.06 ( ( F4 @ ( produc4305682042979456191nt_int @ A2 @ B2 ) )
% 2.86/3.06 => ( produc9098658269643458507_int_o @ F4 @ A2 @ B2 ) ) ).
% 2.86/3.06
% 2.86/3.06 % curryI
% 2.86/3.06 thf(fact_1178_zip__eq__zip__same__len,axiom,
% 2.86/3.06 ! [A2: list_c,B2: list_c,A7: list_c,B6: list_c] :
% 2.86/3.06 ( ( ( size_size_list_c @ A2 )
% 2.86/3.06 = ( size_size_list_c @ B2 ) )
% 2.86/3.06 => ( ( ( size_size_list_c @ A7 )
% 2.86/3.06 = ( size_size_list_c @ B6 ) )
% 2.86/3.06 => ( ( ( zip_c_c @ A2 @ B2 )
% 2.86/3.06 = ( zip_c_c @ A7 @ B6 ) )
% 2.86/3.06 = ( ( A2 = A7 )
% 2.86/3.06 & ( B2 = B6 ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zip_eq_zip_same_len
% 2.86/3.06 thf(fact_1179_zip__eq__zip__same__len,axiom,
% 2.86/3.06 ! [A2: list_c,B2: list_d,A7: list_c,B6: list_d] :
% 2.86/3.06 ( ( ( size_size_list_c @ A2 )
% 2.86/3.06 = ( size_size_list_d @ B2 ) )
% 2.86/3.06 => ( ( ( size_size_list_c @ A7 )
% 2.86/3.06 = ( size_size_list_d @ B6 ) )
% 2.86/3.06 => ( ( ( zip_c_d @ A2 @ B2 )
% 2.86/3.06 = ( zip_c_d @ A7 @ B6 ) )
% 2.86/3.06 = ( ( A2 = A7 )
% 2.86/3.06 & ( B2 = B6 ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zip_eq_zip_same_len
% 2.86/3.06 thf(fact_1180_zip__eq__zip__same__len,axiom,
% 2.86/3.06 ! [A2: list_c,B2: list_nat,A7: list_c,B6: list_nat] :
% 2.86/3.06 ( ( ( size_size_list_c @ A2 )
% 2.86/3.06 = ( size_size_list_nat @ B2 ) )
% 2.86/3.06 => ( ( ( size_size_list_c @ A7 )
% 2.86/3.06 = ( size_size_list_nat @ B6 ) )
% 2.86/3.06 => ( ( ( zip_c_nat @ A2 @ B2 )
% 2.86/3.06 = ( zip_c_nat @ A7 @ B6 ) )
% 2.86/3.06 = ( ( A2 = A7 )
% 2.86/3.06 & ( B2 = B6 ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zip_eq_zip_same_len
% 2.86/3.06 thf(fact_1181_zip__eq__zip__same__len,axiom,
% 2.86/3.06 ! [A2: list_c,B2: list_int,A7: list_c,B6: list_int] :
% 2.86/3.06 ( ( ( size_size_list_c @ A2 )
% 2.86/3.06 = ( size_size_list_int @ B2 ) )
% 2.86/3.06 => ( ( ( size_size_list_c @ A7 )
% 2.86/3.06 = ( size_size_list_int @ B6 ) )
% 2.86/3.06 => ( ( ( zip_c_int @ A2 @ B2 )
% 2.86/3.06 = ( zip_c_int @ A7 @ B6 ) )
% 2.86/3.06 = ( ( A2 = A7 )
% 2.86/3.06 & ( B2 = B6 ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zip_eq_zip_same_len
% 2.86/3.06 thf(fact_1182_zip__eq__zip__same__len,axiom,
% 2.86/3.06 ! [A2: list_d,B2: list_c,A7: list_d,B6: list_c] :
% 2.86/3.06 ( ( ( size_size_list_d @ A2 )
% 2.86/3.06 = ( size_size_list_c @ B2 ) )
% 2.86/3.06 => ( ( ( size_size_list_d @ A7 )
% 2.86/3.06 = ( size_size_list_c @ B6 ) )
% 2.86/3.06 => ( ( ( zip_d_c @ A2 @ B2 )
% 2.86/3.06 = ( zip_d_c @ A7 @ B6 ) )
% 2.86/3.06 = ( ( A2 = A7 )
% 2.86/3.06 & ( B2 = B6 ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zip_eq_zip_same_len
% 2.86/3.06 thf(fact_1183_zip__eq__zip__same__len,axiom,
% 2.86/3.06 ! [A2: list_d,B2: list_d,A7: list_d,B6: list_d] :
% 2.86/3.06 ( ( ( size_size_list_d @ A2 )
% 2.86/3.06 = ( size_size_list_d @ B2 ) )
% 2.86/3.06 => ( ( ( size_size_list_d @ A7 )
% 2.86/3.06 = ( size_size_list_d @ B6 ) )
% 2.86/3.06 => ( ( ( zip_d_d @ A2 @ B2 )
% 2.86/3.06 = ( zip_d_d @ A7 @ B6 ) )
% 2.86/3.06 = ( ( A2 = A7 )
% 2.86/3.06 & ( B2 = B6 ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zip_eq_zip_same_len
% 2.86/3.06 thf(fact_1184_zip__eq__zip__same__len,axiom,
% 2.86/3.06 ! [A2: list_d,B2: list_nat,A7: list_d,B6: list_nat] :
% 2.86/3.06 ( ( ( size_size_list_d @ A2 )
% 2.86/3.06 = ( size_size_list_nat @ B2 ) )
% 2.86/3.06 => ( ( ( size_size_list_d @ A7 )
% 2.86/3.06 = ( size_size_list_nat @ B6 ) )
% 2.86/3.06 => ( ( ( zip_d_nat @ A2 @ B2 )
% 2.86/3.06 = ( zip_d_nat @ A7 @ B6 ) )
% 2.86/3.06 = ( ( A2 = A7 )
% 2.86/3.06 & ( B2 = B6 ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zip_eq_zip_same_len
% 2.86/3.06 thf(fact_1185_zip__eq__zip__same__len,axiom,
% 2.86/3.06 ! [A2: list_d,B2: list_int,A7: list_d,B6: list_int] :
% 2.86/3.06 ( ( ( size_size_list_d @ A2 )
% 2.86/3.06 = ( size_size_list_int @ B2 ) )
% 2.86/3.06 => ( ( ( size_size_list_d @ A7 )
% 2.86/3.06 = ( size_size_list_int @ B6 ) )
% 2.86/3.06 => ( ( ( zip_d_int @ A2 @ B2 )
% 2.86/3.06 = ( zip_d_int @ A7 @ B6 ) )
% 2.86/3.06 = ( ( A2 = A7 )
% 2.86/3.06 & ( B2 = B6 ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zip_eq_zip_same_len
% 2.86/3.06 thf(fact_1186_zip__eq__zip__same__len,axiom,
% 2.86/3.06 ! [A2: list_nat,B2: list_c,A7: list_nat,B6: list_c] :
% 2.86/3.06 ( ( ( size_size_list_nat @ A2 )
% 2.86/3.06 = ( size_size_list_c @ B2 ) )
% 2.86/3.06 => ( ( ( size_size_list_nat @ A7 )
% 2.86/3.06 = ( size_size_list_c @ B6 ) )
% 2.86/3.06 => ( ( ( zip_nat_c @ A2 @ B2 )
% 2.86/3.06 = ( zip_nat_c @ A7 @ B6 ) )
% 2.86/3.06 = ( ( A2 = A7 )
% 2.86/3.06 & ( B2 = B6 ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zip_eq_zip_same_len
% 2.86/3.06 thf(fact_1187_zip__eq__zip__same__len,axiom,
% 2.86/3.06 ! [A2: list_nat,B2: list_d,A7: list_nat,B6: list_d] :
% 2.86/3.06 ( ( ( size_size_list_nat @ A2 )
% 2.86/3.06 = ( size_size_list_d @ B2 ) )
% 2.86/3.06 => ( ( ( size_size_list_nat @ A7 )
% 2.86/3.06 = ( size_size_list_d @ B6 ) )
% 2.86/3.06 => ( ( ( zip_nat_d @ A2 @ B2 )
% 2.86/3.06 = ( zip_nat_d @ A7 @ B6 ) )
% 2.86/3.06 = ( ( A2 = A7 )
% 2.86/3.06 & ( B2 = B6 ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zip_eq_zip_same_len
% 2.86/3.06 thf(fact_1188_zip__inj,axiom,
% 2.86/3.06 ! [A2: list_c,B2: list_c,A7: list_c,B6: list_c] :
% 2.86/3.06 ( ( ( size_size_list_c @ A2 )
% 2.86/3.06 = ( size_size_list_c @ B2 ) )
% 2.86/3.06 => ( ( ( size_size_list_c @ A7 )
% 2.86/3.06 = ( size_size_list_c @ B6 ) )
% 2.86/3.06 => ( ( ( zip_c_c @ A2 @ B2 )
% 2.86/3.06 = ( zip_c_c @ A7 @ B6 ) )
% 2.86/3.06 => ( ( A2 = A7 )
% 2.86/3.06 & ( B2 = B6 ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zip_inj
% 2.86/3.06 thf(fact_1189_zip__inj,axiom,
% 2.86/3.06 ! [A2: list_c,B2: list_d,A7: list_c,B6: list_d] :
% 2.86/3.06 ( ( ( size_size_list_c @ A2 )
% 2.86/3.06 = ( size_size_list_d @ B2 ) )
% 2.86/3.06 => ( ( ( size_size_list_c @ A7 )
% 2.86/3.06 = ( size_size_list_d @ B6 ) )
% 2.86/3.06 => ( ( ( zip_c_d @ A2 @ B2 )
% 2.86/3.06 = ( zip_c_d @ A7 @ B6 ) )
% 2.86/3.06 => ( ( A2 = A7 )
% 2.86/3.06 & ( B2 = B6 ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zip_inj
% 2.86/3.06 thf(fact_1190_zip__inj,axiom,
% 2.86/3.06 ! [A2: list_c,B2: list_nat,A7: list_c,B6: list_nat] :
% 2.86/3.06 ( ( ( size_size_list_c @ A2 )
% 2.86/3.06 = ( size_size_list_nat @ B2 ) )
% 2.86/3.06 => ( ( ( size_size_list_c @ A7 )
% 2.86/3.06 = ( size_size_list_nat @ B6 ) )
% 2.86/3.06 => ( ( ( zip_c_nat @ A2 @ B2 )
% 2.86/3.06 = ( zip_c_nat @ A7 @ B6 ) )
% 2.86/3.06 => ( ( A2 = A7 )
% 2.86/3.06 & ( B2 = B6 ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zip_inj
% 2.86/3.06 thf(fact_1191_zip__inj,axiom,
% 2.86/3.06 ! [A2: list_c,B2: list_int,A7: list_c,B6: list_int] :
% 2.86/3.06 ( ( ( size_size_list_c @ A2 )
% 2.86/3.06 = ( size_size_list_int @ B2 ) )
% 2.86/3.06 => ( ( ( size_size_list_c @ A7 )
% 2.86/3.06 = ( size_size_list_int @ B6 ) )
% 2.86/3.06 => ( ( ( zip_c_int @ A2 @ B2 )
% 2.86/3.06 = ( zip_c_int @ A7 @ B6 ) )
% 2.86/3.06 => ( ( A2 = A7 )
% 2.86/3.06 & ( B2 = B6 ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zip_inj
% 2.86/3.06 thf(fact_1192_zip__inj,axiom,
% 2.86/3.06 ! [A2: list_d,B2: list_c,A7: list_d,B6: list_c] :
% 2.86/3.06 ( ( ( size_size_list_d @ A2 )
% 2.86/3.06 = ( size_size_list_c @ B2 ) )
% 2.86/3.06 => ( ( ( size_size_list_d @ A7 )
% 2.86/3.06 = ( size_size_list_c @ B6 ) )
% 2.86/3.06 => ( ( ( zip_d_c @ A2 @ B2 )
% 2.86/3.06 = ( zip_d_c @ A7 @ B6 ) )
% 2.86/3.06 => ( ( A2 = A7 )
% 2.86/3.06 & ( B2 = B6 ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zip_inj
% 2.86/3.06 thf(fact_1193_zip__inj,axiom,
% 2.86/3.06 ! [A2: list_d,B2: list_d,A7: list_d,B6: list_d] :
% 2.86/3.06 ( ( ( size_size_list_d @ A2 )
% 2.86/3.06 = ( size_size_list_d @ B2 ) )
% 2.86/3.06 => ( ( ( size_size_list_d @ A7 )
% 2.86/3.06 = ( size_size_list_d @ B6 ) )
% 2.86/3.06 => ( ( ( zip_d_d @ A2 @ B2 )
% 2.86/3.06 = ( zip_d_d @ A7 @ B6 ) )
% 2.86/3.06 => ( ( A2 = A7 )
% 2.86/3.06 & ( B2 = B6 ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zip_inj
% 2.86/3.06 thf(fact_1194_zip__inj,axiom,
% 2.86/3.06 ! [A2: list_d,B2: list_nat,A7: list_d,B6: list_nat] :
% 2.86/3.06 ( ( ( size_size_list_d @ A2 )
% 2.86/3.06 = ( size_size_list_nat @ B2 ) )
% 2.86/3.06 => ( ( ( size_size_list_d @ A7 )
% 2.86/3.06 = ( size_size_list_nat @ B6 ) )
% 2.86/3.06 => ( ( ( zip_d_nat @ A2 @ B2 )
% 2.86/3.06 = ( zip_d_nat @ A7 @ B6 ) )
% 2.86/3.06 => ( ( A2 = A7 )
% 2.86/3.06 & ( B2 = B6 ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zip_inj
% 2.86/3.06 thf(fact_1195_zip__inj,axiom,
% 2.86/3.06 ! [A2: list_d,B2: list_int,A7: list_d,B6: list_int] :
% 2.86/3.06 ( ( ( size_size_list_d @ A2 )
% 2.86/3.06 = ( size_size_list_int @ B2 ) )
% 2.86/3.06 => ( ( ( size_size_list_d @ A7 )
% 2.86/3.06 = ( size_size_list_int @ B6 ) )
% 2.86/3.06 => ( ( ( zip_d_int @ A2 @ B2 )
% 2.86/3.06 = ( zip_d_int @ A7 @ B6 ) )
% 2.86/3.06 => ( ( A2 = A7 )
% 2.86/3.06 & ( B2 = B6 ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zip_inj
% 2.86/3.06 thf(fact_1196_zip__inj,axiom,
% 2.86/3.06 ! [A2: list_nat,B2: list_c,A7: list_nat,B6: list_c] :
% 2.86/3.06 ( ( ( size_size_list_nat @ A2 )
% 2.86/3.06 = ( size_size_list_c @ B2 ) )
% 2.86/3.06 => ( ( ( size_size_list_nat @ A7 )
% 2.86/3.06 = ( size_size_list_c @ B6 ) )
% 2.86/3.06 => ( ( ( zip_nat_c @ A2 @ B2 )
% 2.86/3.06 = ( zip_nat_c @ A7 @ B6 ) )
% 2.86/3.06 => ( ( A2 = A7 )
% 2.86/3.06 & ( B2 = B6 ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zip_inj
% 2.86/3.06 thf(fact_1197_zip__inj,axiom,
% 2.86/3.06 ! [A2: list_nat,B2: list_d,A7: list_nat,B6: list_d] :
% 2.86/3.06 ( ( ( size_size_list_nat @ A2 )
% 2.86/3.06 = ( size_size_list_d @ B2 ) )
% 2.86/3.06 => ( ( ( size_size_list_nat @ A7 )
% 2.86/3.06 = ( size_size_list_d @ B6 ) )
% 2.86/3.06 => ( ( ( zip_nat_d @ A2 @ B2 )
% 2.86/3.06 = ( zip_nat_d @ A7 @ B6 ) )
% 2.86/3.06 => ( ( A2 = A7 )
% 2.86/3.06 & ( B2 = B6 ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zip_inj
% 2.86/3.06 thf(fact_1198_pair__list__split,axiom,
% 2.86/3.06 ! [L: list_P267710562049004973od_c_c] :
% 2.86/3.06 ~ ! [L1: list_c,L22: list_c] :
% 2.86/3.06 ( ( L
% 2.86/3.06 = ( zip_c_c @ L1 @ L22 ) )
% 2.86/3.06 => ( ( ( size_size_list_c @ L1 )
% 2.86/3.06 = ( size_size_list_c @ L22 ) )
% 2.86/3.06 => ( ( size_s2756448709718749209od_c_c @ L )
% 2.86/3.06 != ( size_size_list_c @ L22 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % pair_list_split
% 2.86/3.06 thf(fact_1199_pair__list__split,axiom,
% 2.86/3.06 ! [L: list_P338744602095350958od_c_d] :
% 2.86/3.06 ~ ! [L1: list_c,L22: list_d] :
% 2.86/3.06 ( ( L
% 2.86/3.06 = ( zip_c_d @ L1 @ L22 ) )
% 2.86/3.06 => ( ( ( size_size_list_c @ L1 )
% 2.86/3.06 = ( size_size_list_d @ L22 ) )
% 2.86/3.06 => ( ( size_s2827482749765095194od_c_d @ L )
% 2.86/3.06 != ( size_size_list_d @ L22 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % pair_list_split
% 2.86/3.06 thf(fact_1200_pair__list__split,axiom,
% 2.86/3.06 ! [L: list_P5561950507774946575_c_nat] :
% 2.86/3.06 ~ ! [L1: list_c,L22: list_nat] :
% 2.86/3.06 ( ( L
% 2.86/3.06 = ( zip_c_nat @ L1 @ L22 ) )
% 2.86/3.06 => ( ( ( size_size_list_c @ L1 )
% 2.86/3.06 = ( size_size_list_nat @ L22 ) )
% 2.86/3.06 => ( ( size_s2954062820725854115_c_nat @ L )
% 2.86/3.06 != ( size_size_list_nat @ L22 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % pair_list_split
% 2.86/3.06 thf(fact_1201_pair__list__split,axiom,
% 2.86/3.06 ! [L: list_P3071867362843219819_c_int] :
% 2.86/3.06 ~ ! [L1: list_c,L22: list_int] :
% 2.86/3.06 ( ( L
% 2.86/3.06 = ( zip_c_int @ L1 @ L22 ) )
% 2.86/3.06 => ( ( ( size_size_list_c @ L1 )
% 2.86/3.06 = ( size_size_list_int @ L22 ) )
% 2.86/3.06 => ( ( size_s463979675794127359_c_int @ L )
% 2.86/3.06 != ( size_size_list_int @ L22 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % pair_list_split
% 2.86/3.06 thf(fact_1202_pair__list__split,axiom,
% 2.86/3.06 ! [L: list_P8855433598298794092od_d_c] :
% 2.86/3.06 ~ ! [L1: list_d,L22: list_c] :
% 2.86/3.06 ( ( L
% 2.86/3.06 = ( zip_d_c @ L1 @ L22 ) )
% 2.86/3.06 => ( ( ( size_size_list_d @ L1 )
% 2.86/3.06 = ( size_size_list_c @ L22 ) )
% 2.86/3.06 => ( ( size_s2120799709113762520od_d_c @ L )
% 2.86/3.06 != ( size_size_list_c @ L22 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % pair_list_split
% 2.86/3.06 thf(fact_1203_pair__list__split,axiom,
% 2.86/3.06 ! [L: list_P8926467638345140077od_d_d] :
% 2.86/3.06 ~ ! [L1: list_d,L22: list_d] :
% 2.86/3.06 ( ( L
% 2.86/3.06 = ( zip_d_d @ L1 @ L22 ) )
% 2.86/3.06 => ( ( ( size_size_list_d @ L1 )
% 2.86/3.06 = ( size_size_list_d @ L22 ) )
% 2.86/3.06 => ( ( size_s2191833749160108505od_d_d @ L )
% 2.86/3.06 != ( size_size_list_d @ L22 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % pair_list_split
% 2.86/3.06 thf(fact_1204_pair__list__split,axiom,
% 2.86/3.06 ! [L: list_P1934797086108301456_d_nat] :
% 2.86/3.06 ~ ! [L1: list_d,L22: list_nat] :
% 2.86/3.06 ( ( L
% 2.86/3.06 = ( zip_d_nat @ L1 @ L22 ) )
% 2.86/3.06 => ( ( ( size_size_list_d @ L1 )
% 2.86/3.06 = ( size_size_list_nat @ L22 ) )
% 2.86/3.06 => ( ( size_s8550281435913984804_d_nat @ L )
% 2.86/3.06 != ( size_size_list_nat @ L22 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % pair_list_split
% 2.86/3.06 thf(fact_1205_pair__list__split,axiom,
% 2.86/3.06 ! [L: list_P8668085978031350508_d_int] :
% 2.86/3.06 ~ ! [L1: list_d,L22: list_int] :
% 2.86/3.06 ( ( L
% 2.86/3.06 = ( zip_d_int @ L1 @ L22 ) )
% 2.86/3.06 => ( ( ( size_size_list_d @ L1 )
% 2.86/3.06 = ( size_size_list_int @ L22 ) )
% 2.86/3.06 => ( ( size_s6060198290982258048_d_int @ L )
% 2.86/3.06 != ( size_size_list_int @ L22 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % pair_list_split
% 2.86/3.06 thf(fact_1206_pair__list__split,axiom,
% 2.86/3.06 ! [L: list_P2993859830824179253_nat_c] :
% 2.86/3.06 ~ ! [L1: list_nat,L22: list_c] :
% 2.86/3.06 ( ( L
% 2.86/3.06 = ( zip_nat_c @ L1 @ L22 ) )
% 2.86/3.06 => ( ( ( size_size_list_nat @ L1 )
% 2.86/3.06 = ( size_size_list_c @ L22 ) )
% 2.86/3.06 => ( ( size_s385972143775086793_nat_c @ L )
% 2.86/3.06 != ( size_size_list_c @ L22 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % pair_list_split
% 2.86/3.06 thf(fact_1207_pair__list__split,axiom,
% 2.86/3.06 ! [L: list_P3064893870870525238_nat_d] :
% 2.86/3.06 ~ ! [L1: list_nat,L22: list_d] :
% 2.86/3.06 ( ( L
% 2.86/3.06 = ( zip_nat_d @ L1 @ L22 ) )
% 2.86/3.06 => ( ( ( size_size_list_nat @ L1 )
% 2.86/3.06 = ( size_size_list_d @ L22 ) )
% 2.86/3.06 => ( ( size_s457006183821432778_nat_d @ L )
% 2.86/3.06 != ( size_size_list_d @ L22 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % pair_list_split
% 2.86/3.06 thf(fact_1208_curryD,axiom,
% 2.86/3.06 ! [F4: produc1908205239877642774nteger > $o,A2: produc6241069584506657477e_term > option6357759511663192854e_term,B2: produc8923325533196201883nteger] :
% 2.86/3.06 ( ( produc1217013493180205570eger_o @ F4 @ A2 @ B2 )
% 2.86/3.06 => ( F4 @ ( produc8603105652947943368nteger @ A2 @ B2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % curryD
% 2.86/3.06 thf(fact_1209_curryD,axiom,
% 2.86/3.06 ! [F4: produc3925858234332021118et_nat > $o,A2: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat] :
% 2.86/3.06 ( ( produc6216949301066131538_nat_o @ F4 @ A2 @ B2 )
% 2.86/3.06 => ( F4 @ ( produc5001842942810119800et_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % curryD
% 2.86/3.06 thf(fact_1210_curryD,axiom,
% 2.86/3.06 ! [F4: produc2732055786443039994et_nat > $o,A2: produc3658429121746597890et_nat > $o,B2: produc3925858234332021118et_nat] :
% 2.86/3.06 ( ( produc5101573711933517782_nat_o @ F4 @ A2 @ B2 )
% 2.86/3.06 => ( F4 @ ( produc2245416461498447860et_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % curryD
% 2.86/3.06 thf(fact_1211_curryD,axiom,
% 2.86/3.06 ! [F4: produc2285326912895808259nt_int > $o,A2: produc8551481072490612790e_term > option6357759511663192854e_term,B2: product_prod_int_int] :
% 2.86/3.06 ( ( produc730925184835016917_int_o @ F4 @ A2 @ B2 )
% 2.86/3.06 => ( F4 @ ( produc5700946648718959541nt_int @ A2 @ B2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % curryD
% 2.86/3.06 thf(fact_1212_curryD,axiom,
% 2.86/3.06 ! [F4: produc7773217078559923341nt_int > $o,A2: int > option6357759511663192854e_term,B2: product_prod_int_int] :
% 2.86/3.06 ( ( produc9098658269643458507_int_o @ F4 @ A2 @ B2 )
% 2.86/3.06 => ( F4 @ ( produc4305682042979456191nt_int @ A2 @ B2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % curryD
% 2.86/3.06 thf(fact_1213_curryE,axiom,
% 2.86/3.06 ! [F4: produc1908205239877642774nteger > $o,A2: produc6241069584506657477e_term > option6357759511663192854e_term,B2: produc8923325533196201883nteger] :
% 2.86/3.06 ( ( produc1217013493180205570eger_o @ F4 @ A2 @ B2 )
% 2.86/3.06 => ( F4 @ ( produc8603105652947943368nteger @ A2 @ B2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % curryE
% 2.86/3.06 thf(fact_1214_curryE,axiom,
% 2.86/3.06 ! [F4: produc3925858234332021118et_nat > $o,A2: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat] :
% 2.86/3.06 ( ( produc6216949301066131538_nat_o @ F4 @ A2 @ B2 )
% 2.86/3.06 => ( F4 @ ( produc5001842942810119800et_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % curryE
% 2.86/3.06 thf(fact_1215_curryE,axiom,
% 2.86/3.06 ! [F4: produc2732055786443039994et_nat > $o,A2: produc3658429121746597890et_nat > $o,B2: produc3925858234332021118et_nat] :
% 2.86/3.06 ( ( produc5101573711933517782_nat_o @ F4 @ A2 @ B2 )
% 2.86/3.06 => ( F4 @ ( produc2245416461498447860et_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % curryE
% 2.86/3.06 thf(fact_1216_curryE,axiom,
% 2.86/3.06 ! [F4: produc2285326912895808259nt_int > $o,A2: produc8551481072490612790e_term > option6357759511663192854e_term,B2: product_prod_int_int] :
% 2.86/3.06 ( ( produc730925184835016917_int_o @ F4 @ A2 @ B2 )
% 2.86/3.06 => ( F4 @ ( produc5700946648718959541nt_int @ A2 @ B2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % curryE
% 2.86/3.06 thf(fact_1217_curryE,axiom,
% 2.86/3.06 ! [F4: produc7773217078559923341nt_int > $o,A2: int > option6357759511663192854e_term,B2: product_prod_int_int] :
% 2.86/3.06 ( ( produc9098658269643458507_int_o @ F4 @ A2 @ B2 )
% 2.86/3.06 => ( F4 @ ( produc4305682042979456191nt_int @ A2 @ B2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % curryE
% 2.86/3.06 thf(fact_1218_set__zip__rightD,axiom,
% 2.86/3.06 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Xs: list_s1210847774152347623at_nat,Ys: list_s1210847774152347623at_nat] :
% 2.86/3.06 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( set_Pr3765526544606949372at_nat @ ( zip_se5600341670672612855at_nat @ Xs @ Ys ) ) )
% 2.86/3.06 => ( member2643936169264416010at_nat @ Y @ ( set_se5049602875457034614at_nat @ Ys ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % set_zip_rightD
% 2.86/3.06 thf(fact_1219_set__zip__rightD,axiom,
% 2.86/3.06 ! [X: nat,Y: nat,Xs: list_nat,Ys: list_nat] :
% 2.86/3.06 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( set_Pr5648618587558075414at_nat @ ( zip_nat_nat @ Xs @ Ys ) ) )
% 2.86/3.06 => ( member_nat @ Y @ ( set_nat2 @ Ys ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % set_zip_rightD
% 2.86/3.06 thf(fact_1220_set__zip__rightD,axiom,
% 2.86/3.06 ! [X: assn,Y: assn,Xs: list_assn,Ys: list_assn] :
% 2.86/3.06 ( ( member7957490590177025114n_assn @ ( produc118845697133431529n_assn @ X @ Y ) @ ( set_Pr1139785259514867910n_assn @ ( zip_assn_assn @ Xs @ Ys ) ) )
% 2.86/3.06 => ( member_assn @ Y @ ( set_assn2 @ Ys ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % set_zip_rightD
% 2.86/3.06 thf(fact_1221_set__zip__rightD,axiom,
% 2.86/3.06 ! [X: produc6241069584506657477e_term > option6357759511663192854e_term,Y: produc8923325533196201883nteger,Xs: list_P1316552470764441098e_term,Ys: list_P5578671422887162913nteger] :
% 2.86/3.06 ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X @ Y ) @ ( set_Pr2135590979564877377nteger @ ( zip_Pr8292346330294042792nteger @ Xs @ Ys ) ) )
% 2.86/3.06 => ( member157494554546826820nteger @ Y @ ( set_Pr920681315882439344nteger @ Ys ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % set_zip_rightD
% 2.86/3.06 thf(fact_1222_set__zip__rightD,axiom,
% 2.86/3.06 ! [X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat,Xs: list_P7985473006766602707_nat_o,Ys: list_P9062070895058802706et_nat] :
% 2.86/3.06 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X @ Y ) @ ( set_Pr364071364088684201et_nat @ ( zip_Pr7134870689397686104et_nat @ Xs @ Ys ) ) )
% 2.86/3.06 => ( member6260224972018164377et_nat @ Y @ ( set_Pr3864771053587467565et_nat @ Ys ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % set_zip_rightD
% 2.86/3.06 thf(fact_1223_set__zip__rightD,axiom,
% 2.86/3.06 ! [X: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat,Xs: list_P7985473006766602707_nat_o,Ys: list_P2321686559999237006et_nat] :
% 2.86/3.06 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X @ Y ) @ ( set_Pr7458301993993767461et_nat @ ( zip_Pr8136144321567152340et_nat @ Xs @ Ys ) ) )
% 2.86/3.06 => ( member1996754912294343701et_nat @ Y @ ( set_Pr364071364088684201et_nat @ Ys ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % set_zip_rightD
% 2.86/3.06 thf(fact_1224_set__zip__rightD,axiom,
% 2.86/3.06 ! [X: produc8551481072490612790e_term > option6357759511663192854e_term,Y: product_prod_int_int,Xs: list_P1743416141875011707e_term,Ys: list_P5707943133018811711nt_int] :
% 2.86/3.06 ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X @ Y ) @ ( set_Pr4943052134776177454nt_int @ ( zip_Pr4168994715204986005nt_int @ Xs @ Ys ) ) )
% 2.86/3.06 => ( member5262025264175285858nt_int @ Y @ ( set_Pr2470121279949933262nt_int @ Ys ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % set_zip_rightD
% 2.86/3.06 thf(fact_1225_set__zip__rightD,axiom,
% 2.86/3.06 ! [X: int > option6357759511663192854e_term,Y: product_prod_int_int,Xs: list_i8448526496819171953e_term,Ys: list_P5707943133018811711nt_int] :
% 2.86/3.06 ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X @ Y ) @ ( set_Pr1633835384712236856nt_int @ ( zip_in8766932505889695135nt_int @ Xs @ Ys ) ) )
% 2.86/3.06 => ( member5262025264175285858nt_int @ Y @ ( set_Pr2470121279949933262nt_int @ Ys ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % set_zip_rightD
% 2.86/3.06 thf(fact_1226_set__zip__leftD,axiom,
% 2.86/3.06 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Xs: list_s1210847774152347623at_nat,Ys: list_s1210847774152347623at_nat] :
% 2.86/3.06 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( set_Pr3765526544606949372at_nat @ ( zip_se5600341670672612855at_nat @ Xs @ Ys ) ) )
% 2.86/3.06 => ( member2643936169264416010at_nat @ X @ ( set_se5049602875457034614at_nat @ Xs ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % set_zip_leftD
% 2.86/3.06 thf(fact_1227_set__zip__leftD,axiom,
% 2.86/3.06 ! [X: nat,Y: nat,Xs: list_nat,Ys: list_nat] :
% 2.86/3.06 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( set_Pr5648618587558075414at_nat @ ( zip_nat_nat @ Xs @ Ys ) ) )
% 2.86/3.06 => ( member_nat @ X @ ( set_nat2 @ Xs ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % set_zip_leftD
% 2.86/3.06 thf(fact_1228_set__zip__leftD,axiom,
% 2.86/3.06 ! [X: assn,Y: assn,Xs: list_assn,Ys: list_assn] :
% 2.86/3.06 ( ( member7957490590177025114n_assn @ ( produc118845697133431529n_assn @ X @ Y ) @ ( set_Pr1139785259514867910n_assn @ ( zip_assn_assn @ Xs @ Ys ) ) )
% 2.86/3.06 => ( member_assn @ X @ ( set_assn2 @ Xs ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % set_zip_leftD
% 2.86/3.06 thf(fact_1229_set__zip__leftD,axiom,
% 2.86/3.06 ! [X: produc6241069584506657477e_term > option6357759511663192854e_term,Y: produc8923325533196201883nteger,Xs: list_P1316552470764441098e_term,Ys: list_P5578671422887162913nteger] :
% 2.86/3.06 ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X @ Y ) @ ( set_Pr2135590979564877377nteger @ ( zip_Pr8292346330294042792nteger @ Xs @ Ys ) ) )
% 2.86/3.06 => ( member4242434998011752849e_term @ X @ ( set_Pr8342322266483756581e_term @ Xs ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % set_zip_leftD
% 2.86/3.06 thf(fact_1230_set__zip__leftD,axiom,
% 2.86/3.06 ! [X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat,Xs: list_P7985473006766602707_nat_o,Ys: list_P9062070895058802706et_nat] :
% 2.86/3.06 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X @ Y ) @ ( set_Pr364071364088684201et_nat @ ( zip_Pr7134870689397686104et_nat @ Xs @ Ys ) ) )
% 2.86/3.06 => ( member6576561426505652726_nat_o @ X @ ( set_Pr400311997697478754_nat_o @ Xs ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % set_zip_leftD
% 2.86/3.06 thf(fact_1231_set__zip__leftD,axiom,
% 2.86/3.06 ! [X: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat,Xs: list_P7985473006766602707_nat_o,Ys: list_P2321686559999237006et_nat] :
% 2.86/3.06 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X @ Y ) @ ( set_Pr7458301993993767461et_nat @ ( zip_Pr8136144321567152340et_nat @ Xs @ Ys ) ) )
% 2.86/3.06 => ( member6576561426505652726_nat_o @ X @ ( set_Pr400311997697478754_nat_o @ Xs ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % set_zip_leftD
% 2.86/3.06 thf(fact_1232_set__zip__leftD,axiom,
% 2.86/3.06 ! [X: produc8551481072490612790e_term > option6357759511663192854e_term,Y: product_prod_int_int,Xs: list_P1743416141875011707e_term,Ys: list_P5707943133018811711nt_int] :
% 2.86/3.06 ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X @ Y ) @ ( set_Pr4943052134776177454nt_int @ ( zip_Pr4168994715204986005nt_int @ Xs @ Ys ) ) )
% 2.86/3.06 => ( member3222579708246209666e_term @ X @ ( set_Pr16608062948090134e_term @ Xs ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % set_zip_leftD
% 2.86/3.06 thf(fact_1233_set__zip__leftD,axiom,
% 2.86/3.06 ! [X: int > option6357759511663192854e_term,Y: product_prod_int_int,Xs: list_i8448526496819171953e_term,Ys: list_P5707943133018811711nt_int] :
% 2.86/3.06 ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X @ Y ) @ ( set_Pr1633835384712236856nt_int @ ( zip_in8766932505889695135nt_int @ Xs @ Ys ) ) )
% 2.86/3.06 => ( member8845023287901829240e_term @ X @ ( set_in5217446777445088012e_term @ Xs ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % set_zip_leftD
% 2.86/3.06 thf(fact_1234_in__set__zipE,axiom,
% 2.86/3.06 ! [X: int,Y: int,Xs: list_int,Ys: list_int] :
% 2.86/3.06 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( set_Pr2470121279949933262nt_int @ ( zip_int_int @ Xs @ Ys ) ) )
% 2.86/3.06 => ~ ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 2.86/3.06 => ~ ( member_int @ Y @ ( set_int2 @ Ys ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % in_set_zipE
% 2.86/3.06 thf(fact_1235_in__set__zipE,axiom,
% 2.86/3.06 ! [X: int,Y: nat,Xs: list_int,Ys: list_nat] :
% 2.86/3.06 ( ( member216504246829706758nt_nat @ ( product_Pair_int_nat @ X @ Y ) @ ( set_Pr6647972299459129970nt_nat @ ( zip_int_nat @ Xs @ Ys ) ) )
% 2.86/3.06 => ~ ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 2.86/3.06 => ~ ( member_nat @ Y @ ( set_nat2 @ Ys ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % in_set_zipE
% 2.86/3.06 thf(fact_1236_in__set__zipE,axiom,
% 2.86/3.06 ! [X: nat,Y: int,Xs: list_nat,Ys: list_int] :
% 2.86/3.06 ( ( member4262671552274231302at_int @ ( product_Pair_nat_int @ X @ Y ) @ ( set_Pr1470767568048878706at_int @ ( zip_nat_int @ Xs @ Ys ) ) )
% 2.86/3.06 => ~ ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 2.86/3.06 => ~ ( member_int @ Y @ ( set_int2 @ Ys ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % in_set_zipE
% 2.86/3.06 thf(fact_1237_in__set__zipE,axiom,
% 2.86/3.06 ! [X: nat,Y: nat,Xs: list_nat,Ys: list_nat] :
% 2.86/3.06 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( set_Pr5648618587558075414at_nat @ ( zip_nat_nat @ Xs @ Ys ) ) )
% 2.86/3.06 => ~ ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 2.86/3.06 => ~ ( member_nat @ Y @ ( set_nat2 @ Ys ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % in_set_zipE
% 2.86/3.06 thf(fact_1238_in__set__zipE,axiom,
% 2.86/3.06 ! [X: assn,Y: assn,Xs: list_assn,Ys: list_assn] :
% 2.86/3.06 ( ( member7957490590177025114n_assn @ ( produc118845697133431529n_assn @ X @ Y ) @ ( set_Pr1139785259514867910n_assn @ ( zip_assn_assn @ Xs @ Ys ) ) )
% 2.86/3.06 => ~ ( ( member_assn @ X @ ( set_assn2 @ Xs ) )
% 2.86/3.06 => ~ ( member_assn @ Y @ ( set_assn2 @ Ys ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % in_set_zipE
% 2.86/3.06 thf(fact_1239_in__set__zipE,axiom,
% 2.86/3.06 ! [X: product_prod_nat_nat,Y: int,Xs: list_P6011104703257516679at_nat,Ys: list_int] :
% 2.86/3.06 ( ( member8394280151737582451at_int @ ( produc6348220600061155286at_int @ X @ Y ) @ ( set_Pr3658594827066574855at_int @ ( zip_Pr6866960147343648950at_int @ Xs @ Ys ) ) )
% 2.86/3.06 => ~ ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 2.86/3.06 => ~ ( member_int @ Y @ ( set_int2 @ Ys ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % in_set_zipE
% 2.86/3.06 thf(fact_1240_in__set__zipE,axiom,
% 2.86/3.06 ! [X: product_prod_nat_nat,Y: nat,Xs: list_P6011104703257516679at_nat,Ys: list_nat] :
% 2.86/3.06 ( ( member3348759134392003351at_nat @ ( produc6350711070570205562at_nat @ X @ Y ) @ ( set_Pr7836445846575771563at_nat @ ( zip_Pr6869450617852699226at_nat @ Xs @ Ys ) ) )
% 2.86/3.06 => ~ ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 2.86/3.06 => ~ ( member_nat @ Y @ ( set_nat2 @ Ys ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % in_set_zipE
% 2.86/3.06 thf(fact_1241_in__set__zipE,axiom,
% 2.86/3.06 ! [X: int,Y: product_prod_nat_nat,Xs: list_int,Ys: list_P6011104703257516679at_nat] :
% 2.86/3.06 ( ( member5261114234888836065at_nat @ ( produc3525228511222278652at_nat @ X @ Y ) @ ( set_Pr525428910217828469at_nat @ ( zip_in4043968058504772316at_nat @ Xs @ Ys ) ) )
% 2.86/3.06 => ~ ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 2.86/3.06 => ~ ( member8440522571783428010at_nat @ Y @ ( set_Pr5648618587558075414at_nat @ Ys ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % in_set_zipE
% 2.86/3.06 thf(fact_1242_in__set__zipE,axiom,
% 2.86/3.06 ! [X: int,Y: produc6575502325842934193n_assn,Xs: list_int,Ys: list_P8527749157015355191n_assn] :
% 2.86/3.06 ( ( member241480614033477777n_assn @ ( produc3313821056773121708n_assn @ X @ Y ) @ ( set_Pr4510407026980144421n_assn @ ( zip_in7098856637274830732n_assn @ Xs @ Ys ) ) )
% 2.86/3.06 => ~ ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 2.86/3.06 => ~ ( member7957490590177025114n_assn @ Y @ ( set_Pr1139785259514867910n_assn @ Ys ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % in_set_zipE
% 2.86/3.06 thf(fact_1243_in__set__zipE,axiom,
% 2.86/3.06 ! [X: nat,Y: product_prod_nat_nat,Xs: list_nat,Ys: list_P6011104703257516679at_nat] :
% 2.86/3.06 ( ( member2223272150424702269at_nat @ ( produc487386426758144856at_nat @ X @ Y ) @ ( set_Pr6710958862608470481at_nat @ ( zip_na1006125974040638520at_nat @ Xs @ Ys ) ) )
% 2.86/3.06 => ~ ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 2.86/3.06 => ~ ( member8440522571783428010at_nat @ Y @ ( set_Pr5648618587558075414at_nat @ Ys ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % in_set_zipE
% 2.86/3.06 thf(fact_1244_zip__same,axiom,
% 2.86/3.06 ! [A2: produc3843707927480180839at_nat,B2: produc3843707927480180839at_nat,Xs: list_P5464809261938338413at_nat] :
% 2.86/3.06 ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ A2 @ B2 ) @ ( set_Pr4552580085251402108at_nat @ ( zip_Pr2522280425463452279at_nat @ Xs @ Xs ) ) )
% 2.86/3.06 = ( ( member8757157785044589968at_nat @ A2 @ ( set_Pr3765526544606949372at_nat @ Xs ) )
% 2.86/3.06 & ( A2 = B2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zip_same
% 2.86/3.06 thf(fact_1245_zip__same,axiom,
% 2.86/3.06 ! [A2: product_prod_nat_nat,B2: product_prod_nat_nat,Xs: list_P6011104703257516679at_nat] :
% 2.86/3.06 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ A2 @ B2 ) @ ( set_Pr5518436109238095868at_nat @ ( zip_Pr4664179122662387191at_nat @ Xs @ Xs ) ) )
% 2.86/3.06 = ( ( member8440522571783428010at_nat @ A2 @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 2.86/3.06 & ( A2 = B2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zip_same
% 2.86/3.06 thf(fact_1246_zip__same,axiom,
% 2.86/3.06 ! [A2: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat > $o,Xs: list_P7985473006766602707_nat_o] :
% 2.86/3.06 ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ A2 @ B2 ) @ ( set_Pr8666615595052072444_nat_o @ ( zip_Pr2849639184604596727_nat_o @ Xs @ Xs ) ) )
% 2.86/3.06 = ( ( member6576561426505652726_nat_o @ A2 @ ( set_Pr400311997697478754_nat_o @ Xs ) )
% 2.86/3.06 & ( A2 = B2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zip_same
% 2.86/3.06 thf(fact_1247_zip__same,axiom,
% 2.86/3.06 ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,Xs: list_s1210847774152347623at_nat] :
% 2.86/3.06 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A2 @ B2 ) @ ( set_Pr3765526544606949372at_nat @ ( zip_se5600341670672612855at_nat @ Xs @ Xs ) ) )
% 2.86/3.06 = ( ( member2643936169264416010at_nat @ A2 @ ( set_se5049602875457034614at_nat @ Xs ) )
% 2.86/3.06 & ( A2 = B2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zip_same
% 2.86/3.06 thf(fact_1248_zip__same,axiom,
% 2.86/3.06 ! [A2: int,B2: int,Xs: list_int] :
% 2.86/3.06 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B2 ) @ ( set_Pr2470121279949933262nt_int @ ( zip_int_int @ Xs @ Xs ) ) )
% 2.86/3.06 = ( ( member_int @ A2 @ ( set_int2 @ Xs ) )
% 2.86/3.06 & ( A2 = B2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zip_same
% 2.86/3.06 thf(fact_1249_zip__same,axiom,
% 2.86/3.06 ! [A2: nat,B2: nat,Xs: list_nat] :
% 2.86/3.06 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B2 ) @ ( set_Pr5648618587558075414at_nat @ ( zip_nat_nat @ Xs @ Xs ) ) )
% 2.86/3.06 = ( ( member_nat @ A2 @ ( set_nat2 @ Xs ) )
% 2.86/3.06 & ( A2 = B2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zip_same
% 2.86/3.06 thf(fact_1250_zip__same,axiom,
% 2.86/3.06 ! [A2: produc6575502325842934193n_assn,B2: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn] :
% 2.86/3.06 ( ( member4743710847862083984n_assn @ ( produc6128706242671166167n_assn @ A2 @ B2 ) @ ( set_Pr8975451644279219196n_assn @ ( zip_Pr8806919808394484215n_assn @ Xs @ Xs ) ) )
% 2.86/3.06 = ( ( member7957490590177025114n_assn @ A2 @ ( set_Pr1139785259514867910n_assn @ Xs ) )
% 2.86/3.06 & ( A2 = B2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zip_same
% 2.86/3.06 thf(fact_1251_zip__same,axiom,
% 2.86/3.06 ! [A2: assn,B2: assn,Xs: list_assn] :
% 2.86/3.06 ( ( member7957490590177025114n_assn @ ( produc118845697133431529n_assn @ A2 @ B2 ) @ ( set_Pr1139785259514867910n_assn @ ( zip_assn_assn @ Xs @ Xs ) ) )
% 2.86/3.06 = ( ( member_assn @ A2 @ ( set_assn2 @ Xs ) )
% 2.86/3.06 & ( A2 = B2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zip_same
% 2.86/3.06 thf(fact_1252_zip__update,axiom,
% 2.86/3.06 ! [Xs: list_c,I: nat,X: c,Ys: list_c,Y: c] :
% 2.86/3.06 ( ( zip_c_c @ ( list_update_c @ Xs @ I @ X ) @ ( list_update_c @ Ys @ I @ Y ) )
% 2.86/3.06 = ( list_u8616212504517173525od_c_c @ ( zip_c_c @ Xs @ Ys ) @ I @ ( product_Pair_c_c @ X @ Y ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zip_update
% 2.86/3.06 thf(fact_1253_zip__update,axiom,
% 2.86/3.06 ! [Xs: list_c,I: nat,X: c,Ys: list_d,Y: d] :
% 2.86/3.06 ( ( zip_c_d @ ( list_update_c @ Xs @ I @ X ) @ ( list_update_d @ Ys @ I @ Y ) )
% 2.86/3.06 = ( list_u8616212508820402326od_c_d @ ( zip_c_d @ Xs @ Ys ) @ I @ ( product_Pair_c_d @ X @ Y ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zip_update
% 2.86/3.06 thf(fact_1254_zip__update,axiom,
% 2.86/3.06 ! [Xs: list_d,I: nat,X: d,Ys: list_c,Y: c] :
% 2.86/3.06 ( ( zip_d_c @ ( list_update_d @ Xs @ I @ X ) @ ( list_update_c @ Ys @ I @ Y ) )
% 2.86/3.06 = ( list_u5828756922544497492od_d_c @ ( zip_d_c @ Xs @ Ys ) @ I @ ( product_Pair_d_c @ X @ Y ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zip_update
% 2.86/3.06 thf(fact_1255_zip__update,axiom,
% 2.86/3.06 ! [Xs: list_d,I: nat,X: d,Ys: list_d,Y: d] :
% 2.86/3.06 ( ( zip_d_d @ ( list_update_d @ Xs @ I @ X ) @ ( list_update_d @ Ys @ I @ Y ) )
% 2.86/3.06 = ( list_u5828756926847726293od_d_d @ ( zip_d_d @ Xs @ Ys ) @ I @ ( product_Pair_d_d @ X @ Y ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zip_update
% 2.86/3.06 thf(fact_1256_zip__update,axiom,
% 2.86/3.06 ! [Xs: list_P1316552470764441098e_term,I: nat,X: produc6241069584506657477e_term > option6357759511663192854e_term,Ys: list_P5578671422887162913nteger,Y: produc8923325533196201883nteger] :
% 2.86/3.06 ( ( zip_Pr8292346330294042792nteger @ ( list_u877304756163299468e_term @ Xs @ I @ X ) @ ( list_u2254550707601501961nteger @ Ys @ I @ Y ) )
% 2.86/3.06 = ( list_u234853988314817064nteger @ ( zip_Pr8292346330294042792nteger @ Xs @ Ys ) @ I @ ( produc8603105652947943368nteger @ X @ Y ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zip_update
% 2.86/3.06 thf(fact_1257_zip__update,axiom,
% 2.86/3.06 ! [Xs: list_P7985473006766602707_nat_o,I: nat,X: produc3658429121746597890et_nat > $o,Ys: list_P9062070895058802706et_nat,Y: produc3658429121746597890et_nat] :
% 2.86/3.06 ( ( zip_Pr7134870689397686104et_nat @ ( list_u6943956310655620667_nat_o @ Xs @ I @ X ) @ ( list_u9060326803697358356et_nat @ Ys @ I @ Y ) )
% 2.86/3.06 = ( list_u1866171116859985808et_nat @ ( zip_Pr7134870689397686104et_nat @ Xs @ Ys ) @ I @ ( produc5001842942810119800et_nat @ X @ Y ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zip_update
% 2.86/3.06 thf(fact_1258_zip__update,axiom,
% 2.86/3.06 ! [Xs: list_P7985473006766602707_nat_o,I: nat,X: produc3658429121746597890et_nat > $o,Ys: list_P2321686559999237006et_nat,Y: produc3925858234332021118et_nat] :
% 2.86/3.06 ( ( zip_Pr8136144321567152340et_nat @ ( list_u6943956310655620667_nat_o @ Xs @ I @ X ) @ ( list_u1866171116859985808et_nat @ Ys @ I @ Y ) )
% 2.86/3.06 = ( list_u1913845194572276492et_nat @ ( zip_Pr8136144321567152340et_nat @ Xs @ Ys ) @ I @ ( produc2245416461498447860et_nat @ X @ Y ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zip_update
% 2.86/3.06 thf(fact_1259_zip__update,axiom,
% 2.86/3.06 ! [Xs: list_P1743416141875011707e_term,I: nat,X: produc8551481072490612790e_term > option6357759511663192854e_term,Ys: list_P5707943133018811711nt_int,Y: product_prod_int_int] :
% 2.86/3.06 ( ( zip_Pr4168994715204986005nt_int @ ( list_u3533491785856317309e_term @ Xs @ I @ X ) @ ( list_u3002344382305578791nt_int @ Ys @ I @ Y ) )
% 2.86/3.06 = ( list_u7736365598306452245nt_int @ ( zip_Pr4168994715204986005nt_int @ Xs @ Ys ) @ I @ ( produc5700946648718959541nt_int @ X @ Y ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zip_update
% 2.86/3.06 thf(fact_1260_zip__update,axiom,
% 2.86/3.06 ! [Xs: list_i8448526496819171953e_term,I: nat,X: int > option6357759511663192854e_term,Ys: list_P5707943133018811711nt_int,Y: product_prod_int_int] :
% 2.86/3.06 ( ( zip_in8766932505889695135nt_int @ ( list_u8946639151299769843e_term @ Xs @ I @ X ) @ ( list_u3002344382305578791nt_int @ Ys @ I @ Y ) )
% 2.86/3.06 = ( list_u4780935413889332127nt_int @ ( zip_in8766932505889695135nt_int @ Xs @ Ys ) @ I @ ( produc4305682042979456191nt_int @ X @ Y ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zip_update
% 2.86/3.06 thf(fact_1261_in__set__impl__in__set__zip1,axiom,
% 2.86/3.06 ! [Xs: list_assn,Ys: list_assn,X: assn] :
% 2.86/3.06 ( ( ( size_size_list_assn @ Xs )
% 2.86/3.06 = ( size_size_list_assn @ Ys ) )
% 2.86/3.06 => ( ( member_assn @ X @ ( set_assn2 @ Xs ) )
% 2.86/3.06 => ~ ! [Y2: assn] :
% 2.86/3.06 ~ ( member7957490590177025114n_assn @ ( produc118845697133431529n_assn @ X @ Y2 ) @ ( set_Pr1139785259514867910n_assn @ ( zip_assn_assn @ Xs @ Ys ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % in_set_impl_in_set_zip1
% 2.86/3.06 thf(fact_1262_in__set__impl__in__set__zip1,axiom,
% 2.86/3.06 ! [Xs: list_c,Ys: list_c,X: c] :
% 2.86/3.06 ( ( ( size_size_list_c @ Xs )
% 2.86/3.06 = ( size_size_list_c @ Ys ) )
% 2.86/3.06 => ( ( member_c @ X @ ( set_c2 @ Xs ) )
% 2.86/3.06 => ~ ! [Y2: c] :
% 2.86/3.06 ~ ( member5074992359041316560od_c_c @ ( product_Pair_c_c @ X @ Y2 ) @ ( set_Product_prod_c_c2 @ ( zip_c_c @ Xs @ Ys ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % in_set_impl_in_set_zip1
% 2.86/3.06 thf(fact_1263_in__set__impl__in__set__zip1,axiom,
% 2.86/3.06 ! [Xs: list_c,Ys: list_d,X: c] :
% 2.86/3.06 ( ( ( size_size_list_c @ Xs )
% 2.86/3.06 = ( size_size_list_d @ Ys ) )
% 2.86/3.06 => ( ( member_c @ X @ ( set_c2 @ Xs ) )
% 2.86/3.06 => ~ ! [Y2: d] :
% 2.86/3.06 ~ ( member5074992363344545361od_c_d @ ( product_Pair_c_d @ X @ Y2 ) @ ( set_Product_prod_c_d2 @ ( zip_c_d @ Xs @ Ys ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % in_set_impl_in_set_zip1
% 2.86/3.06 thf(fact_1264_in__set__impl__in__set__zip1,axiom,
% 2.86/3.06 ! [Xs: list_c,Ys: list_nat,X: c] :
% 2.86/3.06 ( ( ( size_size_list_c @ Xs )
% 2.86/3.06 = ( size_size_list_nat @ Ys ) )
% 2.86/3.06 => ( ( member_c @ X @ ( set_c2 @ Xs ) )
% 2.86/3.06 => ~ ! [Y2: nat] :
% 2.86/3.06 ~ ( member8195077246299207702_c_nat @ ( product_Pair_c_nat @ X @ Y2 ) @ ( set_Pr3395872032415823530_c_nat @ ( zip_c_nat @ Xs @ Ys ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % in_set_impl_in_set_zip1
% 2.86/3.06 thf(fact_1265_in__set__impl__in__set__zip1,axiom,
% 2.86/3.06 ! [Xs: list_c,Ys: list_int,X: c] :
% 2.86/3.06 ( ( ( size_size_list_c @ Xs )
% 2.86/3.06 = ( size_size_list_int @ Ys ) )
% 2.86/3.06 => ( ( member_c @ X @ ( set_c2 @ Xs ) )
% 2.86/3.06 => ~ ! [Y2: int] :
% 2.86/3.06 ~ ( member4017226226790010994_c_int @ ( product_Pair_c_int @ X @ Y2 ) @ ( set_Pr8441393049761402630_c_int @ ( zip_c_int @ Xs @ Ys ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % in_set_impl_in_set_zip1
% 2.86/3.06 thf(fact_1266_in__set__impl__in__set__zip1,axiom,
% 2.86/3.06 ! [Xs: list_d,Ys: list_c,X: d] :
% 2.86/3.06 ( ( ( size_size_list_d @ Xs )
% 2.86/3.06 = ( size_size_list_c @ Ys ) )
% 2.86/3.06 => ( ( member_d @ X @ ( set_d2 @ Xs ) )
% 2.86/3.06 => ~ ! [Y2: c] :
% 2.86/3.06 ~ ( member2287536777068640527od_d_c @ ( product_Pair_d_c @ X @ Y2 ) @ ( set_Product_prod_d_c2 @ ( zip_d_c @ Xs @ Ys ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % in_set_impl_in_set_zip1
% 2.86/3.06 thf(fact_1267_in__set__impl__in__set__zip1,axiom,
% 2.86/3.06 ! [Xs: list_d,Ys: list_d,X: d] :
% 2.86/3.06 ( ( ( size_size_list_d @ Xs )
% 2.86/3.06 = ( size_size_list_d @ Ys ) )
% 2.86/3.06 => ( ( member_d @ X @ ( set_d2 @ Xs ) )
% 2.86/3.06 => ~ ! [Y2: d] :
% 2.86/3.06 ~ ( member2287536781371869328od_d_d @ ( product_Pair_d_d @ X @ Y2 ) @ ( set_Product_prod_d_d2 @ ( zip_d_d @ Xs @ Ys ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % in_set_impl_in_set_zip1
% 2.86/3.06 thf(fact_1268_in__set__impl__in__set__zip1,axiom,
% 2.86/3.06 ! [Xs: list_d,Ys: list_nat,X: d] :
% 2.86/3.06 ( ( ( size_size_list_d @ Xs )
% 2.86/3.06 = ( size_size_list_nat @ Ys ) )
% 2.86/3.06 => ( ( member_d @ X @ ( set_d2 @ Xs ) )
% 2.86/3.06 => ~ ! [Y2: nat] :
% 2.86/3.06 ~ ( member207149538400826391_d_nat @ ( product_Pair_d_nat @ X @ Y2 ) @ ( set_Pr4631316361372218027_d_nat @ ( zip_d_nat @ Xs @ Ys ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % in_set_impl_in_set_zip1
% 2.86/3.06 thf(fact_1269_in__set__impl__in__set__zip1,axiom,
% 2.86/3.06 ! [Xs: list_d,Ys: list_int,X: d] :
% 2.86/3.06 ( ( ( size_size_list_d @ Xs )
% 2.86/3.06 = ( size_size_list_int @ Ys ) )
% 2.86/3.06 => ( ( member_d @ X @ ( set_d2 @ Xs ) )
% 2.86/3.06 => ~ ! [Y2: int] :
% 2.86/3.06 ~ ( member5252670555746405491_d_int @ ( product_Pair_d_int @ X @ Y2 ) @ ( set_Pr453465341863021319_d_int @ ( zip_d_int @ Xs @ Ys ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % in_set_impl_in_set_zip1
% 2.86/3.06 thf(fact_1270_in__set__impl__in__set__zip1,axiom,
% 2.86/3.06 ! [Xs: list_nat,Ys: list_c,X: nat] :
% 2.86/3.06 ( ( ( size_size_list_nat @ Xs )
% 2.86/3.06 = ( size_size_list_c @ Ys ) )
% 2.86/3.06 => ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 2.86/3.06 => ~ ! [Y2: c] :
% 2.86/3.06 ~ ( member8962352060716553276_nat_c @ ( product_Pair_nat_c @ X @ Y2 ) @ ( set_Pr4163146846833169104_nat_c @ ( zip_nat_c @ Xs @ Ys ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % in_set_impl_in_set_zip1
% 2.86/3.06 thf(fact_1271_in__set__impl__in__set__zip2,axiom,
% 2.86/3.06 ! [Xs: list_assn,Ys: list_assn,Y: assn] :
% 2.86/3.06 ( ( ( size_size_list_assn @ Xs )
% 2.86/3.06 = ( size_size_list_assn @ Ys ) )
% 2.86/3.06 => ( ( member_assn @ Y @ ( set_assn2 @ Ys ) )
% 2.86/3.06 => ~ ! [X3: assn] :
% 2.86/3.06 ~ ( member7957490590177025114n_assn @ ( produc118845697133431529n_assn @ X3 @ Y ) @ ( set_Pr1139785259514867910n_assn @ ( zip_assn_assn @ Xs @ Ys ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % in_set_impl_in_set_zip2
% 2.86/3.06 thf(fact_1272_in__set__impl__in__set__zip2,axiom,
% 2.86/3.06 ! [Xs: list_c,Ys: list_c,Y: c] :
% 2.86/3.06 ( ( ( size_size_list_c @ Xs )
% 2.86/3.06 = ( size_size_list_c @ Ys ) )
% 2.86/3.06 => ( ( member_c @ Y @ ( set_c2 @ Ys ) )
% 2.86/3.06 => ~ ! [X3: c] :
% 2.86/3.06 ~ ( member5074992359041316560od_c_c @ ( product_Pair_c_c @ X3 @ Y ) @ ( set_Product_prod_c_c2 @ ( zip_c_c @ Xs @ Ys ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % in_set_impl_in_set_zip2
% 2.86/3.06 thf(fact_1273_in__set__impl__in__set__zip2,axiom,
% 2.86/3.06 ! [Xs: list_c,Ys: list_d,Y: d] :
% 2.86/3.06 ( ( ( size_size_list_c @ Xs )
% 2.86/3.06 = ( size_size_list_d @ Ys ) )
% 2.86/3.06 => ( ( member_d @ Y @ ( set_d2 @ Ys ) )
% 2.86/3.06 => ~ ! [X3: c] :
% 2.86/3.06 ~ ( member5074992363344545361od_c_d @ ( product_Pair_c_d @ X3 @ Y ) @ ( set_Product_prod_c_d2 @ ( zip_c_d @ Xs @ Ys ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % in_set_impl_in_set_zip2
% 2.86/3.06 thf(fact_1274_in__set__impl__in__set__zip2,axiom,
% 2.86/3.06 ! [Xs: list_c,Ys: list_nat,Y: nat] :
% 2.86/3.06 ( ( ( size_size_list_c @ Xs )
% 2.86/3.06 = ( size_size_list_nat @ Ys ) )
% 2.86/3.06 => ( ( member_nat @ Y @ ( set_nat2 @ Ys ) )
% 2.86/3.06 => ~ ! [X3: c] :
% 2.86/3.06 ~ ( member8195077246299207702_c_nat @ ( product_Pair_c_nat @ X3 @ Y ) @ ( set_Pr3395872032415823530_c_nat @ ( zip_c_nat @ Xs @ Ys ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % in_set_impl_in_set_zip2
% 2.86/3.06 thf(fact_1275_in__set__impl__in__set__zip2,axiom,
% 2.86/3.06 ! [Xs: list_c,Ys: list_int,Y: int] :
% 2.86/3.06 ( ( ( size_size_list_c @ Xs )
% 2.86/3.06 = ( size_size_list_int @ Ys ) )
% 2.86/3.06 => ( ( member_int @ Y @ ( set_int2 @ Ys ) )
% 2.86/3.06 => ~ ! [X3: c] :
% 2.86/3.06 ~ ( member4017226226790010994_c_int @ ( product_Pair_c_int @ X3 @ Y ) @ ( set_Pr8441393049761402630_c_int @ ( zip_c_int @ Xs @ Ys ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % in_set_impl_in_set_zip2
% 2.86/3.06 thf(fact_1276_in__set__impl__in__set__zip2,axiom,
% 2.86/3.06 ! [Xs: list_d,Ys: list_c,Y: c] :
% 2.86/3.06 ( ( ( size_size_list_d @ Xs )
% 2.86/3.06 = ( size_size_list_c @ Ys ) )
% 2.86/3.06 => ( ( member_c @ Y @ ( set_c2 @ Ys ) )
% 2.86/3.06 => ~ ! [X3: d] :
% 2.86/3.06 ~ ( member2287536777068640527od_d_c @ ( product_Pair_d_c @ X3 @ Y ) @ ( set_Product_prod_d_c2 @ ( zip_d_c @ Xs @ Ys ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % in_set_impl_in_set_zip2
% 2.86/3.06 thf(fact_1277_in__set__impl__in__set__zip2,axiom,
% 2.86/3.06 ! [Xs: list_d,Ys: list_d,Y: d] :
% 2.86/3.06 ( ( ( size_size_list_d @ Xs )
% 2.86/3.06 = ( size_size_list_d @ Ys ) )
% 2.86/3.06 => ( ( member_d @ Y @ ( set_d2 @ Ys ) )
% 2.86/3.06 => ~ ! [X3: d] :
% 2.86/3.06 ~ ( member2287536781371869328od_d_d @ ( product_Pair_d_d @ X3 @ Y ) @ ( set_Product_prod_d_d2 @ ( zip_d_d @ Xs @ Ys ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % in_set_impl_in_set_zip2
% 2.86/3.06 thf(fact_1278_in__set__impl__in__set__zip2,axiom,
% 2.86/3.06 ! [Xs: list_d,Ys: list_nat,Y: nat] :
% 2.86/3.06 ( ( ( size_size_list_d @ Xs )
% 2.86/3.06 = ( size_size_list_nat @ Ys ) )
% 2.86/3.06 => ( ( member_nat @ Y @ ( set_nat2 @ Ys ) )
% 2.86/3.06 => ~ ! [X3: d] :
% 2.86/3.06 ~ ( member207149538400826391_d_nat @ ( product_Pair_d_nat @ X3 @ Y ) @ ( set_Pr4631316361372218027_d_nat @ ( zip_d_nat @ Xs @ Ys ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % in_set_impl_in_set_zip2
% 2.86/3.06 thf(fact_1279_in__set__impl__in__set__zip2,axiom,
% 2.86/3.06 ! [Xs: list_d,Ys: list_int,Y: int] :
% 2.86/3.06 ( ( ( size_size_list_d @ Xs )
% 2.86/3.06 = ( size_size_list_int @ Ys ) )
% 2.86/3.06 => ( ( member_int @ Y @ ( set_int2 @ Ys ) )
% 2.86/3.06 => ~ ! [X3: d] :
% 2.86/3.06 ~ ( member5252670555746405491_d_int @ ( product_Pair_d_int @ X3 @ Y ) @ ( set_Pr453465341863021319_d_int @ ( zip_d_int @ Xs @ Ys ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % in_set_impl_in_set_zip2
% 2.86/3.06 thf(fact_1280_in__set__impl__in__set__zip2,axiom,
% 2.86/3.06 ! [Xs: list_nat,Ys: list_c,Y: c] :
% 2.86/3.06 ( ( ( size_size_list_nat @ Xs )
% 2.86/3.06 = ( size_size_list_c @ Ys ) )
% 2.86/3.06 => ( ( member_c @ Y @ ( set_c2 @ Ys ) )
% 2.86/3.06 => ~ ! [X3: nat] :
% 2.86/3.06 ~ ( member8962352060716553276_nat_c @ ( product_Pair_nat_c @ X3 @ Y ) @ ( set_Pr4163146846833169104_nat_c @ ( zip_nat_c @ Xs @ Ys ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % in_set_impl_in_set_zip2
% 2.86/3.06 thf(fact_1281_length__remove1,axiom,
% 2.86/3.06 ! [X: produc3843707927480180839at_nat,Xs: list_P5464809261938338413at_nat] :
% 2.86/3.06 ( ( ( member8757157785044589968at_nat @ X @ ( set_Pr3765526544606949372at_nat @ Xs ) )
% 2.86/3.06 => ( ( size_s1588839187904960729at_nat @ ( remove8895909992688781315at_nat @ X @ Xs ) )
% 2.86/3.06 = ( minus_minus_nat @ ( size_s1588839187904960729at_nat @ Xs ) @ one_one_nat ) ) )
% 2.86/3.06 & ( ~ ( member8757157785044589968at_nat @ X @ ( set_Pr3765526544606949372at_nat @ Xs ) )
% 2.86/3.06 => ( ( size_s1588839187904960729at_nat @ ( remove8895909992688781315at_nat @ X @ Xs ) )
% 2.86/3.06 = ( size_s1588839187904960729at_nat @ Xs ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % length_remove1
% 2.86/3.06 thf(fact_1282_length__remove1,axiom,
% 2.86/3.06 ! [X: product_prod_nat_nat,Xs: list_P6011104703257516679at_nat] :
% 2.86/3.06 ( ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 2.86/3.06 => ( ( size_s5460976970255530739at_nat @ ( remove5766854097993331357at_nat @ X @ Xs ) )
% 2.86/3.06 = ( minus_minus_nat @ ( size_s5460976970255530739at_nat @ Xs ) @ one_one_nat ) ) )
% 2.86/3.06 & ( ~ ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 2.86/3.06 => ( ( size_s5460976970255530739at_nat @ ( remove5766854097993331357at_nat @ X @ Xs ) )
% 2.86/3.06 = ( size_s5460976970255530739at_nat @ Xs ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % length_remove1
% 2.86/3.06 thf(fact_1283_length__remove1,axiom,
% 2.86/3.06 ! [X: produc3658429121746597890et_nat > $o,Xs: list_P7985473006766602707_nat_o] :
% 2.86/3.06 ( ( ( member6576561426505652726_nat_o @ X @ ( set_Pr400311997697478754_nat_o @ Xs ) )
% 2.86/3.06 => ( ( size_s8908918004648414271_nat_o @ ( remove4235003712227595625_nat_o @ X @ Xs ) )
% 2.86/3.06 = ( minus_minus_nat @ ( size_s8908918004648414271_nat_o @ Xs ) @ one_one_nat ) ) )
% 2.86/3.06 & ( ~ ( member6576561426505652726_nat_o @ X @ ( set_Pr400311997697478754_nat_o @ Xs ) )
% 2.86/3.06 => ( ( size_s8908918004648414271_nat_o @ ( remove4235003712227595625_nat_o @ X @ Xs ) )
% 2.86/3.06 = ( size_s8908918004648414271_nat_o @ Xs ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % length_remove1
% 2.86/3.06 thf(fact_1284_length__remove1,axiom,
% 2.86/3.06 ! [X: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn] :
% 2.86/3.06 ( ( ( member7957490590177025114n_assn @ X @ ( set_Pr1139785259514867910n_assn @ Xs ) )
% 2.86/3.06 => ( ( size_s6829681357464350627n_assn @ ( remove1670527618125605709n_assn @ X @ Xs ) )
% 2.86/3.06 = ( minus_minus_nat @ ( size_s6829681357464350627n_assn @ Xs ) @ one_one_nat ) ) )
% 2.86/3.06 & ( ~ ( member7957490590177025114n_assn @ X @ ( set_Pr1139785259514867910n_assn @ Xs ) )
% 2.86/3.06 => ( ( size_s6829681357464350627n_assn @ ( remove1670527618125605709n_assn @ X @ Xs ) )
% 2.86/3.06 = ( size_s6829681357464350627n_assn @ Xs ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % length_remove1
% 2.86/3.06 thf(fact_1285_length__remove1,axiom,
% 2.86/3.06 ! [X: c,Xs: list_c] :
% 2.86/3.06 ( ( ( member_c @ X @ ( set_c2 @ Xs ) )
% 2.86/3.06 => ( ( size_size_list_c @ ( remove1_c @ X @ Xs ) )
% 2.86/3.06 = ( minus_minus_nat @ ( size_size_list_c @ Xs ) @ one_one_nat ) ) )
% 2.86/3.06 & ( ~ ( member_c @ X @ ( set_c2 @ Xs ) )
% 2.86/3.06 => ( ( size_size_list_c @ ( remove1_c @ X @ Xs ) )
% 2.86/3.06 = ( size_size_list_c @ Xs ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % length_remove1
% 2.86/3.06 thf(fact_1286_length__remove1,axiom,
% 2.86/3.06 ! [X: d,Xs: list_d] :
% 2.86/3.06 ( ( ( member_d @ X @ ( set_d2 @ Xs ) )
% 2.86/3.06 => ( ( size_size_list_d @ ( remove1_d @ X @ Xs ) )
% 2.86/3.06 = ( minus_minus_nat @ ( size_size_list_d @ Xs ) @ one_one_nat ) ) )
% 2.86/3.06 & ( ~ ( member_d @ X @ ( set_d2 @ Xs ) )
% 2.86/3.06 => ( ( size_size_list_d @ ( remove1_d @ X @ Xs ) )
% 2.86/3.06 = ( size_size_list_d @ Xs ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % length_remove1
% 2.86/3.06 thf(fact_1287_length__remove1,axiom,
% 2.86/3.06 ! [X: nat,Xs: list_nat] :
% 2.86/3.06 ( ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 2.86/3.06 => ( ( size_size_list_nat @ ( remove1_nat @ X @ Xs ) )
% 2.86/3.06 = ( minus_minus_nat @ ( size_size_list_nat @ Xs ) @ one_one_nat ) ) )
% 2.86/3.06 & ( ~ ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 2.86/3.06 => ( ( size_size_list_nat @ ( remove1_nat @ X @ Xs ) )
% 2.86/3.06 = ( size_size_list_nat @ Xs ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % length_remove1
% 2.86/3.06 thf(fact_1288_length__remove1,axiom,
% 2.86/3.06 ! [X: int,Xs: list_int] :
% 2.86/3.06 ( ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 2.86/3.06 => ( ( size_size_list_int @ ( remove1_int @ X @ Xs ) )
% 2.86/3.06 = ( minus_minus_nat @ ( size_size_list_int @ Xs ) @ one_one_nat ) ) )
% 2.86/3.06 & ( ~ ( member_int @ X @ ( set_int2 @ Xs ) )
% 2.86/3.06 => ( ( size_size_list_int @ ( remove1_int @ X @ Xs ) )
% 2.86/3.06 = ( size_size_list_int @ Xs ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % length_remove1
% 2.86/3.06 thf(fact_1289_insert__code_I2_J,axiom,
% 2.86/3.06 ! [X: nat,Xs: list_nat] :
% 2.86/3.06 ( ( insert_nat2 @ X @ ( coset_nat @ Xs ) )
% 2.86/3.06 = ( coset_nat @ ( removeAll_nat @ X @ Xs ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % insert_code(2)
% 2.86/3.06 thf(fact_1290_insert__code_I2_J,axiom,
% 2.86/3.06 ! [X: int,Xs: list_int] :
% 2.86/3.06 ( ( insert_int2 @ X @ ( coset_int @ Xs ) )
% 2.86/3.06 = ( coset_int @ ( removeAll_int @ X @ Xs ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % insert_code(2)
% 2.86/3.06 thf(fact_1291_insert__code_I2_J,axiom,
% 2.86/3.06 ! [X: product_prod_nat_nat,Xs: list_P6011104703257516679at_nat] :
% 2.86/3.06 ( ( insert8211810215607154385at_nat @ X @ ( coset_6809516720700967924at_nat @ Xs ) )
% 2.86/3.06 = ( coset_6809516720700967924at_nat @ ( remove3673390508374433037at_nat @ X @ Xs ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % insert_code(2)
% 2.86/3.06 thf(fact_1292_insert__code_I2_J,axiom,
% 2.86/3.06 ! [X: produc3843707927480180839at_nat,Xs: list_P5464809261938338413at_nat] :
% 2.86/3.06 ( ( insert9069300056098147895at_nat @ X @ ( coset_5307619257043544794at_nat @ Xs ) )
% 2.86/3.06 = ( coset_5307619257043544794at_nat @ ( remove4908499291543849587at_nat @ X @ Xs ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % insert_code(2)
% 2.86/3.06 thf(fact_1293_insert__code_I2_J,axiom,
% 2.86/3.06 ! [X: $o,Xs: list_o] :
% 2.86/3.06 ( ( insert_o2 @ X @ ( coset_o @ Xs ) )
% 2.86/3.06 = ( coset_o @ ( removeAll_o @ X @ Xs ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % insert_code(2)
% 2.86/3.06 thf(fact_1294_zipf__zip,axiom,
% 2.86/3.06 ! [L12: list_c,L23: list_c] :
% 2.86/3.06 ( ( ( size_size_list_c @ L12 )
% 2.86/3.06 = ( size_size_list_c @ L23 ) )
% 2.86/3.06 => ( ( zipf_c684006316856269033od_c_c @ product_Pair_c_c @ L12 @ L23 )
% 2.86/3.06 = ( zip_c_c @ L12 @ L23 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zipf_zip
% 2.86/3.06 thf(fact_1295_zipf__zip,axiom,
% 2.86/3.06 ! [L12: list_c,L23: list_d] :
% 2.86/3.06 ( ( ( size_size_list_c @ L12 )
% 2.86/3.06 = ( size_size_list_d @ L23 ) )
% 2.86/3.06 => ( ( zipf_c44566020827681705od_c_d @ product_Pair_c_d @ L12 @ L23 )
% 2.86/3.06 = ( zip_c_d @ L12 @ L23 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zipf_zip
% 2.86/3.06 thf(fact_1296_zipf__zip,axiom,
% 2.86/3.06 ! [L12: list_c,L23: list_nat] :
% 2.86/3.06 ( ( ( size_size_list_c @ L12 )
% 2.86/3.06 = ( size_size_list_nat @ L23 ) )
% 2.86/3.06 => ( ( zipf_c7084520048314076179_c_nat @ product_Pair_c_nat @ L12 @ L23 )
% 2.86/3.06 = ( zip_c_nat @ L12 @ L23 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zipf_zip
% 2.86/3.06 thf(fact_1297_zipf__zip,axiom,
% 2.86/3.06 ! [L12: list_c,L23: list_int] :
% 2.86/3.06 ( ( ( size_size_list_c @ L12 )
% 2.86/3.06 = ( size_size_list_int @ L23 ) )
% 2.86/3.06 => ( ( zipf_c230841880303976139_c_int @ product_Pair_c_int @ L12 @ L23 )
% 2.86/3.06 = ( zip_c_int @ L12 @ L23 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zipf_zip
% 2.86/3.06 thf(fact_1298_zipf__zip,axiom,
% 2.86/3.06 ! [L12: list_d,L23: list_c] :
% 2.86/3.06 ( ( ( size_size_list_d @ L12 )
% 2.86/3.06 = ( size_size_list_c @ L23 ) )
% 2.86/3.06 => ( ( zipf_d1836499321508429225od_d_c @ product_Pair_d_c @ L12 @ L23 )
% 2.86/3.06 = ( zip_d_c @ L12 @ L23 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zipf_zip
% 2.86/3.06 thf(fact_1299_zipf__zip,axiom,
% 2.86/3.06 ! [L12: list_d,L23: list_d] :
% 2.86/3.06 ( ( ( size_size_list_d @ L12 )
% 2.86/3.06 = ( size_size_list_d @ L23 ) )
% 2.86/3.06 => ( ( zipf_d1197059025479841897od_d_d @ product_Pair_d_d @ L12 @ L23 )
% 2.86/3.06 = ( zip_d_d @ L12 @ L23 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zipf_zip
% 2.86/3.06 thf(fact_1300_zipf__zip,axiom,
% 2.86/3.06 ! [L12: list_d,L23: list_nat] :
% 2.86/3.06 ( ( ( size_size_list_d @ L12 )
% 2.86/3.06 = ( size_size_list_nat @ L23 ) )
% 2.86/3.06 => ( ( zipf_d7851395264309270293_d_nat @ product_Pair_d_nat @ L12 @ L23 )
% 2.86/3.06 = ( zip_d_nat @ L12 @ L23 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zipf_zip
% 2.86/3.06 thf(fact_1301_zipf__zip,axiom,
% 2.86/3.06 ! [L12: list_d,L23: list_int] :
% 2.86/3.06 ( ( ( size_size_list_d @ L12 )
% 2.86/3.06 = ( size_size_list_int @ L23 ) )
% 2.86/3.06 => ( ( zipf_d997717096299170253_d_int @ product_Pair_d_int @ L12 @ L23 )
% 2.86/3.06 = ( zip_d_int @ L12 @ L23 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zipf_zip
% 2.86/3.06 thf(fact_1302_zipf__zip,axiom,
% 2.86/3.06 ! [L12: list_nat,L23: list_c] :
% 2.86/3.06 ( ( ( size_size_list_nat @ L12 )
% 2.86/3.06 = ( size_size_list_c @ L23 ) )
% 2.86/3.06 => ( ( zipf_n5773672615478942615_nat_c @ product_Pair_nat_c @ L12 @ L23 )
% 2.86/3.06 = ( zip_nat_c @ L12 @ L23 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zipf_zip
% 2.86/3.06 thf(fact_1303_zipf__zip,axiom,
% 2.86/3.06 ! [L12: list_nat,L23: list_d] :
% 2.86/3.06 ( ( ( size_size_list_nat @ L12 )
% 2.86/3.06 = ( size_size_list_d @ L23 ) )
% 2.86/3.06 => ( ( zipf_n3657244561791696409_nat_d @ product_Pair_nat_d @ L12 @ L23 )
% 2.86/3.06 = ( zip_nat_d @ L12 @ L23 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % zipf_zip
% 2.86/3.06 thf(fact_1304_one__assn__raw_Osimps,axiom,
% 2.86/3.06 ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 2.86/3.06 ( ( one_assn_raw @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 2.86/3.06 = ( As2 = bot_bot_set_nat ) ) ).
% 2.86/3.06
% 2.86/3.06 % one_assn_raw.simps
% 2.86/3.06 thf(fact_1305_one__assn__raw_Oelims_I1_J,axiom,
% 2.86/3.06 ! [X: produc3658429121746597890et_nat,Y: $o] :
% 2.86/3.06 ( ( ( one_assn_raw @ X )
% 2.86/3.06 = Y )
% 2.86/3.06 => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.86/3.06 ( ( X
% 2.86/3.06 = ( produc7507926704131184380et_nat @ H @ As ) )
% 2.86/3.06 => ( Y
% 2.86/3.06 = ( As != bot_bot_set_nat ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % one_assn_raw.elims(1)
% 2.86/3.06 thf(fact_1306_one__assn__raw_Oelims_I2_J,axiom,
% 2.86/3.06 ! [X: produc3658429121746597890et_nat] :
% 2.86/3.06 ( ( one_assn_raw @ X )
% 2.86/3.06 => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.86/3.06 ( ( X
% 2.86/3.06 = ( produc7507926704131184380et_nat @ H @ As ) )
% 2.86/3.06 => ( As != bot_bot_set_nat ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % one_assn_raw.elims(2)
% 2.86/3.06 thf(fact_1307_one__assn__raw_Oelims_I3_J,axiom,
% 2.86/3.06 ! [X: produc3658429121746597890et_nat] :
% 2.86/3.06 ( ~ ( one_assn_raw @ X )
% 2.86/3.06 => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.86/3.06 ( ( X
% 2.86/3.06 = ( produc7507926704131184380et_nat @ H @ As ) )
% 2.86/3.06 => ( As = bot_bot_set_nat ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % one_assn_raw.elims(3)
% 2.86/3.06 thf(fact_1308_psubset__insert__iff,axiom,
% 2.86/3.06 ! [A: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o,B: set_Pr4532377907799695533_nat_o] :
% 2.86/3.06 ( ( ord_le2453136405763929_nat_o @ A @ ( insert5175938949040314269_nat_o @ X @ B ) )
% 2.86/3.06 = ( ( ( member6576561426505652726_nat_o @ X @ B )
% 2.86/3.06 => ( ord_le2453136405763929_nat_o @ A @ B ) )
% 2.86/3.06 & ( ~ ( member6576561426505652726_nat_o @ X @ B )
% 2.86/3.06 => ( ( ( member6576561426505652726_nat_o @ X @ A )
% 2.86/3.06 => ( ord_le2453136405763929_nat_o @ ( minus_1801376950450012436_nat_o @ A @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) @ B ) )
% 2.86/3.06 & ( ~ ( member6576561426505652726_nat_o @ X @ A )
% 2.86/3.06 => ( ord_le2965882846123202637_nat_o @ A @ B ) ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % psubset_insert_iff
% 2.86/3.06 thf(fact_1309_psubset__insert__iff,axiom,
% 2.86/3.06 ! [A: set_Pr4329608150637261639at_nat,X: produc3843707927480180839at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.06 ( ( ord_le2604355607129572851at_nat @ A @ ( insert9069300056098147895at_nat @ X @ B ) )
% 2.86/3.06 = ( ( ( member8757157785044589968at_nat @ X @ B )
% 2.86/3.06 => ( ord_le2604355607129572851at_nat @ A @ B ) )
% 2.86/3.06 & ( ~ ( member8757157785044589968at_nat @ X @ B )
% 2.86/3.06 => ( ( ( member8757157785044589968at_nat @ X @ A )
% 2.86/3.06 => ( ord_le2604355607129572851at_nat @ ( minus_3314409938677909166at_nat @ A @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) @ B ) )
% 2.86/3.06 & ( ~ ( member8757157785044589968at_nat @ X @ A )
% 2.86/3.06 => ( ord_le1268244103169919719at_nat @ A @ B ) ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % psubset_insert_iff
% 2.86/3.06 thf(fact_1310_psubset__insert__iff,axiom,
% 2.86/3.06 ! [A: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.06 ( ( ord_le7866589430770878221at_nat @ A @ ( insert8211810215607154385at_nat @ X @ B ) )
% 2.86/3.06 = ( ( ( member8440522571783428010at_nat @ X @ B )
% 2.86/3.06 => ( ord_le7866589430770878221at_nat @ A @ B ) )
% 2.86/3.06 & ( ~ ( member8440522571783428010at_nat @ X @ B )
% 2.86/3.06 => ( ( ( member8440522571783428010at_nat @ X @ A )
% 2.86/3.06 => ( ord_le7866589430770878221at_nat @ ( minus_1356011639430497352at_nat @ A @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) @ B ) )
% 2.86/3.06 & ( ~ ( member8440522571783428010at_nat @ X @ A )
% 2.86/3.06 => ( ord_le3146513528884898305at_nat @ A @ B ) ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % psubset_insert_iff
% 2.86/3.06 thf(fact_1311_psubset__insert__iff,axiom,
% 2.86/3.06 ! [A: set_o,X: $o,B: set_o] :
% 2.86/3.06 ( ( ord_less_set_o @ A @ ( insert_o2 @ X @ B ) )
% 2.86/3.06 = ( ( ( member_o @ X @ B )
% 2.86/3.06 => ( ord_less_set_o @ A @ B ) )
% 2.86/3.06 & ( ~ ( member_o @ X @ B )
% 2.86/3.06 => ( ( ( member_o @ X @ A )
% 2.86/3.06 => ( ord_less_set_o @ ( minus_minus_set_o @ A @ ( insert_o2 @ X @ bot_bot_set_o ) ) @ B ) )
% 2.86/3.06 & ( ~ ( member_o @ X @ A )
% 2.86/3.06 => ( ord_less_eq_set_o @ A @ B ) ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % psubset_insert_iff
% 2.86/3.06 thf(fact_1312_psubset__insert__iff,axiom,
% 2.86/3.06 ! [A: set_int,X: int,B: set_int] :
% 2.86/3.06 ( ( ord_less_set_int @ A @ ( insert_int2 @ X @ B ) )
% 2.86/3.06 = ( ( ( member_int @ X @ B )
% 2.86/3.06 => ( ord_less_set_int @ A @ B ) )
% 2.86/3.06 & ( ~ ( member_int @ X @ B )
% 2.86/3.06 => ( ( ( member_int @ X @ A )
% 2.86/3.06 => ( ord_less_set_int @ ( minus_minus_set_int @ A @ ( insert_int2 @ X @ bot_bot_set_int ) ) @ B ) )
% 2.86/3.06 & ( ~ ( member_int @ X @ A )
% 2.86/3.06 => ( ord_less_eq_set_int @ A @ B ) ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % psubset_insert_iff
% 2.86/3.06 thf(fact_1313_psubset__insert__iff,axiom,
% 2.86/3.06 ! [A: set_nat,X: nat,B: set_nat] :
% 2.86/3.06 ( ( ord_less_set_nat @ A @ ( insert_nat2 @ X @ B ) )
% 2.86/3.06 = ( ( ( member_nat @ X @ B )
% 2.86/3.06 => ( ord_less_set_nat @ A @ B ) )
% 2.86/3.06 & ( ~ ( member_nat @ X @ B )
% 2.86/3.06 => ( ( ( member_nat @ X @ A )
% 2.86/3.06 => ( ord_less_set_nat @ ( minus_minus_set_nat @ A @ ( insert_nat2 @ X @ bot_bot_set_nat ) ) @ B ) )
% 2.86/3.06 & ( ~ ( member_nat @ X @ A )
% 2.86/3.06 => ( ord_less_eq_set_nat @ A @ B ) ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % psubset_insert_iff
% 2.86/3.06 thf(fact_1314_lexn__length,axiom,
% 2.86/3.06 ! [Xs: list_c,Ys: list_c,R2: set_Product_prod_c_c,N: nat] :
% 2.86/3.06 ( ( member7012247553653173456list_c @ ( produc5515445818230282391list_c @ Xs @ Ys ) @ ( lexn_c @ R2 @ N ) )
% 2.86/3.06 => ( ( ( size_size_list_c @ Xs )
% 2.86/3.06 = N )
% 2.86/3.06 & ( ( size_size_list_c @ Ys )
% 2.86/3.06 = N ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % lexn_length
% 2.86/3.06 thf(fact_1315_lexn__length,axiom,
% 2.86/3.06 ! [Xs: list_d,Ys: list_d,R2: set_Product_prod_d_d,N: nat] :
% 2.86/3.06 ( ( member1810801192463332112list_d @ ( produc242965421297323863list_d @ Xs @ Ys ) @ ( lexn_d @ R2 @ N ) )
% 2.86/3.06 => ( ( ( size_size_list_d @ Xs )
% 2.86/3.06 = N )
% 2.86/3.06 & ( ( size_size_list_d @ Ys )
% 2.86/3.06 = N ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % lexn_length
% 2.86/3.06 thf(fact_1316_lexn__length,axiom,
% 2.86/3.06 ! [Xs: list_nat,Ys: list_nat,R2: set_Pr1261947904930325089at_nat,N: nat] :
% 2.86/3.06 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs @ Ys ) @ ( lexn_nat @ R2 @ N ) )
% 2.86/3.06 => ( ( ( size_size_list_nat @ Xs )
% 2.86/3.06 = N )
% 2.86/3.06 & ( ( size_size_list_nat @ Ys )
% 2.86/3.06 = N ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % lexn_length
% 2.86/3.06 thf(fact_1317_lexn__length,axiom,
% 2.86/3.06 ! [Xs: list_int,Ys: list_int,R2: set_Pr958786334691620121nt_int,N: nat] :
% 2.86/3.06 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs @ Ys ) @ ( lexn_int @ R2 @ N ) )
% 2.86/3.06 => ( ( ( size_size_list_int @ Xs )
% 2.86/3.06 = N )
% 2.86/3.06 & ( ( size_size_list_int @ Ys )
% 2.86/3.06 = N ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % lexn_length
% 2.86/3.06 thf(fact_1318_pairwise__alt,axiom,
% 2.86/3.06 ( pairwi3222497012029234898at_nat
% 2.86/3.06 = ( ^ [R3: produc3843707927480180839at_nat > produc3843707927480180839at_nat > $o,S2: set_Pr4329608150637261639at_nat] :
% 2.86/3.06 ! [X2: produc3843707927480180839at_nat] :
% 2.86/3.06 ( ( member8757157785044589968at_nat @ X2 @ S2 )
% 2.86/3.06 => ! [Y5: produc3843707927480180839at_nat] :
% 2.86/3.06 ( ( member8757157785044589968at_nat @ Y5 @ ( minus_3314409938677909166at_nat @ S2 @ ( insert9069300056098147895at_nat @ X2 @ bot_bo228742789529271731at_nat ) ) )
% 2.86/3.06 => ( R3 @ X2 @ Y5 ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % pairwise_alt
% 2.86/3.06 thf(fact_1319_pairwise__alt,axiom,
% 2.86/3.06 ( pairwi6357175311820755948at_nat
% 2.86/3.06 = ( ^ [R3: product_prod_nat_nat > product_prod_nat_nat > $o,S2: set_Pr1261947904930325089at_nat] :
% 2.86/3.06 ! [X2: product_prod_nat_nat] :
% 2.86/3.06 ( ( member8440522571783428010at_nat @ X2 @ S2 )
% 2.86/3.06 => ! [Y5: product_prod_nat_nat] :
% 2.86/3.06 ( ( member8440522571783428010at_nat @ Y5 @ ( minus_1356011639430497352at_nat @ S2 @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) ) )
% 2.86/3.06 => ( R3 @ X2 @ Y5 ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % pairwise_alt
% 2.86/3.06 thf(fact_1320_pairwise__alt,axiom,
% 2.86/3.06 ( pairwise_o
% 2.86/3.06 = ( ^ [R3: $o > $o > $o,S2: set_o] :
% 2.86/3.06 ! [X2: $o] :
% 2.86/3.06 ( ( member_o @ X2 @ S2 )
% 2.86/3.06 => ! [Y5: $o] :
% 2.86/3.06 ( ( member_o @ Y5 @ ( minus_minus_set_o @ S2 @ ( insert_o2 @ X2 @ bot_bot_set_o ) ) )
% 2.86/3.06 => ( R3 @ X2 @ Y5 ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % pairwise_alt
% 2.86/3.06 thf(fact_1321_pairwise__alt,axiom,
% 2.86/3.06 ( pairwise_int
% 2.86/3.06 = ( ^ [R3: int > int > $o,S2: set_int] :
% 2.86/3.06 ! [X2: int] :
% 2.86/3.06 ( ( member_int @ X2 @ S2 )
% 2.86/3.06 => ! [Y5: int] :
% 2.86/3.06 ( ( member_int @ Y5 @ ( minus_minus_set_int @ S2 @ ( insert_int2 @ X2 @ bot_bot_set_int ) ) )
% 2.86/3.06 => ( R3 @ X2 @ Y5 ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % pairwise_alt
% 2.86/3.06 thf(fact_1322_pairwise__alt,axiom,
% 2.86/3.06 ( pairwise_nat
% 2.86/3.06 = ( ^ [R3: nat > nat > $o,S2: set_nat] :
% 2.86/3.06 ! [X2: nat] :
% 2.86/3.06 ( ( member_nat @ X2 @ S2 )
% 2.86/3.06 => ! [Y5: nat] :
% 2.86/3.06 ( ( member_nat @ Y5 @ ( minus_minus_set_nat @ S2 @ ( insert_nat2 @ X2 @ bot_bot_set_nat ) ) )
% 2.86/3.06 => ( R3 @ X2 @ Y5 ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % pairwise_alt
% 2.86/3.06 thf(fact_1323_and__extract__pure__left__iff,axiom,
% 2.86/3.06 ! [B2: $o,Q: assn] :
% 2.86/3.06 ( ( inf_inf_assn @ ( pure_assn @ B2 ) @ Q )
% 2.86/3.06 = ( times_times_assn @ ( inf_inf_assn @ one_one_assn @ Q ) @ ( pure_assn @ B2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % and_extract_pure_left_iff
% 2.86/3.06 thf(fact_1324_and__extract__pure__right__iff,axiom,
% 2.86/3.06 ! [P: assn,B2: $o] :
% 2.86/3.06 ( ( inf_inf_assn @ P @ ( pure_assn @ B2 ) )
% 2.86/3.06 = ( times_times_assn @ ( inf_inf_assn @ one_one_assn @ P ) @ ( pure_assn @ B2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % and_extract_pure_right_iff
% 2.86/3.06 thf(fact_1325_order__refl,axiom,
% 2.86/3.06 ! [X: assn] : ( ord_less_eq_assn @ X @ X ) ).
% 2.86/3.06
% 2.86/3.06 % order_refl
% 2.86/3.06 thf(fact_1326_order__refl,axiom,
% 2.86/3.06 ! [X: filter_nat] : ( ord_le2510731241096832064er_nat @ X @ X ) ).
% 2.86/3.06
% 2.86/3.06 % order_refl
% 2.86/3.06 thf(fact_1327_order__refl,axiom,
% 2.86/3.06 ! [X: set_nat] : ( ord_less_eq_set_nat @ X @ X ) ).
% 2.86/3.06
% 2.86/3.06 % order_refl
% 2.86/3.06 thf(fact_1328_order__refl,axiom,
% 2.86/3.06 ! [X: nat] : ( ord_less_eq_nat @ X @ X ) ).
% 2.86/3.06
% 2.86/3.06 % order_refl
% 2.86/3.06 thf(fact_1329_order__refl,axiom,
% 2.86/3.06 ! [X: int] : ( ord_less_eq_int @ X @ X ) ).
% 2.86/3.06
% 2.86/3.06 % order_refl
% 2.86/3.06 thf(fact_1330_dual__order_Orefl,axiom,
% 2.86/3.06 ! [A2: assn] : ( ord_less_eq_assn @ A2 @ A2 ) ).
% 2.86/3.06
% 2.86/3.06 % dual_order.refl
% 2.86/3.06 thf(fact_1331_dual__order_Orefl,axiom,
% 2.86/3.06 ! [A2: filter_nat] : ( ord_le2510731241096832064er_nat @ A2 @ A2 ) ).
% 2.86/3.06
% 2.86/3.06 % dual_order.refl
% 2.86/3.06 thf(fact_1332_dual__order_Orefl,axiom,
% 2.86/3.06 ! [A2: set_nat] : ( ord_less_eq_set_nat @ A2 @ A2 ) ).
% 2.86/3.06
% 2.86/3.06 % dual_order.refl
% 2.86/3.06 thf(fact_1333_dual__order_Orefl,axiom,
% 2.86/3.06 ! [A2: nat] : ( ord_less_eq_nat @ A2 @ A2 ) ).
% 2.86/3.06
% 2.86/3.06 % dual_order.refl
% 2.86/3.06 thf(fact_1334_dual__order_Orefl,axiom,
% 2.86/3.06 ! [A2: int] : ( ord_less_eq_int @ A2 @ A2 ) ).
% 2.86/3.06
% 2.86/3.06 % dual_order.refl
% 2.86/3.06 thf(fact_1335_subsetI,axiom,
% 2.86/3.06 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.06 ( ! [X3: produc3843707927480180839at_nat] :
% 2.86/3.06 ( ( member8757157785044589968at_nat @ X3 @ A )
% 2.86/3.06 => ( member8757157785044589968at_nat @ X3 @ B ) )
% 2.86/3.06 => ( ord_le1268244103169919719at_nat @ A @ B ) ) ).
% 2.86/3.06
% 2.86/3.06 % subsetI
% 2.86/3.06 thf(fact_1336_subsetI,axiom,
% 2.86/3.06 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.06 ( ! [X3: product_prod_nat_nat] :
% 2.86/3.06 ( ( member8440522571783428010at_nat @ X3 @ A )
% 2.86/3.06 => ( member8440522571783428010at_nat @ X3 @ B ) )
% 2.86/3.06 => ( ord_le3146513528884898305at_nat @ A @ B ) ) ).
% 2.86/3.06
% 2.86/3.06 % subsetI
% 2.86/3.06 thf(fact_1337_subsetI,axiom,
% 2.86/3.06 ! [A: set_int,B: set_int] :
% 2.86/3.06 ( ! [X3: int] :
% 2.86/3.06 ( ( member_int @ X3 @ A )
% 2.86/3.06 => ( member_int @ X3 @ B ) )
% 2.86/3.06 => ( ord_less_eq_set_int @ A @ B ) ) ).
% 2.86/3.06
% 2.86/3.06 % subsetI
% 2.86/3.06 thf(fact_1338_subsetI,axiom,
% 2.86/3.06 ! [A: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o] :
% 2.86/3.06 ( ! [X3: produc3658429121746597890et_nat > $o] :
% 2.86/3.06 ( ( member6576561426505652726_nat_o @ X3 @ A )
% 2.86/3.06 => ( member6576561426505652726_nat_o @ X3 @ B ) )
% 2.86/3.06 => ( ord_le2965882846123202637_nat_o @ A @ B ) ) ).
% 2.86/3.06
% 2.86/3.06 % subsetI
% 2.86/3.06 thf(fact_1339_subsetI,axiom,
% 2.86/3.06 ! [A: set_nat,B: set_nat] :
% 2.86/3.06 ( ! [X3: nat] :
% 2.86/3.06 ( ( member_nat @ X3 @ A )
% 2.86/3.06 => ( member_nat @ X3 @ B ) )
% 2.86/3.06 => ( ord_less_eq_set_nat @ A @ B ) ) ).
% 2.86/3.06
% 2.86/3.06 % subsetI
% 2.86/3.06 thf(fact_1340_subset__antisym,axiom,
% 2.86/3.06 ! [A: set_nat,B: set_nat] :
% 2.86/3.06 ( ( ord_less_eq_set_nat @ A @ B )
% 2.86/3.06 => ( ( ord_less_eq_set_nat @ B @ A )
% 2.86/3.06 => ( A = B ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % subset_antisym
% 2.86/3.06 thf(fact_1341_inf_Oidem,axiom,
% 2.86/3.06 ! [A2: assn] :
% 2.86/3.06 ( ( inf_inf_assn @ A2 @ A2 )
% 2.86/3.06 = A2 ) ).
% 2.86/3.06
% 2.86/3.06 % inf.idem
% 2.86/3.06 thf(fact_1342_inf_Oidem,axiom,
% 2.86/3.06 ! [A2: set_nat] :
% 2.86/3.06 ( ( inf_inf_set_nat @ A2 @ A2 )
% 2.86/3.06 = A2 ) ).
% 2.86/3.06
% 2.86/3.06 % inf.idem
% 2.86/3.06 thf(fact_1343_inf_Oidem,axiom,
% 2.86/3.06 ! [A2: set_Pr1261947904930325089at_nat] :
% 2.86/3.06 ( ( inf_in2572325071724192079at_nat @ A2 @ A2 )
% 2.86/3.06 = A2 ) ).
% 2.86/3.06
% 2.86/3.06 % inf.idem
% 2.86/3.06 thf(fact_1344_inf__idem,axiom,
% 2.86/3.06 ! [X: assn] :
% 2.86/3.06 ( ( inf_inf_assn @ X @ X )
% 2.86/3.06 = X ) ).
% 2.86/3.06
% 2.86/3.06 % inf_idem
% 2.86/3.06 thf(fact_1345_inf__idem,axiom,
% 2.86/3.06 ! [X: set_nat] :
% 2.86/3.06 ( ( inf_inf_set_nat @ X @ X )
% 2.86/3.06 = X ) ).
% 2.86/3.06
% 2.86/3.06 % inf_idem
% 2.86/3.06 thf(fact_1346_inf__idem,axiom,
% 2.86/3.06 ! [X: set_Pr1261947904930325089at_nat] :
% 2.86/3.06 ( ( inf_in2572325071724192079at_nat @ X @ X )
% 2.86/3.06 = X ) ).
% 2.86/3.06
% 2.86/3.06 % inf_idem
% 2.86/3.06 thf(fact_1347_inf_Oleft__idem,axiom,
% 2.86/3.06 ! [A2: assn,B2: assn] :
% 2.86/3.06 ( ( inf_inf_assn @ A2 @ ( inf_inf_assn @ A2 @ B2 ) )
% 2.86/3.06 = ( inf_inf_assn @ A2 @ B2 ) ) ).
% 2.86/3.06
% 2.86/3.06 % inf.left_idem
% 2.86/3.06 thf(fact_1348_inf_Oleft__idem,axiom,
% 2.86/3.06 ! [A2: set_nat,B2: set_nat] :
% 2.86/3.06 ( ( inf_inf_set_nat @ A2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 2.86/3.06 = ( inf_inf_set_nat @ A2 @ B2 ) ) ).
% 2.86/3.06
% 2.86/3.06 % inf.left_idem
% 2.86/3.06 thf(fact_1349_inf_Oleft__idem,axiom,
% 2.86/3.06 ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 2.86/3.06 ( ( inf_in2572325071724192079at_nat @ A2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) )
% 2.86/3.06 = ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ).
% 2.86/3.06
% 2.86/3.06 % inf.left_idem
% 2.86/3.06 thf(fact_1350_inf__left__idem,axiom,
% 2.86/3.06 ! [X: assn,Y: assn] :
% 2.86/3.06 ( ( inf_inf_assn @ X @ ( inf_inf_assn @ X @ Y ) )
% 2.86/3.06 = ( inf_inf_assn @ X @ Y ) ) ).
% 2.86/3.06
% 2.86/3.06 % inf_left_idem
% 2.86/3.06 thf(fact_1351_inf__left__idem,axiom,
% 2.86/3.06 ! [X: set_nat,Y: set_nat] :
% 2.86/3.06 ( ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ X @ Y ) )
% 2.86/3.06 = ( inf_inf_set_nat @ X @ Y ) ) ).
% 2.86/3.06
% 2.86/3.06 % inf_left_idem
% 2.86/3.06 thf(fact_1352_inf__left__idem,axiom,
% 2.86/3.06 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 2.86/3.06 ( ( inf_in2572325071724192079at_nat @ X @ ( inf_in2572325071724192079at_nat @ X @ Y ) )
% 2.86/3.06 = ( inf_in2572325071724192079at_nat @ X @ Y ) ) ).
% 2.86/3.06
% 2.86/3.06 % inf_left_idem
% 2.86/3.06 thf(fact_1353_inf_Oright__idem,axiom,
% 2.86/3.06 ! [A2: assn,B2: assn] :
% 2.86/3.06 ( ( inf_inf_assn @ ( inf_inf_assn @ A2 @ B2 ) @ B2 )
% 2.86/3.06 = ( inf_inf_assn @ A2 @ B2 ) ) ).
% 2.86/3.06
% 2.86/3.06 % inf.right_idem
% 2.86/3.06 thf(fact_1354_inf_Oright__idem,axiom,
% 2.86/3.06 ! [A2: set_nat,B2: set_nat] :
% 2.86/3.06 ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ B2 )
% 2.86/3.06 = ( inf_inf_set_nat @ A2 @ B2 ) ) ).
% 2.86/3.06
% 2.86/3.06 % inf.right_idem
% 2.86/3.06 thf(fact_1355_inf_Oright__idem,axiom,
% 2.86/3.06 ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 2.86/3.06 ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) @ B2 )
% 2.86/3.06 = ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ).
% 2.86/3.06
% 2.86/3.06 % inf.right_idem
% 2.86/3.06 thf(fact_1356_inf__right__idem,axiom,
% 2.86/3.06 ! [X: assn,Y: assn] :
% 2.86/3.06 ( ( inf_inf_assn @ ( inf_inf_assn @ X @ Y ) @ Y )
% 2.86/3.06 = ( inf_inf_assn @ X @ Y ) ) ).
% 2.86/3.06
% 2.86/3.06 % inf_right_idem
% 2.86/3.06 thf(fact_1357_inf__right__idem,axiom,
% 2.86/3.06 ! [X: set_nat,Y: set_nat] :
% 2.86/3.06 ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Y )
% 2.86/3.06 = ( inf_inf_set_nat @ X @ Y ) ) ).
% 2.86/3.06
% 2.86/3.06 % inf_right_idem
% 2.86/3.06 thf(fact_1358_inf__right__idem,axiom,
% 2.86/3.06 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 2.86/3.06 ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Y )
% 2.86/3.06 = ( inf_in2572325071724192079at_nat @ X @ Y ) ) ).
% 2.86/3.06
% 2.86/3.06 % inf_right_idem
% 2.86/3.06 thf(fact_1359_le__inf__iff,axiom,
% 2.86/3.06 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 2.86/3.06 ( ( ord_le3146513528884898305at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) )
% 2.86/3.06 = ( ( ord_le3146513528884898305at_nat @ X @ Y )
% 2.86/3.06 & ( ord_le3146513528884898305at_nat @ X @ Z ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % le_inf_iff
% 2.86/3.06 thf(fact_1360_le__inf__iff,axiom,
% 2.86/3.06 ! [X: assn,Y: assn,Z: assn] :
% 2.86/3.06 ( ( ord_less_eq_assn @ X @ ( inf_inf_assn @ Y @ Z ) )
% 2.86/3.06 = ( ( ord_less_eq_assn @ X @ Y )
% 2.86/3.06 & ( ord_less_eq_assn @ X @ Z ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % le_inf_iff
% 2.86/3.06 thf(fact_1361_le__inf__iff,axiom,
% 2.86/3.06 ! [X: filter_nat,Y: filter_nat,Z: filter_nat] :
% 2.86/3.06 ( ( ord_le2510731241096832064er_nat @ X @ ( inf_inf_filter_nat @ Y @ Z ) )
% 2.86/3.06 = ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 2.86/3.06 & ( ord_le2510731241096832064er_nat @ X @ Z ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % le_inf_iff
% 2.86/3.06 thf(fact_1362_le__inf__iff,axiom,
% 2.86/3.06 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 2.86/3.06 ( ( ord_less_eq_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) )
% 2.86/3.06 = ( ( ord_less_eq_set_nat @ X @ Y )
% 2.86/3.06 & ( ord_less_eq_set_nat @ X @ Z ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % le_inf_iff
% 2.86/3.06 thf(fact_1363_le__inf__iff,axiom,
% 2.86/3.06 ! [X: nat,Y: nat,Z: nat] :
% 2.86/3.06 ( ( ord_less_eq_nat @ X @ ( inf_inf_nat @ Y @ Z ) )
% 2.86/3.06 = ( ( ord_less_eq_nat @ X @ Y )
% 2.86/3.06 & ( ord_less_eq_nat @ X @ Z ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % le_inf_iff
% 2.86/3.06 thf(fact_1364_le__inf__iff,axiom,
% 2.86/3.06 ! [X: int,Y: int,Z: int] :
% 2.86/3.06 ( ( ord_less_eq_int @ X @ ( inf_inf_int @ Y @ Z ) )
% 2.86/3.06 = ( ( ord_less_eq_int @ X @ Y )
% 2.86/3.06 & ( ord_less_eq_int @ X @ Z ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % le_inf_iff
% 2.86/3.06 thf(fact_1365_inf_Obounded__iff,axiom,
% 2.86/3.06 ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat] :
% 2.86/3.06 ( ( ord_le3146513528884898305at_nat @ A2 @ ( inf_in2572325071724192079at_nat @ B2 @ C ) )
% 2.86/3.06 = ( ( ord_le3146513528884898305at_nat @ A2 @ B2 )
% 2.86/3.06 & ( ord_le3146513528884898305at_nat @ A2 @ C ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % inf.bounded_iff
% 2.86/3.06 thf(fact_1366_inf_Obounded__iff,axiom,
% 2.86/3.06 ! [A2: assn,B2: assn,C: assn] :
% 2.86/3.06 ( ( ord_less_eq_assn @ A2 @ ( inf_inf_assn @ B2 @ C ) )
% 2.86/3.06 = ( ( ord_less_eq_assn @ A2 @ B2 )
% 2.86/3.06 & ( ord_less_eq_assn @ A2 @ C ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % inf.bounded_iff
% 2.86/3.06 thf(fact_1367_inf_Obounded__iff,axiom,
% 2.86/3.06 ! [A2: filter_nat,B2: filter_nat,C: filter_nat] :
% 2.86/3.06 ( ( ord_le2510731241096832064er_nat @ A2 @ ( inf_inf_filter_nat @ B2 @ C ) )
% 2.86/3.06 = ( ( ord_le2510731241096832064er_nat @ A2 @ B2 )
% 2.86/3.06 & ( ord_le2510731241096832064er_nat @ A2 @ C ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % inf.bounded_iff
% 2.86/3.06 thf(fact_1368_inf_Obounded__iff,axiom,
% 2.86/3.06 ! [A2: set_nat,B2: set_nat,C: set_nat] :
% 2.86/3.06 ( ( ord_less_eq_set_nat @ A2 @ ( inf_inf_set_nat @ B2 @ C ) )
% 2.86/3.06 = ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 2.86/3.06 & ( ord_less_eq_set_nat @ A2 @ C ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % inf.bounded_iff
% 2.86/3.06 thf(fact_1369_inf_Obounded__iff,axiom,
% 2.86/3.06 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.06 ( ( ord_less_eq_nat @ A2 @ ( inf_inf_nat @ B2 @ C ) )
% 2.86/3.06 = ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.06 & ( ord_less_eq_nat @ A2 @ C ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % inf.bounded_iff
% 2.86/3.06 thf(fact_1370_inf_Obounded__iff,axiom,
% 2.86/3.06 ! [A2: int,B2: int,C: int] :
% 2.86/3.06 ( ( ord_less_eq_int @ A2 @ ( inf_inf_int @ B2 @ C ) )
% 2.86/3.06 = ( ( ord_less_eq_int @ A2 @ B2 )
% 2.86/3.06 & ( ord_less_eq_int @ A2 @ C ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % inf.bounded_iff
% 2.86/3.06 thf(fact_1371_inf__bot__right,axiom,
% 2.86/3.06 ! [X: assn] :
% 2.86/3.06 ( ( inf_inf_assn @ X @ bot_bot_assn )
% 2.86/3.06 = bot_bot_assn ) ).
% 2.86/3.06
% 2.86/3.06 % inf_bot_right
% 2.86/3.06 thf(fact_1372_inf__bot__right,axiom,
% 2.86/3.06 ! [X: set_Pr4329608150637261639at_nat] :
% 2.86/3.06 ( ( inf_in7913087082777306421at_nat @ X @ bot_bo228742789529271731at_nat )
% 2.86/3.06 = bot_bo228742789529271731at_nat ) ).
% 2.86/3.06
% 2.86/3.06 % inf_bot_right
% 2.86/3.06 thf(fact_1373_inf__bot__right,axiom,
% 2.86/3.06 ! [X: set_Pr1261947904930325089at_nat] :
% 2.86/3.06 ( ( inf_in2572325071724192079at_nat @ X @ bot_bo2099793752762293965at_nat )
% 2.86/3.06 = bot_bo2099793752762293965at_nat ) ).
% 2.86/3.06
% 2.86/3.06 % inf_bot_right
% 2.86/3.06 thf(fact_1374_inf__bot__right,axiom,
% 2.86/3.06 ! [X: set_o] :
% 2.86/3.06 ( ( inf_inf_set_o @ X @ bot_bot_set_o )
% 2.86/3.06 = bot_bot_set_o ) ).
% 2.86/3.06
% 2.86/3.06 % inf_bot_right
% 2.86/3.06 thf(fact_1375_inf__bot__right,axiom,
% 2.86/3.06 ! [X: set_nat] :
% 2.86/3.06 ( ( inf_inf_set_nat @ X @ bot_bot_set_nat )
% 2.86/3.06 = bot_bot_set_nat ) ).
% 2.86/3.06
% 2.86/3.06 % inf_bot_right
% 2.86/3.06 thf(fact_1376_inf__bot__right,axiom,
% 2.86/3.06 ! [X: set_int] :
% 2.86/3.06 ( ( inf_inf_set_int @ X @ bot_bot_set_int )
% 2.86/3.06 = bot_bot_set_int ) ).
% 2.86/3.06
% 2.86/3.06 % inf_bot_right
% 2.86/3.06 thf(fact_1377_inf__bot__left,axiom,
% 2.86/3.06 ! [X: assn] :
% 2.86/3.06 ( ( inf_inf_assn @ bot_bot_assn @ X )
% 2.86/3.06 = bot_bot_assn ) ).
% 2.86/3.06
% 2.86/3.06 % inf_bot_left
% 2.86/3.06 thf(fact_1378_inf__bot__left,axiom,
% 2.86/3.06 ! [X: set_Pr4329608150637261639at_nat] :
% 2.86/3.06 ( ( inf_in7913087082777306421at_nat @ bot_bo228742789529271731at_nat @ X )
% 2.86/3.06 = bot_bo228742789529271731at_nat ) ).
% 2.86/3.06
% 2.86/3.06 % inf_bot_left
% 2.86/3.06 thf(fact_1379_inf__bot__left,axiom,
% 2.86/3.06 ! [X: set_Pr1261947904930325089at_nat] :
% 2.86/3.06 ( ( inf_in2572325071724192079at_nat @ bot_bo2099793752762293965at_nat @ X )
% 2.86/3.06 = bot_bo2099793752762293965at_nat ) ).
% 2.86/3.06
% 2.86/3.06 % inf_bot_left
% 2.86/3.06 thf(fact_1380_inf__bot__left,axiom,
% 2.86/3.06 ! [X: set_o] :
% 2.86/3.06 ( ( inf_inf_set_o @ bot_bot_set_o @ X )
% 2.86/3.06 = bot_bot_set_o ) ).
% 2.86/3.06
% 2.86/3.06 % inf_bot_left
% 2.86/3.06 thf(fact_1381_inf__bot__left,axiom,
% 2.86/3.06 ! [X: set_nat] :
% 2.86/3.06 ( ( inf_inf_set_nat @ bot_bot_set_nat @ X )
% 2.86/3.06 = bot_bot_set_nat ) ).
% 2.86/3.06
% 2.86/3.06 % inf_bot_left
% 2.86/3.06 thf(fact_1382_inf__bot__left,axiom,
% 2.86/3.06 ! [X: set_int] :
% 2.86/3.06 ( ( inf_inf_set_int @ bot_bot_set_int @ X )
% 2.86/3.06 = bot_bot_set_int ) ).
% 2.86/3.06
% 2.86/3.06 % inf_bot_left
% 2.86/3.06 thf(fact_1383_subset__empty,axiom,
% 2.86/3.06 ! [A: set_Pr4329608150637261639at_nat] :
% 2.86/3.06 ( ( ord_le1268244103169919719at_nat @ A @ bot_bo228742789529271731at_nat )
% 2.86/3.06 = ( A = bot_bo228742789529271731at_nat ) ) ).
% 2.86/3.06
% 2.86/3.06 % subset_empty
% 2.86/3.06 thf(fact_1384_subset__empty,axiom,
% 2.86/3.06 ! [A: set_Pr1261947904930325089at_nat] :
% 2.86/3.06 ( ( ord_le3146513528884898305at_nat @ A @ bot_bo2099793752762293965at_nat )
% 2.86/3.06 = ( A = bot_bo2099793752762293965at_nat ) ) ).
% 2.86/3.06
% 2.86/3.06 % subset_empty
% 2.86/3.06 thf(fact_1385_subset__empty,axiom,
% 2.86/3.06 ! [A: set_o] :
% 2.86/3.06 ( ( ord_less_eq_set_o @ A @ bot_bot_set_o )
% 2.86/3.06 = ( A = bot_bot_set_o ) ) ).
% 2.86/3.06
% 2.86/3.06 % subset_empty
% 2.86/3.06 thf(fact_1386_subset__empty,axiom,
% 2.86/3.06 ! [A: set_int] :
% 2.86/3.06 ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 2.86/3.06 = ( A = bot_bot_set_int ) ) ).
% 2.86/3.06
% 2.86/3.06 % subset_empty
% 2.86/3.06 thf(fact_1387_subset__empty,axiom,
% 2.86/3.06 ! [A: set_nat] :
% 2.86/3.06 ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 2.86/3.06 = ( A = bot_bot_set_nat ) ) ).
% 2.86/3.06
% 2.86/3.06 % subset_empty
% 2.86/3.06 thf(fact_1388_empty__subsetI,axiom,
% 2.86/3.06 ! [A: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ bot_bo228742789529271731at_nat @ A ) ).
% 2.86/3.06
% 2.86/3.06 % empty_subsetI
% 2.86/3.06 thf(fact_1389_empty__subsetI,axiom,
% 2.86/3.06 ! [A: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ bot_bo2099793752762293965at_nat @ A ) ).
% 2.86/3.06
% 2.86/3.06 % empty_subsetI
% 2.86/3.06 thf(fact_1390_empty__subsetI,axiom,
% 2.86/3.06 ! [A: set_o] : ( ord_less_eq_set_o @ bot_bot_set_o @ A ) ).
% 2.86/3.06
% 2.86/3.06 % empty_subsetI
% 2.86/3.06 thf(fact_1391_empty__subsetI,axiom,
% 2.86/3.06 ! [A: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A ) ).
% 2.86/3.06
% 2.86/3.06 % empty_subsetI
% 2.86/3.06 thf(fact_1392_empty__subsetI,axiom,
% 2.86/3.06 ! [A: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A ) ).
% 2.86/3.06
% 2.86/3.06 % empty_subsetI
% 2.86/3.06 thf(fact_1393_insert__subset,axiom,
% 2.86/3.06 ! [X: $o,A: set_o,B: set_o] :
% 2.86/3.06 ( ( ord_less_eq_set_o @ ( insert_o2 @ X @ A ) @ B )
% 2.86/3.06 = ( ( member_o @ X @ B )
% 2.86/3.06 & ( ord_less_eq_set_o @ A @ B ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % insert_subset
% 2.86/3.06 thf(fact_1394_insert__subset,axiom,
% 2.86/3.06 ! [X: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.06 ( ( ord_le1268244103169919719at_nat @ ( insert9069300056098147895at_nat @ X @ A ) @ B )
% 2.86/3.06 = ( ( member8757157785044589968at_nat @ X @ B )
% 2.86/3.06 & ( ord_le1268244103169919719at_nat @ A @ B ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % insert_subset
% 2.86/3.06 thf(fact_1395_insert__subset,axiom,
% 2.86/3.06 ! [X: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.06 ( ( ord_le3146513528884898305at_nat @ ( insert8211810215607154385at_nat @ X @ A ) @ B )
% 2.86/3.06 = ( ( member8440522571783428010at_nat @ X @ B )
% 2.86/3.06 & ( ord_le3146513528884898305at_nat @ A @ B ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % insert_subset
% 2.86/3.06 thf(fact_1396_insert__subset,axiom,
% 2.86/3.06 ! [X: int,A: set_int,B: set_int] :
% 2.86/3.06 ( ( ord_less_eq_set_int @ ( insert_int2 @ X @ A ) @ B )
% 2.86/3.06 = ( ( member_int @ X @ B )
% 2.86/3.06 & ( ord_less_eq_set_int @ A @ B ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % insert_subset
% 2.86/3.06 thf(fact_1397_insert__subset,axiom,
% 2.86/3.06 ! [X: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o] :
% 2.86/3.06 ( ( ord_le2965882846123202637_nat_o @ ( insert5175938949040314269_nat_o @ X @ A ) @ B )
% 2.86/3.06 = ( ( member6576561426505652726_nat_o @ X @ B )
% 2.86/3.06 & ( ord_le2965882846123202637_nat_o @ A @ B ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % insert_subset
% 2.86/3.06 thf(fact_1398_insert__subset,axiom,
% 2.86/3.06 ! [X: nat,A: set_nat,B: set_nat] :
% 2.86/3.06 ( ( ord_less_eq_set_nat @ ( insert_nat2 @ X @ A ) @ B )
% 2.86/3.06 = ( ( member_nat @ X @ B )
% 2.86/3.06 & ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % insert_subset
% 2.86/3.06 thf(fact_1399_psubsetI,axiom,
% 2.86/3.06 ! [A: set_nat,B: set_nat] :
% 2.86/3.06 ( ( ord_less_eq_set_nat @ A @ B )
% 2.86/3.06 => ( ( A != B )
% 2.86/3.06 => ( ord_less_set_nat @ A @ B ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % psubsetI
% 2.86/3.06 thf(fact_1400_merge__pure__and,axiom,
% 2.86/3.06 ! [A2: $o,B2: $o] :
% 2.86/3.06 ( ( inf_inf_assn @ ( pure_assn @ A2 ) @ ( pure_assn @ B2 ) )
% 2.86/3.06 = ( pure_assn
% 2.86/3.06 @ ( A2
% 2.86/3.06 & B2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % merge_pure_and
% 2.86/3.06 thf(fact_1401_singleton__insert__inj__eq,axiom,
% 2.86/3.06 ! [B2: produc3843707927480180839at_nat,A2: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat] :
% 2.86/3.06 ( ( ( insert9069300056098147895at_nat @ B2 @ bot_bo228742789529271731at_nat )
% 2.86/3.06 = ( insert9069300056098147895at_nat @ A2 @ A ) )
% 2.86/3.06 = ( ( A2 = B2 )
% 2.86/3.06 & ( ord_le1268244103169919719at_nat @ A @ ( insert9069300056098147895at_nat @ B2 @ bot_bo228742789529271731at_nat ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % singleton_insert_inj_eq
% 2.86/3.06 thf(fact_1402_singleton__insert__inj__eq,axiom,
% 2.86/3.06 ! [B2: product_prod_nat_nat,A2: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat] :
% 2.86/3.06 ( ( ( insert8211810215607154385at_nat @ B2 @ bot_bo2099793752762293965at_nat )
% 2.86/3.06 = ( insert8211810215607154385at_nat @ A2 @ A ) )
% 2.86/3.06 = ( ( A2 = B2 )
% 2.86/3.06 & ( ord_le3146513528884898305at_nat @ A @ ( insert8211810215607154385at_nat @ B2 @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % singleton_insert_inj_eq
% 2.86/3.06 thf(fact_1403_singleton__insert__inj__eq,axiom,
% 2.86/3.06 ! [B2: $o,A2: $o,A: set_o] :
% 2.86/3.06 ( ( ( insert_o2 @ B2 @ bot_bot_set_o )
% 2.86/3.06 = ( insert_o2 @ A2 @ A ) )
% 2.86/3.06 = ( ( A2 = B2 )
% 2.86/3.06 & ( ord_less_eq_set_o @ A @ ( insert_o2 @ B2 @ bot_bot_set_o ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % singleton_insert_inj_eq
% 2.86/3.06 thf(fact_1404_singleton__insert__inj__eq,axiom,
% 2.86/3.06 ! [B2: int,A2: int,A: set_int] :
% 2.86/3.06 ( ( ( insert_int2 @ B2 @ bot_bot_set_int )
% 2.86/3.06 = ( insert_int2 @ A2 @ A ) )
% 2.86/3.06 = ( ( A2 = B2 )
% 2.86/3.06 & ( ord_less_eq_set_int @ A @ ( insert_int2 @ B2 @ bot_bot_set_int ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % singleton_insert_inj_eq
% 2.86/3.06 thf(fact_1405_singleton__insert__inj__eq,axiom,
% 2.86/3.06 ! [B2: nat,A2: nat,A: set_nat] :
% 2.86/3.06 ( ( ( insert_nat2 @ B2 @ bot_bot_set_nat )
% 2.86/3.06 = ( insert_nat2 @ A2 @ A ) )
% 2.86/3.06 = ( ( A2 = B2 )
% 2.86/3.06 & ( ord_less_eq_set_nat @ A @ ( insert_nat2 @ B2 @ bot_bot_set_nat ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % singleton_insert_inj_eq
% 2.86/3.06 thf(fact_1406_singleton__insert__inj__eq_H,axiom,
% 2.86/3.06 ! [A2: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat,B2: produc3843707927480180839at_nat] :
% 2.86/3.06 ( ( ( insert9069300056098147895at_nat @ A2 @ A )
% 2.86/3.06 = ( insert9069300056098147895at_nat @ B2 @ bot_bo228742789529271731at_nat ) )
% 2.86/3.06 = ( ( A2 = B2 )
% 2.86/3.06 & ( ord_le1268244103169919719at_nat @ A @ ( insert9069300056098147895at_nat @ B2 @ bot_bo228742789529271731at_nat ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % singleton_insert_inj_eq'
% 2.86/3.06 thf(fact_1407_singleton__insert__inj__eq_H,axiom,
% 2.86/3.06 ! [A2: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat,B2: product_prod_nat_nat] :
% 2.86/3.06 ( ( ( insert8211810215607154385at_nat @ A2 @ A )
% 2.86/3.06 = ( insert8211810215607154385at_nat @ B2 @ bot_bo2099793752762293965at_nat ) )
% 2.86/3.06 = ( ( A2 = B2 )
% 2.86/3.06 & ( ord_le3146513528884898305at_nat @ A @ ( insert8211810215607154385at_nat @ B2 @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % singleton_insert_inj_eq'
% 2.86/3.06 thf(fact_1408_singleton__insert__inj__eq_H,axiom,
% 2.86/3.06 ! [A2: $o,A: set_o,B2: $o] :
% 2.86/3.06 ( ( ( insert_o2 @ A2 @ A )
% 2.86/3.06 = ( insert_o2 @ B2 @ bot_bot_set_o ) )
% 2.86/3.06 = ( ( A2 = B2 )
% 2.86/3.06 & ( ord_less_eq_set_o @ A @ ( insert_o2 @ B2 @ bot_bot_set_o ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % singleton_insert_inj_eq'
% 2.86/3.06 thf(fact_1409_singleton__insert__inj__eq_H,axiom,
% 2.86/3.06 ! [A2: int,A: set_int,B2: int] :
% 2.86/3.06 ( ( ( insert_int2 @ A2 @ A )
% 2.86/3.06 = ( insert_int2 @ B2 @ bot_bot_set_int ) )
% 2.86/3.06 = ( ( A2 = B2 )
% 2.86/3.06 & ( ord_less_eq_set_int @ A @ ( insert_int2 @ B2 @ bot_bot_set_int ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % singleton_insert_inj_eq'
% 2.86/3.06 thf(fact_1410_singleton__insert__inj__eq_H,axiom,
% 2.86/3.06 ! [A2: nat,A: set_nat,B2: nat] :
% 2.86/3.06 ( ( ( insert_nat2 @ A2 @ A )
% 2.86/3.06 = ( insert_nat2 @ B2 @ bot_bot_set_nat ) )
% 2.86/3.06 = ( ( A2 = B2 )
% 2.86/3.06 & ( ord_less_eq_set_nat @ A @ ( insert_nat2 @ B2 @ bot_bot_set_nat ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % singleton_insert_inj_eq'
% 2.86/3.06 thf(fact_1411_Diff__eq__empty__iff,axiom,
% 2.86/3.06 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.06 ( ( ( minus_3314409938677909166at_nat @ A @ B )
% 2.86/3.06 = bot_bo228742789529271731at_nat )
% 2.86/3.06 = ( ord_le1268244103169919719at_nat @ A @ B ) ) ).
% 2.86/3.06
% 2.86/3.06 % Diff_eq_empty_iff
% 2.86/3.06 thf(fact_1412_Diff__eq__empty__iff,axiom,
% 2.86/3.06 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.06 ( ( ( minus_1356011639430497352at_nat @ A @ B )
% 2.86/3.06 = bot_bo2099793752762293965at_nat )
% 2.86/3.06 = ( ord_le3146513528884898305at_nat @ A @ B ) ) ).
% 2.86/3.06
% 2.86/3.06 % Diff_eq_empty_iff
% 2.86/3.06 thf(fact_1413_Diff__eq__empty__iff,axiom,
% 2.86/3.06 ! [A: set_o,B: set_o] :
% 2.86/3.06 ( ( ( minus_minus_set_o @ A @ B )
% 2.86/3.06 = bot_bot_set_o )
% 2.86/3.06 = ( ord_less_eq_set_o @ A @ B ) ) ).
% 2.86/3.06
% 2.86/3.06 % Diff_eq_empty_iff
% 2.86/3.06 thf(fact_1414_Diff__eq__empty__iff,axiom,
% 2.86/3.06 ! [A: set_int,B: set_int] :
% 2.86/3.06 ( ( ( minus_minus_set_int @ A @ B )
% 2.86/3.06 = bot_bot_set_int )
% 2.86/3.06 = ( ord_less_eq_set_int @ A @ B ) ) ).
% 2.86/3.06
% 2.86/3.06 % Diff_eq_empty_iff
% 2.86/3.06 thf(fact_1415_Diff__eq__empty__iff,axiom,
% 2.86/3.06 ! [A: set_nat,B: set_nat] :
% 2.86/3.06 ( ( ( minus_minus_set_nat @ A @ B )
% 2.86/3.06 = bot_bot_set_nat )
% 2.86/3.06 = ( ord_less_eq_set_nat @ A @ B ) ) ).
% 2.86/3.06
% 2.86/3.06 % Diff_eq_empty_iff
% 2.86/3.06 thf(fact_1416_and__extract__pure__right__ctx__iff,axiom,
% 2.86/3.06 ! [P: assn,Q: assn,B2: $o] :
% 2.86/3.06 ( ( inf_inf_assn @ P @ ( times_times_assn @ Q @ ( pure_assn @ B2 ) ) )
% 2.86/3.06 = ( times_times_assn @ ( inf_inf_assn @ P @ Q ) @ ( pure_assn @ B2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % and_extract_pure_right_ctx_iff
% 2.86/3.06 thf(fact_1417_and__extract__pure__left__ctx__iff,axiom,
% 2.86/3.06 ! [P: assn,B2: $o,Q: assn] :
% 2.86/3.06 ( ( inf_inf_assn @ ( times_times_assn @ P @ ( pure_assn @ B2 ) ) @ Q )
% 2.86/3.06 = ( times_times_assn @ ( inf_inf_assn @ P @ Q ) @ ( pure_assn @ B2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % and_extract_pure_left_ctx_iff
% 2.86/3.06 thf(fact_1418_mod__h__bot__iff_I6_J,axiom,
% 2.86/3.06 ! [P: assn,Q: assn,H2: heap_e7401611519738050253t_unit] :
% 2.86/3.06 ( ( rep_assn @ ( inf_inf_assn @ P @ Q ) @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) )
% 2.86/3.06 = ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) )
% 2.86/3.06 & ( rep_assn @ Q @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % mod_h_bot_iff(6)
% 2.86/3.06 thf(fact_1419_in__mono,axiom,
% 2.86/3.06 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,X: produc3843707927480180839at_nat] :
% 2.86/3.06 ( ( ord_le1268244103169919719at_nat @ A @ B )
% 2.86/3.06 => ( ( member8757157785044589968at_nat @ X @ A )
% 2.86/3.06 => ( member8757157785044589968at_nat @ X @ B ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % in_mono
% 2.86/3.06 thf(fact_1420_in__mono,axiom,
% 2.86/3.06 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] :
% 2.86/3.06 ( ( ord_le3146513528884898305at_nat @ A @ B )
% 2.86/3.06 => ( ( member8440522571783428010at_nat @ X @ A )
% 2.86/3.06 => ( member8440522571783428010at_nat @ X @ B ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % in_mono
% 2.86/3.06 thf(fact_1421_in__mono,axiom,
% 2.86/3.06 ! [A: set_int,B: set_int,X: int] :
% 2.86/3.06 ( ( ord_less_eq_set_int @ A @ B )
% 2.86/3.06 => ( ( member_int @ X @ A )
% 2.86/3.06 => ( member_int @ X @ B ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % in_mono
% 2.86/3.06 thf(fact_1422_in__mono,axiom,
% 2.86/3.06 ! [A: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o] :
% 2.86/3.06 ( ( ord_le2965882846123202637_nat_o @ A @ B )
% 2.86/3.06 => ( ( member6576561426505652726_nat_o @ X @ A )
% 2.86/3.06 => ( member6576561426505652726_nat_o @ X @ B ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % in_mono
% 2.86/3.06 thf(fact_1423_in__mono,axiom,
% 2.86/3.06 ! [A: set_nat,B: set_nat,X: nat] :
% 2.86/3.06 ( ( ord_less_eq_set_nat @ A @ B )
% 2.86/3.06 => ( ( member_nat @ X @ A )
% 2.86/3.06 => ( member_nat @ X @ B ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % in_mono
% 2.86/3.06 thf(fact_1424_subsetD,axiom,
% 2.86/3.06 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,C: produc3843707927480180839at_nat] :
% 2.86/3.06 ( ( ord_le1268244103169919719at_nat @ A @ B )
% 2.86/3.06 => ( ( member8757157785044589968at_nat @ C @ A )
% 2.86/3.06 => ( member8757157785044589968at_nat @ C @ B ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % subsetD
% 2.86/3.06 thf(fact_1425_subsetD,axiom,
% 2.86/3.06 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C: product_prod_nat_nat] :
% 2.86/3.06 ( ( ord_le3146513528884898305at_nat @ A @ B )
% 2.86/3.06 => ( ( member8440522571783428010at_nat @ C @ A )
% 2.86/3.06 => ( member8440522571783428010at_nat @ C @ B ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % subsetD
% 2.86/3.06 thf(fact_1426_subsetD,axiom,
% 2.86/3.06 ! [A: set_int,B: set_int,C: int] :
% 2.86/3.06 ( ( ord_less_eq_set_int @ A @ B )
% 2.86/3.06 => ( ( member_int @ C @ A )
% 2.86/3.06 => ( member_int @ C @ B ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % subsetD
% 2.86/3.06 thf(fact_1427_subsetD,axiom,
% 2.86/3.06 ! [A: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o,C: produc3658429121746597890et_nat > $o] :
% 2.86/3.06 ( ( ord_le2965882846123202637_nat_o @ A @ B )
% 2.86/3.06 => ( ( member6576561426505652726_nat_o @ C @ A )
% 2.86/3.06 => ( member6576561426505652726_nat_o @ C @ B ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % subsetD
% 2.86/3.06 thf(fact_1428_subsetD,axiom,
% 2.86/3.06 ! [A: set_nat,B: set_nat,C: nat] :
% 2.86/3.06 ( ( ord_less_eq_set_nat @ A @ B )
% 2.86/3.06 => ( ( member_nat @ C @ A )
% 2.86/3.06 => ( member_nat @ C @ B ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % subsetD
% 2.86/3.06 thf(fact_1429_equalityE,axiom,
% 2.86/3.06 ! [A: set_nat,B: set_nat] :
% 2.86/3.06 ( ( A = B )
% 2.86/3.06 => ~ ( ( ord_less_eq_set_nat @ A @ B )
% 2.86/3.06 => ~ ( ord_less_eq_set_nat @ B @ A ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % equalityE
% 2.86/3.06 thf(fact_1430_pairwiseD,axiom,
% 2.86/3.06 ! [R: produc3843707927480180839at_nat > produc3843707927480180839at_nat > $o,S: set_Pr4329608150637261639at_nat,X: produc3843707927480180839at_nat,Y: produc3843707927480180839at_nat] :
% 2.86/3.06 ( ( pairwi3222497012029234898at_nat @ R @ S )
% 2.86/3.06 => ( ( member8757157785044589968at_nat @ X @ S )
% 2.86/3.06 => ( ( member8757157785044589968at_nat @ Y @ S )
% 2.86/3.06 => ( ( X != Y )
% 2.86/3.06 => ( R @ X @ Y ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % pairwiseD
% 2.86/3.06 thf(fact_1431_pairwiseD,axiom,
% 2.86/3.06 ! [R: product_prod_nat_nat > product_prod_nat_nat > $o,S: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 2.86/3.06 ( ( pairwi6357175311820755948at_nat @ R @ S )
% 2.86/3.06 => ( ( member8440522571783428010at_nat @ X @ S )
% 2.86/3.06 => ( ( member8440522571783428010at_nat @ Y @ S )
% 2.86/3.06 => ( ( X != Y )
% 2.86/3.06 => ( R @ X @ Y ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % pairwiseD
% 2.86/3.06 thf(fact_1432_pairwiseD,axiom,
% 2.86/3.06 ! [R: nat > nat > $o,S: set_nat,X: nat,Y: nat] :
% 2.86/3.06 ( ( pairwise_nat @ R @ S )
% 2.86/3.06 => ( ( member_nat @ X @ S )
% 2.86/3.06 => ( ( member_nat @ Y @ S )
% 2.86/3.06 => ( ( X != Y )
% 2.86/3.06 => ( R @ X @ Y ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % pairwiseD
% 2.86/3.06 thf(fact_1433_pairwiseD,axiom,
% 2.86/3.06 ! [R: int > int > $o,S: set_int,X: int,Y: int] :
% 2.86/3.06 ( ( pairwise_int @ R @ S )
% 2.86/3.06 => ( ( member_int @ X @ S )
% 2.86/3.06 => ( ( member_int @ Y @ S )
% 2.86/3.06 => ( ( X != Y )
% 2.86/3.06 => ( R @ X @ Y ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % pairwiseD
% 2.86/3.06 thf(fact_1434_pairwiseD,axiom,
% 2.86/3.06 ! [R: ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > $o,S: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat > $o] :
% 2.86/3.06 ( ( pairwi2432143822833250616_nat_o @ R @ S )
% 2.86/3.06 => ( ( member6576561426505652726_nat_o @ X @ S )
% 2.86/3.06 => ( ( member6576561426505652726_nat_o @ Y @ S )
% 2.86/3.06 => ( ( X != Y )
% 2.86/3.06 => ( R @ X @ Y ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % pairwiseD
% 2.86/3.06 thf(fact_1435_pairwiseI,axiom,
% 2.86/3.06 ! [S: set_Pr4329608150637261639at_nat,R: produc3843707927480180839at_nat > produc3843707927480180839at_nat > $o] :
% 2.86/3.06 ( ! [X3: produc3843707927480180839at_nat,Y2: produc3843707927480180839at_nat] :
% 2.86/3.06 ( ( member8757157785044589968at_nat @ X3 @ S )
% 2.86/3.06 => ( ( member8757157785044589968at_nat @ Y2 @ S )
% 2.86/3.06 => ( ( X3 != Y2 )
% 2.86/3.06 => ( R @ X3 @ Y2 ) ) ) )
% 2.86/3.06 => ( pairwi3222497012029234898at_nat @ R @ S ) ) ).
% 2.86/3.06
% 2.86/3.06 % pairwiseI
% 2.86/3.06 thf(fact_1436_pairwiseI,axiom,
% 2.86/3.06 ! [S: set_Pr1261947904930325089at_nat,R: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 2.86/3.06 ( ! [X3: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 2.86/3.06 ( ( member8440522571783428010at_nat @ X3 @ S )
% 2.86/3.06 => ( ( member8440522571783428010at_nat @ Y2 @ S )
% 2.86/3.06 => ( ( X3 != Y2 )
% 2.86/3.06 => ( R @ X3 @ Y2 ) ) ) )
% 2.86/3.06 => ( pairwi6357175311820755948at_nat @ R @ S ) ) ).
% 2.86/3.06
% 2.86/3.06 % pairwiseI
% 2.86/3.06 thf(fact_1437_pairwiseI,axiom,
% 2.86/3.06 ! [S: set_nat,R: nat > nat > $o] :
% 2.86/3.06 ( ! [X3: nat,Y2: nat] :
% 2.86/3.06 ( ( member_nat @ X3 @ S )
% 2.86/3.06 => ( ( member_nat @ Y2 @ S )
% 2.86/3.06 => ( ( X3 != Y2 )
% 2.86/3.06 => ( R @ X3 @ Y2 ) ) ) )
% 2.86/3.06 => ( pairwise_nat @ R @ S ) ) ).
% 2.86/3.06
% 2.86/3.06 % pairwiseI
% 2.86/3.06 thf(fact_1438_pairwiseI,axiom,
% 2.86/3.06 ! [S: set_int,R: int > int > $o] :
% 2.86/3.06 ( ! [X3: int,Y2: int] :
% 2.86/3.06 ( ( member_int @ X3 @ S )
% 2.86/3.06 => ( ( member_int @ Y2 @ S )
% 2.86/3.06 => ( ( X3 != Y2 )
% 2.86/3.06 => ( R @ X3 @ Y2 ) ) ) )
% 2.86/3.06 => ( pairwise_int @ R @ S ) ) ).
% 2.86/3.06
% 2.86/3.06 % pairwiseI
% 2.86/3.06 thf(fact_1439_pairwiseI,axiom,
% 2.86/3.06 ! [S: set_Pr4532377907799695533_nat_o,R: ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > $o] :
% 2.86/3.06 ( ! [X3: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat > $o] :
% 2.86/3.06 ( ( member6576561426505652726_nat_o @ X3 @ S )
% 2.86/3.06 => ( ( member6576561426505652726_nat_o @ Y2 @ S )
% 2.86/3.06 => ( ( X3 != Y2 )
% 2.86/3.06 => ( R @ X3 @ Y2 ) ) ) )
% 2.86/3.06 => ( pairwi2432143822833250616_nat_o @ R @ S ) ) ).
% 2.86/3.06
% 2.86/3.06 % pairwiseI
% 2.86/3.06 thf(fact_1440_subset__eq,axiom,
% 2.86/3.06 ( ord_le1268244103169919719at_nat
% 2.86/3.06 = ( ^ [A5: set_Pr4329608150637261639at_nat,B7: set_Pr4329608150637261639at_nat] :
% 2.86/3.06 ! [X2: produc3843707927480180839at_nat] :
% 2.86/3.06 ( ( member8757157785044589968at_nat @ X2 @ A5 )
% 2.86/3.06 => ( member8757157785044589968at_nat @ X2 @ B7 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % subset_eq
% 2.86/3.06 thf(fact_1441_subset__eq,axiom,
% 2.86/3.06 ( ord_le3146513528884898305at_nat
% 2.86/3.06 = ( ^ [A5: set_Pr1261947904930325089at_nat,B7: set_Pr1261947904930325089at_nat] :
% 2.86/3.06 ! [X2: product_prod_nat_nat] :
% 2.86/3.06 ( ( member8440522571783428010at_nat @ X2 @ A5 )
% 2.86/3.06 => ( member8440522571783428010at_nat @ X2 @ B7 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % subset_eq
% 2.86/3.06 thf(fact_1442_subset__eq,axiom,
% 2.86/3.06 ( ord_less_eq_set_int
% 2.86/3.06 = ( ^ [A5: set_int,B7: set_int] :
% 2.86/3.06 ! [X2: int] :
% 2.86/3.06 ( ( member_int @ X2 @ A5 )
% 2.86/3.06 => ( member_int @ X2 @ B7 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % subset_eq
% 2.86/3.06 thf(fact_1443_subset__eq,axiom,
% 2.86/3.06 ( ord_le2965882846123202637_nat_o
% 2.86/3.06 = ( ^ [A5: set_Pr4532377907799695533_nat_o,B7: set_Pr4532377907799695533_nat_o] :
% 2.86/3.06 ! [X2: produc3658429121746597890et_nat > $o] :
% 2.86/3.06 ( ( member6576561426505652726_nat_o @ X2 @ A5 )
% 2.86/3.06 => ( member6576561426505652726_nat_o @ X2 @ B7 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % subset_eq
% 2.86/3.06 thf(fact_1444_subset__eq,axiom,
% 2.86/3.06 ( ord_less_eq_set_nat
% 2.86/3.06 = ( ^ [A5: set_nat,B7: set_nat] :
% 2.86/3.06 ! [X2: nat] :
% 2.86/3.06 ( ( member_nat @ X2 @ A5 )
% 2.86/3.06 => ( member_nat @ X2 @ B7 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % subset_eq
% 2.86/3.06 thf(fact_1445_equalityD1,axiom,
% 2.86/3.06 ! [A: set_nat,B: set_nat] :
% 2.86/3.06 ( ( A = B )
% 2.86/3.06 => ( ord_less_eq_set_nat @ A @ B ) ) ).
% 2.86/3.06
% 2.86/3.06 % equalityD1
% 2.86/3.06 thf(fact_1446_equalityD2,axiom,
% 2.86/3.06 ! [A: set_nat,B: set_nat] :
% 2.86/3.06 ( ( A = B )
% 2.86/3.06 => ( ord_less_eq_set_nat @ B @ A ) ) ).
% 2.86/3.06
% 2.86/3.06 % equalityD2
% 2.86/3.06 thf(fact_1447_subset__iff,axiom,
% 2.86/3.06 ( ord_le1268244103169919719at_nat
% 2.86/3.06 = ( ^ [A5: set_Pr4329608150637261639at_nat,B7: set_Pr4329608150637261639at_nat] :
% 2.86/3.06 ! [T2: produc3843707927480180839at_nat] :
% 2.86/3.06 ( ( member8757157785044589968at_nat @ T2 @ A5 )
% 2.86/3.06 => ( member8757157785044589968at_nat @ T2 @ B7 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % subset_iff
% 2.86/3.06 thf(fact_1448_subset__iff,axiom,
% 2.86/3.06 ( ord_le3146513528884898305at_nat
% 2.86/3.06 = ( ^ [A5: set_Pr1261947904930325089at_nat,B7: set_Pr1261947904930325089at_nat] :
% 2.86/3.06 ! [T2: product_prod_nat_nat] :
% 2.86/3.06 ( ( member8440522571783428010at_nat @ T2 @ A5 )
% 2.86/3.06 => ( member8440522571783428010at_nat @ T2 @ B7 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % subset_iff
% 2.86/3.06 thf(fact_1449_subset__iff,axiom,
% 2.86/3.06 ( ord_less_eq_set_int
% 2.86/3.06 = ( ^ [A5: set_int,B7: set_int] :
% 2.86/3.06 ! [T2: int] :
% 2.86/3.06 ( ( member_int @ T2 @ A5 )
% 2.86/3.06 => ( member_int @ T2 @ B7 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % subset_iff
% 2.86/3.06 thf(fact_1450_subset__iff,axiom,
% 2.86/3.06 ( ord_le2965882846123202637_nat_o
% 2.86/3.06 = ( ^ [A5: set_Pr4532377907799695533_nat_o,B7: set_Pr4532377907799695533_nat_o] :
% 2.86/3.06 ! [T2: produc3658429121746597890et_nat > $o] :
% 2.86/3.06 ( ( member6576561426505652726_nat_o @ T2 @ A5 )
% 2.86/3.06 => ( member6576561426505652726_nat_o @ T2 @ B7 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % subset_iff
% 2.86/3.06 thf(fact_1451_subset__iff,axiom,
% 2.86/3.06 ( ord_less_eq_set_nat
% 2.86/3.06 = ( ^ [A5: set_nat,B7: set_nat] :
% 2.86/3.06 ! [T2: nat] :
% 2.86/3.06 ( ( member_nat @ T2 @ A5 )
% 2.86/3.06 => ( member_nat @ T2 @ B7 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % subset_iff
% 2.86/3.06 thf(fact_1452_subset__refl,axiom,
% 2.86/3.06 ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).
% 2.86/3.06
% 2.86/3.06 % subset_refl
% 2.86/3.06 thf(fact_1453_Collect__mono,axiom,
% 2.86/3.06 ! [P: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
% 2.86/3.06 ( ! [X3: product_prod_nat_nat] :
% 2.86/3.06 ( ( P @ X3 )
% 2.86/3.06 => ( Q @ X3 ) )
% 2.86/3.06 => ( ord_le3146513528884898305at_nat @ ( collec3392354462482085612at_nat @ P ) @ ( collec3392354462482085612at_nat @ Q ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % Collect_mono
% 2.86/3.06 thf(fact_1454_Collect__mono,axiom,
% 2.86/3.06 ! [P: ( produc3658429121746597890et_nat > $o ) > $o,Q: ( produc3658429121746597890et_nat > $o ) > $o] :
% 2.86/3.06 ( ! [X3: produc3658429121746597890et_nat > $o] :
% 2.86/3.06 ( ( P @ X3 )
% 2.86/3.06 => ( Q @ X3 ) )
% 2.86/3.06 => ( ord_le2965882846123202637_nat_o @ ( collec939566748876313656_nat_o @ P ) @ ( collec939566748876313656_nat_o @ Q ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % Collect_mono
% 2.86/3.06 thf(fact_1455_Collect__mono,axiom,
% 2.86/3.06 ! [P: nat > $o,Q: nat > $o] :
% 2.86/3.06 ( ! [X3: nat] :
% 2.86/3.06 ( ( P @ X3 )
% 2.86/3.06 => ( Q @ X3 ) )
% 2.86/3.06 => ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % Collect_mono
% 2.86/3.06 thf(fact_1456_subset__trans,axiom,
% 2.86/3.06 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 2.86/3.06 ( ( ord_less_eq_set_nat @ A @ B )
% 2.86/3.06 => ( ( ord_less_eq_set_nat @ B @ C2 )
% 2.86/3.06 => ( ord_less_eq_set_nat @ A @ C2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % subset_trans
% 2.86/3.06 thf(fact_1457_pairwise__mono,axiom,
% 2.86/3.06 ! [P: nat > nat > $o,A: set_nat,Q: nat > nat > $o,B: set_nat] :
% 2.86/3.06 ( ( pairwise_nat @ P @ A )
% 2.86/3.06 => ( ! [X3: nat,Y2: nat] :
% 2.86/3.06 ( ( P @ X3 @ Y2 )
% 2.86/3.06 => ( Q @ X3 @ Y2 ) )
% 2.86/3.06 => ( ( ord_less_eq_set_nat @ B @ A )
% 2.86/3.06 => ( pairwise_nat @ Q @ B ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % pairwise_mono
% 2.86/3.06 thf(fact_1458_set__eq__subset,axiom,
% 2.86/3.06 ( ( ^ [Y4: set_nat,Z2: set_nat] : ( Y4 = Z2 ) )
% 2.86/3.06 = ( ^ [A5: set_nat,B7: set_nat] :
% 2.86/3.06 ( ( ord_less_eq_set_nat @ A5 @ B7 )
% 2.86/3.06 & ( ord_less_eq_set_nat @ B7 @ A5 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % set_eq_subset
% 2.86/3.06 thf(fact_1459_pairwise__subset,axiom,
% 2.86/3.06 ! [P: nat > nat > $o,S: set_nat,T3: set_nat] :
% 2.86/3.06 ( ( pairwise_nat @ P @ S )
% 2.86/3.06 => ( ( ord_less_eq_set_nat @ T3 @ S )
% 2.86/3.06 => ( pairwise_nat @ P @ T3 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % pairwise_subset
% 2.86/3.06 thf(fact_1460_Collect__mono__iff,axiom,
% 2.86/3.06 ! [P: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
% 2.86/3.06 ( ( ord_le3146513528884898305at_nat @ ( collec3392354462482085612at_nat @ P ) @ ( collec3392354462482085612at_nat @ Q ) )
% 2.86/3.06 = ( ! [X2: product_prod_nat_nat] :
% 2.86/3.06 ( ( P @ X2 )
% 2.86/3.06 => ( Q @ X2 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % Collect_mono_iff
% 2.86/3.06 thf(fact_1461_Collect__mono__iff,axiom,
% 2.86/3.06 ! [P: ( produc3658429121746597890et_nat > $o ) > $o,Q: ( produc3658429121746597890et_nat > $o ) > $o] :
% 2.86/3.06 ( ( ord_le2965882846123202637_nat_o @ ( collec939566748876313656_nat_o @ P ) @ ( collec939566748876313656_nat_o @ Q ) )
% 2.86/3.06 = ( ! [X2: produc3658429121746597890et_nat > $o] :
% 2.86/3.06 ( ( P @ X2 )
% 2.86/3.06 => ( Q @ X2 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % Collect_mono_iff
% 2.86/3.06 thf(fact_1462_Collect__mono__iff,axiom,
% 2.86/3.06 ! [P: nat > $o,Q: nat > $o] :
% 2.86/3.06 ( ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) )
% 2.86/3.06 = ( ! [X2: nat] :
% 2.86/3.06 ( ( P @ X2 )
% 2.86/3.06 => ( Q @ X2 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % Collect_mono_iff
% 2.86/3.06 thf(fact_1463_ord__eq__le__eq__trans,axiom,
% 2.86/3.06 ! [A2: assn,B2: assn,C: assn,D2: assn] :
% 2.86/3.06 ( ( A2 = B2 )
% 2.86/3.06 => ( ( ord_less_eq_assn @ B2 @ C )
% 2.86/3.06 => ( ( C = D2 )
% 2.86/3.06 => ( ord_less_eq_assn @ A2 @ D2 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % ord_eq_le_eq_trans
% 2.86/3.06 thf(fact_1464_ord__eq__le__eq__trans,axiom,
% 2.86/3.06 ! [A2: filter_nat,B2: filter_nat,C: filter_nat,D2: filter_nat] :
% 2.86/3.06 ( ( A2 = B2 )
% 2.86/3.06 => ( ( ord_le2510731241096832064er_nat @ B2 @ C )
% 2.86/3.06 => ( ( C = D2 )
% 2.86/3.06 => ( ord_le2510731241096832064er_nat @ A2 @ D2 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % ord_eq_le_eq_trans
% 2.86/3.06 thf(fact_1465_ord__eq__le__eq__trans,axiom,
% 2.86/3.06 ! [A2: set_nat,B2: set_nat,C: set_nat,D2: set_nat] :
% 2.86/3.06 ( ( A2 = B2 )
% 2.86/3.06 => ( ( ord_less_eq_set_nat @ B2 @ C )
% 2.86/3.06 => ( ( C = D2 )
% 2.86/3.06 => ( ord_less_eq_set_nat @ A2 @ D2 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % ord_eq_le_eq_trans
% 2.86/3.06 thf(fact_1466_ord__eq__le__eq__trans,axiom,
% 2.86/3.06 ! [A2: nat,B2: nat,C: nat,D2: nat] :
% 2.86/3.06 ( ( A2 = B2 )
% 2.86/3.06 => ( ( ord_less_eq_nat @ B2 @ C )
% 2.86/3.06 => ( ( C = D2 )
% 2.86/3.06 => ( ord_less_eq_nat @ A2 @ D2 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % ord_eq_le_eq_trans
% 2.86/3.06 thf(fact_1467_ord__eq__le__eq__trans,axiom,
% 2.86/3.06 ! [A2: int,B2: int,C: int,D2: int] :
% 2.86/3.06 ( ( A2 = B2 )
% 2.86/3.06 => ( ( ord_less_eq_int @ B2 @ C )
% 2.86/3.06 => ( ( C = D2 )
% 2.86/3.06 => ( ord_less_eq_int @ A2 @ D2 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % ord_eq_le_eq_trans
% 2.86/3.06 thf(fact_1468_subset__Collect__conv,axiom,
% 2.86/3.06 ! [S: set_Pr1261947904930325089at_nat,P: product_prod_nat_nat > $o] :
% 2.86/3.06 ( ( ord_le3146513528884898305at_nat @ S @ ( collec3392354462482085612at_nat @ P ) )
% 2.86/3.06 = ( ! [X2: product_prod_nat_nat] :
% 2.86/3.06 ( ( member8440522571783428010at_nat @ X2 @ S )
% 2.86/3.06 => ( P @ X2 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % subset_Collect_conv
% 2.86/3.06 thf(fact_1469_subset__Collect__conv,axiom,
% 2.86/3.06 ! [S: set_Pr4532377907799695533_nat_o,P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 2.86/3.06 ( ( ord_le2965882846123202637_nat_o @ S @ ( collec939566748876313656_nat_o @ P ) )
% 2.86/3.06 = ( ! [X2: produc3658429121746597890et_nat > $o] :
% 2.86/3.06 ( ( member6576561426505652726_nat_o @ X2 @ S )
% 2.86/3.06 => ( P @ X2 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % subset_Collect_conv
% 2.86/3.06 thf(fact_1470_subset__Collect__conv,axiom,
% 2.86/3.06 ! [S: set_nat,P: nat > $o] :
% 2.86/3.06 ( ( ord_less_eq_set_nat @ S @ ( collect_nat @ P ) )
% 2.86/3.06 = ( ! [X2: nat] :
% 2.86/3.06 ( ( member_nat @ X2 @ S )
% 2.86/3.06 => ( P @ X2 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % subset_Collect_conv
% 2.86/3.06 thf(fact_1471_assn__aci_I4_J,axiom,
% 2.86/3.06 ! [X: assn,Y: assn] :
% 2.86/3.06 ( ( inf_inf_assn @ X @ ( inf_inf_assn @ X @ Y ) )
% 2.86/3.06 = ( inf_inf_assn @ X @ Y ) ) ).
% 2.86/3.06
% 2.86/3.06 % assn_aci(4)
% 2.86/3.06 thf(fact_1472_assn__aci_I3_J,axiom,
% 2.86/3.06 ! [X: assn,Y: assn,Z: assn] :
% 2.86/3.06 ( ( inf_inf_assn @ X @ ( inf_inf_assn @ Y @ Z ) )
% 2.86/3.06 = ( inf_inf_assn @ Y @ ( inf_inf_assn @ X @ Z ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % assn_aci(3)
% 2.86/3.06 thf(fact_1473_assn__aci_I1_J,axiom,
% 2.86/3.06 ( inf_inf_assn
% 2.86/3.06 = ( ^ [X2: assn,Y5: assn] : ( inf_inf_assn @ Y5 @ X2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % assn_aci(1)
% 2.86/3.06 thf(fact_1474_norm__assertion__simps_I31_J,axiom,
% 2.86/3.06 ! [X: assn] :
% 2.86/3.06 ( ( inf_inf_assn @ X @ X )
% 2.86/3.06 = X ) ).
% 2.86/3.06
% 2.86/3.06 % norm_assertion_simps(31)
% 2.86/3.06 thf(fact_1475_norm__assertion__simps_I14_J,axiom,
% 2.86/3.06 ! [X: assn,Y: assn,Z: assn] :
% 2.86/3.06 ( ( inf_inf_assn @ ( inf_inf_assn @ X @ Y ) @ Z )
% 2.86/3.06 = ( inf_inf_assn @ X @ ( inf_inf_assn @ Y @ Z ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % norm_assertion_simps(14)
% 2.86/3.06 thf(fact_1476_nle__le,axiom,
% 2.86/3.06 ! [A2: nat,B2: nat] :
% 2.86/3.06 ( ( ~ ( ord_less_eq_nat @ A2 @ B2 ) )
% 2.86/3.06 = ( ( ord_less_eq_nat @ B2 @ A2 )
% 2.86/3.06 & ( B2 != A2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % nle_le
% 2.86/3.06 thf(fact_1477_nle__le,axiom,
% 2.86/3.06 ! [A2: int,B2: int] :
% 2.86/3.06 ( ( ~ ( ord_less_eq_int @ A2 @ B2 ) )
% 2.86/3.06 = ( ( ord_less_eq_int @ B2 @ A2 )
% 2.86/3.06 & ( B2 != A2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % nle_le
% 2.86/3.06 thf(fact_1478_le__cases3,axiom,
% 2.86/3.06 ! [X: nat,Y: nat,Z: nat] :
% 2.86/3.06 ( ( ( ord_less_eq_nat @ X @ Y )
% 2.86/3.06 => ~ ( ord_less_eq_nat @ Y @ Z ) )
% 2.86/3.06 => ( ( ( ord_less_eq_nat @ Y @ X )
% 2.86/3.06 => ~ ( ord_less_eq_nat @ X @ Z ) )
% 2.86/3.06 => ( ( ( ord_less_eq_nat @ X @ Z )
% 2.86/3.06 => ~ ( ord_less_eq_nat @ Z @ Y ) )
% 2.86/3.06 => ( ( ( ord_less_eq_nat @ Z @ Y )
% 2.86/3.06 => ~ ( ord_less_eq_nat @ Y @ X ) )
% 2.86/3.06 => ( ( ( ord_less_eq_nat @ Y @ Z )
% 2.86/3.06 => ~ ( ord_less_eq_nat @ Z @ X ) )
% 2.86/3.06 => ~ ( ( ord_less_eq_nat @ Z @ X )
% 2.86/3.06 => ~ ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % le_cases3
% 2.86/3.06 thf(fact_1479_le__cases3,axiom,
% 2.86/3.06 ! [X: int,Y: int,Z: int] :
% 2.86/3.06 ( ( ( ord_less_eq_int @ X @ Y )
% 2.86/3.06 => ~ ( ord_less_eq_int @ Y @ Z ) )
% 2.86/3.06 => ( ( ( ord_less_eq_int @ Y @ X )
% 2.86/3.06 => ~ ( ord_less_eq_int @ X @ Z ) )
% 2.86/3.06 => ( ( ( ord_less_eq_int @ X @ Z )
% 2.86/3.06 => ~ ( ord_less_eq_int @ Z @ Y ) )
% 2.86/3.06 => ( ( ( ord_less_eq_int @ Z @ Y )
% 2.86/3.06 => ~ ( ord_less_eq_int @ Y @ X ) )
% 2.86/3.06 => ( ( ( ord_less_eq_int @ Y @ Z )
% 2.86/3.06 => ~ ( ord_less_eq_int @ Z @ X ) )
% 2.86/3.06 => ~ ( ( ord_less_eq_int @ Z @ X )
% 2.86/3.06 => ~ ( ord_less_eq_int @ X @ Y ) ) ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % le_cases3
% 2.86/3.06 thf(fact_1480_order__class_Oorder__eq__iff,axiom,
% 2.86/3.06 ( ( ^ [Y4: assn,Z2: assn] : ( Y4 = Z2 ) )
% 2.86/3.06 = ( ^ [X2: assn,Y5: assn] :
% 2.86/3.06 ( ( ord_less_eq_assn @ X2 @ Y5 )
% 2.86/3.06 & ( ord_less_eq_assn @ Y5 @ X2 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % order_class.order_eq_iff
% 2.86/3.06 thf(fact_1481_order__class_Oorder__eq__iff,axiom,
% 2.86/3.06 ( ( ^ [Y4: filter_nat,Z2: filter_nat] : ( Y4 = Z2 ) )
% 2.86/3.06 = ( ^ [X2: filter_nat,Y5: filter_nat] :
% 2.86/3.06 ( ( ord_le2510731241096832064er_nat @ X2 @ Y5 )
% 2.86/3.06 & ( ord_le2510731241096832064er_nat @ Y5 @ X2 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % order_class.order_eq_iff
% 2.86/3.06 thf(fact_1482_order__class_Oorder__eq__iff,axiom,
% 2.86/3.06 ( ( ^ [Y4: set_nat,Z2: set_nat] : ( Y4 = Z2 ) )
% 2.86/3.06 = ( ^ [X2: set_nat,Y5: set_nat] :
% 2.86/3.06 ( ( ord_less_eq_set_nat @ X2 @ Y5 )
% 2.86/3.06 & ( ord_less_eq_set_nat @ Y5 @ X2 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % order_class.order_eq_iff
% 2.86/3.06 thf(fact_1483_order__class_Oorder__eq__iff,axiom,
% 2.86/3.06 ( ( ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 2.86/3.06 = ( ^ [X2: nat,Y5: nat] :
% 2.86/3.06 ( ( ord_less_eq_nat @ X2 @ Y5 )
% 2.86/3.06 & ( ord_less_eq_nat @ Y5 @ X2 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % order_class.order_eq_iff
% 2.86/3.06 thf(fact_1484_order__class_Oorder__eq__iff,axiom,
% 2.86/3.06 ( ( ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 2.86/3.06 = ( ^ [X2: int,Y5: int] :
% 2.86/3.06 ( ( ord_less_eq_int @ X2 @ Y5 )
% 2.86/3.06 & ( ord_less_eq_int @ Y5 @ X2 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % order_class.order_eq_iff
% 2.86/3.06 thf(fact_1485_ord__eq__le__trans,axiom,
% 2.86/3.06 ! [A2: assn,B2: assn,C: assn] :
% 2.86/3.06 ( ( A2 = B2 )
% 2.86/3.06 => ( ( ord_less_eq_assn @ B2 @ C )
% 2.86/3.06 => ( ord_less_eq_assn @ A2 @ C ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % ord_eq_le_trans
% 2.86/3.06 thf(fact_1486_ord__eq__le__trans,axiom,
% 2.86/3.06 ! [A2: filter_nat,B2: filter_nat,C: filter_nat] :
% 2.86/3.06 ( ( A2 = B2 )
% 2.86/3.06 => ( ( ord_le2510731241096832064er_nat @ B2 @ C )
% 2.86/3.06 => ( ord_le2510731241096832064er_nat @ A2 @ C ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % ord_eq_le_trans
% 2.86/3.06 thf(fact_1487_ord__eq__le__trans,axiom,
% 2.86/3.06 ! [A2: set_nat,B2: set_nat,C: set_nat] :
% 2.86/3.06 ( ( A2 = B2 )
% 2.86/3.06 => ( ( ord_less_eq_set_nat @ B2 @ C )
% 2.86/3.06 => ( ord_less_eq_set_nat @ A2 @ C ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % ord_eq_le_trans
% 2.86/3.06 thf(fact_1488_ord__eq__le__trans,axiom,
% 2.86/3.06 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.06 ( ( A2 = B2 )
% 2.86/3.06 => ( ( ord_less_eq_nat @ B2 @ C )
% 2.86/3.06 => ( ord_less_eq_nat @ A2 @ C ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % ord_eq_le_trans
% 2.86/3.06 thf(fact_1489_ord__eq__le__trans,axiom,
% 2.86/3.06 ! [A2: int,B2: int,C: int] :
% 2.86/3.06 ( ( A2 = B2 )
% 2.86/3.06 => ( ( ord_less_eq_int @ B2 @ C )
% 2.86/3.06 => ( ord_less_eq_int @ A2 @ C ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % ord_eq_le_trans
% 2.86/3.06 thf(fact_1490_ord__le__eq__trans,axiom,
% 2.86/3.06 ! [A2: assn,B2: assn,C: assn] :
% 2.86/3.06 ( ( ord_less_eq_assn @ A2 @ B2 )
% 2.86/3.06 => ( ( B2 = C )
% 2.86/3.06 => ( ord_less_eq_assn @ A2 @ C ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % ord_le_eq_trans
% 2.86/3.06 thf(fact_1491_ord__le__eq__trans,axiom,
% 2.86/3.06 ! [A2: filter_nat,B2: filter_nat,C: filter_nat] :
% 2.86/3.06 ( ( ord_le2510731241096832064er_nat @ A2 @ B2 )
% 2.86/3.06 => ( ( B2 = C )
% 2.86/3.06 => ( ord_le2510731241096832064er_nat @ A2 @ C ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % ord_le_eq_trans
% 2.86/3.06 thf(fact_1492_ord__le__eq__trans,axiom,
% 2.86/3.06 ! [A2: set_nat,B2: set_nat,C: set_nat] :
% 2.86/3.06 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 2.86/3.06 => ( ( B2 = C )
% 2.86/3.06 => ( ord_less_eq_set_nat @ A2 @ C ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % ord_le_eq_trans
% 2.86/3.06 thf(fact_1493_ord__le__eq__trans,axiom,
% 2.86/3.06 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.06 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.06 => ( ( B2 = C )
% 2.86/3.06 => ( ord_less_eq_nat @ A2 @ C ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % ord_le_eq_trans
% 2.86/3.06 thf(fact_1494_ord__le__eq__trans,axiom,
% 2.86/3.06 ! [A2: int,B2: int,C: int] :
% 2.86/3.06 ( ( ord_less_eq_int @ A2 @ B2 )
% 2.86/3.06 => ( ( B2 = C )
% 2.86/3.06 => ( ord_less_eq_int @ A2 @ C ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % ord_le_eq_trans
% 2.86/3.06 thf(fact_1495_order__antisym,axiom,
% 2.86/3.06 ! [X: assn,Y: assn] :
% 2.86/3.06 ( ( ord_less_eq_assn @ X @ Y )
% 2.86/3.06 => ( ( ord_less_eq_assn @ Y @ X )
% 2.86/3.06 => ( X = Y ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % order_antisym
% 2.86/3.06 thf(fact_1496_order__antisym,axiom,
% 2.86/3.06 ! [X: filter_nat,Y: filter_nat] :
% 2.86/3.06 ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 2.86/3.06 => ( ( ord_le2510731241096832064er_nat @ Y @ X )
% 2.86/3.06 => ( X = Y ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % order_antisym
% 2.86/3.06 thf(fact_1497_order__antisym,axiom,
% 2.86/3.06 ! [X: set_nat,Y: set_nat] :
% 2.86/3.06 ( ( ord_less_eq_set_nat @ X @ Y )
% 2.86/3.06 => ( ( ord_less_eq_set_nat @ Y @ X )
% 2.86/3.06 => ( X = Y ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % order_antisym
% 2.86/3.06 thf(fact_1498_order__antisym,axiom,
% 2.86/3.06 ! [X: nat,Y: nat] :
% 2.86/3.06 ( ( ord_less_eq_nat @ X @ Y )
% 2.86/3.06 => ( ( ord_less_eq_nat @ Y @ X )
% 2.86/3.06 => ( X = Y ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % order_antisym
% 2.86/3.06 thf(fact_1499_order__antisym,axiom,
% 2.86/3.06 ! [X: int,Y: int] :
% 2.86/3.06 ( ( ord_less_eq_int @ X @ Y )
% 2.86/3.06 => ( ( ord_less_eq_int @ Y @ X )
% 2.86/3.06 => ( X = Y ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % order_antisym
% 2.86/3.06 thf(fact_1500_order_Otrans,axiom,
% 2.86/3.06 ! [A2: assn,B2: assn,C: assn] :
% 2.86/3.06 ( ( ord_less_eq_assn @ A2 @ B2 )
% 2.86/3.06 => ( ( ord_less_eq_assn @ B2 @ C )
% 2.86/3.06 => ( ord_less_eq_assn @ A2 @ C ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % order.trans
% 2.86/3.06 thf(fact_1501_order_Otrans,axiom,
% 2.86/3.06 ! [A2: filter_nat,B2: filter_nat,C: filter_nat] :
% 2.86/3.06 ( ( ord_le2510731241096832064er_nat @ A2 @ B2 )
% 2.86/3.06 => ( ( ord_le2510731241096832064er_nat @ B2 @ C )
% 2.86/3.06 => ( ord_le2510731241096832064er_nat @ A2 @ C ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % order.trans
% 2.86/3.06 thf(fact_1502_order_Otrans,axiom,
% 2.86/3.06 ! [A2: set_nat,B2: set_nat,C: set_nat] :
% 2.86/3.06 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 2.86/3.06 => ( ( ord_less_eq_set_nat @ B2 @ C )
% 2.86/3.06 => ( ord_less_eq_set_nat @ A2 @ C ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % order.trans
% 2.86/3.06 thf(fact_1503_order_Otrans,axiom,
% 2.86/3.06 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.06 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.06 => ( ( ord_less_eq_nat @ B2 @ C )
% 2.86/3.06 => ( ord_less_eq_nat @ A2 @ C ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % order.trans
% 2.86/3.06 thf(fact_1504_order_Otrans,axiom,
% 2.86/3.06 ! [A2: int,B2: int,C: int] :
% 2.86/3.06 ( ( ord_less_eq_int @ A2 @ B2 )
% 2.86/3.06 => ( ( ord_less_eq_int @ B2 @ C )
% 2.86/3.06 => ( ord_less_eq_int @ A2 @ C ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % order.trans
% 2.86/3.06 thf(fact_1505_order__trans,axiom,
% 2.86/3.06 ! [X: assn,Y: assn,Z: assn] :
% 2.86/3.06 ( ( ord_less_eq_assn @ X @ Y )
% 2.86/3.06 => ( ( ord_less_eq_assn @ Y @ Z )
% 2.86/3.06 => ( ord_less_eq_assn @ X @ Z ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % order_trans
% 2.86/3.06 thf(fact_1506_order__trans,axiom,
% 2.86/3.06 ! [X: filter_nat,Y: filter_nat,Z: filter_nat] :
% 2.86/3.06 ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 2.86/3.06 => ( ( ord_le2510731241096832064er_nat @ Y @ Z )
% 2.86/3.06 => ( ord_le2510731241096832064er_nat @ X @ Z ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % order_trans
% 2.86/3.06 thf(fact_1507_order__trans,axiom,
% 2.86/3.06 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 2.86/3.06 ( ( ord_less_eq_set_nat @ X @ Y )
% 2.86/3.06 => ( ( ord_less_eq_set_nat @ Y @ Z )
% 2.86/3.06 => ( ord_less_eq_set_nat @ X @ Z ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % order_trans
% 2.86/3.06 thf(fact_1508_order__trans,axiom,
% 2.86/3.06 ! [X: nat,Y: nat,Z: nat] :
% 2.86/3.06 ( ( ord_less_eq_nat @ X @ Y )
% 2.86/3.06 => ( ( ord_less_eq_nat @ Y @ Z )
% 2.86/3.06 => ( ord_less_eq_nat @ X @ Z ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % order_trans
% 2.86/3.06 thf(fact_1509_order__trans,axiom,
% 2.86/3.06 ! [X: int,Y: int,Z: int] :
% 2.86/3.06 ( ( ord_less_eq_int @ X @ Y )
% 2.86/3.06 => ( ( ord_less_eq_int @ Y @ Z )
% 2.86/3.06 => ( ord_less_eq_int @ X @ Z ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % order_trans
% 2.86/3.06 thf(fact_1510_linorder__wlog,axiom,
% 2.86/3.06 ! [P: nat > nat > $o,A2: nat,B2: nat] :
% 2.86/3.06 ( ! [A4: nat,B4: nat] :
% 2.86/3.06 ( ( ord_less_eq_nat @ A4 @ B4 )
% 2.86/3.06 => ( P @ A4 @ B4 ) )
% 2.86/3.06 => ( ! [A4: nat,B4: nat] :
% 2.86/3.06 ( ( P @ B4 @ A4 )
% 2.86/3.06 => ( P @ A4 @ B4 ) )
% 2.86/3.06 => ( P @ A2 @ B2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % linorder_wlog
% 2.86/3.06 thf(fact_1511_linorder__wlog,axiom,
% 2.86/3.06 ! [P: int > int > $o,A2: int,B2: int] :
% 2.86/3.06 ( ! [A4: int,B4: int] :
% 2.86/3.06 ( ( ord_less_eq_int @ A4 @ B4 )
% 2.86/3.06 => ( P @ A4 @ B4 ) )
% 2.86/3.06 => ( ! [A4: int,B4: int] :
% 2.86/3.06 ( ( P @ B4 @ A4 )
% 2.86/3.06 => ( P @ A4 @ B4 ) )
% 2.86/3.06 => ( P @ A2 @ B2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % linorder_wlog
% 2.86/3.06 thf(fact_1512_dual__order_Oeq__iff,axiom,
% 2.86/3.06 ( ( ^ [Y4: assn,Z2: assn] : ( Y4 = Z2 ) )
% 2.86/3.06 = ( ^ [A3: assn,B3: assn] :
% 2.86/3.06 ( ( ord_less_eq_assn @ B3 @ A3 )
% 2.86/3.06 & ( ord_less_eq_assn @ A3 @ B3 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % dual_order.eq_iff
% 2.86/3.06 thf(fact_1513_dual__order_Oeq__iff,axiom,
% 2.86/3.06 ( ( ^ [Y4: filter_nat,Z2: filter_nat] : ( Y4 = Z2 ) )
% 2.86/3.06 = ( ^ [A3: filter_nat,B3: filter_nat] :
% 2.86/3.06 ( ( ord_le2510731241096832064er_nat @ B3 @ A3 )
% 2.86/3.06 & ( ord_le2510731241096832064er_nat @ A3 @ B3 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % dual_order.eq_iff
% 2.86/3.06 thf(fact_1514_dual__order_Oeq__iff,axiom,
% 2.86/3.06 ( ( ^ [Y4: set_nat,Z2: set_nat] : ( Y4 = Z2 ) )
% 2.86/3.06 = ( ^ [A3: set_nat,B3: set_nat] :
% 2.86/3.06 ( ( ord_less_eq_set_nat @ B3 @ A3 )
% 2.86/3.06 & ( ord_less_eq_set_nat @ A3 @ B3 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % dual_order.eq_iff
% 2.86/3.06 thf(fact_1515_dual__order_Oeq__iff,axiom,
% 2.86/3.06 ( ( ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 2.86/3.06 = ( ^ [A3: nat,B3: nat] :
% 2.86/3.06 ( ( ord_less_eq_nat @ B3 @ A3 )
% 2.86/3.06 & ( ord_less_eq_nat @ A3 @ B3 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % dual_order.eq_iff
% 2.86/3.06 thf(fact_1516_dual__order_Oeq__iff,axiom,
% 2.86/3.06 ( ( ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 2.86/3.06 = ( ^ [A3: int,B3: int] :
% 2.86/3.06 ( ( ord_less_eq_int @ B3 @ A3 )
% 2.86/3.06 & ( ord_less_eq_int @ A3 @ B3 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % dual_order.eq_iff
% 2.86/3.06 thf(fact_1517_dual__order_Oantisym,axiom,
% 2.86/3.06 ! [B2: assn,A2: assn] :
% 2.86/3.06 ( ( ord_less_eq_assn @ B2 @ A2 )
% 2.86/3.06 => ( ( ord_less_eq_assn @ A2 @ B2 )
% 2.86/3.06 => ( A2 = B2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % dual_order.antisym
% 2.86/3.06 thf(fact_1518_dual__order_Oantisym,axiom,
% 2.86/3.06 ! [B2: filter_nat,A2: filter_nat] :
% 2.86/3.06 ( ( ord_le2510731241096832064er_nat @ B2 @ A2 )
% 2.86/3.06 => ( ( ord_le2510731241096832064er_nat @ A2 @ B2 )
% 2.86/3.06 => ( A2 = B2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % dual_order.antisym
% 2.86/3.06 thf(fact_1519_dual__order_Oantisym,axiom,
% 2.86/3.06 ! [B2: set_nat,A2: set_nat] :
% 2.86/3.06 ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 2.86/3.06 => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 2.86/3.06 => ( A2 = B2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % dual_order.antisym
% 2.86/3.06 thf(fact_1520_dual__order_Oantisym,axiom,
% 2.86/3.06 ! [B2: nat,A2: nat] :
% 2.86/3.06 ( ( ord_less_eq_nat @ B2 @ A2 )
% 2.86/3.06 => ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.06 => ( A2 = B2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % dual_order.antisym
% 2.86/3.06 thf(fact_1521_dual__order_Oantisym,axiom,
% 2.86/3.06 ! [B2: int,A2: int] :
% 2.86/3.06 ( ( ord_less_eq_int @ B2 @ A2 )
% 2.86/3.06 => ( ( ord_less_eq_int @ A2 @ B2 )
% 2.86/3.06 => ( A2 = B2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % dual_order.antisym
% 2.86/3.06 thf(fact_1522_dual__order_Otrans,axiom,
% 2.86/3.06 ! [B2: assn,A2: assn,C: assn] :
% 2.86/3.06 ( ( ord_less_eq_assn @ B2 @ A2 )
% 2.86/3.06 => ( ( ord_less_eq_assn @ C @ B2 )
% 2.86/3.06 => ( ord_less_eq_assn @ C @ A2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % dual_order.trans
% 2.86/3.06 thf(fact_1523_dual__order_Otrans,axiom,
% 2.86/3.06 ! [B2: filter_nat,A2: filter_nat,C: filter_nat] :
% 2.86/3.06 ( ( ord_le2510731241096832064er_nat @ B2 @ A2 )
% 2.86/3.06 => ( ( ord_le2510731241096832064er_nat @ C @ B2 )
% 2.86/3.06 => ( ord_le2510731241096832064er_nat @ C @ A2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % dual_order.trans
% 2.86/3.06 thf(fact_1524_dual__order_Otrans,axiom,
% 2.86/3.06 ! [B2: set_nat,A2: set_nat,C: set_nat] :
% 2.86/3.06 ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 2.86/3.06 => ( ( ord_less_eq_set_nat @ C @ B2 )
% 2.86/3.06 => ( ord_less_eq_set_nat @ C @ A2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % dual_order.trans
% 2.86/3.06 thf(fact_1525_dual__order_Otrans,axiom,
% 2.86/3.06 ! [B2: nat,A2: nat,C: nat] :
% 2.86/3.06 ( ( ord_less_eq_nat @ B2 @ A2 )
% 2.86/3.06 => ( ( ord_less_eq_nat @ C @ B2 )
% 2.86/3.06 => ( ord_less_eq_nat @ C @ A2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % dual_order.trans
% 2.86/3.06 thf(fact_1526_dual__order_Otrans,axiom,
% 2.86/3.06 ! [B2: int,A2: int,C: int] :
% 2.86/3.06 ( ( ord_less_eq_int @ B2 @ A2 )
% 2.86/3.06 => ( ( ord_less_eq_int @ C @ B2 )
% 2.86/3.06 => ( ord_less_eq_int @ C @ A2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % dual_order.trans
% 2.86/3.06 thf(fact_1527_antisym,axiom,
% 2.86/3.06 ! [A2: assn,B2: assn] :
% 2.86/3.06 ( ( ord_less_eq_assn @ A2 @ B2 )
% 2.86/3.06 => ( ( ord_less_eq_assn @ B2 @ A2 )
% 2.86/3.06 => ( A2 = B2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % antisym
% 2.86/3.06 thf(fact_1528_antisym,axiom,
% 2.86/3.06 ! [A2: filter_nat,B2: filter_nat] :
% 2.86/3.06 ( ( ord_le2510731241096832064er_nat @ A2 @ B2 )
% 2.86/3.06 => ( ( ord_le2510731241096832064er_nat @ B2 @ A2 )
% 2.86/3.06 => ( A2 = B2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % antisym
% 2.86/3.06 thf(fact_1529_antisym,axiom,
% 2.86/3.06 ! [A2: set_nat,B2: set_nat] :
% 2.86/3.06 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 2.86/3.06 => ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 2.86/3.06 => ( A2 = B2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % antisym
% 2.86/3.06 thf(fact_1530_antisym,axiom,
% 2.86/3.06 ! [A2: nat,B2: nat] :
% 2.86/3.06 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.06 => ( ( ord_less_eq_nat @ B2 @ A2 )
% 2.86/3.06 => ( A2 = B2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % antisym
% 2.86/3.06 thf(fact_1531_antisym,axiom,
% 2.86/3.06 ! [A2: int,B2: int] :
% 2.86/3.06 ( ( ord_less_eq_int @ A2 @ B2 )
% 2.86/3.06 => ( ( ord_less_eq_int @ B2 @ A2 )
% 2.86/3.06 => ( A2 = B2 ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % antisym
% 2.86/3.06 thf(fact_1532_Orderings_Oorder__eq__iff,axiom,
% 2.86/3.06 ( ( ^ [Y4: assn,Z2: assn] : ( Y4 = Z2 ) )
% 2.86/3.06 = ( ^ [A3: assn,B3: assn] :
% 2.86/3.06 ( ( ord_less_eq_assn @ A3 @ B3 )
% 2.86/3.06 & ( ord_less_eq_assn @ B3 @ A3 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % Orderings.order_eq_iff
% 2.86/3.06 thf(fact_1533_Orderings_Oorder__eq__iff,axiom,
% 2.86/3.06 ( ( ^ [Y4: filter_nat,Z2: filter_nat] : ( Y4 = Z2 ) )
% 2.86/3.06 = ( ^ [A3: filter_nat,B3: filter_nat] :
% 2.86/3.06 ( ( ord_le2510731241096832064er_nat @ A3 @ B3 )
% 2.86/3.06 & ( ord_le2510731241096832064er_nat @ B3 @ A3 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % Orderings.order_eq_iff
% 2.86/3.06 thf(fact_1534_Orderings_Oorder__eq__iff,axiom,
% 2.86/3.06 ( ( ^ [Y4: set_nat,Z2: set_nat] : ( Y4 = Z2 ) )
% 2.86/3.06 = ( ^ [A3: set_nat,B3: set_nat] :
% 2.86/3.06 ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 2.86/3.06 & ( ord_less_eq_set_nat @ B3 @ A3 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % Orderings.order_eq_iff
% 2.86/3.06 thf(fact_1535_Orderings_Oorder__eq__iff,axiom,
% 2.86/3.06 ( ( ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 2.86/3.06 = ( ^ [A3: nat,B3: nat] :
% 2.86/3.06 ( ( ord_less_eq_nat @ A3 @ B3 )
% 2.86/3.06 & ( ord_less_eq_nat @ B3 @ A3 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % Orderings.order_eq_iff
% 2.86/3.06 thf(fact_1536_Orderings_Oorder__eq__iff,axiom,
% 2.86/3.06 ( ( ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 2.86/3.06 = ( ^ [A3: int,B3: int] :
% 2.86/3.06 ( ( ord_less_eq_int @ A3 @ B3 )
% 2.86/3.06 & ( ord_less_eq_int @ B3 @ A3 ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % Orderings.order_eq_iff
% 2.86/3.06 thf(fact_1537_order__subst1,axiom,
% 2.86/3.06 ! [A2: assn,F4: assn > assn,B2: assn,C: assn] :
% 2.86/3.06 ( ( ord_less_eq_assn @ A2 @ ( F4 @ B2 ) )
% 2.86/3.06 => ( ( ord_less_eq_assn @ B2 @ C )
% 2.86/3.06 => ( ! [X3: assn,Y2: assn] :
% 2.86/3.06 ( ( ord_less_eq_assn @ X3 @ Y2 )
% 2.86/3.06 => ( ord_less_eq_assn @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.06 => ( ord_less_eq_assn @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % order_subst1
% 2.86/3.06 thf(fact_1538_order__subst1,axiom,
% 2.86/3.06 ! [A2: assn,F4: nat > assn,B2: nat,C: nat] :
% 2.86/3.06 ( ( ord_less_eq_assn @ A2 @ ( F4 @ B2 ) )
% 2.86/3.06 => ( ( ord_less_eq_nat @ B2 @ C )
% 2.86/3.06 => ( ! [X3: nat,Y2: nat] :
% 2.86/3.06 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 2.86/3.06 => ( ord_less_eq_assn @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.06 => ( ord_less_eq_assn @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % order_subst1
% 2.86/3.06 thf(fact_1539_order__subst1,axiom,
% 2.86/3.06 ! [A2: assn,F4: int > assn,B2: int,C: int] :
% 2.86/3.06 ( ( ord_less_eq_assn @ A2 @ ( F4 @ B2 ) )
% 2.86/3.06 => ( ( ord_less_eq_int @ B2 @ C )
% 2.86/3.06 => ( ! [X3: int,Y2: int] :
% 2.86/3.06 ( ( ord_less_eq_int @ X3 @ Y2 )
% 2.86/3.06 => ( ord_less_eq_assn @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.06 => ( ord_less_eq_assn @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % order_subst1
% 2.86/3.06 thf(fact_1540_order__subst1,axiom,
% 2.86/3.06 ! [A2: nat,F4: assn > nat,B2: assn,C: assn] :
% 2.86/3.06 ( ( ord_less_eq_nat @ A2 @ ( F4 @ B2 ) )
% 2.86/3.06 => ( ( ord_less_eq_assn @ B2 @ C )
% 2.86/3.06 => ( ! [X3: assn,Y2: assn] :
% 2.86/3.06 ( ( ord_less_eq_assn @ X3 @ Y2 )
% 2.86/3.06 => ( ord_less_eq_nat @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.06 => ( ord_less_eq_nat @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.86/3.06
% 2.86/3.06 % order_subst1
% 2.86/3.06 thf(fact_1541_order__subst1,axiom,
% 2.86/3.06 ! [A2: nat,F4: nat > nat,B2: nat,C: nat] :
% 2.86/3.06 ( ( ord_less_eq_nat @ A2 @ ( F4 @ B2 ) )
% 2.86/3.06 => ( ( ord_less_eq_nat @ B2 @ C )
% 2.86/3.06 => ( ! [X3: nat,Y2: nat] :
% 2.86/3.06 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 2.86/3.06 => ( ord_less_eq_nat @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.06 => ( ord_less_eq_nat @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_subst1
% 2.86/3.07 thf(fact_1542_order__subst1,axiom,
% 2.86/3.07 ! [A2: nat,F4: int > nat,B2: int,C: int] :
% 2.86/3.07 ( ( ord_less_eq_nat @ A2 @ ( F4 @ B2 ) )
% 2.86/3.07 => ( ( ord_less_eq_int @ B2 @ C )
% 2.86/3.07 => ( ! [X3: int,Y2: int] :
% 2.86/3.07 ( ( ord_less_eq_int @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_nat @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_eq_nat @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_subst1
% 2.86/3.07 thf(fact_1543_order__subst1,axiom,
% 2.86/3.07 ! [A2: int,F4: assn > int,B2: assn,C: assn] :
% 2.86/3.07 ( ( ord_less_eq_int @ A2 @ ( F4 @ B2 ) )
% 2.86/3.07 => ( ( ord_less_eq_assn @ B2 @ C )
% 2.86/3.07 => ( ! [X3: assn,Y2: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_int @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_eq_int @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_subst1
% 2.86/3.07 thf(fact_1544_order__subst1,axiom,
% 2.86/3.07 ! [A2: int,F4: nat > int,B2: nat,C: nat] :
% 2.86/3.07 ( ( ord_less_eq_int @ A2 @ ( F4 @ B2 ) )
% 2.86/3.07 => ( ( ord_less_eq_nat @ B2 @ C )
% 2.86/3.07 => ( ! [X3: nat,Y2: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_int @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_eq_int @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_subst1
% 2.86/3.07 thf(fact_1545_order__subst1,axiom,
% 2.86/3.07 ! [A2: int,F4: int > int,B2: int,C: int] :
% 2.86/3.07 ( ( ord_less_eq_int @ A2 @ ( F4 @ B2 ) )
% 2.86/3.07 => ( ( ord_less_eq_int @ B2 @ C )
% 2.86/3.07 => ( ! [X3: int,Y2: int] :
% 2.86/3.07 ( ( ord_less_eq_int @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_int @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_eq_int @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_subst1
% 2.86/3.07 thf(fact_1546_order__subst1,axiom,
% 2.86/3.07 ! [A2: assn,F4: filter_nat > assn,B2: filter_nat,C: filter_nat] :
% 2.86/3.07 ( ( ord_less_eq_assn @ A2 @ ( F4 @ B2 ) )
% 2.86/3.07 => ( ( ord_le2510731241096832064er_nat @ B2 @ C )
% 2.86/3.07 => ( ! [X3: filter_nat,Y2: filter_nat] :
% 2.86/3.07 ( ( ord_le2510731241096832064er_nat @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_assn @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_eq_assn @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_subst1
% 2.86/3.07 thf(fact_1547_order__subst2,axiom,
% 2.86/3.07 ! [A2: assn,B2: assn,F4: assn > assn,C: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ A2 @ B2 )
% 2.86/3.07 => ( ( ord_less_eq_assn @ ( F4 @ B2 ) @ C )
% 2.86/3.07 => ( ! [X3: assn,Y2: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_assn @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_eq_assn @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_subst2
% 2.86/3.07 thf(fact_1548_order__subst2,axiom,
% 2.86/3.07 ! [A2: assn,B2: assn,F4: assn > nat,C: nat] :
% 2.86/3.07 ( ( ord_less_eq_assn @ A2 @ B2 )
% 2.86/3.07 => ( ( ord_less_eq_nat @ ( F4 @ B2 ) @ C )
% 2.86/3.07 => ( ! [X3: assn,Y2: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_nat @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_eq_nat @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_subst2
% 2.86/3.07 thf(fact_1549_order__subst2,axiom,
% 2.86/3.07 ! [A2: assn,B2: assn,F4: assn > int,C: int] :
% 2.86/3.07 ( ( ord_less_eq_assn @ A2 @ B2 )
% 2.86/3.07 => ( ( ord_less_eq_int @ ( F4 @ B2 ) @ C )
% 2.86/3.07 => ( ! [X3: assn,Y2: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_int @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_eq_int @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_subst2
% 2.86/3.07 thf(fact_1550_order__subst2,axiom,
% 2.86/3.07 ! [A2: nat,B2: nat,F4: nat > assn,C: assn] :
% 2.86/3.07 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.07 => ( ( ord_less_eq_assn @ ( F4 @ B2 ) @ C )
% 2.86/3.07 => ( ! [X3: nat,Y2: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_assn @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_eq_assn @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_subst2
% 2.86/3.07 thf(fact_1551_order__subst2,axiom,
% 2.86/3.07 ! [A2: nat,B2: nat,F4: nat > nat,C: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.07 => ( ( ord_less_eq_nat @ ( F4 @ B2 ) @ C )
% 2.86/3.07 => ( ! [X3: nat,Y2: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_nat @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_eq_nat @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_subst2
% 2.86/3.07 thf(fact_1552_order__subst2,axiom,
% 2.86/3.07 ! [A2: nat,B2: nat,F4: nat > int,C: int] :
% 2.86/3.07 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.07 => ( ( ord_less_eq_int @ ( F4 @ B2 ) @ C )
% 2.86/3.07 => ( ! [X3: nat,Y2: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_int @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_eq_int @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_subst2
% 2.86/3.07 thf(fact_1553_order__subst2,axiom,
% 2.86/3.07 ! [A2: int,B2: int,F4: int > assn,C: assn] :
% 2.86/3.07 ( ( ord_less_eq_int @ A2 @ B2 )
% 2.86/3.07 => ( ( ord_less_eq_assn @ ( F4 @ B2 ) @ C )
% 2.86/3.07 => ( ! [X3: int,Y2: int] :
% 2.86/3.07 ( ( ord_less_eq_int @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_assn @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_eq_assn @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_subst2
% 2.86/3.07 thf(fact_1554_order__subst2,axiom,
% 2.86/3.07 ! [A2: int,B2: int,F4: int > nat,C: nat] :
% 2.86/3.07 ( ( ord_less_eq_int @ A2 @ B2 )
% 2.86/3.07 => ( ( ord_less_eq_nat @ ( F4 @ B2 ) @ C )
% 2.86/3.07 => ( ! [X3: int,Y2: int] :
% 2.86/3.07 ( ( ord_less_eq_int @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_nat @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_eq_nat @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_subst2
% 2.86/3.07 thf(fact_1555_order__subst2,axiom,
% 2.86/3.07 ! [A2: int,B2: int,F4: int > int,C: int] :
% 2.86/3.07 ( ( ord_less_eq_int @ A2 @ B2 )
% 2.86/3.07 => ( ( ord_less_eq_int @ ( F4 @ B2 ) @ C )
% 2.86/3.07 => ( ! [X3: int,Y2: int] :
% 2.86/3.07 ( ( ord_less_eq_int @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_int @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_eq_int @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_subst2
% 2.86/3.07 thf(fact_1556_order__subst2,axiom,
% 2.86/3.07 ! [A2: assn,B2: assn,F4: assn > filter_nat,C: filter_nat] :
% 2.86/3.07 ( ( ord_less_eq_assn @ A2 @ B2 )
% 2.86/3.07 => ( ( ord_le2510731241096832064er_nat @ ( F4 @ B2 ) @ C )
% 2.86/3.07 => ( ! [X3: assn,Y2: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ X3 @ Y2 )
% 2.86/3.07 => ( ord_le2510731241096832064er_nat @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_le2510731241096832064er_nat @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_subst2
% 2.86/3.07 thf(fact_1557_order__eq__refl,axiom,
% 2.86/3.07 ! [X: assn,Y: assn] :
% 2.86/3.07 ( ( X = Y )
% 2.86/3.07 => ( ord_less_eq_assn @ X @ Y ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_eq_refl
% 2.86/3.07 thf(fact_1558_order__eq__refl,axiom,
% 2.86/3.07 ! [X: filter_nat,Y: filter_nat] :
% 2.86/3.07 ( ( X = Y )
% 2.86/3.07 => ( ord_le2510731241096832064er_nat @ X @ Y ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_eq_refl
% 2.86/3.07 thf(fact_1559_order__eq__refl,axiom,
% 2.86/3.07 ! [X: set_nat,Y: set_nat] :
% 2.86/3.07 ( ( X = Y )
% 2.86/3.07 => ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_eq_refl
% 2.86/3.07 thf(fact_1560_order__eq__refl,axiom,
% 2.86/3.07 ! [X: nat,Y: nat] :
% 2.86/3.07 ( ( X = Y )
% 2.86/3.07 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_eq_refl
% 2.86/3.07 thf(fact_1561_order__eq__refl,axiom,
% 2.86/3.07 ! [X: int,Y: int] :
% 2.86/3.07 ( ( X = Y )
% 2.86/3.07 => ( ord_less_eq_int @ X @ Y ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_eq_refl
% 2.86/3.07 thf(fact_1562_linorder__linear,axiom,
% 2.86/3.07 ! [X: nat,Y: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ X @ Y )
% 2.86/3.07 | ( ord_less_eq_nat @ Y @ X ) ) ).
% 2.86/3.07
% 2.86/3.07 % linorder_linear
% 2.86/3.07 thf(fact_1563_linorder__linear,axiom,
% 2.86/3.07 ! [X: int,Y: int] :
% 2.86/3.07 ( ( ord_less_eq_int @ X @ Y )
% 2.86/3.07 | ( ord_less_eq_int @ Y @ X ) ) ).
% 2.86/3.07
% 2.86/3.07 % linorder_linear
% 2.86/3.07 thf(fact_1564_ord__eq__le__subst,axiom,
% 2.86/3.07 ! [A2: assn,F4: assn > assn,B2: assn,C: assn] :
% 2.86/3.07 ( ( A2
% 2.86/3.07 = ( F4 @ B2 ) )
% 2.86/3.07 => ( ( ord_less_eq_assn @ B2 @ C )
% 2.86/3.07 => ( ! [X3: assn,Y2: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_assn @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_eq_assn @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % ord_eq_le_subst
% 2.86/3.07 thf(fact_1565_ord__eq__le__subst,axiom,
% 2.86/3.07 ! [A2: nat,F4: assn > nat,B2: assn,C: assn] :
% 2.86/3.07 ( ( A2
% 2.86/3.07 = ( F4 @ B2 ) )
% 2.86/3.07 => ( ( ord_less_eq_assn @ B2 @ C )
% 2.86/3.07 => ( ! [X3: assn,Y2: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_nat @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_eq_nat @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % ord_eq_le_subst
% 2.86/3.07 thf(fact_1566_ord__eq__le__subst,axiom,
% 2.86/3.07 ! [A2: int,F4: assn > int,B2: assn,C: assn] :
% 2.86/3.07 ( ( A2
% 2.86/3.07 = ( F4 @ B2 ) )
% 2.86/3.07 => ( ( ord_less_eq_assn @ B2 @ C )
% 2.86/3.07 => ( ! [X3: assn,Y2: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_int @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_eq_int @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % ord_eq_le_subst
% 2.86/3.07 thf(fact_1567_ord__eq__le__subst,axiom,
% 2.86/3.07 ! [A2: assn,F4: nat > assn,B2: nat,C: nat] :
% 2.86/3.07 ( ( A2
% 2.86/3.07 = ( F4 @ B2 ) )
% 2.86/3.07 => ( ( ord_less_eq_nat @ B2 @ C )
% 2.86/3.07 => ( ! [X3: nat,Y2: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_assn @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_eq_assn @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % ord_eq_le_subst
% 2.86/3.07 thf(fact_1568_ord__eq__le__subst,axiom,
% 2.86/3.07 ! [A2: nat,F4: nat > nat,B2: nat,C: nat] :
% 2.86/3.07 ( ( A2
% 2.86/3.07 = ( F4 @ B2 ) )
% 2.86/3.07 => ( ( ord_less_eq_nat @ B2 @ C )
% 2.86/3.07 => ( ! [X3: nat,Y2: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_nat @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_eq_nat @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % ord_eq_le_subst
% 2.86/3.07 thf(fact_1569_ord__eq__le__subst,axiom,
% 2.86/3.07 ! [A2: int,F4: nat > int,B2: nat,C: nat] :
% 2.86/3.07 ( ( A2
% 2.86/3.07 = ( F4 @ B2 ) )
% 2.86/3.07 => ( ( ord_less_eq_nat @ B2 @ C )
% 2.86/3.07 => ( ! [X3: nat,Y2: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_int @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_eq_int @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % ord_eq_le_subst
% 2.86/3.07 thf(fact_1570_ord__eq__le__subst,axiom,
% 2.86/3.07 ! [A2: assn,F4: int > assn,B2: int,C: int] :
% 2.86/3.07 ( ( A2
% 2.86/3.07 = ( F4 @ B2 ) )
% 2.86/3.07 => ( ( ord_less_eq_int @ B2 @ C )
% 2.86/3.07 => ( ! [X3: int,Y2: int] :
% 2.86/3.07 ( ( ord_less_eq_int @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_assn @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_eq_assn @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % ord_eq_le_subst
% 2.86/3.07 thf(fact_1571_ord__eq__le__subst,axiom,
% 2.86/3.07 ! [A2: nat,F4: int > nat,B2: int,C: int] :
% 2.86/3.07 ( ( A2
% 2.86/3.07 = ( F4 @ B2 ) )
% 2.86/3.07 => ( ( ord_less_eq_int @ B2 @ C )
% 2.86/3.07 => ( ! [X3: int,Y2: int] :
% 2.86/3.07 ( ( ord_less_eq_int @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_nat @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_eq_nat @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % ord_eq_le_subst
% 2.86/3.07 thf(fact_1572_ord__eq__le__subst,axiom,
% 2.86/3.07 ! [A2: int,F4: int > int,B2: int,C: int] :
% 2.86/3.07 ( ( A2
% 2.86/3.07 = ( F4 @ B2 ) )
% 2.86/3.07 => ( ( ord_less_eq_int @ B2 @ C )
% 2.86/3.07 => ( ! [X3: int,Y2: int] :
% 2.86/3.07 ( ( ord_less_eq_int @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_int @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_eq_int @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % ord_eq_le_subst
% 2.86/3.07 thf(fact_1573_ord__eq__le__subst,axiom,
% 2.86/3.07 ! [A2: filter_nat,F4: assn > filter_nat,B2: assn,C: assn] :
% 2.86/3.07 ( ( A2
% 2.86/3.07 = ( F4 @ B2 ) )
% 2.86/3.07 => ( ( ord_less_eq_assn @ B2 @ C )
% 2.86/3.07 => ( ! [X3: assn,Y2: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ X3 @ Y2 )
% 2.86/3.07 => ( ord_le2510731241096832064er_nat @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_le2510731241096832064er_nat @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % ord_eq_le_subst
% 2.86/3.07 thf(fact_1574_ord__le__eq__subst,axiom,
% 2.86/3.07 ! [A2: assn,B2: assn,F4: assn > assn,C: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ A2 @ B2 )
% 2.86/3.07 => ( ( ( F4 @ B2 )
% 2.86/3.07 = C )
% 2.86/3.07 => ( ! [X3: assn,Y2: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_assn @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_eq_assn @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % ord_le_eq_subst
% 2.86/3.07 thf(fact_1575_ord__le__eq__subst,axiom,
% 2.86/3.07 ! [A2: assn,B2: assn,F4: assn > nat,C: nat] :
% 2.86/3.07 ( ( ord_less_eq_assn @ A2 @ B2 )
% 2.86/3.07 => ( ( ( F4 @ B2 )
% 2.86/3.07 = C )
% 2.86/3.07 => ( ! [X3: assn,Y2: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_nat @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_eq_nat @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % ord_le_eq_subst
% 2.86/3.07 thf(fact_1576_ord__le__eq__subst,axiom,
% 2.86/3.07 ! [A2: assn,B2: assn,F4: assn > int,C: int] :
% 2.86/3.07 ( ( ord_less_eq_assn @ A2 @ B2 )
% 2.86/3.07 => ( ( ( F4 @ B2 )
% 2.86/3.07 = C )
% 2.86/3.07 => ( ! [X3: assn,Y2: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_int @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_eq_int @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % ord_le_eq_subst
% 2.86/3.07 thf(fact_1577_ord__le__eq__subst,axiom,
% 2.86/3.07 ! [A2: nat,B2: nat,F4: nat > assn,C: assn] :
% 2.86/3.07 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.07 => ( ( ( F4 @ B2 )
% 2.86/3.07 = C )
% 2.86/3.07 => ( ! [X3: nat,Y2: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_assn @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_eq_assn @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % ord_le_eq_subst
% 2.86/3.07 thf(fact_1578_ord__le__eq__subst,axiom,
% 2.86/3.07 ! [A2: nat,B2: nat,F4: nat > nat,C: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.07 => ( ( ( F4 @ B2 )
% 2.86/3.07 = C )
% 2.86/3.07 => ( ! [X3: nat,Y2: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_nat @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_eq_nat @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % ord_le_eq_subst
% 2.86/3.07 thf(fact_1579_ord__le__eq__subst,axiom,
% 2.86/3.07 ! [A2: nat,B2: nat,F4: nat > int,C: int] :
% 2.86/3.07 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.07 => ( ( ( F4 @ B2 )
% 2.86/3.07 = C )
% 2.86/3.07 => ( ! [X3: nat,Y2: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_int @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_eq_int @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % ord_le_eq_subst
% 2.86/3.07 thf(fact_1580_ord__le__eq__subst,axiom,
% 2.86/3.07 ! [A2: int,B2: int,F4: int > assn,C: assn] :
% 2.86/3.07 ( ( ord_less_eq_int @ A2 @ B2 )
% 2.86/3.07 => ( ( ( F4 @ B2 )
% 2.86/3.07 = C )
% 2.86/3.07 => ( ! [X3: int,Y2: int] :
% 2.86/3.07 ( ( ord_less_eq_int @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_assn @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_eq_assn @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % ord_le_eq_subst
% 2.86/3.07 thf(fact_1581_ord__le__eq__subst,axiom,
% 2.86/3.07 ! [A2: int,B2: int,F4: int > nat,C: nat] :
% 2.86/3.07 ( ( ord_less_eq_int @ A2 @ B2 )
% 2.86/3.07 => ( ( ( F4 @ B2 )
% 2.86/3.07 = C )
% 2.86/3.07 => ( ! [X3: int,Y2: int] :
% 2.86/3.07 ( ( ord_less_eq_int @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_nat @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_eq_nat @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % ord_le_eq_subst
% 2.86/3.07 thf(fact_1582_ord__le__eq__subst,axiom,
% 2.86/3.07 ! [A2: int,B2: int,F4: int > int,C: int] :
% 2.86/3.07 ( ( ord_less_eq_int @ A2 @ B2 )
% 2.86/3.07 => ( ( ( F4 @ B2 )
% 2.86/3.07 = C )
% 2.86/3.07 => ( ! [X3: int,Y2: int] :
% 2.86/3.07 ( ( ord_less_eq_int @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_int @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_eq_int @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % ord_le_eq_subst
% 2.86/3.07 thf(fact_1583_ord__le__eq__subst,axiom,
% 2.86/3.07 ! [A2: assn,B2: assn,F4: assn > filter_nat,C: filter_nat] :
% 2.86/3.07 ( ( ord_less_eq_assn @ A2 @ B2 )
% 2.86/3.07 => ( ( ( F4 @ B2 )
% 2.86/3.07 = C )
% 2.86/3.07 => ( ! [X3: assn,Y2: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ X3 @ Y2 )
% 2.86/3.07 => ( ord_le2510731241096832064er_nat @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_le2510731241096832064er_nat @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % ord_le_eq_subst
% 2.86/3.07 thf(fact_1584_linorder__le__cases,axiom,
% 2.86/3.07 ! [X: nat,Y: nat] :
% 2.86/3.07 ( ~ ( ord_less_eq_nat @ X @ Y )
% 2.86/3.07 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 2.86/3.07
% 2.86/3.07 % linorder_le_cases
% 2.86/3.07 thf(fact_1585_linorder__le__cases,axiom,
% 2.86/3.07 ! [X: int,Y: int] :
% 2.86/3.07 ( ~ ( ord_less_eq_int @ X @ Y )
% 2.86/3.07 => ( ord_less_eq_int @ Y @ X ) ) ).
% 2.86/3.07
% 2.86/3.07 % linorder_le_cases
% 2.86/3.07 thf(fact_1586_order__antisym__conv,axiom,
% 2.86/3.07 ! [Y: assn,X: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ Y @ X )
% 2.86/3.07 => ( ( ord_less_eq_assn @ X @ Y )
% 2.86/3.07 = ( X = Y ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_antisym_conv
% 2.86/3.07 thf(fact_1587_order__antisym__conv,axiom,
% 2.86/3.07 ! [Y: filter_nat,X: filter_nat] :
% 2.86/3.07 ( ( ord_le2510731241096832064er_nat @ Y @ X )
% 2.86/3.07 => ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 2.86/3.07 = ( X = Y ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_antisym_conv
% 2.86/3.07 thf(fact_1588_order__antisym__conv,axiom,
% 2.86/3.07 ! [Y: set_nat,X: set_nat] :
% 2.86/3.07 ( ( ord_less_eq_set_nat @ Y @ X )
% 2.86/3.07 => ( ( ord_less_eq_set_nat @ X @ Y )
% 2.86/3.07 = ( X = Y ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_antisym_conv
% 2.86/3.07 thf(fact_1589_order__antisym__conv,axiom,
% 2.86/3.07 ! [Y: nat,X: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ Y @ X )
% 2.86/3.07 => ( ( ord_less_eq_nat @ X @ Y )
% 2.86/3.07 = ( X = Y ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_antisym_conv
% 2.86/3.07 thf(fact_1590_order__antisym__conv,axiom,
% 2.86/3.07 ! [Y: int,X: int] :
% 2.86/3.07 ( ( ord_less_eq_int @ Y @ X )
% 2.86/3.07 => ( ( ord_less_eq_int @ X @ Y )
% 2.86/3.07 = ( X = Y ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_antisym_conv
% 2.86/3.07 thf(fact_1591_inf__sup__aci_I4_J,axiom,
% 2.86/3.07 ! [X: assn,Y: assn] :
% 2.86/3.07 ( ( inf_inf_assn @ X @ ( inf_inf_assn @ X @ Y ) )
% 2.86/3.07 = ( inf_inf_assn @ X @ Y ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_sup_aci(4)
% 2.86/3.07 thf(fact_1592_inf__sup__aci_I4_J,axiom,
% 2.86/3.07 ! [X: set_nat,Y: set_nat] :
% 2.86/3.07 ( ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ X @ Y ) )
% 2.86/3.07 = ( inf_inf_set_nat @ X @ Y ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_sup_aci(4)
% 2.86/3.07 thf(fact_1593_inf__sup__aci_I4_J,axiom,
% 2.86/3.07 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 2.86/3.07 ( ( inf_in2572325071724192079at_nat @ X @ ( inf_in2572325071724192079at_nat @ X @ Y ) )
% 2.86/3.07 = ( inf_in2572325071724192079at_nat @ X @ Y ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_sup_aci(4)
% 2.86/3.07 thf(fact_1594_inf__sup__aci_I3_J,axiom,
% 2.86/3.07 ! [X: assn,Y: assn,Z: assn] :
% 2.86/3.07 ( ( inf_inf_assn @ X @ ( inf_inf_assn @ Y @ Z ) )
% 2.86/3.07 = ( inf_inf_assn @ Y @ ( inf_inf_assn @ X @ Z ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_sup_aci(3)
% 2.86/3.07 thf(fact_1595_inf__sup__aci_I3_J,axiom,
% 2.86/3.07 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 2.86/3.07 ( ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) )
% 2.86/3.07 = ( inf_inf_set_nat @ Y @ ( inf_inf_set_nat @ X @ Z ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_sup_aci(3)
% 2.86/3.07 thf(fact_1596_inf__sup__aci_I3_J,axiom,
% 2.86/3.07 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 2.86/3.07 ( ( inf_in2572325071724192079at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) )
% 2.86/3.07 = ( inf_in2572325071724192079at_nat @ Y @ ( inf_in2572325071724192079at_nat @ X @ Z ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_sup_aci(3)
% 2.86/3.07 thf(fact_1597_inf__sup__aci_I2_J,axiom,
% 2.86/3.07 ! [X: assn,Y: assn,Z: assn] :
% 2.86/3.07 ( ( inf_inf_assn @ ( inf_inf_assn @ X @ Y ) @ Z )
% 2.86/3.07 = ( inf_inf_assn @ X @ ( inf_inf_assn @ Y @ Z ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_sup_aci(2)
% 2.86/3.07 thf(fact_1598_inf__sup__aci_I2_J,axiom,
% 2.86/3.07 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 2.86/3.07 ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Z )
% 2.86/3.07 = ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_sup_aci(2)
% 2.86/3.07 thf(fact_1599_inf__sup__aci_I2_J,axiom,
% 2.86/3.07 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 2.86/3.07 ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Z )
% 2.86/3.07 = ( inf_in2572325071724192079at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_sup_aci(2)
% 2.86/3.07 thf(fact_1600_inf__sup__aci_I1_J,axiom,
% 2.86/3.07 ( inf_inf_assn
% 2.86/3.07 = ( ^ [X2: assn,Y5: assn] : ( inf_inf_assn @ Y5 @ X2 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_sup_aci(1)
% 2.86/3.07 thf(fact_1601_inf__sup__aci_I1_J,axiom,
% 2.86/3.07 ( inf_inf_set_nat
% 2.86/3.07 = ( ^ [X2: set_nat,Y5: set_nat] : ( inf_inf_set_nat @ Y5 @ X2 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_sup_aci(1)
% 2.86/3.07 thf(fact_1602_inf__sup__aci_I1_J,axiom,
% 2.86/3.07 ( inf_in2572325071724192079at_nat
% 2.86/3.07 = ( ^ [X2: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( inf_in2572325071724192079at_nat @ Y5 @ X2 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_sup_aci(1)
% 2.86/3.07 thf(fact_1603_inf__sup__ord_I2_J,axiom,
% 2.86/3.07 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Y ) ).
% 2.86/3.07
% 2.86/3.07 % inf_sup_ord(2)
% 2.86/3.07 thf(fact_1604_inf__sup__ord_I2_J,axiom,
% 2.86/3.07 ! [X: assn,Y: assn] : ( ord_less_eq_assn @ ( inf_inf_assn @ X @ Y ) @ Y ) ).
% 2.86/3.07
% 2.86/3.07 % inf_sup_ord(2)
% 2.86/3.07 thf(fact_1605_inf__sup__ord_I2_J,axiom,
% 2.86/3.07 ! [X: filter_nat,Y: filter_nat] : ( ord_le2510731241096832064er_nat @ ( inf_inf_filter_nat @ X @ Y ) @ Y ) ).
% 2.86/3.07
% 2.86/3.07 % inf_sup_ord(2)
% 2.86/3.07 thf(fact_1606_inf__sup__ord_I2_J,axiom,
% 2.86/3.07 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Y ) ).
% 2.86/3.07
% 2.86/3.07 % inf_sup_ord(2)
% 2.86/3.07 thf(fact_1607_inf__sup__ord_I2_J,axiom,
% 2.86/3.07 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ Y ) ).
% 2.86/3.07
% 2.86/3.07 % inf_sup_ord(2)
% 2.86/3.07 thf(fact_1608_inf__sup__ord_I2_J,axiom,
% 2.86/3.07 ! [X: int,Y: int] : ( ord_less_eq_int @ ( inf_inf_int @ X @ Y ) @ Y ) ).
% 2.86/3.07
% 2.86/3.07 % inf_sup_ord(2)
% 2.86/3.07 thf(fact_1609_inf__sup__ord_I1_J,axiom,
% 2.86/3.07 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ X ) ).
% 2.86/3.07
% 2.86/3.07 % inf_sup_ord(1)
% 2.86/3.07 thf(fact_1610_inf__sup__ord_I1_J,axiom,
% 2.86/3.07 ! [X: assn,Y: assn] : ( ord_less_eq_assn @ ( inf_inf_assn @ X @ Y ) @ X ) ).
% 2.86/3.07
% 2.86/3.07 % inf_sup_ord(1)
% 2.86/3.07 thf(fact_1611_inf__sup__ord_I1_J,axiom,
% 2.86/3.07 ! [X: filter_nat,Y: filter_nat] : ( ord_le2510731241096832064er_nat @ ( inf_inf_filter_nat @ X @ Y ) @ X ) ).
% 2.86/3.07
% 2.86/3.07 % inf_sup_ord(1)
% 2.86/3.07 thf(fact_1612_inf__sup__ord_I1_J,axiom,
% 2.86/3.07 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ X ) ).
% 2.86/3.07
% 2.86/3.07 % inf_sup_ord(1)
% 2.86/3.07 thf(fact_1613_inf__sup__ord_I1_J,axiom,
% 2.86/3.07 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ X ) ).
% 2.86/3.07
% 2.86/3.07 % inf_sup_ord(1)
% 2.86/3.07 thf(fact_1614_inf__sup__ord_I1_J,axiom,
% 2.86/3.07 ! [X: int,Y: int] : ( ord_less_eq_int @ ( inf_inf_int @ X @ Y ) @ X ) ).
% 2.86/3.07
% 2.86/3.07 % inf_sup_ord(1)
% 2.86/3.07 thf(fact_1615_inf__le1,axiom,
% 2.86/3.07 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ X ) ).
% 2.86/3.07
% 2.86/3.07 % inf_le1
% 2.86/3.07 thf(fact_1616_inf__le1,axiom,
% 2.86/3.07 ! [X: assn,Y: assn] : ( ord_less_eq_assn @ ( inf_inf_assn @ X @ Y ) @ X ) ).
% 2.86/3.07
% 2.86/3.07 % inf_le1
% 2.86/3.07 thf(fact_1617_inf__le1,axiom,
% 2.86/3.07 ! [X: filter_nat,Y: filter_nat] : ( ord_le2510731241096832064er_nat @ ( inf_inf_filter_nat @ X @ Y ) @ X ) ).
% 2.86/3.07
% 2.86/3.07 % inf_le1
% 2.86/3.07 thf(fact_1618_inf__le1,axiom,
% 2.86/3.07 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ X ) ).
% 2.86/3.07
% 2.86/3.07 % inf_le1
% 2.86/3.07 thf(fact_1619_inf__le1,axiom,
% 2.86/3.07 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ X ) ).
% 2.86/3.07
% 2.86/3.07 % inf_le1
% 2.86/3.07 thf(fact_1620_inf__le1,axiom,
% 2.86/3.07 ! [X: int,Y: int] : ( ord_less_eq_int @ ( inf_inf_int @ X @ Y ) @ X ) ).
% 2.86/3.07
% 2.86/3.07 % inf_le1
% 2.86/3.07 thf(fact_1621_inf__le2,axiom,
% 2.86/3.07 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Y ) ).
% 2.86/3.07
% 2.86/3.07 % inf_le2
% 2.86/3.07 thf(fact_1622_inf__le2,axiom,
% 2.86/3.07 ! [X: assn,Y: assn] : ( ord_less_eq_assn @ ( inf_inf_assn @ X @ Y ) @ Y ) ).
% 2.86/3.07
% 2.86/3.07 % inf_le2
% 2.86/3.07 thf(fact_1623_inf__le2,axiom,
% 2.86/3.07 ! [X: filter_nat,Y: filter_nat] : ( ord_le2510731241096832064er_nat @ ( inf_inf_filter_nat @ X @ Y ) @ Y ) ).
% 2.86/3.07
% 2.86/3.07 % inf_le2
% 2.86/3.07 thf(fact_1624_inf__le2,axiom,
% 2.86/3.07 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Y ) ).
% 2.86/3.07
% 2.86/3.07 % inf_le2
% 2.86/3.07 thf(fact_1625_inf__le2,axiom,
% 2.86/3.07 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ Y ) ).
% 2.86/3.07
% 2.86/3.07 % inf_le2
% 2.86/3.07 thf(fact_1626_inf__le2,axiom,
% 2.86/3.07 ! [X: int,Y: int] : ( ord_less_eq_int @ ( inf_inf_int @ X @ Y ) @ Y ) ).
% 2.86/3.07
% 2.86/3.07 % inf_le2
% 2.86/3.07 thf(fact_1627_le__infE,axiom,
% 2.86/3.07 ! [X: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 2.86/3.07 ( ( ord_le3146513528884898305at_nat @ X @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) )
% 2.86/3.07 => ~ ( ( ord_le3146513528884898305at_nat @ X @ A2 )
% 2.86/3.07 => ~ ( ord_le3146513528884898305at_nat @ X @ B2 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % le_infE
% 2.86/3.07 thf(fact_1628_le__infE,axiom,
% 2.86/3.07 ! [X: assn,A2: assn,B2: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ X @ ( inf_inf_assn @ A2 @ B2 ) )
% 2.86/3.07 => ~ ( ( ord_less_eq_assn @ X @ A2 )
% 2.86/3.07 => ~ ( ord_less_eq_assn @ X @ B2 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % le_infE
% 2.86/3.07 thf(fact_1629_le__infE,axiom,
% 2.86/3.07 ! [X: filter_nat,A2: filter_nat,B2: filter_nat] :
% 2.86/3.07 ( ( ord_le2510731241096832064er_nat @ X @ ( inf_inf_filter_nat @ A2 @ B2 ) )
% 2.86/3.07 => ~ ( ( ord_le2510731241096832064er_nat @ X @ A2 )
% 2.86/3.07 => ~ ( ord_le2510731241096832064er_nat @ X @ B2 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % le_infE
% 2.86/3.07 thf(fact_1630_le__infE,axiom,
% 2.86/3.07 ! [X: set_nat,A2: set_nat,B2: set_nat] :
% 2.86/3.07 ( ( ord_less_eq_set_nat @ X @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 2.86/3.07 => ~ ( ( ord_less_eq_set_nat @ X @ A2 )
% 2.86/3.07 => ~ ( ord_less_eq_set_nat @ X @ B2 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % le_infE
% 2.86/3.07 thf(fact_1631_le__infE,axiom,
% 2.86/3.07 ! [X: nat,A2: nat,B2: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ X @ ( inf_inf_nat @ A2 @ B2 ) )
% 2.86/3.07 => ~ ( ( ord_less_eq_nat @ X @ A2 )
% 2.86/3.07 => ~ ( ord_less_eq_nat @ X @ B2 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % le_infE
% 2.86/3.07 thf(fact_1632_le__infE,axiom,
% 2.86/3.07 ! [X: int,A2: int,B2: int] :
% 2.86/3.07 ( ( ord_less_eq_int @ X @ ( inf_inf_int @ A2 @ B2 ) )
% 2.86/3.07 => ~ ( ( ord_less_eq_int @ X @ A2 )
% 2.86/3.07 => ~ ( ord_less_eq_int @ X @ B2 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % le_infE
% 2.86/3.07 thf(fact_1633_le__infI,axiom,
% 2.86/3.07 ! [X: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 2.86/3.07 ( ( ord_le3146513528884898305at_nat @ X @ A2 )
% 2.86/3.07 => ( ( ord_le3146513528884898305at_nat @ X @ B2 )
% 2.86/3.07 => ( ord_le3146513528884898305at_nat @ X @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % le_infI
% 2.86/3.07 thf(fact_1634_le__infI,axiom,
% 2.86/3.07 ! [X: assn,A2: assn,B2: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ X @ A2 )
% 2.86/3.07 => ( ( ord_less_eq_assn @ X @ B2 )
% 2.86/3.07 => ( ord_less_eq_assn @ X @ ( inf_inf_assn @ A2 @ B2 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % le_infI
% 2.86/3.07 thf(fact_1635_le__infI,axiom,
% 2.86/3.07 ! [X: filter_nat,A2: filter_nat,B2: filter_nat] :
% 2.86/3.07 ( ( ord_le2510731241096832064er_nat @ X @ A2 )
% 2.86/3.07 => ( ( ord_le2510731241096832064er_nat @ X @ B2 )
% 2.86/3.07 => ( ord_le2510731241096832064er_nat @ X @ ( inf_inf_filter_nat @ A2 @ B2 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % le_infI
% 2.86/3.07 thf(fact_1636_le__infI,axiom,
% 2.86/3.07 ! [X: set_nat,A2: set_nat,B2: set_nat] :
% 2.86/3.07 ( ( ord_less_eq_set_nat @ X @ A2 )
% 2.86/3.07 => ( ( ord_less_eq_set_nat @ X @ B2 )
% 2.86/3.07 => ( ord_less_eq_set_nat @ X @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % le_infI
% 2.86/3.07 thf(fact_1637_le__infI,axiom,
% 2.86/3.07 ! [X: nat,A2: nat,B2: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ X @ A2 )
% 2.86/3.07 => ( ( ord_less_eq_nat @ X @ B2 )
% 2.86/3.07 => ( ord_less_eq_nat @ X @ ( inf_inf_nat @ A2 @ B2 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % le_infI
% 2.86/3.07 thf(fact_1638_le__infI,axiom,
% 2.86/3.07 ! [X: int,A2: int,B2: int] :
% 2.86/3.07 ( ( ord_less_eq_int @ X @ A2 )
% 2.86/3.07 => ( ( ord_less_eq_int @ X @ B2 )
% 2.86/3.07 => ( ord_less_eq_int @ X @ ( inf_inf_int @ A2 @ B2 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % le_infI
% 2.86/3.07 thf(fact_1639_inf__mono,axiom,
% 2.86/3.07 ! [A2: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,D2: set_Pr1261947904930325089at_nat] :
% 2.86/3.07 ( ( ord_le3146513528884898305at_nat @ A2 @ C )
% 2.86/3.07 => ( ( ord_le3146513528884898305at_nat @ B2 @ D2 )
% 2.86/3.07 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) @ ( inf_in2572325071724192079at_nat @ C @ D2 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_mono
% 2.86/3.07 thf(fact_1640_inf__mono,axiom,
% 2.86/3.07 ! [A2: assn,C: assn,B2: assn,D2: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ A2 @ C )
% 2.86/3.07 => ( ( ord_less_eq_assn @ B2 @ D2 )
% 2.86/3.07 => ( ord_less_eq_assn @ ( inf_inf_assn @ A2 @ B2 ) @ ( inf_inf_assn @ C @ D2 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_mono
% 2.86/3.07 thf(fact_1641_inf__mono,axiom,
% 2.86/3.07 ! [A2: filter_nat,C: filter_nat,B2: filter_nat,D2: filter_nat] :
% 2.86/3.07 ( ( ord_le2510731241096832064er_nat @ A2 @ C )
% 2.86/3.07 => ( ( ord_le2510731241096832064er_nat @ B2 @ D2 )
% 2.86/3.07 => ( ord_le2510731241096832064er_nat @ ( inf_inf_filter_nat @ A2 @ B2 ) @ ( inf_inf_filter_nat @ C @ D2 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_mono
% 2.86/3.07 thf(fact_1642_inf__mono,axiom,
% 2.86/3.07 ! [A2: set_nat,C: set_nat,B2: set_nat,D2: set_nat] :
% 2.86/3.07 ( ( ord_less_eq_set_nat @ A2 @ C )
% 2.86/3.07 => ( ( ord_less_eq_set_nat @ B2 @ D2 )
% 2.86/3.07 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ ( inf_inf_set_nat @ C @ D2 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_mono
% 2.86/3.07 thf(fact_1643_inf__mono,axiom,
% 2.86/3.07 ! [A2: nat,C: nat,B2: nat,D2: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ A2 @ C )
% 2.86/3.07 => ( ( ord_less_eq_nat @ B2 @ D2 )
% 2.86/3.07 => ( ord_less_eq_nat @ ( inf_inf_nat @ A2 @ B2 ) @ ( inf_inf_nat @ C @ D2 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_mono
% 2.86/3.07 thf(fact_1644_inf__mono,axiom,
% 2.86/3.07 ! [A2: int,C: int,B2: int,D2: int] :
% 2.86/3.07 ( ( ord_less_eq_int @ A2 @ C )
% 2.86/3.07 => ( ( ord_less_eq_int @ B2 @ D2 )
% 2.86/3.07 => ( ord_less_eq_int @ ( inf_inf_int @ A2 @ B2 ) @ ( inf_inf_int @ C @ D2 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_mono
% 2.86/3.07 thf(fact_1645_le__infI1,axiom,
% 2.86/3.07 ! [A2: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 2.86/3.07 ( ( ord_le3146513528884898305at_nat @ A2 @ X )
% 2.86/3.07 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) @ X ) ) ).
% 2.86/3.07
% 2.86/3.07 % le_infI1
% 2.86/3.07 thf(fact_1646_le__infI1,axiom,
% 2.86/3.07 ! [A2: assn,X: assn,B2: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ A2 @ X )
% 2.86/3.07 => ( ord_less_eq_assn @ ( inf_inf_assn @ A2 @ B2 ) @ X ) ) ).
% 2.86/3.07
% 2.86/3.07 % le_infI1
% 2.86/3.07 thf(fact_1647_le__infI1,axiom,
% 2.86/3.07 ! [A2: filter_nat,X: filter_nat,B2: filter_nat] :
% 2.86/3.07 ( ( ord_le2510731241096832064er_nat @ A2 @ X )
% 2.86/3.07 => ( ord_le2510731241096832064er_nat @ ( inf_inf_filter_nat @ A2 @ B2 ) @ X ) ) ).
% 2.86/3.07
% 2.86/3.07 % le_infI1
% 2.86/3.07 thf(fact_1648_le__infI1,axiom,
% 2.86/3.07 ! [A2: set_nat,X: set_nat,B2: set_nat] :
% 2.86/3.07 ( ( ord_less_eq_set_nat @ A2 @ X )
% 2.86/3.07 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ X ) ) ).
% 2.86/3.07
% 2.86/3.07 % le_infI1
% 2.86/3.07 thf(fact_1649_le__infI1,axiom,
% 2.86/3.07 ! [A2: nat,X: nat,B2: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ A2 @ X )
% 2.86/3.07 => ( ord_less_eq_nat @ ( inf_inf_nat @ A2 @ B2 ) @ X ) ) ).
% 2.86/3.07
% 2.86/3.07 % le_infI1
% 2.86/3.07 thf(fact_1650_le__infI1,axiom,
% 2.86/3.07 ! [A2: int,X: int,B2: int] :
% 2.86/3.07 ( ( ord_less_eq_int @ A2 @ X )
% 2.86/3.07 => ( ord_less_eq_int @ ( inf_inf_int @ A2 @ B2 ) @ X ) ) ).
% 2.86/3.07
% 2.86/3.07 % le_infI1
% 2.86/3.07 thf(fact_1651_le__infI2,axiom,
% 2.86/3.07 ! [B2: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 2.86/3.07 ( ( ord_le3146513528884898305at_nat @ B2 @ X )
% 2.86/3.07 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) @ X ) ) ).
% 2.86/3.07
% 2.86/3.07 % le_infI2
% 2.86/3.07 thf(fact_1652_le__infI2,axiom,
% 2.86/3.07 ! [B2: assn,X: assn,A2: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ B2 @ X )
% 2.86/3.07 => ( ord_less_eq_assn @ ( inf_inf_assn @ A2 @ B2 ) @ X ) ) ).
% 2.86/3.07
% 2.86/3.07 % le_infI2
% 2.86/3.07 thf(fact_1653_le__infI2,axiom,
% 2.86/3.07 ! [B2: filter_nat,X: filter_nat,A2: filter_nat] :
% 2.86/3.07 ( ( ord_le2510731241096832064er_nat @ B2 @ X )
% 2.86/3.07 => ( ord_le2510731241096832064er_nat @ ( inf_inf_filter_nat @ A2 @ B2 ) @ X ) ) ).
% 2.86/3.07
% 2.86/3.07 % le_infI2
% 2.86/3.07 thf(fact_1654_le__infI2,axiom,
% 2.86/3.07 ! [B2: set_nat,X: set_nat,A2: set_nat] :
% 2.86/3.07 ( ( ord_less_eq_set_nat @ B2 @ X )
% 2.86/3.07 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ X ) ) ).
% 2.86/3.07
% 2.86/3.07 % le_infI2
% 2.86/3.07 thf(fact_1655_le__infI2,axiom,
% 2.86/3.07 ! [B2: nat,X: nat,A2: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ B2 @ X )
% 2.86/3.07 => ( ord_less_eq_nat @ ( inf_inf_nat @ A2 @ B2 ) @ X ) ) ).
% 2.86/3.07
% 2.86/3.07 % le_infI2
% 2.86/3.07 thf(fact_1656_le__infI2,axiom,
% 2.86/3.07 ! [B2: int,X: int,A2: int] :
% 2.86/3.07 ( ( ord_less_eq_int @ B2 @ X )
% 2.86/3.07 => ( ord_less_eq_int @ ( inf_inf_int @ A2 @ B2 ) @ X ) ) ).
% 2.86/3.07
% 2.86/3.07 % le_infI2
% 2.86/3.07 thf(fact_1657_inf_Oassoc,axiom,
% 2.86/3.07 ! [A2: assn,B2: assn,C: assn] :
% 2.86/3.07 ( ( inf_inf_assn @ ( inf_inf_assn @ A2 @ B2 ) @ C )
% 2.86/3.07 = ( inf_inf_assn @ A2 @ ( inf_inf_assn @ B2 @ C ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.assoc
% 2.86/3.07 thf(fact_1658_inf_Oassoc,axiom,
% 2.86/3.07 ! [A2: set_nat,B2: set_nat,C: set_nat] :
% 2.86/3.07 ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ C )
% 2.86/3.07 = ( inf_inf_set_nat @ A2 @ ( inf_inf_set_nat @ B2 @ C ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.assoc
% 2.86/3.07 thf(fact_1659_inf_Oassoc,axiom,
% 2.86/3.07 ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat] :
% 2.86/3.07 ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) @ C )
% 2.86/3.07 = ( inf_in2572325071724192079at_nat @ A2 @ ( inf_in2572325071724192079at_nat @ B2 @ C ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.assoc
% 2.86/3.07 thf(fact_1660_inf__assoc,axiom,
% 2.86/3.07 ! [X: assn,Y: assn,Z: assn] :
% 2.86/3.07 ( ( inf_inf_assn @ ( inf_inf_assn @ X @ Y ) @ Z )
% 2.86/3.07 = ( inf_inf_assn @ X @ ( inf_inf_assn @ Y @ Z ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_assoc
% 2.86/3.07 thf(fact_1661_inf__assoc,axiom,
% 2.86/3.07 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 2.86/3.07 ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Z )
% 2.86/3.07 = ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_assoc
% 2.86/3.07 thf(fact_1662_inf__assoc,axiom,
% 2.86/3.07 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 2.86/3.07 ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Z )
% 2.86/3.07 = ( inf_in2572325071724192079at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_assoc
% 2.86/3.07 thf(fact_1663_inf_OorderE,axiom,
% 2.86/3.07 ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 2.86/3.07 ( ( ord_le3146513528884898305at_nat @ A2 @ B2 )
% 2.86/3.07 => ( A2
% 2.86/3.07 = ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.orderE
% 2.86/3.07 thf(fact_1664_inf_OorderE,axiom,
% 2.86/3.07 ! [A2: assn,B2: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ A2 @ B2 )
% 2.86/3.07 => ( A2
% 2.86/3.07 = ( inf_inf_assn @ A2 @ B2 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.orderE
% 2.86/3.07 thf(fact_1665_inf_OorderE,axiom,
% 2.86/3.07 ! [A2: filter_nat,B2: filter_nat] :
% 2.86/3.07 ( ( ord_le2510731241096832064er_nat @ A2 @ B2 )
% 2.86/3.07 => ( A2
% 2.86/3.07 = ( inf_inf_filter_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.orderE
% 2.86/3.07 thf(fact_1666_inf_OorderE,axiom,
% 2.86/3.07 ! [A2: set_nat,B2: set_nat] :
% 2.86/3.07 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 2.86/3.07 => ( A2
% 2.86/3.07 = ( inf_inf_set_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.orderE
% 2.86/3.07 thf(fact_1667_inf_OorderE,axiom,
% 2.86/3.07 ! [A2: nat,B2: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.07 => ( A2
% 2.86/3.07 = ( inf_inf_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.orderE
% 2.86/3.07 thf(fact_1668_inf_OorderE,axiom,
% 2.86/3.07 ! [A2: int,B2: int] :
% 2.86/3.07 ( ( ord_less_eq_int @ A2 @ B2 )
% 2.86/3.07 => ( A2
% 2.86/3.07 = ( inf_inf_int @ A2 @ B2 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.orderE
% 2.86/3.07 thf(fact_1669_inf_OorderI,axiom,
% 2.86/3.07 ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 2.86/3.07 ( ( A2
% 2.86/3.07 = ( inf_in2572325071724192079at_nat @ A2 @ B2 ) )
% 2.86/3.07 => ( ord_le3146513528884898305at_nat @ A2 @ B2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.orderI
% 2.86/3.07 thf(fact_1670_inf_OorderI,axiom,
% 2.86/3.07 ! [A2: assn,B2: assn] :
% 2.86/3.07 ( ( A2
% 2.86/3.07 = ( inf_inf_assn @ A2 @ B2 ) )
% 2.86/3.07 => ( ord_less_eq_assn @ A2 @ B2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.orderI
% 2.86/3.07 thf(fact_1671_inf_OorderI,axiom,
% 2.86/3.07 ! [A2: filter_nat,B2: filter_nat] :
% 2.86/3.07 ( ( A2
% 2.86/3.07 = ( inf_inf_filter_nat @ A2 @ B2 ) )
% 2.86/3.07 => ( ord_le2510731241096832064er_nat @ A2 @ B2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.orderI
% 2.86/3.07 thf(fact_1672_inf_OorderI,axiom,
% 2.86/3.07 ! [A2: set_nat,B2: set_nat] :
% 2.86/3.07 ( ( A2
% 2.86/3.07 = ( inf_inf_set_nat @ A2 @ B2 ) )
% 2.86/3.07 => ( ord_less_eq_set_nat @ A2 @ B2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.orderI
% 2.86/3.07 thf(fact_1673_inf_OorderI,axiom,
% 2.86/3.07 ! [A2: nat,B2: nat] :
% 2.86/3.07 ( ( A2
% 2.86/3.07 = ( inf_inf_nat @ A2 @ B2 ) )
% 2.86/3.07 => ( ord_less_eq_nat @ A2 @ B2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.orderI
% 2.86/3.07 thf(fact_1674_inf_OorderI,axiom,
% 2.86/3.07 ! [A2: int,B2: int] :
% 2.86/3.07 ( ( A2
% 2.86/3.07 = ( inf_inf_int @ A2 @ B2 ) )
% 2.86/3.07 => ( ord_less_eq_int @ A2 @ B2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.orderI
% 2.86/3.07 thf(fact_1675_inf__unique,axiom,
% 2.86/3.07 ! [F4: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 2.86/3.07 ( ! [X3: set_Pr1261947904930325089at_nat,Y2: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( F4 @ X3 @ Y2 ) @ X3 )
% 2.86/3.07 => ( ! [X3: set_Pr1261947904930325089at_nat,Y2: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( F4 @ X3 @ Y2 ) @ Y2 )
% 2.86/3.07 => ( ! [X3: set_Pr1261947904930325089at_nat,Y2: set_Pr1261947904930325089at_nat,Z4: set_Pr1261947904930325089at_nat] :
% 2.86/3.07 ( ( ord_le3146513528884898305at_nat @ X3 @ Y2 )
% 2.86/3.07 => ( ( ord_le3146513528884898305at_nat @ X3 @ Z4 )
% 2.86/3.07 => ( ord_le3146513528884898305at_nat @ X3 @ ( F4 @ Y2 @ Z4 ) ) ) )
% 2.86/3.07 => ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 2.86/3.07 = ( F4 @ X @ Y ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_unique
% 2.86/3.07 thf(fact_1676_inf__unique,axiom,
% 2.86/3.07 ! [F4: assn > assn > assn,X: assn,Y: assn] :
% 2.86/3.07 ( ! [X3: assn,Y2: assn] : ( ord_less_eq_assn @ ( F4 @ X3 @ Y2 ) @ X3 )
% 2.86/3.07 => ( ! [X3: assn,Y2: assn] : ( ord_less_eq_assn @ ( F4 @ X3 @ Y2 ) @ Y2 )
% 2.86/3.07 => ( ! [X3: assn,Y2: assn,Z4: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ X3 @ Y2 )
% 2.86/3.07 => ( ( ord_less_eq_assn @ X3 @ Z4 )
% 2.86/3.07 => ( ord_less_eq_assn @ X3 @ ( F4 @ Y2 @ Z4 ) ) ) )
% 2.86/3.07 => ( ( inf_inf_assn @ X @ Y )
% 2.86/3.07 = ( F4 @ X @ Y ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_unique
% 2.86/3.07 thf(fact_1677_inf__unique,axiom,
% 2.86/3.07 ! [F4: filter_nat > filter_nat > filter_nat,X: filter_nat,Y: filter_nat] :
% 2.86/3.07 ( ! [X3: filter_nat,Y2: filter_nat] : ( ord_le2510731241096832064er_nat @ ( F4 @ X3 @ Y2 ) @ X3 )
% 2.86/3.07 => ( ! [X3: filter_nat,Y2: filter_nat] : ( ord_le2510731241096832064er_nat @ ( F4 @ X3 @ Y2 ) @ Y2 )
% 2.86/3.07 => ( ! [X3: filter_nat,Y2: filter_nat,Z4: filter_nat] :
% 2.86/3.07 ( ( ord_le2510731241096832064er_nat @ X3 @ Y2 )
% 2.86/3.07 => ( ( ord_le2510731241096832064er_nat @ X3 @ Z4 )
% 2.86/3.07 => ( ord_le2510731241096832064er_nat @ X3 @ ( F4 @ Y2 @ Z4 ) ) ) )
% 2.86/3.07 => ( ( inf_inf_filter_nat @ X @ Y )
% 2.86/3.07 = ( F4 @ X @ Y ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_unique
% 2.86/3.07 thf(fact_1678_inf__unique,axiom,
% 2.86/3.07 ! [F4: set_nat > set_nat > set_nat,X: set_nat,Y: set_nat] :
% 2.86/3.07 ( ! [X3: set_nat,Y2: set_nat] : ( ord_less_eq_set_nat @ ( F4 @ X3 @ Y2 ) @ X3 )
% 2.86/3.07 => ( ! [X3: set_nat,Y2: set_nat] : ( ord_less_eq_set_nat @ ( F4 @ X3 @ Y2 ) @ Y2 )
% 2.86/3.07 => ( ! [X3: set_nat,Y2: set_nat,Z4: set_nat] :
% 2.86/3.07 ( ( ord_less_eq_set_nat @ X3 @ Y2 )
% 2.86/3.07 => ( ( ord_less_eq_set_nat @ X3 @ Z4 )
% 2.86/3.07 => ( ord_less_eq_set_nat @ X3 @ ( F4 @ Y2 @ Z4 ) ) ) )
% 2.86/3.07 => ( ( inf_inf_set_nat @ X @ Y )
% 2.86/3.07 = ( F4 @ X @ Y ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_unique
% 2.86/3.07 thf(fact_1679_inf__unique,axiom,
% 2.86/3.07 ! [F4: nat > nat > nat,X: nat,Y: nat] :
% 2.86/3.07 ( ! [X3: nat,Y2: nat] : ( ord_less_eq_nat @ ( F4 @ X3 @ Y2 ) @ X3 )
% 2.86/3.07 => ( ! [X3: nat,Y2: nat] : ( ord_less_eq_nat @ ( F4 @ X3 @ Y2 ) @ Y2 )
% 2.86/3.07 => ( ! [X3: nat,Y2: nat,Z4: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 2.86/3.07 => ( ( ord_less_eq_nat @ X3 @ Z4 )
% 2.86/3.07 => ( ord_less_eq_nat @ X3 @ ( F4 @ Y2 @ Z4 ) ) ) )
% 2.86/3.07 => ( ( inf_inf_nat @ X @ Y )
% 2.86/3.07 = ( F4 @ X @ Y ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_unique
% 2.86/3.07 thf(fact_1680_inf__unique,axiom,
% 2.86/3.07 ! [F4: int > int > int,X: int,Y: int] :
% 2.86/3.07 ( ! [X3: int,Y2: int] : ( ord_less_eq_int @ ( F4 @ X3 @ Y2 ) @ X3 )
% 2.86/3.07 => ( ! [X3: int,Y2: int] : ( ord_less_eq_int @ ( F4 @ X3 @ Y2 ) @ Y2 )
% 2.86/3.07 => ( ! [X3: int,Y2: int,Z4: int] :
% 2.86/3.07 ( ( ord_less_eq_int @ X3 @ Y2 )
% 2.86/3.07 => ( ( ord_less_eq_int @ X3 @ Z4 )
% 2.86/3.07 => ( ord_less_eq_int @ X3 @ ( F4 @ Y2 @ Z4 ) ) ) )
% 2.86/3.07 => ( ( inf_inf_int @ X @ Y )
% 2.86/3.07 = ( F4 @ X @ Y ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_unique
% 2.86/3.07 thf(fact_1681_le__iff__inf,axiom,
% 2.86/3.07 ( ord_le3146513528884898305at_nat
% 2.86/3.07 = ( ^ [X2: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] :
% 2.86/3.07 ( ( inf_in2572325071724192079at_nat @ X2 @ Y5 )
% 2.86/3.07 = X2 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % le_iff_inf
% 2.86/3.07 thf(fact_1682_le__iff__inf,axiom,
% 2.86/3.07 ( ord_less_eq_assn
% 2.86/3.07 = ( ^ [X2: assn,Y5: assn] :
% 2.86/3.07 ( ( inf_inf_assn @ X2 @ Y5 )
% 2.86/3.07 = X2 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % le_iff_inf
% 2.86/3.07 thf(fact_1683_le__iff__inf,axiom,
% 2.86/3.07 ( ord_le2510731241096832064er_nat
% 2.86/3.07 = ( ^ [X2: filter_nat,Y5: filter_nat] :
% 2.86/3.07 ( ( inf_inf_filter_nat @ X2 @ Y5 )
% 2.86/3.07 = X2 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % le_iff_inf
% 2.86/3.07 thf(fact_1684_le__iff__inf,axiom,
% 2.86/3.07 ( ord_less_eq_set_nat
% 2.86/3.07 = ( ^ [X2: set_nat,Y5: set_nat] :
% 2.86/3.07 ( ( inf_inf_set_nat @ X2 @ Y5 )
% 2.86/3.07 = X2 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % le_iff_inf
% 2.86/3.07 thf(fact_1685_le__iff__inf,axiom,
% 2.86/3.07 ( ord_less_eq_nat
% 2.86/3.07 = ( ^ [X2: nat,Y5: nat] :
% 2.86/3.07 ( ( inf_inf_nat @ X2 @ Y5 )
% 2.86/3.07 = X2 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % le_iff_inf
% 2.86/3.07 thf(fact_1686_le__iff__inf,axiom,
% 2.86/3.07 ( ord_less_eq_int
% 2.86/3.07 = ( ^ [X2: int,Y5: int] :
% 2.86/3.07 ( ( inf_inf_int @ X2 @ Y5 )
% 2.86/3.07 = X2 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % le_iff_inf
% 2.86/3.07 thf(fact_1687_inf_Oabsorb1,axiom,
% 2.86/3.07 ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 2.86/3.07 ( ( ord_le3146513528884898305at_nat @ A2 @ B2 )
% 2.86/3.07 => ( ( inf_in2572325071724192079at_nat @ A2 @ B2 )
% 2.86/3.07 = A2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.absorb1
% 2.86/3.07 thf(fact_1688_inf_Oabsorb1,axiom,
% 2.86/3.07 ! [A2: assn,B2: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ A2 @ B2 )
% 2.86/3.07 => ( ( inf_inf_assn @ A2 @ B2 )
% 2.86/3.07 = A2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.absorb1
% 2.86/3.07 thf(fact_1689_inf_Oabsorb1,axiom,
% 2.86/3.07 ! [A2: filter_nat,B2: filter_nat] :
% 2.86/3.07 ( ( ord_le2510731241096832064er_nat @ A2 @ B2 )
% 2.86/3.07 => ( ( inf_inf_filter_nat @ A2 @ B2 )
% 2.86/3.07 = A2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.absorb1
% 2.86/3.07 thf(fact_1690_inf_Oabsorb1,axiom,
% 2.86/3.07 ! [A2: set_nat,B2: set_nat] :
% 2.86/3.07 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 2.86/3.07 => ( ( inf_inf_set_nat @ A2 @ B2 )
% 2.86/3.07 = A2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.absorb1
% 2.86/3.07 thf(fact_1691_inf_Oabsorb1,axiom,
% 2.86/3.07 ! [A2: nat,B2: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.07 => ( ( inf_inf_nat @ A2 @ B2 )
% 2.86/3.07 = A2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.absorb1
% 2.86/3.07 thf(fact_1692_inf_Oabsorb1,axiom,
% 2.86/3.07 ! [A2: int,B2: int] :
% 2.86/3.07 ( ( ord_less_eq_int @ A2 @ B2 )
% 2.86/3.07 => ( ( inf_inf_int @ A2 @ B2 )
% 2.86/3.07 = A2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.absorb1
% 2.86/3.07 thf(fact_1693_inf_Oabsorb2,axiom,
% 2.86/3.07 ! [B2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 2.86/3.07 ( ( ord_le3146513528884898305at_nat @ B2 @ A2 )
% 2.86/3.07 => ( ( inf_in2572325071724192079at_nat @ A2 @ B2 )
% 2.86/3.07 = B2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.absorb2
% 2.86/3.07 thf(fact_1694_inf_Oabsorb2,axiom,
% 2.86/3.07 ! [B2: assn,A2: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ B2 @ A2 )
% 2.86/3.07 => ( ( inf_inf_assn @ A2 @ B2 )
% 2.86/3.07 = B2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.absorb2
% 2.86/3.07 thf(fact_1695_inf_Oabsorb2,axiom,
% 2.86/3.07 ! [B2: filter_nat,A2: filter_nat] :
% 2.86/3.07 ( ( ord_le2510731241096832064er_nat @ B2 @ A2 )
% 2.86/3.07 => ( ( inf_inf_filter_nat @ A2 @ B2 )
% 2.86/3.07 = B2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.absorb2
% 2.86/3.07 thf(fact_1696_inf_Oabsorb2,axiom,
% 2.86/3.07 ! [B2: set_nat,A2: set_nat] :
% 2.86/3.07 ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 2.86/3.07 => ( ( inf_inf_set_nat @ A2 @ B2 )
% 2.86/3.07 = B2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.absorb2
% 2.86/3.07 thf(fact_1697_inf_Oabsorb2,axiom,
% 2.86/3.07 ! [B2: nat,A2: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ B2 @ A2 )
% 2.86/3.07 => ( ( inf_inf_nat @ A2 @ B2 )
% 2.86/3.07 = B2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.absorb2
% 2.86/3.07 thf(fact_1698_inf_Oabsorb2,axiom,
% 2.86/3.07 ! [B2: int,A2: int] :
% 2.86/3.07 ( ( ord_less_eq_int @ B2 @ A2 )
% 2.86/3.07 => ( ( inf_inf_int @ A2 @ B2 )
% 2.86/3.07 = B2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.absorb2
% 2.86/3.07 thf(fact_1699_inf_Ocommute,axiom,
% 2.86/3.07 ( inf_inf_assn
% 2.86/3.07 = ( ^ [A3: assn,B3: assn] : ( inf_inf_assn @ B3 @ A3 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.commute
% 2.86/3.07 thf(fact_1700_inf_Ocommute,axiom,
% 2.86/3.07 ( inf_inf_set_nat
% 2.86/3.07 = ( ^ [A3: set_nat,B3: set_nat] : ( inf_inf_set_nat @ B3 @ A3 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.commute
% 2.86/3.07 thf(fact_1701_inf_Ocommute,axiom,
% 2.86/3.07 ( inf_in2572325071724192079at_nat
% 2.86/3.07 = ( ^ [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] : ( inf_in2572325071724192079at_nat @ B3 @ A3 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.commute
% 2.86/3.07 thf(fact_1702_inf__absorb1,axiom,
% 2.86/3.07 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 2.86/3.07 ( ( ord_le3146513528884898305at_nat @ X @ Y )
% 2.86/3.07 => ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 2.86/3.07 = X ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_absorb1
% 2.86/3.07 thf(fact_1703_inf__absorb1,axiom,
% 2.86/3.07 ! [X: assn,Y: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ X @ Y )
% 2.86/3.07 => ( ( inf_inf_assn @ X @ Y )
% 2.86/3.07 = X ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_absorb1
% 2.86/3.07 thf(fact_1704_inf__absorb1,axiom,
% 2.86/3.07 ! [X: filter_nat,Y: filter_nat] :
% 2.86/3.07 ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 2.86/3.07 => ( ( inf_inf_filter_nat @ X @ Y )
% 2.86/3.07 = X ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_absorb1
% 2.86/3.07 thf(fact_1705_inf__absorb1,axiom,
% 2.86/3.07 ! [X: set_nat,Y: set_nat] :
% 2.86/3.07 ( ( ord_less_eq_set_nat @ X @ Y )
% 2.86/3.07 => ( ( inf_inf_set_nat @ X @ Y )
% 2.86/3.07 = X ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_absorb1
% 2.86/3.07 thf(fact_1706_inf__absorb1,axiom,
% 2.86/3.07 ! [X: nat,Y: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ X @ Y )
% 2.86/3.07 => ( ( inf_inf_nat @ X @ Y )
% 2.86/3.07 = X ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_absorb1
% 2.86/3.07 thf(fact_1707_inf__absorb1,axiom,
% 2.86/3.07 ! [X: int,Y: int] :
% 2.86/3.07 ( ( ord_less_eq_int @ X @ Y )
% 2.86/3.07 => ( ( inf_inf_int @ X @ Y )
% 2.86/3.07 = X ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_absorb1
% 2.86/3.07 thf(fact_1708_inf__absorb2,axiom,
% 2.86/3.07 ! [Y: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat] :
% 2.86/3.07 ( ( ord_le3146513528884898305at_nat @ Y @ X )
% 2.86/3.07 => ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 2.86/3.07 = Y ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_absorb2
% 2.86/3.07 thf(fact_1709_inf__absorb2,axiom,
% 2.86/3.07 ! [Y: assn,X: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ Y @ X )
% 2.86/3.07 => ( ( inf_inf_assn @ X @ Y )
% 2.86/3.07 = Y ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_absorb2
% 2.86/3.07 thf(fact_1710_inf__absorb2,axiom,
% 2.86/3.07 ! [Y: filter_nat,X: filter_nat] :
% 2.86/3.07 ( ( ord_le2510731241096832064er_nat @ Y @ X )
% 2.86/3.07 => ( ( inf_inf_filter_nat @ X @ Y )
% 2.86/3.07 = Y ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_absorb2
% 2.86/3.07 thf(fact_1711_inf__absorb2,axiom,
% 2.86/3.07 ! [Y: set_nat,X: set_nat] :
% 2.86/3.07 ( ( ord_less_eq_set_nat @ Y @ X )
% 2.86/3.07 => ( ( inf_inf_set_nat @ X @ Y )
% 2.86/3.07 = Y ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_absorb2
% 2.86/3.07 thf(fact_1712_inf__absorb2,axiom,
% 2.86/3.07 ! [Y: nat,X: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ Y @ X )
% 2.86/3.07 => ( ( inf_inf_nat @ X @ Y )
% 2.86/3.07 = Y ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_absorb2
% 2.86/3.07 thf(fact_1713_inf__absorb2,axiom,
% 2.86/3.07 ! [Y: int,X: int] :
% 2.86/3.07 ( ( ord_less_eq_int @ Y @ X )
% 2.86/3.07 => ( ( inf_inf_int @ X @ Y )
% 2.86/3.07 = Y ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_absorb2
% 2.86/3.07 thf(fact_1714_inf__commute,axiom,
% 2.86/3.07 ( inf_inf_assn
% 2.86/3.07 = ( ^ [X2: assn,Y5: assn] : ( inf_inf_assn @ Y5 @ X2 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_commute
% 2.86/3.07 thf(fact_1715_inf__commute,axiom,
% 2.86/3.07 ( inf_inf_set_nat
% 2.86/3.07 = ( ^ [X2: set_nat,Y5: set_nat] : ( inf_inf_set_nat @ Y5 @ X2 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_commute
% 2.86/3.07 thf(fact_1716_inf__commute,axiom,
% 2.86/3.07 ( inf_in2572325071724192079at_nat
% 2.86/3.07 = ( ^ [X2: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat] : ( inf_in2572325071724192079at_nat @ Y5 @ X2 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_commute
% 2.86/3.07 thf(fact_1717_inf_OboundedE,axiom,
% 2.86/3.07 ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat] :
% 2.86/3.07 ( ( ord_le3146513528884898305at_nat @ A2 @ ( inf_in2572325071724192079at_nat @ B2 @ C ) )
% 2.86/3.07 => ~ ( ( ord_le3146513528884898305at_nat @ A2 @ B2 )
% 2.86/3.07 => ~ ( ord_le3146513528884898305at_nat @ A2 @ C ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.boundedE
% 2.86/3.07 thf(fact_1718_inf_OboundedE,axiom,
% 2.86/3.07 ! [A2: assn,B2: assn,C: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ A2 @ ( inf_inf_assn @ B2 @ C ) )
% 2.86/3.07 => ~ ( ( ord_less_eq_assn @ A2 @ B2 )
% 2.86/3.07 => ~ ( ord_less_eq_assn @ A2 @ C ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.boundedE
% 2.86/3.07 thf(fact_1719_inf_OboundedE,axiom,
% 2.86/3.07 ! [A2: filter_nat,B2: filter_nat,C: filter_nat] :
% 2.86/3.07 ( ( ord_le2510731241096832064er_nat @ A2 @ ( inf_inf_filter_nat @ B2 @ C ) )
% 2.86/3.07 => ~ ( ( ord_le2510731241096832064er_nat @ A2 @ B2 )
% 2.86/3.07 => ~ ( ord_le2510731241096832064er_nat @ A2 @ C ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.boundedE
% 2.86/3.07 thf(fact_1720_inf_OboundedE,axiom,
% 2.86/3.07 ! [A2: set_nat,B2: set_nat,C: set_nat] :
% 2.86/3.07 ( ( ord_less_eq_set_nat @ A2 @ ( inf_inf_set_nat @ B2 @ C ) )
% 2.86/3.07 => ~ ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 2.86/3.07 => ~ ( ord_less_eq_set_nat @ A2 @ C ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.boundedE
% 2.86/3.07 thf(fact_1721_inf_OboundedE,axiom,
% 2.86/3.07 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ A2 @ ( inf_inf_nat @ B2 @ C ) )
% 2.86/3.07 => ~ ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.07 => ~ ( ord_less_eq_nat @ A2 @ C ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.boundedE
% 2.86/3.07 thf(fact_1722_inf_OboundedE,axiom,
% 2.86/3.07 ! [A2: int,B2: int,C: int] :
% 2.86/3.07 ( ( ord_less_eq_int @ A2 @ ( inf_inf_int @ B2 @ C ) )
% 2.86/3.07 => ~ ( ( ord_less_eq_int @ A2 @ B2 )
% 2.86/3.07 => ~ ( ord_less_eq_int @ A2 @ C ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.boundedE
% 2.86/3.07 thf(fact_1723_inf_OboundedI,axiom,
% 2.86/3.07 ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat] :
% 2.86/3.07 ( ( ord_le3146513528884898305at_nat @ A2 @ B2 )
% 2.86/3.07 => ( ( ord_le3146513528884898305at_nat @ A2 @ C )
% 2.86/3.07 => ( ord_le3146513528884898305at_nat @ A2 @ ( inf_in2572325071724192079at_nat @ B2 @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.boundedI
% 2.86/3.07 thf(fact_1724_inf_OboundedI,axiom,
% 2.86/3.07 ! [A2: assn,B2: assn,C: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ A2 @ B2 )
% 2.86/3.07 => ( ( ord_less_eq_assn @ A2 @ C )
% 2.86/3.07 => ( ord_less_eq_assn @ A2 @ ( inf_inf_assn @ B2 @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.boundedI
% 2.86/3.07 thf(fact_1725_inf_OboundedI,axiom,
% 2.86/3.07 ! [A2: filter_nat,B2: filter_nat,C: filter_nat] :
% 2.86/3.07 ( ( ord_le2510731241096832064er_nat @ A2 @ B2 )
% 2.86/3.07 => ( ( ord_le2510731241096832064er_nat @ A2 @ C )
% 2.86/3.07 => ( ord_le2510731241096832064er_nat @ A2 @ ( inf_inf_filter_nat @ B2 @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.boundedI
% 2.86/3.07 thf(fact_1726_inf_OboundedI,axiom,
% 2.86/3.07 ! [A2: set_nat,B2: set_nat,C: set_nat] :
% 2.86/3.07 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 2.86/3.07 => ( ( ord_less_eq_set_nat @ A2 @ C )
% 2.86/3.07 => ( ord_less_eq_set_nat @ A2 @ ( inf_inf_set_nat @ B2 @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.boundedI
% 2.86/3.07 thf(fact_1727_inf_OboundedI,axiom,
% 2.86/3.07 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.07 => ( ( ord_less_eq_nat @ A2 @ C )
% 2.86/3.07 => ( ord_less_eq_nat @ A2 @ ( inf_inf_nat @ B2 @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.boundedI
% 2.86/3.07 thf(fact_1728_inf_OboundedI,axiom,
% 2.86/3.07 ! [A2: int,B2: int,C: int] :
% 2.86/3.07 ( ( ord_less_eq_int @ A2 @ B2 )
% 2.86/3.07 => ( ( ord_less_eq_int @ A2 @ C )
% 2.86/3.07 => ( ord_less_eq_int @ A2 @ ( inf_inf_int @ B2 @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.boundedI
% 2.86/3.07 thf(fact_1729_inf__greatest,axiom,
% 2.86/3.07 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 2.86/3.07 ( ( ord_le3146513528884898305at_nat @ X @ Y )
% 2.86/3.07 => ( ( ord_le3146513528884898305at_nat @ X @ Z )
% 2.86/3.07 => ( ord_le3146513528884898305at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_greatest
% 2.86/3.07 thf(fact_1730_inf__greatest,axiom,
% 2.86/3.07 ! [X: assn,Y: assn,Z: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ X @ Y )
% 2.86/3.07 => ( ( ord_less_eq_assn @ X @ Z )
% 2.86/3.07 => ( ord_less_eq_assn @ X @ ( inf_inf_assn @ Y @ Z ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_greatest
% 2.86/3.07 thf(fact_1731_inf__greatest,axiom,
% 2.86/3.07 ! [X: filter_nat,Y: filter_nat,Z: filter_nat] :
% 2.86/3.07 ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 2.86/3.07 => ( ( ord_le2510731241096832064er_nat @ X @ Z )
% 2.86/3.07 => ( ord_le2510731241096832064er_nat @ X @ ( inf_inf_filter_nat @ Y @ Z ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_greatest
% 2.86/3.07 thf(fact_1732_inf__greatest,axiom,
% 2.86/3.07 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 2.86/3.07 ( ( ord_less_eq_set_nat @ X @ Y )
% 2.86/3.07 => ( ( ord_less_eq_set_nat @ X @ Z )
% 2.86/3.07 => ( ord_less_eq_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_greatest
% 2.86/3.07 thf(fact_1733_inf__greatest,axiom,
% 2.86/3.07 ! [X: nat,Y: nat,Z: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ X @ Y )
% 2.86/3.07 => ( ( ord_less_eq_nat @ X @ Z )
% 2.86/3.07 => ( ord_less_eq_nat @ X @ ( inf_inf_nat @ Y @ Z ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_greatest
% 2.86/3.07 thf(fact_1734_inf__greatest,axiom,
% 2.86/3.07 ! [X: int,Y: int,Z: int] :
% 2.86/3.07 ( ( ord_less_eq_int @ X @ Y )
% 2.86/3.07 => ( ( ord_less_eq_int @ X @ Z )
% 2.86/3.07 => ( ord_less_eq_int @ X @ ( inf_inf_int @ Y @ Z ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_greatest
% 2.86/3.07 thf(fact_1735_inf_Oorder__iff,axiom,
% 2.86/3.07 ( ord_le3146513528884898305at_nat
% 2.86/3.07 = ( ^ [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.86/3.07 ( A3
% 2.86/3.07 = ( inf_in2572325071724192079at_nat @ A3 @ B3 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.order_iff
% 2.86/3.07 thf(fact_1736_inf_Oorder__iff,axiom,
% 2.86/3.07 ( ord_less_eq_assn
% 2.86/3.07 = ( ^ [A3: assn,B3: assn] :
% 2.86/3.07 ( A3
% 2.86/3.07 = ( inf_inf_assn @ A3 @ B3 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.order_iff
% 2.86/3.07 thf(fact_1737_inf_Oorder__iff,axiom,
% 2.86/3.07 ( ord_le2510731241096832064er_nat
% 2.86/3.07 = ( ^ [A3: filter_nat,B3: filter_nat] :
% 2.86/3.07 ( A3
% 2.86/3.07 = ( inf_inf_filter_nat @ A3 @ B3 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.order_iff
% 2.86/3.07 thf(fact_1738_inf_Oorder__iff,axiom,
% 2.86/3.07 ( ord_less_eq_set_nat
% 2.86/3.07 = ( ^ [A3: set_nat,B3: set_nat] :
% 2.86/3.07 ( A3
% 2.86/3.07 = ( inf_inf_set_nat @ A3 @ B3 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.order_iff
% 2.86/3.07 thf(fact_1739_inf_Oorder__iff,axiom,
% 2.86/3.07 ( ord_less_eq_nat
% 2.86/3.07 = ( ^ [A3: nat,B3: nat] :
% 2.86/3.07 ( A3
% 2.86/3.07 = ( inf_inf_nat @ A3 @ B3 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.order_iff
% 2.86/3.07 thf(fact_1740_inf_Oorder__iff,axiom,
% 2.86/3.07 ( ord_less_eq_int
% 2.86/3.07 = ( ^ [A3: int,B3: int] :
% 2.86/3.07 ( A3
% 2.86/3.07 = ( inf_inf_int @ A3 @ B3 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.order_iff
% 2.86/3.07 thf(fact_1741_inf_Ocobounded1,axiom,
% 2.86/3.07 ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) @ A2 ) ).
% 2.86/3.07
% 2.86/3.07 % inf.cobounded1
% 2.86/3.07 thf(fact_1742_inf_Ocobounded1,axiom,
% 2.86/3.07 ! [A2: assn,B2: assn] : ( ord_less_eq_assn @ ( inf_inf_assn @ A2 @ B2 ) @ A2 ) ).
% 2.86/3.07
% 2.86/3.07 % inf.cobounded1
% 2.86/3.07 thf(fact_1743_inf_Ocobounded1,axiom,
% 2.86/3.07 ! [A2: filter_nat,B2: filter_nat] : ( ord_le2510731241096832064er_nat @ ( inf_inf_filter_nat @ A2 @ B2 ) @ A2 ) ).
% 2.86/3.07
% 2.86/3.07 % inf.cobounded1
% 2.86/3.07 thf(fact_1744_inf_Ocobounded1,axiom,
% 2.86/3.07 ! [A2: set_nat,B2: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ A2 ) ).
% 2.86/3.07
% 2.86/3.07 % inf.cobounded1
% 2.86/3.07 thf(fact_1745_inf_Ocobounded1,axiom,
% 2.86/3.07 ! [A2: nat,B2: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ A2 @ B2 ) @ A2 ) ).
% 2.86/3.07
% 2.86/3.07 % inf.cobounded1
% 2.86/3.07 thf(fact_1746_inf_Ocobounded1,axiom,
% 2.86/3.07 ! [A2: int,B2: int] : ( ord_less_eq_int @ ( inf_inf_int @ A2 @ B2 ) @ A2 ) ).
% 2.86/3.07
% 2.86/3.07 % inf.cobounded1
% 2.86/3.07 thf(fact_1747_inf_Ocobounded2,axiom,
% 2.86/3.07 ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) @ B2 ) ).
% 2.86/3.07
% 2.86/3.07 % inf.cobounded2
% 2.86/3.07 thf(fact_1748_inf_Ocobounded2,axiom,
% 2.86/3.07 ! [A2: assn,B2: assn] : ( ord_less_eq_assn @ ( inf_inf_assn @ A2 @ B2 ) @ B2 ) ).
% 2.86/3.07
% 2.86/3.07 % inf.cobounded2
% 2.86/3.07 thf(fact_1749_inf_Ocobounded2,axiom,
% 2.86/3.07 ! [A2: filter_nat,B2: filter_nat] : ( ord_le2510731241096832064er_nat @ ( inf_inf_filter_nat @ A2 @ B2 ) @ B2 ) ).
% 2.86/3.07
% 2.86/3.07 % inf.cobounded2
% 2.86/3.07 thf(fact_1750_inf_Ocobounded2,axiom,
% 2.86/3.07 ! [A2: set_nat,B2: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ B2 ) ).
% 2.86/3.07
% 2.86/3.07 % inf.cobounded2
% 2.86/3.07 thf(fact_1751_inf_Ocobounded2,axiom,
% 2.86/3.07 ! [A2: nat,B2: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ A2 @ B2 ) @ B2 ) ).
% 2.86/3.07
% 2.86/3.07 % inf.cobounded2
% 2.86/3.07 thf(fact_1752_inf_Ocobounded2,axiom,
% 2.86/3.07 ! [A2: int,B2: int] : ( ord_less_eq_int @ ( inf_inf_int @ A2 @ B2 ) @ B2 ) ).
% 2.86/3.07
% 2.86/3.07 % inf.cobounded2
% 2.86/3.07 thf(fact_1753_inf_Oabsorb__iff1,axiom,
% 2.86/3.07 ( ord_le3146513528884898305at_nat
% 2.86/3.07 = ( ^ [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.86/3.07 ( ( inf_in2572325071724192079at_nat @ A3 @ B3 )
% 2.86/3.07 = A3 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.absorb_iff1
% 2.86/3.07 thf(fact_1754_inf_Oabsorb__iff1,axiom,
% 2.86/3.07 ( ord_less_eq_assn
% 2.86/3.07 = ( ^ [A3: assn,B3: assn] :
% 2.86/3.07 ( ( inf_inf_assn @ A3 @ B3 )
% 2.86/3.07 = A3 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.absorb_iff1
% 2.86/3.07 thf(fact_1755_inf_Oabsorb__iff1,axiom,
% 2.86/3.07 ( ord_le2510731241096832064er_nat
% 2.86/3.07 = ( ^ [A3: filter_nat,B3: filter_nat] :
% 2.86/3.07 ( ( inf_inf_filter_nat @ A3 @ B3 )
% 2.86/3.07 = A3 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.absorb_iff1
% 2.86/3.07 thf(fact_1756_inf_Oabsorb__iff1,axiom,
% 2.86/3.07 ( ord_less_eq_set_nat
% 2.86/3.07 = ( ^ [A3: set_nat,B3: set_nat] :
% 2.86/3.07 ( ( inf_inf_set_nat @ A3 @ B3 )
% 2.86/3.07 = A3 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.absorb_iff1
% 2.86/3.07 thf(fact_1757_inf_Oabsorb__iff1,axiom,
% 2.86/3.07 ( ord_less_eq_nat
% 2.86/3.07 = ( ^ [A3: nat,B3: nat] :
% 2.86/3.07 ( ( inf_inf_nat @ A3 @ B3 )
% 2.86/3.07 = A3 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.absorb_iff1
% 2.86/3.07 thf(fact_1758_inf_Oabsorb__iff1,axiom,
% 2.86/3.07 ( ord_less_eq_int
% 2.86/3.07 = ( ^ [A3: int,B3: int] :
% 2.86/3.07 ( ( inf_inf_int @ A3 @ B3 )
% 2.86/3.07 = A3 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.absorb_iff1
% 2.86/3.07 thf(fact_1759_inf_Oabsorb__iff2,axiom,
% 2.86/3.07 ( ord_le3146513528884898305at_nat
% 2.86/3.07 = ( ^ [B3: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat] :
% 2.86/3.07 ( ( inf_in2572325071724192079at_nat @ A3 @ B3 )
% 2.86/3.07 = B3 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.absorb_iff2
% 2.86/3.07 thf(fact_1760_inf_Oabsorb__iff2,axiom,
% 2.86/3.07 ( ord_less_eq_assn
% 2.86/3.07 = ( ^ [B3: assn,A3: assn] :
% 2.86/3.07 ( ( inf_inf_assn @ A3 @ B3 )
% 2.86/3.07 = B3 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.absorb_iff2
% 2.86/3.07 thf(fact_1761_inf_Oabsorb__iff2,axiom,
% 2.86/3.07 ( ord_le2510731241096832064er_nat
% 2.86/3.07 = ( ^ [B3: filter_nat,A3: filter_nat] :
% 2.86/3.07 ( ( inf_inf_filter_nat @ A3 @ B3 )
% 2.86/3.07 = B3 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.absorb_iff2
% 2.86/3.07 thf(fact_1762_inf_Oabsorb__iff2,axiom,
% 2.86/3.07 ( ord_less_eq_set_nat
% 2.86/3.07 = ( ^ [B3: set_nat,A3: set_nat] :
% 2.86/3.07 ( ( inf_inf_set_nat @ A3 @ B3 )
% 2.86/3.07 = B3 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.absorb_iff2
% 2.86/3.07 thf(fact_1763_inf_Oabsorb__iff2,axiom,
% 2.86/3.07 ( ord_less_eq_nat
% 2.86/3.07 = ( ^ [B3: nat,A3: nat] :
% 2.86/3.07 ( ( inf_inf_nat @ A3 @ B3 )
% 2.86/3.07 = B3 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.absorb_iff2
% 2.86/3.07 thf(fact_1764_inf_Oabsorb__iff2,axiom,
% 2.86/3.07 ( ord_less_eq_int
% 2.86/3.07 = ( ^ [B3: int,A3: int] :
% 2.86/3.07 ( ( inf_inf_int @ A3 @ B3 )
% 2.86/3.07 = B3 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.absorb_iff2
% 2.86/3.07 thf(fact_1765_inf_OcoboundedI1,axiom,
% 2.86/3.07 ! [A2: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 2.86/3.07 ( ( ord_le3146513528884898305at_nat @ A2 @ C )
% 2.86/3.07 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.coboundedI1
% 2.86/3.07 thf(fact_1766_inf_OcoboundedI1,axiom,
% 2.86/3.07 ! [A2: assn,C: assn,B2: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ A2 @ C )
% 2.86/3.07 => ( ord_less_eq_assn @ ( inf_inf_assn @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.coboundedI1
% 2.86/3.07 thf(fact_1767_inf_OcoboundedI1,axiom,
% 2.86/3.07 ! [A2: filter_nat,C: filter_nat,B2: filter_nat] :
% 2.86/3.07 ( ( ord_le2510731241096832064er_nat @ A2 @ C )
% 2.86/3.07 => ( ord_le2510731241096832064er_nat @ ( inf_inf_filter_nat @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.coboundedI1
% 2.86/3.07 thf(fact_1768_inf_OcoboundedI1,axiom,
% 2.86/3.07 ! [A2: set_nat,C: set_nat,B2: set_nat] :
% 2.86/3.07 ( ( ord_less_eq_set_nat @ A2 @ C )
% 2.86/3.07 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.coboundedI1
% 2.86/3.07 thf(fact_1769_inf_OcoboundedI1,axiom,
% 2.86/3.07 ! [A2: nat,C: nat,B2: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ A2 @ C )
% 2.86/3.07 => ( ord_less_eq_nat @ ( inf_inf_nat @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.coboundedI1
% 2.86/3.07 thf(fact_1770_inf_OcoboundedI1,axiom,
% 2.86/3.07 ! [A2: int,C: int,B2: int] :
% 2.86/3.07 ( ( ord_less_eq_int @ A2 @ C )
% 2.86/3.07 => ( ord_less_eq_int @ ( inf_inf_int @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.coboundedI1
% 2.86/3.07 thf(fact_1771_inf_OcoboundedI2,axiom,
% 2.86/3.07 ! [B2: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 2.86/3.07 ( ( ord_le3146513528884898305at_nat @ B2 @ C )
% 2.86/3.07 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.coboundedI2
% 2.86/3.07 thf(fact_1772_inf_OcoboundedI2,axiom,
% 2.86/3.07 ! [B2: assn,C: assn,A2: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ B2 @ C )
% 2.86/3.07 => ( ord_less_eq_assn @ ( inf_inf_assn @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.coboundedI2
% 2.86/3.07 thf(fact_1773_inf_OcoboundedI2,axiom,
% 2.86/3.07 ! [B2: filter_nat,C: filter_nat,A2: filter_nat] :
% 2.86/3.07 ( ( ord_le2510731241096832064er_nat @ B2 @ C )
% 2.86/3.07 => ( ord_le2510731241096832064er_nat @ ( inf_inf_filter_nat @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.coboundedI2
% 2.86/3.07 thf(fact_1774_inf_OcoboundedI2,axiom,
% 2.86/3.07 ! [B2: set_nat,C: set_nat,A2: set_nat] :
% 2.86/3.07 ( ( ord_less_eq_set_nat @ B2 @ C )
% 2.86/3.07 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.coboundedI2
% 2.86/3.07 thf(fact_1775_inf_OcoboundedI2,axiom,
% 2.86/3.07 ! [B2: nat,C: nat,A2: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ B2 @ C )
% 2.86/3.07 => ( ord_less_eq_nat @ ( inf_inf_nat @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.coboundedI2
% 2.86/3.07 thf(fact_1776_inf_OcoboundedI2,axiom,
% 2.86/3.07 ! [B2: int,C: int,A2: int] :
% 2.86/3.07 ( ( ord_less_eq_int @ B2 @ C )
% 2.86/3.07 => ( ord_less_eq_int @ ( inf_inf_int @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.coboundedI2
% 2.86/3.07 thf(fact_1777_inf_Oleft__commute,axiom,
% 2.86/3.07 ! [B2: assn,A2: assn,C: assn] :
% 2.86/3.07 ( ( inf_inf_assn @ B2 @ ( inf_inf_assn @ A2 @ C ) )
% 2.86/3.07 = ( inf_inf_assn @ A2 @ ( inf_inf_assn @ B2 @ C ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.left_commute
% 2.86/3.07 thf(fact_1778_inf_Oleft__commute,axiom,
% 2.86/3.07 ! [B2: set_nat,A2: set_nat,C: set_nat] :
% 2.86/3.07 ( ( inf_inf_set_nat @ B2 @ ( inf_inf_set_nat @ A2 @ C ) )
% 2.86/3.07 = ( inf_inf_set_nat @ A2 @ ( inf_inf_set_nat @ B2 @ C ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.left_commute
% 2.86/3.07 thf(fact_1779_inf_Oleft__commute,axiom,
% 2.86/3.07 ! [B2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat] :
% 2.86/3.07 ( ( inf_in2572325071724192079at_nat @ B2 @ ( inf_in2572325071724192079at_nat @ A2 @ C ) )
% 2.86/3.07 = ( inf_in2572325071724192079at_nat @ A2 @ ( inf_in2572325071724192079at_nat @ B2 @ C ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.left_commute
% 2.86/3.07 thf(fact_1780_inf__left__commute,axiom,
% 2.86/3.07 ! [X: assn,Y: assn,Z: assn] :
% 2.86/3.07 ( ( inf_inf_assn @ X @ ( inf_inf_assn @ Y @ Z ) )
% 2.86/3.07 = ( inf_inf_assn @ Y @ ( inf_inf_assn @ X @ Z ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_left_commute
% 2.86/3.07 thf(fact_1781_inf__left__commute,axiom,
% 2.86/3.07 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 2.86/3.07 ( ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) )
% 2.86/3.07 = ( inf_inf_set_nat @ Y @ ( inf_inf_set_nat @ X @ Z ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_left_commute
% 2.86/3.07 thf(fact_1782_inf__left__commute,axiom,
% 2.86/3.07 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 2.86/3.07 ( ( inf_in2572325071724192079at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) )
% 2.86/3.07 = ( inf_in2572325071724192079at_nat @ Y @ ( inf_in2572325071724192079at_nat @ X @ Z ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf_left_commute
% 2.86/3.07 thf(fact_1783_inf_Ostrict__coboundedI2,axiom,
% 2.86/3.07 ! [B2: set_nat,C: set_nat,A2: set_nat] :
% 2.86/3.07 ( ( ord_less_set_nat @ B2 @ C )
% 2.86/3.07 => ( ord_less_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.strict_coboundedI2
% 2.86/3.07 thf(fact_1784_inf_Ostrict__coboundedI2,axiom,
% 2.86/3.07 ! [B2: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 2.86/3.07 ( ( ord_le7866589430770878221at_nat @ B2 @ C )
% 2.86/3.07 => ( ord_le7866589430770878221at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.strict_coboundedI2
% 2.86/3.07 thf(fact_1785_inf_Ostrict__coboundedI2,axiom,
% 2.86/3.07 ! [B2: assn,C: assn,A2: assn] :
% 2.86/3.07 ( ( ord_less_assn @ B2 @ C )
% 2.86/3.07 => ( ord_less_assn @ ( inf_inf_assn @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.strict_coboundedI2
% 2.86/3.07 thf(fact_1786_inf_Ostrict__coboundedI2,axiom,
% 2.86/3.07 ! [B2: nat,C: nat,A2: nat] :
% 2.86/3.07 ( ( ord_less_nat @ B2 @ C )
% 2.86/3.07 => ( ord_less_nat @ ( inf_inf_nat @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.strict_coboundedI2
% 2.86/3.07 thf(fact_1787_inf_Ostrict__coboundedI2,axiom,
% 2.86/3.07 ! [B2: int,C: int,A2: int] :
% 2.86/3.07 ( ( ord_less_int @ B2 @ C )
% 2.86/3.07 => ( ord_less_int @ ( inf_inf_int @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.strict_coboundedI2
% 2.86/3.07 thf(fact_1788_inf_Ostrict__coboundedI1,axiom,
% 2.86/3.07 ! [A2: set_nat,C: set_nat,B2: set_nat] :
% 2.86/3.07 ( ( ord_less_set_nat @ A2 @ C )
% 2.86/3.07 => ( ord_less_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.strict_coboundedI1
% 2.86/3.07 thf(fact_1789_inf_Ostrict__coboundedI1,axiom,
% 2.86/3.07 ! [A2: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 2.86/3.07 ( ( ord_le7866589430770878221at_nat @ A2 @ C )
% 2.86/3.07 => ( ord_le7866589430770878221at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.strict_coboundedI1
% 2.86/3.07 thf(fact_1790_inf_Ostrict__coboundedI1,axiom,
% 2.86/3.07 ! [A2: assn,C: assn,B2: assn] :
% 2.86/3.07 ( ( ord_less_assn @ A2 @ C )
% 2.86/3.07 => ( ord_less_assn @ ( inf_inf_assn @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.strict_coboundedI1
% 2.86/3.07 thf(fact_1791_inf_Ostrict__coboundedI1,axiom,
% 2.86/3.07 ! [A2: nat,C: nat,B2: nat] :
% 2.86/3.07 ( ( ord_less_nat @ A2 @ C )
% 2.86/3.07 => ( ord_less_nat @ ( inf_inf_nat @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.strict_coboundedI1
% 2.86/3.07 thf(fact_1792_inf_Ostrict__coboundedI1,axiom,
% 2.86/3.07 ! [A2: int,C: int,B2: int] :
% 2.86/3.07 ( ( ord_less_int @ A2 @ C )
% 2.86/3.07 => ( ord_less_int @ ( inf_inf_int @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.strict_coboundedI1
% 2.86/3.07 thf(fact_1793_inf_Ostrict__order__iff,axiom,
% 2.86/3.07 ( ord_less_set_nat
% 2.86/3.07 = ( ^ [A3: set_nat,B3: set_nat] :
% 2.86/3.07 ( ( A3
% 2.86/3.07 = ( inf_inf_set_nat @ A3 @ B3 ) )
% 2.86/3.07 & ( A3 != B3 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.strict_order_iff
% 2.86/3.07 thf(fact_1794_inf_Ostrict__order__iff,axiom,
% 2.86/3.07 ( ord_le7866589430770878221at_nat
% 2.86/3.07 = ( ^ [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.86/3.07 ( ( A3
% 2.86/3.07 = ( inf_in2572325071724192079at_nat @ A3 @ B3 ) )
% 2.86/3.07 & ( A3 != B3 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.strict_order_iff
% 2.86/3.07 thf(fact_1795_inf_Ostrict__order__iff,axiom,
% 2.86/3.07 ( ord_less_assn
% 2.86/3.07 = ( ^ [A3: assn,B3: assn] :
% 2.86/3.07 ( ( A3
% 2.86/3.07 = ( inf_inf_assn @ A3 @ B3 ) )
% 2.86/3.07 & ( A3 != B3 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.strict_order_iff
% 2.86/3.07 thf(fact_1796_inf_Ostrict__order__iff,axiom,
% 2.86/3.07 ( ord_less_nat
% 2.86/3.07 = ( ^ [A3: nat,B3: nat] :
% 2.86/3.07 ( ( A3
% 2.86/3.07 = ( inf_inf_nat @ A3 @ B3 ) )
% 2.86/3.07 & ( A3 != B3 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.strict_order_iff
% 2.86/3.07 thf(fact_1797_inf_Ostrict__order__iff,axiom,
% 2.86/3.07 ( ord_less_int
% 2.86/3.07 = ( ^ [A3: int,B3: int] :
% 2.86/3.07 ( ( A3
% 2.86/3.07 = ( inf_inf_int @ A3 @ B3 ) )
% 2.86/3.07 & ( A3 != B3 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.strict_order_iff
% 2.86/3.07 thf(fact_1798_inf_Ostrict__boundedE,axiom,
% 2.86/3.07 ! [A2: set_nat,B2: set_nat,C: set_nat] :
% 2.86/3.07 ( ( ord_less_set_nat @ A2 @ ( inf_inf_set_nat @ B2 @ C ) )
% 2.86/3.07 => ~ ( ( ord_less_set_nat @ A2 @ B2 )
% 2.86/3.07 => ~ ( ord_less_set_nat @ A2 @ C ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.strict_boundedE
% 2.86/3.07 thf(fact_1799_inf_Ostrict__boundedE,axiom,
% 2.86/3.07 ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat] :
% 2.86/3.07 ( ( ord_le7866589430770878221at_nat @ A2 @ ( inf_in2572325071724192079at_nat @ B2 @ C ) )
% 2.86/3.07 => ~ ( ( ord_le7866589430770878221at_nat @ A2 @ B2 )
% 2.86/3.07 => ~ ( ord_le7866589430770878221at_nat @ A2 @ C ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.strict_boundedE
% 2.86/3.07 thf(fact_1800_inf_Ostrict__boundedE,axiom,
% 2.86/3.07 ! [A2: assn,B2: assn,C: assn] :
% 2.86/3.07 ( ( ord_less_assn @ A2 @ ( inf_inf_assn @ B2 @ C ) )
% 2.86/3.07 => ~ ( ( ord_less_assn @ A2 @ B2 )
% 2.86/3.07 => ~ ( ord_less_assn @ A2 @ C ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.strict_boundedE
% 2.86/3.07 thf(fact_1801_inf_Ostrict__boundedE,axiom,
% 2.86/3.07 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.07 ( ( ord_less_nat @ A2 @ ( inf_inf_nat @ B2 @ C ) )
% 2.86/3.07 => ~ ( ( ord_less_nat @ A2 @ B2 )
% 2.86/3.07 => ~ ( ord_less_nat @ A2 @ C ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.strict_boundedE
% 2.86/3.07 thf(fact_1802_inf_Ostrict__boundedE,axiom,
% 2.86/3.07 ! [A2: int,B2: int,C: int] :
% 2.86/3.07 ( ( ord_less_int @ A2 @ ( inf_inf_int @ B2 @ C ) )
% 2.86/3.07 => ~ ( ( ord_less_int @ A2 @ B2 )
% 2.86/3.07 => ~ ( ord_less_int @ A2 @ C ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.strict_boundedE
% 2.86/3.07 thf(fact_1803_inf_Oabsorb4,axiom,
% 2.86/3.07 ! [B2: set_nat,A2: set_nat] :
% 2.86/3.07 ( ( ord_less_set_nat @ B2 @ A2 )
% 2.86/3.07 => ( ( inf_inf_set_nat @ A2 @ B2 )
% 2.86/3.07 = B2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.absorb4
% 2.86/3.07 thf(fact_1804_inf_Oabsorb4,axiom,
% 2.86/3.07 ! [B2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 2.86/3.07 ( ( ord_le7866589430770878221at_nat @ B2 @ A2 )
% 2.86/3.07 => ( ( inf_in2572325071724192079at_nat @ A2 @ B2 )
% 2.86/3.07 = B2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.absorb4
% 2.86/3.07 thf(fact_1805_inf_Oabsorb4,axiom,
% 2.86/3.07 ! [B2: assn,A2: assn] :
% 2.86/3.07 ( ( ord_less_assn @ B2 @ A2 )
% 2.86/3.07 => ( ( inf_inf_assn @ A2 @ B2 )
% 2.86/3.07 = B2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.absorb4
% 2.86/3.07 thf(fact_1806_inf_Oabsorb4,axiom,
% 2.86/3.07 ! [B2: nat,A2: nat] :
% 2.86/3.07 ( ( ord_less_nat @ B2 @ A2 )
% 2.86/3.07 => ( ( inf_inf_nat @ A2 @ B2 )
% 2.86/3.07 = B2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.absorb4
% 2.86/3.07 thf(fact_1807_inf_Oabsorb4,axiom,
% 2.86/3.07 ! [B2: int,A2: int] :
% 2.86/3.07 ( ( ord_less_int @ B2 @ A2 )
% 2.86/3.07 => ( ( inf_inf_int @ A2 @ B2 )
% 2.86/3.07 = B2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.absorb4
% 2.86/3.07 thf(fact_1808_inf_Oabsorb3,axiom,
% 2.86/3.07 ! [A2: set_nat,B2: set_nat] :
% 2.86/3.07 ( ( ord_less_set_nat @ A2 @ B2 )
% 2.86/3.07 => ( ( inf_inf_set_nat @ A2 @ B2 )
% 2.86/3.07 = A2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.absorb3
% 2.86/3.07 thf(fact_1809_inf_Oabsorb3,axiom,
% 2.86/3.07 ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 2.86/3.07 ( ( ord_le7866589430770878221at_nat @ A2 @ B2 )
% 2.86/3.07 => ( ( inf_in2572325071724192079at_nat @ A2 @ B2 )
% 2.86/3.07 = A2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.absorb3
% 2.86/3.07 thf(fact_1810_inf_Oabsorb3,axiom,
% 2.86/3.07 ! [A2: assn,B2: assn] :
% 2.86/3.07 ( ( ord_less_assn @ A2 @ B2 )
% 2.86/3.07 => ( ( inf_inf_assn @ A2 @ B2 )
% 2.86/3.07 = A2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.absorb3
% 2.86/3.07 thf(fact_1811_inf_Oabsorb3,axiom,
% 2.86/3.07 ! [A2: nat,B2: nat] :
% 2.86/3.07 ( ( ord_less_nat @ A2 @ B2 )
% 2.86/3.07 => ( ( inf_inf_nat @ A2 @ B2 )
% 2.86/3.07 = A2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.absorb3
% 2.86/3.07 thf(fact_1812_inf_Oabsorb3,axiom,
% 2.86/3.07 ! [A2: int,B2: int] :
% 2.86/3.07 ( ( ord_less_int @ A2 @ B2 )
% 2.86/3.07 => ( ( inf_inf_int @ A2 @ B2 )
% 2.86/3.07 = A2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % inf.absorb3
% 2.86/3.07 thf(fact_1813_less__infI2,axiom,
% 2.86/3.07 ! [B2: set_nat,X: set_nat,A2: set_nat] :
% 2.86/3.07 ( ( ord_less_set_nat @ B2 @ X )
% 2.86/3.07 => ( ord_less_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ X ) ) ).
% 2.86/3.07
% 2.86/3.07 % less_infI2
% 2.86/3.07 thf(fact_1814_less__infI2,axiom,
% 2.86/3.07 ! [B2: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 2.86/3.07 ( ( ord_le7866589430770878221at_nat @ B2 @ X )
% 2.86/3.07 => ( ord_le7866589430770878221at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) @ X ) ) ).
% 2.86/3.07
% 2.86/3.07 % less_infI2
% 2.86/3.07 thf(fact_1815_less__infI2,axiom,
% 2.86/3.07 ! [B2: assn,X: assn,A2: assn] :
% 2.86/3.07 ( ( ord_less_assn @ B2 @ X )
% 2.86/3.07 => ( ord_less_assn @ ( inf_inf_assn @ A2 @ B2 ) @ X ) ) ).
% 2.86/3.07
% 2.86/3.07 % less_infI2
% 2.86/3.07 thf(fact_1816_less__infI2,axiom,
% 2.86/3.07 ! [B2: nat,X: nat,A2: nat] :
% 2.86/3.07 ( ( ord_less_nat @ B2 @ X )
% 2.86/3.07 => ( ord_less_nat @ ( inf_inf_nat @ A2 @ B2 ) @ X ) ) ).
% 2.86/3.07
% 2.86/3.07 % less_infI2
% 2.86/3.07 thf(fact_1817_less__infI2,axiom,
% 2.86/3.07 ! [B2: int,X: int,A2: int] :
% 2.86/3.07 ( ( ord_less_int @ B2 @ X )
% 2.86/3.07 => ( ord_less_int @ ( inf_inf_int @ A2 @ B2 ) @ X ) ) ).
% 2.86/3.07
% 2.86/3.07 % less_infI2
% 2.86/3.07 thf(fact_1818_less__infI1,axiom,
% 2.86/3.07 ! [A2: set_nat,X: set_nat,B2: set_nat] :
% 2.86/3.07 ( ( ord_less_set_nat @ A2 @ X )
% 2.86/3.07 => ( ord_less_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ X ) ) ).
% 2.86/3.07
% 2.86/3.07 % less_infI1
% 2.86/3.07 thf(fact_1819_less__infI1,axiom,
% 2.86/3.07 ! [A2: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 2.86/3.07 ( ( ord_le7866589430770878221at_nat @ A2 @ X )
% 2.86/3.07 => ( ord_le7866589430770878221at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) @ X ) ) ).
% 2.86/3.07
% 2.86/3.07 % less_infI1
% 2.86/3.07 thf(fact_1820_less__infI1,axiom,
% 2.86/3.07 ! [A2: assn,X: assn,B2: assn] :
% 2.86/3.07 ( ( ord_less_assn @ A2 @ X )
% 2.86/3.07 => ( ord_less_assn @ ( inf_inf_assn @ A2 @ B2 ) @ X ) ) ).
% 2.86/3.07
% 2.86/3.07 % less_infI1
% 2.86/3.07 thf(fact_1821_less__infI1,axiom,
% 2.86/3.07 ! [A2: nat,X: nat,B2: nat] :
% 2.86/3.07 ( ( ord_less_nat @ A2 @ X )
% 2.86/3.07 => ( ord_less_nat @ ( inf_inf_nat @ A2 @ B2 ) @ X ) ) ).
% 2.86/3.07
% 2.86/3.07 % less_infI1
% 2.86/3.07 thf(fact_1822_less__infI1,axiom,
% 2.86/3.07 ! [A2: int,X: int,B2: int] :
% 2.86/3.07 ( ( ord_less_int @ A2 @ X )
% 2.86/3.07 => ( ord_less_int @ ( inf_inf_int @ A2 @ B2 ) @ X ) ) ).
% 2.86/3.07
% 2.86/3.07 % less_infI1
% 2.86/3.07 thf(fact_1823_pinf_I6_J,axiom,
% 2.86/3.07 ! [T: code_integer] :
% 2.86/3.07 ? [Z4: code_integer] :
% 2.86/3.07 ! [X7: code_integer] :
% 2.86/3.07 ( ( ord_le6747313008572928689nteger @ Z4 @ X7 )
% 2.86/3.07 => ~ ( ord_le3102999989581377725nteger @ X7 @ T ) ) ).
% 2.86/3.07
% 2.86/3.07 % pinf(6)
% 2.86/3.07 thf(fact_1824_pinf_I6_J,axiom,
% 2.86/3.07 ! [T: num] :
% 2.86/3.07 ? [Z4: num] :
% 2.86/3.07 ! [X7: num] :
% 2.86/3.07 ( ( ord_less_num @ Z4 @ X7 )
% 2.86/3.07 => ~ ( ord_less_eq_num @ X7 @ T ) ) ).
% 2.86/3.07
% 2.86/3.07 % pinf(6)
% 2.86/3.07 thf(fact_1825_pinf_I6_J,axiom,
% 2.86/3.07 ! [T: nat] :
% 2.86/3.07 ? [Z4: nat] :
% 2.86/3.07 ! [X7: nat] :
% 2.86/3.07 ( ( ord_less_nat @ Z4 @ X7 )
% 2.86/3.07 => ~ ( ord_less_eq_nat @ X7 @ T ) ) ).
% 2.86/3.07
% 2.86/3.07 % pinf(6)
% 2.86/3.07 thf(fact_1826_pinf_I6_J,axiom,
% 2.86/3.07 ! [T: int] :
% 2.86/3.07 ? [Z4: int] :
% 2.86/3.07 ! [X7: int] :
% 2.86/3.07 ( ( ord_less_int @ Z4 @ X7 )
% 2.86/3.07 => ~ ( ord_less_eq_int @ X7 @ T ) ) ).
% 2.86/3.07
% 2.86/3.07 % pinf(6)
% 2.86/3.07 thf(fact_1827_pinf_I8_J,axiom,
% 2.86/3.07 ! [T: code_integer] :
% 2.86/3.07 ? [Z4: code_integer] :
% 2.86/3.07 ! [X7: code_integer] :
% 2.86/3.07 ( ( ord_le6747313008572928689nteger @ Z4 @ X7 )
% 2.86/3.07 => ( ord_le3102999989581377725nteger @ T @ X7 ) ) ).
% 2.86/3.07
% 2.86/3.07 % pinf(8)
% 2.86/3.07 thf(fact_1828_pinf_I8_J,axiom,
% 2.86/3.07 ! [T: num] :
% 2.86/3.07 ? [Z4: num] :
% 2.86/3.07 ! [X7: num] :
% 2.86/3.07 ( ( ord_less_num @ Z4 @ X7 )
% 2.86/3.07 => ( ord_less_eq_num @ T @ X7 ) ) ).
% 2.86/3.07
% 2.86/3.07 % pinf(8)
% 2.86/3.07 thf(fact_1829_pinf_I8_J,axiom,
% 2.86/3.07 ! [T: nat] :
% 2.86/3.07 ? [Z4: nat] :
% 2.86/3.07 ! [X7: nat] :
% 2.86/3.07 ( ( ord_less_nat @ Z4 @ X7 )
% 2.86/3.07 => ( ord_less_eq_nat @ T @ X7 ) ) ).
% 2.86/3.07
% 2.86/3.07 % pinf(8)
% 2.86/3.07 thf(fact_1830_pinf_I8_J,axiom,
% 2.86/3.07 ! [T: int] :
% 2.86/3.07 ? [Z4: int] :
% 2.86/3.07 ! [X7: int] :
% 2.86/3.07 ( ( ord_less_int @ Z4 @ X7 )
% 2.86/3.07 => ( ord_less_eq_int @ T @ X7 ) ) ).
% 2.86/3.07
% 2.86/3.07 % pinf(8)
% 2.86/3.07 thf(fact_1831_minf_I6_J,axiom,
% 2.86/3.07 ! [T: code_integer] :
% 2.86/3.07 ? [Z4: code_integer] :
% 2.86/3.07 ! [X7: code_integer] :
% 2.86/3.07 ( ( ord_le6747313008572928689nteger @ X7 @ Z4 )
% 2.86/3.07 => ( ord_le3102999989581377725nteger @ X7 @ T ) ) ).
% 2.86/3.07
% 2.86/3.07 % minf(6)
% 2.86/3.07 thf(fact_1832_minf_I6_J,axiom,
% 2.86/3.07 ! [T: num] :
% 2.86/3.07 ? [Z4: num] :
% 2.86/3.07 ! [X7: num] :
% 2.86/3.07 ( ( ord_less_num @ X7 @ Z4 )
% 2.86/3.07 => ( ord_less_eq_num @ X7 @ T ) ) ).
% 2.86/3.07
% 2.86/3.07 % minf(6)
% 2.86/3.07 thf(fact_1833_minf_I6_J,axiom,
% 2.86/3.07 ! [T: nat] :
% 2.86/3.07 ? [Z4: nat] :
% 2.86/3.07 ! [X7: nat] :
% 2.86/3.07 ( ( ord_less_nat @ X7 @ Z4 )
% 2.86/3.07 => ( ord_less_eq_nat @ X7 @ T ) ) ).
% 2.86/3.07
% 2.86/3.07 % minf(6)
% 2.86/3.07 thf(fact_1834_minf_I6_J,axiom,
% 2.86/3.07 ! [T: int] :
% 2.86/3.07 ? [Z4: int] :
% 2.86/3.07 ! [X7: int] :
% 2.86/3.07 ( ( ord_less_int @ X7 @ Z4 )
% 2.86/3.07 => ( ord_less_eq_int @ X7 @ T ) ) ).
% 2.86/3.07
% 2.86/3.07 % minf(6)
% 2.86/3.07 thf(fact_1835_minf_I8_J,axiom,
% 2.86/3.07 ! [T: code_integer] :
% 2.86/3.07 ? [Z4: code_integer] :
% 2.86/3.07 ! [X7: code_integer] :
% 2.86/3.07 ( ( ord_le6747313008572928689nteger @ X7 @ Z4 )
% 2.86/3.07 => ~ ( ord_le3102999989581377725nteger @ T @ X7 ) ) ).
% 2.86/3.07
% 2.86/3.07 % minf(8)
% 2.86/3.07 thf(fact_1836_minf_I8_J,axiom,
% 2.86/3.07 ! [T: num] :
% 2.86/3.07 ? [Z4: num] :
% 2.86/3.07 ! [X7: num] :
% 2.86/3.07 ( ( ord_less_num @ X7 @ Z4 )
% 2.86/3.07 => ~ ( ord_less_eq_num @ T @ X7 ) ) ).
% 2.86/3.07
% 2.86/3.07 % minf(8)
% 2.86/3.07 thf(fact_1837_minf_I8_J,axiom,
% 2.86/3.07 ! [T: nat] :
% 2.86/3.07 ? [Z4: nat] :
% 2.86/3.07 ! [X7: nat] :
% 2.86/3.07 ( ( ord_less_nat @ X7 @ Z4 )
% 2.86/3.07 => ~ ( ord_less_eq_nat @ T @ X7 ) ) ).
% 2.86/3.07
% 2.86/3.07 % minf(8)
% 2.86/3.07 thf(fact_1838_minf_I8_J,axiom,
% 2.86/3.07 ! [T: int] :
% 2.86/3.07 ? [Z4: int] :
% 2.86/3.07 ! [X7: int] :
% 2.86/3.07 ( ( ord_less_int @ X7 @ Z4 )
% 2.86/3.07 => ~ ( ord_less_eq_int @ T @ X7 ) ) ).
% 2.86/3.07
% 2.86/3.07 % minf(8)
% 2.86/3.07 thf(fact_1839_order__le__imp__less__or__eq,axiom,
% 2.86/3.07 ! [X: code_integer,Y: code_integer] :
% 2.86/3.07 ( ( ord_le3102999989581377725nteger @ X @ Y )
% 2.86/3.07 => ( ( ord_le6747313008572928689nteger @ X @ Y )
% 2.86/3.07 | ( X = Y ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_imp_less_or_eq
% 2.86/3.07 thf(fact_1840_order__le__imp__less__or__eq,axiom,
% 2.86/3.07 ! [X: num,Y: num] :
% 2.86/3.07 ( ( ord_less_eq_num @ X @ Y )
% 2.86/3.07 => ( ( ord_less_num @ X @ Y )
% 2.86/3.07 | ( X = Y ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_imp_less_or_eq
% 2.86/3.07 thf(fact_1841_order__le__imp__less__or__eq,axiom,
% 2.86/3.07 ! [X: assn,Y: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ X @ Y )
% 2.86/3.07 => ( ( ord_less_assn @ X @ Y )
% 2.86/3.07 | ( X = Y ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_imp_less_or_eq
% 2.86/3.07 thf(fact_1842_order__le__imp__less__or__eq,axiom,
% 2.86/3.07 ! [X: filter_nat,Y: filter_nat] :
% 2.86/3.07 ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 2.86/3.07 => ( ( ord_less_filter_nat @ X @ Y )
% 2.86/3.07 | ( X = Y ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_imp_less_or_eq
% 2.86/3.07 thf(fact_1843_order__le__imp__less__or__eq,axiom,
% 2.86/3.07 ! [X: set_nat,Y: set_nat] :
% 2.86/3.07 ( ( ord_less_eq_set_nat @ X @ Y )
% 2.86/3.07 => ( ( ord_less_set_nat @ X @ Y )
% 2.86/3.07 | ( X = Y ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_imp_less_or_eq
% 2.86/3.07 thf(fact_1844_order__le__imp__less__or__eq,axiom,
% 2.86/3.07 ! [X: nat,Y: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ X @ Y )
% 2.86/3.07 => ( ( ord_less_nat @ X @ Y )
% 2.86/3.07 | ( X = Y ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_imp_less_or_eq
% 2.86/3.07 thf(fact_1845_order__le__imp__less__or__eq,axiom,
% 2.86/3.07 ! [X: int,Y: int] :
% 2.86/3.07 ( ( ord_less_eq_int @ X @ Y )
% 2.86/3.07 => ( ( ord_less_int @ X @ Y )
% 2.86/3.07 | ( X = Y ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_imp_less_or_eq
% 2.86/3.07 thf(fact_1846_linorder__le__less__linear,axiom,
% 2.86/3.07 ! [X: code_integer,Y: code_integer] :
% 2.86/3.07 ( ( ord_le3102999989581377725nteger @ X @ Y )
% 2.86/3.07 | ( ord_le6747313008572928689nteger @ Y @ X ) ) ).
% 2.86/3.07
% 2.86/3.07 % linorder_le_less_linear
% 2.86/3.07 thf(fact_1847_linorder__le__less__linear,axiom,
% 2.86/3.07 ! [X: num,Y: num] :
% 2.86/3.07 ( ( ord_less_eq_num @ X @ Y )
% 2.86/3.07 | ( ord_less_num @ Y @ X ) ) ).
% 2.86/3.07
% 2.86/3.07 % linorder_le_less_linear
% 2.86/3.07 thf(fact_1848_linorder__le__less__linear,axiom,
% 2.86/3.07 ! [X: nat,Y: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ X @ Y )
% 2.86/3.07 | ( ord_less_nat @ Y @ X ) ) ).
% 2.86/3.07
% 2.86/3.07 % linorder_le_less_linear
% 2.86/3.07 thf(fact_1849_linorder__le__less__linear,axiom,
% 2.86/3.07 ! [X: int,Y: int] :
% 2.86/3.07 ( ( ord_less_eq_int @ X @ Y )
% 2.86/3.07 | ( ord_less_int @ Y @ X ) ) ).
% 2.86/3.07
% 2.86/3.07 % linorder_le_less_linear
% 2.86/3.07 thf(fact_1850_order__less__le__subst2,axiom,
% 2.86/3.07 ! [A2: code_integer,B2: code_integer,F4: code_integer > code_integer,C: code_integer] :
% 2.86/3.07 ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 2.86/3.07 => ( ( ord_le3102999989581377725nteger @ ( F4 @ B2 ) @ C )
% 2.86/3.07 => ( ! [X3: code_integer,Y2: code_integer] :
% 2.86/3.07 ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 2.86/3.07 => ( ord_le6747313008572928689nteger @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_le6747313008572928689nteger @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_le_subst2
% 2.86/3.07 thf(fact_1851_order__less__le__subst2,axiom,
% 2.86/3.07 ! [A2: code_integer,B2: code_integer,F4: code_integer > num,C: num] :
% 2.86/3.07 ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 2.86/3.07 => ( ( ord_less_eq_num @ ( F4 @ B2 ) @ C )
% 2.86/3.07 => ( ! [X3: code_integer,Y2: code_integer] :
% 2.86/3.07 ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_num @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_num @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_le_subst2
% 2.86/3.07 thf(fact_1852_order__less__le__subst2,axiom,
% 2.86/3.07 ! [A2: assn,B2: assn,F4: assn > code_integer,C: code_integer] :
% 2.86/3.07 ( ( ord_less_assn @ A2 @ B2 )
% 2.86/3.07 => ( ( ord_le3102999989581377725nteger @ ( F4 @ B2 ) @ C )
% 2.86/3.07 => ( ! [X3: assn,Y2: assn] :
% 2.86/3.07 ( ( ord_less_assn @ X3 @ Y2 )
% 2.86/3.07 => ( ord_le6747313008572928689nteger @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_le6747313008572928689nteger @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_le_subst2
% 2.86/3.07 thf(fact_1853_order__less__le__subst2,axiom,
% 2.86/3.07 ! [A2: assn,B2: assn,F4: assn > num,C: num] :
% 2.86/3.07 ( ( ord_less_assn @ A2 @ B2 )
% 2.86/3.07 => ( ( ord_less_eq_num @ ( F4 @ B2 ) @ C )
% 2.86/3.07 => ( ! [X3: assn,Y2: assn] :
% 2.86/3.07 ( ( ord_less_assn @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_num @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_num @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_le_subst2
% 2.86/3.07 thf(fact_1854_order__less__le__subst2,axiom,
% 2.86/3.07 ! [A2: num,B2: num,F4: num > code_integer,C: code_integer] :
% 2.86/3.07 ( ( ord_less_num @ A2 @ B2 )
% 2.86/3.07 => ( ( ord_le3102999989581377725nteger @ ( F4 @ B2 ) @ C )
% 2.86/3.07 => ( ! [X3: num,Y2: num] :
% 2.86/3.07 ( ( ord_less_num @ X3 @ Y2 )
% 2.86/3.07 => ( ord_le6747313008572928689nteger @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_le6747313008572928689nteger @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_le_subst2
% 2.86/3.07 thf(fact_1855_order__less__le__subst2,axiom,
% 2.86/3.07 ! [A2: num,B2: num,F4: num > num,C: num] :
% 2.86/3.07 ( ( ord_less_num @ A2 @ B2 )
% 2.86/3.07 => ( ( ord_less_eq_num @ ( F4 @ B2 ) @ C )
% 2.86/3.07 => ( ! [X3: num,Y2: num] :
% 2.86/3.07 ( ( ord_less_num @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_num @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_num @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_le_subst2
% 2.86/3.07 thf(fact_1856_order__less__le__subst2,axiom,
% 2.86/3.07 ! [A2: nat,B2: nat,F4: nat > code_integer,C: code_integer] :
% 2.86/3.07 ( ( ord_less_nat @ A2 @ B2 )
% 2.86/3.07 => ( ( ord_le3102999989581377725nteger @ ( F4 @ B2 ) @ C )
% 2.86/3.07 => ( ! [X3: nat,Y2: nat] :
% 2.86/3.07 ( ( ord_less_nat @ X3 @ Y2 )
% 2.86/3.07 => ( ord_le6747313008572928689nteger @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_le6747313008572928689nteger @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_le_subst2
% 2.86/3.07 thf(fact_1857_order__less__le__subst2,axiom,
% 2.86/3.07 ! [A2: nat,B2: nat,F4: nat > num,C: num] :
% 2.86/3.07 ( ( ord_less_nat @ A2 @ B2 )
% 2.86/3.07 => ( ( ord_less_eq_num @ ( F4 @ B2 ) @ C )
% 2.86/3.07 => ( ! [X3: nat,Y2: nat] :
% 2.86/3.07 ( ( ord_less_nat @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_num @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_num @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_le_subst2
% 2.86/3.07 thf(fact_1858_order__less__le__subst2,axiom,
% 2.86/3.07 ! [A2: int,B2: int,F4: int > code_integer,C: code_integer] :
% 2.86/3.07 ( ( ord_less_int @ A2 @ B2 )
% 2.86/3.07 => ( ( ord_le3102999989581377725nteger @ ( F4 @ B2 ) @ C )
% 2.86/3.07 => ( ! [X3: int,Y2: int] :
% 2.86/3.07 ( ( ord_less_int @ X3 @ Y2 )
% 2.86/3.07 => ( ord_le6747313008572928689nteger @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_le6747313008572928689nteger @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_le_subst2
% 2.86/3.07 thf(fact_1859_order__less__le__subst2,axiom,
% 2.86/3.07 ! [A2: int,B2: int,F4: int > num,C: num] :
% 2.86/3.07 ( ( ord_less_int @ A2 @ B2 )
% 2.86/3.07 => ( ( ord_less_eq_num @ ( F4 @ B2 ) @ C )
% 2.86/3.07 => ( ! [X3: int,Y2: int] :
% 2.86/3.07 ( ( ord_less_int @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_num @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_num @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_le_subst2
% 2.86/3.07 thf(fact_1860_order__less__le__subst1,axiom,
% 2.86/3.07 ! [A2: code_integer,F4: assn > code_integer,B2: assn,C: assn] :
% 2.86/3.07 ( ( ord_le6747313008572928689nteger @ A2 @ ( F4 @ B2 ) )
% 2.86/3.07 => ( ( ord_less_eq_assn @ B2 @ C )
% 2.86/3.07 => ( ! [X3: assn,Y2: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ X3 @ Y2 )
% 2.86/3.07 => ( ord_le3102999989581377725nteger @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_le6747313008572928689nteger @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_le_subst1
% 2.86/3.07 thf(fact_1861_order__less__le__subst1,axiom,
% 2.86/3.07 ! [A2: num,F4: assn > num,B2: assn,C: assn] :
% 2.86/3.07 ( ( ord_less_num @ A2 @ ( F4 @ B2 ) )
% 2.86/3.07 => ( ( ord_less_eq_assn @ B2 @ C )
% 2.86/3.07 => ( ! [X3: assn,Y2: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_num @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_num @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_le_subst1
% 2.86/3.07 thf(fact_1862_order__less__le__subst1,axiom,
% 2.86/3.07 ! [A2: assn,F4: assn > assn,B2: assn,C: assn] :
% 2.86/3.07 ( ( ord_less_assn @ A2 @ ( F4 @ B2 ) )
% 2.86/3.07 => ( ( ord_less_eq_assn @ B2 @ C )
% 2.86/3.07 => ( ! [X3: assn,Y2: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_assn @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_assn @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_le_subst1
% 2.86/3.07 thf(fact_1863_order__less__le__subst1,axiom,
% 2.86/3.07 ! [A2: nat,F4: assn > nat,B2: assn,C: assn] :
% 2.86/3.07 ( ( ord_less_nat @ A2 @ ( F4 @ B2 ) )
% 2.86/3.07 => ( ( ord_less_eq_assn @ B2 @ C )
% 2.86/3.07 => ( ! [X3: assn,Y2: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_nat @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_nat @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_le_subst1
% 2.86/3.07 thf(fact_1864_order__less__le__subst1,axiom,
% 2.86/3.07 ! [A2: int,F4: assn > int,B2: assn,C: assn] :
% 2.86/3.07 ( ( ord_less_int @ A2 @ ( F4 @ B2 ) )
% 2.86/3.07 => ( ( ord_less_eq_assn @ B2 @ C )
% 2.86/3.07 => ( ! [X3: assn,Y2: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_int @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_int @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_le_subst1
% 2.86/3.07 thf(fact_1865_order__less__le__subst1,axiom,
% 2.86/3.07 ! [A2: code_integer,F4: nat > code_integer,B2: nat,C: nat] :
% 2.86/3.07 ( ( ord_le6747313008572928689nteger @ A2 @ ( F4 @ B2 ) )
% 2.86/3.07 => ( ( ord_less_eq_nat @ B2 @ C )
% 2.86/3.07 => ( ! [X3: nat,Y2: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 2.86/3.07 => ( ord_le3102999989581377725nteger @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_le6747313008572928689nteger @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_le_subst1
% 2.86/3.07 thf(fact_1866_order__less__le__subst1,axiom,
% 2.86/3.07 ! [A2: num,F4: nat > num,B2: nat,C: nat] :
% 2.86/3.07 ( ( ord_less_num @ A2 @ ( F4 @ B2 ) )
% 2.86/3.07 => ( ( ord_less_eq_nat @ B2 @ C )
% 2.86/3.07 => ( ! [X3: nat,Y2: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_num @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_num @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_le_subst1
% 2.86/3.07 thf(fact_1867_order__less__le__subst1,axiom,
% 2.86/3.07 ! [A2: assn,F4: nat > assn,B2: nat,C: nat] :
% 2.86/3.07 ( ( ord_less_assn @ A2 @ ( F4 @ B2 ) )
% 2.86/3.07 => ( ( ord_less_eq_nat @ B2 @ C )
% 2.86/3.07 => ( ! [X3: nat,Y2: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_assn @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_assn @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_le_subst1
% 2.86/3.07 thf(fact_1868_order__less__le__subst1,axiom,
% 2.86/3.07 ! [A2: nat,F4: nat > nat,B2: nat,C: nat] :
% 2.86/3.07 ( ( ord_less_nat @ A2 @ ( F4 @ B2 ) )
% 2.86/3.07 => ( ( ord_less_eq_nat @ B2 @ C )
% 2.86/3.07 => ( ! [X3: nat,Y2: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_nat @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_nat @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_le_subst1
% 2.86/3.07 thf(fact_1869_order__less__le__subst1,axiom,
% 2.86/3.07 ! [A2: int,F4: nat > int,B2: nat,C: nat] :
% 2.86/3.07 ( ( ord_less_int @ A2 @ ( F4 @ B2 ) )
% 2.86/3.07 => ( ( ord_less_eq_nat @ B2 @ C )
% 2.86/3.07 => ( ! [X3: nat,Y2: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_int @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_int @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_le_subst1
% 2.86/3.07 thf(fact_1870_order__le__less__subst2,axiom,
% 2.86/3.07 ! [A2: assn,B2: assn,F4: assn > code_integer,C: code_integer] :
% 2.86/3.07 ( ( ord_less_eq_assn @ A2 @ B2 )
% 2.86/3.07 => ( ( ord_le6747313008572928689nteger @ ( F4 @ B2 ) @ C )
% 2.86/3.07 => ( ! [X3: assn,Y2: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ X3 @ Y2 )
% 2.86/3.07 => ( ord_le3102999989581377725nteger @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_le6747313008572928689nteger @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_less_subst2
% 2.86/3.07 thf(fact_1871_order__le__less__subst2,axiom,
% 2.86/3.07 ! [A2: assn,B2: assn,F4: assn > num,C: num] :
% 2.86/3.07 ( ( ord_less_eq_assn @ A2 @ B2 )
% 2.86/3.07 => ( ( ord_less_num @ ( F4 @ B2 ) @ C )
% 2.86/3.07 => ( ! [X3: assn,Y2: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_num @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_num @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_less_subst2
% 2.86/3.07 thf(fact_1872_order__le__less__subst2,axiom,
% 2.86/3.07 ! [A2: assn,B2: assn,F4: assn > assn,C: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ A2 @ B2 )
% 2.86/3.07 => ( ( ord_less_assn @ ( F4 @ B2 ) @ C )
% 2.86/3.07 => ( ! [X3: assn,Y2: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_assn @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_assn @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_less_subst2
% 2.86/3.07 thf(fact_1873_order__le__less__subst2,axiom,
% 2.86/3.07 ! [A2: assn,B2: assn,F4: assn > nat,C: nat] :
% 2.86/3.07 ( ( ord_less_eq_assn @ A2 @ B2 )
% 2.86/3.07 => ( ( ord_less_nat @ ( F4 @ B2 ) @ C )
% 2.86/3.07 => ( ! [X3: assn,Y2: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_nat @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_nat @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_less_subst2
% 2.86/3.07 thf(fact_1874_order__le__less__subst2,axiom,
% 2.86/3.07 ! [A2: assn,B2: assn,F4: assn > int,C: int] :
% 2.86/3.07 ( ( ord_less_eq_assn @ A2 @ B2 )
% 2.86/3.07 => ( ( ord_less_int @ ( F4 @ B2 ) @ C )
% 2.86/3.07 => ( ! [X3: assn,Y2: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_int @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_int @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_less_subst2
% 2.86/3.07 thf(fact_1875_order__le__less__subst2,axiom,
% 2.86/3.07 ! [A2: nat,B2: nat,F4: nat > code_integer,C: code_integer] :
% 2.86/3.07 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.07 => ( ( ord_le6747313008572928689nteger @ ( F4 @ B2 ) @ C )
% 2.86/3.07 => ( ! [X3: nat,Y2: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 2.86/3.07 => ( ord_le3102999989581377725nteger @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_le6747313008572928689nteger @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_less_subst2
% 2.86/3.07 thf(fact_1876_order__le__less__subst2,axiom,
% 2.86/3.07 ! [A2: nat,B2: nat,F4: nat > num,C: num] :
% 2.86/3.07 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.07 => ( ( ord_less_num @ ( F4 @ B2 ) @ C )
% 2.86/3.07 => ( ! [X3: nat,Y2: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_num @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_num @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_less_subst2
% 2.86/3.07 thf(fact_1877_order__le__less__subst2,axiom,
% 2.86/3.07 ! [A2: nat,B2: nat,F4: nat > assn,C: assn] :
% 2.86/3.07 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.07 => ( ( ord_less_assn @ ( F4 @ B2 ) @ C )
% 2.86/3.07 => ( ! [X3: nat,Y2: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_assn @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_assn @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_less_subst2
% 2.86/3.07 thf(fact_1878_order__le__less__subst2,axiom,
% 2.86/3.07 ! [A2: nat,B2: nat,F4: nat > nat,C: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.07 => ( ( ord_less_nat @ ( F4 @ B2 ) @ C )
% 2.86/3.07 => ( ! [X3: nat,Y2: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_nat @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_nat @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_less_subst2
% 2.86/3.07 thf(fact_1879_order__le__less__subst2,axiom,
% 2.86/3.07 ! [A2: nat,B2: nat,F4: nat > int,C: int] :
% 2.86/3.07 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.07 => ( ( ord_less_int @ ( F4 @ B2 ) @ C )
% 2.86/3.07 => ( ! [X3: nat,Y2: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_eq_int @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_int @ ( F4 @ A2 ) @ C ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_less_subst2
% 2.86/3.07 thf(fact_1880_order__le__less__subst1,axiom,
% 2.86/3.07 ! [A2: code_integer,F4: code_integer > code_integer,B2: code_integer,C: code_integer] :
% 2.86/3.07 ( ( ord_le3102999989581377725nteger @ A2 @ ( F4 @ B2 ) )
% 2.86/3.07 => ( ( ord_le6747313008572928689nteger @ B2 @ C )
% 2.86/3.07 => ( ! [X3: code_integer,Y2: code_integer] :
% 2.86/3.07 ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 2.86/3.07 => ( ord_le6747313008572928689nteger @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_le6747313008572928689nteger @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_less_subst1
% 2.86/3.07 thf(fact_1881_order__le__less__subst1,axiom,
% 2.86/3.07 ! [A2: num,F4: code_integer > num,B2: code_integer,C: code_integer] :
% 2.86/3.07 ( ( ord_less_eq_num @ A2 @ ( F4 @ B2 ) )
% 2.86/3.07 => ( ( ord_le6747313008572928689nteger @ B2 @ C )
% 2.86/3.07 => ( ! [X3: code_integer,Y2: code_integer] :
% 2.86/3.07 ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_num @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_num @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_less_subst1
% 2.86/3.07 thf(fact_1882_order__le__less__subst1,axiom,
% 2.86/3.07 ! [A2: code_integer,F4: assn > code_integer,B2: assn,C: assn] :
% 2.86/3.07 ( ( ord_le3102999989581377725nteger @ A2 @ ( F4 @ B2 ) )
% 2.86/3.07 => ( ( ord_less_assn @ B2 @ C )
% 2.86/3.07 => ( ! [X3: assn,Y2: assn] :
% 2.86/3.07 ( ( ord_less_assn @ X3 @ Y2 )
% 2.86/3.07 => ( ord_le6747313008572928689nteger @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_le6747313008572928689nteger @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_less_subst1
% 2.86/3.07 thf(fact_1883_order__le__less__subst1,axiom,
% 2.86/3.07 ! [A2: num,F4: assn > num,B2: assn,C: assn] :
% 2.86/3.07 ( ( ord_less_eq_num @ A2 @ ( F4 @ B2 ) )
% 2.86/3.07 => ( ( ord_less_assn @ B2 @ C )
% 2.86/3.07 => ( ! [X3: assn,Y2: assn] :
% 2.86/3.07 ( ( ord_less_assn @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_num @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_num @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_less_subst1
% 2.86/3.07 thf(fact_1884_order__le__less__subst1,axiom,
% 2.86/3.07 ! [A2: code_integer,F4: num > code_integer,B2: num,C: num] :
% 2.86/3.07 ( ( ord_le3102999989581377725nteger @ A2 @ ( F4 @ B2 ) )
% 2.86/3.07 => ( ( ord_less_num @ B2 @ C )
% 2.86/3.07 => ( ! [X3: num,Y2: num] :
% 2.86/3.07 ( ( ord_less_num @ X3 @ Y2 )
% 2.86/3.07 => ( ord_le6747313008572928689nteger @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_le6747313008572928689nteger @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_less_subst1
% 2.86/3.07 thf(fact_1885_order__le__less__subst1,axiom,
% 2.86/3.07 ! [A2: num,F4: num > num,B2: num,C: num] :
% 2.86/3.07 ( ( ord_less_eq_num @ A2 @ ( F4 @ B2 ) )
% 2.86/3.07 => ( ( ord_less_num @ B2 @ C )
% 2.86/3.07 => ( ! [X3: num,Y2: num] :
% 2.86/3.07 ( ( ord_less_num @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_num @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_num @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_less_subst1
% 2.86/3.07 thf(fact_1886_order__le__less__subst1,axiom,
% 2.86/3.07 ! [A2: code_integer,F4: nat > code_integer,B2: nat,C: nat] :
% 2.86/3.07 ( ( ord_le3102999989581377725nteger @ A2 @ ( F4 @ B2 ) )
% 2.86/3.07 => ( ( ord_less_nat @ B2 @ C )
% 2.86/3.07 => ( ! [X3: nat,Y2: nat] :
% 2.86/3.07 ( ( ord_less_nat @ X3 @ Y2 )
% 2.86/3.07 => ( ord_le6747313008572928689nteger @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_le6747313008572928689nteger @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_less_subst1
% 2.86/3.07 thf(fact_1887_order__le__less__subst1,axiom,
% 2.86/3.07 ! [A2: num,F4: nat > num,B2: nat,C: nat] :
% 2.86/3.07 ( ( ord_less_eq_num @ A2 @ ( F4 @ B2 ) )
% 2.86/3.07 => ( ( ord_less_nat @ B2 @ C )
% 2.86/3.07 => ( ! [X3: nat,Y2: nat] :
% 2.86/3.07 ( ( ord_less_nat @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_num @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_num @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_less_subst1
% 2.86/3.07 thf(fact_1888_order__le__less__subst1,axiom,
% 2.86/3.07 ! [A2: code_integer,F4: int > code_integer,B2: int,C: int] :
% 2.86/3.07 ( ( ord_le3102999989581377725nteger @ A2 @ ( F4 @ B2 ) )
% 2.86/3.07 => ( ( ord_less_int @ B2 @ C )
% 2.86/3.07 => ( ! [X3: int,Y2: int] :
% 2.86/3.07 ( ( ord_less_int @ X3 @ Y2 )
% 2.86/3.07 => ( ord_le6747313008572928689nteger @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_le6747313008572928689nteger @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_less_subst1
% 2.86/3.07 thf(fact_1889_order__le__less__subst1,axiom,
% 2.86/3.07 ! [A2: num,F4: int > num,B2: int,C: int] :
% 2.86/3.07 ( ( ord_less_eq_num @ A2 @ ( F4 @ B2 ) )
% 2.86/3.07 => ( ( ord_less_int @ B2 @ C )
% 2.86/3.07 => ( ! [X3: int,Y2: int] :
% 2.86/3.07 ( ( ord_less_int @ X3 @ Y2 )
% 2.86/3.07 => ( ord_less_num @ ( F4 @ X3 ) @ ( F4 @ Y2 ) ) )
% 2.86/3.07 => ( ord_less_num @ A2 @ ( F4 @ C ) ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_less_subst1
% 2.86/3.07 thf(fact_1890_order__less__le__trans,axiom,
% 2.86/3.07 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 2.86/3.07 ( ( ord_le6747313008572928689nteger @ X @ Y )
% 2.86/3.07 => ( ( ord_le3102999989581377725nteger @ Y @ Z )
% 2.86/3.07 => ( ord_le6747313008572928689nteger @ X @ Z ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_le_trans
% 2.86/3.07 thf(fact_1891_order__less__le__trans,axiom,
% 2.86/3.07 ! [X: num,Y: num,Z: num] :
% 2.86/3.07 ( ( ord_less_num @ X @ Y )
% 2.86/3.07 => ( ( ord_less_eq_num @ Y @ Z )
% 2.86/3.07 => ( ord_less_num @ X @ Z ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_le_trans
% 2.86/3.07 thf(fact_1892_order__less__le__trans,axiom,
% 2.86/3.07 ! [X: assn,Y: assn,Z: assn] :
% 2.86/3.07 ( ( ord_less_assn @ X @ Y )
% 2.86/3.07 => ( ( ord_less_eq_assn @ Y @ Z )
% 2.86/3.07 => ( ord_less_assn @ X @ Z ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_le_trans
% 2.86/3.07 thf(fact_1893_order__less__le__trans,axiom,
% 2.86/3.07 ! [X: filter_nat,Y: filter_nat,Z: filter_nat] :
% 2.86/3.07 ( ( ord_less_filter_nat @ X @ Y )
% 2.86/3.07 => ( ( ord_le2510731241096832064er_nat @ Y @ Z )
% 2.86/3.07 => ( ord_less_filter_nat @ X @ Z ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_le_trans
% 2.86/3.07 thf(fact_1894_order__less__le__trans,axiom,
% 2.86/3.07 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 2.86/3.07 ( ( ord_less_set_nat @ X @ Y )
% 2.86/3.07 => ( ( ord_less_eq_set_nat @ Y @ Z )
% 2.86/3.07 => ( ord_less_set_nat @ X @ Z ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_le_trans
% 2.86/3.07 thf(fact_1895_order__less__le__trans,axiom,
% 2.86/3.07 ! [X: nat,Y: nat,Z: nat] :
% 2.86/3.07 ( ( ord_less_nat @ X @ Y )
% 2.86/3.07 => ( ( ord_less_eq_nat @ Y @ Z )
% 2.86/3.07 => ( ord_less_nat @ X @ Z ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_le_trans
% 2.86/3.07 thf(fact_1896_order__less__le__trans,axiom,
% 2.86/3.07 ! [X: int,Y: int,Z: int] :
% 2.86/3.07 ( ( ord_less_int @ X @ Y )
% 2.86/3.07 => ( ( ord_less_eq_int @ Y @ Z )
% 2.86/3.07 => ( ord_less_int @ X @ Z ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_le_trans
% 2.86/3.07 thf(fact_1897_order__le__less__trans,axiom,
% 2.86/3.07 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 2.86/3.07 ( ( ord_le3102999989581377725nteger @ X @ Y )
% 2.86/3.07 => ( ( ord_le6747313008572928689nteger @ Y @ Z )
% 2.86/3.07 => ( ord_le6747313008572928689nteger @ X @ Z ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_less_trans
% 2.86/3.07 thf(fact_1898_order__le__less__trans,axiom,
% 2.86/3.07 ! [X: num,Y: num,Z: num] :
% 2.86/3.07 ( ( ord_less_eq_num @ X @ Y )
% 2.86/3.07 => ( ( ord_less_num @ Y @ Z )
% 2.86/3.07 => ( ord_less_num @ X @ Z ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_less_trans
% 2.86/3.07 thf(fact_1899_order__le__less__trans,axiom,
% 2.86/3.07 ! [X: assn,Y: assn,Z: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ X @ Y )
% 2.86/3.07 => ( ( ord_less_assn @ Y @ Z )
% 2.86/3.07 => ( ord_less_assn @ X @ Z ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_less_trans
% 2.86/3.07 thf(fact_1900_order__le__less__trans,axiom,
% 2.86/3.07 ! [X: filter_nat,Y: filter_nat,Z: filter_nat] :
% 2.86/3.07 ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 2.86/3.07 => ( ( ord_less_filter_nat @ Y @ Z )
% 2.86/3.07 => ( ord_less_filter_nat @ X @ Z ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_less_trans
% 2.86/3.07 thf(fact_1901_order__le__less__trans,axiom,
% 2.86/3.07 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 2.86/3.07 ( ( ord_less_eq_set_nat @ X @ Y )
% 2.86/3.07 => ( ( ord_less_set_nat @ Y @ Z )
% 2.86/3.07 => ( ord_less_set_nat @ X @ Z ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_less_trans
% 2.86/3.07 thf(fact_1902_order__le__less__trans,axiom,
% 2.86/3.07 ! [X: nat,Y: nat,Z: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ X @ Y )
% 2.86/3.07 => ( ( ord_less_nat @ Y @ Z )
% 2.86/3.07 => ( ord_less_nat @ X @ Z ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_less_trans
% 2.86/3.07 thf(fact_1903_order__le__less__trans,axiom,
% 2.86/3.07 ! [X: int,Y: int,Z: int] :
% 2.86/3.07 ( ( ord_less_eq_int @ X @ Y )
% 2.86/3.07 => ( ( ord_less_int @ Y @ Z )
% 2.86/3.07 => ( ord_less_int @ X @ Z ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_less_trans
% 2.86/3.07 thf(fact_1904_order__neq__le__trans,axiom,
% 2.86/3.07 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.07 ( ( A2 != B2 )
% 2.86/3.07 => ( ( ord_le3102999989581377725nteger @ A2 @ B2 )
% 2.86/3.07 => ( ord_le6747313008572928689nteger @ A2 @ B2 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_neq_le_trans
% 2.86/3.07 thf(fact_1905_order__neq__le__trans,axiom,
% 2.86/3.07 ! [A2: num,B2: num] :
% 2.86/3.07 ( ( A2 != B2 )
% 2.86/3.07 => ( ( ord_less_eq_num @ A2 @ B2 )
% 2.86/3.07 => ( ord_less_num @ A2 @ B2 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_neq_le_trans
% 2.86/3.07 thf(fact_1906_order__neq__le__trans,axiom,
% 2.86/3.07 ! [A2: assn,B2: assn] :
% 2.86/3.07 ( ( A2 != B2 )
% 2.86/3.07 => ( ( ord_less_eq_assn @ A2 @ B2 )
% 2.86/3.07 => ( ord_less_assn @ A2 @ B2 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_neq_le_trans
% 2.86/3.07 thf(fact_1907_order__neq__le__trans,axiom,
% 2.86/3.07 ! [A2: filter_nat,B2: filter_nat] :
% 2.86/3.07 ( ( A2 != B2 )
% 2.86/3.07 => ( ( ord_le2510731241096832064er_nat @ A2 @ B2 )
% 2.86/3.07 => ( ord_less_filter_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_neq_le_trans
% 2.86/3.07 thf(fact_1908_order__neq__le__trans,axiom,
% 2.86/3.07 ! [A2: set_nat,B2: set_nat] :
% 2.86/3.07 ( ( A2 != B2 )
% 2.86/3.07 => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 2.86/3.07 => ( ord_less_set_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_neq_le_trans
% 2.86/3.07 thf(fact_1909_order__neq__le__trans,axiom,
% 2.86/3.07 ! [A2: nat,B2: nat] :
% 2.86/3.07 ( ( A2 != B2 )
% 2.86/3.07 => ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.07 => ( ord_less_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_neq_le_trans
% 2.86/3.07 thf(fact_1910_order__neq__le__trans,axiom,
% 2.86/3.07 ! [A2: int,B2: int] :
% 2.86/3.07 ( ( A2 != B2 )
% 2.86/3.07 => ( ( ord_less_eq_int @ A2 @ B2 )
% 2.86/3.07 => ( ord_less_int @ A2 @ B2 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_neq_le_trans
% 2.86/3.07 thf(fact_1911_order__le__neq__trans,axiom,
% 2.86/3.07 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.07 ( ( ord_le3102999989581377725nteger @ A2 @ B2 )
% 2.86/3.07 => ( ( A2 != B2 )
% 2.86/3.07 => ( ord_le6747313008572928689nteger @ A2 @ B2 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_neq_trans
% 2.86/3.07 thf(fact_1912_order__le__neq__trans,axiom,
% 2.86/3.07 ! [A2: num,B2: num] :
% 2.86/3.07 ( ( ord_less_eq_num @ A2 @ B2 )
% 2.86/3.07 => ( ( A2 != B2 )
% 2.86/3.07 => ( ord_less_num @ A2 @ B2 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_neq_trans
% 2.86/3.07 thf(fact_1913_order__le__neq__trans,axiom,
% 2.86/3.07 ! [A2: assn,B2: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ A2 @ B2 )
% 2.86/3.07 => ( ( A2 != B2 )
% 2.86/3.07 => ( ord_less_assn @ A2 @ B2 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_neq_trans
% 2.86/3.07 thf(fact_1914_order__le__neq__trans,axiom,
% 2.86/3.07 ! [A2: filter_nat,B2: filter_nat] :
% 2.86/3.07 ( ( ord_le2510731241096832064er_nat @ A2 @ B2 )
% 2.86/3.07 => ( ( A2 != B2 )
% 2.86/3.07 => ( ord_less_filter_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_neq_trans
% 2.86/3.07 thf(fact_1915_order__le__neq__trans,axiom,
% 2.86/3.07 ! [A2: set_nat,B2: set_nat] :
% 2.86/3.07 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 2.86/3.07 => ( ( A2 != B2 )
% 2.86/3.07 => ( ord_less_set_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_neq_trans
% 2.86/3.07 thf(fact_1916_order__le__neq__trans,axiom,
% 2.86/3.07 ! [A2: nat,B2: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.07 => ( ( A2 != B2 )
% 2.86/3.07 => ( ord_less_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_neq_trans
% 2.86/3.07 thf(fact_1917_order__le__neq__trans,axiom,
% 2.86/3.07 ! [A2: int,B2: int] :
% 2.86/3.07 ( ( ord_less_eq_int @ A2 @ B2 )
% 2.86/3.07 => ( ( A2 != B2 )
% 2.86/3.07 => ( ord_less_int @ A2 @ B2 ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_neq_trans
% 2.86/3.07 thf(fact_1918_order__less__imp__le,axiom,
% 2.86/3.07 ! [X: code_integer,Y: code_integer] :
% 2.86/3.07 ( ( ord_le6747313008572928689nteger @ X @ Y )
% 2.86/3.07 => ( ord_le3102999989581377725nteger @ X @ Y ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_imp_le
% 2.86/3.07 thf(fact_1919_order__less__imp__le,axiom,
% 2.86/3.07 ! [X: num,Y: num] :
% 2.86/3.07 ( ( ord_less_num @ X @ Y )
% 2.86/3.07 => ( ord_less_eq_num @ X @ Y ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_imp_le
% 2.86/3.07 thf(fact_1920_order__less__imp__le,axiom,
% 2.86/3.07 ! [X: assn,Y: assn] :
% 2.86/3.07 ( ( ord_less_assn @ X @ Y )
% 2.86/3.07 => ( ord_less_eq_assn @ X @ Y ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_imp_le
% 2.86/3.07 thf(fact_1921_order__less__imp__le,axiom,
% 2.86/3.07 ! [X: filter_nat,Y: filter_nat] :
% 2.86/3.07 ( ( ord_less_filter_nat @ X @ Y )
% 2.86/3.07 => ( ord_le2510731241096832064er_nat @ X @ Y ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_imp_le
% 2.86/3.07 thf(fact_1922_order__less__imp__le,axiom,
% 2.86/3.07 ! [X: set_nat,Y: set_nat] :
% 2.86/3.07 ( ( ord_less_set_nat @ X @ Y )
% 2.86/3.07 => ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_imp_le
% 2.86/3.07 thf(fact_1923_order__less__imp__le,axiom,
% 2.86/3.07 ! [X: nat,Y: nat] :
% 2.86/3.07 ( ( ord_less_nat @ X @ Y )
% 2.86/3.07 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_imp_le
% 2.86/3.07 thf(fact_1924_order__less__imp__le,axiom,
% 2.86/3.07 ! [X: int,Y: int] :
% 2.86/3.07 ( ( ord_less_int @ X @ Y )
% 2.86/3.07 => ( ord_less_eq_int @ X @ Y ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_imp_le
% 2.86/3.07 thf(fact_1925_linorder__not__less,axiom,
% 2.86/3.07 ! [X: code_integer,Y: code_integer] :
% 2.86/3.07 ( ( ~ ( ord_le6747313008572928689nteger @ X @ Y ) )
% 2.86/3.07 = ( ord_le3102999989581377725nteger @ Y @ X ) ) ).
% 2.86/3.07
% 2.86/3.07 % linorder_not_less
% 2.86/3.07 thf(fact_1926_linorder__not__less,axiom,
% 2.86/3.07 ! [X: num,Y: num] :
% 2.86/3.07 ( ( ~ ( ord_less_num @ X @ Y ) )
% 2.86/3.07 = ( ord_less_eq_num @ Y @ X ) ) ).
% 2.86/3.07
% 2.86/3.07 % linorder_not_less
% 2.86/3.07 thf(fact_1927_linorder__not__less,axiom,
% 2.86/3.07 ! [X: nat,Y: nat] :
% 2.86/3.07 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 2.86/3.07 = ( ord_less_eq_nat @ Y @ X ) ) ).
% 2.86/3.07
% 2.86/3.07 % linorder_not_less
% 2.86/3.07 thf(fact_1928_linorder__not__less,axiom,
% 2.86/3.07 ! [X: int,Y: int] :
% 2.86/3.07 ( ( ~ ( ord_less_int @ X @ Y ) )
% 2.86/3.07 = ( ord_less_eq_int @ Y @ X ) ) ).
% 2.86/3.07
% 2.86/3.07 % linorder_not_less
% 2.86/3.07 thf(fact_1929_linorder__not__le,axiom,
% 2.86/3.07 ! [X: code_integer,Y: code_integer] :
% 2.86/3.07 ( ( ~ ( ord_le3102999989581377725nteger @ X @ Y ) )
% 2.86/3.07 = ( ord_le6747313008572928689nteger @ Y @ X ) ) ).
% 2.86/3.07
% 2.86/3.07 % linorder_not_le
% 2.86/3.07 thf(fact_1930_linorder__not__le,axiom,
% 2.86/3.07 ! [X: num,Y: num] :
% 2.86/3.07 ( ( ~ ( ord_less_eq_num @ X @ Y ) )
% 2.86/3.07 = ( ord_less_num @ Y @ X ) ) ).
% 2.86/3.07
% 2.86/3.07 % linorder_not_le
% 2.86/3.07 thf(fact_1931_linorder__not__le,axiom,
% 2.86/3.07 ! [X: nat,Y: nat] :
% 2.86/3.07 ( ( ~ ( ord_less_eq_nat @ X @ Y ) )
% 2.86/3.07 = ( ord_less_nat @ Y @ X ) ) ).
% 2.86/3.07
% 2.86/3.07 % linorder_not_le
% 2.86/3.07 thf(fact_1932_linorder__not__le,axiom,
% 2.86/3.07 ! [X: int,Y: int] :
% 2.86/3.07 ( ( ~ ( ord_less_eq_int @ X @ Y ) )
% 2.86/3.07 = ( ord_less_int @ Y @ X ) ) ).
% 2.86/3.07
% 2.86/3.07 % linorder_not_le
% 2.86/3.07 thf(fact_1933_order__less__le,axiom,
% 2.86/3.07 ( ord_le6747313008572928689nteger
% 2.86/3.07 = ( ^ [X2: code_integer,Y5: code_integer] :
% 2.86/3.07 ( ( ord_le3102999989581377725nteger @ X2 @ Y5 )
% 2.86/3.07 & ( X2 != Y5 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_le
% 2.86/3.07 thf(fact_1934_order__less__le,axiom,
% 2.86/3.07 ( ord_less_num
% 2.86/3.07 = ( ^ [X2: num,Y5: num] :
% 2.86/3.07 ( ( ord_less_eq_num @ X2 @ Y5 )
% 2.86/3.07 & ( X2 != Y5 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_le
% 2.86/3.07 thf(fact_1935_order__less__le,axiom,
% 2.86/3.07 ( ord_less_assn
% 2.86/3.07 = ( ^ [X2: assn,Y5: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ X2 @ Y5 )
% 2.86/3.07 & ( X2 != Y5 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_le
% 2.86/3.07 thf(fact_1936_order__less__le,axiom,
% 2.86/3.07 ( ord_less_filter_nat
% 2.86/3.07 = ( ^ [X2: filter_nat,Y5: filter_nat] :
% 2.86/3.07 ( ( ord_le2510731241096832064er_nat @ X2 @ Y5 )
% 2.86/3.07 & ( X2 != Y5 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_le
% 2.86/3.07 thf(fact_1937_order__less__le,axiom,
% 2.86/3.07 ( ord_less_set_nat
% 2.86/3.07 = ( ^ [X2: set_nat,Y5: set_nat] :
% 2.86/3.07 ( ( ord_less_eq_set_nat @ X2 @ Y5 )
% 2.86/3.07 & ( X2 != Y5 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_le
% 2.86/3.07 thf(fact_1938_order__less__le,axiom,
% 2.86/3.07 ( ord_less_nat
% 2.86/3.07 = ( ^ [X2: nat,Y5: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ X2 @ Y5 )
% 2.86/3.07 & ( X2 != Y5 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_le
% 2.86/3.07 thf(fact_1939_order__less__le,axiom,
% 2.86/3.07 ( ord_less_int
% 2.86/3.07 = ( ^ [X2: int,Y5: int] :
% 2.86/3.07 ( ( ord_less_eq_int @ X2 @ Y5 )
% 2.86/3.07 & ( X2 != Y5 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_less_le
% 2.86/3.07 thf(fact_1940_order__le__less,axiom,
% 2.86/3.07 ( ord_le3102999989581377725nteger
% 2.86/3.07 = ( ^ [X2: code_integer,Y5: code_integer] :
% 2.86/3.07 ( ( ord_le6747313008572928689nteger @ X2 @ Y5 )
% 2.86/3.07 | ( X2 = Y5 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_less
% 2.86/3.07 thf(fact_1941_order__le__less,axiom,
% 2.86/3.07 ( ord_less_eq_num
% 2.86/3.07 = ( ^ [X2: num,Y5: num] :
% 2.86/3.07 ( ( ord_less_num @ X2 @ Y5 )
% 2.86/3.07 | ( X2 = Y5 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_less
% 2.86/3.07 thf(fact_1942_order__le__less,axiom,
% 2.86/3.07 ( ord_less_eq_assn
% 2.86/3.07 = ( ^ [X2: assn,Y5: assn] :
% 2.86/3.07 ( ( ord_less_assn @ X2 @ Y5 )
% 2.86/3.07 | ( X2 = Y5 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_less
% 2.86/3.07 thf(fact_1943_order__le__less,axiom,
% 2.86/3.07 ( ord_le2510731241096832064er_nat
% 2.86/3.07 = ( ^ [X2: filter_nat,Y5: filter_nat] :
% 2.86/3.07 ( ( ord_less_filter_nat @ X2 @ Y5 )
% 2.86/3.07 | ( X2 = Y5 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_less
% 2.86/3.07 thf(fact_1944_order__le__less,axiom,
% 2.86/3.07 ( ord_less_eq_set_nat
% 2.86/3.07 = ( ^ [X2: set_nat,Y5: set_nat] :
% 2.86/3.07 ( ( ord_less_set_nat @ X2 @ Y5 )
% 2.86/3.07 | ( X2 = Y5 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_less
% 2.86/3.07 thf(fact_1945_order__le__less,axiom,
% 2.86/3.07 ( ord_less_eq_nat
% 2.86/3.07 = ( ^ [X2: nat,Y5: nat] :
% 2.86/3.07 ( ( ord_less_nat @ X2 @ Y5 )
% 2.86/3.07 | ( X2 = Y5 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_less
% 2.86/3.07 thf(fact_1946_order__le__less,axiom,
% 2.86/3.07 ( ord_less_eq_int
% 2.86/3.07 = ( ^ [X2: int,Y5: int] :
% 2.86/3.07 ( ( ord_less_int @ X2 @ Y5 )
% 2.86/3.07 | ( X2 = Y5 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % order_le_less
% 2.86/3.07 thf(fact_1947_dual__order_Ostrict__implies__order,axiom,
% 2.86/3.07 ! [B2: code_integer,A2: code_integer] :
% 2.86/3.07 ( ( ord_le6747313008572928689nteger @ B2 @ A2 )
% 2.86/3.07 => ( ord_le3102999989581377725nteger @ B2 @ A2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % dual_order.strict_implies_order
% 2.86/3.07 thf(fact_1948_dual__order_Ostrict__implies__order,axiom,
% 2.86/3.07 ! [B2: num,A2: num] :
% 2.86/3.07 ( ( ord_less_num @ B2 @ A2 )
% 2.86/3.07 => ( ord_less_eq_num @ B2 @ A2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % dual_order.strict_implies_order
% 2.86/3.07 thf(fact_1949_dual__order_Ostrict__implies__order,axiom,
% 2.86/3.07 ! [B2: assn,A2: assn] :
% 2.86/3.07 ( ( ord_less_assn @ B2 @ A2 )
% 2.86/3.07 => ( ord_less_eq_assn @ B2 @ A2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % dual_order.strict_implies_order
% 2.86/3.07 thf(fact_1950_dual__order_Ostrict__implies__order,axiom,
% 2.86/3.07 ! [B2: filter_nat,A2: filter_nat] :
% 2.86/3.07 ( ( ord_less_filter_nat @ B2 @ A2 )
% 2.86/3.07 => ( ord_le2510731241096832064er_nat @ B2 @ A2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % dual_order.strict_implies_order
% 2.86/3.07 thf(fact_1951_dual__order_Ostrict__implies__order,axiom,
% 2.86/3.07 ! [B2: set_nat,A2: set_nat] :
% 2.86/3.07 ( ( ord_less_set_nat @ B2 @ A2 )
% 2.86/3.07 => ( ord_less_eq_set_nat @ B2 @ A2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % dual_order.strict_implies_order
% 2.86/3.07 thf(fact_1952_dual__order_Ostrict__implies__order,axiom,
% 2.86/3.07 ! [B2: nat,A2: nat] :
% 2.86/3.07 ( ( ord_less_nat @ B2 @ A2 )
% 2.86/3.07 => ( ord_less_eq_nat @ B2 @ A2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % dual_order.strict_implies_order
% 2.86/3.07 thf(fact_1953_dual__order_Ostrict__implies__order,axiom,
% 2.86/3.07 ! [B2: int,A2: int] :
% 2.86/3.07 ( ( ord_less_int @ B2 @ A2 )
% 2.86/3.07 => ( ord_less_eq_int @ B2 @ A2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % dual_order.strict_implies_order
% 2.86/3.07 thf(fact_1954_order_Ostrict__implies__order,axiom,
% 2.86/3.07 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.07 ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 2.86/3.07 => ( ord_le3102999989581377725nteger @ A2 @ B2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % order.strict_implies_order
% 2.86/3.07 thf(fact_1955_order_Ostrict__implies__order,axiom,
% 2.86/3.07 ! [A2: num,B2: num] :
% 2.86/3.07 ( ( ord_less_num @ A2 @ B2 )
% 2.86/3.07 => ( ord_less_eq_num @ A2 @ B2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % order.strict_implies_order
% 2.86/3.07 thf(fact_1956_order_Ostrict__implies__order,axiom,
% 2.86/3.07 ! [A2: assn,B2: assn] :
% 2.86/3.07 ( ( ord_less_assn @ A2 @ B2 )
% 2.86/3.07 => ( ord_less_eq_assn @ A2 @ B2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % order.strict_implies_order
% 2.86/3.07 thf(fact_1957_order_Ostrict__implies__order,axiom,
% 2.86/3.07 ! [A2: filter_nat,B2: filter_nat] :
% 2.86/3.07 ( ( ord_less_filter_nat @ A2 @ B2 )
% 2.86/3.07 => ( ord_le2510731241096832064er_nat @ A2 @ B2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % order.strict_implies_order
% 2.86/3.07 thf(fact_1958_order_Ostrict__implies__order,axiom,
% 2.86/3.07 ! [A2: set_nat,B2: set_nat] :
% 2.86/3.07 ( ( ord_less_set_nat @ A2 @ B2 )
% 2.86/3.07 => ( ord_less_eq_set_nat @ A2 @ B2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % order.strict_implies_order
% 2.86/3.07 thf(fact_1959_order_Ostrict__implies__order,axiom,
% 2.86/3.07 ! [A2: nat,B2: nat] :
% 2.86/3.07 ( ( ord_less_nat @ A2 @ B2 )
% 2.86/3.07 => ( ord_less_eq_nat @ A2 @ B2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % order.strict_implies_order
% 2.86/3.07 thf(fact_1960_order_Ostrict__implies__order,axiom,
% 2.86/3.07 ! [A2: int,B2: int] :
% 2.86/3.07 ( ( ord_less_int @ A2 @ B2 )
% 2.86/3.07 => ( ord_less_eq_int @ A2 @ B2 ) ) ).
% 2.86/3.07
% 2.86/3.07 % order.strict_implies_order
% 2.86/3.07 thf(fact_1961_dual__order_Ostrict__iff__not,axiom,
% 2.86/3.07 ( ord_le6747313008572928689nteger
% 2.86/3.07 = ( ^ [B3: code_integer,A3: code_integer] :
% 2.86/3.07 ( ( ord_le3102999989581377725nteger @ B3 @ A3 )
% 2.86/3.07 & ~ ( ord_le3102999989581377725nteger @ A3 @ B3 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % dual_order.strict_iff_not
% 2.86/3.07 thf(fact_1962_dual__order_Ostrict__iff__not,axiom,
% 2.86/3.07 ( ord_less_num
% 2.86/3.07 = ( ^ [B3: num,A3: num] :
% 2.86/3.07 ( ( ord_less_eq_num @ B3 @ A3 )
% 2.86/3.07 & ~ ( ord_less_eq_num @ A3 @ B3 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % dual_order.strict_iff_not
% 2.86/3.07 thf(fact_1963_dual__order_Ostrict__iff__not,axiom,
% 2.86/3.07 ( ord_less_assn
% 2.86/3.07 = ( ^ [B3: assn,A3: assn] :
% 2.86/3.07 ( ( ord_less_eq_assn @ B3 @ A3 )
% 2.86/3.07 & ~ ( ord_less_eq_assn @ A3 @ B3 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % dual_order.strict_iff_not
% 2.86/3.07 thf(fact_1964_dual__order_Ostrict__iff__not,axiom,
% 2.86/3.07 ( ord_less_filter_nat
% 2.86/3.07 = ( ^ [B3: filter_nat,A3: filter_nat] :
% 2.86/3.07 ( ( ord_le2510731241096832064er_nat @ B3 @ A3 )
% 2.86/3.07 & ~ ( ord_le2510731241096832064er_nat @ A3 @ B3 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % dual_order.strict_iff_not
% 2.86/3.07 thf(fact_1965_dual__order_Ostrict__iff__not,axiom,
% 2.86/3.07 ( ord_less_set_nat
% 2.86/3.07 = ( ^ [B3: set_nat,A3: set_nat] :
% 2.86/3.07 ( ( ord_less_eq_set_nat @ B3 @ A3 )
% 2.86/3.07 & ~ ( ord_less_eq_set_nat @ A3 @ B3 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % dual_order.strict_iff_not
% 2.86/3.07 thf(fact_1966_dual__order_Ostrict__iff__not,axiom,
% 2.86/3.07 ( ord_less_nat
% 2.86/3.07 = ( ^ [B3: nat,A3: nat] :
% 2.86/3.07 ( ( ord_less_eq_nat @ B3 @ A3 )
% 2.86/3.07 & ~ ( ord_less_eq_nat @ A3 @ B3 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % dual_order.strict_iff_not
% 2.86/3.07 thf(fact_1967_dual__order_Ostrict__iff__not,axiom,
% 2.86/3.07 ( ord_less_int
% 2.86/3.07 = ( ^ [B3: int,A3: int] :
% 2.86/3.07 ( ( ord_less_eq_int @ B3 @ A3 )
% 2.86/3.07 & ~ ( ord_less_eq_int @ A3 @ B3 ) ) ) ) ).
% 2.86/3.07
% 2.86/3.07 % dual_order.strict_iff_not
% 2.86/3.07 thf(fact_1968_dual__order_Ostrict__trans2,axiom,
% 2.86/3.07 ! [B2: code_integer,A2: code_integer,C: code_integer] :
% 2.86/3.07 ( ( ord_le6747313008572928689nteger @ B2 @ A2 )
% 2.86/3.08 => ( ( ord_le3102999989581377725nteger @ C @ B2 )
% 2.86/3.08 => ( ord_le6747313008572928689nteger @ C @ A2 ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % dual_order.strict_trans2
% 2.86/3.08 thf(fact_1969_dual__order_Ostrict__trans2,axiom,
% 2.86/3.08 ! [B2: num,A2: num,C: num] :
% 2.86/3.08 ( ( ord_less_num @ B2 @ A2 )
% 2.86/3.08 => ( ( ord_less_eq_num @ C @ B2 )
% 2.86/3.08 => ( ord_less_num @ C @ A2 ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % dual_order.strict_trans2
% 2.86/3.08 thf(fact_1970_dual__order_Ostrict__trans2,axiom,
% 2.86/3.08 ! [B2: assn,A2: assn,C: assn] :
% 2.86/3.08 ( ( ord_less_assn @ B2 @ A2 )
% 2.86/3.08 => ( ( ord_less_eq_assn @ C @ B2 )
% 2.86/3.08 => ( ord_less_assn @ C @ A2 ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % dual_order.strict_trans2
% 2.86/3.08 thf(fact_1971_dual__order_Ostrict__trans2,axiom,
% 2.86/3.08 ! [B2: filter_nat,A2: filter_nat,C: filter_nat] :
% 2.86/3.08 ( ( ord_less_filter_nat @ B2 @ A2 )
% 2.86/3.08 => ( ( ord_le2510731241096832064er_nat @ C @ B2 )
% 2.86/3.08 => ( ord_less_filter_nat @ C @ A2 ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % dual_order.strict_trans2
% 2.86/3.08 thf(fact_1972_dual__order_Ostrict__trans2,axiom,
% 2.86/3.08 ! [B2: set_nat,A2: set_nat,C: set_nat] :
% 2.86/3.08 ( ( ord_less_set_nat @ B2 @ A2 )
% 2.86/3.08 => ( ( ord_less_eq_set_nat @ C @ B2 )
% 2.86/3.08 => ( ord_less_set_nat @ C @ A2 ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % dual_order.strict_trans2
% 2.86/3.08 thf(fact_1973_dual__order_Ostrict__trans2,axiom,
% 2.86/3.08 ! [B2: nat,A2: nat,C: nat] :
% 2.86/3.08 ( ( ord_less_nat @ B2 @ A2 )
% 2.86/3.08 => ( ( ord_less_eq_nat @ C @ B2 )
% 2.86/3.08 => ( ord_less_nat @ C @ A2 ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % dual_order.strict_trans2
% 2.86/3.08 thf(fact_1974_dual__order_Ostrict__trans2,axiom,
% 2.86/3.08 ! [B2: int,A2: int,C: int] :
% 2.86/3.08 ( ( ord_less_int @ B2 @ A2 )
% 2.86/3.08 => ( ( ord_less_eq_int @ C @ B2 )
% 2.86/3.08 => ( ord_less_int @ C @ A2 ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % dual_order.strict_trans2
% 2.86/3.08 thf(fact_1975_dual__order_Ostrict__trans1,axiom,
% 2.86/3.08 ! [B2: code_integer,A2: code_integer,C: code_integer] :
% 2.86/3.08 ( ( ord_le3102999989581377725nteger @ B2 @ A2 )
% 2.86/3.08 => ( ( ord_le6747313008572928689nteger @ C @ B2 )
% 2.86/3.08 => ( ord_le6747313008572928689nteger @ C @ A2 ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % dual_order.strict_trans1
% 2.86/3.08 thf(fact_1976_dual__order_Ostrict__trans1,axiom,
% 2.86/3.08 ! [B2: num,A2: num,C: num] :
% 2.86/3.08 ( ( ord_less_eq_num @ B2 @ A2 )
% 2.86/3.08 => ( ( ord_less_num @ C @ B2 )
% 2.86/3.08 => ( ord_less_num @ C @ A2 ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % dual_order.strict_trans1
% 2.86/3.08 thf(fact_1977_dual__order_Ostrict__trans1,axiom,
% 2.86/3.08 ! [B2: assn,A2: assn,C: assn] :
% 2.86/3.08 ( ( ord_less_eq_assn @ B2 @ A2 )
% 2.86/3.08 => ( ( ord_less_assn @ C @ B2 )
% 2.86/3.08 => ( ord_less_assn @ C @ A2 ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % dual_order.strict_trans1
% 2.86/3.08 thf(fact_1978_dual__order_Ostrict__trans1,axiom,
% 2.86/3.08 ! [B2: filter_nat,A2: filter_nat,C: filter_nat] :
% 2.86/3.08 ( ( ord_le2510731241096832064er_nat @ B2 @ A2 )
% 2.86/3.08 => ( ( ord_less_filter_nat @ C @ B2 )
% 2.86/3.08 => ( ord_less_filter_nat @ C @ A2 ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % dual_order.strict_trans1
% 2.86/3.08 thf(fact_1979_dual__order_Ostrict__trans1,axiom,
% 2.86/3.08 ! [B2: set_nat,A2: set_nat,C: set_nat] :
% 2.86/3.08 ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 2.86/3.08 => ( ( ord_less_set_nat @ C @ B2 )
% 2.86/3.08 => ( ord_less_set_nat @ C @ A2 ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % dual_order.strict_trans1
% 2.86/3.08 thf(fact_1980_dual__order_Ostrict__trans1,axiom,
% 2.86/3.08 ! [B2: nat,A2: nat,C: nat] :
% 2.86/3.08 ( ( ord_less_eq_nat @ B2 @ A2 )
% 2.86/3.08 => ( ( ord_less_nat @ C @ B2 )
% 2.86/3.08 => ( ord_less_nat @ C @ A2 ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % dual_order.strict_trans1
% 2.86/3.08 thf(fact_1981_dual__order_Ostrict__trans1,axiom,
% 2.86/3.08 ! [B2: int,A2: int,C: int] :
% 2.86/3.08 ( ( ord_less_eq_int @ B2 @ A2 )
% 2.86/3.08 => ( ( ord_less_int @ C @ B2 )
% 2.86/3.08 => ( ord_less_int @ C @ A2 ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % dual_order.strict_trans1
% 2.86/3.08 thf(fact_1982_dual__order_Ostrict__iff__order,axiom,
% 2.86/3.08 ( ord_le6747313008572928689nteger
% 2.86/3.08 = ( ^ [B3: code_integer,A3: code_integer] :
% 2.86/3.08 ( ( ord_le3102999989581377725nteger @ B3 @ A3 )
% 2.86/3.08 & ( A3 != B3 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % dual_order.strict_iff_order
% 2.86/3.08 thf(fact_1983_dual__order_Ostrict__iff__order,axiom,
% 2.86/3.08 ( ord_less_num
% 2.86/3.08 = ( ^ [B3: num,A3: num] :
% 2.86/3.08 ( ( ord_less_eq_num @ B3 @ A3 )
% 2.86/3.08 & ( A3 != B3 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % dual_order.strict_iff_order
% 2.86/3.08 thf(fact_1984_dual__order_Ostrict__iff__order,axiom,
% 2.86/3.08 ( ord_less_assn
% 2.86/3.08 = ( ^ [B3: assn,A3: assn] :
% 2.86/3.08 ( ( ord_less_eq_assn @ B3 @ A3 )
% 2.86/3.08 & ( A3 != B3 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % dual_order.strict_iff_order
% 2.86/3.08 thf(fact_1985_dual__order_Ostrict__iff__order,axiom,
% 2.86/3.08 ( ord_less_filter_nat
% 2.86/3.08 = ( ^ [B3: filter_nat,A3: filter_nat] :
% 2.86/3.08 ( ( ord_le2510731241096832064er_nat @ B3 @ A3 )
% 2.86/3.08 & ( A3 != B3 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % dual_order.strict_iff_order
% 2.86/3.08 thf(fact_1986_dual__order_Ostrict__iff__order,axiom,
% 2.86/3.08 ( ord_less_set_nat
% 2.86/3.08 = ( ^ [B3: set_nat,A3: set_nat] :
% 2.86/3.08 ( ( ord_less_eq_set_nat @ B3 @ A3 )
% 2.86/3.08 & ( A3 != B3 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % dual_order.strict_iff_order
% 2.86/3.08 thf(fact_1987_dual__order_Ostrict__iff__order,axiom,
% 2.86/3.08 ( ord_less_nat
% 2.86/3.08 = ( ^ [B3: nat,A3: nat] :
% 2.86/3.08 ( ( ord_less_eq_nat @ B3 @ A3 )
% 2.86/3.08 & ( A3 != B3 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % dual_order.strict_iff_order
% 2.86/3.08 thf(fact_1988_dual__order_Ostrict__iff__order,axiom,
% 2.86/3.08 ( ord_less_int
% 2.86/3.08 = ( ^ [B3: int,A3: int] :
% 2.86/3.08 ( ( ord_less_eq_int @ B3 @ A3 )
% 2.86/3.08 & ( A3 != B3 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % dual_order.strict_iff_order
% 2.86/3.08 thf(fact_1989_dual__order_Oorder__iff__strict,axiom,
% 2.86/3.08 ( ord_le3102999989581377725nteger
% 2.86/3.08 = ( ^ [B3: code_integer,A3: code_integer] :
% 2.86/3.08 ( ( ord_le6747313008572928689nteger @ B3 @ A3 )
% 2.86/3.08 | ( A3 = B3 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % dual_order.order_iff_strict
% 2.86/3.08 thf(fact_1990_dual__order_Oorder__iff__strict,axiom,
% 2.86/3.08 ( ord_less_eq_num
% 2.86/3.08 = ( ^ [B3: num,A3: num] :
% 2.86/3.08 ( ( ord_less_num @ B3 @ A3 )
% 2.86/3.08 | ( A3 = B3 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % dual_order.order_iff_strict
% 2.86/3.08 thf(fact_1991_dual__order_Oorder__iff__strict,axiom,
% 2.86/3.08 ( ord_less_eq_assn
% 2.86/3.08 = ( ^ [B3: assn,A3: assn] :
% 2.86/3.08 ( ( ord_less_assn @ B3 @ A3 )
% 2.86/3.08 | ( A3 = B3 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % dual_order.order_iff_strict
% 2.86/3.08 thf(fact_1992_dual__order_Oorder__iff__strict,axiom,
% 2.86/3.08 ( ord_le2510731241096832064er_nat
% 2.86/3.08 = ( ^ [B3: filter_nat,A3: filter_nat] :
% 2.86/3.08 ( ( ord_less_filter_nat @ B3 @ A3 )
% 2.86/3.08 | ( A3 = B3 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % dual_order.order_iff_strict
% 2.86/3.08 thf(fact_1993_dual__order_Oorder__iff__strict,axiom,
% 2.86/3.08 ( ord_less_eq_set_nat
% 2.86/3.08 = ( ^ [B3: set_nat,A3: set_nat] :
% 2.86/3.08 ( ( ord_less_set_nat @ B3 @ A3 )
% 2.86/3.08 | ( A3 = B3 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % dual_order.order_iff_strict
% 2.86/3.08 thf(fact_1994_dual__order_Oorder__iff__strict,axiom,
% 2.86/3.08 ( ord_less_eq_nat
% 2.86/3.08 = ( ^ [B3: nat,A3: nat] :
% 2.86/3.08 ( ( ord_less_nat @ B3 @ A3 )
% 2.86/3.08 | ( A3 = B3 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % dual_order.order_iff_strict
% 2.86/3.08 thf(fact_1995_dual__order_Oorder__iff__strict,axiom,
% 2.86/3.08 ( ord_less_eq_int
% 2.86/3.08 = ( ^ [B3: int,A3: int] :
% 2.86/3.08 ( ( ord_less_int @ B3 @ A3 )
% 2.86/3.08 | ( A3 = B3 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % dual_order.order_iff_strict
% 2.86/3.08 thf(fact_1996_order_Ostrict__iff__not,axiom,
% 2.86/3.08 ( ord_le6747313008572928689nteger
% 2.86/3.08 = ( ^ [A3: code_integer,B3: code_integer] :
% 2.86/3.08 ( ( ord_le3102999989581377725nteger @ A3 @ B3 )
% 2.86/3.08 & ~ ( ord_le3102999989581377725nteger @ B3 @ A3 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % order.strict_iff_not
% 2.86/3.08 thf(fact_1997_order_Ostrict__iff__not,axiom,
% 2.86/3.08 ( ord_less_num
% 2.86/3.08 = ( ^ [A3: num,B3: num] :
% 2.86/3.08 ( ( ord_less_eq_num @ A3 @ B3 )
% 2.86/3.08 & ~ ( ord_less_eq_num @ B3 @ A3 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % order.strict_iff_not
% 2.86/3.08 thf(fact_1998_order_Ostrict__iff__not,axiom,
% 2.86/3.08 ( ord_less_assn
% 2.86/3.08 = ( ^ [A3: assn,B3: assn] :
% 2.86/3.08 ( ( ord_less_eq_assn @ A3 @ B3 )
% 2.86/3.08 & ~ ( ord_less_eq_assn @ B3 @ A3 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % order.strict_iff_not
% 2.86/3.08 thf(fact_1999_order_Ostrict__iff__not,axiom,
% 2.86/3.08 ( ord_less_filter_nat
% 2.86/3.08 = ( ^ [A3: filter_nat,B3: filter_nat] :
% 2.86/3.08 ( ( ord_le2510731241096832064er_nat @ A3 @ B3 )
% 2.86/3.08 & ~ ( ord_le2510731241096832064er_nat @ B3 @ A3 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % order.strict_iff_not
% 2.86/3.08 thf(fact_2000_order_Ostrict__iff__not,axiom,
% 2.86/3.08 ( ord_less_set_nat
% 2.86/3.08 = ( ^ [A3: set_nat,B3: set_nat] :
% 2.86/3.08 ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 2.86/3.08 & ~ ( ord_less_eq_set_nat @ B3 @ A3 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % order.strict_iff_not
% 2.86/3.08 thf(fact_2001_order_Ostrict__iff__not,axiom,
% 2.86/3.08 ( ord_less_nat
% 2.86/3.08 = ( ^ [A3: nat,B3: nat] :
% 2.86/3.08 ( ( ord_less_eq_nat @ A3 @ B3 )
% 2.86/3.08 & ~ ( ord_less_eq_nat @ B3 @ A3 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % order.strict_iff_not
% 2.86/3.08 thf(fact_2002_order_Ostrict__iff__not,axiom,
% 2.86/3.08 ( ord_less_int
% 2.86/3.08 = ( ^ [A3: int,B3: int] :
% 2.86/3.08 ( ( ord_less_eq_int @ A3 @ B3 )
% 2.86/3.08 & ~ ( ord_less_eq_int @ B3 @ A3 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % order.strict_iff_not
% 2.86/3.08 thf(fact_2003_order_Ostrict__trans2,axiom,
% 2.86/3.08 ! [A2: code_integer,B2: code_integer,C: code_integer] :
% 2.86/3.08 ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 2.86/3.08 => ( ( ord_le3102999989581377725nteger @ B2 @ C )
% 2.86/3.08 => ( ord_le6747313008572928689nteger @ A2 @ C ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % order.strict_trans2
% 2.86/3.08 thf(fact_2004_order_Ostrict__trans2,axiom,
% 2.86/3.08 ! [A2: num,B2: num,C: num] :
% 2.86/3.08 ( ( ord_less_num @ A2 @ B2 )
% 2.86/3.08 => ( ( ord_less_eq_num @ B2 @ C )
% 2.86/3.08 => ( ord_less_num @ A2 @ C ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % order.strict_trans2
% 2.86/3.08 thf(fact_2005_order_Ostrict__trans2,axiom,
% 2.86/3.08 ! [A2: assn,B2: assn,C: assn] :
% 2.86/3.08 ( ( ord_less_assn @ A2 @ B2 )
% 2.86/3.08 => ( ( ord_less_eq_assn @ B2 @ C )
% 2.86/3.08 => ( ord_less_assn @ A2 @ C ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % order.strict_trans2
% 2.86/3.08 thf(fact_2006_order_Ostrict__trans2,axiom,
% 2.86/3.08 ! [A2: filter_nat,B2: filter_nat,C: filter_nat] :
% 2.86/3.08 ( ( ord_less_filter_nat @ A2 @ B2 )
% 2.86/3.08 => ( ( ord_le2510731241096832064er_nat @ B2 @ C )
% 2.86/3.08 => ( ord_less_filter_nat @ A2 @ C ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % order.strict_trans2
% 2.86/3.08 thf(fact_2007_order_Ostrict__trans2,axiom,
% 2.86/3.08 ! [A2: set_nat,B2: set_nat,C: set_nat] :
% 2.86/3.08 ( ( ord_less_set_nat @ A2 @ B2 )
% 2.86/3.08 => ( ( ord_less_eq_set_nat @ B2 @ C )
% 2.86/3.08 => ( ord_less_set_nat @ A2 @ C ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % order.strict_trans2
% 2.86/3.08 thf(fact_2008_order_Ostrict__trans2,axiom,
% 2.86/3.08 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.08 ( ( ord_less_nat @ A2 @ B2 )
% 2.86/3.08 => ( ( ord_less_eq_nat @ B2 @ C )
% 2.86/3.08 => ( ord_less_nat @ A2 @ C ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % order.strict_trans2
% 2.86/3.08 thf(fact_2009_order_Ostrict__trans2,axiom,
% 2.86/3.08 ! [A2: int,B2: int,C: int] :
% 2.86/3.08 ( ( ord_less_int @ A2 @ B2 )
% 2.86/3.08 => ( ( ord_less_eq_int @ B2 @ C )
% 2.86/3.08 => ( ord_less_int @ A2 @ C ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % order.strict_trans2
% 2.86/3.08 thf(fact_2010_order_Ostrict__trans1,axiom,
% 2.86/3.08 ! [A2: code_integer,B2: code_integer,C: code_integer] :
% 2.86/3.08 ( ( ord_le3102999989581377725nteger @ A2 @ B2 )
% 2.86/3.08 => ( ( ord_le6747313008572928689nteger @ B2 @ C )
% 2.86/3.08 => ( ord_le6747313008572928689nteger @ A2 @ C ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % order.strict_trans1
% 2.86/3.08 thf(fact_2011_order_Ostrict__trans1,axiom,
% 2.86/3.08 ! [A2: num,B2: num,C: num] :
% 2.86/3.08 ( ( ord_less_eq_num @ A2 @ B2 )
% 2.86/3.08 => ( ( ord_less_num @ B2 @ C )
% 2.86/3.08 => ( ord_less_num @ A2 @ C ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % order.strict_trans1
% 2.86/3.08 thf(fact_2012_order_Ostrict__trans1,axiom,
% 2.86/3.08 ! [A2: assn,B2: assn,C: assn] :
% 2.86/3.08 ( ( ord_less_eq_assn @ A2 @ B2 )
% 2.86/3.08 => ( ( ord_less_assn @ B2 @ C )
% 2.86/3.08 => ( ord_less_assn @ A2 @ C ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % order.strict_trans1
% 2.86/3.08 thf(fact_2013_order_Ostrict__trans1,axiom,
% 2.86/3.08 ! [A2: filter_nat,B2: filter_nat,C: filter_nat] :
% 2.86/3.08 ( ( ord_le2510731241096832064er_nat @ A2 @ B2 )
% 2.86/3.08 => ( ( ord_less_filter_nat @ B2 @ C )
% 2.86/3.08 => ( ord_less_filter_nat @ A2 @ C ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % order.strict_trans1
% 2.86/3.08 thf(fact_2014_order_Ostrict__trans1,axiom,
% 2.86/3.08 ! [A2: set_nat,B2: set_nat,C: set_nat] :
% 2.86/3.08 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 2.86/3.08 => ( ( ord_less_set_nat @ B2 @ C )
% 2.86/3.08 => ( ord_less_set_nat @ A2 @ C ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % order.strict_trans1
% 2.86/3.08 thf(fact_2015_order_Ostrict__trans1,axiom,
% 2.86/3.08 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.08 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.08 => ( ( ord_less_nat @ B2 @ C )
% 2.86/3.08 => ( ord_less_nat @ A2 @ C ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % order.strict_trans1
% 2.86/3.08 thf(fact_2016_order_Ostrict__trans1,axiom,
% 2.86/3.08 ! [A2: int,B2: int,C: int] :
% 2.86/3.08 ( ( ord_less_eq_int @ A2 @ B2 )
% 2.86/3.08 => ( ( ord_less_int @ B2 @ C )
% 2.86/3.08 => ( ord_less_int @ A2 @ C ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % order.strict_trans1
% 2.86/3.08 thf(fact_2017_order_Ostrict__iff__order,axiom,
% 2.86/3.08 ( ord_le6747313008572928689nteger
% 2.86/3.08 = ( ^ [A3: code_integer,B3: code_integer] :
% 2.86/3.08 ( ( ord_le3102999989581377725nteger @ A3 @ B3 )
% 2.86/3.08 & ( A3 != B3 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % order.strict_iff_order
% 2.86/3.08 thf(fact_2018_order_Ostrict__iff__order,axiom,
% 2.86/3.08 ( ord_less_num
% 2.86/3.08 = ( ^ [A3: num,B3: num] :
% 2.86/3.08 ( ( ord_less_eq_num @ A3 @ B3 )
% 2.86/3.08 & ( A3 != B3 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % order.strict_iff_order
% 2.86/3.08 thf(fact_2019_order_Ostrict__iff__order,axiom,
% 2.86/3.08 ( ord_less_assn
% 2.86/3.08 = ( ^ [A3: assn,B3: assn] :
% 2.86/3.08 ( ( ord_less_eq_assn @ A3 @ B3 )
% 2.86/3.08 & ( A3 != B3 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % order.strict_iff_order
% 2.86/3.08 thf(fact_2020_order_Ostrict__iff__order,axiom,
% 2.86/3.08 ( ord_less_filter_nat
% 2.86/3.08 = ( ^ [A3: filter_nat,B3: filter_nat] :
% 2.86/3.08 ( ( ord_le2510731241096832064er_nat @ A3 @ B3 )
% 2.86/3.08 & ( A3 != B3 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % order.strict_iff_order
% 2.86/3.08 thf(fact_2021_order_Ostrict__iff__order,axiom,
% 2.86/3.08 ( ord_less_set_nat
% 2.86/3.08 = ( ^ [A3: set_nat,B3: set_nat] :
% 2.86/3.08 ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 2.86/3.08 & ( A3 != B3 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % order.strict_iff_order
% 2.86/3.08 thf(fact_2022_order_Ostrict__iff__order,axiom,
% 2.86/3.08 ( ord_less_nat
% 2.86/3.08 = ( ^ [A3: nat,B3: nat] :
% 2.86/3.08 ( ( ord_less_eq_nat @ A3 @ B3 )
% 2.86/3.08 & ( A3 != B3 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % order.strict_iff_order
% 2.86/3.08 thf(fact_2023_order_Ostrict__iff__order,axiom,
% 2.86/3.08 ( ord_less_int
% 2.86/3.08 = ( ^ [A3: int,B3: int] :
% 2.86/3.08 ( ( ord_less_eq_int @ A3 @ B3 )
% 2.86/3.08 & ( A3 != B3 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % order.strict_iff_order
% 2.86/3.08 thf(fact_2024_order_Oorder__iff__strict,axiom,
% 2.86/3.08 ( ord_le3102999989581377725nteger
% 2.86/3.08 = ( ^ [A3: code_integer,B3: code_integer] :
% 2.86/3.08 ( ( ord_le6747313008572928689nteger @ A3 @ B3 )
% 2.86/3.08 | ( A3 = B3 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % order.order_iff_strict
% 2.86/3.08 thf(fact_2025_order_Oorder__iff__strict,axiom,
% 2.86/3.08 ( ord_less_eq_num
% 2.86/3.08 = ( ^ [A3: num,B3: num] :
% 2.86/3.08 ( ( ord_less_num @ A3 @ B3 )
% 2.86/3.08 | ( A3 = B3 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % order.order_iff_strict
% 2.86/3.08 thf(fact_2026_order_Oorder__iff__strict,axiom,
% 2.86/3.08 ( ord_less_eq_assn
% 2.86/3.08 = ( ^ [A3: assn,B3: assn] :
% 2.86/3.08 ( ( ord_less_assn @ A3 @ B3 )
% 2.86/3.08 | ( A3 = B3 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % order.order_iff_strict
% 2.86/3.08 thf(fact_2027_order_Oorder__iff__strict,axiom,
% 2.86/3.08 ( ord_le2510731241096832064er_nat
% 2.86/3.08 = ( ^ [A3: filter_nat,B3: filter_nat] :
% 2.86/3.08 ( ( ord_less_filter_nat @ A3 @ B3 )
% 2.86/3.08 | ( A3 = B3 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % order.order_iff_strict
% 2.86/3.08 thf(fact_2028_order_Oorder__iff__strict,axiom,
% 2.86/3.08 ( ord_less_eq_set_nat
% 2.86/3.08 = ( ^ [A3: set_nat,B3: set_nat] :
% 2.86/3.08 ( ( ord_less_set_nat @ A3 @ B3 )
% 2.86/3.08 | ( A3 = B3 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % order.order_iff_strict
% 2.86/3.08 thf(fact_2029_order_Oorder__iff__strict,axiom,
% 2.86/3.08 ( ord_less_eq_nat
% 2.86/3.08 = ( ^ [A3: nat,B3: nat] :
% 2.86/3.08 ( ( ord_less_nat @ A3 @ B3 )
% 2.86/3.08 | ( A3 = B3 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % order.order_iff_strict
% 2.86/3.08 thf(fact_2030_order_Oorder__iff__strict,axiom,
% 2.86/3.08 ( ord_less_eq_int
% 2.86/3.08 = ( ^ [A3: int,B3: int] :
% 2.86/3.08 ( ( ord_less_int @ A3 @ B3 )
% 2.86/3.08 | ( A3 = B3 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % order.order_iff_strict
% 2.86/3.08 thf(fact_2031_not__le__imp__less,axiom,
% 2.86/3.08 ! [Y: code_integer,X: code_integer] :
% 2.86/3.08 ( ~ ( ord_le3102999989581377725nteger @ Y @ X )
% 2.86/3.08 => ( ord_le6747313008572928689nteger @ X @ Y ) ) ).
% 2.86/3.08
% 2.86/3.08 % not_le_imp_less
% 2.86/3.08 thf(fact_2032_not__le__imp__less,axiom,
% 2.86/3.08 ! [Y: num,X: num] :
% 2.86/3.08 ( ~ ( ord_less_eq_num @ Y @ X )
% 2.86/3.08 => ( ord_less_num @ X @ Y ) ) ).
% 2.86/3.08
% 2.86/3.08 % not_le_imp_less
% 2.86/3.08 thf(fact_2033_not__le__imp__less,axiom,
% 2.86/3.08 ! [Y: nat,X: nat] :
% 2.86/3.08 ( ~ ( ord_less_eq_nat @ Y @ X )
% 2.86/3.08 => ( ord_less_nat @ X @ Y ) ) ).
% 2.86/3.08
% 2.86/3.08 % not_le_imp_less
% 2.86/3.08 thf(fact_2034_not__le__imp__less,axiom,
% 2.86/3.08 ! [Y: int,X: int] :
% 2.86/3.08 ( ~ ( ord_less_eq_int @ Y @ X )
% 2.86/3.08 => ( ord_less_int @ X @ Y ) ) ).
% 2.86/3.08
% 2.86/3.08 % not_le_imp_less
% 2.86/3.08 thf(fact_2035_less__le__not__le,axiom,
% 2.86/3.08 ( ord_le6747313008572928689nteger
% 2.86/3.08 = ( ^ [X2: code_integer,Y5: code_integer] :
% 2.86/3.08 ( ( ord_le3102999989581377725nteger @ X2 @ Y5 )
% 2.86/3.08 & ~ ( ord_le3102999989581377725nteger @ Y5 @ X2 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % less_le_not_le
% 2.86/3.08 thf(fact_2036_less__le__not__le,axiom,
% 2.86/3.08 ( ord_less_num
% 2.86/3.08 = ( ^ [X2: num,Y5: num] :
% 2.86/3.08 ( ( ord_less_eq_num @ X2 @ Y5 )
% 2.86/3.08 & ~ ( ord_less_eq_num @ Y5 @ X2 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % less_le_not_le
% 2.86/3.08 thf(fact_2037_less__le__not__le,axiom,
% 2.86/3.08 ( ord_less_assn
% 2.86/3.08 = ( ^ [X2: assn,Y5: assn] :
% 2.86/3.08 ( ( ord_less_eq_assn @ X2 @ Y5 )
% 2.86/3.08 & ~ ( ord_less_eq_assn @ Y5 @ X2 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % less_le_not_le
% 2.86/3.08 thf(fact_2038_less__le__not__le,axiom,
% 2.86/3.08 ( ord_less_filter_nat
% 2.86/3.08 = ( ^ [X2: filter_nat,Y5: filter_nat] :
% 2.86/3.08 ( ( ord_le2510731241096832064er_nat @ X2 @ Y5 )
% 2.86/3.08 & ~ ( ord_le2510731241096832064er_nat @ Y5 @ X2 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % less_le_not_le
% 2.86/3.08 thf(fact_2039_less__le__not__le,axiom,
% 2.86/3.08 ( ord_less_set_nat
% 2.86/3.08 = ( ^ [X2: set_nat,Y5: set_nat] :
% 2.86/3.08 ( ( ord_less_eq_set_nat @ X2 @ Y5 )
% 2.86/3.08 & ~ ( ord_less_eq_set_nat @ Y5 @ X2 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % less_le_not_le
% 2.86/3.08 thf(fact_2040_less__le__not__le,axiom,
% 2.86/3.08 ( ord_less_nat
% 2.86/3.08 = ( ^ [X2: nat,Y5: nat] :
% 2.86/3.08 ( ( ord_less_eq_nat @ X2 @ Y5 )
% 2.86/3.08 & ~ ( ord_less_eq_nat @ Y5 @ X2 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % less_le_not_le
% 2.86/3.08 thf(fact_2041_less__le__not__le,axiom,
% 2.86/3.08 ( ord_less_int
% 2.86/3.08 = ( ^ [X2: int,Y5: int] :
% 2.86/3.08 ( ( ord_less_eq_int @ X2 @ Y5 )
% 2.86/3.08 & ~ ( ord_less_eq_int @ Y5 @ X2 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % less_le_not_le
% 2.86/3.08 thf(fact_2042_antisym__conv2,axiom,
% 2.86/3.08 ! [X: code_integer,Y: code_integer] :
% 2.86/3.08 ( ( ord_le3102999989581377725nteger @ X @ Y )
% 2.86/3.08 => ( ( ~ ( ord_le6747313008572928689nteger @ X @ Y ) )
% 2.86/3.08 = ( X = Y ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % antisym_conv2
% 2.86/3.08 thf(fact_2043_antisym__conv2,axiom,
% 2.86/3.08 ! [X: num,Y: num] :
% 2.86/3.08 ( ( ord_less_eq_num @ X @ Y )
% 2.86/3.08 => ( ( ~ ( ord_less_num @ X @ Y ) )
% 2.86/3.08 = ( X = Y ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % antisym_conv2
% 2.86/3.08 thf(fact_2044_antisym__conv2,axiom,
% 2.86/3.08 ! [X: assn,Y: assn] :
% 2.86/3.08 ( ( ord_less_eq_assn @ X @ Y )
% 2.86/3.08 => ( ( ~ ( ord_less_assn @ X @ Y ) )
% 2.86/3.08 = ( X = Y ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % antisym_conv2
% 2.86/3.08 thf(fact_2045_antisym__conv2,axiom,
% 2.86/3.08 ! [X: filter_nat,Y: filter_nat] :
% 2.86/3.08 ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 2.86/3.08 => ( ( ~ ( ord_less_filter_nat @ X @ Y ) )
% 2.86/3.08 = ( X = Y ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % antisym_conv2
% 2.86/3.08 thf(fact_2046_antisym__conv2,axiom,
% 2.86/3.08 ! [X: set_nat,Y: set_nat] :
% 2.86/3.08 ( ( ord_less_eq_set_nat @ X @ Y )
% 2.86/3.08 => ( ( ~ ( ord_less_set_nat @ X @ Y ) )
% 2.86/3.08 = ( X = Y ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % antisym_conv2
% 2.86/3.08 thf(fact_2047_antisym__conv2,axiom,
% 2.86/3.08 ! [X: nat,Y: nat] :
% 2.86/3.08 ( ( ord_less_eq_nat @ X @ Y )
% 2.86/3.08 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 2.86/3.08 = ( X = Y ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % antisym_conv2
% 2.86/3.08 thf(fact_2048_antisym__conv2,axiom,
% 2.86/3.08 ! [X: int,Y: int] :
% 2.86/3.08 ( ( ord_less_eq_int @ X @ Y )
% 2.86/3.08 => ( ( ~ ( ord_less_int @ X @ Y ) )
% 2.86/3.08 = ( X = Y ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % antisym_conv2
% 2.86/3.08 thf(fact_2049_antisym__conv1,axiom,
% 2.86/3.08 ! [X: code_integer,Y: code_integer] :
% 2.86/3.08 ( ~ ( ord_le6747313008572928689nteger @ X @ Y )
% 2.86/3.08 => ( ( ord_le3102999989581377725nteger @ X @ Y )
% 2.86/3.08 = ( X = Y ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % antisym_conv1
% 2.86/3.08 thf(fact_2050_antisym__conv1,axiom,
% 2.86/3.08 ! [X: num,Y: num] :
% 2.86/3.08 ( ~ ( ord_less_num @ X @ Y )
% 2.86/3.08 => ( ( ord_less_eq_num @ X @ Y )
% 2.86/3.08 = ( X = Y ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % antisym_conv1
% 2.86/3.08 thf(fact_2051_antisym__conv1,axiom,
% 2.86/3.08 ! [X: assn,Y: assn] :
% 2.86/3.08 ( ~ ( ord_less_assn @ X @ Y )
% 2.86/3.08 => ( ( ord_less_eq_assn @ X @ Y )
% 2.86/3.08 = ( X = Y ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % antisym_conv1
% 2.86/3.08 thf(fact_2052_antisym__conv1,axiom,
% 2.86/3.08 ! [X: filter_nat,Y: filter_nat] :
% 2.86/3.08 ( ~ ( ord_less_filter_nat @ X @ Y )
% 2.86/3.08 => ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 2.86/3.08 = ( X = Y ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % antisym_conv1
% 2.86/3.08 thf(fact_2053_antisym__conv1,axiom,
% 2.86/3.08 ! [X: set_nat,Y: set_nat] :
% 2.86/3.08 ( ~ ( ord_less_set_nat @ X @ Y )
% 2.86/3.08 => ( ( ord_less_eq_set_nat @ X @ Y )
% 2.86/3.08 = ( X = Y ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % antisym_conv1
% 2.86/3.08 thf(fact_2054_antisym__conv1,axiom,
% 2.86/3.08 ! [X: nat,Y: nat] :
% 2.86/3.08 ( ~ ( ord_less_nat @ X @ Y )
% 2.86/3.08 => ( ( ord_less_eq_nat @ X @ Y )
% 2.86/3.08 = ( X = Y ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % antisym_conv1
% 2.86/3.08 thf(fact_2055_antisym__conv1,axiom,
% 2.86/3.08 ! [X: int,Y: int] :
% 2.86/3.08 ( ~ ( ord_less_int @ X @ Y )
% 2.86/3.08 => ( ( ord_less_eq_int @ X @ Y )
% 2.86/3.08 = ( X = Y ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % antisym_conv1
% 2.86/3.08 thf(fact_2056_nless__le,axiom,
% 2.86/3.08 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.08 ( ( ~ ( ord_le6747313008572928689nteger @ A2 @ B2 ) )
% 2.86/3.08 = ( ~ ( ord_le3102999989581377725nteger @ A2 @ B2 )
% 2.86/3.08 | ( A2 = B2 ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % nless_le
% 2.86/3.08 thf(fact_2057_nless__le,axiom,
% 2.86/3.08 ! [A2: num,B2: num] :
% 2.86/3.08 ( ( ~ ( ord_less_num @ A2 @ B2 ) )
% 2.86/3.08 = ( ~ ( ord_less_eq_num @ A2 @ B2 )
% 2.86/3.08 | ( A2 = B2 ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % nless_le
% 2.86/3.08 thf(fact_2058_nless__le,axiom,
% 2.86/3.08 ! [A2: assn,B2: assn] :
% 2.86/3.08 ( ( ~ ( ord_less_assn @ A2 @ B2 ) )
% 2.86/3.08 = ( ~ ( ord_less_eq_assn @ A2 @ B2 )
% 2.86/3.08 | ( A2 = B2 ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % nless_le
% 2.86/3.08 thf(fact_2059_nless__le,axiom,
% 2.86/3.08 ! [A2: filter_nat,B2: filter_nat] :
% 2.86/3.08 ( ( ~ ( ord_less_filter_nat @ A2 @ B2 ) )
% 2.86/3.08 = ( ~ ( ord_le2510731241096832064er_nat @ A2 @ B2 )
% 2.86/3.08 | ( A2 = B2 ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % nless_le
% 2.86/3.08 thf(fact_2060_nless__le,axiom,
% 2.86/3.08 ! [A2: set_nat,B2: set_nat] :
% 2.86/3.08 ( ( ~ ( ord_less_set_nat @ A2 @ B2 ) )
% 2.86/3.08 = ( ~ ( ord_less_eq_set_nat @ A2 @ B2 )
% 2.86/3.08 | ( A2 = B2 ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % nless_le
% 2.86/3.08 thf(fact_2061_nless__le,axiom,
% 2.86/3.08 ! [A2: nat,B2: nat] :
% 2.86/3.08 ( ( ~ ( ord_less_nat @ A2 @ B2 ) )
% 2.86/3.08 = ( ~ ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.08 | ( A2 = B2 ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % nless_le
% 2.86/3.08 thf(fact_2062_nless__le,axiom,
% 2.86/3.08 ! [A2: int,B2: int] :
% 2.86/3.08 ( ( ~ ( ord_less_int @ A2 @ B2 ) )
% 2.86/3.08 = ( ~ ( ord_less_eq_int @ A2 @ B2 )
% 2.86/3.08 | ( A2 = B2 ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % nless_le
% 2.86/3.08 thf(fact_2063_leI,axiom,
% 2.86/3.08 ! [X: code_integer,Y: code_integer] :
% 2.86/3.08 ( ~ ( ord_le6747313008572928689nteger @ X @ Y )
% 2.86/3.08 => ( ord_le3102999989581377725nteger @ Y @ X ) ) ).
% 2.86/3.08
% 2.86/3.08 % leI
% 2.86/3.08 thf(fact_2064_leI,axiom,
% 2.86/3.08 ! [X: num,Y: num] :
% 2.86/3.08 ( ~ ( ord_less_num @ X @ Y )
% 2.86/3.08 => ( ord_less_eq_num @ Y @ X ) ) ).
% 2.86/3.08
% 2.86/3.08 % leI
% 2.86/3.08 thf(fact_2065_leI,axiom,
% 2.86/3.08 ! [X: nat,Y: nat] :
% 2.86/3.08 ( ~ ( ord_less_nat @ X @ Y )
% 2.86/3.08 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 2.86/3.08
% 2.86/3.08 % leI
% 2.86/3.08 thf(fact_2066_leI,axiom,
% 2.86/3.08 ! [X: int,Y: int] :
% 2.86/3.08 ( ~ ( ord_less_int @ X @ Y )
% 2.86/3.08 => ( ord_less_eq_int @ Y @ X ) ) ).
% 2.86/3.08
% 2.86/3.08 % leI
% 2.86/3.08 thf(fact_2067_leD,axiom,
% 2.86/3.08 ! [Y: code_integer,X: code_integer] :
% 2.86/3.08 ( ( ord_le3102999989581377725nteger @ Y @ X )
% 2.86/3.08 => ~ ( ord_le6747313008572928689nteger @ X @ Y ) ) ).
% 2.86/3.08
% 2.86/3.08 % leD
% 2.86/3.08 thf(fact_2068_leD,axiom,
% 2.86/3.08 ! [Y: num,X: num] :
% 2.86/3.08 ( ( ord_less_eq_num @ Y @ X )
% 2.86/3.08 => ~ ( ord_less_num @ X @ Y ) ) ).
% 2.86/3.08
% 2.86/3.08 % leD
% 2.86/3.08 thf(fact_2069_leD,axiom,
% 2.86/3.08 ! [Y: assn,X: assn] :
% 2.86/3.08 ( ( ord_less_eq_assn @ Y @ X )
% 2.86/3.08 => ~ ( ord_less_assn @ X @ Y ) ) ).
% 2.86/3.08
% 2.86/3.08 % leD
% 2.86/3.08 thf(fact_2070_leD,axiom,
% 2.86/3.08 ! [Y: filter_nat,X: filter_nat] :
% 2.86/3.08 ( ( ord_le2510731241096832064er_nat @ Y @ X )
% 2.86/3.08 => ~ ( ord_less_filter_nat @ X @ Y ) ) ).
% 2.86/3.08
% 2.86/3.08 % leD
% 2.86/3.08 thf(fact_2071_leD,axiom,
% 2.86/3.08 ! [Y: set_nat,X: set_nat] :
% 2.86/3.08 ( ( ord_less_eq_set_nat @ Y @ X )
% 2.86/3.08 => ~ ( ord_less_set_nat @ X @ Y ) ) ).
% 2.86/3.08
% 2.86/3.08 % leD
% 2.86/3.08 thf(fact_2072_leD,axiom,
% 2.86/3.08 ! [Y: nat,X: nat] :
% 2.86/3.08 ( ( ord_less_eq_nat @ Y @ X )
% 2.86/3.08 => ~ ( ord_less_nat @ X @ Y ) ) ).
% 2.86/3.08
% 2.86/3.08 % leD
% 2.86/3.08 thf(fact_2073_leD,axiom,
% 2.86/3.08 ! [Y: int,X: int] :
% 2.86/3.08 ( ( ord_less_eq_int @ Y @ X )
% 2.86/3.08 => ~ ( ord_less_int @ X @ Y ) ) ).
% 2.86/3.08
% 2.86/3.08 % leD
% 2.86/3.08 thf(fact_2074_bot_Oextremum__uniqueI,axiom,
% 2.86/3.08 ! [A2: set_Pr4329608150637261639at_nat] :
% 2.86/3.08 ( ( ord_le1268244103169919719at_nat @ A2 @ bot_bo228742789529271731at_nat )
% 2.86/3.08 => ( A2 = bot_bo228742789529271731at_nat ) ) ).
% 2.86/3.08
% 2.86/3.08 % bot.extremum_uniqueI
% 2.86/3.08 thf(fact_2075_bot_Oextremum__uniqueI,axiom,
% 2.86/3.08 ! [A2: set_Pr1261947904930325089at_nat] :
% 2.86/3.08 ( ( ord_le3146513528884898305at_nat @ A2 @ bot_bo2099793752762293965at_nat )
% 2.86/3.08 => ( A2 = bot_bo2099793752762293965at_nat ) ) ).
% 2.86/3.08
% 2.86/3.08 % bot.extremum_uniqueI
% 2.86/3.08 thf(fact_2076_bot_Oextremum__uniqueI,axiom,
% 2.86/3.08 ! [A2: set_o] :
% 2.86/3.08 ( ( ord_less_eq_set_o @ A2 @ bot_bot_set_o )
% 2.86/3.08 => ( A2 = bot_bot_set_o ) ) ).
% 2.86/3.08
% 2.86/3.08 % bot.extremum_uniqueI
% 2.86/3.08 thf(fact_2077_bot_Oextremum__uniqueI,axiom,
% 2.86/3.08 ! [A2: set_int] :
% 2.86/3.08 ( ( ord_less_eq_set_int @ A2 @ bot_bot_set_int )
% 2.86/3.08 => ( A2 = bot_bot_set_int ) ) ).
% 2.86/3.08
% 2.86/3.08 % bot.extremum_uniqueI
% 2.86/3.08 thf(fact_2078_bot_Oextremum__uniqueI,axiom,
% 2.86/3.08 ! [A2: assn] :
% 2.86/3.08 ( ( ord_less_eq_assn @ A2 @ bot_bot_assn )
% 2.86/3.08 => ( A2 = bot_bot_assn ) ) ).
% 2.86/3.08
% 2.86/3.08 % bot.extremum_uniqueI
% 2.86/3.08 thf(fact_2079_bot_Oextremum__uniqueI,axiom,
% 2.86/3.08 ! [A2: filter_nat] :
% 2.86/3.08 ( ( ord_le2510731241096832064er_nat @ A2 @ bot_bot_filter_nat )
% 2.86/3.08 => ( A2 = bot_bot_filter_nat ) ) ).
% 2.86/3.08
% 2.86/3.08 % bot.extremum_uniqueI
% 2.86/3.08 thf(fact_2080_bot_Oextremum__uniqueI,axiom,
% 2.86/3.08 ! [A2: set_nat] :
% 2.86/3.08 ( ( ord_less_eq_set_nat @ A2 @ bot_bot_set_nat )
% 2.86/3.08 => ( A2 = bot_bot_set_nat ) ) ).
% 2.86/3.08
% 2.86/3.08 % bot.extremum_uniqueI
% 2.86/3.08 thf(fact_2081_bot_Oextremum__uniqueI,axiom,
% 2.86/3.08 ! [A2: nat] :
% 2.86/3.08 ( ( ord_less_eq_nat @ A2 @ bot_bot_nat )
% 2.86/3.08 => ( A2 = bot_bot_nat ) ) ).
% 2.86/3.08
% 2.86/3.08 % bot.extremum_uniqueI
% 2.86/3.08 thf(fact_2082_bot_Oextremum__unique,axiom,
% 2.86/3.08 ! [A2: set_Pr4329608150637261639at_nat] :
% 2.86/3.08 ( ( ord_le1268244103169919719at_nat @ A2 @ bot_bo228742789529271731at_nat )
% 2.86/3.08 = ( A2 = bot_bo228742789529271731at_nat ) ) ).
% 2.86/3.08
% 2.86/3.08 % bot.extremum_unique
% 2.86/3.08 thf(fact_2083_bot_Oextremum__unique,axiom,
% 2.86/3.08 ! [A2: set_Pr1261947904930325089at_nat] :
% 2.86/3.08 ( ( ord_le3146513528884898305at_nat @ A2 @ bot_bo2099793752762293965at_nat )
% 2.86/3.08 = ( A2 = bot_bo2099793752762293965at_nat ) ) ).
% 2.86/3.08
% 2.86/3.08 % bot.extremum_unique
% 2.86/3.08 thf(fact_2084_bot_Oextremum__unique,axiom,
% 2.86/3.08 ! [A2: set_o] :
% 2.86/3.08 ( ( ord_less_eq_set_o @ A2 @ bot_bot_set_o )
% 2.86/3.08 = ( A2 = bot_bot_set_o ) ) ).
% 2.86/3.08
% 2.86/3.08 % bot.extremum_unique
% 2.86/3.08 thf(fact_2085_bot_Oextremum__unique,axiom,
% 2.86/3.08 ! [A2: set_int] :
% 2.86/3.08 ( ( ord_less_eq_set_int @ A2 @ bot_bot_set_int )
% 2.86/3.08 = ( A2 = bot_bot_set_int ) ) ).
% 2.86/3.08
% 2.86/3.08 % bot.extremum_unique
% 2.86/3.08 thf(fact_2086_bot_Oextremum__unique,axiom,
% 2.86/3.08 ! [A2: assn] :
% 2.86/3.08 ( ( ord_less_eq_assn @ A2 @ bot_bot_assn )
% 2.86/3.08 = ( A2 = bot_bot_assn ) ) ).
% 2.86/3.08
% 2.86/3.08 % bot.extremum_unique
% 2.86/3.08 thf(fact_2087_bot_Oextremum__unique,axiom,
% 2.86/3.08 ! [A2: filter_nat] :
% 2.86/3.08 ( ( ord_le2510731241096832064er_nat @ A2 @ bot_bot_filter_nat )
% 2.86/3.08 = ( A2 = bot_bot_filter_nat ) ) ).
% 2.86/3.08
% 2.86/3.08 % bot.extremum_unique
% 2.86/3.08 thf(fact_2088_bot_Oextremum__unique,axiom,
% 2.86/3.08 ! [A2: set_nat] :
% 2.86/3.08 ( ( ord_less_eq_set_nat @ A2 @ bot_bot_set_nat )
% 2.86/3.08 = ( A2 = bot_bot_set_nat ) ) ).
% 2.86/3.08
% 2.86/3.08 % bot.extremum_unique
% 2.86/3.08 thf(fact_2089_bot_Oextremum__unique,axiom,
% 2.86/3.08 ! [A2: nat] :
% 2.86/3.08 ( ( ord_less_eq_nat @ A2 @ bot_bot_nat )
% 2.86/3.08 = ( A2 = bot_bot_nat ) ) ).
% 2.86/3.08
% 2.86/3.08 % bot.extremum_unique
% 2.86/3.08 thf(fact_2090_bot_Oextremum,axiom,
% 2.86/3.08 ! [A2: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ bot_bo228742789529271731at_nat @ A2 ) ).
% 2.86/3.08
% 2.86/3.08 % bot.extremum
% 2.86/3.08 thf(fact_2091_bot_Oextremum,axiom,
% 2.86/3.08 ! [A2: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ bot_bo2099793752762293965at_nat @ A2 ) ).
% 2.86/3.08
% 2.86/3.08 % bot.extremum
% 2.86/3.08 thf(fact_2092_bot_Oextremum,axiom,
% 2.86/3.08 ! [A2: set_o] : ( ord_less_eq_set_o @ bot_bot_set_o @ A2 ) ).
% 2.86/3.08
% 2.86/3.08 % bot.extremum
% 2.86/3.08 thf(fact_2093_bot_Oextremum,axiom,
% 2.86/3.08 ! [A2: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A2 ) ).
% 2.86/3.08
% 2.86/3.08 % bot.extremum
% 2.86/3.08 thf(fact_2094_bot_Oextremum,axiom,
% 2.86/3.08 ! [A2: assn] : ( ord_less_eq_assn @ bot_bot_assn @ A2 ) ).
% 2.86/3.08
% 2.86/3.08 % bot.extremum
% 2.86/3.08 thf(fact_2095_bot_Oextremum,axiom,
% 2.86/3.08 ! [A2: filter_nat] : ( ord_le2510731241096832064er_nat @ bot_bot_filter_nat @ A2 ) ).
% 2.86/3.08
% 2.86/3.08 % bot.extremum
% 2.86/3.08 thf(fact_2096_bot_Oextremum,axiom,
% 2.86/3.08 ! [A2: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A2 ) ).
% 2.86/3.08
% 2.86/3.08 % bot.extremum
% 2.86/3.08 thf(fact_2097_bot_Oextremum,axiom,
% 2.86/3.08 ! [A2: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A2 ) ).
% 2.86/3.08
% 2.86/3.08 % bot.extremum
% 2.86/3.08 thf(fact_2098_subrelI,axiom,
% 2.86/3.08 ! [R2: set_Pr4329608150637261639at_nat,S3: set_Pr4329608150637261639at_nat] :
% 2.86/3.08 ( ! [X3: set_Pr1261947904930325089at_nat,Y2: set_Pr1261947904930325089at_nat] :
% 2.86/3.08 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y2 ) @ R2 )
% 2.86/3.08 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y2 ) @ S3 ) )
% 2.86/3.08 => ( ord_le1268244103169919719at_nat @ R2 @ S3 ) ) ).
% 2.86/3.08
% 2.86/3.08 % subrelI
% 2.86/3.08 thf(fact_2099_subrelI,axiom,
% 2.86/3.08 ! [R2: set_Pr1261947904930325089at_nat,S3: set_Pr1261947904930325089at_nat] :
% 2.86/3.08 ( ! [X3: nat,Y2: nat] :
% 2.86/3.08 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y2 ) @ R2 )
% 2.86/3.08 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y2 ) @ S3 ) )
% 2.86/3.08 => ( ord_le3146513528884898305at_nat @ R2 @ S3 ) ) ).
% 2.86/3.08
% 2.86/3.08 % subrelI
% 2.86/3.08 thf(fact_2100_subrelI,axiom,
% 2.86/3.08 ! [R2: set_Pr1281608226676607948nteger,S3: set_Pr1281608226676607948nteger] :
% 2.86/3.08 ( ! [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y2: produc8923325533196201883nteger] :
% 2.86/3.08 ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y2 ) @ R2 )
% 2.86/3.08 => ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y2 ) @ S3 ) )
% 2.86/3.08 => ( ord_le653643898420964396nteger @ R2 @ S3 ) ) ).
% 2.86/3.08
% 2.86/3.08 % subrelI
% 2.86/3.08 thf(fact_2101_subrelI,axiom,
% 2.86/3.08 ! [R2: set_Pr3286484037609594932et_nat,S3: set_Pr3286484037609594932et_nat] :
% 2.86/3.08 ( ! [X3: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat] :
% 2.86/3.08 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y2 ) @ R2 )
% 2.86/3.08 => ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y2 ) @ S3 ) )
% 2.86/3.08 => ( ord_le5966269811547037844et_nat @ R2 @ S3 ) ) ).
% 2.86/3.08
% 2.86/3.08 % subrelI
% 2.86/3.08 thf(fact_2102_subrelI,axiom,
% 2.86/3.08 ! [R2: set_Pr8536935166611901872et_nat,S3: set_Pr8536935166611901872et_nat] :
% 2.86/3.08 ( ! [X3: produc3658429121746597890et_nat > $o,Y2: produc3925858234332021118et_nat] :
% 2.86/3.08 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y2 ) @ R2 )
% 2.86/3.08 => ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y2 ) @ S3 ) )
% 2.86/3.08 => ( ord_le4763372923235995152et_nat @ R2 @ S3 ) ) ).
% 2.86/3.08
% 2.86/3.08 % subrelI
% 2.86/3.08 thf(fact_2103_subrelI,axiom,
% 2.86/3.08 ! [R2: set_Pr9222295170931077689nt_int,S3: set_Pr9222295170931077689nt_int] :
% 2.86/3.08 ( ! [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y2: product_prod_int_int] :
% 2.86/3.08 ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y2 ) @ R2 )
% 2.86/3.08 => ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y2 ) @ S3 ) )
% 2.86/3.08 => ( ord_le8725513860283290265nt_int @ R2 @ S3 ) ) ).
% 2.86/3.08
% 2.86/3.08 % subrelI
% 2.86/3.08 thf(fact_2104_subrelI,axiom,
% 2.86/3.08 ! [R2: set_Pr1872883991513573699nt_int,S3: set_Pr1872883991513573699nt_int] :
% 2.86/3.08 ( ! [X3: int > option6357759511663192854e_term,Y2: product_prod_int_int] :
% 2.86/3.08 ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y2 ) @ R2 )
% 2.86/3.08 => ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y2 ) @ S3 ) )
% 2.86/3.08 => ( ord_le135402666524580259nt_int @ R2 @ S3 ) ) ).
% 2.86/3.08
% 2.86/3.08 % subrelI
% 2.86/3.08 thf(fact_2105_diff__eq__diff__less__eq,axiom,
% 2.86/3.08 ! [A2: rat,B2: rat,C: rat,D2: rat] :
% 2.86/3.08 ( ( ( minus_minus_rat @ A2 @ B2 )
% 2.86/3.08 = ( minus_minus_rat @ C @ D2 ) )
% 2.86/3.08 => ( ( ord_less_eq_rat @ A2 @ B2 )
% 2.86/3.08 = ( ord_less_eq_rat @ C @ D2 ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % diff_eq_diff_less_eq
% 2.86/3.08 thf(fact_2106_diff__eq__diff__less__eq,axiom,
% 2.86/3.08 ! [A2: int,B2: int,C: int,D2: int] :
% 2.86/3.08 ( ( ( minus_minus_int @ A2 @ B2 )
% 2.86/3.08 = ( minus_minus_int @ C @ D2 ) )
% 2.86/3.08 => ( ( ord_less_eq_int @ A2 @ B2 )
% 2.86/3.08 = ( ord_less_eq_int @ C @ D2 ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % diff_eq_diff_less_eq
% 2.86/3.08 thf(fact_2107_diff__right__mono,axiom,
% 2.86/3.08 ! [A2: rat,B2: rat,C: rat] :
% 2.86/3.08 ( ( ord_less_eq_rat @ A2 @ B2 )
% 2.86/3.08 => ( ord_less_eq_rat @ ( minus_minus_rat @ A2 @ C ) @ ( minus_minus_rat @ B2 @ C ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % diff_right_mono
% 2.86/3.08 thf(fact_2108_diff__right__mono,axiom,
% 2.86/3.08 ! [A2: int,B2: int,C: int] :
% 2.86/3.08 ( ( ord_less_eq_int @ A2 @ B2 )
% 2.86/3.08 => ( ord_less_eq_int @ ( minus_minus_int @ A2 @ C ) @ ( minus_minus_int @ B2 @ C ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % diff_right_mono
% 2.86/3.08 thf(fact_2109_diff__left__mono,axiom,
% 2.86/3.08 ! [B2: rat,A2: rat,C: rat] :
% 2.86/3.08 ( ( ord_less_eq_rat @ B2 @ A2 )
% 2.86/3.08 => ( ord_less_eq_rat @ ( minus_minus_rat @ C @ A2 ) @ ( minus_minus_rat @ C @ B2 ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % diff_left_mono
% 2.86/3.08 thf(fact_2110_diff__left__mono,axiom,
% 2.86/3.08 ! [B2: int,A2: int,C: int] :
% 2.86/3.08 ( ( ord_less_eq_int @ B2 @ A2 )
% 2.86/3.08 => ( ord_less_eq_int @ ( minus_minus_int @ C @ A2 ) @ ( minus_minus_int @ C @ B2 ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % diff_left_mono
% 2.86/3.08 thf(fact_2111_diff__mono,axiom,
% 2.86/3.08 ! [A2: rat,B2: rat,D2: rat,C: rat] :
% 2.86/3.08 ( ( ord_less_eq_rat @ A2 @ B2 )
% 2.86/3.08 => ( ( ord_less_eq_rat @ D2 @ C )
% 2.86/3.08 => ( ord_less_eq_rat @ ( minus_minus_rat @ A2 @ C ) @ ( minus_minus_rat @ B2 @ D2 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % diff_mono
% 2.86/3.08 thf(fact_2112_diff__mono,axiom,
% 2.86/3.08 ! [A2: int,B2: int,D2: int,C: int] :
% 2.86/3.08 ( ( ord_less_eq_int @ A2 @ B2 )
% 2.86/3.08 => ( ( ord_less_eq_int @ D2 @ C )
% 2.86/3.08 => ( ord_less_eq_int @ ( minus_minus_int @ A2 @ C ) @ ( minus_minus_int @ B2 @ D2 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % diff_mono
% 2.86/3.08 thf(fact_2113_mod__and__dist,axiom,
% 2.86/3.08 ! [P: assn,Q: assn,H2: produc3658429121746597890et_nat] :
% 2.86/3.08 ( ( rep_assn @ ( inf_inf_assn @ P @ Q ) @ H2 )
% 2.86/3.08 = ( ( rep_assn @ P @ H2 )
% 2.86/3.08 & ( rep_assn @ Q @ H2 ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % mod_and_dist
% 2.86/3.08 thf(fact_2114_ent__conjI,axiom,
% 2.86/3.08 ! [A: assn,B: assn,C2: assn] :
% 2.86/3.08 ( ( entails @ A @ B )
% 2.86/3.08 => ( ( entails @ A @ C2 )
% 2.86/3.08 => ( entails @ A @ ( inf_inf_assn @ B @ C2 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % ent_conjI
% 2.86/3.08 thf(fact_2115_ent__conjE1,axiom,
% 2.86/3.08 ! [A: assn,C2: assn,B: assn] :
% 2.86/3.08 ( ( entails @ A @ C2 )
% 2.86/3.08 => ( entails @ ( inf_inf_assn @ A @ B ) @ C2 ) ) ).
% 2.86/3.08
% 2.86/3.08 % ent_conjE1
% 2.86/3.08 thf(fact_2116_ent__conjE2,axiom,
% 2.86/3.08 ! [B: assn,C2: assn,A: assn] :
% 2.86/3.08 ( ( entails @ B @ C2 )
% 2.86/3.08 => ( entails @ ( inf_inf_assn @ A @ B ) @ C2 ) ) ).
% 2.86/3.08
% 2.86/3.08 % ent_conjE2
% 2.86/3.08 thf(fact_2117_subset__insertI2,axiom,
% 2.86/3.08 ! [A: set_int,B: set_int,B2: int] :
% 2.86/3.08 ( ( ord_less_eq_set_int @ A @ B )
% 2.86/3.08 => ( ord_less_eq_set_int @ A @ ( insert_int2 @ B2 @ B ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_insertI2
% 2.86/3.08 thf(fact_2118_subset__insertI2,axiom,
% 2.86/3.08 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,B2: product_prod_nat_nat] :
% 2.86/3.08 ( ( ord_le3146513528884898305at_nat @ A @ B )
% 2.86/3.08 => ( ord_le3146513528884898305at_nat @ A @ ( insert8211810215607154385at_nat @ B2 @ B ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_insertI2
% 2.86/3.08 thf(fact_2119_subset__insertI2,axiom,
% 2.86/3.08 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,B2: produc3843707927480180839at_nat] :
% 2.86/3.08 ( ( ord_le1268244103169919719at_nat @ A @ B )
% 2.86/3.08 => ( ord_le1268244103169919719at_nat @ A @ ( insert9069300056098147895at_nat @ B2 @ B ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_insertI2
% 2.86/3.08 thf(fact_2120_subset__insertI2,axiom,
% 2.86/3.08 ! [A: set_o,B: set_o,B2: $o] :
% 2.86/3.08 ( ( ord_less_eq_set_o @ A @ B )
% 2.86/3.08 => ( ord_less_eq_set_o @ A @ ( insert_o2 @ B2 @ B ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_insertI2
% 2.86/3.08 thf(fact_2121_subset__insertI2,axiom,
% 2.86/3.08 ! [A: set_nat,B: set_nat,B2: nat] :
% 2.86/3.08 ( ( ord_less_eq_set_nat @ A @ B )
% 2.86/3.08 => ( ord_less_eq_set_nat @ A @ ( insert_nat2 @ B2 @ B ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_insertI2
% 2.86/3.08 thf(fact_2122_subset__insertI,axiom,
% 2.86/3.08 ! [B: set_int,A2: int] : ( ord_less_eq_set_int @ B @ ( insert_int2 @ A2 @ B ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_insertI
% 2.86/3.08 thf(fact_2123_subset__insertI,axiom,
% 2.86/3.08 ! [B: set_Pr1261947904930325089at_nat,A2: product_prod_nat_nat] : ( ord_le3146513528884898305at_nat @ B @ ( insert8211810215607154385at_nat @ A2 @ B ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_insertI
% 2.86/3.08 thf(fact_2124_subset__insertI,axiom,
% 2.86/3.08 ! [B: set_Pr4329608150637261639at_nat,A2: produc3843707927480180839at_nat] : ( ord_le1268244103169919719at_nat @ B @ ( insert9069300056098147895at_nat @ A2 @ B ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_insertI
% 2.86/3.08 thf(fact_2125_subset__insertI,axiom,
% 2.86/3.08 ! [B: set_o,A2: $o] : ( ord_less_eq_set_o @ B @ ( insert_o2 @ A2 @ B ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_insertI
% 2.86/3.08 thf(fact_2126_subset__insertI,axiom,
% 2.86/3.08 ! [B: set_nat,A2: nat] : ( ord_less_eq_set_nat @ B @ ( insert_nat2 @ A2 @ B ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_insertI
% 2.86/3.08 thf(fact_2127_subset__insert,axiom,
% 2.86/3.08 ! [X: $o,A: set_o,B: set_o] :
% 2.86/3.08 ( ~ ( member_o @ X @ A )
% 2.86/3.08 => ( ( ord_less_eq_set_o @ A @ ( insert_o2 @ X @ B ) )
% 2.86/3.08 = ( ord_less_eq_set_o @ A @ B ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_insert
% 2.86/3.08 thf(fact_2128_subset__insert,axiom,
% 2.86/3.08 ! [X: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.08 ( ~ ( member8757157785044589968at_nat @ X @ A )
% 2.86/3.08 => ( ( ord_le1268244103169919719at_nat @ A @ ( insert9069300056098147895at_nat @ X @ B ) )
% 2.86/3.08 = ( ord_le1268244103169919719at_nat @ A @ B ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_insert
% 2.86/3.08 thf(fact_2129_subset__insert,axiom,
% 2.86/3.08 ! [X: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.08 ( ~ ( member8440522571783428010at_nat @ X @ A )
% 2.86/3.08 => ( ( ord_le3146513528884898305at_nat @ A @ ( insert8211810215607154385at_nat @ X @ B ) )
% 2.86/3.08 = ( ord_le3146513528884898305at_nat @ A @ B ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_insert
% 2.86/3.08 thf(fact_2130_subset__insert,axiom,
% 2.86/3.08 ! [X: int,A: set_int,B: set_int] :
% 2.86/3.08 ( ~ ( member_int @ X @ A )
% 2.86/3.08 => ( ( ord_less_eq_set_int @ A @ ( insert_int2 @ X @ B ) )
% 2.86/3.08 = ( ord_less_eq_set_int @ A @ B ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_insert
% 2.86/3.08 thf(fact_2131_subset__insert,axiom,
% 2.86/3.08 ! [X: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o] :
% 2.86/3.08 ( ~ ( member6576561426505652726_nat_o @ X @ A )
% 2.86/3.08 => ( ( ord_le2965882846123202637_nat_o @ A @ ( insert5175938949040314269_nat_o @ X @ B ) )
% 2.86/3.08 = ( ord_le2965882846123202637_nat_o @ A @ B ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_insert
% 2.86/3.08 thf(fact_2132_subset__insert,axiom,
% 2.86/3.08 ! [X: nat,A: set_nat,B: set_nat] :
% 2.86/3.08 ( ~ ( member_nat @ X @ A )
% 2.86/3.08 => ( ( ord_less_eq_set_nat @ A @ ( insert_nat2 @ X @ B ) )
% 2.86/3.08 = ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_insert
% 2.86/3.08 thf(fact_2133_insert__mono,axiom,
% 2.86/3.08 ! [C2: set_int,D: set_int,A2: int] :
% 2.86/3.08 ( ( ord_less_eq_set_int @ C2 @ D )
% 2.86/3.08 => ( ord_less_eq_set_int @ ( insert_int2 @ A2 @ C2 ) @ ( insert_int2 @ A2 @ D ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % insert_mono
% 2.86/3.08 thf(fact_2134_insert__mono,axiom,
% 2.86/3.08 ! [C2: set_Pr1261947904930325089at_nat,D: set_Pr1261947904930325089at_nat,A2: product_prod_nat_nat] :
% 2.86/3.08 ( ( ord_le3146513528884898305at_nat @ C2 @ D )
% 2.86/3.08 => ( ord_le3146513528884898305at_nat @ ( insert8211810215607154385at_nat @ A2 @ C2 ) @ ( insert8211810215607154385at_nat @ A2 @ D ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % insert_mono
% 2.86/3.08 thf(fact_2135_insert__mono,axiom,
% 2.86/3.08 ! [C2: set_Pr4329608150637261639at_nat,D: set_Pr4329608150637261639at_nat,A2: produc3843707927480180839at_nat] :
% 2.86/3.08 ( ( ord_le1268244103169919719at_nat @ C2 @ D )
% 2.86/3.08 => ( ord_le1268244103169919719at_nat @ ( insert9069300056098147895at_nat @ A2 @ C2 ) @ ( insert9069300056098147895at_nat @ A2 @ D ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % insert_mono
% 2.86/3.08 thf(fact_2136_insert__mono,axiom,
% 2.86/3.08 ! [C2: set_o,D: set_o,A2: $o] :
% 2.86/3.08 ( ( ord_less_eq_set_o @ C2 @ D )
% 2.86/3.08 => ( ord_less_eq_set_o @ ( insert_o2 @ A2 @ C2 ) @ ( insert_o2 @ A2 @ D ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % insert_mono
% 2.86/3.08 thf(fact_2137_insert__mono,axiom,
% 2.86/3.08 ! [C2: set_nat,D: set_nat,A2: nat] :
% 2.86/3.08 ( ( ord_less_eq_set_nat @ C2 @ D )
% 2.86/3.08 => ( ord_less_eq_set_nat @ ( insert_nat2 @ A2 @ C2 ) @ ( insert_nat2 @ A2 @ D ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % insert_mono
% 2.86/3.08 thf(fact_2138_subset__code_I1_J,axiom,
% 2.86/3.08 ! [Xs: list_P5464809261938338413at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.08 ( ( ord_le1268244103169919719at_nat @ ( set_Pr3765526544606949372at_nat @ Xs ) @ B )
% 2.86/3.08 = ( ! [X2: produc3843707927480180839at_nat] :
% 2.86/3.08 ( ( member8757157785044589968at_nat @ X2 @ ( set_Pr3765526544606949372at_nat @ Xs ) )
% 2.86/3.08 => ( member8757157785044589968at_nat @ X2 @ B ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_code(1)
% 2.86/3.08 thf(fact_2139_subset__code_I1_J,axiom,
% 2.86/3.08 ! [Xs: list_P6011104703257516679at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.08 ( ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ Xs ) @ B )
% 2.86/3.08 = ( ! [X2: product_prod_nat_nat] :
% 2.86/3.08 ( ( member8440522571783428010at_nat @ X2 @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 2.86/3.08 => ( member8440522571783428010at_nat @ X2 @ B ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_code(1)
% 2.86/3.08 thf(fact_2140_subset__code_I1_J,axiom,
% 2.86/3.08 ! [Xs: list_P7985473006766602707_nat_o,B: set_Pr4532377907799695533_nat_o] :
% 2.86/3.08 ( ( ord_le2965882846123202637_nat_o @ ( set_Pr400311997697478754_nat_o @ Xs ) @ B )
% 2.86/3.08 = ( ! [X2: produc3658429121746597890et_nat > $o] :
% 2.86/3.08 ( ( member6576561426505652726_nat_o @ X2 @ ( set_Pr400311997697478754_nat_o @ Xs ) )
% 2.86/3.08 => ( member6576561426505652726_nat_o @ X2 @ B ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_code(1)
% 2.86/3.08 thf(fact_2141_subset__code_I1_J,axiom,
% 2.86/3.08 ! [Xs: list_int,B: set_int] :
% 2.86/3.08 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ B )
% 2.86/3.08 = ( ! [X2: int] :
% 2.86/3.08 ( ( member_int @ X2 @ ( set_int2 @ Xs ) )
% 2.86/3.08 => ( member_int @ X2 @ B ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_code(1)
% 2.86/3.08 thf(fact_2142_subset__code_I1_J,axiom,
% 2.86/3.08 ! [Xs: list_P8527749157015355191n_assn,B: set_Pr5949110396991348497n_assn] :
% 2.86/3.08 ( ( ord_le171416862856029873n_assn @ ( set_Pr1139785259514867910n_assn @ Xs ) @ B )
% 2.86/3.08 = ( ! [X2: produc6575502325842934193n_assn] :
% 2.86/3.08 ( ( member7957490590177025114n_assn @ X2 @ ( set_Pr1139785259514867910n_assn @ Xs ) )
% 2.86/3.08 => ( member7957490590177025114n_assn @ X2 @ B ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_code(1)
% 2.86/3.08 thf(fact_2143_subset__code_I1_J,axiom,
% 2.86/3.08 ! [Xs: list_nat,B: set_nat] :
% 2.86/3.08 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ B )
% 2.86/3.08 = ( ! [X2: nat] :
% 2.86/3.08 ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 2.86/3.08 => ( member_nat @ X2 @ B ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_code(1)
% 2.86/3.08 thf(fact_2144_double__diff,axiom,
% 2.86/3.08 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 2.86/3.08 ( ( ord_less_eq_set_nat @ A @ B )
% 2.86/3.08 => ( ( ord_less_eq_set_nat @ B @ C2 )
% 2.86/3.08 => ( ( minus_minus_set_nat @ B @ ( minus_minus_set_nat @ C2 @ A ) )
% 2.86/3.08 = A ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % double_diff
% 2.86/3.08 thf(fact_2145_Diff__subset,axiom,
% 2.86/3.08 ! [A: set_nat,B: set_nat] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A @ B ) @ A ) ).
% 2.86/3.08
% 2.86/3.08 % Diff_subset
% 2.86/3.08 thf(fact_2146_Diff__mono,axiom,
% 2.86/3.08 ! [A: set_nat,C2: set_nat,D: set_nat,B: set_nat] :
% 2.86/3.08 ( ( ord_less_eq_set_nat @ A @ C2 )
% 2.86/3.08 => ( ( ord_less_eq_set_nat @ D @ B )
% 2.86/3.08 => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A @ B ) @ ( minus_minus_set_nat @ C2 @ D ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Diff_mono
% 2.86/3.08 thf(fact_2147_subset__iff__psubset__eq,axiom,
% 2.86/3.08 ( ord_less_eq_set_nat
% 2.86/3.08 = ( ^ [A5: set_nat,B7: set_nat] :
% 2.86/3.08 ( ( ord_less_set_nat @ A5 @ B7 )
% 2.86/3.08 | ( A5 = B7 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_iff_psubset_eq
% 2.86/3.08 thf(fact_2148_subset__psubset__trans,axiom,
% 2.86/3.08 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 2.86/3.08 ( ( ord_less_eq_set_nat @ A @ B )
% 2.86/3.08 => ( ( ord_less_set_nat @ B @ C2 )
% 2.86/3.08 => ( ord_less_set_nat @ A @ C2 ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_psubset_trans
% 2.86/3.08 thf(fact_2149_subset__not__subset__eq,axiom,
% 2.86/3.08 ( ord_less_set_nat
% 2.86/3.08 = ( ^ [A5: set_nat,B7: set_nat] :
% 2.86/3.08 ( ( ord_less_eq_set_nat @ A5 @ B7 )
% 2.86/3.08 & ~ ( ord_less_eq_set_nat @ B7 @ A5 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_not_subset_eq
% 2.86/3.08 thf(fact_2150_psubset__subset__trans,axiom,
% 2.86/3.08 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 2.86/3.08 ( ( ord_less_set_nat @ A @ B )
% 2.86/3.08 => ( ( ord_less_eq_set_nat @ B @ C2 )
% 2.86/3.08 => ( ord_less_set_nat @ A @ C2 ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % psubset_subset_trans
% 2.86/3.08 thf(fact_2151_psubset__imp__subset,axiom,
% 2.86/3.08 ! [A: set_nat,B: set_nat] :
% 2.86/3.08 ( ( ord_less_set_nat @ A @ B )
% 2.86/3.08 => ( ord_less_eq_set_nat @ A @ B ) ) ).
% 2.86/3.08
% 2.86/3.08 % psubset_imp_subset
% 2.86/3.08 thf(fact_2152_psubset__eq,axiom,
% 2.86/3.08 ( ord_less_set_nat
% 2.86/3.08 = ( ^ [A5: set_nat,B7: set_nat] :
% 2.86/3.08 ( ( ord_less_eq_set_nat @ A5 @ B7 )
% 2.86/3.08 & ( A5 != B7 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % psubset_eq
% 2.86/3.08 thf(fact_2153_psubsetE,axiom,
% 2.86/3.08 ! [A: set_nat,B: set_nat] :
% 2.86/3.08 ( ( ord_less_set_nat @ A @ B )
% 2.86/3.08 => ~ ( ( ord_less_eq_set_nat @ A @ B )
% 2.86/3.08 => ( ord_less_eq_set_nat @ B @ A ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % psubsetE
% 2.86/3.08 thf(fact_2154_norm__assertion__simps_I9_J,axiom,
% 2.86/3.08 ! [X: assn] :
% 2.86/3.08 ( ( inf_inf_assn @ bot_bot_assn @ X )
% 2.86/3.08 = bot_bot_assn ) ).
% 2.86/3.08
% 2.86/3.08 % norm_assertion_simps(9)
% 2.86/3.08 thf(fact_2155_norm__assertion__simps_I10_J,axiom,
% 2.86/3.08 ! [X: assn] :
% 2.86/3.08 ( ( inf_inf_assn @ X @ bot_bot_assn )
% 2.86/3.08 = bot_bot_assn ) ).
% 2.86/3.08
% 2.86/3.08 % norm_assertion_simps(10)
% 2.86/3.08 thf(fact_2156_pairwise__empty,axiom,
% 2.86/3.08 ! [P: produc3843707927480180839at_nat > produc3843707927480180839at_nat > $o] : ( pairwi3222497012029234898at_nat @ P @ bot_bo228742789529271731at_nat ) ).
% 2.86/3.08
% 2.86/3.08 % pairwise_empty
% 2.86/3.08 thf(fact_2157_pairwise__empty,axiom,
% 2.86/3.08 ! [P: product_prod_nat_nat > product_prod_nat_nat > $o] : ( pairwi6357175311820755948at_nat @ P @ bot_bo2099793752762293965at_nat ) ).
% 2.86/3.08
% 2.86/3.08 % pairwise_empty
% 2.86/3.08 thf(fact_2158_pairwise__empty,axiom,
% 2.86/3.08 ! [P: $o > $o > $o] : ( pairwise_o @ P @ bot_bot_set_o ) ).
% 2.86/3.08
% 2.86/3.08 % pairwise_empty
% 2.86/3.08 thf(fact_2159_pairwise__empty,axiom,
% 2.86/3.08 ! [P: nat > nat > $o] : ( pairwise_nat @ P @ bot_bot_set_nat ) ).
% 2.86/3.08
% 2.86/3.08 % pairwise_empty
% 2.86/3.08 thf(fact_2160_pairwise__empty,axiom,
% 2.86/3.08 ! [P: int > int > $o] : ( pairwise_int @ P @ bot_bot_set_int ) ).
% 2.86/3.08
% 2.86/3.08 % pairwise_empty
% 2.86/3.08 thf(fact_2161_pairwise__insert,axiom,
% 2.86/3.08 ! [R2: $o > $o > $o,X: $o,S3: set_o] :
% 2.86/3.08 ( ( pairwise_o @ R2 @ ( insert_o2 @ X @ S3 ) )
% 2.86/3.08 = ( ! [Y5: $o] :
% 2.86/3.08 ( ( ( member_o @ Y5 @ S3 )
% 2.86/3.08 & ( Y5 != X ) )
% 2.86/3.08 => ( ( R2 @ X @ Y5 )
% 2.86/3.08 & ( R2 @ Y5 @ X ) ) )
% 2.86/3.08 & ( pairwise_o @ R2 @ S3 ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % pairwise_insert
% 2.86/3.08 thf(fact_2162_pairwise__insert,axiom,
% 2.86/3.08 ! [R2: produc3843707927480180839at_nat > produc3843707927480180839at_nat > $o,X: produc3843707927480180839at_nat,S3: set_Pr4329608150637261639at_nat] :
% 2.86/3.08 ( ( pairwi3222497012029234898at_nat @ R2 @ ( insert9069300056098147895at_nat @ X @ S3 ) )
% 2.86/3.08 = ( ! [Y5: produc3843707927480180839at_nat] :
% 2.86/3.08 ( ( ( member8757157785044589968at_nat @ Y5 @ S3 )
% 2.86/3.08 & ( Y5 != X ) )
% 2.86/3.08 => ( ( R2 @ X @ Y5 )
% 2.86/3.08 & ( R2 @ Y5 @ X ) ) )
% 2.86/3.08 & ( pairwi3222497012029234898at_nat @ R2 @ S3 ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % pairwise_insert
% 2.86/3.08 thf(fact_2163_pairwise__insert,axiom,
% 2.86/3.08 ! [R2: product_prod_nat_nat > product_prod_nat_nat > $o,X: product_prod_nat_nat,S3: set_Pr1261947904930325089at_nat] :
% 2.86/3.08 ( ( pairwi6357175311820755948at_nat @ R2 @ ( insert8211810215607154385at_nat @ X @ S3 ) )
% 2.86/3.08 = ( ! [Y5: product_prod_nat_nat] :
% 2.86/3.08 ( ( ( member8440522571783428010at_nat @ Y5 @ S3 )
% 2.86/3.08 & ( Y5 != X ) )
% 2.86/3.08 => ( ( R2 @ X @ Y5 )
% 2.86/3.08 & ( R2 @ Y5 @ X ) ) )
% 2.86/3.08 & ( pairwi6357175311820755948at_nat @ R2 @ S3 ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % pairwise_insert
% 2.86/3.08 thf(fact_2164_pairwise__insert,axiom,
% 2.86/3.08 ! [R2: nat > nat > $o,X: nat,S3: set_nat] :
% 2.86/3.08 ( ( pairwise_nat @ R2 @ ( insert_nat2 @ X @ S3 ) )
% 2.86/3.08 = ( ! [Y5: nat] :
% 2.86/3.08 ( ( ( member_nat @ Y5 @ S3 )
% 2.86/3.08 & ( Y5 != X ) )
% 2.86/3.08 => ( ( R2 @ X @ Y5 )
% 2.86/3.08 & ( R2 @ Y5 @ X ) ) )
% 2.86/3.08 & ( pairwise_nat @ R2 @ S3 ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % pairwise_insert
% 2.86/3.08 thf(fact_2165_pairwise__insert,axiom,
% 2.86/3.08 ! [R2: int > int > $o,X: int,S3: set_int] :
% 2.86/3.08 ( ( pairwise_int @ R2 @ ( insert_int2 @ X @ S3 ) )
% 2.86/3.08 = ( ! [Y5: int] :
% 2.86/3.08 ( ( ( member_int @ Y5 @ S3 )
% 2.86/3.08 & ( Y5 != X ) )
% 2.86/3.08 => ( ( R2 @ X @ Y5 )
% 2.86/3.08 & ( R2 @ Y5 @ X ) ) )
% 2.86/3.08 & ( pairwise_int @ R2 @ S3 ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % pairwise_insert
% 2.86/3.08 thf(fact_2166_pairwise__insert,axiom,
% 2.86/3.08 ! [R2: ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > $o,X: produc3658429121746597890et_nat > $o,S3: set_Pr4532377907799695533_nat_o] :
% 2.86/3.08 ( ( pairwi2432143822833250616_nat_o @ R2 @ ( insert5175938949040314269_nat_o @ X @ S3 ) )
% 2.86/3.08 = ( ! [Y5: produc3658429121746597890et_nat > $o] :
% 2.86/3.08 ( ( ( member6576561426505652726_nat_o @ Y5 @ S3 )
% 2.86/3.08 & ( Y5 != X ) )
% 2.86/3.08 => ( ( R2 @ X @ Y5 )
% 2.86/3.08 & ( R2 @ Y5 @ X ) ) )
% 2.86/3.08 & ( pairwi2432143822833250616_nat_o @ R2 @ S3 ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % pairwise_insert
% 2.86/3.08 thf(fact_2167_subset__singletonD,axiom,
% 2.86/3.08 ! [A: set_Pr4329608150637261639at_nat,X: produc3843707927480180839at_nat] :
% 2.86/3.08 ( ( ord_le1268244103169919719at_nat @ A @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 2.86/3.08 => ( ( A = bot_bo228742789529271731at_nat )
% 2.86/3.08 | ( A
% 2.86/3.08 = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_singletonD
% 2.86/3.08 thf(fact_2168_subset__singletonD,axiom,
% 2.86/3.08 ! [A: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] :
% 2.86/3.08 ( ( ord_le3146513528884898305at_nat @ A @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 2.86/3.08 => ( ( A = bot_bo2099793752762293965at_nat )
% 2.86/3.08 | ( A
% 2.86/3.08 = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_singletonD
% 2.86/3.08 thf(fact_2169_subset__singletonD,axiom,
% 2.86/3.08 ! [A: set_o,X: $o] :
% 2.86/3.08 ( ( ord_less_eq_set_o @ A @ ( insert_o2 @ X @ bot_bot_set_o ) )
% 2.86/3.08 => ( ( A = bot_bot_set_o )
% 2.86/3.08 | ( A
% 2.86/3.08 = ( insert_o2 @ X @ bot_bot_set_o ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_singletonD
% 2.86/3.08 thf(fact_2170_subset__singletonD,axiom,
% 2.86/3.08 ! [A: set_int,X: int] :
% 2.86/3.08 ( ( ord_less_eq_set_int @ A @ ( insert_int2 @ X @ bot_bot_set_int ) )
% 2.86/3.08 => ( ( A = bot_bot_set_int )
% 2.86/3.08 | ( A
% 2.86/3.08 = ( insert_int2 @ X @ bot_bot_set_int ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_singletonD
% 2.86/3.08 thf(fact_2171_subset__singletonD,axiom,
% 2.86/3.08 ! [A: set_nat,X: nat] :
% 2.86/3.08 ( ( ord_less_eq_set_nat @ A @ ( insert_nat2 @ X @ bot_bot_set_nat ) )
% 2.86/3.08 => ( ( A = bot_bot_set_nat )
% 2.86/3.08 | ( A
% 2.86/3.08 = ( insert_nat2 @ X @ bot_bot_set_nat ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_singletonD
% 2.86/3.08 thf(fact_2172_subset__singleton__iff,axiom,
% 2.86/3.08 ! [X4: set_Pr4329608150637261639at_nat,A2: produc3843707927480180839at_nat] :
% 2.86/3.08 ( ( ord_le1268244103169919719at_nat @ X4 @ ( insert9069300056098147895at_nat @ A2 @ bot_bo228742789529271731at_nat ) )
% 2.86/3.08 = ( ( X4 = bot_bo228742789529271731at_nat )
% 2.86/3.08 | ( X4
% 2.86/3.08 = ( insert9069300056098147895at_nat @ A2 @ bot_bo228742789529271731at_nat ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_singleton_iff
% 2.86/3.08 thf(fact_2173_subset__singleton__iff,axiom,
% 2.86/3.08 ! [X4: set_Pr1261947904930325089at_nat,A2: product_prod_nat_nat] :
% 2.86/3.08 ( ( ord_le3146513528884898305at_nat @ X4 @ ( insert8211810215607154385at_nat @ A2 @ bot_bo2099793752762293965at_nat ) )
% 2.86/3.08 = ( ( X4 = bot_bo2099793752762293965at_nat )
% 2.86/3.08 | ( X4
% 2.86/3.08 = ( insert8211810215607154385at_nat @ A2 @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_singleton_iff
% 2.86/3.08 thf(fact_2174_subset__singleton__iff,axiom,
% 2.86/3.08 ! [X4: set_o,A2: $o] :
% 2.86/3.08 ( ( ord_less_eq_set_o @ X4 @ ( insert_o2 @ A2 @ bot_bot_set_o ) )
% 2.86/3.08 = ( ( X4 = bot_bot_set_o )
% 2.86/3.08 | ( X4
% 2.86/3.08 = ( insert_o2 @ A2 @ bot_bot_set_o ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_singleton_iff
% 2.86/3.08 thf(fact_2175_subset__singleton__iff,axiom,
% 2.86/3.08 ! [X4: set_int,A2: int] :
% 2.86/3.08 ( ( ord_less_eq_set_int @ X4 @ ( insert_int2 @ A2 @ bot_bot_set_int ) )
% 2.86/3.08 = ( ( X4 = bot_bot_set_int )
% 2.86/3.08 | ( X4
% 2.86/3.08 = ( insert_int2 @ A2 @ bot_bot_set_int ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_singleton_iff
% 2.86/3.08 thf(fact_2176_subset__singleton__iff,axiom,
% 2.86/3.08 ! [X4: set_nat,A2: nat] :
% 2.86/3.08 ( ( ord_less_eq_set_nat @ X4 @ ( insert_nat2 @ A2 @ bot_bot_set_nat ) )
% 2.86/3.08 = ( ( X4 = bot_bot_set_nat )
% 2.86/3.08 | ( X4
% 2.86/3.08 = ( insert_nat2 @ A2 @ bot_bot_set_nat ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_singleton_iff
% 2.86/3.08 thf(fact_2177_subset__minus__empty,axiom,
% 2.86/3.08 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.08 ( ( ord_le1268244103169919719at_nat @ A @ B )
% 2.86/3.08 => ( ( minus_3314409938677909166at_nat @ A @ B )
% 2.86/3.08 = bot_bo228742789529271731at_nat ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_minus_empty
% 2.86/3.08 thf(fact_2178_subset__minus__empty,axiom,
% 2.86/3.08 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.08 ( ( ord_le3146513528884898305at_nat @ A @ B )
% 2.86/3.08 => ( ( minus_1356011639430497352at_nat @ A @ B )
% 2.86/3.08 = bot_bo2099793752762293965at_nat ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_minus_empty
% 2.86/3.08 thf(fact_2179_subset__minus__empty,axiom,
% 2.86/3.08 ! [A: set_o,B: set_o] :
% 2.86/3.08 ( ( ord_less_eq_set_o @ A @ B )
% 2.86/3.08 => ( ( minus_minus_set_o @ A @ B )
% 2.86/3.08 = bot_bot_set_o ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_minus_empty
% 2.86/3.08 thf(fact_2180_subset__minus__empty,axiom,
% 2.86/3.08 ! [A: set_int,B: set_int] :
% 2.86/3.08 ( ( ord_less_eq_set_int @ A @ B )
% 2.86/3.08 => ( ( minus_minus_set_int @ A @ B )
% 2.86/3.08 = bot_bot_set_int ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_minus_empty
% 2.86/3.08 thf(fact_2181_subset__minus__empty,axiom,
% 2.86/3.08 ! [A: set_nat,B: set_nat] :
% 2.86/3.08 ( ( ord_less_eq_set_nat @ A @ B )
% 2.86/3.08 => ( ( minus_minus_set_nat @ A @ B )
% 2.86/3.08 = bot_bot_set_nat ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_minus_empty
% 2.86/3.08 thf(fact_2182_subset__Diff__insert,axiom,
% 2.86/3.08 ! [A: set_o,B: set_o,X: $o,C2: set_o] :
% 2.86/3.08 ( ( ord_less_eq_set_o @ A @ ( minus_minus_set_o @ B @ ( insert_o2 @ X @ C2 ) ) )
% 2.86/3.08 = ( ( ord_less_eq_set_o @ A @ ( minus_minus_set_o @ B @ C2 ) )
% 2.86/3.08 & ~ ( member_o @ X @ A ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_Diff_insert
% 2.86/3.08 thf(fact_2183_subset__Diff__insert,axiom,
% 2.86/3.08 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,X: produc3843707927480180839at_nat,C2: set_Pr4329608150637261639at_nat] :
% 2.86/3.08 ( ( ord_le1268244103169919719at_nat @ A @ ( minus_3314409938677909166at_nat @ B @ ( insert9069300056098147895at_nat @ X @ C2 ) ) )
% 2.86/3.08 = ( ( ord_le1268244103169919719at_nat @ A @ ( minus_3314409938677909166at_nat @ B @ C2 ) )
% 2.86/3.08 & ~ ( member8757157785044589968at_nat @ X @ A ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_Diff_insert
% 2.86/3.08 thf(fact_2184_subset__Diff__insert,axiom,
% 2.86/3.08 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,C2: set_Pr1261947904930325089at_nat] :
% 2.86/3.08 ( ( ord_le3146513528884898305at_nat @ A @ ( minus_1356011639430497352at_nat @ B @ ( insert8211810215607154385at_nat @ X @ C2 ) ) )
% 2.86/3.08 = ( ( ord_le3146513528884898305at_nat @ A @ ( minus_1356011639430497352at_nat @ B @ C2 ) )
% 2.86/3.08 & ~ ( member8440522571783428010at_nat @ X @ A ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_Diff_insert
% 2.86/3.08 thf(fact_2185_subset__Diff__insert,axiom,
% 2.86/3.08 ! [A: set_int,B: set_int,X: int,C2: set_int] :
% 2.86/3.08 ( ( ord_less_eq_set_int @ A @ ( minus_minus_set_int @ B @ ( insert_int2 @ X @ C2 ) ) )
% 2.86/3.08 = ( ( ord_less_eq_set_int @ A @ ( minus_minus_set_int @ B @ C2 ) )
% 2.86/3.08 & ~ ( member_int @ X @ A ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_Diff_insert
% 2.86/3.08 thf(fact_2186_subset__Diff__insert,axiom,
% 2.86/3.08 ! [A: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o,C2: set_Pr4532377907799695533_nat_o] :
% 2.86/3.08 ( ( ord_le2965882846123202637_nat_o @ A @ ( minus_1801376950450012436_nat_o @ B @ ( insert5175938949040314269_nat_o @ X @ C2 ) ) )
% 2.86/3.08 = ( ( ord_le2965882846123202637_nat_o @ A @ ( minus_1801376950450012436_nat_o @ B @ C2 ) )
% 2.86/3.08 & ~ ( member6576561426505652726_nat_o @ X @ A ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_Diff_insert
% 2.86/3.08 thf(fact_2187_subset__Diff__insert,axiom,
% 2.86/3.08 ! [A: set_nat,B: set_nat,X: nat,C2: set_nat] :
% 2.86/3.08 ( ( ord_less_eq_set_nat @ A @ ( minus_minus_set_nat @ B @ ( insert_nat2 @ X @ C2 ) ) )
% 2.86/3.08 = ( ( ord_less_eq_set_nat @ A @ ( minus_minus_set_nat @ B @ C2 ) )
% 2.86/3.08 & ~ ( member_nat @ X @ A ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_Diff_insert
% 2.86/3.08 thf(fact_2188_set__update__subsetI,axiom,
% 2.86/3.08 ! [Xs: list_P5464809261938338413at_nat,A: set_Pr4329608150637261639at_nat,X: produc3843707927480180839at_nat,I: nat] :
% 2.86/3.08 ( ( ord_le1268244103169919719at_nat @ ( set_Pr3765526544606949372at_nat @ Xs ) @ A )
% 2.86/3.08 => ( ( member8757157785044589968at_nat @ X @ A )
% 2.86/3.08 => ( ord_le1268244103169919719at_nat @ ( set_Pr3765526544606949372at_nat @ ( list_u4696772448584712917at_nat @ Xs @ I @ X ) ) @ A ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % set_update_subsetI
% 2.86/3.08 thf(fact_2189_set__update__subsetI,axiom,
% 2.86/3.08 ! [Xs: list_P6011104703257516679at_nat,A: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,I: nat] :
% 2.86/3.08 ( ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ Xs ) @ A )
% 2.86/3.08 => ( ( member8440522571783428010at_nat @ X @ A )
% 2.86/3.08 => ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ ( list_u6180841689913720943at_nat @ Xs @ I @ X ) ) @ A ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % set_update_subsetI
% 2.86/3.08 thf(fact_2190_set__update__subsetI,axiom,
% 2.86/3.08 ! [Xs: list_P7985473006766602707_nat_o,A: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o,I: nat] :
% 2.86/3.08 ( ( ord_le2965882846123202637_nat_o @ ( set_Pr400311997697478754_nat_o @ Xs ) @ A )
% 2.86/3.08 => ( ( member6576561426505652726_nat_o @ X @ A )
% 2.86/3.08 => ( ord_le2965882846123202637_nat_o @ ( set_Pr400311997697478754_nat_o @ ( list_u6943956310655620667_nat_o @ Xs @ I @ X ) ) @ A ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % set_update_subsetI
% 2.86/3.08 thf(fact_2191_set__update__subsetI,axiom,
% 2.86/3.08 ! [Xs: list_int,A: set_int,X: int,I: nat] :
% 2.86/3.08 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A )
% 2.86/3.08 => ( ( member_int @ X @ A )
% 2.86/3.08 => ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs @ I @ X ) ) @ A ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % set_update_subsetI
% 2.86/3.08 thf(fact_2192_set__update__subsetI,axiom,
% 2.86/3.08 ! [Xs: list_P8527749157015355191n_assn,A: set_Pr5949110396991348497n_assn,X: produc6575502325842934193n_assn,I: nat] :
% 2.86/3.08 ( ( ord_le171416862856029873n_assn @ ( set_Pr1139785259514867910n_assn @ Xs ) @ A )
% 2.86/3.08 => ( ( member7957490590177025114n_assn @ X @ A )
% 2.86/3.08 => ( ord_le171416862856029873n_assn @ ( set_Pr1139785259514867910n_assn @ ( list_u4534839942911652127n_assn @ Xs @ I @ X ) ) @ A ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % set_update_subsetI
% 2.86/3.08 thf(fact_2193_set__update__subsetI,axiom,
% 2.86/3.08 ! [Xs: list_c,A: set_c,X: c,I: nat] :
% 2.86/3.08 ( ( ord_less_eq_set_c @ ( set_c2 @ Xs ) @ A )
% 2.86/3.08 => ( ( member_c @ X @ A )
% 2.86/3.08 => ( ord_less_eq_set_c @ ( set_c2 @ ( list_update_c @ Xs @ I @ X ) ) @ A ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % set_update_subsetI
% 2.86/3.08 thf(fact_2194_set__update__subsetI,axiom,
% 2.86/3.08 ! [Xs: list_d,A: set_d,X: d,I: nat] :
% 2.86/3.08 ( ( ord_less_eq_set_d @ ( set_d2 @ Xs ) @ A )
% 2.86/3.08 => ( ( member_d @ X @ A )
% 2.86/3.08 => ( ord_less_eq_set_d @ ( set_d2 @ ( list_update_d @ Xs @ I @ X ) ) @ A ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % set_update_subsetI
% 2.86/3.08 thf(fact_2195_set__update__subsetI,axiom,
% 2.86/3.08 ! [Xs: list_nat,A: set_nat,X: nat,I: nat] :
% 2.86/3.08 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A )
% 2.86/3.08 => ( ( member_nat @ X @ A )
% 2.86/3.08 => ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs @ I @ X ) ) @ A ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % set_update_subsetI
% 2.86/3.08 thf(fact_2196_set__remove1__subset,axiom,
% 2.86/3.08 ! [X: int,Xs: list_int] : ( ord_less_eq_set_int @ ( set_int2 @ ( remove1_int @ X @ Xs ) ) @ ( set_int2 @ Xs ) ) ).
% 2.86/3.08
% 2.86/3.08 % set_remove1_subset
% 2.86/3.08 thf(fact_2197_set__remove1__subset,axiom,
% 2.86/3.08 ! [X: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn] : ( ord_le171416862856029873n_assn @ ( set_Pr1139785259514867910n_assn @ ( remove1670527618125605709n_assn @ X @ Xs ) ) @ ( set_Pr1139785259514867910n_assn @ Xs ) ) ).
% 2.86/3.08
% 2.86/3.08 % set_remove1_subset
% 2.86/3.08 thf(fact_2198_set__remove1__subset,axiom,
% 2.86/3.08 ! [X: nat,Xs: list_nat] : ( ord_less_eq_set_nat @ ( set_nat2 @ ( remove1_nat @ X @ Xs ) ) @ ( set_nat2 @ Xs ) ) ).
% 2.86/3.08
% 2.86/3.08 % set_remove1_subset
% 2.86/3.08 thf(fact_2199_subset__code_I2_J,axiom,
% 2.86/3.08 ! [A: set_Pr4329608150637261639at_nat,Ys: list_P5464809261938338413at_nat] :
% 2.86/3.08 ( ( ord_le1268244103169919719at_nat @ A @ ( coset_5307619257043544794at_nat @ Ys ) )
% 2.86/3.08 = ( ! [X2: produc3843707927480180839at_nat] :
% 2.86/3.08 ( ( member8757157785044589968at_nat @ X2 @ ( set_Pr3765526544606949372at_nat @ Ys ) )
% 2.86/3.08 => ~ ( member8757157785044589968at_nat @ X2 @ A ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_code(2)
% 2.86/3.08 thf(fact_2200_subset__code_I2_J,axiom,
% 2.86/3.08 ! [A: set_Pr1261947904930325089at_nat,Ys: list_P6011104703257516679at_nat] :
% 2.86/3.08 ( ( ord_le3146513528884898305at_nat @ A @ ( coset_6809516720700967924at_nat @ Ys ) )
% 2.86/3.08 = ( ! [X2: product_prod_nat_nat] :
% 2.86/3.08 ( ( member8440522571783428010at_nat @ X2 @ ( set_Pr5648618587558075414at_nat @ Ys ) )
% 2.86/3.08 => ~ ( member8440522571783428010at_nat @ X2 @ A ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_code(2)
% 2.86/3.08 thf(fact_2201_subset__code_I2_J,axiom,
% 2.86/3.08 ! [A: set_Pr4532377907799695533_nat_o,Ys: list_P7985473006766602707_nat_o] :
% 2.86/3.08 ( ( ord_le2965882846123202637_nat_o @ A @ ( coset_9017067850271954240_nat_o @ Ys ) )
% 2.86/3.08 = ( ! [X2: produc3658429121746597890et_nat > $o] :
% 2.86/3.08 ( ( member6576561426505652726_nat_o @ X2 @ ( set_Pr400311997697478754_nat_o @ Ys ) )
% 2.86/3.08 => ~ ( member6576561426505652726_nat_o @ X2 @ A ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_code(2)
% 2.86/3.08 thf(fact_2202_subset__code_I2_J,axiom,
% 2.86/3.08 ! [A: set_int,Ys: list_int] :
% 2.86/3.08 ( ( ord_less_eq_set_int @ A @ ( coset_int @ Ys ) )
% 2.86/3.08 = ( ! [X2: int] :
% 2.86/3.08 ( ( member_int @ X2 @ ( set_int2 @ Ys ) )
% 2.86/3.08 => ~ ( member_int @ X2 @ A ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_code(2)
% 2.86/3.08 thf(fact_2203_subset__code_I2_J,axiom,
% 2.86/3.08 ! [A: set_Pr5949110396991348497n_assn,Ys: list_P8527749157015355191n_assn] :
% 2.86/3.08 ( ( ord_le171416862856029873n_assn @ A @ ( coset_703488708621576356n_assn @ Ys ) )
% 2.86/3.08 = ( ! [X2: produc6575502325842934193n_assn] :
% 2.86/3.08 ( ( member7957490590177025114n_assn @ X2 @ ( set_Pr1139785259514867910n_assn @ Ys ) )
% 2.86/3.08 => ~ ( member7957490590177025114n_assn @ X2 @ A ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_code(2)
% 2.86/3.08 thf(fact_2204_subset__code_I2_J,axiom,
% 2.86/3.08 ! [A: set_nat,Ys: list_nat] :
% 2.86/3.08 ( ( ord_less_eq_set_nat @ A @ ( coset_nat @ Ys ) )
% 2.86/3.08 = ( ! [X2: nat] :
% 2.86/3.08 ( ( member_nat @ X2 @ ( set_nat2 @ Ys ) )
% 2.86/3.08 => ~ ( member_nat @ X2 @ A ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_code(2)
% 2.86/3.08 thf(fact_2205_pairwise__singleton,axiom,
% 2.86/3.08 ! [P: produc3843707927480180839at_nat > produc3843707927480180839at_nat > $o,A: produc3843707927480180839at_nat] : ( pairwi3222497012029234898at_nat @ P @ ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) ).
% 2.86/3.08
% 2.86/3.08 % pairwise_singleton
% 2.86/3.08 thf(fact_2206_pairwise__singleton,axiom,
% 2.86/3.08 ! [P: product_prod_nat_nat > product_prod_nat_nat > $o,A: product_prod_nat_nat] : ( pairwi6357175311820755948at_nat @ P @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) ).
% 2.86/3.08
% 2.86/3.08 % pairwise_singleton
% 2.86/3.08 thf(fact_2207_pairwise__singleton,axiom,
% 2.86/3.08 ! [P: $o > $o > $o,A: $o] : ( pairwise_o @ P @ ( insert_o2 @ A @ bot_bot_set_o ) ) ).
% 2.86/3.08
% 2.86/3.08 % pairwise_singleton
% 2.86/3.08 thf(fact_2208_pairwise__singleton,axiom,
% 2.86/3.08 ! [P: nat > nat > $o,A: nat] : ( pairwise_nat @ P @ ( insert_nat2 @ A @ bot_bot_set_nat ) ) ).
% 2.86/3.08
% 2.86/3.08 % pairwise_singleton
% 2.86/3.08 thf(fact_2209_pairwise__singleton,axiom,
% 2.86/3.08 ! [P: int > int > $o,A: int] : ( pairwise_int @ P @ ( insert_int2 @ A @ bot_bot_set_int ) ) ).
% 2.86/3.08
% 2.86/3.08 % pairwise_singleton
% 2.86/3.08 thf(fact_2210_subset__insert__iff,axiom,
% 2.86/3.08 ! [A: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o,B: set_Pr4532377907799695533_nat_o] :
% 2.86/3.08 ( ( ord_le2965882846123202637_nat_o @ A @ ( insert5175938949040314269_nat_o @ X @ B ) )
% 2.86/3.08 = ( ( ( member6576561426505652726_nat_o @ X @ A )
% 2.86/3.08 => ( ord_le2965882846123202637_nat_o @ ( minus_1801376950450012436_nat_o @ A @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) @ B ) )
% 2.86/3.08 & ( ~ ( member6576561426505652726_nat_o @ X @ A )
% 2.86/3.08 => ( ord_le2965882846123202637_nat_o @ A @ B ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_insert_iff
% 2.86/3.08 thf(fact_2211_subset__insert__iff,axiom,
% 2.86/3.08 ! [A: set_Pr4329608150637261639at_nat,X: produc3843707927480180839at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.08 ( ( ord_le1268244103169919719at_nat @ A @ ( insert9069300056098147895at_nat @ X @ B ) )
% 2.86/3.08 = ( ( ( member8757157785044589968at_nat @ X @ A )
% 2.86/3.08 => ( ord_le1268244103169919719at_nat @ ( minus_3314409938677909166at_nat @ A @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) @ B ) )
% 2.86/3.08 & ( ~ ( member8757157785044589968at_nat @ X @ A )
% 2.86/3.08 => ( ord_le1268244103169919719at_nat @ A @ B ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_insert_iff
% 2.86/3.08 thf(fact_2212_subset__insert__iff,axiom,
% 2.86/3.08 ! [A: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.08 ( ( ord_le3146513528884898305at_nat @ A @ ( insert8211810215607154385at_nat @ X @ B ) )
% 2.86/3.08 = ( ( ( member8440522571783428010at_nat @ X @ A )
% 2.86/3.08 => ( ord_le3146513528884898305at_nat @ ( minus_1356011639430497352at_nat @ A @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) @ B ) )
% 2.86/3.08 & ( ~ ( member8440522571783428010at_nat @ X @ A )
% 2.86/3.08 => ( ord_le3146513528884898305at_nat @ A @ B ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_insert_iff
% 2.86/3.08 thf(fact_2213_subset__insert__iff,axiom,
% 2.86/3.08 ! [A: set_o,X: $o,B: set_o] :
% 2.86/3.08 ( ( ord_less_eq_set_o @ A @ ( insert_o2 @ X @ B ) )
% 2.86/3.08 = ( ( ( member_o @ X @ A )
% 2.86/3.08 => ( ord_less_eq_set_o @ ( minus_minus_set_o @ A @ ( insert_o2 @ X @ bot_bot_set_o ) ) @ B ) )
% 2.86/3.08 & ( ~ ( member_o @ X @ A )
% 2.86/3.08 => ( ord_less_eq_set_o @ A @ B ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_insert_iff
% 2.86/3.08 thf(fact_2214_subset__insert__iff,axiom,
% 2.86/3.08 ! [A: set_int,X: int,B: set_int] :
% 2.86/3.08 ( ( ord_less_eq_set_int @ A @ ( insert_int2 @ X @ B ) )
% 2.86/3.08 = ( ( ( member_int @ X @ A )
% 2.86/3.08 => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A @ ( insert_int2 @ X @ bot_bot_set_int ) ) @ B ) )
% 2.86/3.08 & ( ~ ( member_int @ X @ A )
% 2.86/3.08 => ( ord_less_eq_set_int @ A @ B ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_insert_iff
% 2.86/3.08 thf(fact_2215_subset__insert__iff,axiom,
% 2.86/3.08 ! [A: set_nat,X: nat,B: set_nat] :
% 2.86/3.08 ( ( ord_less_eq_set_nat @ A @ ( insert_nat2 @ X @ B ) )
% 2.86/3.08 = ( ( ( member_nat @ X @ A )
% 2.86/3.08 => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A @ ( insert_nat2 @ X @ bot_bot_set_nat ) ) @ B ) )
% 2.86/3.08 & ( ~ ( member_nat @ X @ A )
% 2.86/3.08 => ( ord_less_eq_set_nat @ A @ B ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_insert_iff
% 2.86/3.08 thf(fact_2216_Diff__single__insert,axiom,
% 2.86/3.08 ! [A: set_Pr4329608150637261639at_nat,X: produc3843707927480180839at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.08 ( ( ord_le1268244103169919719at_nat @ ( minus_3314409938677909166at_nat @ A @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) @ B )
% 2.86/3.08 => ( ord_le1268244103169919719at_nat @ A @ ( insert9069300056098147895at_nat @ X @ B ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Diff_single_insert
% 2.86/3.08 thf(fact_2217_Diff__single__insert,axiom,
% 2.86/3.08 ! [A: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.08 ( ( ord_le3146513528884898305at_nat @ ( minus_1356011639430497352at_nat @ A @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) @ B )
% 2.86/3.08 => ( ord_le3146513528884898305at_nat @ A @ ( insert8211810215607154385at_nat @ X @ B ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Diff_single_insert
% 2.86/3.08 thf(fact_2218_Diff__single__insert,axiom,
% 2.86/3.08 ! [A: set_o,X: $o,B: set_o] :
% 2.86/3.08 ( ( ord_less_eq_set_o @ ( minus_minus_set_o @ A @ ( insert_o2 @ X @ bot_bot_set_o ) ) @ B )
% 2.86/3.08 => ( ord_less_eq_set_o @ A @ ( insert_o2 @ X @ B ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Diff_single_insert
% 2.86/3.08 thf(fact_2219_Diff__single__insert,axiom,
% 2.86/3.08 ! [A: set_int,X: int,B: set_int] :
% 2.86/3.08 ( ( ord_less_eq_set_int @ ( minus_minus_set_int @ A @ ( insert_int2 @ X @ bot_bot_set_int ) ) @ B )
% 2.86/3.08 => ( ord_less_eq_set_int @ A @ ( insert_int2 @ X @ B ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Diff_single_insert
% 2.86/3.08 thf(fact_2220_Diff__single__insert,axiom,
% 2.86/3.08 ! [A: set_nat,X: nat,B: set_nat] :
% 2.86/3.08 ( ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A @ ( insert_nat2 @ X @ bot_bot_set_nat ) ) @ B )
% 2.86/3.08 => ( ord_less_eq_set_nat @ A @ ( insert_nat2 @ X @ B ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Diff_single_insert
% 2.86/3.08 thf(fact_2221_set__update__subset__insert,axiom,
% 2.86/3.08 ! [Xs: list_P6011104703257516679at_nat,I: nat,X: product_prod_nat_nat] : ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ ( list_u6180841689913720943at_nat @ Xs @ I @ X ) ) @ ( insert8211810215607154385at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % set_update_subset_insert
% 2.86/3.08 thf(fact_2222_set__update__subset__insert,axiom,
% 2.86/3.08 ! [Xs: list_P5464809261938338413at_nat,I: nat,X: produc3843707927480180839at_nat] : ( ord_le1268244103169919719at_nat @ ( set_Pr3765526544606949372at_nat @ ( list_u4696772448584712917at_nat @ Xs @ I @ X ) ) @ ( insert9069300056098147895at_nat @ X @ ( set_Pr3765526544606949372at_nat @ Xs ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % set_update_subset_insert
% 2.86/3.08 thf(fact_2223_set__update__subset__insert,axiom,
% 2.86/3.08 ! [Xs: list_o,I: nat,X: $o] : ( ord_less_eq_set_o @ ( set_o2 @ ( list_update_o @ Xs @ I @ X ) ) @ ( insert_o2 @ X @ ( set_o2 @ Xs ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % set_update_subset_insert
% 2.86/3.08 thf(fact_2224_set__update__subset__insert,axiom,
% 2.86/3.08 ! [Xs: list_int,I: nat,X: int] : ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs @ I @ X ) ) @ ( insert_int2 @ X @ ( set_int2 @ Xs ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % set_update_subset_insert
% 2.86/3.08 thf(fact_2225_set__update__subset__insert,axiom,
% 2.86/3.08 ! [Xs: list_P8527749157015355191n_assn,I: nat,X: produc6575502325842934193n_assn] : ( ord_le171416862856029873n_assn @ ( set_Pr1139785259514867910n_assn @ ( list_u4534839942911652127n_assn @ Xs @ I @ X ) ) @ ( insert5290817439147925377n_assn @ X @ ( set_Pr1139785259514867910n_assn @ Xs ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % set_update_subset_insert
% 2.86/3.08 thf(fact_2226_set__update__subset__insert,axiom,
% 2.86/3.08 ! [Xs: list_c,I: nat,X: c] : ( ord_less_eq_set_c @ ( set_c2 @ ( list_update_c @ Xs @ I @ X ) ) @ ( insert_c @ X @ ( set_c2 @ Xs ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % set_update_subset_insert
% 2.86/3.08 thf(fact_2227_set__update__subset__insert,axiom,
% 2.86/3.08 ! [Xs: list_d,I: nat,X: d] : ( ord_less_eq_set_d @ ( set_d2 @ ( list_update_d @ Xs @ I @ X ) ) @ ( insert_d @ X @ ( set_d2 @ Xs ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % set_update_subset_insert
% 2.86/3.08 thf(fact_2228_set__update__subset__insert,axiom,
% 2.86/3.08 ! [Xs: list_nat,I: nat,X: nat] : ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs @ I @ X ) ) @ ( insert_nat2 @ X @ ( set_nat2 @ Xs ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % set_update_subset_insert
% 2.86/3.08 thf(fact_2229_boolean__algebra_Oconj__zero__right,axiom,
% 2.86/3.08 ! [X: assn] :
% 2.86/3.08 ( ( inf_inf_assn @ X @ bot_bot_assn )
% 2.86/3.08 = bot_bot_assn ) ).
% 2.86/3.08
% 2.86/3.08 % boolean_algebra.conj_zero_right
% 2.86/3.08 thf(fact_2230_boolean__algebra_Oconj__zero__right,axiom,
% 2.86/3.08 ! [X: set_Pr4329608150637261639at_nat] :
% 2.86/3.08 ( ( inf_in7913087082777306421at_nat @ X @ bot_bo228742789529271731at_nat )
% 2.86/3.08 = bot_bo228742789529271731at_nat ) ).
% 2.86/3.08
% 2.86/3.08 % boolean_algebra.conj_zero_right
% 2.86/3.08 thf(fact_2231_boolean__algebra_Oconj__zero__right,axiom,
% 2.86/3.08 ! [X: set_Pr1261947904930325089at_nat] :
% 2.86/3.08 ( ( inf_in2572325071724192079at_nat @ X @ bot_bo2099793752762293965at_nat )
% 2.86/3.08 = bot_bo2099793752762293965at_nat ) ).
% 2.86/3.08
% 2.86/3.08 % boolean_algebra.conj_zero_right
% 2.86/3.08 thf(fact_2232_boolean__algebra_Oconj__zero__right,axiom,
% 2.86/3.08 ! [X: set_o] :
% 2.86/3.08 ( ( inf_inf_set_o @ X @ bot_bot_set_o )
% 2.86/3.08 = bot_bot_set_o ) ).
% 2.86/3.08
% 2.86/3.08 % boolean_algebra.conj_zero_right
% 2.86/3.08 thf(fact_2233_boolean__algebra_Oconj__zero__right,axiom,
% 2.86/3.08 ! [X: set_nat] :
% 2.86/3.08 ( ( inf_inf_set_nat @ X @ bot_bot_set_nat )
% 2.86/3.08 = bot_bot_set_nat ) ).
% 2.86/3.08
% 2.86/3.08 % boolean_algebra.conj_zero_right
% 2.86/3.08 thf(fact_2234_boolean__algebra_Oconj__zero__right,axiom,
% 2.86/3.08 ! [X: set_int] :
% 2.86/3.08 ( ( inf_inf_set_int @ X @ bot_bot_set_int )
% 2.86/3.08 = bot_bot_set_int ) ).
% 2.86/3.08
% 2.86/3.08 % boolean_algebra.conj_zero_right
% 2.86/3.08 thf(fact_2235_boolean__algebra_Oconj__zero__left,axiom,
% 2.86/3.08 ! [X: assn] :
% 2.86/3.08 ( ( inf_inf_assn @ bot_bot_assn @ X )
% 2.86/3.08 = bot_bot_assn ) ).
% 2.86/3.08
% 2.86/3.08 % boolean_algebra.conj_zero_left
% 2.86/3.08 thf(fact_2236_boolean__algebra_Oconj__zero__left,axiom,
% 2.86/3.08 ! [X: set_Pr4329608150637261639at_nat] :
% 2.86/3.08 ( ( inf_in7913087082777306421at_nat @ bot_bo228742789529271731at_nat @ X )
% 2.86/3.08 = bot_bo228742789529271731at_nat ) ).
% 2.86/3.08
% 2.86/3.08 % boolean_algebra.conj_zero_left
% 2.86/3.08 thf(fact_2237_boolean__algebra_Oconj__zero__left,axiom,
% 2.86/3.08 ! [X: set_Pr1261947904930325089at_nat] :
% 2.86/3.08 ( ( inf_in2572325071724192079at_nat @ bot_bo2099793752762293965at_nat @ X )
% 2.86/3.08 = bot_bo2099793752762293965at_nat ) ).
% 2.86/3.08
% 2.86/3.08 % boolean_algebra.conj_zero_left
% 2.86/3.08 thf(fact_2238_boolean__algebra_Oconj__zero__left,axiom,
% 2.86/3.08 ! [X: set_o] :
% 2.86/3.08 ( ( inf_inf_set_o @ bot_bot_set_o @ X )
% 2.86/3.08 = bot_bot_set_o ) ).
% 2.86/3.08
% 2.86/3.08 % boolean_algebra.conj_zero_left
% 2.86/3.08 thf(fact_2239_boolean__algebra_Oconj__zero__left,axiom,
% 2.86/3.08 ! [X: set_nat] :
% 2.86/3.08 ( ( inf_inf_set_nat @ bot_bot_set_nat @ X )
% 2.86/3.08 = bot_bot_set_nat ) ).
% 2.86/3.08
% 2.86/3.08 % boolean_algebra.conj_zero_left
% 2.86/3.08 thf(fact_2240_boolean__algebra_Oconj__zero__left,axiom,
% 2.86/3.08 ! [X: set_int] :
% 2.86/3.08 ( ( inf_inf_set_int @ bot_bot_set_int @ X )
% 2.86/3.08 = bot_bot_set_int ) ).
% 2.86/3.08
% 2.86/3.08 % boolean_algebra.conj_zero_left
% 2.86/3.08 thf(fact_2241_diff__shunt__var,axiom,
% 2.86/3.08 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 2.86/3.08 ( ( ( minus_3314409938677909166at_nat @ X @ Y )
% 2.86/3.08 = bot_bo228742789529271731at_nat )
% 2.86/3.08 = ( ord_le1268244103169919719at_nat @ X @ Y ) ) ).
% 2.86/3.08
% 2.86/3.08 % diff_shunt_var
% 2.86/3.08 thf(fact_2242_diff__shunt__var,axiom,
% 2.86/3.08 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 2.86/3.08 ( ( ( minus_1356011639430497352at_nat @ X @ Y )
% 2.86/3.08 = bot_bo2099793752762293965at_nat )
% 2.86/3.08 = ( ord_le3146513528884898305at_nat @ X @ Y ) ) ).
% 2.86/3.08
% 2.86/3.08 % diff_shunt_var
% 2.86/3.08 thf(fact_2243_diff__shunt__var,axiom,
% 2.86/3.08 ! [X: set_o,Y: set_o] :
% 2.86/3.08 ( ( ( minus_minus_set_o @ X @ Y )
% 2.86/3.08 = bot_bot_set_o )
% 2.86/3.08 = ( ord_less_eq_set_o @ X @ Y ) ) ).
% 2.86/3.08
% 2.86/3.08 % diff_shunt_var
% 2.86/3.08 thf(fact_2244_diff__shunt__var,axiom,
% 2.86/3.08 ! [X: set_int,Y: set_int] :
% 2.86/3.08 ( ( ( minus_minus_set_int @ X @ Y )
% 2.86/3.08 = bot_bot_set_int )
% 2.86/3.08 = ( ord_less_eq_set_int @ X @ Y ) ) ).
% 2.86/3.08
% 2.86/3.08 % diff_shunt_var
% 2.86/3.08 thf(fact_2245_diff__shunt__var,axiom,
% 2.86/3.08 ! [X: assn,Y: assn] :
% 2.86/3.08 ( ( ( minus_minus_assn @ X @ Y )
% 2.86/3.08 = bot_bot_assn )
% 2.86/3.08 = ( ord_less_eq_assn @ X @ Y ) ) ).
% 2.86/3.08
% 2.86/3.08 % diff_shunt_var
% 2.86/3.08 thf(fact_2246_diff__shunt__var,axiom,
% 2.86/3.08 ! [X: set_nat,Y: set_nat] :
% 2.86/3.08 ( ( ( minus_minus_set_nat @ X @ Y )
% 2.86/3.08 = bot_bot_set_nat )
% 2.86/3.08 = ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 2.86/3.08
% 2.86/3.08 % diff_shunt_var
% 2.86/3.08 thf(fact_2247_length__product,axiom,
% 2.86/3.08 ! [Xs: list_c,Ys: list_c] :
% 2.86/3.08 ( ( size_s2756448709718749209od_c_c @ ( product_c_c @ Xs @ Ys ) )
% 2.86/3.08 = ( times_times_nat @ ( size_size_list_c @ Xs ) @ ( size_size_list_c @ Ys ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % length_product
% 2.86/3.08 thf(fact_2248_length__product,axiom,
% 2.86/3.08 ! [Xs: list_c,Ys: list_d] :
% 2.86/3.08 ( ( size_s2827482749765095194od_c_d @ ( product_c_d @ Xs @ Ys ) )
% 2.86/3.08 = ( times_times_nat @ ( size_size_list_c @ Xs ) @ ( size_size_list_d @ Ys ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % length_product
% 2.86/3.08 thf(fact_2249_length__product,axiom,
% 2.86/3.08 ! [Xs: list_c,Ys: list_nat] :
% 2.86/3.08 ( ( size_s2954062820725854115_c_nat @ ( product_c_nat @ Xs @ Ys ) )
% 2.86/3.08 = ( times_times_nat @ ( size_size_list_c @ Xs ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % length_product
% 2.86/3.08 thf(fact_2250_length__product,axiom,
% 2.86/3.08 ! [Xs: list_c,Ys: list_int] :
% 2.86/3.08 ( ( size_s463979675794127359_c_int @ ( product_c_int @ Xs @ Ys ) )
% 2.86/3.08 = ( times_times_nat @ ( size_size_list_c @ Xs ) @ ( size_size_list_int @ Ys ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % length_product
% 2.86/3.08 thf(fact_2251_length__product,axiom,
% 2.86/3.08 ! [Xs: list_d,Ys: list_c] :
% 2.86/3.08 ( ( size_s2120799709113762520od_d_c @ ( product_d_c @ Xs @ Ys ) )
% 2.86/3.08 = ( times_times_nat @ ( size_size_list_d @ Xs ) @ ( size_size_list_c @ Ys ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % length_product
% 2.86/3.08 thf(fact_2252_length__product,axiom,
% 2.86/3.08 ! [Xs: list_d,Ys: list_d] :
% 2.86/3.08 ( ( size_s2191833749160108505od_d_d @ ( product_d_d @ Xs @ Ys ) )
% 2.86/3.08 = ( times_times_nat @ ( size_size_list_d @ Xs ) @ ( size_size_list_d @ Ys ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % length_product
% 2.86/3.08 thf(fact_2253_length__product,axiom,
% 2.86/3.08 ! [Xs: list_d,Ys: list_nat] :
% 2.86/3.08 ( ( size_s8550281435913984804_d_nat @ ( product_d_nat @ Xs @ Ys ) )
% 2.86/3.08 = ( times_times_nat @ ( size_size_list_d @ Xs ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % length_product
% 2.86/3.08 thf(fact_2254_length__product,axiom,
% 2.86/3.08 ! [Xs: list_d,Ys: list_int] :
% 2.86/3.08 ( ( size_s6060198290982258048_d_int @ ( product_d_int @ Xs @ Ys ) )
% 2.86/3.08 = ( times_times_nat @ ( size_size_list_d @ Xs ) @ ( size_size_list_int @ Ys ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % length_product
% 2.86/3.08 thf(fact_2255_length__product,axiom,
% 2.86/3.08 ! [Xs: list_nat,Ys: list_c] :
% 2.86/3.08 ( ( size_s385972143775086793_nat_c @ ( product_nat_c @ Xs @ Ys ) )
% 2.86/3.08 = ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_c @ Ys ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % length_product
% 2.86/3.08 thf(fact_2256_length__product,axiom,
% 2.86/3.08 ! [Xs: list_nat,Ys: list_d] :
% 2.86/3.08 ( ( size_s457006183821432778_nat_d @ ( product_nat_d @ Xs @ Ys ) )
% 2.86/3.08 = ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_d @ Ys ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % length_product
% 2.86/3.08 thf(fact_2257_less__imp__diff__less,axiom,
% 2.86/3.08 ! [J: nat,K3: nat,N: nat] :
% 2.86/3.08 ( ( ord_less_nat @ J @ K3 )
% 2.86/3.08 => ( ord_less_nat @ ( minus_minus_nat @ J @ N ) @ K3 ) ) ).
% 2.86/3.08
% 2.86/3.08 % less_imp_diff_less
% 2.86/3.08 thf(fact_2258_diff__less__mono2,axiom,
% 2.86/3.08 ! [M2: nat,N: nat,L: nat] :
% 2.86/3.08 ( ( ord_less_nat @ M2 @ N )
% 2.86/3.08 => ( ( ord_less_nat @ M2 @ L )
% 2.86/3.08 => ( ord_less_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M2 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % diff_less_mono2
% 2.86/3.08 thf(fact_2259_insert__subsetI,axiom,
% 2.86/3.08 ! [X: $o,A: set_o,X4: set_o] :
% 2.86/3.08 ( ( member_o @ X @ A )
% 2.86/3.08 => ( ( ord_less_eq_set_o @ X4 @ A )
% 2.86/3.08 => ( ord_less_eq_set_o @ ( insert_o2 @ X @ X4 ) @ A ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % insert_subsetI
% 2.86/3.08 thf(fact_2260_insert__subsetI,axiom,
% 2.86/3.08 ! [X: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat,X4: set_Pr4329608150637261639at_nat] :
% 2.86/3.08 ( ( member8757157785044589968at_nat @ X @ A )
% 2.86/3.08 => ( ( ord_le1268244103169919719at_nat @ X4 @ A )
% 2.86/3.08 => ( ord_le1268244103169919719at_nat @ ( insert9069300056098147895at_nat @ X @ X4 ) @ A ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % insert_subsetI
% 2.86/3.08 thf(fact_2261_insert__subsetI,axiom,
% 2.86/3.08 ! [X: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat,X4: set_Pr1261947904930325089at_nat] :
% 2.86/3.08 ( ( member8440522571783428010at_nat @ X @ A )
% 2.86/3.08 => ( ( ord_le3146513528884898305at_nat @ X4 @ A )
% 2.86/3.08 => ( ord_le3146513528884898305at_nat @ ( insert8211810215607154385at_nat @ X @ X4 ) @ A ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % insert_subsetI
% 2.86/3.08 thf(fact_2262_insert__subsetI,axiom,
% 2.86/3.08 ! [X: int,A: set_int,X4: set_int] :
% 2.86/3.08 ( ( member_int @ X @ A )
% 2.86/3.08 => ( ( ord_less_eq_set_int @ X4 @ A )
% 2.86/3.08 => ( ord_less_eq_set_int @ ( insert_int2 @ X @ X4 ) @ A ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % insert_subsetI
% 2.86/3.08 thf(fact_2263_insert__subsetI,axiom,
% 2.86/3.08 ! [X: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,X4: set_Pr4532377907799695533_nat_o] :
% 2.86/3.08 ( ( member6576561426505652726_nat_o @ X @ A )
% 2.86/3.08 => ( ( ord_le2965882846123202637_nat_o @ X4 @ A )
% 2.86/3.08 => ( ord_le2965882846123202637_nat_o @ ( insert5175938949040314269_nat_o @ X @ X4 ) @ A ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % insert_subsetI
% 2.86/3.08 thf(fact_2264_insert__subsetI,axiom,
% 2.86/3.08 ! [X: nat,A: set_nat,X4: set_nat] :
% 2.86/3.08 ( ( member_nat @ X @ A )
% 2.86/3.08 => ( ( ord_less_eq_set_nat @ X4 @ A )
% 2.86/3.08 => ( ord_less_eq_set_nat @ ( insert_nat2 @ X @ X4 ) @ A ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % insert_subsetI
% 2.86/3.08 thf(fact_2265_subset__emptyI,axiom,
% 2.86/3.08 ! [A: set_Pr4532377907799695533_nat_o] :
% 2.86/3.08 ( ! [X3: produc3658429121746597890et_nat > $o] :
% 2.86/3.08 ~ ( member6576561426505652726_nat_o @ X3 @ A )
% 2.86/3.08 => ( ord_le2965882846123202637_nat_o @ A @ bot_bo7824918357723582233_nat_o ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_emptyI
% 2.86/3.08 thf(fact_2266_subset__emptyI,axiom,
% 2.86/3.08 ! [A: set_Pr4329608150637261639at_nat] :
% 2.86/3.08 ( ! [X3: produc3843707927480180839at_nat] :
% 2.86/3.08 ~ ( member8757157785044589968at_nat @ X3 @ A )
% 2.86/3.08 => ( ord_le1268244103169919719at_nat @ A @ bot_bo228742789529271731at_nat ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_emptyI
% 2.86/3.08 thf(fact_2267_subset__emptyI,axiom,
% 2.86/3.08 ! [A: set_Pr1261947904930325089at_nat] :
% 2.86/3.08 ( ! [X3: product_prod_nat_nat] :
% 2.86/3.08 ~ ( member8440522571783428010at_nat @ X3 @ A )
% 2.86/3.08 => ( ord_le3146513528884898305at_nat @ A @ bot_bo2099793752762293965at_nat ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_emptyI
% 2.86/3.08 thf(fact_2268_subset__emptyI,axiom,
% 2.86/3.08 ! [A: set_o] :
% 2.86/3.08 ( ! [X3: $o] :
% 2.86/3.08 ~ ( member_o @ X3 @ A )
% 2.86/3.08 => ( ord_less_eq_set_o @ A @ bot_bot_set_o ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_emptyI
% 2.86/3.08 thf(fact_2269_subset__emptyI,axiom,
% 2.86/3.08 ! [A: set_int] :
% 2.86/3.08 ( ! [X3: int] :
% 2.86/3.08 ~ ( member_int @ X3 @ A )
% 2.86/3.08 => ( ord_less_eq_set_int @ A @ bot_bot_set_int ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_emptyI
% 2.86/3.08 thf(fact_2270_subset__emptyI,axiom,
% 2.86/3.08 ! [A: set_nat] :
% 2.86/3.08 ( ! [X3: nat] :
% 2.86/3.08 ~ ( member_nat @ X3 @ A )
% 2.86/3.08 => ( ord_less_eq_set_nat @ A @ bot_bot_set_nat ) ) ).
% 2.86/3.08
% 2.86/3.08 % subset_emptyI
% 2.86/3.08 thf(fact_2271_complete__interval,axiom,
% 2.86/3.08 ! [A2: nat,B2: nat,P: nat > $o] :
% 2.86/3.08 ( ( ord_less_nat @ A2 @ B2 )
% 2.86/3.08 => ( ( P @ A2 )
% 2.86/3.08 => ( ~ ( P @ B2 )
% 2.86/3.08 => ? [C4: nat] :
% 2.86/3.08 ( ( ord_less_eq_nat @ A2 @ C4 )
% 2.86/3.08 & ( ord_less_eq_nat @ C4 @ B2 )
% 2.86/3.08 & ! [X7: nat] :
% 2.86/3.08 ( ( ( ord_less_eq_nat @ A2 @ X7 )
% 2.86/3.08 & ( ord_less_nat @ X7 @ C4 ) )
% 2.86/3.08 => ( P @ X7 ) )
% 2.86/3.08 & ! [D4: nat] :
% 2.86/3.08 ( ! [X3: nat] :
% 2.86/3.08 ( ( ( ord_less_eq_nat @ A2 @ X3 )
% 2.86/3.08 & ( ord_less_nat @ X3 @ D4 ) )
% 2.86/3.08 => ( P @ X3 ) )
% 2.86/3.08 => ( ord_less_eq_nat @ D4 @ C4 ) ) ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % complete_interval
% 2.86/3.08 thf(fact_2272_complete__interval,axiom,
% 2.86/3.08 ! [A2: int,B2: int,P: int > $o] :
% 2.86/3.08 ( ( ord_less_int @ A2 @ B2 )
% 2.86/3.08 => ( ( P @ A2 )
% 2.86/3.08 => ( ~ ( P @ B2 )
% 2.86/3.08 => ? [C4: int] :
% 2.86/3.08 ( ( ord_less_eq_int @ A2 @ C4 )
% 2.86/3.08 & ( ord_less_eq_int @ C4 @ B2 )
% 2.86/3.08 & ! [X7: int] :
% 2.86/3.08 ( ( ( ord_less_eq_int @ A2 @ X7 )
% 2.86/3.08 & ( ord_less_int @ X7 @ C4 ) )
% 2.86/3.08 => ( P @ X7 ) )
% 2.86/3.08 & ! [D4: int] :
% 2.86/3.08 ( ! [X3: int] :
% 2.86/3.08 ( ( ( ord_less_eq_int @ A2 @ X3 )
% 2.86/3.08 & ( ord_less_int @ X3 @ D4 ) )
% 2.86/3.08 => ( P @ X3 ) )
% 2.86/3.08 => ( ord_less_eq_int @ D4 @ C4 ) ) ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % complete_interval
% 2.86/3.08 thf(fact_2273_verit__comp__simplify1_I3_J,axiom,
% 2.86/3.08 ! [B6: code_integer,A7: code_integer] :
% 2.86/3.08 ( ( ~ ( ord_le3102999989581377725nteger @ B6 @ A7 ) )
% 2.86/3.08 = ( ord_le6747313008572928689nteger @ A7 @ B6 ) ) ).
% 2.86/3.08
% 2.86/3.08 % verit_comp_simplify1(3)
% 2.86/3.08 thf(fact_2274_verit__comp__simplify1_I3_J,axiom,
% 2.86/3.08 ! [B6: num,A7: num] :
% 2.86/3.08 ( ( ~ ( ord_less_eq_num @ B6 @ A7 ) )
% 2.86/3.08 = ( ord_less_num @ A7 @ B6 ) ) ).
% 2.86/3.08
% 2.86/3.08 % verit_comp_simplify1(3)
% 2.86/3.08 thf(fact_2275_verit__comp__simplify1_I3_J,axiom,
% 2.86/3.08 ! [B6: nat,A7: nat] :
% 2.86/3.08 ( ( ~ ( ord_less_eq_nat @ B6 @ A7 ) )
% 2.86/3.08 = ( ord_less_nat @ A7 @ B6 ) ) ).
% 2.86/3.08
% 2.86/3.08 % verit_comp_simplify1(3)
% 2.86/3.08 thf(fact_2276_verit__comp__simplify1_I3_J,axiom,
% 2.86/3.08 ! [B6: int,A7: int] :
% 2.86/3.08 ( ( ~ ( ord_less_eq_int @ B6 @ A7 ) )
% 2.86/3.08 = ( ord_less_int @ A7 @ B6 ) ) ).
% 2.86/3.08
% 2.86/3.08 % verit_comp_simplify1(3)
% 2.86/3.08 thf(fact_2277_Int__subset__iff,axiom,
% 2.86/3.08 ! [C2: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.08 ( ( ord_le3146513528884898305at_nat @ C2 @ ( inf_in2572325071724192079at_nat @ A @ B ) )
% 2.86/3.08 = ( ( ord_le3146513528884898305at_nat @ C2 @ A )
% 2.86/3.08 & ( ord_le3146513528884898305at_nat @ C2 @ B ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_subset_iff
% 2.86/3.08 thf(fact_2278_Int__subset__iff,axiom,
% 2.86/3.08 ! [C2: set_nat,A: set_nat,B: set_nat] :
% 2.86/3.08 ( ( ord_less_eq_set_nat @ C2 @ ( inf_inf_set_nat @ A @ B ) )
% 2.86/3.08 = ( ( ord_less_eq_set_nat @ C2 @ A )
% 2.86/3.08 & ( ord_less_eq_set_nat @ C2 @ B ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_subset_iff
% 2.86/3.08 thf(fact_2279_Int__insert__left__if0,axiom,
% 2.86/3.08 ! [A2: $o,C2: set_o,B: set_o] :
% 2.86/3.08 ( ~ ( member_o @ A2 @ C2 )
% 2.86/3.08 => ( ( inf_inf_set_o @ ( insert_o2 @ A2 @ B ) @ C2 )
% 2.86/3.08 = ( inf_inf_set_o @ B @ C2 ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_insert_left_if0
% 2.86/3.08 thf(fact_2280_Int__insert__left__if0,axiom,
% 2.86/3.08 ! [A2: produc3843707927480180839at_nat,C2: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.08 ( ~ ( member8757157785044589968at_nat @ A2 @ C2 )
% 2.86/3.08 => ( ( inf_in7913087082777306421at_nat @ ( insert9069300056098147895at_nat @ A2 @ B ) @ C2 )
% 2.86/3.08 = ( inf_in7913087082777306421at_nat @ B @ C2 ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_insert_left_if0
% 2.86/3.08 thf(fact_2281_Int__insert__left__if0,axiom,
% 2.86/3.08 ! [A2: int,C2: set_int,B: set_int] :
% 2.86/3.08 ( ~ ( member_int @ A2 @ C2 )
% 2.86/3.08 => ( ( inf_inf_set_int @ ( insert_int2 @ A2 @ B ) @ C2 )
% 2.86/3.08 = ( inf_inf_set_int @ B @ C2 ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_insert_left_if0
% 2.86/3.08 thf(fact_2282_Int__insert__left__if0,axiom,
% 2.86/3.08 ! [A2: produc3658429121746597890et_nat > $o,C2: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o] :
% 2.86/3.08 ( ~ ( member6576561426505652726_nat_o @ A2 @ C2 )
% 2.86/3.08 => ( ( inf_in1906310914598751387_nat_o @ ( insert5175938949040314269_nat_o @ A2 @ B ) @ C2 )
% 2.86/3.08 = ( inf_in1906310914598751387_nat_o @ B @ C2 ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_insert_left_if0
% 2.86/3.08 thf(fact_2283_Int__insert__left__if0,axiom,
% 2.86/3.08 ! [A2: nat,C2: set_nat,B: set_nat] :
% 2.86/3.08 ( ~ ( member_nat @ A2 @ C2 )
% 2.86/3.08 => ( ( inf_inf_set_nat @ ( insert_nat2 @ A2 @ B ) @ C2 )
% 2.86/3.08 = ( inf_inf_set_nat @ B @ C2 ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_insert_left_if0
% 2.86/3.08 thf(fact_2284_Int__insert__left__if0,axiom,
% 2.86/3.08 ! [A2: product_prod_nat_nat,C2: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.08 ( ~ ( member8440522571783428010at_nat @ A2 @ C2 )
% 2.86/3.08 => ( ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A2 @ B ) @ C2 )
% 2.86/3.08 = ( inf_in2572325071724192079at_nat @ B @ C2 ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_insert_left_if0
% 2.86/3.08 thf(fact_2285_Int__insert__left__if1,axiom,
% 2.86/3.08 ! [A2: $o,C2: set_o,B: set_o] :
% 2.86/3.08 ( ( member_o @ A2 @ C2 )
% 2.86/3.08 => ( ( inf_inf_set_o @ ( insert_o2 @ A2 @ B ) @ C2 )
% 2.86/3.08 = ( insert_o2 @ A2 @ ( inf_inf_set_o @ B @ C2 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_insert_left_if1
% 2.86/3.08 thf(fact_2286_Int__insert__left__if1,axiom,
% 2.86/3.08 ! [A2: produc3843707927480180839at_nat,C2: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.08 ( ( member8757157785044589968at_nat @ A2 @ C2 )
% 2.86/3.08 => ( ( inf_in7913087082777306421at_nat @ ( insert9069300056098147895at_nat @ A2 @ B ) @ C2 )
% 2.86/3.08 = ( insert9069300056098147895at_nat @ A2 @ ( inf_in7913087082777306421at_nat @ B @ C2 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_insert_left_if1
% 2.86/3.08 thf(fact_2287_Int__insert__left__if1,axiom,
% 2.86/3.08 ! [A2: int,C2: set_int,B: set_int] :
% 2.86/3.08 ( ( member_int @ A2 @ C2 )
% 2.86/3.08 => ( ( inf_inf_set_int @ ( insert_int2 @ A2 @ B ) @ C2 )
% 2.86/3.08 = ( insert_int2 @ A2 @ ( inf_inf_set_int @ B @ C2 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_insert_left_if1
% 2.86/3.08 thf(fact_2288_Int__insert__left__if1,axiom,
% 2.86/3.08 ! [A2: produc3658429121746597890et_nat > $o,C2: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o] :
% 2.86/3.08 ( ( member6576561426505652726_nat_o @ A2 @ C2 )
% 2.86/3.08 => ( ( inf_in1906310914598751387_nat_o @ ( insert5175938949040314269_nat_o @ A2 @ B ) @ C2 )
% 2.86/3.08 = ( insert5175938949040314269_nat_o @ A2 @ ( inf_in1906310914598751387_nat_o @ B @ C2 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_insert_left_if1
% 2.86/3.08 thf(fact_2289_Int__insert__left__if1,axiom,
% 2.86/3.08 ! [A2: nat,C2: set_nat,B: set_nat] :
% 2.86/3.08 ( ( member_nat @ A2 @ C2 )
% 2.86/3.08 => ( ( inf_inf_set_nat @ ( insert_nat2 @ A2 @ B ) @ C2 )
% 2.86/3.08 = ( insert_nat2 @ A2 @ ( inf_inf_set_nat @ B @ C2 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_insert_left_if1
% 2.86/3.08 thf(fact_2290_Int__insert__left__if1,axiom,
% 2.86/3.08 ! [A2: product_prod_nat_nat,C2: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.08 ( ( member8440522571783428010at_nat @ A2 @ C2 )
% 2.86/3.08 => ( ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A2 @ B ) @ C2 )
% 2.86/3.08 = ( insert8211810215607154385at_nat @ A2 @ ( inf_in2572325071724192079at_nat @ B @ C2 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_insert_left_if1
% 2.86/3.08 thf(fact_2291_insert__inter__insert,axiom,
% 2.86/3.08 ! [A2: int,A: set_int,B: set_int] :
% 2.86/3.08 ( ( inf_inf_set_int @ ( insert_int2 @ A2 @ A ) @ ( insert_int2 @ A2 @ B ) )
% 2.86/3.08 = ( insert_int2 @ A2 @ ( inf_inf_set_int @ A @ B ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % insert_inter_insert
% 2.86/3.08 thf(fact_2292_insert__inter__insert,axiom,
% 2.86/3.08 ! [A2: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.08 ( ( inf_in7913087082777306421at_nat @ ( insert9069300056098147895at_nat @ A2 @ A ) @ ( insert9069300056098147895at_nat @ A2 @ B ) )
% 2.86/3.08 = ( insert9069300056098147895at_nat @ A2 @ ( inf_in7913087082777306421at_nat @ A @ B ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % insert_inter_insert
% 2.86/3.08 thf(fact_2293_insert__inter__insert,axiom,
% 2.86/3.08 ! [A2: $o,A: set_o,B: set_o] :
% 2.86/3.08 ( ( inf_inf_set_o @ ( insert_o2 @ A2 @ A ) @ ( insert_o2 @ A2 @ B ) )
% 2.86/3.08 = ( insert_o2 @ A2 @ ( inf_inf_set_o @ A @ B ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % insert_inter_insert
% 2.86/3.08 thf(fact_2294_insert__inter__insert,axiom,
% 2.86/3.08 ! [A2: nat,A: set_nat,B: set_nat] :
% 2.86/3.08 ( ( inf_inf_set_nat @ ( insert_nat2 @ A2 @ A ) @ ( insert_nat2 @ A2 @ B ) )
% 2.86/3.08 = ( insert_nat2 @ A2 @ ( inf_inf_set_nat @ A @ B ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % insert_inter_insert
% 2.86/3.08 thf(fact_2295_insert__inter__insert,axiom,
% 2.86/3.08 ! [A2: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.08 ( ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A2 @ A ) @ ( insert8211810215607154385at_nat @ A2 @ B ) )
% 2.86/3.08 = ( insert8211810215607154385at_nat @ A2 @ ( inf_in2572325071724192079at_nat @ A @ B ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % insert_inter_insert
% 2.86/3.08 thf(fact_2296_Int__insert__right__if0,axiom,
% 2.86/3.08 ! [A2: $o,A: set_o,B: set_o] :
% 2.86/3.08 ( ~ ( member_o @ A2 @ A )
% 2.86/3.08 => ( ( inf_inf_set_o @ A @ ( insert_o2 @ A2 @ B ) )
% 2.86/3.08 = ( inf_inf_set_o @ A @ B ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_insert_right_if0
% 2.86/3.08 thf(fact_2297_Int__insert__right__if0,axiom,
% 2.86/3.08 ! [A2: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.08 ( ~ ( member8757157785044589968at_nat @ A2 @ A )
% 2.86/3.08 => ( ( inf_in7913087082777306421at_nat @ A @ ( insert9069300056098147895at_nat @ A2 @ B ) )
% 2.86/3.08 = ( inf_in7913087082777306421at_nat @ A @ B ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_insert_right_if0
% 2.86/3.08 thf(fact_2298_Int__insert__right__if0,axiom,
% 2.86/3.08 ! [A2: int,A: set_int,B: set_int] :
% 2.86/3.08 ( ~ ( member_int @ A2 @ A )
% 2.86/3.08 => ( ( inf_inf_set_int @ A @ ( insert_int2 @ A2 @ B ) )
% 2.86/3.08 = ( inf_inf_set_int @ A @ B ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_insert_right_if0
% 2.86/3.08 thf(fact_2299_Int__insert__right__if0,axiom,
% 2.86/3.08 ! [A2: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o] :
% 2.86/3.08 ( ~ ( member6576561426505652726_nat_o @ A2 @ A )
% 2.86/3.08 => ( ( inf_in1906310914598751387_nat_o @ A @ ( insert5175938949040314269_nat_o @ A2 @ B ) )
% 2.86/3.08 = ( inf_in1906310914598751387_nat_o @ A @ B ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_insert_right_if0
% 2.86/3.08 thf(fact_2300_Int__insert__right__if0,axiom,
% 2.86/3.08 ! [A2: nat,A: set_nat,B: set_nat] :
% 2.86/3.08 ( ~ ( member_nat @ A2 @ A )
% 2.86/3.08 => ( ( inf_inf_set_nat @ A @ ( insert_nat2 @ A2 @ B ) )
% 2.86/3.08 = ( inf_inf_set_nat @ A @ B ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_insert_right_if0
% 2.86/3.08 thf(fact_2301_Int__insert__right__if0,axiom,
% 2.86/3.08 ! [A2: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.08 ( ~ ( member8440522571783428010at_nat @ A2 @ A )
% 2.86/3.08 => ( ( inf_in2572325071724192079at_nat @ A @ ( insert8211810215607154385at_nat @ A2 @ B ) )
% 2.86/3.08 = ( inf_in2572325071724192079at_nat @ A @ B ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_insert_right_if0
% 2.86/3.08 thf(fact_2302_Int__insert__right__if1,axiom,
% 2.86/3.08 ! [A2: $o,A: set_o,B: set_o] :
% 2.86/3.08 ( ( member_o @ A2 @ A )
% 2.86/3.08 => ( ( inf_inf_set_o @ A @ ( insert_o2 @ A2 @ B ) )
% 2.86/3.08 = ( insert_o2 @ A2 @ ( inf_inf_set_o @ A @ B ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_insert_right_if1
% 2.86/3.08 thf(fact_2303_Int__insert__right__if1,axiom,
% 2.86/3.08 ! [A2: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.08 ( ( member8757157785044589968at_nat @ A2 @ A )
% 2.86/3.08 => ( ( inf_in7913087082777306421at_nat @ A @ ( insert9069300056098147895at_nat @ A2 @ B ) )
% 2.86/3.08 = ( insert9069300056098147895at_nat @ A2 @ ( inf_in7913087082777306421at_nat @ A @ B ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_insert_right_if1
% 2.86/3.08 thf(fact_2304_Int__insert__right__if1,axiom,
% 2.86/3.08 ! [A2: int,A: set_int,B: set_int] :
% 2.86/3.08 ( ( member_int @ A2 @ A )
% 2.86/3.08 => ( ( inf_inf_set_int @ A @ ( insert_int2 @ A2 @ B ) )
% 2.86/3.08 = ( insert_int2 @ A2 @ ( inf_inf_set_int @ A @ B ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_insert_right_if1
% 2.86/3.08 thf(fact_2305_Int__insert__right__if1,axiom,
% 2.86/3.08 ! [A2: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o] :
% 2.86/3.08 ( ( member6576561426505652726_nat_o @ A2 @ A )
% 2.86/3.08 => ( ( inf_in1906310914598751387_nat_o @ A @ ( insert5175938949040314269_nat_o @ A2 @ B ) )
% 2.86/3.08 = ( insert5175938949040314269_nat_o @ A2 @ ( inf_in1906310914598751387_nat_o @ A @ B ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_insert_right_if1
% 2.86/3.08 thf(fact_2306_Int__insert__right__if1,axiom,
% 2.86/3.08 ! [A2: nat,A: set_nat,B: set_nat] :
% 2.86/3.08 ( ( member_nat @ A2 @ A )
% 2.86/3.08 => ( ( inf_inf_set_nat @ A @ ( insert_nat2 @ A2 @ B ) )
% 2.86/3.08 = ( insert_nat2 @ A2 @ ( inf_inf_set_nat @ A @ B ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_insert_right_if1
% 2.86/3.08 thf(fact_2307_Int__insert__right__if1,axiom,
% 2.86/3.08 ! [A2: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.08 ( ( member8440522571783428010at_nat @ A2 @ A )
% 2.86/3.08 => ( ( inf_in2572325071724192079at_nat @ A @ ( insert8211810215607154385at_nat @ A2 @ B ) )
% 2.86/3.08 = ( insert8211810215607154385at_nat @ A2 @ ( inf_in2572325071724192079at_nat @ A @ B ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_insert_right_if1
% 2.86/3.08 thf(fact_2308_insert__disjoint_I1_J,axiom,
% 2.86/3.08 ! [A2: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o] :
% 2.86/3.08 ( ( ( inf_in1906310914598751387_nat_o @ ( insert5175938949040314269_nat_o @ A2 @ A ) @ B )
% 2.86/3.08 = bot_bo7824918357723582233_nat_o )
% 2.86/3.08 = ( ~ ( member6576561426505652726_nat_o @ A2 @ B )
% 2.86/3.08 & ( ( inf_in1906310914598751387_nat_o @ A @ B )
% 2.86/3.08 = bot_bo7824918357723582233_nat_o ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % insert_disjoint(1)
% 2.86/3.08 thf(fact_2309_insert__disjoint_I1_J,axiom,
% 2.86/3.08 ! [A2: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.08 ( ( ( inf_in7913087082777306421at_nat @ ( insert9069300056098147895at_nat @ A2 @ A ) @ B )
% 2.86/3.08 = bot_bo228742789529271731at_nat )
% 2.86/3.08 = ( ~ ( member8757157785044589968at_nat @ A2 @ B )
% 2.86/3.08 & ( ( inf_in7913087082777306421at_nat @ A @ B )
% 2.86/3.08 = bot_bo228742789529271731at_nat ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % insert_disjoint(1)
% 2.86/3.08 thf(fact_2310_insert__disjoint_I1_J,axiom,
% 2.86/3.08 ! [A2: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.08 ( ( ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A2 @ A ) @ B )
% 2.86/3.08 = bot_bo2099793752762293965at_nat )
% 2.86/3.08 = ( ~ ( member8440522571783428010at_nat @ A2 @ B )
% 2.86/3.08 & ( ( inf_in2572325071724192079at_nat @ A @ B )
% 2.86/3.08 = bot_bo2099793752762293965at_nat ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % insert_disjoint(1)
% 2.86/3.08 thf(fact_2311_insert__disjoint_I1_J,axiom,
% 2.86/3.08 ! [A2: $o,A: set_o,B: set_o] :
% 2.86/3.08 ( ( ( inf_inf_set_o @ ( insert_o2 @ A2 @ A ) @ B )
% 2.86/3.08 = bot_bot_set_o )
% 2.86/3.08 = ( ~ ( member_o @ A2 @ B )
% 2.86/3.08 & ( ( inf_inf_set_o @ A @ B )
% 2.86/3.08 = bot_bot_set_o ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % insert_disjoint(1)
% 2.86/3.08 thf(fact_2312_insert__disjoint_I1_J,axiom,
% 2.86/3.08 ! [A2: nat,A: set_nat,B: set_nat] :
% 2.86/3.08 ( ( ( inf_inf_set_nat @ ( insert_nat2 @ A2 @ A ) @ B )
% 2.86/3.08 = bot_bot_set_nat )
% 2.86/3.08 = ( ~ ( member_nat @ A2 @ B )
% 2.86/3.08 & ( ( inf_inf_set_nat @ A @ B )
% 2.86/3.08 = bot_bot_set_nat ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % insert_disjoint(1)
% 2.86/3.08 thf(fact_2313_insert__disjoint_I1_J,axiom,
% 2.86/3.08 ! [A2: int,A: set_int,B: set_int] :
% 2.86/3.08 ( ( ( inf_inf_set_int @ ( insert_int2 @ A2 @ A ) @ B )
% 2.86/3.08 = bot_bot_set_int )
% 2.86/3.08 = ( ~ ( member_int @ A2 @ B )
% 2.86/3.08 & ( ( inf_inf_set_int @ A @ B )
% 2.86/3.08 = bot_bot_set_int ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % insert_disjoint(1)
% 2.86/3.08 thf(fact_2314_insert__disjoint_I2_J,axiom,
% 2.86/3.08 ! [A2: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o] :
% 2.86/3.08 ( ( bot_bo7824918357723582233_nat_o
% 2.86/3.08 = ( inf_in1906310914598751387_nat_o @ ( insert5175938949040314269_nat_o @ A2 @ A ) @ B ) )
% 2.86/3.08 = ( ~ ( member6576561426505652726_nat_o @ A2 @ B )
% 2.86/3.08 & ( bot_bo7824918357723582233_nat_o
% 2.86/3.08 = ( inf_in1906310914598751387_nat_o @ A @ B ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % insert_disjoint(2)
% 2.86/3.08 thf(fact_2315_insert__disjoint_I2_J,axiom,
% 2.86/3.08 ! [A2: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.08 ( ( bot_bo228742789529271731at_nat
% 2.86/3.08 = ( inf_in7913087082777306421at_nat @ ( insert9069300056098147895at_nat @ A2 @ A ) @ B ) )
% 2.86/3.08 = ( ~ ( member8757157785044589968at_nat @ A2 @ B )
% 2.86/3.08 & ( bot_bo228742789529271731at_nat
% 2.86/3.08 = ( inf_in7913087082777306421at_nat @ A @ B ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % insert_disjoint(2)
% 2.86/3.08 thf(fact_2316_insert__disjoint_I2_J,axiom,
% 2.86/3.08 ! [A2: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.08 ( ( bot_bo2099793752762293965at_nat
% 2.86/3.08 = ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A2 @ A ) @ B ) )
% 2.86/3.08 = ( ~ ( member8440522571783428010at_nat @ A2 @ B )
% 2.86/3.08 & ( bot_bo2099793752762293965at_nat
% 2.86/3.08 = ( inf_in2572325071724192079at_nat @ A @ B ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % insert_disjoint(2)
% 2.86/3.08 thf(fact_2317_insert__disjoint_I2_J,axiom,
% 2.86/3.08 ! [A2: $o,A: set_o,B: set_o] :
% 2.86/3.08 ( ( bot_bot_set_o
% 2.86/3.08 = ( inf_inf_set_o @ ( insert_o2 @ A2 @ A ) @ B ) )
% 2.86/3.08 = ( ~ ( member_o @ A2 @ B )
% 2.86/3.08 & ( bot_bot_set_o
% 2.86/3.08 = ( inf_inf_set_o @ A @ B ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % insert_disjoint(2)
% 2.86/3.08 thf(fact_2318_insert__disjoint_I2_J,axiom,
% 2.86/3.08 ! [A2: nat,A: set_nat,B: set_nat] :
% 2.86/3.08 ( ( bot_bot_set_nat
% 2.86/3.08 = ( inf_inf_set_nat @ ( insert_nat2 @ A2 @ A ) @ B ) )
% 2.86/3.08 = ( ~ ( member_nat @ A2 @ B )
% 2.86/3.08 & ( bot_bot_set_nat
% 2.86/3.08 = ( inf_inf_set_nat @ A @ B ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % insert_disjoint(2)
% 2.86/3.08 thf(fact_2319_insert__disjoint_I2_J,axiom,
% 2.86/3.08 ! [A2: int,A: set_int,B: set_int] :
% 2.86/3.08 ( ( bot_bot_set_int
% 2.86/3.08 = ( inf_inf_set_int @ ( insert_int2 @ A2 @ A ) @ B ) )
% 2.86/3.08 = ( ~ ( member_int @ A2 @ B )
% 2.86/3.08 & ( bot_bot_set_int
% 2.86/3.08 = ( inf_inf_set_int @ A @ B ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % insert_disjoint(2)
% 2.86/3.08 thf(fact_2320_disjoint__insert_I1_J,axiom,
% 2.86/3.08 ! [B: set_Pr4532377907799695533_nat_o,A2: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o] :
% 2.86/3.08 ( ( ( inf_in1906310914598751387_nat_o @ B @ ( insert5175938949040314269_nat_o @ A2 @ A ) )
% 2.86/3.08 = bot_bo7824918357723582233_nat_o )
% 2.86/3.08 = ( ~ ( member6576561426505652726_nat_o @ A2 @ B )
% 2.86/3.08 & ( ( inf_in1906310914598751387_nat_o @ B @ A )
% 2.86/3.08 = bot_bo7824918357723582233_nat_o ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % disjoint_insert(1)
% 2.86/3.08 thf(fact_2321_disjoint__insert_I1_J,axiom,
% 2.86/3.08 ! [B: set_Pr4329608150637261639at_nat,A2: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat] :
% 2.86/3.08 ( ( ( inf_in7913087082777306421at_nat @ B @ ( insert9069300056098147895at_nat @ A2 @ A ) )
% 2.86/3.08 = bot_bo228742789529271731at_nat )
% 2.86/3.08 = ( ~ ( member8757157785044589968at_nat @ A2 @ B )
% 2.86/3.08 & ( ( inf_in7913087082777306421at_nat @ B @ A )
% 2.86/3.08 = bot_bo228742789529271731at_nat ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % disjoint_insert(1)
% 2.86/3.08 thf(fact_2322_disjoint__insert_I1_J,axiom,
% 2.86/3.08 ! [B: set_Pr1261947904930325089at_nat,A2: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat] :
% 2.86/3.08 ( ( ( inf_in2572325071724192079at_nat @ B @ ( insert8211810215607154385at_nat @ A2 @ A ) )
% 2.86/3.08 = bot_bo2099793752762293965at_nat )
% 2.86/3.08 = ( ~ ( member8440522571783428010at_nat @ A2 @ B )
% 2.86/3.08 & ( ( inf_in2572325071724192079at_nat @ B @ A )
% 2.86/3.08 = bot_bo2099793752762293965at_nat ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % disjoint_insert(1)
% 2.86/3.08 thf(fact_2323_disjoint__insert_I1_J,axiom,
% 2.86/3.08 ! [B: set_o,A2: $o,A: set_o] :
% 2.86/3.08 ( ( ( inf_inf_set_o @ B @ ( insert_o2 @ A2 @ A ) )
% 2.86/3.08 = bot_bot_set_o )
% 2.86/3.08 = ( ~ ( member_o @ A2 @ B )
% 2.86/3.08 & ( ( inf_inf_set_o @ B @ A )
% 2.86/3.08 = bot_bot_set_o ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % disjoint_insert(1)
% 2.86/3.08 thf(fact_2324_disjoint__insert_I1_J,axiom,
% 2.86/3.08 ! [B: set_nat,A2: nat,A: set_nat] :
% 2.86/3.08 ( ( ( inf_inf_set_nat @ B @ ( insert_nat2 @ A2 @ A ) )
% 2.86/3.08 = bot_bot_set_nat )
% 2.86/3.08 = ( ~ ( member_nat @ A2 @ B )
% 2.86/3.08 & ( ( inf_inf_set_nat @ B @ A )
% 2.86/3.08 = bot_bot_set_nat ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % disjoint_insert(1)
% 2.86/3.08 thf(fact_2325_disjoint__insert_I1_J,axiom,
% 2.86/3.08 ! [B: set_int,A2: int,A: set_int] :
% 2.86/3.08 ( ( ( inf_inf_set_int @ B @ ( insert_int2 @ A2 @ A ) )
% 2.86/3.08 = bot_bot_set_int )
% 2.86/3.08 = ( ~ ( member_int @ A2 @ B )
% 2.86/3.08 & ( ( inf_inf_set_int @ B @ A )
% 2.86/3.08 = bot_bot_set_int ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % disjoint_insert(1)
% 2.86/3.08 thf(fact_2326_disjoint__insert_I2_J,axiom,
% 2.86/3.08 ! [A: set_Pr4532377907799695533_nat_o,B2: produc3658429121746597890et_nat > $o,B: set_Pr4532377907799695533_nat_o] :
% 2.86/3.08 ( ( bot_bo7824918357723582233_nat_o
% 2.86/3.08 = ( inf_in1906310914598751387_nat_o @ A @ ( insert5175938949040314269_nat_o @ B2 @ B ) ) )
% 2.86/3.08 = ( ~ ( member6576561426505652726_nat_o @ B2 @ A )
% 2.86/3.08 & ( bot_bo7824918357723582233_nat_o
% 2.86/3.08 = ( inf_in1906310914598751387_nat_o @ A @ B ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % disjoint_insert(2)
% 2.86/3.08 thf(fact_2327_disjoint__insert_I2_J,axiom,
% 2.86/3.08 ! [A: set_Pr4329608150637261639at_nat,B2: produc3843707927480180839at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.08 ( ( bot_bo228742789529271731at_nat
% 2.86/3.08 = ( inf_in7913087082777306421at_nat @ A @ ( insert9069300056098147895at_nat @ B2 @ B ) ) )
% 2.86/3.08 = ( ~ ( member8757157785044589968at_nat @ B2 @ A )
% 2.86/3.08 & ( bot_bo228742789529271731at_nat
% 2.86/3.08 = ( inf_in7913087082777306421at_nat @ A @ B ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % disjoint_insert(2)
% 2.86/3.08 thf(fact_2328_disjoint__insert_I2_J,axiom,
% 2.86/3.08 ! [A: set_Pr1261947904930325089at_nat,B2: product_prod_nat_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.08 ( ( bot_bo2099793752762293965at_nat
% 2.86/3.08 = ( inf_in2572325071724192079at_nat @ A @ ( insert8211810215607154385at_nat @ B2 @ B ) ) )
% 2.86/3.08 = ( ~ ( member8440522571783428010at_nat @ B2 @ A )
% 2.86/3.08 & ( bot_bo2099793752762293965at_nat
% 2.86/3.08 = ( inf_in2572325071724192079at_nat @ A @ B ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % disjoint_insert(2)
% 2.86/3.08 thf(fact_2329_disjoint__insert_I2_J,axiom,
% 2.86/3.08 ! [A: set_o,B2: $o,B: set_o] :
% 2.86/3.08 ( ( bot_bot_set_o
% 2.86/3.08 = ( inf_inf_set_o @ A @ ( insert_o2 @ B2 @ B ) ) )
% 2.86/3.08 = ( ~ ( member_o @ B2 @ A )
% 2.86/3.08 & ( bot_bot_set_o
% 2.86/3.08 = ( inf_inf_set_o @ A @ B ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % disjoint_insert(2)
% 2.86/3.08 thf(fact_2330_disjoint__insert_I2_J,axiom,
% 2.86/3.08 ! [A: set_nat,B2: nat,B: set_nat] :
% 2.86/3.08 ( ( bot_bot_set_nat
% 2.86/3.08 = ( inf_inf_set_nat @ A @ ( insert_nat2 @ B2 @ B ) ) )
% 2.86/3.08 = ( ~ ( member_nat @ B2 @ A )
% 2.86/3.08 & ( bot_bot_set_nat
% 2.86/3.08 = ( inf_inf_set_nat @ A @ B ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % disjoint_insert(2)
% 2.86/3.08 thf(fact_2331_disjoint__insert_I2_J,axiom,
% 2.86/3.08 ! [A: set_int,B2: int,B: set_int] :
% 2.86/3.08 ( ( bot_bot_set_int
% 2.86/3.08 = ( inf_inf_set_int @ A @ ( insert_int2 @ B2 @ B ) ) )
% 2.86/3.08 = ( ~ ( member_int @ B2 @ A )
% 2.86/3.08 & ( bot_bot_set_int
% 2.86/3.08 = ( inf_inf_set_int @ A @ B ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % disjoint_insert(2)
% 2.86/3.08 thf(fact_2332_Diff__disjoint,axiom,
% 2.86/3.08 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.08 ( ( inf_in7913087082777306421at_nat @ A @ ( minus_3314409938677909166at_nat @ B @ A ) )
% 2.86/3.08 = bot_bo228742789529271731at_nat ) ).
% 2.86/3.08
% 2.86/3.08 % Diff_disjoint
% 2.86/3.08 thf(fact_2333_Diff__disjoint,axiom,
% 2.86/3.08 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.08 ( ( inf_in2572325071724192079at_nat @ A @ ( minus_1356011639430497352at_nat @ B @ A ) )
% 2.86/3.08 = bot_bo2099793752762293965at_nat ) ).
% 2.86/3.08
% 2.86/3.08 % Diff_disjoint
% 2.86/3.08 thf(fact_2334_Diff__disjoint,axiom,
% 2.86/3.08 ! [A: set_o,B: set_o] :
% 2.86/3.08 ( ( inf_inf_set_o @ A @ ( minus_minus_set_o @ B @ A ) )
% 2.86/3.08 = bot_bot_set_o ) ).
% 2.86/3.08
% 2.86/3.08 % Diff_disjoint
% 2.86/3.08 thf(fact_2335_Diff__disjoint,axiom,
% 2.86/3.08 ! [A: set_int,B: set_int] :
% 2.86/3.08 ( ( inf_inf_set_int @ A @ ( minus_minus_set_int @ B @ A ) )
% 2.86/3.08 = bot_bot_set_int ) ).
% 2.86/3.08
% 2.86/3.08 % Diff_disjoint
% 2.86/3.08 thf(fact_2336_Diff__disjoint,axiom,
% 2.86/3.08 ! [A: set_nat,B: set_nat] :
% 2.86/3.08 ( ( inf_inf_set_nat @ A @ ( minus_minus_set_nat @ B @ A ) )
% 2.86/3.08 = bot_bot_set_nat ) ).
% 2.86/3.08
% 2.86/3.08 % Diff_disjoint
% 2.86/3.08 thf(fact_2337_list__update__beyond,axiom,
% 2.86/3.08 ! [Xs: list_c,I: nat,X: c] :
% 2.86/3.08 ( ( ord_less_eq_nat @ ( size_size_list_c @ Xs ) @ I )
% 2.86/3.08 => ( ( list_update_c @ Xs @ I @ X )
% 2.86/3.08 = Xs ) ) ).
% 2.86/3.08
% 2.86/3.08 % list_update_beyond
% 2.86/3.08 thf(fact_2338_list__update__beyond,axiom,
% 2.86/3.08 ! [Xs: list_d,I: nat,X: d] :
% 2.86/3.08 ( ( ord_less_eq_nat @ ( size_size_list_d @ Xs ) @ I )
% 2.86/3.08 => ( ( list_update_d @ Xs @ I @ X )
% 2.86/3.08 = Xs ) ) ).
% 2.86/3.08
% 2.86/3.08 % list_update_beyond
% 2.86/3.08 thf(fact_2339_list__update__beyond,axiom,
% 2.86/3.08 ! [Xs: list_nat,I: nat,X: nat] :
% 2.86/3.08 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ I )
% 2.86/3.08 => ( ( list_update_nat @ Xs @ I @ X )
% 2.86/3.08 = Xs ) ) ).
% 2.86/3.08
% 2.86/3.08 % list_update_beyond
% 2.86/3.08 thf(fact_2340_list__update__beyond,axiom,
% 2.86/3.08 ! [Xs: list_int,I: nat,X: int] :
% 2.86/3.08 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ I )
% 2.86/3.08 => ( ( list_update_int @ Xs @ I @ X )
% 2.86/3.08 = Xs ) ) ).
% 2.86/3.08
% 2.86/3.08 % list_update_beyond
% 2.86/3.08 thf(fact_2341_nat__less__le,axiom,
% 2.86/3.08 ( ord_less_nat
% 2.86/3.08 = ( ^ [M: nat,N2: nat] :
% 2.86/3.08 ( ( ord_less_eq_nat @ M @ N2 )
% 2.86/3.08 & ( M != N2 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % nat_less_le
% 2.86/3.08 thf(fact_2342_less__imp__le__nat,axiom,
% 2.86/3.08 ! [M2: nat,N: nat] :
% 2.86/3.08 ( ( ord_less_nat @ M2 @ N )
% 2.86/3.08 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 2.86/3.08
% 2.86/3.08 % less_imp_le_nat
% 2.86/3.08 thf(fact_2343_le__eq__less__or__eq,axiom,
% 2.86/3.08 ( ord_less_eq_nat
% 2.86/3.08 = ( ^ [M: nat,N2: nat] :
% 2.86/3.08 ( ( ord_less_nat @ M @ N2 )
% 2.86/3.08 | ( M = N2 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % le_eq_less_or_eq
% 2.86/3.08 thf(fact_2344_less__or__eq__imp__le,axiom,
% 2.86/3.08 ! [M2: nat,N: nat] :
% 2.86/3.08 ( ( ( ord_less_nat @ M2 @ N )
% 2.86/3.08 | ( M2 = N ) )
% 2.86/3.08 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 2.86/3.08
% 2.86/3.08 % less_or_eq_imp_le
% 2.86/3.08 thf(fact_2345_le__neq__implies__less,axiom,
% 2.86/3.08 ! [M2: nat,N: nat] :
% 2.86/3.08 ( ( ord_less_eq_nat @ M2 @ N )
% 2.86/3.08 => ( ( M2 != N )
% 2.86/3.08 => ( ord_less_nat @ M2 @ N ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % le_neq_implies_less
% 2.86/3.08 thf(fact_2346_less__mono__imp__le__mono,axiom,
% 2.86/3.08 ! [F4: nat > nat,I: nat,J: nat] :
% 2.86/3.08 ( ! [I5: nat,J3: nat] :
% 2.86/3.08 ( ( ord_less_nat @ I5 @ J3 )
% 2.86/3.08 => ( ord_less_nat @ ( F4 @ I5 ) @ ( F4 @ J3 ) ) )
% 2.86/3.08 => ( ( ord_less_eq_nat @ I @ J )
% 2.86/3.08 => ( ord_less_eq_nat @ ( F4 @ I ) @ ( F4 @ J ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % less_mono_imp_le_mono
% 2.86/3.08 thf(fact_2347_disjoint__iff__not__equal,axiom,
% 2.86/3.08 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.08 ( ( ( inf_in7913087082777306421at_nat @ A @ B )
% 2.86/3.08 = bot_bo228742789529271731at_nat )
% 2.86/3.08 = ( ! [X2: produc3843707927480180839at_nat] :
% 2.86/3.08 ( ( member8757157785044589968at_nat @ X2 @ A )
% 2.86/3.08 => ! [Y5: produc3843707927480180839at_nat] :
% 2.86/3.08 ( ( member8757157785044589968at_nat @ Y5 @ B )
% 2.86/3.08 => ( X2 != Y5 ) ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % disjoint_iff_not_equal
% 2.86/3.08 thf(fact_2348_disjoint__iff__not__equal,axiom,
% 2.86/3.08 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.08 ( ( ( inf_in2572325071724192079at_nat @ A @ B )
% 2.86/3.08 = bot_bo2099793752762293965at_nat )
% 2.86/3.08 = ( ! [X2: product_prod_nat_nat] :
% 2.86/3.08 ( ( member8440522571783428010at_nat @ X2 @ A )
% 2.86/3.08 => ! [Y5: product_prod_nat_nat] :
% 2.86/3.08 ( ( member8440522571783428010at_nat @ Y5 @ B )
% 2.86/3.08 => ( X2 != Y5 ) ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % disjoint_iff_not_equal
% 2.86/3.08 thf(fact_2349_disjoint__iff__not__equal,axiom,
% 2.86/3.08 ! [A: set_o,B: set_o] :
% 2.86/3.08 ( ( ( inf_inf_set_o @ A @ B )
% 2.86/3.08 = bot_bot_set_o )
% 2.86/3.08 = ( ! [X2: $o] :
% 2.86/3.08 ( ( member_o @ X2 @ A )
% 2.86/3.08 => ! [Y5: $o] :
% 2.86/3.08 ( ( member_o @ Y5 @ B )
% 2.86/3.08 => ( X2 = ~ Y5 ) ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % disjoint_iff_not_equal
% 2.86/3.08 thf(fact_2350_disjoint__iff__not__equal,axiom,
% 2.86/3.08 ! [A: set_nat,B: set_nat] :
% 2.86/3.08 ( ( ( inf_inf_set_nat @ A @ B )
% 2.86/3.08 = bot_bot_set_nat )
% 2.86/3.08 = ( ! [X2: nat] :
% 2.86/3.08 ( ( member_nat @ X2 @ A )
% 2.86/3.08 => ! [Y5: nat] :
% 2.86/3.08 ( ( member_nat @ Y5 @ B )
% 2.86/3.08 => ( X2 != Y5 ) ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % disjoint_iff_not_equal
% 2.86/3.08 thf(fact_2351_disjoint__iff__not__equal,axiom,
% 2.86/3.08 ! [A: set_int,B: set_int] :
% 2.86/3.08 ( ( ( inf_inf_set_int @ A @ B )
% 2.86/3.08 = bot_bot_set_int )
% 2.86/3.08 = ( ! [X2: int] :
% 2.86/3.08 ( ( member_int @ X2 @ A )
% 2.86/3.08 => ! [Y5: int] :
% 2.86/3.08 ( ( member_int @ Y5 @ B )
% 2.86/3.08 => ( X2 != Y5 ) ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % disjoint_iff_not_equal
% 2.86/3.08 thf(fact_2352_Int__empty__right,axiom,
% 2.86/3.08 ! [A: set_Pr4329608150637261639at_nat] :
% 2.86/3.08 ( ( inf_in7913087082777306421at_nat @ A @ bot_bo228742789529271731at_nat )
% 2.86/3.08 = bot_bo228742789529271731at_nat ) ).
% 2.86/3.08
% 2.86/3.08 % Int_empty_right
% 2.86/3.08 thf(fact_2353_Int__empty__right,axiom,
% 2.86/3.08 ! [A: set_Pr1261947904930325089at_nat] :
% 2.86/3.08 ( ( inf_in2572325071724192079at_nat @ A @ bot_bo2099793752762293965at_nat )
% 2.86/3.08 = bot_bo2099793752762293965at_nat ) ).
% 2.86/3.08
% 2.86/3.08 % Int_empty_right
% 2.86/3.08 thf(fact_2354_Int__empty__right,axiom,
% 2.86/3.08 ! [A: set_o] :
% 2.86/3.08 ( ( inf_inf_set_o @ A @ bot_bot_set_o )
% 2.86/3.08 = bot_bot_set_o ) ).
% 2.86/3.08
% 2.86/3.08 % Int_empty_right
% 2.86/3.08 thf(fact_2355_Int__empty__right,axiom,
% 2.86/3.08 ! [A: set_nat] :
% 2.86/3.08 ( ( inf_inf_set_nat @ A @ bot_bot_set_nat )
% 2.86/3.08 = bot_bot_set_nat ) ).
% 2.86/3.08
% 2.86/3.08 % Int_empty_right
% 2.86/3.08 thf(fact_2356_Int__empty__right,axiom,
% 2.86/3.08 ! [A: set_int] :
% 2.86/3.08 ( ( inf_inf_set_int @ A @ bot_bot_set_int )
% 2.86/3.08 = bot_bot_set_int ) ).
% 2.86/3.08
% 2.86/3.08 % Int_empty_right
% 2.86/3.08 thf(fact_2357_Int__empty__left,axiom,
% 2.86/3.08 ! [B: set_Pr4329608150637261639at_nat] :
% 2.86/3.08 ( ( inf_in7913087082777306421at_nat @ bot_bo228742789529271731at_nat @ B )
% 2.86/3.08 = bot_bo228742789529271731at_nat ) ).
% 2.86/3.08
% 2.86/3.08 % Int_empty_left
% 2.86/3.08 thf(fact_2358_Int__empty__left,axiom,
% 2.86/3.08 ! [B: set_Pr1261947904930325089at_nat] :
% 2.86/3.08 ( ( inf_in2572325071724192079at_nat @ bot_bo2099793752762293965at_nat @ B )
% 2.86/3.08 = bot_bo2099793752762293965at_nat ) ).
% 2.86/3.08
% 2.86/3.08 % Int_empty_left
% 2.86/3.08 thf(fact_2359_Int__empty__left,axiom,
% 2.86/3.08 ! [B: set_o] :
% 2.86/3.08 ( ( inf_inf_set_o @ bot_bot_set_o @ B )
% 2.86/3.08 = bot_bot_set_o ) ).
% 2.86/3.08
% 2.86/3.08 % Int_empty_left
% 2.86/3.08 thf(fact_2360_Int__empty__left,axiom,
% 2.86/3.08 ! [B: set_nat] :
% 2.86/3.08 ( ( inf_inf_set_nat @ bot_bot_set_nat @ B )
% 2.86/3.08 = bot_bot_set_nat ) ).
% 2.86/3.08
% 2.86/3.08 % Int_empty_left
% 2.86/3.08 thf(fact_2361_Int__empty__left,axiom,
% 2.86/3.08 ! [B: set_int] :
% 2.86/3.08 ( ( inf_inf_set_int @ bot_bot_set_int @ B )
% 2.86/3.08 = bot_bot_set_int ) ).
% 2.86/3.08
% 2.86/3.08 % Int_empty_left
% 2.86/3.08 thf(fact_2362_disjoint__iff,axiom,
% 2.86/3.08 ! [A: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o] :
% 2.86/3.08 ( ( ( inf_in1906310914598751387_nat_o @ A @ B )
% 2.86/3.08 = bot_bo7824918357723582233_nat_o )
% 2.86/3.08 = ( ! [X2: produc3658429121746597890et_nat > $o] :
% 2.86/3.08 ( ( member6576561426505652726_nat_o @ X2 @ A )
% 2.86/3.08 => ~ ( member6576561426505652726_nat_o @ X2 @ B ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % disjoint_iff
% 2.86/3.08 thf(fact_2363_disjoint__iff,axiom,
% 2.86/3.08 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.08 ( ( ( inf_in7913087082777306421at_nat @ A @ B )
% 2.86/3.08 = bot_bo228742789529271731at_nat )
% 2.86/3.08 = ( ! [X2: produc3843707927480180839at_nat] :
% 2.86/3.08 ( ( member8757157785044589968at_nat @ X2 @ A )
% 2.86/3.08 => ~ ( member8757157785044589968at_nat @ X2 @ B ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % disjoint_iff
% 2.86/3.08 thf(fact_2364_disjoint__iff,axiom,
% 2.86/3.08 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.08 ( ( ( inf_in2572325071724192079at_nat @ A @ B )
% 2.86/3.08 = bot_bo2099793752762293965at_nat )
% 2.86/3.08 = ( ! [X2: product_prod_nat_nat] :
% 2.86/3.08 ( ( member8440522571783428010at_nat @ X2 @ A )
% 2.86/3.08 => ~ ( member8440522571783428010at_nat @ X2 @ B ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % disjoint_iff
% 2.86/3.08 thf(fact_2365_disjoint__iff,axiom,
% 2.86/3.08 ! [A: set_o,B: set_o] :
% 2.86/3.08 ( ( ( inf_inf_set_o @ A @ B )
% 2.86/3.08 = bot_bot_set_o )
% 2.86/3.08 = ( ! [X2: $o] :
% 2.86/3.08 ( ( member_o @ X2 @ A )
% 2.86/3.08 => ~ ( member_o @ X2 @ B ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % disjoint_iff
% 2.86/3.08 thf(fact_2366_disjoint__iff,axiom,
% 2.86/3.08 ! [A: set_nat,B: set_nat] :
% 2.86/3.08 ( ( ( inf_inf_set_nat @ A @ B )
% 2.86/3.08 = bot_bot_set_nat )
% 2.86/3.08 = ( ! [X2: nat] :
% 2.86/3.08 ( ( member_nat @ X2 @ A )
% 2.86/3.08 => ~ ( member_nat @ X2 @ B ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % disjoint_iff
% 2.86/3.08 thf(fact_2367_disjoint__iff,axiom,
% 2.86/3.08 ! [A: set_int,B: set_int] :
% 2.86/3.08 ( ( ( inf_inf_set_int @ A @ B )
% 2.86/3.08 = bot_bot_set_int )
% 2.86/3.08 = ( ! [X2: int] :
% 2.86/3.08 ( ( member_int @ X2 @ A )
% 2.86/3.08 => ~ ( member_int @ X2 @ B ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % disjoint_iff
% 2.86/3.08 thf(fact_2368_Int__emptyI,axiom,
% 2.86/3.08 ! [A: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o] :
% 2.86/3.08 ( ! [X3: produc3658429121746597890et_nat > $o] :
% 2.86/3.08 ( ( member6576561426505652726_nat_o @ X3 @ A )
% 2.86/3.08 => ~ ( member6576561426505652726_nat_o @ X3 @ B ) )
% 2.86/3.08 => ( ( inf_in1906310914598751387_nat_o @ A @ B )
% 2.86/3.08 = bot_bo7824918357723582233_nat_o ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_emptyI
% 2.86/3.08 thf(fact_2369_Int__emptyI,axiom,
% 2.86/3.08 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.08 ( ! [X3: produc3843707927480180839at_nat] :
% 2.86/3.08 ( ( member8757157785044589968at_nat @ X3 @ A )
% 2.86/3.08 => ~ ( member8757157785044589968at_nat @ X3 @ B ) )
% 2.86/3.08 => ( ( inf_in7913087082777306421at_nat @ A @ B )
% 2.86/3.08 = bot_bo228742789529271731at_nat ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_emptyI
% 2.86/3.08 thf(fact_2370_Int__emptyI,axiom,
% 2.86/3.08 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.08 ( ! [X3: product_prod_nat_nat] :
% 2.86/3.08 ( ( member8440522571783428010at_nat @ X3 @ A )
% 2.86/3.08 => ~ ( member8440522571783428010at_nat @ X3 @ B ) )
% 2.86/3.08 => ( ( inf_in2572325071724192079at_nat @ A @ B )
% 2.86/3.08 = bot_bo2099793752762293965at_nat ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_emptyI
% 2.86/3.08 thf(fact_2371_Int__emptyI,axiom,
% 2.86/3.08 ! [A: set_o,B: set_o] :
% 2.86/3.08 ( ! [X3: $o] :
% 2.86/3.08 ( ( member_o @ X3 @ A )
% 2.86/3.08 => ~ ( member_o @ X3 @ B ) )
% 2.86/3.08 => ( ( inf_inf_set_o @ A @ B )
% 2.86/3.08 = bot_bot_set_o ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_emptyI
% 2.86/3.08 thf(fact_2372_Int__emptyI,axiom,
% 2.86/3.08 ! [A: set_nat,B: set_nat] :
% 2.86/3.08 ( ! [X3: nat] :
% 2.86/3.08 ( ( member_nat @ X3 @ A )
% 2.86/3.08 => ~ ( member_nat @ X3 @ B ) )
% 2.86/3.08 => ( ( inf_inf_set_nat @ A @ B )
% 2.86/3.08 = bot_bot_set_nat ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_emptyI
% 2.86/3.08 thf(fact_2373_Int__emptyI,axiom,
% 2.86/3.08 ! [A: set_int,B: set_int] :
% 2.86/3.08 ( ! [X3: int] :
% 2.86/3.08 ( ( member_int @ X3 @ A )
% 2.86/3.08 => ~ ( member_int @ X3 @ B ) )
% 2.86/3.08 => ( ( inf_inf_set_int @ A @ B )
% 2.86/3.08 = bot_bot_set_int ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_emptyI
% 2.86/3.08 thf(fact_2374_disjointI,axiom,
% 2.86/3.08 ! [A2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o] :
% 2.86/3.08 ( ! [X3: produc3658429121746597890et_nat > $o] :
% 2.86/3.08 ( ( member6576561426505652726_nat_o @ X3 @ A2 )
% 2.86/3.08 => ~ ( member6576561426505652726_nat_o @ X3 @ B2 ) )
% 2.86/3.08 => ( ( inf_in1906310914598751387_nat_o @ A2 @ B2 )
% 2.86/3.08 = bot_bo7824918357723582233_nat_o ) ) ).
% 2.86/3.08
% 2.86/3.08 % disjointI
% 2.86/3.08 thf(fact_2375_disjointI,axiom,
% 2.86/3.08 ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 2.86/3.08 ( ! [X3: produc3843707927480180839at_nat] :
% 2.86/3.08 ( ( member8757157785044589968at_nat @ X3 @ A2 )
% 2.86/3.08 => ~ ( member8757157785044589968at_nat @ X3 @ B2 ) )
% 2.86/3.08 => ( ( inf_in7913087082777306421at_nat @ A2 @ B2 )
% 2.86/3.08 = bot_bo228742789529271731at_nat ) ) ).
% 2.86/3.08
% 2.86/3.08 % disjointI
% 2.86/3.08 thf(fact_2376_disjointI,axiom,
% 2.86/3.08 ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 2.86/3.08 ( ! [X3: product_prod_nat_nat] :
% 2.86/3.08 ( ( member8440522571783428010at_nat @ X3 @ A2 )
% 2.86/3.08 => ~ ( member8440522571783428010at_nat @ X3 @ B2 ) )
% 2.86/3.08 => ( ( inf_in2572325071724192079at_nat @ A2 @ B2 )
% 2.86/3.08 = bot_bo2099793752762293965at_nat ) ) ).
% 2.86/3.08
% 2.86/3.08 % disjointI
% 2.86/3.08 thf(fact_2377_disjointI,axiom,
% 2.86/3.08 ! [A2: set_o,B2: set_o] :
% 2.86/3.08 ( ! [X3: $o] :
% 2.86/3.08 ( ( member_o @ X3 @ A2 )
% 2.86/3.08 => ~ ( member_o @ X3 @ B2 ) )
% 2.86/3.08 => ( ( inf_inf_set_o @ A2 @ B2 )
% 2.86/3.08 = bot_bot_set_o ) ) ).
% 2.86/3.08
% 2.86/3.08 % disjointI
% 2.86/3.08 thf(fact_2378_disjointI,axiom,
% 2.86/3.08 ! [A2: set_nat,B2: set_nat] :
% 2.86/3.08 ( ! [X3: nat] :
% 2.86/3.08 ( ( member_nat @ X3 @ A2 )
% 2.86/3.08 => ~ ( member_nat @ X3 @ B2 ) )
% 2.86/3.08 => ( ( inf_inf_set_nat @ A2 @ B2 )
% 2.86/3.08 = bot_bot_set_nat ) ) ).
% 2.86/3.08
% 2.86/3.08 % disjointI
% 2.86/3.08 thf(fact_2379_disjointI,axiom,
% 2.86/3.08 ! [A2: set_int,B2: set_int] :
% 2.86/3.08 ( ! [X3: int] :
% 2.86/3.08 ( ( member_int @ X3 @ A2 )
% 2.86/3.08 => ~ ( member_int @ X3 @ B2 ) )
% 2.86/3.08 => ( ( inf_inf_set_int @ A2 @ B2 )
% 2.86/3.08 = bot_bot_set_int ) ) ).
% 2.86/3.08
% 2.86/3.08 % disjointI
% 2.86/3.08 thf(fact_2380_inter__eq__subsetI,axiom,
% 2.86/3.08 ! [S: set_Pr1261947904930325089at_nat,S4: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.08 ( ( ord_le3146513528884898305at_nat @ S @ S4 )
% 2.86/3.08 => ( ( ( inf_in2572325071724192079at_nat @ A @ S4 )
% 2.86/3.08 = ( inf_in2572325071724192079at_nat @ B @ S4 ) )
% 2.86/3.08 => ( ( inf_in2572325071724192079at_nat @ A @ S )
% 2.86/3.08 = ( inf_in2572325071724192079at_nat @ B @ S ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % inter_eq_subsetI
% 2.86/3.08 thf(fact_2381_inter__eq__subsetI,axiom,
% 2.86/3.08 ! [S: set_nat,S4: set_nat,A: set_nat,B: set_nat] :
% 2.86/3.08 ( ( ord_less_eq_set_nat @ S @ S4 )
% 2.86/3.08 => ( ( ( inf_inf_set_nat @ A @ S4 )
% 2.86/3.08 = ( inf_inf_set_nat @ B @ S4 ) )
% 2.86/3.08 => ( ( inf_inf_set_nat @ A @ S )
% 2.86/3.08 = ( inf_inf_set_nat @ B @ S ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % inter_eq_subsetI
% 2.86/3.08 thf(fact_2382_Int__Collect__mono,axiom,
% 2.86/3.08 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,P: produc3843707927480180839at_nat > $o,Q: produc3843707927480180839at_nat > $o] :
% 2.86/3.08 ( ( ord_le1268244103169919719at_nat @ A @ B )
% 2.86/3.08 => ( ! [X3: produc3843707927480180839at_nat] :
% 2.86/3.08 ( ( member8757157785044589968at_nat @ X3 @ A )
% 2.86/3.08 => ( ( P @ X3 )
% 2.86/3.08 => ( Q @ X3 ) ) )
% 2.86/3.08 => ( ord_le1268244103169919719at_nat @ ( inf_in7913087082777306421at_nat @ A @ ( collec6321179662152712658at_nat @ P ) ) @ ( inf_in7913087082777306421at_nat @ B @ ( collec6321179662152712658at_nat @ Q ) ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_Collect_mono
% 2.86/3.08 thf(fact_2383_Int__Collect__mono,axiom,
% 2.86/3.08 ! [A: set_int,B: set_int,P: int > $o,Q: int > $o] :
% 2.86/3.08 ( ( ord_less_eq_set_int @ A @ B )
% 2.86/3.08 => ( ! [X3: int] :
% 2.86/3.08 ( ( member_int @ X3 @ A )
% 2.86/3.08 => ( ( P @ X3 )
% 2.86/3.08 => ( Q @ X3 ) ) )
% 2.86/3.08 => ( ord_less_eq_set_int @ ( inf_inf_set_int @ A @ ( collect_int @ P ) ) @ ( inf_inf_set_int @ B @ ( collect_int @ Q ) ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_Collect_mono
% 2.86/3.08 thf(fact_2384_Int__Collect__mono,axiom,
% 2.86/3.08 ! [A: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o,P: ( produc3658429121746597890et_nat > $o ) > $o,Q: ( produc3658429121746597890et_nat > $o ) > $o] :
% 2.86/3.08 ( ( ord_le2965882846123202637_nat_o @ A @ B )
% 2.86/3.08 => ( ! [X3: produc3658429121746597890et_nat > $o] :
% 2.86/3.08 ( ( member6576561426505652726_nat_o @ X3 @ A )
% 2.86/3.08 => ( ( P @ X3 )
% 2.86/3.08 => ( Q @ X3 ) ) )
% 2.86/3.08 => ( ord_le2965882846123202637_nat_o @ ( inf_in1906310914598751387_nat_o @ A @ ( collec939566748876313656_nat_o @ P ) ) @ ( inf_in1906310914598751387_nat_o @ B @ ( collec939566748876313656_nat_o @ Q ) ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_Collect_mono
% 2.86/3.08 thf(fact_2385_Int__Collect__mono,axiom,
% 2.86/3.08 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,P: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
% 2.86/3.08 ( ( ord_le3146513528884898305at_nat @ A @ B )
% 2.86/3.08 => ( ! [X3: product_prod_nat_nat] :
% 2.86/3.08 ( ( member8440522571783428010at_nat @ X3 @ A )
% 2.86/3.08 => ( ( P @ X3 )
% 2.86/3.08 => ( Q @ X3 ) ) )
% 2.86/3.08 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ ( collec3392354462482085612at_nat @ P ) ) @ ( inf_in2572325071724192079at_nat @ B @ ( collec3392354462482085612at_nat @ Q ) ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_Collect_mono
% 2.86/3.08 thf(fact_2386_Int__Collect__mono,axiom,
% 2.86/3.08 ! [A: set_nat,B: set_nat,P: nat > $o,Q: nat > $o] :
% 2.86/3.08 ( ( ord_less_eq_set_nat @ A @ B )
% 2.86/3.08 => ( ! [X3: nat] :
% 2.86/3.08 ( ( member_nat @ X3 @ A )
% 2.86/3.08 => ( ( P @ X3 )
% 2.86/3.08 => ( Q @ X3 ) ) )
% 2.86/3.08 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ ( collect_nat @ P ) ) @ ( inf_inf_set_nat @ B @ ( collect_nat @ Q ) ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_Collect_mono
% 2.86/3.08 thf(fact_2387_Int__greatest,axiom,
% 2.86/3.08 ! [C2: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.08 ( ( ord_le3146513528884898305at_nat @ C2 @ A )
% 2.86/3.08 => ( ( ord_le3146513528884898305at_nat @ C2 @ B )
% 2.86/3.08 => ( ord_le3146513528884898305at_nat @ C2 @ ( inf_in2572325071724192079at_nat @ A @ B ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_greatest
% 2.86/3.08 thf(fact_2388_Int__greatest,axiom,
% 2.86/3.08 ! [C2: set_nat,A: set_nat,B: set_nat] :
% 2.86/3.08 ( ( ord_less_eq_set_nat @ C2 @ A )
% 2.86/3.08 => ( ( ord_less_eq_set_nat @ C2 @ B )
% 2.86/3.08 => ( ord_less_eq_set_nat @ C2 @ ( inf_inf_set_nat @ A @ B ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_greatest
% 2.86/3.08 thf(fact_2389_Int__absorb2,axiom,
% 2.86/3.08 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.08 ( ( ord_le3146513528884898305at_nat @ A @ B )
% 2.86/3.08 => ( ( inf_in2572325071724192079at_nat @ A @ B )
% 2.86/3.08 = A ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_absorb2
% 2.86/3.08 thf(fact_2390_Int__absorb2,axiom,
% 2.86/3.08 ! [A: set_nat,B: set_nat] :
% 2.86/3.08 ( ( ord_less_eq_set_nat @ A @ B )
% 2.86/3.08 => ( ( inf_inf_set_nat @ A @ B )
% 2.86/3.08 = A ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_absorb2
% 2.86/3.08 thf(fact_2391_Int__absorb1,axiom,
% 2.86/3.08 ! [B: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 2.86/3.08 ( ( ord_le3146513528884898305at_nat @ B @ A )
% 2.86/3.08 => ( ( inf_in2572325071724192079at_nat @ A @ B )
% 2.86/3.08 = B ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_absorb1
% 2.86/3.08 thf(fact_2392_Int__absorb1,axiom,
% 2.86/3.08 ! [B: set_nat,A: set_nat] :
% 2.86/3.08 ( ( ord_less_eq_set_nat @ B @ A )
% 2.86/3.08 => ( ( inf_inf_set_nat @ A @ B )
% 2.86/3.08 = B ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_absorb1
% 2.86/3.08 thf(fact_2393_Int__lower2,axiom,
% 2.86/3.08 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ B ) ).
% 2.86/3.08
% 2.86/3.08 % Int_lower2
% 2.86/3.08 thf(fact_2394_Int__lower2,axiom,
% 2.86/3.08 ! [A: set_nat,B: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ B ) ).
% 2.86/3.08
% 2.86/3.08 % Int_lower2
% 2.86/3.08 thf(fact_2395_Int__lower1,axiom,
% 2.86/3.08 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ A ) ).
% 2.86/3.08
% 2.86/3.08 % Int_lower1
% 2.86/3.08 thf(fact_2396_Int__lower1,axiom,
% 2.86/3.08 ! [A: set_nat,B: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ A ) ).
% 2.86/3.08
% 2.86/3.08 % Int_lower1
% 2.86/3.08 thf(fact_2397_Int__mono,axiom,
% 2.86/3.08 ! [A: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,D: set_Pr1261947904930325089at_nat] :
% 2.86/3.08 ( ( ord_le3146513528884898305at_nat @ A @ C2 )
% 2.86/3.08 => ( ( ord_le3146513528884898305at_nat @ B @ D )
% 2.86/3.08 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ ( inf_in2572325071724192079at_nat @ C2 @ D ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_mono
% 2.86/3.08 thf(fact_2398_Int__mono,axiom,
% 2.86/3.08 ! [A: set_nat,C2: set_nat,B: set_nat,D: set_nat] :
% 2.86/3.08 ( ( ord_less_eq_set_nat @ A @ C2 )
% 2.86/3.08 => ( ( ord_less_eq_set_nat @ B @ D )
% 2.86/3.08 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ ( inf_inf_set_nat @ C2 @ D ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_mono
% 2.86/3.08 thf(fact_2399_Int__insert__left,axiom,
% 2.86/3.08 ! [A2: $o,C2: set_o,B: set_o] :
% 2.86/3.08 ( ( ( member_o @ A2 @ C2 )
% 2.86/3.08 => ( ( inf_inf_set_o @ ( insert_o2 @ A2 @ B ) @ C2 )
% 2.86/3.08 = ( insert_o2 @ A2 @ ( inf_inf_set_o @ B @ C2 ) ) ) )
% 2.86/3.08 & ( ~ ( member_o @ A2 @ C2 )
% 2.86/3.08 => ( ( inf_inf_set_o @ ( insert_o2 @ A2 @ B ) @ C2 )
% 2.86/3.08 = ( inf_inf_set_o @ B @ C2 ) ) ) ) ).
% 2.86/3.08
% 2.86/3.08 % Int_insert_left
% 2.86/3.08 thf(fact_2400_Int__insert__left,axiom,
% 2.86/3.08 ! [A2: produc3843707927480180839at_nat,C2: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.08 ( ( ( member8757157785044589968at_nat @ A2 @ C2 )
% 2.86/3.09 => ( ( inf_in7913087082777306421at_nat @ ( insert9069300056098147895at_nat @ A2 @ B ) @ C2 )
% 2.86/3.09 = ( insert9069300056098147895at_nat @ A2 @ ( inf_in7913087082777306421at_nat @ B @ C2 ) ) ) )
% 2.86/3.09 & ( ~ ( member8757157785044589968at_nat @ A2 @ C2 )
% 2.86/3.09 => ( ( inf_in7913087082777306421at_nat @ ( insert9069300056098147895at_nat @ A2 @ B ) @ C2 )
% 2.86/3.09 = ( inf_in7913087082777306421at_nat @ B @ C2 ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Int_insert_left
% 2.86/3.09 thf(fact_2401_Int__insert__left,axiom,
% 2.86/3.09 ! [A2: int,C2: set_int,B: set_int] :
% 2.86/3.09 ( ( ( member_int @ A2 @ C2 )
% 2.86/3.09 => ( ( inf_inf_set_int @ ( insert_int2 @ A2 @ B ) @ C2 )
% 2.86/3.09 = ( insert_int2 @ A2 @ ( inf_inf_set_int @ B @ C2 ) ) ) )
% 2.86/3.09 & ( ~ ( member_int @ A2 @ C2 )
% 2.86/3.09 => ( ( inf_inf_set_int @ ( insert_int2 @ A2 @ B ) @ C2 )
% 2.86/3.09 = ( inf_inf_set_int @ B @ C2 ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Int_insert_left
% 2.86/3.09 thf(fact_2402_Int__insert__left,axiom,
% 2.86/3.09 ! [A2: produc3658429121746597890et_nat > $o,C2: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o] :
% 2.86/3.09 ( ( ( member6576561426505652726_nat_o @ A2 @ C2 )
% 2.86/3.09 => ( ( inf_in1906310914598751387_nat_o @ ( insert5175938949040314269_nat_o @ A2 @ B ) @ C2 )
% 2.86/3.09 = ( insert5175938949040314269_nat_o @ A2 @ ( inf_in1906310914598751387_nat_o @ B @ C2 ) ) ) )
% 2.86/3.09 & ( ~ ( member6576561426505652726_nat_o @ A2 @ C2 )
% 2.86/3.09 => ( ( inf_in1906310914598751387_nat_o @ ( insert5175938949040314269_nat_o @ A2 @ B ) @ C2 )
% 2.86/3.09 = ( inf_in1906310914598751387_nat_o @ B @ C2 ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Int_insert_left
% 2.86/3.09 thf(fact_2403_Int__insert__left,axiom,
% 2.86/3.09 ! [A2: nat,C2: set_nat,B: set_nat] :
% 2.86/3.09 ( ( ( member_nat @ A2 @ C2 )
% 2.86/3.09 => ( ( inf_inf_set_nat @ ( insert_nat2 @ A2 @ B ) @ C2 )
% 2.86/3.09 = ( insert_nat2 @ A2 @ ( inf_inf_set_nat @ B @ C2 ) ) ) )
% 2.86/3.09 & ( ~ ( member_nat @ A2 @ C2 )
% 2.86/3.09 => ( ( inf_inf_set_nat @ ( insert_nat2 @ A2 @ B ) @ C2 )
% 2.86/3.09 = ( inf_inf_set_nat @ B @ C2 ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Int_insert_left
% 2.86/3.09 thf(fact_2404_Int__insert__left,axiom,
% 2.86/3.09 ! [A2: product_prod_nat_nat,C2: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( ( member8440522571783428010at_nat @ A2 @ C2 )
% 2.86/3.09 => ( ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A2 @ B ) @ C2 )
% 2.86/3.09 = ( insert8211810215607154385at_nat @ A2 @ ( inf_in2572325071724192079at_nat @ B @ C2 ) ) ) )
% 2.86/3.09 & ( ~ ( member8440522571783428010at_nat @ A2 @ C2 )
% 2.86/3.09 => ( ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A2 @ B ) @ C2 )
% 2.86/3.09 = ( inf_in2572325071724192079at_nat @ B @ C2 ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Int_insert_left
% 2.86/3.09 thf(fact_2405_Int__insert__right,axiom,
% 2.86/3.09 ! [A2: $o,A: set_o,B: set_o] :
% 2.86/3.09 ( ( ( member_o @ A2 @ A )
% 2.86/3.09 => ( ( inf_inf_set_o @ A @ ( insert_o2 @ A2 @ B ) )
% 2.86/3.09 = ( insert_o2 @ A2 @ ( inf_inf_set_o @ A @ B ) ) ) )
% 2.86/3.09 & ( ~ ( member_o @ A2 @ A )
% 2.86/3.09 => ( ( inf_inf_set_o @ A @ ( insert_o2 @ A2 @ B ) )
% 2.86/3.09 = ( inf_inf_set_o @ A @ B ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Int_insert_right
% 2.86/3.09 thf(fact_2406_Int__insert__right,axiom,
% 2.86/3.09 ! [A2: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( ( member8757157785044589968at_nat @ A2 @ A )
% 2.86/3.09 => ( ( inf_in7913087082777306421at_nat @ A @ ( insert9069300056098147895at_nat @ A2 @ B ) )
% 2.86/3.09 = ( insert9069300056098147895at_nat @ A2 @ ( inf_in7913087082777306421at_nat @ A @ B ) ) ) )
% 2.86/3.09 & ( ~ ( member8757157785044589968at_nat @ A2 @ A )
% 2.86/3.09 => ( ( inf_in7913087082777306421at_nat @ A @ ( insert9069300056098147895at_nat @ A2 @ B ) )
% 2.86/3.09 = ( inf_in7913087082777306421at_nat @ A @ B ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Int_insert_right
% 2.86/3.09 thf(fact_2407_Int__insert__right,axiom,
% 2.86/3.09 ! [A2: int,A: set_int,B: set_int] :
% 2.86/3.09 ( ( ( member_int @ A2 @ A )
% 2.86/3.09 => ( ( inf_inf_set_int @ A @ ( insert_int2 @ A2 @ B ) )
% 2.86/3.09 = ( insert_int2 @ A2 @ ( inf_inf_set_int @ A @ B ) ) ) )
% 2.86/3.09 & ( ~ ( member_int @ A2 @ A )
% 2.86/3.09 => ( ( inf_inf_set_int @ A @ ( insert_int2 @ A2 @ B ) )
% 2.86/3.09 = ( inf_inf_set_int @ A @ B ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Int_insert_right
% 2.86/3.09 thf(fact_2408_Int__insert__right,axiom,
% 2.86/3.09 ! [A2: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o] :
% 2.86/3.09 ( ( ( member6576561426505652726_nat_o @ A2 @ A )
% 2.86/3.09 => ( ( inf_in1906310914598751387_nat_o @ A @ ( insert5175938949040314269_nat_o @ A2 @ B ) )
% 2.86/3.09 = ( insert5175938949040314269_nat_o @ A2 @ ( inf_in1906310914598751387_nat_o @ A @ B ) ) ) )
% 2.86/3.09 & ( ~ ( member6576561426505652726_nat_o @ A2 @ A )
% 2.86/3.09 => ( ( inf_in1906310914598751387_nat_o @ A @ ( insert5175938949040314269_nat_o @ A2 @ B ) )
% 2.86/3.09 = ( inf_in1906310914598751387_nat_o @ A @ B ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Int_insert_right
% 2.86/3.09 thf(fact_2409_Int__insert__right,axiom,
% 2.86/3.09 ! [A2: nat,A: set_nat,B: set_nat] :
% 2.86/3.09 ( ( ( member_nat @ A2 @ A )
% 2.86/3.09 => ( ( inf_inf_set_nat @ A @ ( insert_nat2 @ A2 @ B ) )
% 2.86/3.09 = ( insert_nat2 @ A2 @ ( inf_inf_set_nat @ A @ B ) ) ) )
% 2.86/3.09 & ( ~ ( member_nat @ A2 @ A )
% 2.86/3.09 => ( ( inf_inf_set_nat @ A @ ( insert_nat2 @ A2 @ B ) )
% 2.86/3.09 = ( inf_inf_set_nat @ A @ B ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Int_insert_right
% 2.86/3.09 thf(fact_2410_Int__insert__right,axiom,
% 2.86/3.09 ! [A2: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( ( member8440522571783428010at_nat @ A2 @ A )
% 2.86/3.09 => ( ( inf_in2572325071724192079at_nat @ A @ ( insert8211810215607154385at_nat @ A2 @ B ) )
% 2.86/3.09 = ( insert8211810215607154385at_nat @ A2 @ ( inf_in2572325071724192079at_nat @ A @ B ) ) ) )
% 2.86/3.09 & ( ~ ( member8440522571783428010at_nat @ A2 @ A )
% 2.86/3.09 => ( ( inf_in2572325071724192079at_nat @ A @ ( insert8211810215607154385at_nat @ A2 @ B ) )
% 2.86/3.09 = ( inf_in2572325071724192079at_nat @ A @ B ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Int_insert_right
% 2.86/3.09 thf(fact_2411_Int__Diff,axiom,
% 2.86/3.09 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( minus_1356011639430497352at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ C2 )
% 2.86/3.09 = ( inf_in2572325071724192079at_nat @ A @ ( minus_1356011639430497352at_nat @ B @ C2 ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Int_Diff
% 2.86/3.09 thf(fact_2412_Int__Diff,axiom,
% 2.86/3.09 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 2.86/3.09 ( ( minus_minus_set_nat @ ( inf_inf_set_nat @ A @ B ) @ C2 )
% 2.86/3.09 = ( inf_inf_set_nat @ A @ ( minus_minus_set_nat @ B @ C2 ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Int_Diff
% 2.86/3.09 thf(fact_2413_Diff__Int2,axiom,
% 2.86/3.09 ! [A: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( minus_1356011639430497352at_nat @ ( inf_in2572325071724192079at_nat @ A @ C2 ) @ ( inf_in2572325071724192079at_nat @ B @ C2 ) )
% 2.86/3.09 = ( minus_1356011639430497352at_nat @ ( inf_in2572325071724192079at_nat @ A @ C2 ) @ B ) ) ).
% 2.86/3.09
% 2.86/3.09 % Diff_Int2
% 2.86/3.09 thf(fact_2414_Diff__Int2,axiom,
% 2.86/3.09 ! [A: set_nat,C2: set_nat,B: set_nat] :
% 2.86/3.09 ( ( minus_minus_set_nat @ ( inf_inf_set_nat @ A @ C2 ) @ ( inf_inf_set_nat @ B @ C2 ) )
% 2.86/3.09 = ( minus_minus_set_nat @ ( inf_inf_set_nat @ A @ C2 ) @ B ) ) ).
% 2.86/3.09
% 2.86/3.09 % Diff_Int2
% 2.86/3.09 thf(fact_2415_Diff__Diff__Int,axiom,
% 2.86/3.09 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( minus_1356011639430497352at_nat @ A @ ( minus_1356011639430497352at_nat @ A @ B ) )
% 2.86/3.09 = ( inf_in2572325071724192079at_nat @ A @ B ) ) ).
% 2.86/3.09
% 2.86/3.09 % Diff_Diff_Int
% 2.86/3.09 thf(fact_2416_Diff__Diff__Int,axiom,
% 2.86/3.09 ! [A: set_nat,B: set_nat] :
% 2.86/3.09 ( ( minus_minus_set_nat @ A @ ( minus_minus_set_nat @ A @ B ) )
% 2.86/3.09 = ( inf_inf_set_nat @ A @ B ) ) ).
% 2.86/3.09
% 2.86/3.09 % Diff_Diff_Int
% 2.86/3.09 thf(fact_2417_Diff__Int__distrib,axiom,
% 2.86/3.09 ! [C2: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( inf_in2572325071724192079at_nat @ C2 @ ( minus_1356011639430497352at_nat @ A @ B ) )
% 2.86/3.09 = ( minus_1356011639430497352at_nat @ ( inf_in2572325071724192079at_nat @ C2 @ A ) @ ( inf_in2572325071724192079at_nat @ C2 @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Diff_Int_distrib
% 2.86/3.09 thf(fact_2418_Diff__Int__distrib,axiom,
% 2.86/3.09 ! [C2: set_nat,A: set_nat,B: set_nat] :
% 2.86/3.09 ( ( inf_inf_set_nat @ C2 @ ( minus_minus_set_nat @ A @ B ) )
% 2.86/3.09 = ( minus_minus_set_nat @ ( inf_inf_set_nat @ C2 @ A ) @ ( inf_inf_set_nat @ C2 @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Diff_Int_distrib
% 2.86/3.09 thf(fact_2419_Diff__Int__distrib2,axiom,
% 2.86/3.09 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( inf_in2572325071724192079at_nat @ ( minus_1356011639430497352at_nat @ A @ B ) @ C2 )
% 2.86/3.09 = ( minus_1356011639430497352at_nat @ ( inf_in2572325071724192079at_nat @ A @ C2 ) @ ( inf_in2572325071724192079at_nat @ B @ C2 ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Diff_Int_distrib2
% 2.86/3.09 thf(fact_2420_Diff__Int__distrib2,axiom,
% 2.86/3.09 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 2.86/3.09 ( ( inf_inf_set_nat @ ( minus_minus_set_nat @ A @ B ) @ C2 )
% 2.86/3.09 = ( minus_minus_set_nat @ ( inf_inf_set_nat @ A @ C2 ) @ ( inf_inf_set_nat @ B @ C2 ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Diff_Int_distrib2
% 2.86/3.09 thf(fact_2421_exists__leI,axiom,
% 2.86/3.09 ! [N: nat,P: nat > $o] :
% 2.86/3.09 ( ( ! [N3: nat] :
% 2.86/3.09 ( ( ord_less_nat @ N3 @ N )
% 2.86/3.09 => ~ ( P @ N3 ) )
% 2.86/3.09 => ( P @ N ) )
% 2.86/3.09 => ? [N4: nat] :
% 2.86/3.09 ( ( ord_less_eq_nat @ N4 @ N )
% 2.86/3.09 & ( P @ N4 ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % exists_leI
% 2.86/3.09 thf(fact_2422_less__eq__assn__def,axiom,
% 2.86/3.09 ( ord_less_eq_assn
% 2.86/3.09 = ( ^ [A3: assn,B3: assn] :
% 2.86/3.09 ( A3
% 2.86/3.09 = ( inf_inf_assn @ A3 @ B3 ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % less_eq_assn_def
% 2.86/3.09 thf(fact_2423_less__diff__iff,axiom,
% 2.86/3.09 ! [K3: nat,M2: nat,N: nat] :
% 2.86/3.09 ( ( ord_less_eq_nat @ K3 @ M2 )
% 2.86/3.09 => ( ( ord_less_eq_nat @ K3 @ N )
% 2.86/3.09 => ( ( ord_less_nat @ ( minus_minus_nat @ M2 @ K3 ) @ ( minus_minus_nat @ N @ K3 ) )
% 2.86/3.09 = ( ord_less_nat @ M2 @ N ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % less_diff_iff
% 2.86/3.09 thf(fact_2424_diff__less__mono,axiom,
% 2.86/3.09 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.09 ( ( ord_less_nat @ A2 @ B2 )
% 2.86/3.09 => ( ( ord_less_eq_nat @ C @ A2 )
% 2.86/3.09 => ( ord_less_nat @ ( minus_minus_nat @ A2 @ C ) @ ( minus_minus_nat @ B2 @ C ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % diff_less_mono
% 2.86/3.09 thf(fact_2425_disjoint__mono,axiom,
% 2.86/3.09 ! [A2: set_Pr4329608150637261639at_nat,A7: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,B6: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( ord_le1268244103169919719at_nat @ A2 @ A7 )
% 2.86/3.09 => ( ( ord_le1268244103169919719at_nat @ B2 @ B6 )
% 2.86/3.09 => ( ( ( inf_in7913087082777306421at_nat @ A7 @ B6 )
% 2.86/3.09 = bot_bo228742789529271731at_nat )
% 2.86/3.09 => ( ( inf_in7913087082777306421at_nat @ A2 @ B2 )
% 2.86/3.09 = bot_bo228742789529271731at_nat ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % disjoint_mono
% 2.86/3.09 thf(fact_2426_disjoint__mono,axiom,
% 2.86/3.09 ! [A2: set_Pr1261947904930325089at_nat,A7: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( ord_le3146513528884898305at_nat @ A2 @ A7 )
% 2.86/3.09 => ( ( ord_le3146513528884898305at_nat @ B2 @ B6 )
% 2.86/3.09 => ( ( ( inf_in2572325071724192079at_nat @ A7 @ B6 )
% 2.86/3.09 = bot_bo2099793752762293965at_nat )
% 2.86/3.09 => ( ( inf_in2572325071724192079at_nat @ A2 @ B2 )
% 2.86/3.09 = bot_bo2099793752762293965at_nat ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % disjoint_mono
% 2.86/3.09 thf(fact_2427_disjoint__mono,axiom,
% 2.86/3.09 ! [A2: set_o,A7: set_o,B2: set_o,B6: set_o] :
% 2.86/3.09 ( ( ord_less_eq_set_o @ A2 @ A7 )
% 2.86/3.09 => ( ( ord_less_eq_set_o @ B2 @ B6 )
% 2.86/3.09 => ( ( ( inf_inf_set_o @ A7 @ B6 )
% 2.86/3.09 = bot_bot_set_o )
% 2.86/3.09 => ( ( inf_inf_set_o @ A2 @ B2 )
% 2.86/3.09 = bot_bot_set_o ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % disjoint_mono
% 2.86/3.09 thf(fact_2428_disjoint__mono,axiom,
% 2.86/3.09 ! [A2: set_int,A7: set_int,B2: set_int,B6: set_int] :
% 2.86/3.09 ( ( ord_less_eq_set_int @ A2 @ A7 )
% 2.86/3.09 => ( ( ord_less_eq_set_int @ B2 @ B6 )
% 2.86/3.09 => ( ( ( inf_inf_set_int @ A7 @ B6 )
% 2.86/3.09 = bot_bot_set_int )
% 2.86/3.09 => ( ( inf_inf_set_int @ A2 @ B2 )
% 2.86/3.09 = bot_bot_set_int ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % disjoint_mono
% 2.86/3.09 thf(fact_2429_disjoint__mono,axiom,
% 2.86/3.09 ! [A2: set_nat,A7: set_nat,B2: set_nat,B6: set_nat] :
% 2.86/3.09 ( ( ord_less_eq_set_nat @ A2 @ A7 )
% 2.86/3.09 => ( ( ord_less_eq_set_nat @ B2 @ B6 )
% 2.86/3.09 => ( ( ( inf_inf_set_nat @ A7 @ B6 )
% 2.86/3.09 = bot_bot_set_nat )
% 2.86/3.09 => ( ( inf_inf_set_nat @ A2 @ B2 )
% 2.86/3.09 = bot_bot_set_nat ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % disjoint_mono
% 2.86/3.09 thf(fact_2430_disjoint__alt__simp2,axiom,
% 2.86/3.09 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( ( minus_3314409938677909166at_nat @ A @ B )
% 2.86/3.09 != A )
% 2.86/3.09 = ( ( inf_in7913087082777306421at_nat @ A @ B )
% 2.86/3.09 != bot_bo228742789529271731at_nat ) ) ).
% 2.86/3.09
% 2.86/3.09 % disjoint_alt_simp2
% 2.86/3.09 thf(fact_2431_disjoint__alt__simp2,axiom,
% 2.86/3.09 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( ( minus_1356011639430497352at_nat @ A @ B )
% 2.86/3.09 != A )
% 2.86/3.09 = ( ( inf_in2572325071724192079at_nat @ A @ B )
% 2.86/3.09 != bot_bo2099793752762293965at_nat ) ) ).
% 2.86/3.09
% 2.86/3.09 % disjoint_alt_simp2
% 2.86/3.09 thf(fact_2432_disjoint__alt__simp2,axiom,
% 2.86/3.09 ! [A: set_o,B: set_o] :
% 2.86/3.09 ( ( ( minus_minus_set_o @ A @ B )
% 2.86/3.09 != A )
% 2.86/3.09 = ( ( inf_inf_set_o @ A @ B )
% 2.86/3.09 != bot_bot_set_o ) ) ).
% 2.86/3.09
% 2.86/3.09 % disjoint_alt_simp2
% 2.86/3.09 thf(fact_2433_disjoint__alt__simp2,axiom,
% 2.86/3.09 ! [A: set_int,B: set_int] :
% 2.86/3.09 ( ( ( minus_minus_set_int @ A @ B )
% 2.86/3.09 != A )
% 2.86/3.09 = ( ( inf_inf_set_int @ A @ B )
% 2.86/3.09 != bot_bot_set_int ) ) ).
% 2.86/3.09
% 2.86/3.09 % disjoint_alt_simp2
% 2.86/3.09 thf(fact_2434_disjoint__alt__simp2,axiom,
% 2.86/3.09 ! [A: set_nat,B: set_nat] :
% 2.86/3.09 ( ( ( minus_minus_set_nat @ A @ B )
% 2.86/3.09 != A )
% 2.86/3.09 = ( ( inf_inf_set_nat @ A @ B )
% 2.86/3.09 != bot_bot_set_nat ) ) ).
% 2.86/3.09
% 2.86/3.09 % disjoint_alt_simp2
% 2.86/3.09 thf(fact_2435_disjoint__alt__simp1,axiom,
% 2.86/3.09 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( ( minus_3314409938677909166at_nat @ A @ B )
% 2.86/3.09 = A )
% 2.86/3.09 = ( ( inf_in7913087082777306421at_nat @ A @ B )
% 2.86/3.09 = bot_bo228742789529271731at_nat ) ) ).
% 2.86/3.09
% 2.86/3.09 % disjoint_alt_simp1
% 2.86/3.09 thf(fact_2436_disjoint__alt__simp1,axiom,
% 2.86/3.09 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( ( minus_1356011639430497352at_nat @ A @ B )
% 2.86/3.09 = A )
% 2.86/3.09 = ( ( inf_in2572325071724192079at_nat @ A @ B )
% 2.86/3.09 = bot_bo2099793752762293965at_nat ) ) ).
% 2.86/3.09
% 2.86/3.09 % disjoint_alt_simp1
% 2.86/3.09 thf(fact_2437_disjoint__alt__simp1,axiom,
% 2.86/3.09 ! [A: set_o,B: set_o] :
% 2.86/3.09 ( ( ( minus_minus_set_o @ A @ B )
% 2.86/3.09 = A )
% 2.86/3.09 = ( ( inf_inf_set_o @ A @ B )
% 2.86/3.09 = bot_bot_set_o ) ) ).
% 2.86/3.09
% 2.86/3.09 % disjoint_alt_simp1
% 2.86/3.09 thf(fact_2438_disjoint__alt__simp1,axiom,
% 2.86/3.09 ! [A: set_int,B: set_int] :
% 2.86/3.09 ( ( ( minus_minus_set_int @ A @ B )
% 2.86/3.09 = A )
% 2.86/3.09 = ( ( inf_inf_set_int @ A @ B )
% 2.86/3.09 = bot_bot_set_int ) ) ).
% 2.86/3.09
% 2.86/3.09 % disjoint_alt_simp1
% 2.86/3.09 thf(fact_2439_disjoint__alt__simp1,axiom,
% 2.86/3.09 ! [A: set_nat,B: set_nat] :
% 2.86/3.09 ( ( ( minus_minus_set_nat @ A @ B )
% 2.86/3.09 = A )
% 2.86/3.09 = ( ( inf_inf_set_nat @ A @ B )
% 2.86/3.09 = bot_bot_set_nat ) ) ).
% 2.86/3.09
% 2.86/3.09 % disjoint_alt_simp1
% 2.86/3.09 thf(fact_2440_Int__Diff__disjoint,axiom,
% 2.86/3.09 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( inf_in7913087082777306421at_nat @ ( inf_in7913087082777306421at_nat @ A @ B ) @ ( minus_3314409938677909166at_nat @ A @ B ) )
% 2.86/3.09 = bot_bo228742789529271731at_nat ) ).
% 2.86/3.09
% 2.86/3.09 % Int_Diff_disjoint
% 2.86/3.09 thf(fact_2441_Int__Diff__disjoint,axiom,
% 2.86/3.09 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ ( minus_1356011639430497352at_nat @ A @ B ) )
% 2.86/3.09 = bot_bo2099793752762293965at_nat ) ).
% 2.86/3.09
% 2.86/3.09 % Int_Diff_disjoint
% 2.86/3.09 thf(fact_2442_Int__Diff__disjoint,axiom,
% 2.86/3.09 ! [A: set_o,B: set_o] :
% 2.86/3.09 ( ( inf_inf_set_o @ ( inf_inf_set_o @ A @ B ) @ ( minus_minus_set_o @ A @ B ) )
% 2.86/3.09 = bot_bot_set_o ) ).
% 2.86/3.09
% 2.86/3.09 % Int_Diff_disjoint
% 2.86/3.09 thf(fact_2443_Int__Diff__disjoint,axiom,
% 2.86/3.09 ! [A: set_int,B: set_int] :
% 2.86/3.09 ( ( inf_inf_set_int @ ( inf_inf_set_int @ A @ B ) @ ( minus_minus_set_int @ A @ B ) )
% 2.86/3.09 = bot_bot_set_int ) ).
% 2.86/3.09
% 2.86/3.09 % Int_Diff_disjoint
% 2.86/3.09 thf(fact_2444_Int__Diff__disjoint,axiom,
% 2.86/3.09 ! [A: set_nat,B: set_nat] :
% 2.86/3.09 ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ A @ B ) @ ( minus_minus_set_nat @ A @ B ) )
% 2.86/3.09 = bot_bot_set_nat ) ).
% 2.86/3.09
% 2.86/3.09 % Int_Diff_disjoint
% 2.86/3.09 thf(fact_2445_Diff__triv,axiom,
% 2.86/3.09 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( ( inf_in7913087082777306421at_nat @ A @ B )
% 2.86/3.09 = bot_bo228742789529271731at_nat )
% 2.86/3.09 => ( ( minus_3314409938677909166at_nat @ A @ B )
% 2.86/3.09 = A ) ) ).
% 2.86/3.09
% 2.86/3.09 % Diff_triv
% 2.86/3.09 thf(fact_2446_Diff__triv,axiom,
% 2.86/3.09 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( ( inf_in2572325071724192079at_nat @ A @ B )
% 2.86/3.09 = bot_bo2099793752762293965at_nat )
% 2.86/3.09 => ( ( minus_1356011639430497352at_nat @ A @ B )
% 2.86/3.09 = A ) ) ).
% 2.86/3.09
% 2.86/3.09 % Diff_triv
% 2.86/3.09 thf(fact_2447_Diff__triv,axiom,
% 2.86/3.09 ! [A: set_o,B: set_o] :
% 2.86/3.09 ( ( ( inf_inf_set_o @ A @ B )
% 2.86/3.09 = bot_bot_set_o )
% 2.86/3.09 => ( ( minus_minus_set_o @ A @ B )
% 2.86/3.09 = A ) ) ).
% 2.86/3.09
% 2.86/3.09 % Diff_triv
% 2.86/3.09 thf(fact_2448_Diff__triv,axiom,
% 2.86/3.09 ! [A: set_int,B: set_int] :
% 2.86/3.09 ( ( ( inf_inf_set_int @ A @ B )
% 2.86/3.09 = bot_bot_set_int )
% 2.86/3.09 => ( ( minus_minus_set_int @ A @ B )
% 2.86/3.09 = A ) ) ).
% 2.86/3.09
% 2.86/3.09 % Diff_triv
% 2.86/3.09 thf(fact_2449_Diff__triv,axiom,
% 2.86/3.09 ! [A: set_nat,B: set_nat] :
% 2.86/3.09 ( ( ( inf_inf_set_nat @ A @ B )
% 2.86/3.09 = bot_bot_set_nat )
% 2.86/3.09 => ( ( minus_minus_set_nat @ A @ B )
% 2.86/3.09 = A ) ) ).
% 2.86/3.09
% 2.86/3.09 % Diff_triv
% 2.86/3.09 thf(fact_2450_foldl__absorb1,axiom,
% 2.86/3.09 ! [X: code_integer,Zs: list_Code_integer] :
% 2.86/3.09 ( ( times_3573771949741848930nteger @ X @ ( foldl_1542389171486570077nteger @ times_3573771949741848930nteger @ one_one_Code_integer @ Zs ) )
% 2.86/3.09 = ( foldl_1542389171486570077nteger @ times_3573771949741848930nteger @ X @ Zs ) ) ).
% 2.86/3.09
% 2.86/3.09 % foldl_absorb1
% 2.86/3.09 thf(fact_2451_foldl__absorb1,axiom,
% 2.86/3.09 ! [X: assn,Zs: list_assn] :
% 2.86/3.09 ( ( times_times_assn @ X @ ( foldl_assn_assn @ times_times_assn @ one_one_assn @ Zs ) )
% 2.86/3.09 = ( foldl_assn_assn @ times_times_assn @ X @ Zs ) ) ).
% 2.86/3.09
% 2.86/3.09 % foldl_absorb1
% 2.86/3.09 thf(fact_2452_foldl__absorb1,axiom,
% 2.86/3.09 ! [X: rat,Zs: list_rat] :
% 2.86/3.09 ( ( times_times_rat @ X @ ( foldl_rat_rat @ times_times_rat @ one_one_rat @ Zs ) )
% 2.86/3.09 = ( foldl_rat_rat @ times_times_rat @ X @ Zs ) ) ).
% 2.86/3.09
% 2.86/3.09 % foldl_absorb1
% 2.86/3.09 thf(fact_2453_foldl__absorb1,axiom,
% 2.86/3.09 ! [X: nat,Zs: list_nat] :
% 2.86/3.09 ( ( times_times_nat @ X @ ( foldl_nat_nat @ times_times_nat @ one_one_nat @ Zs ) )
% 2.86/3.09 = ( foldl_nat_nat @ times_times_nat @ X @ Zs ) ) ).
% 2.86/3.09
% 2.86/3.09 % foldl_absorb1
% 2.86/3.09 thf(fact_2454_foldl__absorb1,axiom,
% 2.86/3.09 ! [X: int,Zs: list_int] :
% 2.86/3.09 ( ( times_times_int @ X @ ( foldl_int_int @ times_times_int @ one_one_int @ Zs ) )
% 2.86/3.09 = ( foldl_int_int @ times_times_int @ X @ Zs ) ) ).
% 2.86/3.09
% 2.86/3.09 % foldl_absorb1
% 2.86/3.09 thf(fact_2455_length__removeAll__less__eq,axiom,
% 2.86/3.09 ! [X: c,Xs: list_c] : ( ord_less_eq_nat @ ( size_size_list_c @ ( removeAll_c @ X @ Xs ) ) @ ( size_size_list_c @ Xs ) ) ).
% 2.86/3.09
% 2.86/3.09 % length_removeAll_less_eq
% 2.86/3.09 thf(fact_2456_length__removeAll__less__eq,axiom,
% 2.86/3.09 ! [X: d,Xs: list_d] : ( ord_less_eq_nat @ ( size_size_list_d @ ( removeAll_d @ X @ Xs ) ) @ ( size_size_list_d @ Xs ) ) ).
% 2.86/3.09
% 2.86/3.09 % length_removeAll_less_eq
% 2.86/3.09 thf(fact_2457_length__removeAll__less__eq,axiom,
% 2.86/3.09 ! [X: nat,Xs: list_nat] : ( ord_less_eq_nat @ ( size_size_list_nat @ ( removeAll_nat @ X @ Xs ) ) @ ( size_size_list_nat @ Xs ) ) ).
% 2.86/3.09
% 2.86/3.09 % length_removeAll_less_eq
% 2.86/3.09 thf(fact_2458_length__removeAll__less__eq,axiom,
% 2.86/3.09 ! [X: int,Xs: list_int] : ( ord_less_eq_nat @ ( size_size_list_int @ ( removeAll_int @ X @ Xs ) ) @ ( size_size_list_int @ Xs ) ) ).
% 2.86/3.09
% 2.86/3.09 % length_removeAll_less_eq
% 2.86/3.09 thf(fact_2459_disjoint__alt__simp3,axiom,
% 2.86/3.09 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( ord_le2604355607129572851at_nat @ ( minus_3314409938677909166at_nat @ A @ B ) @ A )
% 2.86/3.09 = ( ( inf_in7913087082777306421at_nat @ A @ B )
% 2.86/3.09 != bot_bo228742789529271731at_nat ) ) ).
% 2.86/3.09
% 2.86/3.09 % disjoint_alt_simp3
% 2.86/3.09 thf(fact_2460_disjoint__alt__simp3,axiom,
% 2.86/3.09 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( ord_le7866589430770878221at_nat @ ( minus_1356011639430497352at_nat @ A @ B ) @ A )
% 2.86/3.09 = ( ( inf_in2572325071724192079at_nat @ A @ B )
% 2.86/3.09 != bot_bo2099793752762293965at_nat ) ) ).
% 2.86/3.09
% 2.86/3.09 % disjoint_alt_simp3
% 2.86/3.09 thf(fact_2461_disjoint__alt__simp3,axiom,
% 2.86/3.09 ! [A: set_o,B: set_o] :
% 2.86/3.09 ( ( ord_less_set_o @ ( minus_minus_set_o @ A @ B ) @ A )
% 2.86/3.09 = ( ( inf_inf_set_o @ A @ B )
% 2.86/3.09 != bot_bot_set_o ) ) ).
% 2.86/3.09
% 2.86/3.09 % disjoint_alt_simp3
% 2.86/3.09 thf(fact_2462_disjoint__alt__simp3,axiom,
% 2.86/3.09 ! [A: set_int,B: set_int] :
% 2.86/3.09 ( ( ord_less_set_int @ ( minus_minus_set_int @ A @ B ) @ A )
% 2.86/3.09 = ( ( inf_inf_set_int @ A @ B )
% 2.86/3.09 != bot_bot_set_int ) ) ).
% 2.86/3.09
% 2.86/3.09 % disjoint_alt_simp3
% 2.86/3.09 thf(fact_2463_disjoint__alt__simp3,axiom,
% 2.86/3.09 ! [A: set_nat,B: set_nat] :
% 2.86/3.09 ( ( ord_less_set_nat @ ( minus_minus_set_nat @ A @ B ) @ A )
% 2.86/3.09 = ( ( inf_inf_set_nat @ A @ B )
% 2.86/3.09 != bot_bot_set_nat ) ) ).
% 2.86/3.09
% 2.86/3.09 % disjoint_alt_simp3
% 2.86/3.09 thf(fact_2464_verit__comp__simplify1_I1_J,axiom,
% 2.86/3.09 ! [A2: code_integer] :
% 2.86/3.09 ~ ( ord_le6747313008572928689nteger @ A2 @ A2 ) ).
% 2.86/3.09
% 2.86/3.09 % verit_comp_simplify1(1)
% 2.86/3.09 thf(fact_2465_verit__comp__simplify1_I1_J,axiom,
% 2.86/3.09 ! [A2: assn] :
% 2.86/3.09 ~ ( ord_less_assn @ A2 @ A2 ) ).
% 2.86/3.09
% 2.86/3.09 % verit_comp_simplify1(1)
% 2.86/3.09 thf(fact_2466_verit__comp__simplify1_I1_J,axiom,
% 2.86/3.09 ! [A2: num] :
% 2.86/3.09 ~ ( ord_less_num @ A2 @ A2 ) ).
% 2.86/3.09
% 2.86/3.09 % verit_comp_simplify1(1)
% 2.86/3.09 thf(fact_2467_verit__comp__simplify1_I1_J,axiom,
% 2.86/3.09 ! [A2: nat] :
% 2.86/3.09 ~ ( ord_less_nat @ A2 @ A2 ) ).
% 2.86/3.09
% 2.86/3.09 % verit_comp_simplify1(1)
% 2.86/3.09 thf(fact_2468_verit__comp__simplify1_I1_J,axiom,
% 2.86/3.09 ! [A2: int] :
% 2.86/3.09 ~ ( ord_less_int @ A2 @ A2 ) ).
% 2.86/3.09
% 2.86/3.09 % verit_comp_simplify1(1)
% 2.86/3.09 thf(fact_2469_ssubst__Pair__rhs,axiom,
% 2.86/3.09 ! [R2: set_Pr1261947904930325089at_nat,S3: set_Pr1261947904930325089at_nat,R: set_Pr4329608150637261639at_nat,S5: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R2 @ S3 ) @ R )
% 2.86/3.09 => ( ( S5 = S3 )
% 2.86/3.09 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ R2 @ S5 ) @ R ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % ssubst_Pair_rhs
% 2.86/3.09 thf(fact_2470_ssubst__Pair__rhs,axiom,
% 2.86/3.09 ! [R2: nat,S3: nat,R: set_Pr1261947904930325089at_nat,S5: nat] :
% 2.86/3.09 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ R2 @ S3 ) @ R )
% 2.86/3.09 => ( ( S5 = S3 )
% 2.86/3.09 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ R2 @ S5 ) @ R ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % ssubst_Pair_rhs
% 2.86/3.09 thf(fact_2471_ssubst__Pair__rhs,axiom,
% 2.86/3.09 ! [R2: produc6241069584506657477e_term > option6357759511663192854e_term,S3: produc8923325533196201883nteger,R: set_Pr1281608226676607948nteger,S5: produc8923325533196201883nteger] :
% 2.86/3.09 ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ R2 @ S3 ) @ R )
% 2.86/3.09 => ( ( S5 = S3 )
% 2.86/3.09 => ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ R2 @ S5 ) @ R ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % ssubst_Pair_rhs
% 2.86/3.09 thf(fact_2472_ssubst__Pair__rhs,axiom,
% 2.86/3.09 ! [R2: produc3658429121746597890et_nat > $o,S3: produc3658429121746597890et_nat,R: set_Pr3286484037609594932et_nat,S5: produc3658429121746597890et_nat] :
% 2.86/3.09 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ R2 @ S3 ) @ R )
% 2.86/3.09 => ( ( S5 = S3 )
% 2.86/3.09 => ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ R2 @ S5 ) @ R ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % ssubst_Pair_rhs
% 2.86/3.09 thf(fact_2473_ssubst__Pair__rhs,axiom,
% 2.86/3.09 ! [R2: produc3658429121746597890et_nat > $o,S3: produc3925858234332021118et_nat,R: set_Pr8536935166611901872et_nat,S5: produc3925858234332021118et_nat] :
% 2.86/3.09 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ R2 @ S3 ) @ R )
% 2.86/3.09 => ( ( S5 = S3 )
% 2.86/3.09 => ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ R2 @ S5 ) @ R ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % ssubst_Pair_rhs
% 2.86/3.09 thf(fact_2474_ssubst__Pair__rhs,axiom,
% 2.86/3.09 ! [R2: produc8551481072490612790e_term > option6357759511663192854e_term,S3: product_prod_int_int,R: set_Pr9222295170931077689nt_int,S5: product_prod_int_int] :
% 2.86/3.09 ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ R2 @ S3 ) @ R )
% 2.86/3.09 => ( ( S5 = S3 )
% 2.86/3.09 => ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ R2 @ S5 ) @ R ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % ssubst_Pair_rhs
% 2.86/3.09 thf(fact_2475_ssubst__Pair__rhs,axiom,
% 2.86/3.09 ! [R2: int > option6357759511663192854e_term,S3: product_prod_int_int,R: set_Pr1872883991513573699nt_int,S5: product_prod_int_int] :
% 2.86/3.09 ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ R2 @ S3 ) @ R )
% 2.86/3.09 => ( ( S5 = S3 )
% 2.86/3.09 => ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ R2 @ S5 ) @ R ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % ssubst_Pair_rhs
% 2.86/3.09 thf(fact_2476_distinct__length__le,axiom,
% 2.86/3.09 ! [Ys: list_P8527749157015355191n_assn,Xs: list_P8527749157015355191n_assn] :
% 2.86/3.09 ( ( distin4809818325527169450n_assn @ Ys )
% 2.86/3.09 => ( ( ( set_Pr1139785259514867910n_assn @ Ys )
% 2.86/3.09 = ( set_Pr1139785259514867910n_assn @ Xs ) )
% 2.86/3.09 => ( ord_less_eq_nat @ ( size_s6829681357464350627n_assn @ Ys ) @ ( size_s6829681357464350627n_assn @ Xs ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % distinct_length_le
% 2.86/3.09 thf(fact_2477_distinct__length__le,axiom,
% 2.86/3.09 ! [Ys: list_c,Xs: list_c] :
% 2.86/3.09 ( ( distinct_c @ Ys )
% 2.86/3.09 => ( ( ( set_c2 @ Ys )
% 2.86/3.09 = ( set_c2 @ Xs ) )
% 2.86/3.09 => ( ord_less_eq_nat @ ( size_size_list_c @ Ys ) @ ( size_size_list_c @ Xs ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % distinct_length_le
% 2.86/3.09 thf(fact_2478_distinct__length__le,axiom,
% 2.86/3.09 ! [Ys: list_d,Xs: list_d] :
% 2.86/3.09 ( ( distinct_d @ Ys )
% 2.86/3.09 => ( ( ( set_d2 @ Ys )
% 2.86/3.09 = ( set_d2 @ Xs ) )
% 2.86/3.09 => ( ord_less_eq_nat @ ( size_size_list_d @ Ys ) @ ( size_size_list_d @ Xs ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % distinct_length_le
% 2.86/3.09 thf(fact_2479_distinct__length__le,axiom,
% 2.86/3.09 ! [Ys: list_nat,Xs: list_nat] :
% 2.86/3.09 ( ( distinct_nat @ Ys )
% 2.86/3.09 => ( ( ( set_nat2 @ Ys )
% 2.86/3.09 = ( set_nat2 @ Xs ) )
% 2.86/3.09 => ( ord_less_eq_nat @ ( size_size_list_nat @ Ys ) @ ( size_size_list_nat @ Xs ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % distinct_length_le
% 2.86/3.09 thf(fact_2480_distinct__length__le,axiom,
% 2.86/3.09 ! [Ys: list_int,Xs: list_int] :
% 2.86/3.09 ( ( distinct_int @ Ys )
% 2.86/3.09 => ( ( ( set_int2 @ Ys )
% 2.86/3.09 = ( set_int2 @ Xs ) )
% 2.86/3.09 => ( ord_less_eq_nat @ ( size_size_list_int @ Ys ) @ ( size_size_list_int @ Xs ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % distinct_length_le
% 2.86/3.09 thf(fact_2481_nat__neq__iff,axiom,
% 2.86/3.09 ! [M2: nat,N: nat] :
% 2.86/3.09 ( ( M2 != N )
% 2.86/3.09 = ( ( ord_less_nat @ M2 @ N )
% 2.86/3.09 | ( ord_less_nat @ N @ M2 ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % nat_neq_iff
% 2.86/3.09 thf(fact_2482_less__not__refl,axiom,
% 2.86/3.09 ! [N: nat] :
% 2.86/3.09 ~ ( ord_less_nat @ N @ N ) ).
% 2.86/3.09
% 2.86/3.09 % less_not_refl
% 2.86/3.09 thf(fact_2483_less__not__refl2,axiom,
% 2.86/3.09 ! [N: nat,M2: nat] :
% 2.86/3.09 ( ( ord_less_nat @ N @ M2 )
% 2.86/3.09 => ( M2 != N ) ) ).
% 2.86/3.09
% 2.86/3.09 % less_not_refl2
% 2.86/3.09 thf(fact_2484_less__not__refl3,axiom,
% 2.86/3.09 ! [S3: nat,T: nat] :
% 2.86/3.09 ( ( ord_less_nat @ S3 @ T )
% 2.86/3.09 => ( S3 != T ) ) ).
% 2.86/3.09
% 2.86/3.09 % less_not_refl3
% 2.86/3.09 thf(fact_2485_less__irrefl__nat,axiom,
% 2.86/3.09 ! [N: nat] :
% 2.86/3.09 ~ ( ord_less_nat @ N @ N ) ).
% 2.86/3.09
% 2.86/3.09 % less_irrefl_nat
% 2.86/3.09 thf(fact_2486_nat__less__induct,axiom,
% 2.86/3.09 ! [P: nat > $o,N: nat] :
% 2.86/3.09 ( ! [N5: nat] :
% 2.86/3.09 ( ! [M3: nat] :
% 2.86/3.09 ( ( ord_less_nat @ M3 @ N5 )
% 2.86/3.09 => ( P @ M3 ) )
% 2.86/3.09 => ( P @ N5 ) )
% 2.86/3.09 => ( P @ N ) ) ).
% 2.86/3.09
% 2.86/3.09 % nat_less_induct
% 2.86/3.09 thf(fact_2487_infinite__descent,axiom,
% 2.86/3.09 ! [P: nat > $o,N: nat] :
% 2.86/3.09 ( ! [N5: nat] :
% 2.86/3.09 ( ~ ( P @ N5 )
% 2.86/3.09 => ? [M3: nat] :
% 2.86/3.09 ( ( ord_less_nat @ M3 @ N5 )
% 2.86/3.09 & ~ ( P @ M3 ) ) )
% 2.86/3.09 => ( P @ N ) ) ).
% 2.86/3.09
% 2.86/3.09 % infinite_descent
% 2.86/3.09 thf(fact_2488_linorder__neqE__nat,axiom,
% 2.86/3.09 ! [X: nat,Y: nat] :
% 2.86/3.09 ( ( X != Y )
% 2.86/3.09 => ( ~ ( ord_less_nat @ X @ Y )
% 2.86/3.09 => ( ord_less_nat @ Y @ X ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % linorder_neqE_nat
% 2.86/3.09 thf(fact_2489_size__neq__size__imp__neq,axiom,
% 2.86/3.09 ! [X: list_c,Y: list_c] :
% 2.86/3.09 ( ( ( size_size_list_c @ X )
% 2.86/3.09 != ( size_size_list_c @ Y ) )
% 2.86/3.09 => ( X != Y ) ) ).
% 2.86/3.09
% 2.86/3.09 % size_neq_size_imp_neq
% 2.86/3.09 thf(fact_2490_size__neq__size__imp__neq,axiom,
% 2.86/3.09 ! [X: list_d,Y: list_d] :
% 2.86/3.09 ( ( ( size_size_list_d @ X )
% 2.86/3.09 != ( size_size_list_d @ Y ) )
% 2.86/3.09 => ( X != Y ) ) ).
% 2.86/3.09
% 2.86/3.09 % size_neq_size_imp_neq
% 2.86/3.09 thf(fact_2491_size__neq__size__imp__neq,axiom,
% 2.86/3.09 ! [X: list_nat,Y: list_nat] :
% 2.86/3.09 ( ( ( size_size_list_nat @ X )
% 2.86/3.09 != ( size_size_list_nat @ Y ) )
% 2.86/3.09 => ( X != Y ) ) ).
% 2.86/3.09
% 2.86/3.09 % size_neq_size_imp_neq
% 2.86/3.09 thf(fact_2492_size__neq__size__imp__neq,axiom,
% 2.86/3.09 ! [X: list_int,Y: list_int] :
% 2.86/3.09 ( ( ( size_size_list_int @ X )
% 2.86/3.09 != ( size_size_list_int @ Y ) )
% 2.86/3.09 => ( X != Y ) ) ).
% 2.86/3.09
% 2.86/3.09 % size_neq_size_imp_neq
% 2.86/3.09 thf(fact_2493_distinct__product,axiom,
% 2.86/3.09 ! [Xs: list_int,Ys: list_int] :
% 2.86/3.09 ( ( distinct_int @ Xs )
% 2.86/3.09 => ( ( distinct_int @ Ys )
% 2.86/3.09 => ( distin3744728255968310194nt_int @ ( product_int_int @ Xs @ Ys ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % distinct_product
% 2.86/3.09 thf(fact_2494_distinct__product,axiom,
% 2.86/3.09 ! [Xs: list_int,Ys: list_nat] :
% 2.86/3.09 ( ( distinct_int @ Xs )
% 2.86/3.09 => ( ( distinct_nat @ Ys )
% 2.86/3.09 => ( distin7922579275477506902nt_nat @ ( product_int_nat @ Xs @ Ys ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % distinct_product
% 2.86/3.09 thf(fact_2495_distinct__product,axiom,
% 2.86/3.09 ! [Xs: list_nat,Ys: list_int] :
% 2.86/3.09 ( ( distinct_nat @ Xs )
% 2.86/3.09 => ( ( distinct_int @ Ys )
% 2.86/3.09 => ( distin2745374544067255638at_int @ ( product_nat_int @ Xs @ Ys ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % distinct_product
% 2.86/3.09 thf(fact_2496_distinct__product,axiom,
% 2.86/3.09 ! [Xs: list_nat,Ys: list_nat] :
% 2.86/3.09 ( ( distinct_nat @ Xs )
% 2.86/3.09 => ( ( distinct_nat @ Ys )
% 2.86/3.09 => ( distin6923225563576452346at_nat @ ( product_nat_nat @ Xs @ Ys ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % distinct_product
% 2.86/3.09 thf(fact_2497_distinct__sorted__mono,axiom,
% 2.86/3.09 ! [L: list_Code_integer,I: nat,J: nat] :
% 2.86/3.09 ( ( sorted710888440204495920nteger @ ord_le3102999989581377725nteger @ L )
% 2.86/3.09 => ( ( distin1543349897113766820nteger @ L )
% 2.86/3.09 => ( ( ord_less_nat @ I @ J )
% 2.86/3.09 => ( ( ord_less_nat @ J @ ( size_s3445333598471063425nteger @ L ) )
% 2.86/3.09 => ( ord_le6747313008572928689nteger @ ( nth_Code_integer @ L @ I ) @ ( nth_Code_integer @ L @ J ) ) ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % distinct_sorted_mono
% 2.86/3.09 thf(fact_2498_distinct__sorted__mono,axiom,
% 2.86/3.09 ! [L: list_num,I: nat,J: nat] :
% 2.86/3.09 ( ( sorted_wrt_num @ ord_less_eq_num @ L )
% 2.86/3.09 => ( ( distinct_num @ L )
% 2.86/3.09 => ( ( ord_less_nat @ I @ J )
% 2.86/3.09 => ( ( ord_less_nat @ J @ ( size_size_list_num @ L ) )
% 2.86/3.09 => ( ord_less_num @ ( nth_num @ L @ I ) @ ( nth_num @ L @ J ) ) ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % distinct_sorted_mono
% 2.86/3.09 thf(fact_2499_distinct__sorted__mono,axiom,
% 2.86/3.09 ! [L: list_nat,I: nat,J: nat] :
% 2.86/3.09 ( ( sorted_wrt_nat @ ord_less_eq_nat @ L )
% 2.86/3.09 => ( ( distinct_nat @ L )
% 2.86/3.09 => ( ( ord_less_nat @ I @ J )
% 2.86/3.09 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ L ) )
% 2.86/3.09 => ( ord_less_nat @ ( nth_nat @ L @ I ) @ ( nth_nat @ L @ J ) ) ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % distinct_sorted_mono
% 2.86/3.09 thf(fact_2500_distinct__sorted__mono,axiom,
% 2.86/3.09 ! [L: list_int,I: nat,J: nat] :
% 2.86/3.09 ( ( sorted_wrt_int @ ord_less_eq_int @ L )
% 2.86/3.09 => ( ( distinct_int @ L )
% 2.86/3.09 => ( ( ord_less_nat @ I @ J )
% 2.86/3.09 => ( ( ord_less_nat @ J @ ( size_size_list_int @ L ) )
% 2.86/3.09 => ( ord_less_int @ ( nth_int @ L @ I ) @ ( nth_int @ L @ J ) ) ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % distinct_sorted_mono
% 2.86/3.09 thf(fact_2501_distinct__sorted__strict__mono__iff,axiom,
% 2.86/3.09 ! [L: list_Code_integer,I: nat,J: nat] :
% 2.86/3.09 ( ( distin1543349897113766820nteger @ L )
% 2.86/3.09 => ( ( sorted710888440204495920nteger @ ord_le3102999989581377725nteger @ L )
% 2.86/3.09 => ( ( ord_less_nat @ I @ ( size_s3445333598471063425nteger @ L ) )
% 2.86/3.09 => ( ( ord_less_nat @ J @ ( size_s3445333598471063425nteger @ L ) )
% 2.86/3.09 => ( ( ord_le6747313008572928689nteger @ ( nth_Code_integer @ L @ I ) @ ( nth_Code_integer @ L @ J ) )
% 2.86/3.09 = ( ord_less_nat @ I @ J ) ) ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % distinct_sorted_strict_mono_iff
% 2.86/3.09 thf(fact_2502_distinct__sorted__strict__mono__iff,axiom,
% 2.86/3.09 ! [L: list_num,I: nat,J: nat] :
% 2.86/3.09 ( ( distinct_num @ L )
% 2.86/3.09 => ( ( sorted_wrt_num @ ord_less_eq_num @ L )
% 2.86/3.09 => ( ( ord_less_nat @ I @ ( size_size_list_num @ L ) )
% 2.86/3.09 => ( ( ord_less_nat @ J @ ( size_size_list_num @ L ) )
% 2.86/3.09 => ( ( ord_less_num @ ( nth_num @ L @ I ) @ ( nth_num @ L @ J ) )
% 2.86/3.09 = ( ord_less_nat @ I @ J ) ) ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % distinct_sorted_strict_mono_iff
% 2.86/3.09 thf(fact_2503_distinct__sorted__strict__mono__iff,axiom,
% 2.86/3.09 ! [L: list_nat,I: nat,J: nat] :
% 2.86/3.09 ( ( distinct_nat @ L )
% 2.86/3.09 => ( ( sorted_wrt_nat @ ord_less_eq_nat @ L )
% 2.86/3.09 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ L ) )
% 2.86/3.09 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ L ) )
% 2.86/3.09 => ( ( ord_less_nat @ ( nth_nat @ L @ I ) @ ( nth_nat @ L @ J ) )
% 2.86/3.09 = ( ord_less_nat @ I @ J ) ) ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % distinct_sorted_strict_mono_iff
% 2.86/3.09 thf(fact_2504_distinct__sorted__strict__mono__iff,axiom,
% 2.86/3.09 ! [L: list_int,I: nat,J: nat] :
% 2.86/3.09 ( ( distinct_int @ L )
% 2.86/3.09 => ( ( sorted_wrt_int @ ord_less_eq_int @ L )
% 2.86/3.09 => ( ( ord_less_nat @ I @ ( size_size_list_int @ L ) )
% 2.86/3.09 => ( ( ord_less_nat @ J @ ( size_size_list_int @ L ) )
% 2.86/3.09 => ( ( ord_less_int @ ( nth_int @ L @ I ) @ ( nth_int @ L @ J ) )
% 2.86/3.09 = ( ord_less_nat @ I @ J ) ) ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % distinct_sorted_strict_mono_iff
% 2.86/3.09 thf(fact_2505_slice__len,axiom,
% 2.86/3.09 ! [From: nat,To: nat,Xs: list_c] :
% 2.86/3.09 ( ( ord_less_eq_nat @ From @ To )
% 2.86/3.09 => ( ( ord_less_eq_nat @ To @ ( size_size_list_c @ Xs ) )
% 2.86/3.09 => ( ( size_size_list_c @ ( slice_c @ From @ To @ Xs ) )
% 2.86/3.09 = ( minus_minus_nat @ To @ From ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % slice_len
% 2.86/3.09 thf(fact_2506_slice__len,axiom,
% 2.86/3.09 ! [From: nat,To: nat,Xs: list_d] :
% 2.86/3.09 ( ( ord_less_eq_nat @ From @ To )
% 2.86/3.09 => ( ( ord_less_eq_nat @ To @ ( size_size_list_d @ Xs ) )
% 2.86/3.09 => ( ( size_size_list_d @ ( slice_d @ From @ To @ Xs ) )
% 2.86/3.09 = ( minus_minus_nat @ To @ From ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % slice_len
% 2.86/3.09 thf(fact_2507_slice__len,axiom,
% 2.86/3.09 ! [From: nat,To: nat,Xs: list_nat] :
% 2.86/3.09 ( ( ord_less_eq_nat @ From @ To )
% 2.86/3.09 => ( ( ord_less_eq_nat @ To @ ( size_size_list_nat @ Xs ) )
% 2.86/3.09 => ( ( size_size_list_nat @ ( slice_nat @ From @ To @ Xs ) )
% 2.86/3.09 = ( minus_minus_nat @ To @ From ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % slice_len
% 2.86/3.09 thf(fact_2508_slice__len,axiom,
% 2.86/3.09 ! [From: nat,To: nat,Xs: list_int] :
% 2.86/3.09 ( ( ord_less_eq_nat @ From @ To )
% 2.86/3.09 => ( ( ord_less_eq_nat @ To @ ( size_size_list_int @ Xs ) )
% 2.86/3.09 => ( ( size_size_list_int @ ( slice_int @ From @ To @ Xs ) )
% 2.86/3.09 = ( minus_minus_nat @ To @ From ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % slice_len
% 2.86/3.09 thf(fact_2509_rev__update,axiom,
% 2.86/3.09 ! [K3: nat,Xs: list_c,Y: c] :
% 2.86/3.09 ( ( ord_less_nat @ K3 @ ( size_size_list_c @ Xs ) )
% 2.86/3.09 => ( ( rev_c @ ( list_update_c @ Xs @ K3 @ Y ) )
% 2.86/3.09 = ( list_update_c @ ( rev_c @ Xs ) @ ( minus_minus_nat @ ( minus_minus_nat @ ( size_size_list_c @ Xs ) @ K3 ) @ one_one_nat ) @ Y ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % rev_update
% 2.86/3.09 thf(fact_2510_rev__update,axiom,
% 2.86/3.09 ! [K3: nat,Xs: list_d,Y: d] :
% 2.86/3.09 ( ( ord_less_nat @ K3 @ ( size_size_list_d @ Xs ) )
% 2.86/3.09 => ( ( rev_d @ ( list_update_d @ Xs @ K3 @ Y ) )
% 2.86/3.09 = ( list_update_d @ ( rev_d @ Xs ) @ ( minus_minus_nat @ ( minus_minus_nat @ ( size_size_list_d @ Xs ) @ K3 ) @ one_one_nat ) @ Y ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % rev_update
% 2.86/3.09 thf(fact_2511_rev__update,axiom,
% 2.86/3.09 ! [K3: nat,Xs: list_nat,Y: nat] :
% 2.86/3.09 ( ( ord_less_nat @ K3 @ ( size_size_list_nat @ Xs ) )
% 2.86/3.09 => ( ( rev_nat @ ( list_update_nat @ Xs @ K3 @ Y ) )
% 2.86/3.09 = ( list_update_nat @ ( rev_nat @ Xs ) @ ( minus_minus_nat @ ( minus_minus_nat @ ( size_size_list_nat @ Xs ) @ K3 ) @ one_one_nat ) @ Y ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % rev_update
% 2.86/3.09 thf(fact_2512_rev__update,axiom,
% 2.86/3.09 ! [K3: nat,Xs: list_int,Y: int] :
% 2.86/3.09 ( ( ord_less_nat @ K3 @ ( size_size_list_int @ Xs ) )
% 2.86/3.09 => ( ( rev_int @ ( list_update_int @ Xs @ K3 @ Y ) )
% 2.86/3.09 = ( list_update_int @ ( rev_int @ Xs ) @ ( minus_minus_nat @ ( minus_minus_nat @ ( size_size_list_int @ Xs ) @ K3 ) @ one_one_nat ) @ Y ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % rev_update
% 2.86/3.09 thf(fact_2513_butlast__list__update,axiom,
% 2.86/3.09 ! [K3: nat,Xs: list_c,X: c] :
% 2.86/3.09 ( ( ( K3
% 2.86/3.09 = ( minus_minus_nat @ ( size_size_list_c @ Xs ) @ one_one_nat ) )
% 2.86/3.09 => ( ( butlast_c @ ( list_update_c @ Xs @ K3 @ X ) )
% 2.86/3.09 = ( butlast_c @ Xs ) ) )
% 2.86/3.09 & ( ( K3
% 2.86/3.09 != ( minus_minus_nat @ ( size_size_list_c @ Xs ) @ one_one_nat ) )
% 2.86/3.09 => ( ( butlast_c @ ( list_update_c @ Xs @ K3 @ X ) )
% 2.86/3.09 = ( list_update_c @ ( butlast_c @ Xs ) @ K3 @ X ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % butlast_list_update
% 2.86/3.09 thf(fact_2514_butlast__list__update,axiom,
% 2.86/3.09 ! [K3: nat,Xs: list_d,X: d] :
% 2.86/3.09 ( ( ( K3
% 2.86/3.09 = ( minus_minus_nat @ ( size_size_list_d @ Xs ) @ one_one_nat ) )
% 2.86/3.09 => ( ( butlast_d @ ( list_update_d @ Xs @ K3 @ X ) )
% 2.86/3.09 = ( butlast_d @ Xs ) ) )
% 2.86/3.09 & ( ( K3
% 2.86/3.09 != ( minus_minus_nat @ ( size_size_list_d @ Xs ) @ one_one_nat ) )
% 2.86/3.09 => ( ( butlast_d @ ( list_update_d @ Xs @ K3 @ X ) )
% 2.86/3.09 = ( list_update_d @ ( butlast_d @ Xs ) @ K3 @ X ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % butlast_list_update
% 2.86/3.09 thf(fact_2515_butlast__list__update,axiom,
% 2.86/3.09 ! [K3: nat,Xs: list_nat,X: nat] :
% 2.86/3.09 ( ( ( K3
% 2.86/3.09 = ( minus_minus_nat @ ( size_size_list_nat @ Xs ) @ one_one_nat ) )
% 2.86/3.09 => ( ( butlast_nat @ ( list_update_nat @ Xs @ K3 @ X ) )
% 2.86/3.09 = ( butlast_nat @ Xs ) ) )
% 2.86/3.09 & ( ( K3
% 2.86/3.09 != ( minus_minus_nat @ ( size_size_list_nat @ Xs ) @ one_one_nat ) )
% 2.86/3.09 => ( ( butlast_nat @ ( list_update_nat @ Xs @ K3 @ X ) )
% 2.86/3.09 = ( list_update_nat @ ( butlast_nat @ Xs ) @ K3 @ X ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % butlast_list_update
% 2.86/3.09 thf(fact_2516_butlast__list__update,axiom,
% 2.86/3.09 ! [K3: nat,Xs: list_int,X: int] :
% 2.86/3.09 ( ( ( K3
% 2.86/3.09 = ( minus_minus_nat @ ( size_size_list_int @ Xs ) @ one_one_nat ) )
% 2.86/3.09 => ( ( butlast_int @ ( list_update_int @ Xs @ K3 @ X ) )
% 2.86/3.09 = ( butlast_int @ Xs ) ) )
% 2.86/3.09 & ( ( K3
% 2.86/3.09 != ( minus_minus_nat @ ( size_size_list_int @ Xs ) @ one_one_nat ) )
% 2.86/3.09 => ( ( butlast_int @ ( list_update_int @ Xs @ K3 @ X ) )
% 2.86/3.09 = ( list_update_int @ ( butlast_int @ Xs ) @ K3 @ X ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % butlast_list_update
% 2.86/3.09 thf(fact_2517_distinct__sorted__mono__iff,axiom,
% 2.86/3.09 ! [L: list_nat,I: nat,J: nat] :
% 2.86/3.09 ( ( distinct_nat @ L )
% 2.86/3.09 => ( ( sorted_wrt_nat @ ord_less_eq_nat @ L )
% 2.86/3.09 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ L ) )
% 2.86/3.09 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ L ) )
% 2.86/3.09 => ( ( ord_less_eq_nat @ ( nth_nat @ L @ I ) @ ( nth_nat @ L @ J ) )
% 2.86/3.09 = ( ord_less_eq_nat @ I @ J ) ) ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % distinct_sorted_mono_iff
% 2.86/3.09 thf(fact_2518_distinct__sorted__mono__iff,axiom,
% 2.86/3.09 ! [L: list_int,I: nat,J: nat] :
% 2.86/3.09 ( ( distinct_int @ L )
% 2.86/3.09 => ( ( sorted_wrt_int @ ord_less_eq_int @ L )
% 2.86/3.09 => ( ( ord_less_nat @ I @ ( size_size_list_int @ L ) )
% 2.86/3.09 => ( ( ord_less_nat @ J @ ( size_size_list_int @ L ) )
% 2.86/3.09 => ( ( ord_less_eq_int @ ( nth_int @ L @ I ) @ ( nth_int @ L @ J ) )
% 2.86/3.09 = ( ord_less_eq_nat @ I @ J ) ) ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % distinct_sorted_mono_iff
% 2.86/3.09 thf(fact_2519_length__zip,axiom,
% 2.86/3.09 ! [Xs: list_c,Ys: list_c] :
% 2.86/3.09 ( ( size_s2756448709718749209od_c_c @ ( zip_c_c @ Xs @ Ys ) )
% 2.86/3.09 = ( ord_min_nat @ ( size_size_list_c @ Xs ) @ ( size_size_list_c @ Ys ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % length_zip
% 2.86/3.09 thf(fact_2520_length__zip,axiom,
% 2.86/3.09 ! [Xs: list_c,Ys: list_d] :
% 2.86/3.09 ( ( size_s2827482749765095194od_c_d @ ( zip_c_d @ Xs @ Ys ) )
% 2.86/3.09 = ( ord_min_nat @ ( size_size_list_c @ Xs ) @ ( size_size_list_d @ Ys ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % length_zip
% 2.86/3.09 thf(fact_2521_length__zip,axiom,
% 2.86/3.09 ! [Xs: list_c,Ys: list_nat] :
% 2.86/3.09 ( ( size_s2954062820725854115_c_nat @ ( zip_c_nat @ Xs @ Ys ) )
% 2.86/3.09 = ( ord_min_nat @ ( size_size_list_c @ Xs ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % length_zip
% 2.86/3.09 thf(fact_2522_length__zip,axiom,
% 2.86/3.09 ! [Xs: list_c,Ys: list_int] :
% 2.86/3.09 ( ( size_s463979675794127359_c_int @ ( zip_c_int @ Xs @ Ys ) )
% 2.86/3.09 = ( ord_min_nat @ ( size_size_list_c @ Xs ) @ ( size_size_list_int @ Ys ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % length_zip
% 2.86/3.09 thf(fact_2523_length__zip,axiom,
% 2.86/3.09 ! [Xs: list_d,Ys: list_c] :
% 2.86/3.09 ( ( size_s2120799709113762520od_d_c @ ( zip_d_c @ Xs @ Ys ) )
% 2.86/3.09 = ( ord_min_nat @ ( size_size_list_d @ Xs ) @ ( size_size_list_c @ Ys ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % length_zip
% 2.86/3.09 thf(fact_2524_length__zip,axiom,
% 2.86/3.09 ! [Xs: list_d,Ys: list_d] :
% 2.86/3.09 ( ( size_s2191833749160108505od_d_d @ ( zip_d_d @ Xs @ Ys ) )
% 2.86/3.09 = ( ord_min_nat @ ( size_size_list_d @ Xs ) @ ( size_size_list_d @ Ys ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % length_zip
% 2.86/3.09 thf(fact_2525_length__zip,axiom,
% 2.86/3.09 ! [Xs: list_d,Ys: list_nat] :
% 2.86/3.09 ( ( size_s8550281435913984804_d_nat @ ( zip_d_nat @ Xs @ Ys ) )
% 2.86/3.09 = ( ord_min_nat @ ( size_size_list_d @ Xs ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % length_zip
% 2.86/3.09 thf(fact_2526_length__zip,axiom,
% 2.86/3.09 ! [Xs: list_d,Ys: list_int] :
% 2.86/3.09 ( ( size_s6060198290982258048_d_int @ ( zip_d_int @ Xs @ Ys ) )
% 2.86/3.09 = ( ord_min_nat @ ( size_size_list_d @ Xs ) @ ( size_size_list_int @ Ys ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % length_zip
% 2.86/3.09 thf(fact_2527_length__zip,axiom,
% 2.86/3.09 ! [Xs: list_nat,Ys: list_c] :
% 2.86/3.09 ( ( size_s385972143775086793_nat_c @ ( zip_nat_c @ Xs @ Ys ) )
% 2.86/3.09 = ( ord_min_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_c @ Ys ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % length_zip
% 2.86/3.09 thf(fact_2528_length__zip,axiom,
% 2.86/3.09 ! [Xs: list_nat,Ys: list_d] :
% 2.86/3.09 ( ( size_s457006183821432778_nat_d @ ( zip_nat_d @ Xs @ Ys ) )
% 2.86/3.09 = ( ord_min_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_d @ Ys ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % length_zip
% 2.86/3.09 thf(fact_2529_star__assnI,axiom,
% 2.86/3.09 ! [P: assn,H2: heap_e7401611519738050253t_unit,As2: set_nat,Q: assn,As3: set_nat] :
% 2.86/3.09 ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 2.86/3.09 => ( ( rep_assn @ Q @ ( produc7507926704131184380et_nat @ H2 @ As3 ) )
% 2.86/3.09 => ( ( ( inf_inf_set_nat @ As2 @ As3 )
% 2.86/3.09 = bot_bot_set_nat )
% 2.86/3.09 => ( rep_assn @ ( times_times_assn @ P @ Q ) @ ( produc7507926704131184380et_nat @ H2 @ ( sup_sup_set_nat @ As2 @ As3 ) ) ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % star_assnI
% 2.86/3.09 thf(fact_2530_mod__star__conv,axiom,
% 2.86/3.09 ! [A: assn,B: assn,H2: produc3658429121746597890et_nat] :
% 2.86/3.09 ( ( rep_assn @ ( times_times_assn @ A @ B ) @ H2 )
% 2.86/3.09 = ( ? [Hr: heap_e7401611519738050253t_unit,As1: set_nat,As22: set_nat] :
% 2.86/3.09 ( ( H2
% 2.86/3.09 = ( produc7507926704131184380et_nat @ Hr @ ( sup_sup_set_nat @ As1 @ As22 ) ) )
% 2.86/3.09 & ( ( inf_inf_set_nat @ As1 @ As22 )
% 2.86/3.09 = bot_bot_set_nat )
% 2.86/3.09 & ( rep_assn @ A @ ( produc7507926704131184380et_nat @ Hr @ As1 ) )
% 2.86/3.09 & ( rep_assn @ B @ ( produc7507926704131184380et_nat @ Hr @ As22 ) ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % mod_star_conv
% 2.86/3.09 thf(fact_2531_rotate1__length01,axiom,
% 2.86/3.09 ! [Xs: list_c] :
% 2.86/3.09 ( ( ord_less_eq_nat @ ( size_size_list_c @ Xs ) @ one_one_nat )
% 2.86/3.09 => ( ( rotate1_c @ Xs )
% 2.86/3.09 = Xs ) ) ).
% 2.86/3.09
% 2.86/3.09 % rotate1_length01
% 2.86/3.09 thf(fact_2532_rotate1__length01,axiom,
% 2.86/3.09 ! [Xs: list_d] :
% 2.86/3.09 ( ( ord_less_eq_nat @ ( size_size_list_d @ Xs ) @ one_one_nat )
% 2.86/3.09 => ( ( rotate1_d @ Xs )
% 2.86/3.09 = Xs ) ) ).
% 2.86/3.09
% 2.86/3.09 % rotate1_length01
% 2.86/3.09 thf(fact_2533_rotate1__length01,axiom,
% 2.86/3.09 ! [Xs: list_nat] :
% 2.86/3.09 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ one_one_nat )
% 2.86/3.09 => ( ( rotate1_nat @ Xs )
% 2.86/3.09 = Xs ) ) ).
% 2.86/3.09
% 2.86/3.09 % rotate1_length01
% 2.86/3.09 thf(fact_2534_rotate1__length01,axiom,
% 2.86/3.09 ! [Xs: list_int] :
% 2.86/3.09 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ one_one_nat )
% 2.86/3.09 => ( ( rotate1_int @ Xs )
% 2.86/3.09 = Xs ) ) ).
% 2.86/3.09
% 2.86/3.09 % rotate1_length01
% 2.86/3.09 thf(fact_2535_sup_Oidem,axiom,
% 2.86/3.09 ! [A2: set_nat] :
% 2.86/3.09 ( ( sup_sup_set_nat @ A2 @ A2 )
% 2.86/3.09 = A2 ) ).
% 2.86/3.09
% 2.86/3.09 % sup.idem
% 2.86/3.09 thf(fact_2536_sup_Oidem,axiom,
% 2.86/3.09 ! [A2: assn] :
% 2.86/3.09 ( ( sup_sup_assn @ A2 @ A2 )
% 2.86/3.09 = A2 ) ).
% 2.86/3.09
% 2.86/3.09 % sup.idem
% 2.86/3.09 thf(fact_2537_sup_Oidem,axiom,
% 2.86/3.09 ! [A2: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( sup_su5525570899277871387at_nat @ A2 @ A2 )
% 2.86/3.09 = A2 ) ).
% 2.86/3.09
% 2.86/3.09 % sup.idem
% 2.86/3.09 thf(fact_2538_sup__idem,axiom,
% 2.86/3.09 ! [X: set_nat] :
% 2.86/3.09 ( ( sup_sup_set_nat @ X @ X )
% 2.86/3.09 = X ) ).
% 2.86/3.09
% 2.86/3.09 % sup_idem
% 2.86/3.09 thf(fact_2539_sup__idem,axiom,
% 2.86/3.09 ! [X: assn] :
% 2.86/3.09 ( ( sup_sup_assn @ X @ X )
% 2.86/3.09 = X ) ).
% 2.86/3.09
% 2.86/3.09 % sup_idem
% 2.86/3.09 thf(fact_2540_sup__idem,axiom,
% 2.86/3.09 ! [X: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( sup_su5525570899277871387at_nat @ X @ X )
% 2.86/3.09 = X ) ).
% 2.86/3.09
% 2.86/3.09 % sup_idem
% 2.86/3.09 thf(fact_2541_sup_Oleft__idem,axiom,
% 2.86/3.09 ! [A2: set_nat,B2: set_nat] :
% 2.86/3.09 ( ( sup_sup_set_nat @ A2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 2.86/3.09 = ( sup_sup_set_nat @ A2 @ B2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % sup.left_idem
% 2.86/3.09 thf(fact_2542_sup_Oleft__idem,axiom,
% 2.86/3.09 ! [A2: assn,B2: assn] :
% 2.86/3.09 ( ( sup_sup_assn @ A2 @ ( sup_sup_assn @ A2 @ B2 ) )
% 2.86/3.09 = ( sup_sup_assn @ A2 @ B2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % sup.left_idem
% 2.86/3.09 thf(fact_2543_sup_Oleft__idem,axiom,
% 2.86/3.09 ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( sup_su5525570899277871387at_nat @ A2 @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) )
% 2.86/3.09 = ( sup_su5525570899277871387at_nat @ A2 @ B2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % sup.left_idem
% 2.86/3.09 thf(fact_2544_sup__left__idem,axiom,
% 2.86/3.09 ! [X: set_nat,Y: set_nat] :
% 2.86/3.09 ( ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ X @ Y ) )
% 2.86/3.09 = ( sup_sup_set_nat @ X @ Y ) ) ).
% 2.86/3.09
% 2.86/3.09 % sup_left_idem
% 2.86/3.09 thf(fact_2545_sup__left__idem,axiom,
% 2.86/3.09 ! [X: assn,Y: assn] :
% 2.86/3.09 ( ( sup_sup_assn @ X @ ( sup_sup_assn @ X @ Y ) )
% 2.86/3.09 = ( sup_sup_assn @ X @ Y ) ) ).
% 2.86/3.09
% 2.86/3.09 % sup_left_idem
% 2.86/3.09 thf(fact_2546_sup__left__idem,axiom,
% 2.86/3.09 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( sup_su5525570899277871387at_nat @ X @ ( sup_su5525570899277871387at_nat @ X @ Y ) )
% 2.86/3.09 = ( sup_su5525570899277871387at_nat @ X @ Y ) ) ).
% 2.86/3.09
% 2.86/3.09 % sup_left_idem
% 2.86/3.09 thf(fact_2547_sup_Oright__idem,axiom,
% 2.86/3.09 ! [A2: set_nat,B2: set_nat] :
% 2.86/3.09 ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ A2 @ B2 ) @ B2 )
% 2.86/3.09 = ( sup_sup_set_nat @ A2 @ B2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % sup.right_idem
% 2.86/3.09 thf(fact_2548_sup_Oright__idem,axiom,
% 2.86/3.09 ! [A2: assn,B2: assn] :
% 2.86/3.09 ( ( sup_sup_assn @ ( sup_sup_assn @ A2 @ B2 ) @ B2 )
% 2.86/3.09 = ( sup_sup_assn @ A2 @ B2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % sup.right_idem
% 2.86/3.09 thf(fact_2549_sup_Oright__idem,axiom,
% 2.86/3.09 ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( sup_su5525570899277871387at_nat @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) @ B2 )
% 2.86/3.09 = ( sup_su5525570899277871387at_nat @ A2 @ B2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % sup.right_idem
% 2.86/3.09 thf(fact_2550_IntI,axiom,
% 2.86/3.09 ! [C: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( member8757157785044589968at_nat @ C @ A )
% 2.86/3.09 => ( ( member8757157785044589968at_nat @ C @ B )
% 2.86/3.09 => ( member8757157785044589968at_nat @ C @ ( inf_in7913087082777306421at_nat @ A @ B ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % IntI
% 2.86/3.09 thf(fact_2551_IntI,axiom,
% 2.86/3.09 ! [C: int,A: set_int,B: set_int] :
% 2.86/3.09 ( ( member_int @ C @ A )
% 2.86/3.09 => ( ( member_int @ C @ B )
% 2.86/3.09 => ( member_int @ C @ ( inf_inf_set_int @ A @ B ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % IntI
% 2.86/3.09 thf(fact_2552_IntI,axiom,
% 2.86/3.09 ! [C: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o] :
% 2.86/3.09 ( ( member6576561426505652726_nat_o @ C @ A )
% 2.86/3.09 => ( ( member6576561426505652726_nat_o @ C @ B )
% 2.86/3.09 => ( member6576561426505652726_nat_o @ C @ ( inf_in1906310914598751387_nat_o @ A @ B ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % IntI
% 2.86/3.09 thf(fact_2553_IntI,axiom,
% 2.86/3.09 ! [C: nat,A: set_nat,B: set_nat] :
% 2.86/3.09 ( ( member_nat @ C @ A )
% 2.86/3.09 => ( ( member_nat @ C @ B )
% 2.86/3.09 => ( member_nat @ C @ ( inf_inf_set_nat @ A @ B ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % IntI
% 2.86/3.09 thf(fact_2554_IntI,axiom,
% 2.86/3.09 ! [C: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( member8440522571783428010at_nat @ C @ A )
% 2.86/3.09 => ( ( member8440522571783428010at_nat @ C @ B )
% 2.86/3.09 => ( member8440522571783428010at_nat @ C @ ( inf_in2572325071724192079at_nat @ A @ B ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % IntI
% 2.86/3.09 thf(fact_2555_Int__iff,axiom,
% 2.86/3.09 ! [C: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( member8757157785044589968at_nat @ C @ ( inf_in7913087082777306421at_nat @ A @ B ) )
% 2.86/3.09 = ( ( member8757157785044589968at_nat @ C @ A )
% 2.86/3.09 & ( member8757157785044589968at_nat @ C @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Int_iff
% 2.86/3.09 thf(fact_2556_Int__iff,axiom,
% 2.86/3.09 ! [C: int,A: set_int,B: set_int] :
% 2.86/3.09 ( ( member_int @ C @ ( inf_inf_set_int @ A @ B ) )
% 2.86/3.09 = ( ( member_int @ C @ A )
% 2.86/3.09 & ( member_int @ C @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Int_iff
% 2.86/3.09 thf(fact_2557_Int__iff,axiom,
% 2.86/3.09 ! [C: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o] :
% 2.86/3.09 ( ( member6576561426505652726_nat_o @ C @ ( inf_in1906310914598751387_nat_o @ A @ B ) )
% 2.86/3.09 = ( ( member6576561426505652726_nat_o @ C @ A )
% 2.86/3.09 & ( member6576561426505652726_nat_o @ C @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Int_iff
% 2.86/3.09 thf(fact_2558_Int__iff,axiom,
% 2.86/3.09 ! [C: nat,A: set_nat,B: set_nat] :
% 2.86/3.09 ( ( member_nat @ C @ ( inf_inf_set_nat @ A @ B ) )
% 2.86/3.09 = ( ( member_nat @ C @ A )
% 2.86/3.09 & ( member_nat @ C @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Int_iff
% 2.86/3.09 thf(fact_2559_Int__iff,axiom,
% 2.86/3.09 ! [C: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( member8440522571783428010at_nat @ C @ ( inf_in2572325071724192079at_nat @ A @ B ) )
% 2.86/3.09 = ( ( member8440522571783428010at_nat @ C @ A )
% 2.86/3.09 & ( member8440522571783428010at_nat @ C @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Int_iff
% 2.86/3.09 thf(fact_2560_UnCI,axiom,
% 2.86/3.09 ! [C: product_prod_nat_nat,B: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( ~ ( member8440522571783428010at_nat @ C @ B )
% 2.86/3.09 => ( member8440522571783428010at_nat @ C @ A ) )
% 2.86/3.09 => ( member8440522571783428010at_nat @ C @ ( sup_su6327502436637775413at_nat @ A @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % UnCI
% 2.86/3.09 thf(fact_2561_UnCI,axiom,
% 2.86/3.09 ! [C: int,B: set_int,A: set_int] :
% 2.86/3.09 ( ( ~ ( member_int @ C @ B )
% 2.86/3.09 => ( member_int @ C @ A ) )
% 2.86/3.09 => ( member_int @ C @ ( sup_sup_set_int @ A @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % UnCI
% 2.86/3.09 thf(fact_2562_UnCI,axiom,
% 2.86/3.09 ! [C: produc3658429121746597890et_nat > $o,B: set_Pr4532377907799695533_nat_o,A: set_Pr4532377907799695533_nat_o] :
% 2.86/3.09 ( ( ~ ( member6576561426505652726_nat_o @ C @ B )
% 2.86/3.09 => ( member6576561426505652726_nat_o @ C @ A ) )
% 2.86/3.09 => ( member6576561426505652726_nat_o @ C @ ( sup_su5209123915105501825_nat_o @ A @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % UnCI
% 2.86/3.09 thf(fact_2563_UnCI,axiom,
% 2.86/3.09 ! [C: nat,B: set_nat,A: set_nat] :
% 2.86/3.09 ( ( ~ ( member_nat @ C @ B )
% 2.86/3.09 => ( member_nat @ C @ A ) )
% 2.86/3.09 => ( member_nat @ C @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % UnCI
% 2.86/3.09 thf(fact_2564_UnCI,axiom,
% 2.86/3.09 ! [C: produc3843707927480180839at_nat,B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( ~ ( member8757157785044589968at_nat @ C @ B )
% 2.86/3.09 => ( member8757157785044589968at_nat @ C @ A ) )
% 2.86/3.09 => ( member8757157785044589968at_nat @ C @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % UnCI
% 2.86/3.09 thf(fact_2565_Un__iff,axiom,
% 2.86/3.09 ! [C: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( member8440522571783428010at_nat @ C @ ( sup_su6327502436637775413at_nat @ A @ B ) )
% 2.86/3.09 = ( ( member8440522571783428010at_nat @ C @ A )
% 2.86/3.09 | ( member8440522571783428010at_nat @ C @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Un_iff
% 2.86/3.09 thf(fact_2566_Un__iff,axiom,
% 2.86/3.09 ! [C: int,A: set_int,B: set_int] :
% 2.86/3.09 ( ( member_int @ C @ ( sup_sup_set_int @ A @ B ) )
% 2.86/3.09 = ( ( member_int @ C @ A )
% 2.86/3.09 | ( member_int @ C @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Un_iff
% 2.86/3.09 thf(fact_2567_Un__iff,axiom,
% 2.86/3.09 ! [C: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o] :
% 2.86/3.09 ( ( member6576561426505652726_nat_o @ C @ ( sup_su5209123915105501825_nat_o @ A @ B ) )
% 2.86/3.09 = ( ( member6576561426505652726_nat_o @ C @ A )
% 2.86/3.09 | ( member6576561426505652726_nat_o @ C @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Un_iff
% 2.86/3.09 thf(fact_2568_Un__iff,axiom,
% 2.86/3.09 ! [C: nat,A: set_nat,B: set_nat] :
% 2.86/3.09 ( ( member_nat @ C @ ( sup_sup_set_nat @ A @ B ) )
% 2.86/3.09 = ( ( member_nat @ C @ A )
% 2.86/3.09 | ( member_nat @ C @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Un_iff
% 2.86/3.09 thf(fact_2569_Un__iff,axiom,
% 2.86/3.09 ! [C: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( member8757157785044589968at_nat @ C @ ( sup_su5525570899277871387at_nat @ A @ B ) )
% 2.86/3.09 = ( ( member8757157785044589968at_nat @ C @ A )
% 2.86/3.09 | ( member8757157785044589968at_nat @ C @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Un_iff
% 2.86/3.09 thf(fact_2570_min_Oidem,axiom,
% 2.86/3.09 ! [A2: nat] :
% 2.86/3.09 ( ( ord_min_nat @ A2 @ A2 )
% 2.86/3.09 = A2 ) ).
% 2.86/3.09
% 2.86/3.09 % min.idem
% 2.86/3.09 thf(fact_2571_min_Oleft__idem,axiom,
% 2.86/3.09 ! [A2: nat,B2: nat] :
% 2.86/3.09 ( ( ord_min_nat @ A2 @ ( ord_min_nat @ A2 @ B2 ) )
% 2.86/3.09 = ( ord_min_nat @ A2 @ B2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min.left_idem
% 2.86/3.09 thf(fact_2572_min_Oright__idem,axiom,
% 2.86/3.09 ! [A2: nat,B2: nat] :
% 2.86/3.09 ( ( ord_min_nat @ ( ord_min_nat @ A2 @ B2 ) @ B2 )
% 2.86/3.09 = ( ord_min_nat @ A2 @ B2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min.right_idem
% 2.86/3.09 thf(fact_2573_le__sup__iff,axiom,
% 2.86/3.09 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) @ Z )
% 2.86/3.09 = ( ( ord_le1268244103169919719at_nat @ X @ Z )
% 2.86/3.09 & ( ord_le1268244103169919719at_nat @ Y @ Z ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % le_sup_iff
% 2.86/3.09 thf(fact_2574_le__sup__iff,axiom,
% 2.86/3.09 ! [X: assn,Y: assn,Z: assn] :
% 2.86/3.09 ( ( ord_less_eq_assn @ ( sup_sup_assn @ X @ Y ) @ Z )
% 2.86/3.09 = ( ( ord_less_eq_assn @ X @ Z )
% 2.86/3.09 & ( ord_less_eq_assn @ Y @ Z ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % le_sup_iff
% 2.86/3.09 thf(fact_2575_le__sup__iff,axiom,
% 2.86/3.09 ! [X: filter_nat,Y: filter_nat,Z: filter_nat] :
% 2.86/3.09 ( ( ord_le2510731241096832064er_nat @ ( sup_sup_filter_nat @ X @ Y ) @ Z )
% 2.86/3.09 = ( ( ord_le2510731241096832064er_nat @ X @ Z )
% 2.86/3.09 & ( ord_le2510731241096832064er_nat @ Y @ Z ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % le_sup_iff
% 2.86/3.09 thf(fact_2576_le__sup__iff,axiom,
% 2.86/3.09 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 2.86/3.09 ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ Z )
% 2.86/3.09 = ( ( ord_less_eq_set_nat @ X @ Z )
% 2.86/3.09 & ( ord_less_eq_set_nat @ Y @ Z ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % le_sup_iff
% 2.86/3.09 thf(fact_2577_le__sup__iff,axiom,
% 2.86/3.09 ! [X: nat,Y: nat,Z: nat] :
% 2.86/3.09 ( ( ord_less_eq_nat @ ( sup_sup_nat @ X @ Y ) @ Z )
% 2.86/3.09 = ( ( ord_less_eq_nat @ X @ Z )
% 2.86/3.09 & ( ord_less_eq_nat @ Y @ Z ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % le_sup_iff
% 2.86/3.09 thf(fact_2578_le__sup__iff,axiom,
% 2.86/3.09 ! [X: int,Y: int,Z: int] :
% 2.86/3.09 ( ( ord_less_eq_int @ ( sup_sup_int @ X @ Y ) @ Z )
% 2.86/3.09 = ( ( ord_less_eq_int @ X @ Z )
% 2.86/3.09 & ( ord_less_eq_int @ Y @ Z ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % le_sup_iff
% 2.86/3.09 thf(fact_2579_sup_Obounded__iff,axiom,
% 2.86/3.09 ! [B2: set_Pr4329608150637261639at_nat,C: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ B2 @ C ) @ A2 )
% 2.86/3.09 = ( ( ord_le1268244103169919719at_nat @ B2 @ A2 )
% 2.86/3.09 & ( ord_le1268244103169919719at_nat @ C @ A2 ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % sup.bounded_iff
% 2.86/3.09 thf(fact_2580_sup_Obounded__iff,axiom,
% 2.86/3.09 ! [B2: assn,C: assn,A2: assn] :
% 2.86/3.09 ( ( ord_less_eq_assn @ ( sup_sup_assn @ B2 @ C ) @ A2 )
% 2.86/3.09 = ( ( ord_less_eq_assn @ B2 @ A2 )
% 2.86/3.09 & ( ord_less_eq_assn @ C @ A2 ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % sup.bounded_iff
% 2.86/3.09 thf(fact_2581_sup_Obounded__iff,axiom,
% 2.86/3.09 ! [B2: filter_nat,C: filter_nat,A2: filter_nat] :
% 2.86/3.09 ( ( ord_le2510731241096832064er_nat @ ( sup_sup_filter_nat @ B2 @ C ) @ A2 )
% 2.86/3.09 = ( ( ord_le2510731241096832064er_nat @ B2 @ A2 )
% 2.86/3.09 & ( ord_le2510731241096832064er_nat @ C @ A2 ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % sup.bounded_iff
% 2.86/3.09 thf(fact_2582_sup_Obounded__iff,axiom,
% 2.86/3.09 ! [B2: set_nat,C: set_nat,A2: set_nat] :
% 2.86/3.09 ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ B2 @ C ) @ A2 )
% 2.86/3.09 = ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 2.86/3.09 & ( ord_less_eq_set_nat @ C @ A2 ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % sup.bounded_iff
% 2.86/3.09 thf(fact_2583_sup_Obounded__iff,axiom,
% 2.86/3.09 ! [B2: nat,C: nat,A2: nat] :
% 2.86/3.09 ( ( ord_less_eq_nat @ ( sup_sup_nat @ B2 @ C ) @ A2 )
% 2.86/3.09 = ( ( ord_less_eq_nat @ B2 @ A2 )
% 2.86/3.09 & ( ord_less_eq_nat @ C @ A2 ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % sup.bounded_iff
% 2.86/3.09 thf(fact_2584_sup_Obounded__iff,axiom,
% 2.86/3.09 ! [B2: int,C: int,A2: int] :
% 2.86/3.09 ( ( ord_less_eq_int @ ( sup_sup_int @ B2 @ C ) @ A2 )
% 2.86/3.09 = ( ( ord_less_eq_int @ B2 @ A2 )
% 2.86/3.09 & ( ord_less_eq_int @ C @ A2 ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % sup.bounded_iff
% 2.86/3.09 thf(fact_2585_sup__bot_Oright__neutral,axiom,
% 2.86/3.09 ! [A2: assn] :
% 2.86/3.09 ( ( sup_sup_assn @ A2 @ bot_bot_assn )
% 2.86/3.09 = A2 ) ).
% 2.86/3.09
% 2.86/3.09 % sup_bot.right_neutral
% 2.86/3.09 thf(fact_2586_sup__bot_Oright__neutral,axiom,
% 2.86/3.09 ! [A2: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( sup_su5525570899277871387at_nat @ A2 @ bot_bo228742789529271731at_nat )
% 2.86/3.09 = A2 ) ).
% 2.86/3.09
% 2.86/3.09 % sup_bot.right_neutral
% 2.86/3.09 thf(fact_2587_sup__bot_Oright__neutral,axiom,
% 2.86/3.09 ! [A2: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( sup_su6327502436637775413at_nat @ A2 @ bot_bo2099793752762293965at_nat )
% 2.86/3.09 = A2 ) ).
% 2.86/3.09
% 2.86/3.09 % sup_bot.right_neutral
% 2.86/3.09 thf(fact_2588_sup__bot_Oright__neutral,axiom,
% 2.86/3.09 ! [A2: set_o] :
% 2.86/3.09 ( ( sup_sup_set_o @ A2 @ bot_bot_set_o )
% 2.86/3.09 = A2 ) ).
% 2.86/3.09
% 2.86/3.09 % sup_bot.right_neutral
% 2.86/3.09 thf(fact_2589_sup__bot_Oright__neutral,axiom,
% 2.86/3.09 ! [A2: set_nat] :
% 2.86/3.09 ( ( sup_sup_set_nat @ A2 @ bot_bot_set_nat )
% 2.86/3.09 = A2 ) ).
% 2.86/3.09
% 2.86/3.09 % sup_bot.right_neutral
% 2.86/3.09 thf(fact_2590_sup__bot_Oright__neutral,axiom,
% 2.86/3.09 ! [A2: set_int] :
% 2.86/3.09 ( ( sup_sup_set_int @ A2 @ bot_bot_set_int )
% 2.86/3.09 = A2 ) ).
% 2.86/3.09
% 2.86/3.09 % sup_bot.right_neutral
% 2.86/3.09 thf(fact_2591_sup__bot_Oneutr__eq__iff,axiom,
% 2.86/3.09 ! [A2: assn,B2: assn] :
% 2.86/3.09 ( ( bot_bot_assn
% 2.86/3.09 = ( sup_sup_assn @ A2 @ B2 ) )
% 2.86/3.09 = ( ( A2 = bot_bot_assn )
% 2.86/3.09 & ( B2 = bot_bot_assn ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % sup_bot.neutr_eq_iff
% 2.86/3.09 thf(fact_2592_sup__bot_Oneutr__eq__iff,axiom,
% 2.86/3.09 ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( bot_bo228742789529271731at_nat
% 2.86/3.09 = ( sup_su5525570899277871387at_nat @ A2 @ B2 ) )
% 2.86/3.09 = ( ( A2 = bot_bo228742789529271731at_nat )
% 2.86/3.09 & ( B2 = bot_bo228742789529271731at_nat ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % sup_bot.neutr_eq_iff
% 2.86/3.09 thf(fact_2593_sup__bot_Oneutr__eq__iff,axiom,
% 2.86/3.09 ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( bot_bo2099793752762293965at_nat
% 2.86/3.09 = ( sup_su6327502436637775413at_nat @ A2 @ B2 ) )
% 2.86/3.09 = ( ( A2 = bot_bo2099793752762293965at_nat )
% 2.86/3.09 & ( B2 = bot_bo2099793752762293965at_nat ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % sup_bot.neutr_eq_iff
% 2.86/3.09 thf(fact_2594_sup__bot_Oneutr__eq__iff,axiom,
% 2.86/3.09 ! [A2: set_o,B2: set_o] :
% 2.86/3.09 ( ( bot_bot_set_o
% 2.86/3.09 = ( sup_sup_set_o @ A2 @ B2 ) )
% 2.86/3.09 = ( ( A2 = bot_bot_set_o )
% 2.86/3.09 & ( B2 = bot_bot_set_o ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % sup_bot.neutr_eq_iff
% 2.86/3.09 thf(fact_2595_sup__bot_Oneutr__eq__iff,axiom,
% 2.86/3.09 ! [A2: set_nat,B2: set_nat] :
% 2.86/3.09 ( ( bot_bot_set_nat
% 2.86/3.09 = ( sup_sup_set_nat @ A2 @ B2 ) )
% 2.86/3.09 = ( ( A2 = bot_bot_set_nat )
% 2.86/3.09 & ( B2 = bot_bot_set_nat ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % sup_bot.neutr_eq_iff
% 2.86/3.09 thf(fact_2596_sup__bot_Oneutr__eq__iff,axiom,
% 2.86/3.09 ! [A2: set_int,B2: set_int] :
% 2.86/3.09 ( ( bot_bot_set_int
% 2.86/3.09 = ( sup_sup_set_int @ A2 @ B2 ) )
% 2.86/3.09 = ( ( A2 = bot_bot_set_int )
% 2.86/3.09 & ( B2 = bot_bot_set_int ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % sup_bot.neutr_eq_iff
% 2.86/3.09 thf(fact_2597_sup__bot_Oleft__neutral,axiom,
% 2.86/3.09 ! [A2: assn] :
% 2.86/3.09 ( ( sup_sup_assn @ bot_bot_assn @ A2 )
% 2.86/3.09 = A2 ) ).
% 2.86/3.09
% 2.86/3.09 % sup_bot.left_neutral
% 2.86/3.09 thf(fact_2598_sup__bot_Oleft__neutral,axiom,
% 2.86/3.09 ! [A2: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( sup_su5525570899277871387at_nat @ bot_bo228742789529271731at_nat @ A2 )
% 2.86/3.09 = A2 ) ).
% 2.86/3.09
% 2.86/3.09 % sup_bot.left_neutral
% 2.86/3.09 thf(fact_2599_sup__bot_Oleft__neutral,axiom,
% 2.86/3.09 ! [A2: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( sup_su6327502436637775413at_nat @ bot_bo2099793752762293965at_nat @ A2 )
% 2.86/3.09 = A2 ) ).
% 2.86/3.09
% 2.86/3.09 % sup_bot.left_neutral
% 2.86/3.09 thf(fact_2600_sup__bot_Oleft__neutral,axiom,
% 2.86/3.09 ! [A2: set_o] :
% 2.86/3.09 ( ( sup_sup_set_o @ bot_bot_set_o @ A2 )
% 2.86/3.09 = A2 ) ).
% 2.86/3.09
% 2.86/3.09 % sup_bot.left_neutral
% 2.86/3.09 thf(fact_2601_sup__bot_Oleft__neutral,axiom,
% 2.86/3.09 ! [A2: set_nat] :
% 2.86/3.09 ( ( sup_sup_set_nat @ bot_bot_set_nat @ A2 )
% 2.86/3.09 = A2 ) ).
% 2.86/3.09
% 2.86/3.09 % sup_bot.left_neutral
% 2.86/3.09 thf(fact_2602_sup__bot_Oleft__neutral,axiom,
% 2.86/3.09 ! [A2: set_int] :
% 2.86/3.09 ( ( sup_sup_set_int @ bot_bot_set_int @ A2 )
% 2.86/3.09 = A2 ) ).
% 2.86/3.09
% 2.86/3.09 % sup_bot.left_neutral
% 2.86/3.09 thf(fact_2603_sup__bot_Oeq__neutr__iff,axiom,
% 2.86/3.09 ! [A2: assn,B2: assn] :
% 2.86/3.09 ( ( ( sup_sup_assn @ A2 @ B2 )
% 2.86/3.09 = bot_bot_assn )
% 2.86/3.09 = ( ( A2 = bot_bot_assn )
% 2.86/3.09 & ( B2 = bot_bot_assn ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % sup_bot.eq_neutr_iff
% 2.86/3.09 thf(fact_2604_sup__bot_Oeq__neutr__iff,axiom,
% 2.86/3.09 ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( ( sup_su5525570899277871387at_nat @ A2 @ B2 )
% 2.86/3.09 = bot_bo228742789529271731at_nat )
% 2.86/3.09 = ( ( A2 = bot_bo228742789529271731at_nat )
% 2.86/3.09 & ( B2 = bot_bo228742789529271731at_nat ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % sup_bot.eq_neutr_iff
% 2.86/3.09 thf(fact_2605_sup__bot_Oeq__neutr__iff,axiom,
% 2.86/3.09 ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( ( sup_su6327502436637775413at_nat @ A2 @ B2 )
% 2.86/3.09 = bot_bo2099793752762293965at_nat )
% 2.86/3.09 = ( ( A2 = bot_bo2099793752762293965at_nat )
% 2.86/3.09 & ( B2 = bot_bo2099793752762293965at_nat ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % sup_bot.eq_neutr_iff
% 2.86/3.09 thf(fact_2606_sup__bot_Oeq__neutr__iff,axiom,
% 2.86/3.09 ! [A2: set_o,B2: set_o] :
% 2.86/3.09 ( ( ( sup_sup_set_o @ A2 @ B2 )
% 2.86/3.09 = bot_bot_set_o )
% 2.86/3.09 = ( ( A2 = bot_bot_set_o )
% 2.86/3.09 & ( B2 = bot_bot_set_o ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % sup_bot.eq_neutr_iff
% 2.86/3.09 thf(fact_2607_sup__bot_Oeq__neutr__iff,axiom,
% 2.86/3.09 ! [A2: set_nat,B2: set_nat] :
% 2.86/3.09 ( ( ( sup_sup_set_nat @ A2 @ B2 )
% 2.86/3.09 = bot_bot_set_nat )
% 2.86/3.09 = ( ( A2 = bot_bot_set_nat )
% 2.86/3.09 & ( B2 = bot_bot_set_nat ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % sup_bot.eq_neutr_iff
% 2.86/3.09 thf(fact_2608_sup__bot_Oeq__neutr__iff,axiom,
% 2.86/3.09 ! [A2: set_int,B2: set_int] :
% 2.86/3.09 ( ( ( sup_sup_set_int @ A2 @ B2 )
% 2.86/3.09 = bot_bot_set_int )
% 2.86/3.09 = ( ( A2 = bot_bot_set_int )
% 2.86/3.09 & ( B2 = bot_bot_set_int ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % sup_bot.eq_neutr_iff
% 2.86/3.09 thf(fact_2609_sup__eq__bot__iff,axiom,
% 2.86/3.09 ! [X: assn,Y: assn] :
% 2.86/3.09 ( ( ( sup_sup_assn @ X @ Y )
% 2.86/3.09 = bot_bot_assn )
% 2.86/3.09 = ( ( X = bot_bot_assn )
% 2.86/3.09 & ( Y = bot_bot_assn ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % sup_eq_bot_iff
% 2.86/3.09 thf(fact_2610_sup__eq__bot__iff,axiom,
% 2.86/3.09 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( ( sup_su5525570899277871387at_nat @ X @ Y )
% 2.86/3.09 = bot_bo228742789529271731at_nat )
% 2.86/3.09 = ( ( X = bot_bo228742789529271731at_nat )
% 2.86/3.09 & ( Y = bot_bo228742789529271731at_nat ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % sup_eq_bot_iff
% 2.86/3.09 thf(fact_2611_sup__eq__bot__iff,axiom,
% 2.86/3.09 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( ( sup_su6327502436637775413at_nat @ X @ Y )
% 2.86/3.09 = bot_bo2099793752762293965at_nat )
% 2.86/3.09 = ( ( X = bot_bo2099793752762293965at_nat )
% 2.86/3.09 & ( Y = bot_bo2099793752762293965at_nat ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % sup_eq_bot_iff
% 2.86/3.09 thf(fact_2612_sup__eq__bot__iff,axiom,
% 2.86/3.09 ! [X: set_o,Y: set_o] :
% 2.86/3.09 ( ( ( sup_sup_set_o @ X @ Y )
% 2.86/3.09 = bot_bot_set_o )
% 2.86/3.09 = ( ( X = bot_bot_set_o )
% 2.86/3.09 & ( Y = bot_bot_set_o ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % sup_eq_bot_iff
% 2.86/3.09 thf(fact_2613_sup__eq__bot__iff,axiom,
% 2.86/3.09 ! [X: set_nat,Y: set_nat] :
% 2.86/3.09 ( ( ( sup_sup_set_nat @ X @ Y )
% 2.86/3.09 = bot_bot_set_nat )
% 2.86/3.09 = ( ( X = bot_bot_set_nat )
% 2.86/3.09 & ( Y = bot_bot_set_nat ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % sup_eq_bot_iff
% 2.86/3.09 thf(fact_2614_sup__eq__bot__iff,axiom,
% 2.86/3.09 ! [X: set_int,Y: set_int] :
% 2.86/3.09 ( ( ( sup_sup_set_int @ X @ Y )
% 2.86/3.09 = bot_bot_set_int )
% 2.86/3.09 = ( ( X = bot_bot_set_int )
% 2.86/3.09 & ( Y = bot_bot_set_int ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % sup_eq_bot_iff
% 2.86/3.09 thf(fact_2615_bot__eq__sup__iff,axiom,
% 2.86/3.09 ! [X: assn,Y: assn] :
% 2.86/3.09 ( ( bot_bot_assn
% 2.86/3.09 = ( sup_sup_assn @ X @ Y ) )
% 2.86/3.09 = ( ( X = bot_bot_assn )
% 2.86/3.09 & ( Y = bot_bot_assn ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % bot_eq_sup_iff
% 2.86/3.09 thf(fact_2616_bot__eq__sup__iff,axiom,
% 2.86/3.09 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( bot_bo228742789529271731at_nat
% 2.86/3.09 = ( sup_su5525570899277871387at_nat @ X @ Y ) )
% 2.86/3.09 = ( ( X = bot_bo228742789529271731at_nat )
% 2.86/3.09 & ( Y = bot_bo228742789529271731at_nat ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % bot_eq_sup_iff
% 2.86/3.09 thf(fact_2617_bot__eq__sup__iff,axiom,
% 2.86/3.09 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( bot_bo2099793752762293965at_nat
% 2.86/3.09 = ( sup_su6327502436637775413at_nat @ X @ Y ) )
% 2.86/3.09 = ( ( X = bot_bo2099793752762293965at_nat )
% 2.86/3.09 & ( Y = bot_bo2099793752762293965at_nat ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % bot_eq_sup_iff
% 2.86/3.09 thf(fact_2618_bot__eq__sup__iff,axiom,
% 2.86/3.09 ! [X: set_o,Y: set_o] :
% 2.86/3.09 ( ( bot_bot_set_o
% 2.86/3.09 = ( sup_sup_set_o @ X @ Y ) )
% 2.86/3.09 = ( ( X = bot_bot_set_o )
% 2.86/3.09 & ( Y = bot_bot_set_o ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % bot_eq_sup_iff
% 2.86/3.09 thf(fact_2619_bot__eq__sup__iff,axiom,
% 2.86/3.09 ! [X: set_nat,Y: set_nat] :
% 2.86/3.09 ( ( bot_bot_set_nat
% 2.86/3.09 = ( sup_sup_set_nat @ X @ Y ) )
% 2.86/3.09 = ( ( X = bot_bot_set_nat )
% 2.86/3.09 & ( Y = bot_bot_set_nat ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % bot_eq_sup_iff
% 2.86/3.09 thf(fact_2620_bot__eq__sup__iff,axiom,
% 2.86/3.09 ! [X: set_int,Y: set_int] :
% 2.86/3.09 ( ( bot_bot_set_int
% 2.86/3.09 = ( sup_sup_set_int @ X @ Y ) )
% 2.86/3.09 = ( ( X = bot_bot_set_int )
% 2.86/3.09 & ( Y = bot_bot_set_int ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % bot_eq_sup_iff
% 2.86/3.09 thf(fact_2621_sup__bot__right,axiom,
% 2.86/3.09 ! [X: assn] :
% 2.86/3.09 ( ( sup_sup_assn @ X @ bot_bot_assn )
% 2.86/3.09 = X ) ).
% 2.86/3.09
% 2.86/3.09 % sup_bot_right
% 2.86/3.09 thf(fact_2622_sup__bot__right,axiom,
% 2.86/3.09 ! [X: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( sup_su5525570899277871387at_nat @ X @ bot_bo228742789529271731at_nat )
% 2.86/3.09 = X ) ).
% 2.86/3.09
% 2.86/3.09 % sup_bot_right
% 2.86/3.09 thf(fact_2623_sup__bot__right,axiom,
% 2.86/3.09 ! [X: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( sup_su6327502436637775413at_nat @ X @ bot_bo2099793752762293965at_nat )
% 2.86/3.09 = X ) ).
% 2.86/3.09
% 2.86/3.09 % sup_bot_right
% 2.86/3.09 thf(fact_2624_sup__bot__right,axiom,
% 2.86/3.09 ! [X: set_o] :
% 2.86/3.09 ( ( sup_sup_set_o @ X @ bot_bot_set_o )
% 2.86/3.09 = X ) ).
% 2.86/3.09
% 2.86/3.09 % sup_bot_right
% 2.86/3.09 thf(fact_2625_sup__bot__right,axiom,
% 2.86/3.09 ! [X: set_nat] :
% 2.86/3.09 ( ( sup_sup_set_nat @ X @ bot_bot_set_nat )
% 2.86/3.09 = X ) ).
% 2.86/3.09
% 2.86/3.09 % sup_bot_right
% 2.86/3.09 thf(fact_2626_sup__bot__right,axiom,
% 2.86/3.09 ! [X: set_int] :
% 2.86/3.09 ( ( sup_sup_set_int @ X @ bot_bot_set_int )
% 2.86/3.09 = X ) ).
% 2.86/3.09
% 2.86/3.09 % sup_bot_right
% 2.86/3.09 thf(fact_2627_sup__bot__left,axiom,
% 2.86/3.09 ! [X: assn] :
% 2.86/3.09 ( ( sup_sup_assn @ bot_bot_assn @ X )
% 2.86/3.09 = X ) ).
% 2.86/3.09
% 2.86/3.09 % sup_bot_left
% 2.86/3.09 thf(fact_2628_sup__bot__left,axiom,
% 2.86/3.09 ! [X: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( sup_su5525570899277871387at_nat @ bot_bo228742789529271731at_nat @ X )
% 2.86/3.09 = X ) ).
% 2.86/3.09
% 2.86/3.09 % sup_bot_left
% 2.86/3.09 thf(fact_2629_sup__bot__left,axiom,
% 2.86/3.09 ! [X: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( sup_su6327502436637775413at_nat @ bot_bo2099793752762293965at_nat @ X )
% 2.86/3.09 = X ) ).
% 2.86/3.09
% 2.86/3.09 % sup_bot_left
% 2.86/3.09 thf(fact_2630_sup__bot__left,axiom,
% 2.86/3.09 ! [X: set_o] :
% 2.86/3.09 ( ( sup_sup_set_o @ bot_bot_set_o @ X )
% 2.86/3.09 = X ) ).
% 2.86/3.09
% 2.86/3.09 % sup_bot_left
% 2.86/3.09 thf(fact_2631_sup__bot__left,axiom,
% 2.86/3.09 ! [X: set_nat] :
% 2.86/3.09 ( ( sup_sup_set_nat @ bot_bot_set_nat @ X )
% 2.86/3.09 = X ) ).
% 2.86/3.09
% 2.86/3.09 % sup_bot_left
% 2.86/3.09 thf(fact_2632_sup__bot__left,axiom,
% 2.86/3.09 ! [X: set_int] :
% 2.86/3.09 ( ( sup_sup_set_int @ bot_bot_set_int @ X )
% 2.86/3.09 = X ) ).
% 2.86/3.09
% 2.86/3.09 % sup_bot_left
% 2.86/3.09 thf(fact_2633_inf__sup__absorb,axiom,
% 2.86/3.09 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( inf_in2572325071724192079at_nat @ X @ ( sup_su6327502436637775413at_nat @ X @ Y ) )
% 2.86/3.09 = X ) ).
% 2.86/3.09
% 2.86/3.09 % inf_sup_absorb
% 2.86/3.09 thf(fact_2634_inf__sup__absorb,axiom,
% 2.86/3.09 ! [X: set_nat,Y: set_nat] :
% 2.86/3.09 ( ( inf_inf_set_nat @ X @ ( sup_sup_set_nat @ X @ Y ) )
% 2.86/3.09 = X ) ).
% 2.86/3.09
% 2.86/3.09 % inf_sup_absorb
% 2.86/3.09 thf(fact_2635_inf__sup__absorb,axiom,
% 2.86/3.09 ! [X: assn,Y: assn] :
% 2.86/3.09 ( ( inf_inf_assn @ X @ ( sup_sup_assn @ X @ Y ) )
% 2.86/3.09 = X ) ).
% 2.86/3.09
% 2.86/3.09 % inf_sup_absorb
% 2.86/3.09 thf(fact_2636_inf__sup__absorb,axiom,
% 2.86/3.09 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( inf_in7913087082777306421at_nat @ X @ ( sup_su5525570899277871387at_nat @ X @ Y ) )
% 2.86/3.09 = X ) ).
% 2.86/3.09
% 2.86/3.09 % inf_sup_absorb
% 2.86/3.09 thf(fact_2637_sup__inf__absorb,axiom,
% 2.86/3.09 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( sup_su6327502436637775413at_nat @ X @ ( inf_in2572325071724192079at_nat @ X @ Y ) )
% 2.86/3.09 = X ) ).
% 2.86/3.09
% 2.86/3.09 % sup_inf_absorb
% 2.86/3.09 thf(fact_2638_sup__inf__absorb,axiom,
% 2.86/3.09 ! [X: set_nat,Y: set_nat] :
% 2.86/3.09 ( ( sup_sup_set_nat @ X @ ( inf_inf_set_nat @ X @ Y ) )
% 2.86/3.09 = X ) ).
% 2.86/3.09
% 2.86/3.09 % sup_inf_absorb
% 2.86/3.09 thf(fact_2639_sup__inf__absorb,axiom,
% 2.86/3.09 ! [X: assn,Y: assn] :
% 2.86/3.09 ( ( sup_sup_assn @ X @ ( inf_inf_assn @ X @ Y ) )
% 2.86/3.09 = X ) ).
% 2.86/3.09
% 2.86/3.09 % sup_inf_absorb
% 2.86/3.09 thf(fact_2640_sup__inf__absorb,axiom,
% 2.86/3.09 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( sup_su5525570899277871387at_nat @ X @ ( inf_in7913087082777306421at_nat @ X @ Y ) )
% 2.86/3.09 = X ) ).
% 2.86/3.09
% 2.86/3.09 % sup_inf_absorb
% 2.86/3.09 thf(fact_2641_Un__empty,axiom,
% 2.86/3.09 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( ( sup_su5525570899277871387at_nat @ A @ B )
% 2.86/3.09 = bot_bo228742789529271731at_nat )
% 2.86/3.09 = ( ( A = bot_bo228742789529271731at_nat )
% 2.86/3.09 & ( B = bot_bo228742789529271731at_nat ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Un_empty
% 2.86/3.09 thf(fact_2642_Un__empty,axiom,
% 2.86/3.09 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( ( sup_su6327502436637775413at_nat @ A @ B )
% 2.86/3.09 = bot_bo2099793752762293965at_nat )
% 2.86/3.09 = ( ( A = bot_bo2099793752762293965at_nat )
% 2.86/3.09 & ( B = bot_bo2099793752762293965at_nat ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Un_empty
% 2.86/3.09 thf(fact_2643_Un__empty,axiom,
% 2.86/3.09 ! [A: set_o,B: set_o] :
% 2.86/3.09 ( ( ( sup_sup_set_o @ A @ B )
% 2.86/3.09 = bot_bot_set_o )
% 2.86/3.09 = ( ( A = bot_bot_set_o )
% 2.86/3.09 & ( B = bot_bot_set_o ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Un_empty
% 2.86/3.09 thf(fact_2644_Un__empty,axiom,
% 2.86/3.09 ! [A: set_nat,B: set_nat] :
% 2.86/3.09 ( ( ( sup_sup_set_nat @ A @ B )
% 2.86/3.09 = bot_bot_set_nat )
% 2.86/3.09 = ( ( A = bot_bot_set_nat )
% 2.86/3.09 & ( B = bot_bot_set_nat ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Un_empty
% 2.86/3.09 thf(fact_2645_Un__empty,axiom,
% 2.86/3.09 ! [A: set_int,B: set_int] :
% 2.86/3.09 ( ( ( sup_sup_set_int @ A @ B )
% 2.86/3.09 = bot_bot_set_int )
% 2.86/3.09 = ( ( A = bot_bot_set_int )
% 2.86/3.09 & ( B = bot_bot_set_int ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Un_empty
% 2.86/3.09 thf(fact_2646_min__arg__le_I2_J,axiom,
% 2.86/3.09 ! [M2: assn,N: assn] :
% 2.86/3.09 ( ( ord_less_eq_assn @ M2 @ ( ord_min_assn @ M2 @ N ) )
% 2.86/3.09 = ( ( ord_min_assn @ M2 @ N )
% 2.86/3.09 = M2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_arg_le(2)
% 2.86/3.09 thf(fact_2647_min__arg__le_I2_J,axiom,
% 2.86/3.09 ! [M2: filter_nat,N: filter_nat] :
% 2.86/3.09 ( ( ord_le2510731241096832064er_nat @ M2 @ ( ord_min_filter_nat @ M2 @ N ) )
% 2.86/3.09 = ( ( ord_min_filter_nat @ M2 @ N )
% 2.86/3.09 = M2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_arg_le(2)
% 2.86/3.09 thf(fact_2648_min__arg__le_I2_J,axiom,
% 2.86/3.09 ! [M2: set_nat,N: set_nat] :
% 2.86/3.09 ( ( ord_less_eq_set_nat @ M2 @ ( ord_min_set_nat @ M2 @ N ) )
% 2.86/3.09 = ( ( ord_min_set_nat @ M2 @ N )
% 2.86/3.09 = M2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_arg_le(2)
% 2.86/3.09 thf(fact_2649_min__arg__le_I2_J,axiom,
% 2.86/3.09 ! [M2: nat,N: nat] :
% 2.86/3.09 ( ( ord_less_eq_nat @ M2 @ ( ord_min_nat @ M2 @ N ) )
% 2.86/3.09 = ( ( ord_min_nat @ M2 @ N )
% 2.86/3.09 = M2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_arg_le(2)
% 2.86/3.09 thf(fact_2650_min__arg__le_I2_J,axiom,
% 2.86/3.09 ! [M2: int,N: int] :
% 2.86/3.09 ( ( ord_less_eq_int @ M2 @ ( ord_min_int @ M2 @ N ) )
% 2.86/3.09 = ( ( ord_min_int @ M2 @ N )
% 2.86/3.09 = M2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_arg_le(2)
% 2.86/3.09 thf(fact_2651_min__arg__le_I1_J,axiom,
% 2.86/3.09 ! [N: assn,M2: assn] :
% 2.86/3.09 ( ( ord_less_eq_assn @ N @ ( ord_min_assn @ M2 @ N ) )
% 2.86/3.09 = ( ( ord_min_assn @ M2 @ N )
% 2.86/3.09 = N ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_arg_le(1)
% 2.86/3.09 thf(fact_2652_min__arg__le_I1_J,axiom,
% 2.86/3.09 ! [N: filter_nat,M2: filter_nat] :
% 2.86/3.09 ( ( ord_le2510731241096832064er_nat @ N @ ( ord_min_filter_nat @ M2 @ N ) )
% 2.86/3.09 = ( ( ord_min_filter_nat @ M2 @ N )
% 2.86/3.09 = N ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_arg_le(1)
% 2.86/3.09 thf(fact_2653_min__arg__le_I1_J,axiom,
% 2.86/3.09 ! [N: set_nat,M2: set_nat] :
% 2.86/3.09 ( ( ord_less_eq_set_nat @ N @ ( ord_min_set_nat @ M2 @ N ) )
% 2.86/3.09 = ( ( ord_min_set_nat @ M2 @ N )
% 2.86/3.09 = N ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_arg_le(1)
% 2.86/3.09 thf(fact_2654_min__arg__le_I1_J,axiom,
% 2.86/3.09 ! [N: nat,M2: nat] :
% 2.86/3.09 ( ( ord_less_eq_nat @ N @ ( ord_min_nat @ M2 @ N ) )
% 2.86/3.09 = ( ( ord_min_nat @ M2 @ N )
% 2.86/3.09 = N ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_arg_le(1)
% 2.86/3.09 thf(fact_2655_min__arg__le_I1_J,axiom,
% 2.86/3.09 ! [N: int,M2: int] :
% 2.86/3.09 ( ( ord_less_eq_int @ N @ ( ord_min_int @ M2 @ N ) )
% 2.86/3.09 = ( ( ord_min_int @ M2 @ N )
% 2.86/3.09 = N ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_arg_le(1)
% 2.86/3.09 thf(fact_2656_min__eq__arg_I2_J,axiom,
% 2.86/3.09 ! [M2: nat,N: nat] :
% 2.86/3.09 ( ( ( ord_min_nat @ M2 @ N )
% 2.86/3.09 = N )
% 2.86/3.09 = ( ord_less_eq_nat @ N @ M2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_eq_arg(2)
% 2.86/3.09 thf(fact_2657_min__eq__arg_I2_J,axiom,
% 2.86/3.09 ! [M2: int,N: int] :
% 2.86/3.09 ( ( ( ord_min_int @ M2 @ N )
% 2.86/3.09 = N )
% 2.86/3.09 = ( ord_less_eq_int @ N @ M2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_eq_arg(2)
% 2.86/3.09 thf(fact_2658_min__eq__arg_I1_J,axiom,
% 2.86/3.09 ! [M2: nat,N: nat] :
% 2.86/3.09 ( ( ( ord_min_nat @ M2 @ N )
% 2.86/3.09 = M2 )
% 2.86/3.09 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_eq_arg(1)
% 2.86/3.09 thf(fact_2659_min__eq__arg_I1_J,axiom,
% 2.86/3.09 ! [M2: int,N: int] :
% 2.86/3.09 ( ( ( ord_min_int @ M2 @ N )
% 2.86/3.09 = M2 )
% 2.86/3.09 = ( ord_less_eq_int @ M2 @ N ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_eq_arg(1)
% 2.86/3.09 thf(fact_2660_min_Oabsorb1,axiom,
% 2.86/3.09 ! [A2: nat,B2: nat] :
% 2.86/3.09 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.09 => ( ( ord_min_nat @ A2 @ B2 )
% 2.86/3.09 = A2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min.absorb1
% 2.86/3.09 thf(fact_2661_min_Oabsorb1,axiom,
% 2.86/3.09 ! [A2: int,B2: int] :
% 2.86/3.09 ( ( ord_less_eq_int @ A2 @ B2 )
% 2.86/3.09 => ( ( ord_min_int @ A2 @ B2 )
% 2.86/3.09 = A2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min.absorb1
% 2.86/3.09 thf(fact_2662_min_Oabsorb2,axiom,
% 2.86/3.09 ! [B2: nat,A2: nat] :
% 2.86/3.09 ( ( ord_less_eq_nat @ B2 @ A2 )
% 2.86/3.09 => ( ( ord_min_nat @ A2 @ B2 )
% 2.86/3.09 = B2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min.absorb2
% 2.86/3.09 thf(fact_2663_min_Oabsorb2,axiom,
% 2.86/3.09 ! [B2: int,A2: int] :
% 2.86/3.09 ( ( ord_less_eq_int @ B2 @ A2 )
% 2.86/3.09 => ( ( ord_min_int @ A2 @ B2 )
% 2.86/3.09 = B2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min.absorb2
% 2.86/3.09 thf(fact_2664_min_Obounded__iff,axiom,
% 2.86/3.09 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.09 ( ( ord_less_eq_nat @ A2 @ ( ord_min_nat @ B2 @ C ) )
% 2.86/3.09 = ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.09 & ( ord_less_eq_nat @ A2 @ C ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % min.bounded_iff
% 2.86/3.09 thf(fact_2665_min_Obounded__iff,axiom,
% 2.86/3.09 ! [A2: int,B2: int,C: int] :
% 2.86/3.09 ( ( ord_less_eq_int @ A2 @ ( ord_min_int @ B2 @ C ) )
% 2.86/3.09 = ( ( ord_less_eq_int @ A2 @ B2 )
% 2.86/3.09 & ( ord_less_eq_int @ A2 @ C ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % min.bounded_iff
% 2.86/3.09 thf(fact_2666_Un__subset__iff,axiom,
% 2.86/3.09 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ A @ B ) @ C2 )
% 2.86/3.09 = ( ( ord_le1268244103169919719at_nat @ A @ C2 )
% 2.86/3.09 & ( ord_le1268244103169919719at_nat @ B @ C2 ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Un_subset_iff
% 2.86/3.09 thf(fact_2667_Un__subset__iff,axiom,
% 2.86/3.09 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 2.86/3.09 ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A @ B ) @ C2 )
% 2.86/3.09 = ( ( ord_less_eq_set_nat @ A @ C2 )
% 2.86/3.09 & ( ord_less_eq_set_nat @ B @ C2 ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Un_subset_iff
% 2.86/3.09 thf(fact_2668_Un__insert__right,axiom,
% 2.86/3.09 ! [A: set_int,A2: int,B: set_int] :
% 2.86/3.09 ( ( sup_sup_set_int @ A @ ( insert_int2 @ A2 @ B ) )
% 2.86/3.09 = ( insert_int2 @ A2 @ ( sup_sup_set_int @ A @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Un_insert_right
% 2.86/3.09 thf(fact_2669_Un__insert__right,axiom,
% 2.86/3.09 ! [A: set_Pr1261947904930325089at_nat,A2: product_prod_nat_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( sup_su6327502436637775413at_nat @ A @ ( insert8211810215607154385at_nat @ A2 @ B ) )
% 2.86/3.09 = ( insert8211810215607154385at_nat @ A2 @ ( sup_su6327502436637775413at_nat @ A @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Un_insert_right
% 2.86/3.09 thf(fact_2670_Un__insert__right,axiom,
% 2.86/3.09 ! [A: set_o,A2: $o,B: set_o] :
% 2.86/3.09 ( ( sup_sup_set_o @ A @ ( insert_o2 @ A2 @ B ) )
% 2.86/3.09 = ( insert_o2 @ A2 @ ( sup_sup_set_o @ A @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Un_insert_right
% 2.86/3.09 thf(fact_2671_Un__insert__right,axiom,
% 2.86/3.09 ! [A: set_nat,A2: nat,B: set_nat] :
% 2.86/3.09 ( ( sup_sup_set_nat @ A @ ( insert_nat2 @ A2 @ B ) )
% 2.86/3.09 = ( insert_nat2 @ A2 @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Un_insert_right
% 2.86/3.09 thf(fact_2672_Un__insert__right,axiom,
% 2.86/3.09 ! [A: set_Pr4329608150637261639at_nat,A2: produc3843707927480180839at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( sup_su5525570899277871387at_nat @ A @ ( insert9069300056098147895at_nat @ A2 @ B ) )
% 2.86/3.09 = ( insert9069300056098147895at_nat @ A2 @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Un_insert_right
% 2.86/3.09 thf(fact_2673_Un__insert__left,axiom,
% 2.86/3.09 ! [A2: int,B: set_int,C2: set_int] :
% 2.86/3.09 ( ( sup_sup_set_int @ ( insert_int2 @ A2 @ B ) @ C2 )
% 2.86/3.09 = ( insert_int2 @ A2 @ ( sup_sup_set_int @ B @ C2 ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Un_insert_left
% 2.86/3.09 thf(fact_2674_Un__insert__left,axiom,
% 2.86/3.09 ! [A2: product_prod_nat_nat,B: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( sup_su6327502436637775413at_nat @ ( insert8211810215607154385at_nat @ A2 @ B ) @ C2 )
% 2.86/3.09 = ( insert8211810215607154385at_nat @ A2 @ ( sup_su6327502436637775413at_nat @ B @ C2 ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Un_insert_left
% 2.86/3.09 thf(fact_2675_Un__insert__left,axiom,
% 2.86/3.09 ! [A2: $o,B: set_o,C2: set_o] :
% 2.86/3.09 ( ( sup_sup_set_o @ ( insert_o2 @ A2 @ B ) @ C2 )
% 2.86/3.09 = ( insert_o2 @ A2 @ ( sup_sup_set_o @ B @ C2 ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Un_insert_left
% 2.86/3.09 thf(fact_2676_Un__insert__left,axiom,
% 2.86/3.09 ! [A2: nat,B: set_nat,C2: set_nat] :
% 2.86/3.09 ( ( sup_sup_set_nat @ ( insert_nat2 @ A2 @ B ) @ C2 )
% 2.86/3.09 = ( insert_nat2 @ A2 @ ( sup_sup_set_nat @ B @ C2 ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Un_insert_left
% 2.86/3.09 thf(fact_2677_Un__insert__left,axiom,
% 2.86/3.09 ! [A2: produc3843707927480180839at_nat,B: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( sup_su5525570899277871387at_nat @ ( insert9069300056098147895at_nat @ A2 @ B ) @ C2 )
% 2.86/3.09 = ( insert9069300056098147895at_nat @ A2 @ ( sup_su5525570899277871387at_nat @ B @ C2 ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Un_insert_left
% 2.86/3.09 thf(fact_2678_min__less__iff__conj,axiom,
% 2.86/3.09 ! [Z: code_integer,X: code_integer,Y: code_integer] :
% 2.86/3.09 ( ( ord_le6747313008572928689nteger @ Z @ ( ord_min_Code_integer @ X @ Y ) )
% 2.86/3.09 = ( ( ord_le6747313008572928689nteger @ Z @ X )
% 2.86/3.09 & ( ord_le6747313008572928689nteger @ Z @ Y ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_less_iff_conj
% 2.86/3.09 thf(fact_2679_min__less__iff__conj,axiom,
% 2.86/3.09 ! [Z: num,X: num,Y: num] :
% 2.86/3.09 ( ( ord_less_num @ Z @ ( ord_min_num @ X @ Y ) )
% 2.86/3.09 = ( ( ord_less_num @ Z @ X )
% 2.86/3.09 & ( ord_less_num @ Z @ Y ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_less_iff_conj
% 2.86/3.09 thf(fact_2680_min__less__iff__conj,axiom,
% 2.86/3.09 ! [Z: nat,X: nat,Y: nat] :
% 2.86/3.09 ( ( ord_less_nat @ Z @ ( ord_min_nat @ X @ Y ) )
% 2.86/3.09 = ( ( ord_less_nat @ Z @ X )
% 2.86/3.09 & ( ord_less_nat @ Z @ Y ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_less_iff_conj
% 2.86/3.09 thf(fact_2681_min__less__iff__conj,axiom,
% 2.86/3.09 ! [Z: int,X: int,Y: int] :
% 2.86/3.09 ( ( ord_less_int @ Z @ ( ord_min_int @ X @ Y ) )
% 2.86/3.09 = ( ( ord_less_int @ Z @ X )
% 2.86/3.09 & ( ord_less_int @ Z @ Y ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_less_iff_conj
% 2.86/3.09 thf(fact_2682_min_Oabsorb4,axiom,
% 2.86/3.09 ! [B2: code_integer,A2: code_integer] :
% 2.86/3.09 ( ( ord_le6747313008572928689nteger @ B2 @ A2 )
% 2.86/3.09 => ( ( ord_min_Code_integer @ A2 @ B2 )
% 2.86/3.09 = B2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min.absorb4
% 2.86/3.09 thf(fact_2683_min_Oabsorb4,axiom,
% 2.86/3.09 ! [B2: num,A2: num] :
% 2.86/3.09 ( ( ord_less_num @ B2 @ A2 )
% 2.86/3.09 => ( ( ord_min_num @ A2 @ B2 )
% 2.86/3.09 = B2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min.absorb4
% 2.86/3.09 thf(fact_2684_min_Oabsorb4,axiom,
% 2.86/3.09 ! [B2: nat,A2: nat] :
% 2.86/3.09 ( ( ord_less_nat @ B2 @ A2 )
% 2.86/3.09 => ( ( ord_min_nat @ A2 @ B2 )
% 2.86/3.09 = B2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min.absorb4
% 2.86/3.09 thf(fact_2685_min_Oabsorb4,axiom,
% 2.86/3.09 ! [B2: int,A2: int] :
% 2.86/3.09 ( ( ord_less_int @ B2 @ A2 )
% 2.86/3.09 => ( ( ord_min_int @ A2 @ B2 )
% 2.86/3.09 = B2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min.absorb4
% 2.86/3.09 thf(fact_2686_min_Oabsorb3,axiom,
% 2.86/3.09 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.09 ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 2.86/3.09 => ( ( ord_min_Code_integer @ A2 @ B2 )
% 2.86/3.09 = A2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min.absorb3
% 2.86/3.09 thf(fact_2687_min_Oabsorb3,axiom,
% 2.86/3.09 ! [A2: num,B2: num] :
% 2.86/3.09 ( ( ord_less_num @ A2 @ B2 )
% 2.86/3.09 => ( ( ord_min_num @ A2 @ B2 )
% 2.86/3.09 = A2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min.absorb3
% 2.86/3.09 thf(fact_2688_min_Oabsorb3,axiom,
% 2.86/3.09 ! [A2: nat,B2: nat] :
% 2.86/3.09 ( ( ord_less_nat @ A2 @ B2 )
% 2.86/3.09 => ( ( ord_min_nat @ A2 @ B2 )
% 2.86/3.09 = A2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min.absorb3
% 2.86/3.09 thf(fact_2689_min_Oabsorb3,axiom,
% 2.86/3.09 ! [A2: int,B2: int] :
% 2.86/3.09 ( ( ord_less_int @ A2 @ B2 )
% 2.86/3.09 => ( ( ord_min_int @ A2 @ B2 )
% 2.86/3.09 = A2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min.absorb3
% 2.86/3.09 thf(fact_2690_min__arg__not__ge_I1_J,axiom,
% 2.86/3.09 ! [M2: code_integer,N: code_integer] :
% 2.86/3.09 ( ( ~ ( ord_le6747313008572928689nteger @ ( ord_min_Code_integer @ M2 @ N ) @ M2 ) )
% 2.86/3.09 = ( ( ord_min_Code_integer @ M2 @ N )
% 2.86/3.09 = M2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_arg_not_ge(1)
% 2.86/3.09 thf(fact_2691_min__arg__not__ge_I1_J,axiom,
% 2.86/3.09 ! [M2: num,N: num] :
% 2.86/3.09 ( ( ~ ( ord_less_num @ ( ord_min_num @ M2 @ N ) @ M2 ) )
% 2.86/3.09 = ( ( ord_min_num @ M2 @ N )
% 2.86/3.09 = M2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_arg_not_ge(1)
% 2.86/3.09 thf(fact_2692_min__arg__not__ge_I1_J,axiom,
% 2.86/3.09 ! [M2: nat,N: nat] :
% 2.86/3.09 ( ( ~ ( ord_less_nat @ ( ord_min_nat @ M2 @ N ) @ M2 ) )
% 2.86/3.09 = ( ( ord_min_nat @ M2 @ N )
% 2.86/3.09 = M2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_arg_not_ge(1)
% 2.86/3.09 thf(fact_2693_min__arg__not__ge_I1_J,axiom,
% 2.86/3.09 ! [M2: int,N: int] :
% 2.86/3.09 ( ( ~ ( ord_less_int @ ( ord_min_int @ M2 @ N ) @ M2 ) )
% 2.86/3.09 = ( ( ord_min_int @ M2 @ N )
% 2.86/3.09 = M2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_arg_not_ge(1)
% 2.86/3.09 thf(fact_2694_min__arg__not__ge_I2_J,axiom,
% 2.86/3.09 ! [M2: code_integer,N: code_integer] :
% 2.86/3.09 ( ( ~ ( ord_le6747313008572928689nteger @ ( ord_min_Code_integer @ M2 @ N ) @ N ) )
% 2.86/3.09 = ( ( ord_min_Code_integer @ M2 @ N )
% 2.86/3.09 = N ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_arg_not_ge(2)
% 2.86/3.09 thf(fact_2695_min__arg__not__ge_I2_J,axiom,
% 2.86/3.09 ! [M2: num,N: num] :
% 2.86/3.09 ( ( ~ ( ord_less_num @ ( ord_min_num @ M2 @ N ) @ N ) )
% 2.86/3.09 = ( ( ord_min_num @ M2 @ N )
% 2.86/3.09 = N ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_arg_not_ge(2)
% 2.86/3.09 thf(fact_2696_min__arg__not__ge_I2_J,axiom,
% 2.86/3.09 ! [M2: nat,N: nat] :
% 2.86/3.09 ( ( ~ ( ord_less_nat @ ( ord_min_nat @ M2 @ N ) @ N ) )
% 2.86/3.09 = ( ( ord_min_nat @ M2 @ N )
% 2.86/3.09 = N ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_arg_not_ge(2)
% 2.86/3.09 thf(fact_2697_min__arg__not__ge_I2_J,axiom,
% 2.86/3.09 ! [M2: int,N: int] :
% 2.86/3.09 ( ( ~ ( ord_less_int @ ( ord_min_int @ M2 @ N ) @ N ) )
% 2.86/3.09 = ( ( ord_min_int @ M2 @ N )
% 2.86/3.09 = N ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_arg_not_ge(2)
% 2.86/3.09 thf(fact_2698_min__less__self__conv_I1_J,axiom,
% 2.86/3.09 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.09 ( ( ord_le6747313008572928689nteger @ ( ord_min_Code_integer @ A2 @ B2 ) @ A2 )
% 2.86/3.09 = ( ord_le6747313008572928689nteger @ B2 @ A2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_less_self_conv(1)
% 2.86/3.09 thf(fact_2699_min__less__self__conv_I1_J,axiom,
% 2.86/3.09 ! [A2: num,B2: num] :
% 2.86/3.09 ( ( ord_less_num @ ( ord_min_num @ A2 @ B2 ) @ A2 )
% 2.86/3.09 = ( ord_less_num @ B2 @ A2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_less_self_conv(1)
% 2.86/3.09 thf(fact_2700_min__less__self__conv_I1_J,axiom,
% 2.86/3.09 ! [A2: nat,B2: nat] :
% 2.86/3.09 ( ( ord_less_nat @ ( ord_min_nat @ A2 @ B2 ) @ A2 )
% 2.86/3.09 = ( ord_less_nat @ B2 @ A2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_less_self_conv(1)
% 2.86/3.09 thf(fact_2701_min__less__self__conv_I1_J,axiom,
% 2.86/3.09 ! [A2: int,B2: int] :
% 2.86/3.09 ( ( ord_less_int @ ( ord_min_int @ A2 @ B2 ) @ A2 )
% 2.86/3.09 = ( ord_less_int @ B2 @ A2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_less_self_conv(1)
% 2.86/3.09 thf(fact_2702_min__less__self__conv_I2_J,axiom,
% 2.86/3.09 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.09 ( ( ord_le6747313008572928689nteger @ ( ord_min_Code_integer @ A2 @ B2 ) @ B2 )
% 2.86/3.09 = ( ord_le6747313008572928689nteger @ A2 @ B2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_less_self_conv(2)
% 2.86/3.09 thf(fact_2703_min__less__self__conv_I2_J,axiom,
% 2.86/3.09 ! [A2: num,B2: num] :
% 2.86/3.09 ( ( ord_less_num @ ( ord_min_num @ A2 @ B2 ) @ B2 )
% 2.86/3.09 = ( ord_less_num @ A2 @ B2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_less_self_conv(2)
% 2.86/3.09 thf(fact_2704_min__less__self__conv_I2_J,axiom,
% 2.86/3.09 ! [A2: nat,B2: nat] :
% 2.86/3.09 ( ( ord_less_nat @ ( ord_min_nat @ A2 @ B2 ) @ B2 )
% 2.86/3.09 = ( ord_less_nat @ A2 @ B2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_less_self_conv(2)
% 2.86/3.09 thf(fact_2705_min__less__self__conv_I2_J,axiom,
% 2.86/3.09 ! [A2: int,B2: int] :
% 2.86/3.09 ( ( ord_less_int @ ( ord_min_int @ A2 @ B2 ) @ B2 )
% 2.86/3.09 = ( ord_less_int @ A2 @ B2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_less_self_conv(2)
% 2.86/3.09 thf(fact_2706_min__simps_I1_J,axiom,
% 2.86/3.09 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.09 ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 2.86/3.09 => ( ( ord_min_Code_integer @ A2 @ B2 )
% 2.86/3.09 = A2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_simps(1)
% 2.86/3.09 thf(fact_2707_min__simps_I1_J,axiom,
% 2.86/3.09 ! [A2: assn,B2: assn] :
% 2.86/3.09 ( ( ord_less_assn @ A2 @ B2 )
% 2.86/3.09 => ( ( ord_min_assn @ A2 @ B2 )
% 2.86/3.09 = A2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_simps(1)
% 2.86/3.09 thf(fact_2708_min__simps_I1_J,axiom,
% 2.86/3.09 ! [A2: num,B2: num] :
% 2.86/3.09 ( ( ord_less_num @ A2 @ B2 )
% 2.86/3.09 => ( ( ord_min_num @ A2 @ B2 )
% 2.86/3.09 = A2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_simps(1)
% 2.86/3.09 thf(fact_2709_min__simps_I1_J,axiom,
% 2.86/3.09 ! [A2: nat,B2: nat] :
% 2.86/3.09 ( ( ord_less_nat @ A2 @ B2 )
% 2.86/3.09 => ( ( ord_min_nat @ A2 @ B2 )
% 2.86/3.09 = A2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_simps(1)
% 2.86/3.09 thf(fact_2710_min__simps_I1_J,axiom,
% 2.86/3.09 ! [A2: int,B2: int] :
% 2.86/3.09 ( ( ord_less_int @ A2 @ B2 )
% 2.86/3.09 => ( ( ord_min_int @ A2 @ B2 )
% 2.86/3.09 = A2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_simps(1)
% 2.86/3.09 thf(fact_2711_min__simps_I2_J,axiom,
% 2.86/3.09 ! [B2: code_integer,A2: code_integer] :
% 2.86/3.09 ( ( ord_le6747313008572928689nteger @ B2 @ A2 )
% 2.86/3.09 => ( ( ord_min_Code_integer @ A2 @ B2 )
% 2.86/3.09 = B2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_simps(2)
% 2.86/3.09 thf(fact_2712_min__simps_I2_J,axiom,
% 2.86/3.09 ! [B2: assn,A2: assn] :
% 2.86/3.09 ( ( ord_less_assn @ B2 @ A2 )
% 2.86/3.09 => ( ( ord_min_assn @ A2 @ B2 )
% 2.86/3.09 = B2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_simps(2)
% 2.86/3.09 thf(fact_2713_min__simps_I2_J,axiom,
% 2.86/3.09 ! [B2: num,A2: num] :
% 2.86/3.09 ( ( ord_less_num @ B2 @ A2 )
% 2.86/3.09 => ( ( ord_min_num @ A2 @ B2 )
% 2.86/3.09 = B2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_simps(2)
% 2.86/3.09 thf(fact_2714_min__simps_I2_J,axiom,
% 2.86/3.09 ! [B2: nat,A2: nat] :
% 2.86/3.09 ( ( ord_less_nat @ B2 @ A2 )
% 2.86/3.09 => ( ( ord_min_nat @ A2 @ B2 )
% 2.86/3.09 = B2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_simps(2)
% 2.86/3.09 thf(fact_2715_min__simps_I2_J,axiom,
% 2.86/3.09 ! [B2: int,A2: int] :
% 2.86/3.09 ( ( ord_less_int @ B2 @ A2 )
% 2.86/3.09 => ( ( ord_min_int @ A2 @ B2 )
% 2.86/3.09 = B2 ) ) ).
% 2.86/3.09
% 2.86/3.09 % min_simps(2)
% 2.86/3.09 thf(fact_2716_min__bot2,axiom,
% 2.86/3.09 ! [X: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( ord_mi6693596345299712430at_nat @ X @ bot_bo228742789529271731at_nat )
% 2.86/3.09 = bot_bo228742789529271731at_nat ) ).
% 2.86/3.09
% 2.86/3.09 % min_bot2
% 2.86/3.09 thf(fact_2717_min__bot2,axiom,
% 2.86/3.09 ! [X: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( ord_mi4194197829855655752at_nat @ X @ bot_bo2099793752762293965at_nat )
% 2.86/3.09 = bot_bo2099793752762293965at_nat ) ).
% 2.86/3.09
% 2.86/3.09 % min_bot2
% 2.86/3.09 thf(fact_2718_min__bot2,axiom,
% 2.86/3.09 ! [X: set_o] :
% 2.86/3.09 ( ( ord_min_set_o @ X @ bot_bot_set_o )
% 2.86/3.09 = bot_bot_set_o ) ).
% 2.86/3.09
% 2.86/3.09 % min_bot2
% 2.86/3.09 thf(fact_2719_min__bot2,axiom,
% 2.86/3.09 ! [X: set_nat] :
% 2.86/3.09 ( ( ord_min_set_nat @ X @ bot_bot_set_nat )
% 2.86/3.09 = bot_bot_set_nat ) ).
% 2.86/3.09
% 2.86/3.09 % min_bot2
% 2.86/3.09 thf(fact_2720_min__bot2,axiom,
% 2.86/3.09 ! [X: set_int] :
% 2.86/3.09 ( ( ord_min_set_int @ X @ bot_bot_set_int )
% 2.86/3.09 = bot_bot_set_int ) ).
% 2.86/3.09
% 2.86/3.09 % min_bot2
% 2.86/3.09 thf(fact_2721_min__bot2,axiom,
% 2.86/3.09 ! [X: nat] :
% 2.86/3.09 ( ( ord_min_nat @ X @ bot_bot_nat )
% 2.86/3.09 = bot_bot_nat ) ).
% 2.86/3.09
% 2.86/3.09 % min_bot2
% 2.86/3.09 thf(fact_2722_min__bot,axiom,
% 2.86/3.09 ! [X: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( ord_mi6693596345299712430at_nat @ bot_bo228742789529271731at_nat @ X )
% 2.86/3.09 = bot_bo228742789529271731at_nat ) ).
% 2.86/3.09
% 2.86/3.09 % min_bot
% 2.86/3.09 thf(fact_2723_min__bot,axiom,
% 2.86/3.09 ! [X: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( ord_mi4194197829855655752at_nat @ bot_bo2099793752762293965at_nat @ X )
% 2.86/3.09 = bot_bo2099793752762293965at_nat ) ).
% 2.86/3.09
% 2.86/3.09 % min_bot
% 2.86/3.09 thf(fact_2724_min__bot,axiom,
% 2.86/3.09 ! [X: set_o] :
% 2.86/3.09 ( ( ord_min_set_o @ bot_bot_set_o @ X )
% 2.86/3.09 = bot_bot_set_o ) ).
% 2.86/3.09
% 2.86/3.09 % min_bot
% 2.86/3.09 thf(fact_2725_min__bot,axiom,
% 2.86/3.09 ! [X: set_nat] :
% 2.86/3.09 ( ( ord_min_set_nat @ bot_bot_set_nat @ X )
% 2.86/3.09 = bot_bot_set_nat ) ).
% 2.86/3.09
% 2.86/3.09 % min_bot
% 2.86/3.09 thf(fact_2726_min__bot,axiom,
% 2.86/3.09 ! [X: set_int] :
% 2.86/3.09 ( ( ord_min_set_int @ bot_bot_set_int @ X )
% 2.86/3.09 = bot_bot_set_int ) ).
% 2.86/3.09
% 2.86/3.09 % min_bot
% 2.86/3.09 thf(fact_2727_min__bot,axiom,
% 2.86/3.09 ! [X: nat] :
% 2.86/3.09 ( ( ord_min_nat @ bot_bot_nat @ X )
% 2.86/3.09 = bot_bot_nat ) ).
% 2.86/3.09
% 2.86/3.09 % min_bot
% 2.86/3.09 thf(fact_2728_Int__Un__eq_I4_J,axiom,
% 2.86/3.09 ! [T3: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( sup_su6327502436637775413at_nat @ T3 @ ( inf_in2572325071724192079at_nat @ S @ T3 ) )
% 2.86/3.09 = T3 ) ).
% 2.86/3.09
% 2.86/3.09 % Int_Un_eq(4)
% 2.86/3.09 thf(fact_2729_Int__Un__eq_I4_J,axiom,
% 2.86/3.09 ! [T3: set_nat,S: set_nat] :
% 2.86/3.09 ( ( sup_sup_set_nat @ T3 @ ( inf_inf_set_nat @ S @ T3 ) )
% 2.86/3.09 = T3 ) ).
% 2.86/3.09
% 2.86/3.09 % Int_Un_eq(4)
% 2.86/3.09 thf(fact_2730_Int__Un__eq_I4_J,axiom,
% 2.86/3.09 ! [T3: set_Pr4329608150637261639at_nat,S: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( sup_su5525570899277871387at_nat @ T3 @ ( inf_in7913087082777306421at_nat @ S @ T3 ) )
% 2.86/3.09 = T3 ) ).
% 2.86/3.09
% 2.86/3.09 % Int_Un_eq(4)
% 2.86/3.09 thf(fact_2731_Int__Un__eq_I3_J,axiom,
% 2.86/3.09 ! [S: set_Pr1261947904930325089at_nat,T3: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( sup_su6327502436637775413at_nat @ S @ ( inf_in2572325071724192079at_nat @ S @ T3 ) )
% 2.86/3.09 = S ) ).
% 2.86/3.09
% 2.86/3.09 % Int_Un_eq(3)
% 2.86/3.09 thf(fact_2732_Int__Un__eq_I3_J,axiom,
% 2.86/3.09 ! [S: set_nat,T3: set_nat] :
% 2.86/3.09 ( ( sup_sup_set_nat @ S @ ( inf_inf_set_nat @ S @ T3 ) )
% 2.86/3.09 = S ) ).
% 2.86/3.09
% 2.86/3.09 % Int_Un_eq(3)
% 2.86/3.09 thf(fact_2733_Int__Un__eq_I3_J,axiom,
% 2.86/3.09 ! [S: set_Pr4329608150637261639at_nat,T3: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( sup_su5525570899277871387at_nat @ S @ ( inf_in7913087082777306421at_nat @ S @ T3 ) )
% 2.86/3.09 = S ) ).
% 2.86/3.09
% 2.86/3.09 % Int_Un_eq(3)
% 2.86/3.09 thf(fact_2734_Int__Un__eq_I2_J,axiom,
% 2.86/3.09 ! [S: set_Pr1261947904930325089at_nat,T3: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ S @ T3 ) @ T3 )
% 2.86/3.09 = T3 ) ).
% 2.86/3.09
% 2.86/3.09 % Int_Un_eq(2)
% 2.86/3.09 thf(fact_2735_Int__Un__eq_I2_J,axiom,
% 2.86/3.09 ! [S: set_nat,T3: set_nat] :
% 2.86/3.09 ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ S @ T3 ) @ T3 )
% 2.86/3.09 = T3 ) ).
% 2.86/3.09
% 2.86/3.09 % Int_Un_eq(2)
% 2.86/3.09 thf(fact_2736_Int__Un__eq_I2_J,axiom,
% 2.86/3.09 ! [S: set_Pr4329608150637261639at_nat,T3: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ S @ T3 ) @ T3 )
% 2.86/3.09 = T3 ) ).
% 2.86/3.09
% 2.86/3.09 % Int_Un_eq(2)
% 2.86/3.09 thf(fact_2737_Int__Un__eq_I1_J,axiom,
% 2.86/3.09 ! [S: set_Pr1261947904930325089at_nat,T3: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ S @ T3 ) @ S )
% 2.86/3.09 = S ) ).
% 2.86/3.09
% 2.86/3.09 % Int_Un_eq(1)
% 2.86/3.09 thf(fact_2738_Int__Un__eq_I1_J,axiom,
% 2.86/3.09 ! [S: set_nat,T3: set_nat] :
% 2.86/3.09 ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ S @ T3 ) @ S )
% 2.86/3.09 = S ) ).
% 2.86/3.09
% 2.86/3.09 % Int_Un_eq(1)
% 2.86/3.09 thf(fact_2739_Int__Un__eq_I1_J,axiom,
% 2.86/3.09 ! [S: set_Pr4329608150637261639at_nat,T3: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ S @ T3 ) @ S )
% 2.86/3.09 = S ) ).
% 2.86/3.09
% 2.86/3.09 % Int_Un_eq(1)
% 2.86/3.09 thf(fact_2740_Un__Int__eq_I4_J,axiom,
% 2.86/3.09 ! [T3: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( inf_in2572325071724192079at_nat @ T3 @ ( sup_su6327502436637775413at_nat @ S @ T3 ) )
% 2.86/3.09 = T3 ) ).
% 2.86/3.09
% 2.86/3.09 % Un_Int_eq(4)
% 2.86/3.09 thf(fact_2741_Un__Int__eq_I4_J,axiom,
% 2.86/3.09 ! [T3: set_nat,S: set_nat] :
% 2.86/3.09 ( ( inf_inf_set_nat @ T3 @ ( sup_sup_set_nat @ S @ T3 ) )
% 2.86/3.09 = T3 ) ).
% 2.86/3.09
% 2.86/3.09 % Un_Int_eq(4)
% 2.86/3.09 thf(fact_2742_Un__Int__eq_I4_J,axiom,
% 2.86/3.09 ! [T3: set_Pr4329608150637261639at_nat,S: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( inf_in7913087082777306421at_nat @ T3 @ ( sup_su5525570899277871387at_nat @ S @ T3 ) )
% 2.86/3.09 = T3 ) ).
% 2.86/3.09
% 2.86/3.09 % Un_Int_eq(4)
% 2.86/3.09 thf(fact_2743_Un__Int__eq_I3_J,axiom,
% 2.86/3.09 ! [S: set_Pr1261947904930325089at_nat,T3: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( inf_in2572325071724192079at_nat @ S @ ( sup_su6327502436637775413at_nat @ S @ T3 ) )
% 2.86/3.09 = S ) ).
% 2.86/3.09
% 2.86/3.09 % Un_Int_eq(3)
% 2.86/3.09 thf(fact_2744_Un__Int__eq_I3_J,axiom,
% 2.86/3.09 ! [S: set_nat,T3: set_nat] :
% 2.86/3.09 ( ( inf_inf_set_nat @ S @ ( sup_sup_set_nat @ S @ T3 ) )
% 2.86/3.09 = S ) ).
% 2.86/3.09
% 2.86/3.09 % Un_Int_eq(3)
% 2.86/3.09 thf(fact_2745_Un__Int__eq_I3_J,axiom,
% 2.86/3.09 ! [S: set_Pr4329608150637261639at_nat,T3: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( inf_in7913087082777306421at_nat @ S @ ( sup_su5525570899277871387at_nat @ S @ T3 ) )
% 2.86/3.09 = S ) ).
% 2.86/3.09
% 2.86/3.09 % Un_Int_eq(3)
% 2.86/3.09 thf(fact_2746_Un__Int__eq_I2_J,axiom,
% 2.86/3.09 ! [S: set_Pr1261947904930325089at_nat,T3: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ S @ T3 ) @ T3 )
% 2.86/3.09 = T3 ) ).
% 2.86/3.09
% 2.86/3.09 % Un_Int_eq(2)
% 2.86/3.09 thf(fact_2747_Un__Int__eq_I2_J,axiom,
% 2.86/3.09 ! [S: set_nat,T3: set_nat] :
% 2.86/3.09 ( ( inf_inf_set_nat @ ( sup_sup_set_nat @ S @ T3 ) @ T3 )
% 2.86/3.09 = T3 ) ).
% 2.86/3.09
% 2.86/3.09 % Un_Int_eq(2)
% 2.86/3.09 thf(fact_2748_Un__Int__eq_I2_J,axiom,
% 2.86/3.09 ! [S: set_Pr4329608150637261639at_nat,T3: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ S @ T3 ) @ T3 )
% 2.86/3.09 = T3 ) ).
% 2.86/3.09
% 2.86/3.09 % Un_Int_eq(2)
% 2.86/3.09 thf(fact_2749_Un__Int__eq_I1_J,axiom,
% 2.86/3.09 ! [S: set_Pr1261947904930325089at_nat,T3: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ S @ T3 ) @ S )
% 2.86/3.09 = S ) ).
% 2.86/3.09
% 2.86/3.09 % Un_Int_eq(1)
% 2.86/3.09 thf(fact_2750_Un__Int__eq_I1_J,axiom,
% 2.86/3.09 ! [S: set_nat,T3: set_nat] :
% 2.86/3.09 ( ( inf_inf_set_nat @ ( sup_sup_set_nat @ S @ T3 ) @ S )
% 2.86/3.09 = S ) ).
% 2.86/3.09
% 2.86/3.09 % Un_Int_eq(1)
% 2.86/3.09 thf(fact_2751_Un__Int__eq_I1_J,axiom,
% 2.86/3.09 ! [S: set_Pr4329608150637261639at_nat,T3: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ S @ T3 ) @ S )
% 2.86/3.09 = S ) ).
% 2.86/3.09
% 2.86/3.09 % Un_Int_eq(1)
% 2.86/3.09 thf(fact_2752_Un__Diff__cancel2,axiom,
% 2.86/3.09 ! [B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( sup_su5525570899277871387at_nat @ ( minus_3314409938677909166at_nat @ B @ A ) @ A )
% 2.86/3.09 = ( sup_su5525570899277871387at_nat @ B @ A ) ) ).
% 2.86/3.09
% 2.86/3.09 % Un_Diff_cancel2
% 2.86/3.09 thf(fact_2753_Un__Diff__cancel2,axiom,
% 2.86/3.09 ! [B: set_nat,A: set_nat] :
% 2.86/3.09 ( ( sup_sup_set_nat @ ( minus_minus_set_nat @ B @ A ) @ A )
% 2.86/3.09 = ( sup_sup_set_nat @ B @ A ) ) ).
% 2.86/3.09
% 2.86/3.09 % Un_Diff_cancel2
% 2.86/3.09 thf(fact_2754_Un__Diff__cancel,axiom,
% 2.86/3.09 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( sup_su5525570899277871387at_nat @ A @ ( minus_3314409938677909166at_nat @ B @ A ) )
% 2.86/3.09 = ( sup_su5525570899277871387at_nat @ A @ B ) ) ).
% 2.86/3.09
% 2.86/3.09 % Un_Diff_cancel
% 2.86/3.09 thf(fact_2755_Un__Diff__cancel,axiom,
% 2.86/3.09 ! [A: set_nat,B: set_nat] :
% 2.86/3.09 ( ( sup_sup_set_nat @ A @ ( minus_minus_set_nat @ B @ A ) )
% 2.86/3.09 = ( sup_sup_set_nat @ A @ B ) ) ).
% 2.86/3.09
% 2.86/3.09 % Un_Diff_cancel
% 2.86/3.09 thf(fact_2756_set__rev,axiom,
% 2.86/3.09 ! [Xs: list_int] :
% 2.86/3.09 ( ( set_int2 @ ( rev_int @ Xs ) )
% 2.86/3.09 = ( set_int2 @ Xs ) ) ).
% 2.86/3.09
% 2.86/3.09 % set_rev
% 2.86/3.09 thf(fact_2757_set__rev,axiom,
% 2.86/3.09 ! [Xs: list_nat] :
% 2.86/3.09 ( ( set_nat2 @ ( rev_nat @ Xs ) )
% 2.86/3.09 = ( set_nat2 @ Xs ) ) ).
% 2.86/3.09
% 2.86/3.09 % set_rev
% 2.86/3.09 thf(fact_2758_set__rev,axiom,
% 2.86/3.09 ! [Xs: list_P8527749157015355191n_assn] :
% 2.86/3.09 ( ( set_Pr1139785259514867910n_assn @ ( rev_Pr4855572775806611735n_assn @ Xs ) )
% 2.86/3.09 = ( set_Pr1139785259514867910n_assn @ Xs ) ) ).
% 2.86/3.09
% 2.86/3.09 % set_rev
% 2.86/3.09 thf(fact_2759_length__rev,axiom,
% 2.86/3.09 ! [Xs: list_c] :
% 2.86/3.09 ( ( size_size_list_c @ ( rev_c @ Xs ) )
% 2.86/3.09 = ( size_size_list_c @ Xs ) ) ).
% 2.86/3.09
% 2.86/3.09 % length_rev
% 2.86/3.09 thf(fact_2760_length__rev,axiom,
% 2.86/3.09 ! [Xs: list_d] :
% 2.86/3.09 ( ( size_size_list_d @ ( rev_d @ Xs ) )
% 2.86/3.09 = ( size_size_list_d @ Xs ) ) ).
% 2.86/3.09
% 2.86/3.09 % length_rev
% 2.86/3.09 thf(fact_2761_length__rev,axiom,
% 2.86/3.09 ! [Xs: list_nat] :
% 2.86/3.09 ( ( size_size_list_nat @ ( rev_nat @ Xs ) )
% 2.86/3.09 = ( size_size_list_nat @ Xs ) ) ).
% 2.86/3.09
% 2.86/3.09 % length_rev
% 2.86/3.09 thf(fact_2762_length__rev,axiom,
% 2.86/3.09 ! [Xs: list_int] :
% 2.86/3.09 ( ( size_size_list_int @ ( rev_int @ Xs ) )
% 2.86/3.09 = ( size_size_list_int @ Xs ) ) ).
% 2.86/3.09
% 2.86/3.09 % length_rev
% 2.86/3.09 thf(fact_2763_distinct__rev,axiom,
% 2.86/3.09 ! [Xs: list_int] :
% 2.86/3.09 ( ( distinct_int @ ( rev_int @ Xs ) )
% 2.86/3.09 = ( distinct_int @ Xs ) ) ).
% 2.86/3.09
% 2.86/3.09 % distinct_rev
% 2.86/3.09 thf(fact_2764_distinct__rev,axiom,
% 2.86/3.09 ! [Xs: list_nat] :
% 2.86/3.09 ( ( distinct_nat @ ( rev_nat @ Xs ) )
% 2.86/3.09 = ( distinct_nat @ Xs ) ) ).
% 2.86/3.09
% 2.86/3.09 % distinct_rev
% 2.86/3.09 thf(fact_2765_set__rotate1,axiom,
% 2.86/3.09 ! [Xs: list_int] :
% 2.86/3.09 ( ( set_int2 @ ( rotate1_int @ Xs ) )
% 2.86/3.09 = ( set_int2 @ Xs ) ) ).
% 2.86/3.09
% 2.86/3.09 % set_rotate1
% 2.86/3.09 thf(fact_2766_set__rotate1,axiom,
% 2.86/3.09 ! [Xs: list_nat] :
% 2.86/3.09 ( ( set_nat2 @ ( rotate1_nat @ Xs ) )
% 2.86/3.09 = ( set_nat2 @ Xs ) ) ).
% 2.86/3.09
% 2.86/3.09 % set_rotate1
% 2.86/3.09 thf(fact_2767_set__rotate1,axiom,
% 2.86/3.09 ! [Xs: list_P8527749157015355191n_assn] :
% 2.86/3.09 ( ( set_Pr1139785259514867910n_assn @ ( rotate328796349445179396n_assn @ Xs ) )
% 2.86/3.09 = ( set_Pr1139785259514867910n_assn @ Xs ) ) ).
% 2.86/3.09
% 2.86/3.09 % set_rotate1
% 2.86/3.09 thf(fact_2768_length__rotate1,axiom,
% 2.86/3.09 ! [Xs: list_c] :
% 2.86/3.09 ( ( size_size_list_c @ ( rotate1_c @ Xs ) )
% 2.86/3.09 = ( size_size_list_c @ Xs ) ) ).
% 2.86/3.09
% 2.86/3.09 % length_rotate1
% 2.86/3.09 thf(fact_2769_length__rotate1,axiom,
% 2.86/3.09 ! [Xs: list_d] :
% 2.86/3.09 ( ( size_size_list_d @ ( rotate1_d @ Xs ) )
% 2.86/3.09 = ( size_size_list_d @ Xs ) ) ).
% 2.86/3.09
% 2.86/3.09 % length_rotate1
% 2.86/3.09 thf(fact_2770_length__rotate1,axiom,
% 2.86/3.09 ! [Xs: list_nat] :
% 2.86/3.09 ( ( size_size_list_nat @ ( rotate1_nat @ Xs ) )
% 2.86/3.09 = ( size_size_list_nat @ Xs ) ) ).
% 2.86/3.09
% 2.86/3.09 % length_rotate1
% 2.86/3.09 thf(fact_2771_length__rotate1,axiom,
% 2.86/3.09 ! [Xs: list_int] :
% 2.86/3.09 ( ( size_size_list_int @ ( rotate1_int @ Xs ) )
% 2.86/3.09 = ( size_size_list_int @ Xs ) ) ).
% 2.86/3.09
% 2.86/3.09 % length_rotate1
% 2.86/3.09 thf(fact_2772_distinct1__rotate,axiom,
% 2.86/3.09 ! [Xs: list_int] :
% 2.86/3.09 ( ( distinct_int @ ( rotate1_int @ Xs ) )
% 2.86/3.09 = ( distinct_int @ Xs ) ) ).
% 2.86/3.09
% 2.86/3.09 % distinct1_rotate
% 2.86/3.09 thf(fact_2773_distinct1__rotate,axiom,
% 2.86/3.09 ! [Xs: list_nat] :
% 2.86/3.09 ( ( distinct_nat @ ( rotate1_nat @ Xs ) )
% 2.86/3.09 = ( distinct_nat @ Xs ) ) ).
% 2.86/3.09
% 2.86/3.09 % distinct1_rotate
% 2.86/3.09 thf(fact_2774_list__ex__rev,axiom,
% 2.86/3.09 ! [P: int > $o,Xs: list_int] :
% 2.86/3.09 ( ( list_ex_int @ P @ ( rev_int @ Xs ) )
% 2.86/3.09 = ( list_ex_int @ P @ Xs ) ) ).
% 2.86/3.09
% 2.86/3.09 % list_ex_rev
% 2.86/3.09 thf(fact_2775_list__ex__rev,axiom,
% 2.86/3.09 ! [P: nat > $o,Xs: list_nat] :
% 2.86/3.09 ( ( list_ex_nat @ P @ ( rev_nat @ Xs ) )
% 2.86/3.09 = ( list_ex_nat @ P @ Xs ) ) ).
% 2.86/3.09
% 2.86/3.09 % list_ex_rev
% 2.86/3.09 thf(fact_2776_set__union,axiom,
% 2.86/3.09 ! [Xs: list_int,Ys: list_int] :
% 2.86/3.09 ( ( set_int2 @ ( union_int @ Xs @ Ys ) )
% 2.86/3.09 = ( sup_sup_set_int @ ( set_int2 @ Xs ) @ ( set_int2 @ Ys ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % set_union
% 2.86/3.09 thf(fact_2777_set__union,axiom,
% 2.86/3.09 ! [Xs: list_P8527749157015355191n_assn,Ys: list_P8527749157015355191n_assn] :
% 2.86/3.09 ( ( set_Pr1139785259514867910n_assn @ ( union_944050417204428971n_assn @ Xs @ Ys ) )
% 2.86/3.09 = ( sup_su1735938885662425829n_assn @ ( set_Pr1139785259514867910n_assn @ Xs ) @ ( set_Pr1139785259514867910n_assn @ Ys ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % set_union
% 2.86/3.09 thf(fact_2778_set__union,axiom,
% 2.86/3.09 ! [Xs: list_nat,Ys: list_nat] :
% 2.86/3.09 ( ( set_nat2 @ ( union_nat @ Xs @ Ys ) )
% 2.86/3.09 = ( sup_sup_set_nat @ ( set_nat2 @ Xs ) @ ( set_nat2 @ Ys ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % set_union
% 2.86/3.09 thf(fact_2779_set__union,axiom,
% 2.86/3.09 ! [Xs: list_P5464809261938338413at_nat,Ys: list_P5464809261938338413at_nat] :
% 2.86/3.09 ( ( set_Pr3765526544606949372at_nat @ ( union_4462254032241401953at_nat @ Xs @ Ys ) )
% 2.86/3.09 = ( sup_su5525570899277871387at_nat @ ( set_Pr3765526544606949372at_nat @ Xs ) @ ( set_Pr3765526544606949372at_nat @ Ys ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % set_union
% 2.86/3.09 thf(fact_2780_length__butlast,axiom,
% 2.86/3.09 ! [Xs: list_c] :
% 2.86/3.09 ( ( size_size_list_c @ ( butlast_c @ Xs ) )
% 2.86/3.09 = ( minus_minus_nat @ ( size_size_list_c @ Xs ) @ one_one_nat ) ) ).
% 2.86/3.09
% 2.86/3.09 % length_butlast
% 2.86/3.09 thf(fact_2781_length__butlast,axiom,
% 2.86/3.09 ! [Xs: list_d] :
% 2.86/3.09 ( ( size_size_list_d @ ( butlast_d @ Xs ) )
% 2.86/3.09 = ( minus_minus_nat @ ( size_size_list_d @ Xs ) @ one_one_nat ) ) ).
% 2.86/3.09
% 2.86/3.09 % length_butlast
% 2.86/3.09 thf(fact_2782_length__butlast,axiom,
% 2.86/3.09 ! [Xs: list_nat] :
% 2.86/3.09 ( ( size_size_list_nat @ ( butlast_nat @ Xs ) )
% 2.86/3.09 = ( minus_minus_nat @ ( size_size_list_nat @ Xs ) @ one_one_nat ) ) ).
% 2.86/3.09
% 2.86/3.09 % length_butlast
% 2.86/3.09 thf(fact_2783_length__butlast,axiom,
% 2.86/3.09 ! [Xs: list_int] :
% 2.86/3.09 ( ( size_size_list_int @ ( butlast_int @ Xs ) )
% 2.86/3.09 = ( minus_minus_nat @ ( size_size_list_int @ Xs ) @ one_one_nat ) ) ).
% 2.86/3.09
% 2.86/3.09 % length_butlast
% 2.86/3.09 thf(fact_2784_IntE,axiom,
% 2.86/3.09 ! [C: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( member8757157785044589968at_nat @ C @ ( inf_in7913087082777306421at_nat @ A @ B ) )
% 2.86/3.09 => ~ ( ( member8757157785044589968at_nat @ C @ A )
% 2.86/3.09 => ~ ( member8757157785044589968at_nat @ C @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % IntE
% 2.86/3.09 thf(fact_2785_IntE,axiom,
% 2.86/3.09 ! [C: int,A: set_int,B: set_int] :
% 2.86/3.09 ( ( member_int @ C @ ( inf_inf_set_int @ A @ B ) )
% 2.86/3.09 => ~ ( ( member_int @ C @ A )
% 2.86/3.09 => ~ ( member_int @ C @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % IntE
% 2.86/3.09 thf(fact_2786_IntE,axiom,
% 2.86/3.09 ! [C: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o] :
% 2.86/3.09 ( ( member6576561426505652726_nat_o @ C @ ( inf_in1906310914598751387_nat_o @ A @ B ) )
% 2.86/3.09 => ~ ( ( member6576561426505652726_nat_o @ C @ A )
% 2.86/3.09 => ~ ( member6576561426505652726_nat_o @ C @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % IntE
% 2.86/3.09 thf(fact_2787_IntE,axiom,
% 2.86/3.09 ! [C: nat,A: set_nat,B: set_nat] :
% 2.86/3.09 ( ( member_nat @ C @ ( inf_inf_set_nat @ A @ B ) )
% 2.86/3.09 => ~ ( ( member_nat @ C @ A )
% 2.86/3.09 => ~ ( member_nat @ C @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % IntE
% 2.86/3.09 thf(fact_2788_IntE,axiom,
% 2.86/3.09 ! [C: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( member8440522571783428010at_nat @ C @ ( inf_in2572325071724192079at_nat @ A @ B ) )
% 2.86/3.09 => ~ ( ( member8440522571783428010at_nat @ C @ A )
% 2.86/3.09 => ~ ( member8440522571783428010at_nat @ C @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % IntE
% 2.86/3.09 thf(fact_2789_IntD1,axiom,
% 2.86/3.09 ! [C: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( member8757157785044589968at_nat @ C @ ( inf_in7913087082777306421at_nat @ A @ B ) )
% 2.86/3.09 => ( member8757157785044589968at_nat @ C @ A ) ) ).
% 2.86/3.09
% 2.86/3.09 % IntD1
% 2.86/3.09 thf(fact_2790_IntD1,axiom,
% 2.86/3.09 ! [C: int,A: set_int,B: set_int] :
% 2.86/3.09 ( ( member_int @ C @ ( inf_inf_set_int @ A @ B ) )
% 2.86/3.09 => ( member_int @ C @ A ) ) ).
% 2.86/3.09
% 2.86/3.09 % IntD1
% 2.86/3.09 thf(fact_2791_IntD1,axiom,
% 2.86/3.09 ! [C: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o] :
% 2.86/3.09 ( ( member6576561426505652726_nat_o @ C @ ( inf_in1906310914598751387_nat_o @ A @ B ) )
% 2.86/3.09 => ( member6576561426505652726_nat_o @ C @ A ) ) ).
% 2.86/3.09
% 2.86/3.09 % IntD1
% 2.86/3.09 thf(fact_2792_IntD1,axiom,
% 2.86/3.09 ! [C: nat,A: set_nat,B: set_nat] :
% 2.86/3.09 ( ( member_nat @ C @ ( inf_inf_set_nat @ A @ B ) )
% 2.86/3.09 => ( member_nat @ C @ A ) ) ).
% 2.86/3.09
% 2.86/3.09 % IntD1
% 2.86/3.09 thf(fact_2793_IntD1,axiom,
% 2.86/3.09 ! [C: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( member8440522571783428010at_nat @ C @ ( inf_in2572325071724192079at_nat @ A @ B ) )
% 2.86/3.09 => ( member8440522571783428010at_nat @ C @ A ) ) ).
% 2.86/3.09
% 2.86/3.09 % IntD1
% 2.86/3.09 thf(fact_2794_IntD2,axiom,
% 2.86/3.09 ! [C: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( member8757157785044589968at_nat @ C @ ( inf_in7913087082777306421at_nat @ A @ B ) )
% 2.86/3.09 => ( member8757157785044589968at_nat @ C @ B ) ) ).
% 2.86/3.09
% 2.86/3.09 % IntD2
% 2.86/3.09 thf(fact_2795_IntD2,axiom,
% 2.86/3.09 ! [C: int,A: set_int,B: set_int] :
% 2.86/3.09 ( ( member_int @ C @ ( inf_inf_set_int @ A @ B ) )
% 2.86/3.09 => ( member_int @ C @ B ) ) ).
% 2.86/3.09
% 2.86/3.09 % IntD2
% 2.86/3.09 thf(fact_2796_IntD2,axiom,
% 2.86/3.09 ! [C: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o] :
% 2.86/3.09 ( ( member6576561426505652726_nat_o @ C @ ( inf_in1906310914598751387_nat_o @ A @ B ) )
% 2.86/3.09 => ( member6576561426505652726_nat_o @ C @ B ) ) ).
% 2.86/3.09
% 2.86/3.09 % IntD2
% 2.86/3.09 thf(fact_2797_IntD2,axiom,
% 2.86/3.09 ! [C: nat,A: set_nat,B: set_nat] :
% 2.86/3.09 ( ( member_nat @ C @ ( inf_inf_set_nat @ A @ B ) )
% 2.86/3.09 => ( member_nat @ C @ B ) ) ).
% 2.86/3.09
% 2.86/3.09 % IntD2
% 2.86/3.09 thf(fact_2798_IntD2,axiom,
% 2.86/3.09 ! [C: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( member8440522571783428010at_nat @ C @ ( inf_in2572325071724192079at_nat @ A @ B ) )
% 2.86/3.09 => ( member8440522571783428010at_nat @ C @ B ) ) ).
% 2.86/3.09
% 2.86/3.09 % IntD2
% 2.86/3.09 thf(fact_2799_Int__assoc,axiom,
% 2.86/3.09 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 2.86/3.09 ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ A @ B ) @ C2 )
% 2.86/3.09 = ( inf_inf_set_nat @ A @ ( inf_inf_set_nat @ B @ C2 ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Int_assoc
% 2.86/3.09 thf(fact_2800_Int__assoc,axiom,
% 2.86/3.09 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ C2 )
% 2.86/3.09 = ( inf_in2572325071724192079at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C2 ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Int_assoc
% 2.86/3.09 thf(fact_2801_Int__absorb,axiom,
% 2.86/3.09 ! [A: set_nat] :
% 2.86/3.09 ( ( inf_inf_set_nat @ A @ A )
% 2.86/3.09 = A ) ).
% 2.86/3.09
% 2.86/3.09 % Int_absorb
% 2.86/3.09 thf(fact_2802_Int__absorb,axiom,
% 2.86/3.09 ! [A: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( inf_in2572325071724192079at_nat @ A @ A )
% 2.86/3.09 = A ) ).
% 2.86/3.09
% 2.86/3.09 % Int_absorb
% 2.86/3.09 thf(fact_2803_Int__commute,axiom,
% 2.86/3.09 ( inf_inf_set_nat
% 2.86/3.09 = ( ^ [A5: set_nat,B7: set_nat] : ( inf_inf_set_nat @ B7 @ A5 ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Int_commute
% 2.86/3.09 thf(fact_2804_Int__commute,axiom,
% 2.86/3.09 ( inf_in2572325071724192079at_nat
% 2.86/3.09 = ( ^ [A5: set_Pr1261947904930325089at_nat,B7: set_Pr1261947904930325089at_nat] : ( inf_in2572325071724192079at_nat @ B7 @ A5 ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Int_commute
% 2.86/3.09 thf(fact_2805_Un__Int__crazy,axiom,
% 2.86/3.09 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( sup_su6327502436637775413at_nat @ ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ ( inf_in2572325071724192079at_nat @ B @ C2 ) ) @ ( inf_in2572325071724192079at_nat @ C2 @ A ) )
% 2.86/3.09 = ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ A @ B ) @ ( sup_su6327502436637775413at_nat @ B @ C2 ) ) @ ( sup_su6327502436637775413at_nat @ C2 @ A ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Un_Int_crazy
% 2.86/3.09 thf(fact_2806_Un__Int__crazy,axiom,
% 2.86/3.09 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 2.86/3.09 ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ ( inf_inf_set_nat @ A @ B ) @ ( inf_inf_set_nat @ B @ C2 ) ) @ ( inf_inf_set_nat @ C2 @ A ) )
% 2.86/3.09 = ( inf_inf_set_nat @ ( inf_inf_set_nat @ ( sup_sup_set_nat @ A @ B ) @ ( sup_sup_set_nat @ B @ C2 ) ) @ ( sup_sup_set_nat @ C2 @ A ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Un_Int_crazy
% 2.86/3.09 thf(fact_2807_Un__Int__crazy,axiom,
% 2.86/3.09 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( sup_su5525570899277871387at_nat @ ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ A @ B ) @ ( inf_in7913087082777306421at_nat @ B @ C2 ) ) @ ( inf_in7913087082777306421at_nat @ C2 @ A ) )
% 2.86/3.09 = ( inf_in7913087082777306421at_nat @ ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ A @ B ) @ ( sup_su5525570899277871387at_nat @ B @ C2 ) ) @ ( sup_su5525570899277871387at_nat @ C2 @ A ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Un_Int_crazy
% 2.86/3.09 thf(fact_2808_Int__Un__distrib,axiom,
% 2.86/3.09 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( inf_in2572325071724192079at_nat @ A @ ( sup_su6327502436637775413at_nat @ B @ C2 ) )
% 2.86/3.09 = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ ( inf_in2572325071724192079at_nat @ A @ C2 ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Int_Un_distrib
% 2.86/3.09 thf(fact_2809_Int__Un__distrib,axiom,
% 2.86/3.09 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 2.86/3.09 ( ( inf_inf_set_nat @ A @ ( sup_sup_set_nat @ B @ C2 ) )
% 2.86/3.09 = ( sup_sup_set_nat @ ( inf_inf_set_nat @ A @ B ) @ ( inf_inf_set_nat @ A @ C2 ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Int_Un_distrib
% 2.86/3.09 thf(fact_2810_Int__Un__distrib,axiom,
% 2.86/3.09 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( inf_in7913087082777306421at_nat @ A @ ( sup_su5525570899277871387at_nat @ B @ C2 ) )
% 2.86/3.09 = ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ A @ B ) @ ( inf_in7913087082777306421at_nat @ A @ C2 ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Int_Un_distrib
% 2.86/3.09 thf(fact_2811_Un__Int__distrib,axiom,
% 2.86/3.09 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( sup_su6327502436637775413at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C2 ) )
% 2.86/3.09 = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ A @ B ) @ ( sup_su6327502436637775413at_nat @ A @ C2 ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Un_Int_distrib
% 2.86/3.09 thf(fact_2812_Un__Int__distrib,axiom,
% 2.86/3.09 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 2.86/3.09 ( ( sup_sup_set_nat @ A @ ( inf_inf_set_nat @ B @ C2 ) )
% 2.86/3.09 = ( inf_inf_set_nat @ ( sup_sup_set_nat @ A @ B ) @ ( sup_sup_set_nat @ A @ C2 ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Un_Int_distrib
% 2.86/3.09 thf(fact_2813_Un__Int__distrib,axiom,
% 2.86/3.09 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( sup_su5525570899277871387at_nat @ A @ ( inf_in7913087082777306421at_nat @ B @ C2 ) )
% 2.86/3.09 = ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ A @ B ) @ ( sup_su5525570899277871387at_nat @ A @ C2 ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Un_Int_distrib
% 2.86/3.09 thf(fact_2814_Int__Un__distrib2,axiom,
% 2.86/3.09 ! [B: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ B @ C2 ) @ A )
% 2.86/3.09 = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ B @ A ) @ ( inf_in2572325071724192079at_nat @ C2 @ A ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Int_Un_distrib2
% 2.86/3.09 thf(fact_2815_Int__Un__distrib2,axiom,
% 2.86/3.09 ! [B: set_nat,C2: set_nat,A: set_nat] :
% 2.86/3.09 ( ( inf_inf_set_nat @ ( sup_sup_set_nat @ B @ C2 ) @ A )
% 2.86/3.09 = ( sup_sup_set_nat @ ( inf_inf_set_nat @ B @ A ) @ ( inf_inf_set_nat @ C2 @ A ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Int_Un_distrib2
% 2.86/3.09 thf(fact_2816_Int__Un__distrib2,axiom,
% 2.86/3.09 ! [B: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ B @ C2 ) @ A )
% 2.86/3.09 = ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ B @ A ) @ ( inf_in7913087082777306421at_nat @ C2 @ A ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Int_Un_distrib2
% 2.86/3.09 thf(fact_2817_Int__left__absorb,axiom,
% 2.86/3.09 ! [A: set_nat,B: set_nat] :
% 2.86/3.09 ( ( inf_inf_set_nat @ A @ ( inf_inf_set_nat @ A @ B ) )
% 2.86/3.09 = ( inf_inf_set_nat @ A @ B ) ) ).
% 2.86/3.09
% 2.86/3.09 % Int_left_absorb
% 2.86/3.09 thf(fact_2818_Int__left__absorb,axiom,
% 2.86/3.09 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( inf_in2572325071724192079at_nat @ A @ ( inf_in2572325071724192079at_nat @ A @ B ) )
% 2.86/3.09 = ( inf_in2572325071724192079at_nat @ A @ B ) ) ).
% 2.86/3.09
% 2.86/3.09 % Int_left_absorb
% 2.86/3.09 thf(fact_2819_Un__Int__distrib2,axiom,
% 2.86/3.09 ! [B: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ B @ C2 ) @ A )
% 2.86/3.09 = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ B @ A ) @ ( sup_su6327502436637775413at_nat @ C2 @ A ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Un_Int_distrib2
% 2.86/3.09 thf(fact_2820_Un__Int__distrib2,axiom,
% 2.86/3.09 ! [B: set_nat,C2: set_nat,A: set_nat] :
% 2.86/3.09 ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ B @ C2 ) @ A )
% 2.86/3.09 = ( inf_inf_set_nat @ ( sup_sup_set_nat @ B @ A ) @ ( sup_sup_set_nat @ C2 @ A ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Un_Int_distrib2
% 2.86/3.09 thf(fact_2821_Un__Int__distrib2,axiom,
% 2.86/3.09 ! [B: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ B @ C2 ) @ A )
% 2.86/3.09 = ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ B @ A ) @ ( sup_su5525570899277871387at_nat @ C2 @ A ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Un_Int_distrib2
% 2.86/3.09 thf(fact_2822_Int__left__commute,axiom,
% 2.86/3.09 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 2.86/3.09 ( ( inf_inf_set_nat @ A @ ( inf_inf_set_nat @ B @ C2 ) )
% 2.86/3.09 = ( inf_inf_set_nat @ B @ ( inf_inf_set_nat @ A @ C2 ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Int_left_commute
% 2.86/3.09 thf(fact_2823_Int__left__commute,axiom,
% 2.86/3.09 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( inf_in2572325071724192079at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C2 ) )
% 2.86/3.09 = ( inf_in2572325071724192079at_nat @ B @ ( inf_in2572325071724192079at_nat @ A @ C2 ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Int_left_commute
% 2.86/3.09 thf(fact_2824_less__assn__def,axiom,
% 2.86/3.09 ( ord_less_assn
% 2.86/3.09 = ( ^ [A3: assn,B3: assn] :
% 2.86/3.09 ( ( ord_less_eq_assn @ A3 @ B3 )
% 2.86/3.09 & ( A3 != B3 ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % less_assn_def
% 2.86/3.09 thf(fact_2825_UnE,axiom,
% 2.86/3.09 ! [C: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( member8440522571783428010at_nat @ C @ ( sup_su6327502436637775413at_nat @ A @ B ) )
% 2.86/3.09 => ( ~ ( member8440522571783428010at_nat @ C @ A )
% 2.86/3.09 => ( member8440522571783428010at_nat @ C @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % UnE
% 2.86/3.09 thf(fact_2826_UnE,axiom,
% 2.86/3.09 ! [C: int,A: set_int,B: set_int] :
% 2.86/3.09 ( ( member_int @ C @ ( sup_sup_set_int @ A @ B ) )
% 2.86/3.09 => ( ~ ( member_int @ C @ A )
% 2.86/3.09 => ( member_int @ C @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % UnE
% 2.86/3.09 thf(fact_2827_UnE,axiom,
% 2.86/3.09 ! [C: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o] :
% 2.86/3.09 ( ( member6576561426505652726_nat_o @ C @ ( sup_su5209123915105501825_nat_o @ A @ B ) )
% 2.86/3.09 => ( ~ ( member6576561426505652726_nat_o @ C @ A )
% 2.86/3.09 => ( member6576561426505652726_nat_o @ C @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % UnE
% 2.86/3.09 thf(fact_2828_UnE,axiom,
% 2.86/3.09 ! [C: nat,A: set_nat,B: set_nat] :
% 2.86/3.09 ( ( member_nat @ C @ ( sup_sup_set_nat @ A @ B ) )
% 2.86/3.09 => ( ~ ( member_nat @ C @ A )
% 2.86/3.09 => ( member_nat @ C @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % UnE
% 2.86/3.09 thf(fact_2829_UnE,axiom,
% 2.86/3.09 ! [C: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( member8757157785044589968at_nat @ C @ ( sup_su5525570899277871387at_nat @ A @ B ) )
% 2.86/3.09 => ( ~ ( member8757157785044589968at_nat @ C @ A )
% 2.86/3.09 => ( member8757157785044589968at_nat @ C @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % UnE
% 2.86/3.09 thf(fact_2830_UnI1,axiom,
% 2.86/3.09 ! [C: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( member8440522571783428010at_nat @ C @ A )
% 2.86/3.09 => ( member8440522571783428010at_nat @ C @ ( sup_su6327502436637775413at_nat @ A @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % UnI1
% 2.86/3.09 thf(fact_2831_UnI1,axiom,
% 2.86/3.09 ! [C: int,A: set_int,B: set_int] :
% 2.86/3.09 ( ( member_int @ C @ A )
% 2.86/3.09 => ( member_int @ C @ ( sup_sup_set_int @ A @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % UnI1
% 2.86/3.09 thf(fact_2832_UnI1,axiom,
% 2.86/3.09 ! [C: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o] :
% 2.86/3.09 ( ( member6576561426505652726_nat_o @ C @ A )
% 2.86/3.09 => ( member6576561426505652726_nat_o @ C @ ( sup_su5209123915105501825_nat_o @ A @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % UnI1
% 2.86/3.09 thf(fact_2833_UnI1,axiom,
% 2.86/3.09 ! [C: nat,A: set_nat,B: set_nat] :
% 2.86/3.09 ( ( member_nat @ C @ A )
% 2.86/3.09 => ( member_nat @ C @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % UnI1
% 2.86/3.09 thf(fact_2834_UnI1,axiom,
% 2.86/3.09 ! [C: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( member8757157785044589968at_nat @ C @ A )
% 2.86/3.09 => ( member8757157785044589968at_nat @ C @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % UnI1
% 2.86/3.09 thf(fact_2835_UnI2,axiom,
% 2.86/3.09 ! [C: product_prod_nat_nat,B: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 2.86/3.09 ( ( member8440522571783428010at_nat @ C @ B )
% 2.86/3.09 => ( member8440522571783428010at_nat @ C @ ( sup_su6327502436637775413at_nat @ A @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % UnI2
% 2.86/3.09 thf(fact_2836_UnI2,axiom,
% 2.86/3.09 ! [C: int,B: set_int,A: set_int] :
% 2.86/3.09 ( ( member_int @ C @ B )
% 2.86/3.09 => ( member_int @ C @ ( sup_sup_set_int @ A @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % UnI2
% 2.86/3.09 thf(fact_2837_UnI2,axiom,
% 2.86/3.09 ! [C: produc3658429121746597890et_nat > $o,B: set_Pr4532377907799695533_nat_o,A: set_Pr4532377907799695533_nat_o] :
% 2.86/3.09 ( ( member6576561426505652726_nat_o @ C @ B )
% 2.86/3.09 => ( member6576561426505652726_nat_o @ C @ ( sup_su5209123915105501825_nat_o @ A @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % UnI2
% 2.86/3.09 thf(fact_2838_UnI2,axiom,
% 2.86/3.09 ! [C: nat,B: set_nat,A: set_nat] :
% 2.86/3.09 ( ( member_nat @ C @ B )
% 2.86/3.09 => ( member_nat @ C @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % UnI2
% 2.86/3.09 thf(fact_2839_UnI2,axiom,
% 2.86/3.09 ! [C: produc3843707927480180839at_nat,B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( member8757157785044589968at_nat @ C @ B )
% 2.86/3.09 => ( member8757157785044589968at_nat @ C @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % UnI2
% 2.86/3.09 thf(fact_2840_bex__Un,axiom,
% 2.86/3.09 ! [A: set_nat,B: set_nat,P: nat > $o] :
% 2.86/3.09 ( ( ? [X2: nat] :
% 2.86/3.09 ( ( member_nat @ X2 @ ( sup_sup_set_nat @ A @ B ) )
% 2.86/3.09 & ( P @ X2 ) ) )
% 2.86/3.09 = ( ? [X2: nat] :
% 2.86/3.09 ( ( member_nat @ X2 @ A )
% 2.86/3.09 & ( P @ X2 ) )
% 2.86/3.09 | ? [X2: nat] :
% 2.86/3.09 ( ( member_nat @ X2 @ B )
% 2.86/3.09 & ( P @ X2 ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % bex_Un
% 2.86/3.09 thf(fact_2841_bex__Un,axiom,
% 2.86/3.09 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,P: produc3843707927480180839at_nat > $o] :
% 2.86/3.09 ( ( ? [X2: produc3843707927480180839at_nat] :
% 2.86/3.09 ( ( member8757157785044589968at_nat @ X2 @ ( sup_su5525570899277871387at_nat @ A @ B ) )
% 2.86/3.09 & ( P @ X2 ) ) )
% 2.86/3.09 = ( ? [X2: produc3843707927480180839at_nat] :
% 2.86/3.09 ( ( member8757157785044589968at_nat @ X2 @ A )
% 2.86/3.09 & ( P @ X2 ) )
% 2.86/3.09 | ? [X2: produc3843707927480180839at_nat] :
% 2.86/3.09 ( ( member8757157785044589968at_nat @ X2 @ B )
% 2.86/3.09 & ( P @ X2 ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % bex_Un
% 2.86/3.09 thf(fact_2842_ball__Un,axiom,
% 2.86/3.09 ! [A: set_nat,B: set_nat,P: nat > $o] :
% 2.86/3.09 ( ( ! [X2: nat] :
% 2.86/3.09 ( ( member_nat @ X2 @ ( sup_sup_set_nat @ A @ B ) )
% 2.86/3.09 => ( P @ X2 ) ) )
% 2.86/3.09 = ( ! [X2: nat] :
% 2.86/3.09 ( ( member_nat @ X2 @ A )
% 2.86/3.09 => ( P @ X2 ) )
% 2.86/3.09 & ! [X2: nat] :
% 2.86/3.09 ( ( member_nat @ X2 @ B )
% 2.86/3.09 => ( P @ X2 ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % ball_Un
% 2.86/3.09 thf(fact_2843_ball__Un,axiom,
% 2.86/3.09 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,P: produc3843707927480180839at_nat > $o] :
% 2.86/3.09 ( ( ! [X2: produc3843707927480180839at_nat] :
% 2.86/3.09 ( ( member8757157785044589968at_nat @ X2 @ ( sup_su5525570899277871387at_nat @ A @ B ) )
% 2.86/3.09 => ( P @ X2 ) ) )
% 2.86/3.09 = ( ! [X2: produc3843707927480180839at_nat] :
% 2.86/3.09 ( ( member8757157785044589968at_nat @ X2 @ A )
% 2.86/3.09 => ( P @ X2 ) )
% 2.86/3.09 & ! [X2: produc3843707927480180839at_nat] :
% 2.86/3.09 ( ( member8757157785044589968at_nat @ X2 @ B )
% 2.86/3.09 => ( P @ X2 ) ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % ball_Un
% 2.86/3.09 thf(fact_2844_Un__assoc,axiom,
% 2.86/3.09 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 2.86/3.09 ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ A @ B ) @ C2 )
% 2.86/3.09 = ( sup_sup_set_nat @ A @ ( sup_sup_set_nat @ B @ C2 ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Un_assoc
% 2.86/3.09 thf(fact_2845_Un__assoc,axiom,
% 2.86/3.09 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 2.86/3.09 ( ( sup_su5525570899277871387at_nat @ ( sup_su5525570899277871387at_nat @ A @ B ) @ C2 )
% 2.86/3.09 = ( sup_su5525570899277871387at_nat @ A @ ( sup_su5525570899277871387at_nat @ B @ C2 ) ) ) ).
% 2.86/3.09
% 2.86/3.09 % Un_assoc
% 2.86/3.09 thf(fact_2846_Un__absorb,axiom,
% 2.86/3.09 ! [A: set_nat] :
% 2.86/3.09 ( ( sup_sup_set_nat @ A @ A )
% 2.86/3.09 = A ) ).
% 2.86/3.09
% 2.86/3.09 % Un_absorb
% 2.86/3.10 thf(fact_2847_Un__absorb,axiom,
% 2.86/3.10 ! [A: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( sup_su5525570899277871387at_nat @ A @ A )
% 2.86/3.10 = A ) ).
% 2.86/3.10
% 2.86/3.10 % Un_absorb
% 2.86/3.10 thf(fact_2848_Un__commute,axiom,
% 2.86/3.10 ( sup_sup_set_nat
% 2.86/3.10 = ( ^ [A5: set_nat,B7: set_nat] : ( sup_sup_set_nat @ B7 @ A5 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % Un_commute
% 2.86/3.10 thf(fact_2849_Un__commute,axiom,
% 2.86/3.10 ( sup_su5525570899277871387at_nat
% 2.86/3.10 = ( ^ [A5: set_Pr4329608150637261639at_nat,B7: set_Pr4329608150637261639at_nat] : ( sup_su5525570899277871387at_nat @ B7 @ A5 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % Un_commute
% 2.86/3.10 thf(fact_2850_Un__left__absorb,axiom,
% 2.86/3.10 ! [A: set_nat,B: set_nat] :
% 2.86/3.10 ( ( sup_sup_set_nat @ A @ ( sup_sup_set_nat @ A @ B ) )
% 2.86/3.10 = ( sup_sup_set_nat @ A @ B ) ) ).
% 2.86/3.10
% 2.86/3.10 % Un_left_absorb
% 2.86/3.10 thf(fact_2851_Un__left__absorb,axiom,
% 2.86/3.10 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( sup_su5525570899277871387at_nat @ A @ ( sup_su5525570899277871387at_nat @ A @ B ) )
% 2.86/3.10 = ( sup_su5525570899277871387at_nat @ A @ B ) ) ).
% 2.86/3.10
% 2.86/3.10 % Un_left_absorb
% 2.86/3.10 thf(fact_2852_Un__left__commute,axiom,
% 2.86/3.10 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 2.86/3.10 ( ( sup_sup_set_nat @ A @ ( sup_sup_set_nat @ B @ C2 ) )
% 2.86/3.10 = ( sup_sup_set_nat @ B @ ( sup_sup_set_nat @ A @ C2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % Un_left_commute
% 2.86/3.10 thf(fact_2853_Un__left__commute,axiom,
% 2.86/3.10 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( sup_su5525570899277871387at_nat @ A @ ( sup_su5525570899277871387at_nat @ B @ C2 ) )
% 2.86/3.10 = ( sup_su5525570899277871387at_nat @ B @ ( sup_su5525570899277871387at_nat @ A @ C2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % Un_left_commute
% 2.86/3.10 thf(fact_2854_inf__sup__aci_I8_J,axiom,
% 2.86/3.10 ! [X: set_nat,Y: set_nat] :
% 2.86/3.10 ( ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ X @ Y ) )
% 2.86/3.10 = ( sup_sup_set_nat @ X @ Y ) ) ).
% 2.86/3.10
% 2.86/3.10 % inf_sup_aci(8)
% 2.86/3.10 thf(fact_2855_inf__sup__aci_I8_J,axiom,
% 2.86/3.10 ! [X: assn,Y: assn] :
% 2.86/3.10 ( ( sup_sup_assn @ X @ ( sup_sup_assn @ X @ Y ) )
% 2.86/3.10 = ( sup_sup_assn @ X @ Y ) ) ).
% 2.86/3.10
% 2.86/3.10 % inf_sup_aci(8)
% 2.86/3.10 thf(fact_2856_inf__sup__aci_I8_J,axiom,
% 2.86/3.10 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( sup_su5525570899277871387at_nat @ X @ ( sup_su5525570899277871387at_nat @ X @ Y ) )
% 2.86/3.10 = ( sup_su5525570899277871387at_nat @ X @ Y ) ) ).
% 2.86/3.10
% 2.86/3.10 % inf_sup_aci(8)
% 2.86/3.10 thf(fact_2857_inf__sup__aci_I7_J,axiom,
% 2.86/3.10 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 2.86/3.10 ( ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) )
% 2.86/3.10 = ( sup_sup_set_nat @ Y @ ( sup_sup_set_nat @ X @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % inf_sup_aci(7)
% 2.86/3.10 thf(fact_2858_inf__sup__aci_I7_J,axiom,
% 2.86/3.10 ! [X: assn,Y: assn,Z: assn] :
% 2.86/3.10 ( ( sup_sup_assn @ X @ ( sup_sup_assn @ Y @ Z ) )
% 2.86/3.10 = ( sup_sup_assn @ Y @ ( sup_sup_assn @ X @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % inf_sup_aci(7)
% 2.86/3.10 thf(fact_2859_inf__sup__aci_I7_J,axiom,
% 2.86/3.10 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( sup_su5525570899277871387at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z ) )
% 2.86/3.10 = ( sup_su5525570899277871387at_nat @ Y @ ( sup_su5525570899277871387at_nat @ X @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % inf_sup_aci(7)
% 2.86/3.10 thf(fact_2860_inf__sup__aci_I6_J,axiom,
% 2.86/3.10 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 2.86/3.10 ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ Z )
% 2.86/3.10 = ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % inf_sup_aci(6)
% 2.86/3.10 thf(fact_2861_inf__sup__aci_I6_J,axiom,
% 2.86/3.10 ! [X: assn,Y: assn,Z: assn] :
% 2.86/3.10 ( ( sup_sup_assn @ ( sup_sup_assn @ X @ Y ) @ Z )
% 2.86/3.10 = ( sup_sup_assn @ X @ ( sup_sup_assn @ Y @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % inf_sup_aci(6)
% 2.86/3.10 thf(fact_2862_inf__sup__aci_I6_J,axiom,
% 2.86/3.10 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( sup_su5525570899277871387at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) @ Z )
% 2.86/3.10 = ( sup_su5525570899277871387at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % inf_sup_aci(6)
% 2.86/3.10 thf(fact_2863_inf__sup__aci_I5_J,axiom,
% 2.86/3.10 ( sup_sup_set_nat
% 2.86/3.10 = ( ^ [X2: set_nat,Y5: set_nat] : ( sup_sup_set_nat @ Y5 @ X2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % inf_sup_aci(5)
% 2.86/3.10 thf(fact_2864_inf__sup__aci_I5_J,axiom,
% 2.86/3.10 ( sup_sup_assn
% 2.86/3.10 = ( ^ [X2: assn,Y5: assn] : ( sup_sup_assn @ Y5 @ X2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % inf_sup_aci(5)
% 2.86/3.10 thf(fact_2865_inf__sup__aci_I5_J,axiom,
% 2.86/3.10 ( sup_su5525570899277871387at_nat
% 2.86/3.10 = ( ^ [X2: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( sup_su5525570899277871387at_nat @ Y5 @ X2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % inf_sup_aci(5)
% 2.86/3.10 thf(fact_2866_min_Oassoc,axiom,
% 2.86/3.10 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.10 ( ( ord_min_nat @ ( ord_min_nat @ A2 @ B2 ) @ C )
% 2.86/3.10 = ( ord_min_nat @ A2 @ ( ord_min_nat @ B2 @ C ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % min.assoc
% 2.86/3.10 thf(fact_2867_min_Ocommute,axiom,
% 2.86/3.10 ( ord_min_nat
% 2.86/3.10 = ( ^ [A3: nat,B3: nat] : ( ord_min_nat @ B3 @ A3 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % min.commute
% 2.86/3.10 thf(fact_2868_min_Oleft__commute,axiom,
% 2.86/3.10 ! [B2: nat,A2: nat,C: nat] :
% 2.86/3.10 ( ( ord_min_nat @ B2 @ ( ord_min_nat @ A2 @ C ) )
% 2.86/3.10 = ( ord_min_nat @ A2 @ ( ord_min_nat @ B2 @ C ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % min.left_commute
% 2.86/3.10 thf(fact_2869_sup_Oassoc,axiom,
% 2.86/3.10 ! [A2: set_nat,B2: set_nat,C: set_nat] :
% 2.86/3.10 ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ A2 @ B2 ) @ C )
% 2.86/3.10 = ( sup_sup_set_nat @ A2 @ ( sup_sup_set_nat @ B2 @ C ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.assoc
% 2.86/3.10 thf(fact_2870_sup_Oassoc,axiom,
% 2.86/3.10 ! [A2: assn,B2: assn,C: assn] :
% 2.86/3.10 ( ( sup_sup_assn @ ( sup_sup_assn @ A2 @ B2 ) @ C )
% 2.86/3.10 = ( sup_sup_assn @ A2 @ ( sup_sup_assn @ B2 @ C ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.assoc
% 2.86/3.10 thf(fact_2871_sup_Oassoc,axiom,
% 2.86/3.10 ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,C: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( sup_su5525570899277871387at_nat @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) @ C )
% 2.86/3.10 = ( sup_su5525570899277871387at_nat @ A2 @ ( sup_su5525570899277871387at_nat @ B2 @ C ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.assoc
% 2.86/3.10 thf(fact_2872_sup__assoc,axiom,
% 2.86/3.10 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 2.86/3.10 ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ Z )
% 2.86/3.10 = ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_assoc
% 2.86/3.10 thf(fact_2873_sup__assoc,axiom,
% 2.86/3.10 ! [X: assn,Y: assn,Z: assn] :
% 2.86/3.10 ( ( sup_sup_assn @ ( sup_sup_assn @ X @ Y ) @ Z )
% 2.86/3.10 = ( sup_sup_assn @ X @ ( sup_sup_assn @ Y @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_assoc
% 2.86/3.10 thf(fact_2874_sup__assoc,axiom,
% 2.86/3.10 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( sup_su5525570899277871387at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) @ Z )
% 2.86/3.10 = ( sup_su5525570899277871387at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_assoc
% 2.86/3.10 thf(fact_2875_sup_Ocommute,axiom,
% 2.86/3.10 ( sup_sup_set_nat
% 2.86/3.10 = ( ^ [A3: set_nat,B3: set_nat] : ( sup_sup_set_nat @ B3 @ A3 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.commute
% 2.86/3.10 thf(fact_2876_sup_Ocommute,axiom,
% 2.86/3.10 ( sup_sup_assn
% 2.86/3.10 = ( ^ [A3: assn,B3: assn] : ( sup_sup_assn @ B3 @ A3 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.commute
% 2.86/3.10 thf(fact_2877_sup_Ocommute,axiom,
% 2.86/3.10 ( sup_su5525570899277871387at_nat
% 2.86/3.10 = ( ^ [A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] : ( sup_su5525570899277871387at_nat @ B3 @ A3 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.commute
% 2.86/3.10 thf(fact_2878_sup__commute,axiom,
% 2.86/3.10 ( sup_sup_set_nat
% 2.86/3.10 = ( ^ [X2: set_nat,Y5: set_nat] : ( sup_sup_set_nat @ Y5 @ X2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_commute
% 2.86/3.10 thf(fact_2879_sup__commute,axiom,
% 2.86/3.10 ( sup_sup_assn
% 2.86/3.10 = ( ^ [X2: assn,Y5: assn] : ( sup_sup_assn @ Y5 @ X2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_commute
% 2.86/3.10 thf(fact_2880_sup__commute,axiom,
% 2.86/3.10 ( sup_su5525570899277871387at_nat
% 2.86/3.10 = ( ^ [X2: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] : ( sup_su5525570899277871387at_nat @ Y5 @ X2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_commute
% 2.86/3.10 thf(fact_2881_sup_Oleft__commute,axiom,
% 2.86/3.10 ! [B2: set_nat,A2: set_nat,C: set_nat] :
% 2.86/3.10 ( ( sup_sup_set_nat @ B2 @ ( sup_sup_set_nat @ A2 @ C ) )
% 2.86/3.10 = ( sup_sup_set_nat @ A2 @ ( sup_sup_set_nat @ B2 @ C ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.left_commute
% 2.86/3.10 thf(fact_2882_sup_Oleft__commute,axiom,
% 2.86/3.10 ! [B2: assn,A2: assn,C: assn] :
% 2.86/3.10 ( ( sup_sup_assn @ B2 @ ( sup_sup_assn @ A2 @ C ) )
% 2.86/3.10 = ( sup_sup_assn @ A2 @ ( sup_sup_assn @ B2 @ C ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.left_commute
% 2.86/3.10 thf(fact_2883_sup_Oleft__commute,axiom,
% 2.86/3.10 ! [B2: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat,C: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( sup_su5525570899277871387at_nat @ B2 @ ( sup_su5525570899277871387at_nat @ A2 @ C ) )
% 2.86/3.10 = ( sup_su5525570899277871387at_nat @ A2 @ ( sup_su5525570899277871387at_nat @ B2 @ C ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.left_commute
% 2.86/3.10 thf(fact_2884_sup__left__commute,axiom,
% 2.86/3.10 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 2.86/3.10 ( ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) )
% 2.86/3.10 = ( sup_sup_set_nat @ Y @ ( sup_sup_set_nat @ X @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_left_commute
% 2.86/3.10 thf(fact_2885_sup__left__commute,axiom,
% 2.86/3.10 ! [X: assn,Y: assn,Z: assn] :
% 2.86/3.10 ( ( sup_sup_assn @ X @ ( sup_sup_assn @ Y @ Z ) )
% 2.86/3.10 = ( sup_sup_assn @ Y @ ( sup_sup_assn @ X @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_left_commute
% 2.86/3.10 thf(fact_2886_sup__left__commute,axiom,
% 2.86/3.10 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( sup_su5525570899277871387at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z ) )
% 2.86/3.10 = ( sup_su5525570899277871387at_nat @ Y @ ( sup_su5525570899277871387at_nat @ X @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_left_commute
% 2.86/3.10 thf(fact_2887_zip__rev,axiom,
% 2.86/3.10 ! [Xs: list_c,Ys: list_c] :
% 2.86/3.10 ( ( ( size_size_list_c @ Xs )
% 2.86/3.10 = ( size_size_list_c @ Ys ) )
% 2.86/3.10 => ( ( zip_c_c @ ( rev_c @ Xs ) @ ( rev_c @ Ys ) )
% 2.86/3.10 = ( rev_Product_prod_c_c @ ( zip_c_c @ Xs @ Ys ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % zip_rev
% 2.86/3.10 thf(fact_2888_zip__rev,axiom,
% 2.86/3.10 ! [Xs: list_c,Ys: list_d] :
% 2.86/3.10 ( ( ( size_size_list_c @ Xs )
% 2.86/3.10 = ( size_size_list_d @ Ys ) )
% 2.86/3.10 => ( ( zip_c_d @ ( rev_c @ Xs ) @ ( rev_d @ Ys ) )
% 2.86/3.10 = ( rev_Product_prod_c_d @ ( zip_c_d @ Xs @ Ys ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % zip_rev
% 2.86/3.10 thf(fact_2889_zip__rev,axiom,
% 2.86/3.10 ! [Xs: list_c,Ys: list_nat] :
% 2.86/3.10 ( ( ( size_size_list_c @ Xs )
% 2.86/3.10 = ( size_size_list_nat @ Ys ) )
% 2.86/3.10 => ( ( zip_c_nat @ ( rev_c @ Xs ) @ ( rev_nat @ Ys ) )
% 2.86/3.10 = ( rev_Pr3799340238495523993_c_nat @ ( zip_c_nat @ Xs @ Ys ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % zip_rev
% 2.86/3.10 thf(fact_2890_zip__rev,axiom,
% 2.86/3.10 ! [Xs: list_c,Ys: list_int] :
% 2.86/3.10 ( ( ( size_size_list_c @ Xs )
% 2.86/3.10 = ( size_size_list_int @ Ys ) )
% 2.86/3.10 => ( ( zip_c_int @ ( rev_c @ Xs ) @ ( rev_int @ Ys ) )
% 2.86/3.10 = ( rev_Pr8844861255841103093_c_int @ ( zip_c_int @ Xs @ Ys ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % zip_rev
% 2.86/3.10 thf(fact_2891_zip__rev,axiom,
% 2.86/3.10 ! [Xs: list_d,Ys: list_c] :
% 2.86/3.10 ( ( ( size_size_list_d @ Xs )
% 2.86/3.10 = ( size_size_list_c @ Ys ) )
% 2.86/3.10 => ( ( zip_d_c @ ( rev_d @ Xs ) @ ( rev_c @ Ys ) )
% 2.86/3.10 = ( rev_Product_prod_d_c @ ( zip_d_c @ Xs @ Ys ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % zip_rev
% 2.86/3.10 thf(fact_2892_zip__rev,axiom,
% 2.86/3.10 ! [Xs: list_d,Ys: list_d] :
% 2.86/3.10 ( ( ( size_size_list_d @ Xs )
% 2.86/3.10 = ( size_size_list_d @ Ys ) )
% 2.86/3.10 => ( ( zip_d_d @ ( rev_d @ Xs ) @ ( rev_d @ Ys ) )
% 2.86/3.10 = ( rev_Product_prod_d_d @ ( zip_d_d @ Xs @ Ys ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % zip_rev
% 2.86/3.10 thf(fact_2893_zip__rev,axiom,
% 2.86/3.10 ! [Xs: list_d,Ys: list_nat] :
% 2.86/3.10 ( ( ( size_size_list_d @ Xs )
% 2.86/3.10 = ( size_size_list_nat @ Ys ) )
% 2.86/3.10 => ( ( zip_d_nat @ ( rev_d @ Xs ) @ ( rev_nat @ Ys ) )
% 2.86/3.10 = ( rev_Pr5034784567451918490_d_nat @ ( zip_d_nat @ Xs @ Ys ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % zip_rev
% 2.86/3.10 thf(fact_2894_zip__rev,axiom,
% 2.86/3.10 ! [Xs: list_d,Ys: list_int] :
% 2.86/3.10 ( ( ( size_size_list_d @ Xs )
% 2.86/3.10 = ( size_size_list_int @ Ys ) )
% 2.86/3.10 => ( ( zip_d_int @ ( rev_d @ Xs ) @ ( rev_int @ Ys ) )
% 2.86/3.10 = ( rev_Pr856933547942721782_d_int @ ( zip_d_int @ Xs @ Ys ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % zip_rev
% 2.86/3.10 thf(fact_2895_zip__rev,axiom,
% 2.86/3.10 ! [Xs: list_nat,Ys: list_c] :
% 2.86/3.10 ( ( ( size_size_list_nat @ Xs )
% 2.86/3.10 = ( size_size_list_c @ Ys ) )
% 2.86/3.10 => ( ( zip_nat_c @ ( rev_nat @ Xs ) @ ( rev_c @ Ys ) )
% 2.86/3.10 = ( rev_Pr4566615052912869567_nat_c @ ( zip_nat_c @ Xs @ Ys ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % zip_rev
% 2.86/3.10 thf(fact_2896_zip__rev,axiom,
% 2.86/3.10 ! [Xs: list_nat,Ys: list_d] :
% 2.86/3.10 ( ( ( size_size_list_nat @ Xs )
% 2.86/3.10 = ( size_size_list_d @ Ys ) )
% 2.86/3.10 => ( ( zip_nat_d @ ( rev_nat @ Xs ) @ ( rev_d @ Ys ) )
% 2.86/3.10 = ( rev_Pr4566615057216098368_nat_d @ ( zip_nat_d @ Xs @ Ys ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % zip_rev
% 2.86/3.10 thf(fact_2897_sorted__wrt__less__idx,axiom,
% 2.86/3.10 ! [Ns: list_nat,I: nat] :
% 2.86/3.10 ( ( sorted_wrt_nat @ ord_less_nat @ Ns )
% 2.86/3.10 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Ns ) )
% 2.86/3.10 => ( ord_less_eq_nat @ I @ ( nth_nat @ Ns @ I ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sorted_wrt_less_idx
% 2.86/3.10 thf(fact_2898_sorted__wrt__mono__rel,axiom,
% 2.86/3.10 ! [Xs: list_P5464809261938338413at_nat,P: produc3843707927480180839at_nat > produc3843707927480180839at_nat > $o,Q: produc3843707927480180839at_nat > produc3843707927480180839at_nat > $o] :
% 2.86/3.10 ( ! [X3: produc3843707927480180839at_nat,Y2: produc3843707927480180839at_nat] :
% 2.86/3.10 ( ( member8757157785044589968at_nat @ X3 @ ( set_Pr3765526544606949372at_nat @ Xs ) )
% 2.86/3.10 => ( ( member8757157785044589968at_nat @ Y2 @ ( set_Pr3765526544606949372at_nat @ Xs ) )
% 2.86/3.10 => ( ( P @ X3 @ Y2 )
% 2.86/3.10 => ( Q @ X3 @ Y2 ) ) ) )
% 2.86/3.10 => ( ( sorted8831241538929206612at_nat @ P @ Xs )
% 2.86/3.10 => ( sorted8831241538929206612at_nat @ Q @ Xs ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sorted_wrt_mono_rel
% 2.86/3.10 thf(fact_2899_sorted__wrt__mono__rel,axiom,
% 2.86/3.10 ! [Xs: list_P6011104703257516679at_nat,P: product_prod_nat_nat > product_prod_nat_nat > $o,Q: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 2.86/3.10 ( ! [X3: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 2.86/3.10 ( ( member8440522571783428010at_nat @ X3 @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 2.86/3.10 => ( ( member8440522571783428010at_nat @ Y2 @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 2.86/3.10 => ( ( P @ X3 @ Y2 )
% 2.86/3.10 => ( Q @ X3 @ Y2 ) ) ) )
% 2.86/3.10 => ( ( sorted5214655850825725294at_nat @ P @ Xs )
% 2.86/3.10 => ( sorted5214655850825725294at_nat @ Q @ Xs ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sorted_wrt_mono_rel
% 2.86/3.10 thf(fact_2900_sorted__wrt__mono__rel,axiom,
% 2.86/3.10 ! [Xs: list_P7985473006766602707_nat_o,P: ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > $o,Q: ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > $o] :
% 2.86/3.10 ( ! [X3: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat > $o] :
% 2.86/3.10 ( ( member6576561426505652726_nat_o @ X3 @ ( set_Pr400311997697478754_nat_o @ Xs ) )
% 2.86/3.10 => ( ( member6576561426505652726_nat_o @ Y2 @ ( set_Pr400311997697478754_nat_o @ Xs ) )
% 2.86/3.10 => ( ( P @ X3 @ Y2 )
% 2.86/3.10 => ( Q @ X3 @ Y2 ) ) ) )
% 2.86/3.10 => ( ( sorted9199660237762088378_nat_o @ P @ Xs )
% 2.86/3.10 => ( sorted9199660237762088378_nat_o @ Q @ Xs ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sorted_wrt_mono_rel
% 2.86/3.10 thf(fact_2901_sorted__wrt__mono__rel,axiom,
% 2.86/3.10 ! [Xs: list_P8527749157015355191n_assn,P: produc6575502325842934193n_assn > produc6575502325842934193n_assn > $o,Q: produc6575502325842934193n_assn > produc6575502325842934193n_assn > $o] :
% 2.86/3.10 ( ! [X3: produc6575502325842934193n_assn,Y2: produc6575502325842934193n_assn] :
% 2.86/3.10 ( ( member7957490590177025114n_assn @ X3 @ ( set_Pr1139785259514867910n_assn @ Xs ) )
% 2.86/3.10 => ( ( member7957490590177025114n_assn @ Y2 @ ( set_Pr1139785259514867910n_assn @ Xs ) )
% 2.86/3.10 => ( ( P @ X3 @ Y2 )
% 2.86/3.10 => ( Q @ X3 @ Y2 ) ) ) )
% 2.86/3.10 => ( ( sorted3986126766855596574n_assn @ P @ Xs )
% 2.86/3.10 => ( sorted3986126766855596574n_assn @ Q @ Xs ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sorted_wrt_mono_rel
% 2.86/3.10 thf(fact_2902_sorted__wrt__mono__rel,axiom,
% 2.86/3.10 ! [Xs: list_nat,P: nat > nat > $o,Q: nat > nat > $o] :
% 2.86/3.10 ( ! [X3: nat,Y2: nat] :
% 2.86/3.10 ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 2.86/3.10 => ( ( member_nat @ Y2 @ ( set_nat2 @ Xs ) )
% 2.86/3.10 => ( ( P @ X3 @ Y2 )
% 2.86/3.10 => ( Q @ X3 @ Y2 ) ) ) )
% 2.86/3.10 => ( ( sorted_wrt_nat @ P @ Xs )
% 2.86/3.10 => ( sorted_wrt_nat @ Q @ Xs ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sorted_wrt_mono_rel
% 2.86/3.10 thf(fact_2903_sorted__wrt__mono__rel,axiom,
% 2.86/3.10 ! [Xs: list_int,P: int > int > $o,Q: int > int > $o] :
% 2.86/3.10 ( ! [X3: int,Y2: int] :
% 2.86/3.10 ( ( member_int @ X3 @ ( set_int2 @ Xs ) )
% 2.86/3.10 => ( ( member_int @ Y2 @ ( set_int2 @ Xs ) )
% 2.86/3.10 => ( ( P @ X3 @ Y2 )
% 2.86/3.10 => ( Q @ X3 @ Y2 ) ) ) )
% 2.86/3.10 => ( ( sorted_wrt_int @ P @ Xs )
% 2.86/3.10 => ( sorted_wrt_int @ Q @ Xs ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sorted_wrt_mono_rel
% 2.86/3.10 thf(fact_2904_min__def,axiom,
% 2.86/3.10 ( ord_min_assn
% 2.86/3.10 = ( ^ [A3: assn,B3: assn] : ( if_assn @ ( ord_less_eq_assn @ A3 @ B3 ) @ A3 @ B3 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % min_def
% 2.86/3.10 thf(fact_2905_min__def,axiom,
% 2.86/3.10 ( ord_min_filter_nat
% 2.86/3.10 = ( ^ [A3: filter_nat,B3: filter_nat] : ( if_filter_nat @ ( ord_le2510731241096832064er_nat @ A3 @ B3 ) @ A3 @ B3 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % min_def
% 2.86/3.10 thf(fact_2906_min__def,axiom,
% 2.86/3.10 ( ord_min_set_nat
% 2.86/3.10 = ( ^ [A3: set_nat,B3: set_nat] : ( if_set_nat @ ( ord_less_eq_set_nat @ A3 @ B3 ) @ A3 @ B3 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % min_def
% 2.86/3.10 thf(fact_2907_min__def,axiom,
% 2.86/3.10 ( ord_min_nat
% 2.86/3.10 = ( ^ [A3: nat,B3: nat] : ( if_nat @ ( ord_less_eq_nat @ A3 @ B3 ) @ A3 @ B3 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % min_def
% 2.86/3.10 thf(fact_2908_min__def,axiom,
% 2.86/3.10 ( ord_min_int
% 2.86/3.10 = ( ^ [A3: int,B3: int] : ( if_int @ ( ord_less_eq_int @ A3 @ B3 ) @ A3 @ B3 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % min_def
% 2.86/3.10 thf(fact_2909_min__absorb1,axiom,
% 2.86/3.10 ! [X: assn,Y: assn] :
% 2.86/3.10 ( ( ord_less_eq_assn @ X @ Y )
% 2.86/3.10 => ( ( ord_min_assn @ X @ Y )
% 2.86/3.10 = X ) ) ).
% 2.86/3.10
% 2.86/3.10 % min_absorb1
% 2.86/3.10 thf(fact_2910_min__absorb1,axiom,
% 2.86/3.10 ! [X: filter_nat,Y: filter_nat] :
% 2.86/3.10 ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 2.86/3.10 => ( ( ord_min_filter_nat @ X @ Y )
% 2.86/3.10 = X ) ) ).
% 2.86/3.10
% 2.86/3.10 % min_absorb1
% 2.86/3.10 thf(fact_2911_min__absorb1,axiom,
% 2.86/3.10 ! [X: set_nat,Y: set_nat] :
% 2.86/3.10 ( ( ord_less_eq_set_nat @ X @ Y )
% 2.86/3.10 => ( ( ord_min_set_nat @ X @ Y )
% 2.86/3.10 = X ) ) ).
% 2.86/3.10
% 2.86/3.10 % min_absorb1
% 2.86/3.10 thf(fact_2912_min__absorb1,axiom,
% 2.86/3.10 ! [X: nat,Y: nat] :
% 2.86/3.10 ( ( ord_less_eq_nat @ X @ Y )
% 2.86/3.10 => ( ( ord_min_nat @ X @ Y )
% 2.86/3.10 = X ) ) ).
% 2.86/3.10
% 2.86/3.10 % min_absorb1
% 2.86/3.10 thf(fact_2913_min__absorb1,axiom,
% 2.86/3.10 ! [X: int,Y: int] :
% 2.86/3.10 ( ( ord_less_eq_int @ X @ Y )
% 2.86/3.10 => ( ( ord_min_int @ X @ Y )
% 2.86/3.10 = X ) ) ).
% 2.86/3.10
% 2.86/3.10 % min_absorb1
% 2.86/3.10 thf(fact_2914_min__absorb2,axiom,
% 2.86/3.10 ! [Y: assn,X: assn] :
% 2.86/3.10 ( ( ord_less_eq_assn @ Y @ X )
% 2.86/3.10 => ( ( ord_min_assn @ X @ Y )
% 2.86/3.10 = Y ) ) ).
% 2.86/3.10
% 2.86/3.10 % min_absorb2
% 2.86/3.10 thf(fact_2915_min__absorb2,axiom,
% 2.86/3.10 ! [Y: filter_nat,X: filter_nat] :
% 2.86/3.10 ( ( ord_le2510731241096832064er_nat @ Y @ X )
% 2.86/3.10 => ( ( ord_min_filter_nat @ X @ Y )
% 2.86/3.10 = Y ) ) ).
% 2.86/3.10
% 2.86/3.10 % min_absorb2
% 2.86/3.10 thf(fact_2916_min__absorb2,axiom,
% 2.86/3.10 ! [Y: set_nat,X: set_nat] :
% 2.86/3.10 ( ( ord_less_eq_set_nat @ Y @ X )
% 2.86/3.10 => ( ( ord_min_set_nat @ X @ Y )
% 2.86/3.10 = Y ) ) ).
% 2.86/3.10
% 2.86/3.10 % min_absorb2
% 2.86/3.10 thf(fact_2917_min__absorb2,axiom,
% 2.86/3.10 ! [Y: nat,X: nat] :
% 2.86/3.10 ( ( ord_less_eq_nat @ Y @ X )
% 2.86/3.10 => ( ( ord_min_nat @ X @ Y )
% 2.86/3.10 = Y ) ) ).
% 2.86/3.10
% 2.86/3.10 % min_absorb2
% 2.86/3.10 thf(fact_2918_min__absorb2,axiom,
% 2.86/3.10 ! [Y: int,X: int] :
% 2.86/3.10 ( ( ord_less_eq_int @ Y @ X )
% 2.86/3.10 => ( ( ord_min_int @ X @ Y )
% 2.86/3.10 = Y ) ) ).
% 2.86/3.10
% 2.86/3.10 % min_absorb2
% 2.86/3.10 thf(fact_2919_min_Omono,axiom,
% 2.86/3.10 ! [A2: nat,C: nat,B2: nat,D2: nat] :
% 2.86/3.10 ( ( ord_less_eq_nat @ A2 @ C )
% 2.86/3.10 => ( ( ord_less_eq_nat @ B2 @ D2 )
% 2.86/3.10 => ( ord_less_eq_nat @ ( ord_min_nat @ A2 @ B2 ) @ ( ord_min_nat @ C @ D2 ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % min.mono
% 2.86/3.10 thf(fact_2920_min_Omono,axiom,
% 2.86/3.10 ! [A2: int,C: int,B2: int,D2: int] :
% 2.86/3.10 ( ( ord_less_eq_int @ A2 @ C )
% 2.86/3.10 => ( ( ord_less_eq_int @ B2 @ D2 )
% 2.86/3.10 => ( ord_less_eq_int @ ( ord_min_int @ A2 @ B2 ) @ ( ord_min_int @ C @ D2 ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % min.mono
% 2.86/3.10 thf(fact_2921_min_OorderE,axiom,
% 2.86/3.10 ! [A2: nat,B2: nat] :
% 2.86/3.10 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.10 => ( A2
% 2.86/3.10 = ( ord_min_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % min.orderE
% 2.86/3.10 thf(fact_2922_min_OorderE,axiom,
% 2.86/3.10 ! [A2: int,B2: int] :
% 2.86/3.10 ( ( ord_less_eq_int @ A2 @ B2 )
% 2.86/3.10 => ( A2
% 2.86/3.10 = ( ord_min_int @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % min.orderE
% 2.86/3.10 thf(fact_2923_min_OorderI,axiom,
% 2.86/3.10 ! [A2: nat,B2: nat] :
% 2.86/3.10 ( ( A2
% 2.86/3.10 = ( ord_min_nat @ A2 @ B2 ) )
% 2.86/3.10 => ( ord_less_eq_nat @ A2 @ B2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % min.orderI
% 2.86/3.10 thf(fact_2924_min_OorderI,axiom,
% 2.86/3.10 ! [A2: int,B2: int] :
% 2.86/3.10 ( ( A2
% 2.86/3.10 = ( ord_min_int @ A2 @ B2 ) )
% 2.86/3.10 => ( ord_less_eq_int @ A2 @ B2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % min.orderI
% 2.86/3.10 thf(fact_2925_min_OboundedE,axiom,
% 2.86/3.10 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.10 ( ( ord_less_eq_nat @ A2 @ ( ord_min_nat @ B2 @ C ) )
% 2.86/3.10 => ~ ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.10 => ~ ( ord_less_eq_nat @ A2 @ C ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % min.boundedE
% 2.86/3.10 thf(fact_2926_min_OboundedE,axiom,
% 2.86/3.10 ! [A2: int,B2: int,C: int] :
% 2.86/3.10 ( ( ord_less_eq_int @ A2 @ ( ord_min_int @ B2 @ C ) )
% 2.86/3.10 => ~ ( ( ord_less_eq_int @ A2 @ B2 )
% 2.86/3.10 => ~ ( ord_less_eq_int @ A2 @ C ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % min.boundedE
% 2.86/3.10 thf(fact_2927_min_OboundedI,axiom,
% 2.86/3.10 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.10 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.10 => ( ( ord_less_eq_nat @ A2 @ C )
% 2.86/3.10 => ( ord_less_eq_nat @ A2 @ ( ord_min_nat @ B2 @ C ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % min.boundedI
% 2.86/3.10 thf(fact_2928_min_OboundedI,axiom,
% 2.86/3.10 ! [A2: int,B2: int,C: int] :
% 2.86/3.10 ( ( ord_less_eq_int @ A2 @ B2 )
% 2.86/3.10 => ( ( ord_less_eq_int @ A2 @ C )
% 2.86/3.10 => ( ord_less_eq_int @ A2 @ ( ord_min_int @ B2 @ C ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % min.boundedI
% 2.86/3.10 thf(fact_2929_min_Oorder__iff,axiom,
% 2.86/3.10 ( ord_less_eq_nat
% 2.86/3.10 = ( ^ [A3: nat,B3: nat] :
% 2.86/3.10 ( A3
% 2.86/3.10 = ( ord_min_nat @ A3 @ B3 ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % min.order_iff
% 2.86/3.10 thf(fact_2930_min_Oorder__iff,axiom,
% 2.86/3.10 ( ord_less_eq_int
% 2.86/3.10 = ( ^ [A3: int,B3: int] :
% 2.86/3.10 ( A3
% 2.86/3.10 = ( ord_min_int @ A3 @ B3 ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % min.order_iff
% 2.86/3.10 thf(fact_2931_min_Ocobounded1,axiom,
% 2.86/3.10 ! [A2: nat,B2: nat] : ( ord_less_eq_nat @ ( ord_min_nat @ A2 @ B2 ) @ A2 ) ).
% 2.86/3.10
% 2.86/3.10 % min.cobounded1
% 2.86/3.10 thf(fact_2932_min_Ocobounded1,axiom,
% 2.86/3.10 ! [A2: int,B2: int] : ( ord_less_eq_int @ ( ord_min_int @ A2 @ B2 ) @ A2 ) ).
% 2.86/3.10
% 2.86/3.10 % min.cobounded1
% 2.86/3.10 thf(fact_2933_min_Ocobounded2,axiom,
% 2.86/3.10 ! [A2: nat,B2: nat] : ( ord_less_eq_nat @ ( ord_min_nat @ A2 @ B2 ) @ B2 ) ).
% 2.86/3.10
% 2.86/3.10 % min.cobounded2
% 2.86/3.10 thf(fact_2934_min_Ocobounded2,axiom,
% 2.86/3.10 ! [A2: int,B2: int] : ( ord_less_eq_int @ ( ord_min_int @ A2 @ B2 ) @ B2 ) ).
% 2.86/3.10
% 2.86/3.10 % min.cobounded2
% 2.86/3.10 thf(fact_2935_min_Oabsorb__iff1,axiom,
% 2.86/3.10 ( ord_less_eq_nat
% 2.86/3.10 = ( ^ [A3: nat,B3: nat] :
% 2.86/3.10 ( ( ord_min_nat @ A3 @ B3 )
% 2.86/3.10 = A3 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % min.absorb_iff1
% 2.86/3.10 thf(fact_2936_min_Oabsorb__iff1,axiom,
% 2.86/3.10 ( ord_less_eq_int
% 2.86/3.10 = ( ^ [A3: int,B3: int] :
% 2.86/3.10 ( ( ord_min_int @ A3 @ B3 )
% 2.86/3.10 = A3 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % min.absorb_iff1
% 2.86/3.10 thf(fact_2937_min_Oabsorb__iff2,axiom,
% 2.86/3.10 ( ord_less_eq_nat
% 2.86/3.10 = ( ^ [B3: nat,A3: nat] :
% 2.86/3.10 ( ( ord_min_nat @ A3 @ B3 )
% 2.86/3.10 = B3 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % min.absorb_iff2
% 2.86/3.10 thf(fact_2938_min_Oabsorb__iff2,axiom,
% 2.86/3.10 ( ord_less_eq_int
% 2.86/3.10 = ( ^ [B3: int,A3: int] :
% 2.86/3.10 ( ( ord_min_int @ A3 @ B3 )
% 2.86/3.10 = B3 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % min.absorb_iff2
% 2.86/3.10 thf(fact_2939_min_OcoboundedI1,axiom,
% 2.86/3.10 ! [A2: nat,C: nat,B2: nat] :
% 2.86/3.10 ( ( ord_less_eq_nat @ A2 @ C )
% 2.86/3.10 => ( ord_less_eq_nat @ ( ord_min_nat @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.10
% 2.86/3.10 % min.coboundedI1
% 2.86/3.10 thf(fact_2940_min_OcoboundedI1,axiom,
% 2.86/3.10 ! [A2: int,C: int,B2: int] :
% 2.86/3.10 ( ( ord_less_eq_int @ A2 @ C )
% 2.86/3.10 => ( ord_less_eq_int @ ( ord_min_int @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.10
% 2.86/3.10 % min.coboundedI1
% 2.86/3.10 thf(fact_2941_min_OcoboundedI2,axiom,
% 2.86/3.10 ! [B2: nat,C: nat,A2: nat] :
% 2.86/3.10 ( ( ord_less_eq_nat @ B2 @ C )
% 2.86/3.10 => ( ord_less_eq_nat @ ( ord_min_nat @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.10
% 2.86/3.10 % min.coboundedI2
% 2.86/3.10 thf(fact_2942_min_OcoboundedI2,axiom,
% 2.86/3.10 ! [B2: int,C: int,A2: int] :
% 2.86/3.10 ( ( ord_less_eq_int @ B2 @ C )
% 2.86/3.10 => ( ord_less_eq_int @ ( ord_min_int @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.10
% 2.86/3.10 % min.coboundedI2
% 2.86/3.10 thf(fact_2943_min__le__iff__disj,axiom,
% 2.86/3.10 ! [X: nat,Y: nat,Z: nat] :
% 2.86/3.10 ( ( ord_less_eq_nat @ ( ord_min_nat @ X @ Y ) @ Z )
% 2.86/3.10 = ( ( ord_less_eq_nat @ X @ Z )
% 2.86/3.10 | ( ord_less_eq_nat @ Y @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % min_le_iff_disj
% 2.86/3.10 thf(fact_2944_min__le__iff__disj,axiom,
% 2.86/3.10 ! [X: int,Y: int,Z: int] :
% 2.86/3.10 ( ( ord_less_eq_int @ ( ord_min_int @ X @ Y ) @ Z )
% 2.86/3.10 = ( ( ord_less_eq_int @ X @ Z )
% 2.86/3.10 | ( ord_less_eq_int @ Y @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % min_le_iff_disj
% 2.86/3.10 thf(fact_2945_min_Ostrict__coboundedI2,axiom,
% 2.86/3.10 ! [B2: code_integer,C: code_integer,A2: code_integer] :
% 2.86/3.10 ( ( ord_le6747313008572928689nteger @ B2 @ C )
% 2.86/3.10 => ( ord_le6747313008572928689nteger @ ( ord_min_Code_integer @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.10
% 2.86/3.10 % min.strict_coboundedI2
% 2.86/3.10 thf(fact_2946_min_Ostrict__coboundedI2,axiom,
% 2.86/3.10 ! [B2: num,C: num,A2: num] :
% 2.86/3.10 ( ( ord_less_num @ B2 @ C )
% 2.86/3.10 => ( ord_less_num @ ( ord_min_num @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.10
% 2.86/3.10 % min.strict_coboundedI2
% 2.86/3.10 thf(fact_2947_min_Ostrict__coboundedI2,axiom,
% 2.86/3.10 ! [B2: nat,C: nat,A2: nat] :
% 2.86/3.10 ( ( ord_less_nat @ B2 @ C )
% 2.86/3.10 => ( ord_less_nat @ ( ord_min_nat @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.10
% 2.86/3.10 % min.strict_coboundedI2
% 2.86/3.10 thf(fact_2948_min_Ostrict__coboundedI2,axiom,
% 2.86/3.10 ! [B2: int,C: int,A2: int] :
% 2.86/3.10 ( ( ord_less_int @ B2 @ C )
% 2.86/3.10 => ( ord_less_int @ ( ord_min_int @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.10
% 2.86/3.10 % min.strict_coboundedI2
% 2.86/3.10 thf(fact_2949_min_Ostrict__coboundedI1,axiom,
% 2.86/3.10 ! [A2: code_integer,C: code_integer,B2: code_integer] :
% 2.86/3.10 ( ( ord_le6747313008572928689nteger @ A2 @ C )
% 2.86/3.10 => ( ord_le6747313008572928689nteger @ ( ord_min_Code_integer @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.10
% 2.86/3.10 % min.strict_coboundedI1
% 2.86/3.10 thf(fact_2950_min_Ostrict__coboundedI1,axiom,
% 2.86/3.10 ! [A2: num,C: num,B2: num] :
% 2.86/3.10 ( ( ord_less_num @ A2 @ C )
% 2.86/3.10 => ( ord_less_num @ ( ord_min_num @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.10
% 2.86/3.10 % min.strict_coboundedI1
% 2.86/3.10 thf(fact_2951_min_Ostrict__coboundedI1,axiom,
% 2.86/3.10 ! [A2: nat,C: nat,B2: nat] :
% 2.86/3.10 ( ( ord_less_nat @ A2 @ C )
% 2.86/3.10 => ( ord_less_nat @ ( ord_min_nat @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.10
% 2.86/3.10 % min.strict_coboundedI1
% 2.86/3.10 thf(fact_2952_min_Ostrict__coboundedI1,axiom,
% 2.86/3.10 ! [A2: int,C: int,B2: int] :
% 2.86/3.10 ( ( ord_less_int @ A2 @ C )
% 2.86/3.10 => ( ord_less_int @ ( ord_min_int @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.10
% 2.86/3.10 % min.strict_coboundedI1
% 2.86/3.10 thf(fact_2953_min_Ostrict__order__iff,axiom,
% 2.86/3.10 ( ord_le6747313008572928689nteger
% 2.86/3.10 = ( ^ [A3: code_integer,B3: code_integer] :
% 2.86/3.10 ( ( A3
% 2.86/3.10 = ( ord_min_Code_integer @ A3 @ B3 ) )
% 2.86/3.10 & ( A3 != B3 ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % min.strict_order_iff
% 2.86/3.10 thf(fact_2954_min_Ostrict__order__iff,axiom,
% 2.86/3.10 ( ord_less_num
% 2.86/3.10 = ( ^ [A3: num,B3: num] :
% 2.86/3.10 ( ( A3
% 2.86/3.10 = ( ord_min_num @ A3 @ B3 ) )
% 2.86/3.10 & ( A3 != B3 ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % min.strict_order_iff
% 2.86/3.10 thf(fact_2955_min_Ostrict__order__iff,axiom,
% 2.86/3.10 ( ord_less_nat
% 2.86/3.10 = ( ^ [A3: nat,B3: nat] :
% 2.86/3.10 ( ( A3
% 2.86/3.10 = ( ord_min_nat @ A3 @ B3 ) )
% 2.86/3.10 & ( A3 != B3 ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % min.strict_order_iff
% 2.86/3.10 thf(fact_2956_min_Ostrict__order__iff,axiom,
% 2.86/3.10 ( ord_less_int
% 2.86/3.10 = ( ^ [A3: int,B3: int] :
% 2.86/3.10 ( ( A3
% 2.86/3.10 = ( ord_min_int @ A3 @ B3 ) )
% 2.86/3.10 & ( A3 != B3 ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % min.strict_order_iff
% 2.86/3.10 thf(fact_2957_min_Ostrict__boundedE,axiom,
% 2.86/3.10 ! [A2: code_integer,B2: code_integer,C: code_integer] :
% 2.86/3.10 ( ( ord_le6747313008572928689nteger @ A2 @ ( ord_min_Code_integer @ B2 @ C ) )
% 2.86/3.10 => ~ ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 2.86/3.10 => ~ ( ord_le6747313008572928689nteger @ A2 @ C ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % min.strict_boundedE
% 2.86/3.10 thf(fact_2958_min_Ostrict__boundedE,axiom,
% 2.86/3.10 ! [A2: num,B2: num,C: num] :
% 2.86/3.10 ( ( ord_less_num @ A2 @ ( ord_min_num @ B2 @ C ) )
% 2.86/3.10 => ~ ( ( ord_less_num @ A2 @ B2 )
% 2.86/3.10 => ~ ( ord_less_num @ A2 @ C ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % min.strict_boundedE
% 2.86/3.10 thf(fact_2959_min_Ostrict__boundedE,axiom,
% 2.86/3.10 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.10 ( ( ord_less_nat @ A2 @ ( ord_min_nat @ B2 @ C ) )
% 2.86/3.10 => ~ ( ( ord_less_nat @ A2 @ B2 )
% 2.86/3.10 => ~ ( ord_less_nat @ A2 @ C ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % min.strict_boundedE
% 2.86/3.10 thf(fact_2960_min_Ostrict__boundedE,axiom,
% 2.86/3.10 ! [A2: int,B2: int,C: int] :
% 2.86/3.10 ( ( ord_less_int @ A2 @ ( ord_min_int @ B2 @ C ) )
% 2.86/3.10 => ~ ( ( ord_less_int @ A2 @ B2 )
% 2.86/3.10 => ~ ( ord_less_int @ A2 @ C ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % min.strict_boundedE
% 2.86/3.10 thf(fact_2961_min__less__iff__disj,axiom,
% 2.86/3.10 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 2.86/3.10 ( ( ord_le6747313008572928689nteger @ ( ord_min_Code_integer @ X @ Y ) @ Z )
% 2.86/3.10 = ( ( ord_le6747313008572928689nteger @ X @ Z )
% 2.86/3.10 | ( ord_le6747313008572928689nteger @ Y @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % min_less_iff_disj
% 2.86/3.10 thf(fact_2962_min__less__iff__disj,axiom,
% 2.86/3.10 ! [X: num,Y: num,Z: num] :
% 2.86/3.10 ( ( ord_less_num @ ( ord_min_num @ X @ Y ) @ Z )
% 2.86/3.10 = ( ( ord_less_num @ X @ Z )
% 2.86/3.10 | ( ord_less_num @ Y @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % min_less_iff_disj
% 2.86/3.10 thf(fact_2963_min__less__iff__disj,axiom,
% 2.86/3.10 ! [X: nat,Y: nat,Z: nat] :
% 2.86/3.10 ( ( ord_less_nat @ ( ord_min_nat @ X @ Y ) @ Z )
% 2.86/3.10 = ( ( ord_less_nat @ X @ Z )
% 2.86/3.10 | ( ord_less_nat @ Y @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % min_less_iff_disj
% 2.86/3.10 thf(fact_2964_min__less__iff__disj,axiom,
% 2.86/3.10 ! [X: int,Y: int,Z: int] :
% 2.86/3.10 ( ( ord_less_int @ ( ord_min_int @ X @ Y ) @ Z )
% 2.86/3.10 = ( ( ord_less_int @ X @ Z )
% 2.86/3.10 | ( ord_less_int @ Y @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % min_less_iff_disj
% 2.86/3.10 thf(fact_2965_min__diff__distrib__left,axiom,
% 2.86/3.10 ! [X: rat,Y: rat,Z: rat] :
% 2.86/3.10 ( ( minus_minus_rat @ ( ord_min_rat @ X @ Y ) @ Z )
% 2.86/3.10 = ( ord_min_rat @ ( minus_minus_rat @ X @ Z ) @ ( minus_minus_rat @ Y @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % min_diff_distrib_left
% 2.86/3.10 thf(fact_2966_min__diff__distrib__left,axiom,
% 2.86/3.10 ! [X: int,Y: int,Z: int] :
% 2.86/3.10 ( ( minus_minus_int @ ( ord_min_int @ X @ Y ) @ Z )
% 2.86/3.10 = ( ord_min_int @ ( minus_minus_int @ X @ Z ) @ ( minus_minus_int @ Y @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % min_diff_distrib_left
% 2.86/3.10 thf(fact_2967_inf__sup__ord_I4_J,axiom,
% 2.86/3.10 ! [Y: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ Y @ ( sup_su5525570899277871387at_nat @ X @ Y ) ) ).
% 2.86/3.10
% 2.86/3.10 % inf_sup_ord(4)
% 2.86/3.10 thf(fact_2968_inf__sup__ord_I4_J,axiom,
% 2.86/3.10 ! [Y: assn,X: assn] : ( ord_less_eq_assn @ Y @ ( sup_sup_assn @ X @ Y ) ) ).
% 2.86/3.10
% 2.86/3.10 % inf_sup_ord(4)
% 2.86/3.10 thf(fact_2969_inf__sup__ord_I4_J,axiom,
% 2.86/3.10 ! [Y: filter_nat,X: filter_nat] : ( ord_le2510731241096832064er_nat @ Y @ ( sup_sup_filter_nat @ X @ Y ) ) ).
% 2.86/3.10
% 2.86/3.10 % inf_sup_ord(4)
% 2.86/3.10 thf(fact_2970_inf__sup__ord_I4_J,axiom,
% 2.86/3.10 ! [Y: set_nat,X: set_nat] : ( ord_less_eq_set_nat @ Y @ ( sup_sup_set_nat @ X @ Y ) ) ).
% 2.86/3.10
% 2.86/3.10 % inf_sup_ord(4)
% 2.86/3.10 thf(fact_2971_inf__sup__ord_I4_J,axiom,
% 2.86/3.10 ! [Y: nat,X: nat] : ( ord_less_eq_nat @ Y @ ( sup_sup_nat @ X @ Y ) ) ).
% 2.86/3.10
% 2.86/3.10 % inf_sup_ord(4)
% 2.86/3.10 thf(fact_2972_inf__sup__ord_I4_J,axiom,
% 2.86/3.10 ! [Y: int,X: int] : ( ord_less_eq_int @ Y @ ( sup_sup_int @ X @ Y ) ) ).
% 2.86/3.10
% 2.86/3.10 % inf_sup_ord(4)
% 2.86/3.10 thf(fact_2973_inf__sup__ord_I3_J,axiom,
% 2.86/3.10 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ X @ ( sup_su5525570899277871387at_nat @ X @ Y ) ) ).
% 2.86/3.10
% 2.86/3.10 % inf_sup_ord(3)
% 2.86/3.10 thf(fact_2974_inf__sup__ord_I3_J,axiom,
% 2.86/3.10 ! [X: assn,Y: assn] : ( ord_less_eq_assn @ X @ ( sup_sup_assn @ X @ Y ) ) ).
% 2.86/3.10
% 2.86/3.10 % inf_sup_ord(3)
% 2.86/3.10 thf(fact_2975_inf__sup__ord_I3_J,axiom,
% 2.86/3.10 ! [X: filter_nat,Y: filter_nat] : ( ord_le2510731241096832064er_nat @ X @ ( sup_sup_filter_nat @ X @ Y ) ) ).
% 2.86/3.10
% 2.86/3.10 % inf_sup_ord(3)
% 2.86/3.10 thf(fact_2976_inf__sup__ord_I3_J,axiom,
% 2.86/3.10 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ X @ Y ) ) ).
% 2.86/3.10
% 2.86/3.10 % inf_sup_ord(3)
% 2.86/3.10 thf(fact_2977_inf__sup__ord_I3_J,axiom,
% 2.86/3.10 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ X @ ( sup_sup_nat @ X @ Y ) ) ).
% 2.86/3.10
% 2.86/3.10 % inf_sup_ord(3)
% 2.86/3.10 thf(fact_2978_inf__sup__ord_I3_J,axiom,
% 2.86/3.10 ! [X: int,Y: int] : ( ord_less_eq_int @ X @ ( sup_sup_int @ X @ Y ) ) ).
% 2.86/3.10
% 2.86/3.10 % inf_sup_ord(3)
% 2.86/3.10 thf(fact_2979_le__supE,axiom,
% 2.86/3.10 ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) @ X )
% 2.86/3.10 => ~ ( ( ord_le1268244103169919719at_nat @ A2 @ X )
% 2.86/3.10 => ~ ( ord_le1268244103169919719at_nat @ B2 @ X ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % le_supE
% 2.86/3.10 thf(fact_2980_le__supE,axiom,
% 2.86/3.10 ! [A2: assn,B2: assn,X: assn] :
% 2.86/3.10 ( ( ord_less_eq_assn @ ( sup_sup_assn @ A2 @ B2 ) @ X )
% 2.86/3.10 => ~ ( ( ord_less_eq_assn @ A2 @ X )
% 2.86/3.10 => ~ ( ord_less_eq_assn @ B2 @ X ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % le_supE
% 2.86/3.10 thf(fact_2981_le__supE,axiom,
% 2.86/3.10 ! [A2: filter_nat,B2: filter_nat,X: filter_nat] :
% 2.86/3.10 ( ( ord_le2510731241096832064er_nat @ ( sup_sup_filter_nat @ A2 @ B2 ) @ X )
% 2.86/3.10 => ~ ( ( ord_le2510731241096832064er_nat @ A2 @ X )
% 2.86/3.10 => ~ ( ord_le2510731241096832064er_nat @ B2 @ X ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % le_supE
% 2.86/3.10 thf(fact_2982_le__supE,axiom,
% 2.86/3.10 ! [A2: set_nat,B2: set_nat,X: set_nat] :
% 2.86/3.10 ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A2 @ B2 ) @ X )
% 2.86/3.10 => ~ ( ( ord_less_eq_set_nat @ A2 @ X )
% 2.86/3.10 => ~ ( ord_less_eq_set_nat @ B2 @ X ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % le_supE
% 2.86/3.10 thf(fact_2983_le__supE,axiom,
% 2.86/3.10 ! [A2: nat,B2: nat,X: nat] :
% 2.86/3.10 ( ( ord_less_eq_nat @ ( sup_sup_nat @ A2 @ B2 ) @ X )
% 2.86/3.10 => ~ ( ( ord_less_eq_nat @ A2 @ X )
% 2.86/3.10 => ~ ( ord_less_eq_nat @ B2 @ X ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % le_supE
% 2.86/3.10 thf(fact_2984_le__supE,axiom,
% 2.86/3.10 ! [A2: int,B2: int,X: int] :
% 2.86/3.10 ( ( ord_less_eq_int @ ( sup_sup_int @ A2 @ B2 ) @ X )
% 2.86/3.10 => ~ ( ( ord_less_eq_int @ A2 @ X )
% 2.86/3.10 => ~ ( ord_less_eq_int @ B2 @ X ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % le_supE
% 2.86/3.10 thf(fact_2985_le__supI,axiom,
% 2.86/3.10 ! [A2: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( ord_le1268244103169919719at_nat @ A2 @ X )
% 2.86/3.10 => ( ( ord_le1268244103169919719at_nat @ B2 @ X )
% 2.86/3.10 => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) @ X ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % le_supI
% 2.86/3.10 thf(fact_2986_le__supI,axiom,
% 2.86/3.10 ! [A2: assn,X: assn,B2: assn] :
% 2.86/3.10 ( ( ord_less_eq_assn @ A2 @ X )
% 2.86/3.10 => ( ( ord_less_eq_assn @ B2 @ X )
% 2.86/3.10 => ( ord_less_eq_assn @ ( sup_sup_assn @ A2 @ B2 ) @ X ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % le_supI
% 2.86/3.10 thf(fact_2987_le__supI,axiom,
% 2.86/3.10 ! [A2: filter_nat,X: filter_nat,B2: filter_nat] :
% 2.86/3.10 ( ( ord_le2510731241096832064er_nat @ A2 @ X )
% 2.86/3.10 => ( ( ord_le2510731241096832064er_nat @ B2 @ X )
% 2.86/3.10 => ( ord_le2510731241096832064er_nat @ ( sup_sup_filter_nat @ A2 @ B2 ) @ X ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % le_supI
% 2.86/3.10 thf(fact_2988_le__supI,axiom,
% 2.86/3.10 ! [A2: set_nat,X: set_nat,B2: set_nat] :
% 2.86/3.10 ( ( ord_less_eq_set_nat @ A2 @ X )
% 2.86/3.10 => ( ( ord_less_eq_set_nat @ B2 @ X )
% 2.86/3.10 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A2 @ B2 ) @ X ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % le_supI
% 2.86/3.10 thf(fact_2989_le__supI,axiom,
% 2.86/3.10 ! [A2: nat,X: nat,B2: nat] :
% 2.86/3.10 ( ( ord_less_eq_nat @ A2 @ X )
% 2.86/3.10 => ( ( ord_less_eq_nat @ B2 @ X )
% 2.86/3.10 => ( ord_less_eq_nat @ ( sup_sup_nat @ A2 @ B2 ) @ X ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % le_supI
% 2.86/3.10 thf(fact_2990_le__supI,axiom,
% 2.86/3.10 ! [A2: int,X: int,B2: int] :
% 2.86/3.10 ( ( ord_less_eq_int @ A2 @ X )
% 2.86/3.10 => ( ( ord_less_eq_int @ B2 @ X )
% 2.86/3.10 => ( ord_less_eq_int @ ( sup_sup_int @ A2 @ B2 ) @ X ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % le_supI
% 2.86/3.10 thf(fact_2991_sup__ge1,axiom,
% 2.86/3.10 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ X @ ( sup_su5525570899277871387at_nat @ X @ Y ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_ge1
% 2.86/3.10 thf(fact_2992_sup__ge1,axiom,
% 2.86/3.10 ! [X: assn,Y: assn] : ( ord_less_eq_assn @ X @ ( sup_sup_assn @ X @ Y ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_ge1
% 2.86/3.10 thf(fact_2993_sup__ge1,axiom,
% 2.86/3.10 ! [X: filter_nat,Y: filter_nat] : ( ord_le2510731241096832064er_nat @ X @ ( sup_sup_filter_nat @ X @ Y ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_ge1
% 2.86/3.10 thf(fact_2994_sup__ge1,axiom,
% 2.86/3.10 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ X @ Y ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_ge1
% 2.86/3.10 thf(fact_2995_sup__ge1,axiom,
% 2.86/3.10 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ X @ ( sup_sup_nat @ X @ Y ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_ge1
% 2.86/3.10 thf(fact_2996_sup__ge1,axiom,
% 2.86/3.10 ! [X: int,Y: int] : ( ord_less_eq_int @ X @ ( sup_sup_int @ X @ Y ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_ge1
% 2.86/3.10 thf(fact_2997_sup__ge2,axiom,
% 2.86/3.10 ! [Y: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ Y @ ( sup_su5525570899277871387at_nat @ X @ Y ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_ge2
% 2.86/3.10 thf(fact_2998_sup__ge2,axiom,
% 2.86/3.10 ! [Y: assn,X: assn] : ( ord_less_eq_assn @ Y @ ( sup_sup_assn @ X @ Y ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_ge2
% 2.86/3.10 thf(fact_2999_sup__ge2,axiom,
% 2.86/3.10 ! [Y: filter_nat,X: filter_nat] : ( ord_le2510731241096832064er_nat @ Y @ ( sup_sup_filter_nat @ X @ Y ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_ge2
% 2.86/3.10 thf(fact_3000_sup__ge2,axiom,
% 2.86/3.10 ! [Y: set_nat,X: set_nat] : ( ord_less_eq_set_nat @ Y @ ( sup_sup_set_nat @ X @ Y ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_ge2
% 2.86/3.10 thf(fact_3001_sup__ge2,axiom,
% 2.86/3.10 ! [Y: nat,X: nat] : ( ord_less_eq_nat @ Y @ ( sup_sup_nat @ X @ Y ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_ge2
% 2.86/3.10 thf(fact_3002_sup__ge2,axiom,
% 2.86/3.10 ! [Y: int,X: int] : ( ord_less_eq_int @ Y @ ( sup_sup_int @ X @ Y ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_ge2
% 2.86/3.10 thf(fact_3003_le__supI1,axiom,
% 2.86/3.10 ! [X: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( ord_le1268244103169919719at_nat @ X @ A2 )
% 2.86/3.10 => ( ord_le1268244103169919719at_nat @ X @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % le_supI1
% 2.86/3.10 thf(fact_3004_le__supI1,axiom,
% 2.86/3.10 ! [X: assn,A2: assn,B2: assn] :
% 2.86/3.10 ( ( ord_less_eq_assn @ X @ A2 )
% 2.86/3.10 => ( ord_less_eq_assn @ X @ ( sup_sup_assn @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % le_supI1
% 2.86/3.10 thf(fact_3005_le__supI1,axiom,
% 2.86/3.10 ! [X: filter_nat,A2: filter_nat,B2: filter_nat] :
% 2.86/3.10 ( ( ord_le2510731241096832064er_nat @ X @ A2 )
% 2.86/3.10 => ( ord_le2510731241096832064er_nat @ X @ ( sup_sup_filter_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % le_supI1
% 2.86/3.10 thf(fact_3006_le__supI1,axiom,
% 2.86/3.10 ! [X: set_nat,A2: set_nat,B2: set_nat] :
% 2.86/3.10 ( ( ord_less_eq_set_nat @ X @ A2 )
% 2.86/3.10 => ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % le_supI1
% 2.86/3.10 thf(fact_3007_le__supI1,axiom,
% 2.86/3.10 ! [X: nat,A2: nat,B2: nat] :
% 2.86/3.10 ( ( ord_less_eq_nat @ X @ A2 )
% 2.86/3.10 => ( ord_less_eq_nat @ X @ ( sup_sup_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % le_supI1
% 2.86/3.10 thf(fact_3008_le__supI1,axiom,
% 2.86/3.10 ! [X: int,A2: int,B2: int] :
% 2.86/3.10 ( ( ord_less_eq_int @ X @ A2 )
% 2.86/3.10 => ( ord_less_eq_int @ X @ ( sup_sup_int @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % le_supI1
% 2.86/3.10 thf(fact_3009_le__supI2,axiom,
% 2.86/3.10 ! [X: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( ord_le1268244103169919719at_nat @ X @ B2 )
% 2.86/3.10 => ( ord_le1268244103169919719at_nat @ X @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % le_supI2
% 2.86/3.10 thf(fact_3010_le__supI2,axiom,
% 2.86/3.10 ! [X: assn,B2: assn,A2: assn] :
% 2.86/3.10 ( ( ord_less_eq_assn @ X @ B2 )
% 2.86/3.10 => ( ord_less_eq_assn @ X @ ( sup_sup_assn @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % le_supI2
% 2.86/3.10 thf(fact_3011_le__supI2,axiom,
% 2.86/3.10 ! [X: filter_nat,B2: filter_nat,A2: filter_nat] :
% 2.86/3.10 ( ( ord_le2510731241096832064er_nat @ X @ B2 )
% 2.86/3.10 => ( ord_le2510731241096832064er_nat @ X @ ( sup_sup_filter_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % le_supI2
% 2.86/3.10 thf(fact_3012_le__supI2,axiom,
% 2.86/3.10 ! [X: set_nat,B2: set_nat,A2: set_nat] :
% 2.86/3.10 ( ( ord_less_eq_set_nat @ X @ B2 )
% 2.86/3.10 => ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % le_supI2
% 2.86/3.10 thf(fact_3013_le__supI2,axiom,
% 2.86/3.10 ! [X: nat,B2: nat,A2: nat] :
% 2.86/3.10 ( ( ord_less_eq_nat @ X @ B2 )
% 2.86/3.10 => ( ord_less_eq_nat @ X @ ( sup_sup_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % le_supI2
% 2.86/3.10 thf(fact_3014_le__supI2,axiom,
% 2.86/3.10 ! [X: int,B2: int,A2: int] :
% 2.86/3.10 ( ( ord_less_eq_int @ X @ B2 )
% 2.86/3.10 => ( ord_less_eq_int @ X @ ( sup_sup_int @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % le_supI2
% 2.86/3.10 thf(fact_3015_sup_Omono,axiom,
% 2.86/3.10 ! [C: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat,D2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( ord_le1268244103169919719at_nat @ C @ A2 )
% 2.86/3.10 => ( ( ord_le1268244103169919719at_nat @ D2 @ B2 )
% 2.86/3.10 => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ C @ D2 ) @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.mono
% 2.86/3.10 thf(fact_3016_sup_Omono,axiom,
% 2.86/3.10 ! [C: assn,A2: assn,D2: assn,B2: assn] :
% 2.86/3.10 ( ( ord_less_eq_assn @ C @ A2 )
% 2.86/3.10 => ( ( ord_less_eq_assn @ D2 @ B2 )
% 2.86/3.10 => ( ord_less_eq_assn @ ( sup_sup_assn @ C @ D2 ) @ ( sup_sup_assn @ A2 @ B2 ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.mono
% 2.86/3.10 thf(fact_3017_sup_Omono,axiom,
% 2.86/3.10 ! [C: filter_nat,A2: filter_nat,D2: filter_nat,B2: filter_nat] :
% 2.86/3.10 ( ( ord_le2510731241096832064er_nat @ C @ A2 )
% 2.86/3.10 => ( ( ord_le2510731241096832064er_nat @ D2 @ B2 )
% 2.86/3.10 => ( ord_le2510731241096832064er_nat @ ( sup_sup_filter_nat @ C @ D2 ) @ ( sup_sup_filter_nat @ A2 @ B2 ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.mono
% 2.86/3.10 thf(fact_3018_sup_Omono,axiom,
% 2.86/3.10 ! [C: set_nat,A2: set_nat,D2: set_nat,B2: set_nat] :
% 2.86/3.10 ( ( ord_less_eq_set_nat @ C @ A2 )
% 2.86/3.10 => ( ( ord_less_eq_set_nat @ D2 @ B2 )
% 2.86/3.10 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ C @ D2 ) @ ( sup_sup_set_nat @ A2 @ B2 ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.mono
% 2.86/3.10 thf(fact_3019_sup_Omono,axiom,
% 2.86/3.10 ! [C: nat,A2: nat,D2: nat,B2: nat] :
% 2.86/3.10 ( ( ord_less_eq_nat @ C @ A2 )
% 2.86/3.10 => ( ( ord_less_eq_nat @ D2 @ B2 )
% 2.86/3.10 => ( ord_less_eq_nat @ ( sup_sup_nat @ C @ D2 ) @ ( sup_sup_nat @ A2 @ B2 ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.mono
% 2.86/3.10 thf(fact_3020_sup_Omono,axiom,
% 2.86/3.10 ! [C: int,A2: int,D2: int,B2: int] :
% 2.86/3.10 ( ( ord_less_eq_int @ C @ A2 )
% 2.86/3.10 => ( ( ord_less_eq_int @ D2 @ B2 )
% 2.86/3.10 => ( ord_less_eq_int @ ( sup_sup_int @ C @ D2 ) @ ( sup_sup_int @ A2 @ B2 ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.mono
% 2.86/3.10 thf(fact_3021_sup__mono,axiom,
% 2.86/3.10 ! [A2: set_Pr4329608150637261639at_nat,C: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,D2: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( ord_le1268244103169919719at_nat @ A2 @ C )
% 2.86/3.10 => ( ( ord_le1268244103169919719at_nat @ B2 @ D2 )
% 2.86/3.10 => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) @ ( sup_su5525570899277871387at_nat @ C @ D2 ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_mono
% 2.86/3.10 thf(fact_3022_sup__mono,axiom,
% 2.86/3.10 ! [A2: assn,C: assn,B2: assn,D2: assn] :
% 2.86/3.10 ( ( ord_less_eq_assn @ A2 @ C )
% 2.86/3.10 => ( ( ord_less_eq_assn @ B2 @ D2 )
% 2.86/3.10 => ( ord_less_eq_assn @ ( sup_sup_assn @ A2 @ B2 ) @ ( sup_sup_assn @ C @ D2 ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_mono
% 2.86/3.10 thf(fact_3023_sup__mono,axiom,
% 2.86/3.10 ! [A2: filter_nat,C: filter_nat,B2: filter_nat,D2: filter_nat] :
% 2.86/3.10 ( ( ord_le2510731241096832064er_nat @ A2 @ C )
% 2.86/3.10 => ( ( ord_le2510731241096832064er_nat @ B2 @ D2 )
% 2.86/3.10 => ( ord_le2510731241096832064er_nat @ ( sup_sup_filter_nat @ A2 @ B2 ) @ ( sup_sup_filter_nat @ C @ D2 ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_mono
% 2.86/3.10 thf(fact_3024_sup__mono,axiom,
% 2.86/3.10 ! [A2: set_nat,C: set_nat,B2: set_nat,D2: set_nat] :
% 2.86/3.10 ( ( ord_less_eq_set_nat @ A2 @ C )
% 2.86/3.10 => ( ( ord_less_eq_set_nat @ B2 @ D2 )
% 2.86/3.10 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A2 @ B2 ) @ ( sup_sup_set_nat @ C @ D2 ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_mono
% 2.86/3.10 thf(fact_3025_sup__mono,axiom,
% 2.86/3.10 ! [A2: nat,C: nat,B2: nat,D2: nat] :
% 2.86/3.10 ( ( ord_less_eq_nat @ A2 @ C )
% 2.86/3.10 => ( ( ord_less_eq_nat @ B2 @ D2 )
% 2.86/3.10 => ( ord_less_eq_nat @ ( sup_sup_nat @ A2 @ B2 ) @ ( sup_sup_nat @ C @ D2 ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_mono
% 2.86/3.10 thf(fact_3026_sup__mono,axiom,
% 2.86/3.10 ! [A2: int,C: int,B2: int,D2: int] :
% 2.86/3.10 ( ( ord_less_eq_int @ A2 @ C )
% 2.86/3.10 => ( ( ord_less_eq_int @ B2 @ D2 )
% 2.86/3.10 => ( ord_less_eq_int @ ( sup_sup_int @ A2 @ B2 ) @ ( sup_sup_int @ C @ D2 ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_mono
% 2.86/3.10 thf(fact_3027_sup__least,axiom,
% 2.86/3.10 ! [Y: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( ord_le1268244103169919719at_nat @ Y @ X )
% 2.86/3.10 => ( ( ord_le1268244103169919719at_nat @ Z @ X )
% 2.86/3.10 => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ Y @ Z ) @ X ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_least
% 2.86/3.10 thf(fact_3028_sup__least,axiom,
% 2.86/3.10 ! [Y: assn,X: assn,Z: assn] :
% 2.86/3.10 ( ( ord_less_eq_assn @ Y @ X )
% 2.86/3.10 => ( ( ord_less_eq_assn @ Z @ X )
% 2.86/3.10 => ( ord_less_eq_assn @ ( sup_sup_assn @ Y @ Z ) @ X ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_least
% 2.86/3.10 thf(fact_3029_sup__least,axiom,
% 2.86/3.10 ! [Y: filter_nat,X: filter_nat,Z: filter_nat] :
% 2.86/3.10 ( ( ord_le2510731241096832064er_nat @ Y @ X )
% 2.86/3.10 => ( ( ord_le2510731241096832064er_nat @ Z @ X )
% 2.86/3.10 => ( ord_le2510731241096832064er_nat @ ( sup_sup_filter_nat @ Y @ Z ) @ X ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_least
% 2.86/3.10 thf(fact_3030_sup__least,axiom,
% 2.86/3.10 ! [Y: set_nat,X: set_nat,Z: set_nat] :
% 2.86/3.10 ( ( ord_less_eq_set_nat @ Y @ X )
% 2.86/3.10 => ( ( ord_less_eq_set_nat @ Z @ X )
% 2.86/3.10 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ Y @ Z ) @ X ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_least
% 2.86/3.10 thf(fact_3031_sup__least,axiom,
% 2.86/3.10 ! [Y: nat,X: nat,Z: nat] :
% 2.86/3.10 ( ( ord_less_eq_nat @ Y @ X )
% 2.86/3.10 => ( ( ord_less_eq_nat @ Z @ X )
% 2.86/3.10 => ( ord_less_eq_nat @ ( sup_sup_nat @ Y @ Z ) @ X ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_least
% 2.86/3.10 thf(fact_3032_sup__least,axiom,
% 2.86/3.10 ! [Y: int,X: int,Z: int] :
% 2.86/3.10 ( ( ord_less_eq_int @ Y @ X )
% 2.86/3.10 => ( ( ord_less_eq_int @ Z @ X )
% 2.86/3.10 => ( ord_less_eq_int @ ( sup_sup_int @ Y @ Z ) @ X ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_least
% 2.86/3.10 thf(fact_3033_le__iff__sup,axiom,
% 2.86/3.10 ( ord_le1268244103169919719at_nat
% 2.86/3.10 = ( ^ [X2: set_Pr4329608150637261639at_nat,Y5: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( sup_su5525570899277871387at_nat @ X2 @ Y5 )
% 2.86/3.10 = Y5 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % le_iff_sup
% 2.86/3.10 thf(fact_3034_le__iff__sup,axiom,
% 2.86/3.10 ( ord_less_eq_assn
% 2.86/3.10 = ( ^ [X2: assn,Y5: assn] :
% 2.86/3.10 ( ( sup_sup_assn @ X2 @ Y5 )
% 2.86/3.10 = Y5 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % le_iff_sup
% 2.86/3.10 thf(fact_3035_le__iff__sup,axiom,
% 2.86/3.10 ( ord_le2510731241096832064er_nat
% 2.86/3.10 = ( ^ [X2: filter_nat,Y5: filter_nat] :
% 2.86/3.10 ( ( sup_sup_filter_nat @ X2 @ Y5 )
% 2.86/3.10 = Y5 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % le_iff_sup
% 2.86/3.10 thf(fact_3036_le__iff__sup,axiom,
% 2.86/3.10 ( ord_less_eq_set_nat
% 2.86/3.10 = ( ^ [X2: set_nat,Y5: set_nat] :
% 2.86/3.10 ( ( sup_sup_set_nat @ X2 @ Y5 )
% 2.86/3.10 = Y5 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % le_iff_sup
% 2.86/3.10 thf(fact_3037_le__iff__sup,axiom,
% 2.86/3.10 ( ord_less_eq_nat
% 2.86/3.10 = ( ^ [X2: nat,Y5: nat] :
% 2.86/3.10 ( ( sup_sup_nat @ X2 @ Y5 )
% 2.86/3.10 = Y5 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % le_iff_sup
% 2.86/3.10 thf(fact_3038_le__iff__sup,axiom,
% 2.86/3.10 ( ord_less_eq_int
% 2.86/3.10 = ( ^ [X2: int,Y5: int] :
% 2.86/3.10 ( ( sup_sup_int @ X2 @ Y5 )
% 2.86/3.10 = Y5 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % le_iff_sup
% 2.86/3.10 thf(fact_3039_sup_OorderE,axiom,
% 2.86/3.10 ! [B2: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( ord_le1268244103169919719at_nat @ B2 @ A2 )
% 2.86/3.10 => ( A2
% 2.86/3.10 = ( sup_su5525570899277871387at_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.orderE
% 2.86/3.10 thf(fact_3040_sup_OorderE,axiom,
% 2.86/3.10 ! [B2: assn,A2: assn] :
% 2.86/3.10 ( ( ord_less_eq_assn @ B2 @ A2 )
% 2.86/3.10 => ( A2
% 2.86/3.10 = ( sup_sup_assn @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.orderE
% 2.86/3.10 thf(fact_3041_sup_OorderE,axiom,
% 2.86/3.10 ! [B2: filter_nat,A2: filter_nat] :
% 2.86/3.10 ( ( ord_le2510731241096832064er_nat @ B2 @ A2 )
% 2.86/3.10 => ( A2
% 2.86/3.10 = ( sup_sup_filter_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.orderE
% 2.86/3.10 thf(fact_3042_sup_OorderE,axiom,
% 2.86/3.10 ! [B2: set_nat,A2: set_nat] :
% 2.86/3.10 ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 2.86/3.10 => ( A2
% 2.86/3.10 = ( sup_sup_set_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.orderE
% 2.86/3.10 thf(fact_3043_sup_OorderE,axiom,
% 2.86/3.10 ! [B2: nat,A2: nat] :
% 2.86/3.10 ( ( ord_less_eq_nat @ B2 @ A2 )
% 2.86/3.10 => ( A2
% 2.86/3.10 = ( sup_sup_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.orderE
% 2.86/3.10 thf(fact_3044_sup_OorderE,axiom,
% 2.86/3.10 ! [B2: int,A2: int] :
% 2.86/3.10 ( ( ord_less_eq_int @ B2 @ A2 )
% 2.86/3.10 => ( A2
% 2.86/3.10 = ( sup_sup_int @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.orderE
% 2.86/3.10 thf(fact_3045_sup_OorderI,axiom,
% 2.86/3.10 ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( A2
% 2.86/3.10 = ( sup_su5525570899277871387at_nat @ A2 @ B2 ) )
% 2.86/3.10 => ( ord_le1268244103169919719at_nat @ B2 @ A2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.orderI
% 2.86/3.10 thf(fact_3046_sup_OorderI,axiom,
% 2.86/3.10 ! [A2: assn,B2: assn] :
% 2.86/3.10 ( ( A2
% 2.86/3.10 = ( sup_sup_assn @ A2 @ B2 ) )
% 2.86/3.10 => ( ord_less_eq_assn @ B2 @ A2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.orderI
% 2.86/3.10 thf(fact_3047_sup_OorderI,axiom,
% 2.86/3.10 ! [A2: filter_nat,B2: filter_nat] :
% 2.86/3.10 ( ( A2
% 2.86/3.10 = ( sup_sup_filter_nat @ A2 @ B2 ) )
% 2.86/3.10 => ( ord_le2510731241096832064er_nat @ B2 @ A2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.orderI
% 2.86/3.10 thf(fact_3048_sup_OorderI,axiom,
% 2.86/3.10 ! [A2: set_nat,B2: set_nat] :
% 2.86/3.10 ( ( A2
% 2.86/3.10 = ( sup_sup_set_nat @ A2 @ B2 ) )
% 2.86/3.10 => ( ord_less_eq_set_nat @ B2 @ A2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.orderI
% 2.86/3.10 thf(fact_3049_sup_OorderI,axiom,
% 2.86/3.10 ! [A2: nat,B2: nat] :
% 2.86/3.10 ( ( A2
% 2.86/3.10 = ( sup_sup_nat @ A2 @ B2 ) )
% 2.86/3.10 => ( ord_less_eq_nat @ B2 @ A2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.orderI
% 2.86/3.10 thf(fact_3050_sup_OorderI,axiom,
% 2.86/3.10 ! [A2: int,B2: int] :
% 2.86/3.10 ( ( A2
% 2.86/3.10 = ( sup_sup_int @ A2 @ B2 ) )
% 2.86/3.10 => ( ord_less_eq_int @ B2 @ A2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.orderI
% 2.86/3.10 thf(fact_3051_sup__unique,axiom,
% 2.86/3.10 ! [F4: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ! [X3: set_Pr4329608150637261639at_nat,Y2: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ X3 @ ( F4 @ X3 @ Y2 ) )
% 2.86/3.10 => ( ! [X3: set_Pr4329608150637261639at_nat,Y2: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ Y2 @ ( F4 @ X3 @ Y2 ) )
% 2.86/3.10 => ( ! [X3: set_Pr4329608150637261639at_nat,Y2: set_Pr4329608150637261639at_nat,Z4: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( ord_le1268244103169919719at_nat @ Y2 @ X3 )
% 2.86/3.10 => ( ( ord_le1268244103169919719at_nat @ Z4 @ X3 )
% 2.86/3.10 => ( ord_le1268244103169919719at_nat @ ( F4 @ Y2 @ Z4 ) @ X3 ) ) )
% 2.86/3.10 => ( ( sup_su5525570899277871387at_nat @ X @ Y )
% 2.86/3.10 = ( F4 @ X @ Y ) ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_unique
% 2.86/3.10 thf(fact_3052_sup__unique,axiom,
% 2.86/3.10 ! [F4: assn > assn > assn,X: assn,Y: assn] :
% 2.86/3.10 ( ! [X3: assn,Y2: assn] : ( ord_less_eq_assn @ X3 @ ( F4 @ X3 @ Y2 ) )
% 2.86/3.10 => ( ! [X3: assn,Y2: assn] : ( ord_less_eq_assn @ Y2 @ ( F4 @ X3 @ Y2 ) )
% 2.86/3.10 => ( ! [X3: assn,Y2: assn,Z4: assn] :
% 2.86/3.10 ( ( ord_less_eq_assn @ Y2 @ X3 )
% 2.86/3.10 => ( ( ord_less_eq_assn @ Z4 @ X3 )
% 2.86/3.10 => ( ord_less_eq_assn @ ( F4 @ Y2 @ Z4 ) @ X3 ) ) )
% 2.86/3.10 => ( ( sup_sup_assn @ X @ Y )
% 2.86/3.10 = ( F4 @ X @ Y ) ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_unique
% 2.86/3.10 thf(fact_3053_sup__unique,axiom,
% 2.86/3.10 ! [F4: filter_nat > filter_nat > filter_nat,X: filter_nat,Y: filter_nat] :
% 2.86/3.10 ( ! [X3: filter_nat,Y2: filter_nat] : ( ord_le2510731241096832064er_nat @ X3 @ ( F4 @ X3 @ Y2 ) )
% 2.86/3.10 => ( ! [X3: filter_nat,Y2: filter_nat] : ( ord_le2510731241096832064er_nat @ Y2 @ ( F4 @ X3 @ Y2 ) )
% 2.86/3.10 => ( ! [X3: filter_nat,Y2: filter_nat,Z4: filter_nat] :
% 2.86/3.10 ( ( ord_le2510731241096832064er_nat @ Y2 @ X3 )
% 2.86/3.10 => ( ( ord_le2510731241096832064er_nat @ Z4 @ X3 )
% 2.86/3.10 => ( ord_le2510731241096832064er_nat @ ( F4 @ Y2 @ Z4 ) @ X3 ) ) )
% 2.86/3.10 => ( ( sup_sup_filter_nat @ X @ Y )
% 2.86/3.10 = ( F4 @ X @ Y ) ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_unique
% 2.86/3.10 thf(fact_3054_sup__unique,axiom,
% 2.86/3.10 ! [F4: set_nat > set_nat > set_nat,X: set_nat,Y: set_nat] :
% 2.86/3.10 ( ! [X3: set_nat,Y2: set_nat] : ( ord_less_eq_set_nat @ X3 @ ( F4 @ X3 @ Y2 ) )
% 2.86/3.10 => ( ! [X3: set_nat,Y2: set_nat] : ( ord_less_eq_set_nat @ Y2 @ ( F4 @ X3 @ Y2 ) )
% 2.86/3.10 => ( ! [X3: set_nat,Y2: set_nat,Z4: set_nat] :
% 2.86/3.10 ( ( ord_less_eq_set_nat @ Y2 @ X3 )
% 2.86/3.10 => ( ( ord_less_eq_set_nat @ Z4 @ X3 )
% 2.86/3.10 => ( ord_less_eq_set_nat @ ( F4 @ Y2 @ Z4 ) @ X3 ) ) )
% 2.86/3.10 => ( ( sup_sup_set_nat @ X @ Y )
% 2.86/3.10 = ( F4 @ X @ Y ) ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_unique
% 2.86/3.10 thf(fact_3055_sup__unique,axiom,
% 2.86/3.10 ! [F4: nat > nat > nat,X: nat,Y: nat] :
% 2.86/3.10 ( ! [X3: nat,Y2: nat] : ( ord_less_eq_nat @ X3 @ ( F4 @ X3 @ Y2 ) )
% 2.86/3.10 => ( ! [X3: nat,Y2: nat] : ( ord_less_eq_nat @ Y2 @ ( F4 @ X3 @ Y2 ) )
% 2.86/3.10 => ( ! [X3: nat,Y2: nat,Z4: nat] :
% 2.86/3.10 ( ( ord_less_eq_nat @ Y2 @ X3 )
% 2.86/3.10 => ( ( ord_less_eq_nat @ Z4 @ X3 )
% 2.86/3.10 => ( ord_less_eq_nat @ ( F4 @ Y2 @ Z4 ) @ X3 ) ) )
% 2.86/3.10 => ( ( sup_sup_nat @ X @ Y )
% 2.86/3.10 = ( F4 @ X @ Y ) ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_unique
% 2.86/3.10 thf(fact_3056_sup__unique,axiom,
% 2.86/3.10 ! [F4: int > int > int,X: int,Y: int] :
% 2.86/3.10 ( ! [X3: int,Y2: int] : ( ord_less_eq_int @ X3 @ ( F4 @ X3 @ Y2 ) )
% 2.86/3.10 => ( ! [X3: int,Y2: int] : ( ord_less_eq_int @ Y2 @ ( F4 @ X3 @ Y2 ) )
% 2.86/3.10 => ( ! [X3: int,Y2: int,Z4: int] :
% 2.86/3.10 ( ( ord_less_eq_int @ Y2 @ X3 )
% 2.86/3.10 => ( ( ord_less_eq_int @ Z4 @ X3 )
% 2.86/3.10 => ( ord_less_eq_int @ ( F4 @ Y2 @ Z4 ) @ X3 ) ) )
% 2.86/3.10 => ( ( sup_sup_int @ X @ Y )
% 2.86/3.10 = ( F4 @ X @ Y ) ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_unique
% 2.86/3.10 thf(fact_3057_sup_Oabsorb1,axiom,
% 2.86/3.10 ! [B2: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( ord_le1268244103169919719at_nat @ B2 @ A2 )
% 2.86/3.10 => ( ( sup_su5525570899277871387at_nat @ A2 @ B2 )
% 2.86/3.10 = A2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.absorb1
% 2.86/3.10 thf(fact_3058_sup_Oabsorb1,axiom,
% 2.86/3.10 ! [B2: assn,A2: assn] :
% 2.86/3.10 ( ( ord_less_eq_assn @ B2 @ A2 )
% 2.86/3.10 => ( ( sup_sup_assn @ A2 @ B2 )
% 2.86/3.10 = A2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.absorb1
% 2.86/3.10 thf(fact_3059_sup_Oabsorb1,axiom,
% 2.86/3.10 ! [B2: filter_nat,A2: filter_nat] :
% 2.86/3.10 ( ( ord_le2510731241096832064er_nat @ B2 @ A2 )
% 2.86/3.10 => ( ( sup_sup_filter_nat @ A2 @ B2 )
% 2.86/3.10 = A2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.absorb1
% 2.86/3.10 thf(fact_3060_sup_Oabsorb1,axiom,
% 2.86/3.10 ! [B2: set_nat,A2: set_nat] :
% 2.86/3.10 ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 2.86/3.10 => ( ( sup_sup_set_nat @ A2 @ B2 )
% 2.86/3.10 = A2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.absorb1
% 2.86/3.10 thf(fact_3061_sup_Oabsorb1,axiom,
% 2.86/3.10 ! [B2: nat,A2: nat] :
% 2.86/3.10 ( ( ord_less_eq_nat @ B2 @ A2 )
% 2.86/3.10 => ( ( sup_sup_nat @ A2 @ B2 )
% 2.86/3.10 = A2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.absorb1
% 2.86/3.10 thf(fact_3062_sup_Oabsorb1,axiom,
% 2.86/3.10 ! [B2: int,A2: int] :
% 2.86/3.10 ( ( ord_less_eq_int @ B2 @ A2 )
% 2.86/3.10 => ( ( sup_sup_int @ A2 @ B2 )
% 2.86/3.10 = A2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.absorb1
% 2.86/3.10 thf(fact_3063_sup_Oabsorb2,axiom,
% 2.86/3.10 ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( ord_le1268244103169919719at_nat @ A2 @ B2 )
% 2.86/3.10 => ( ( sup_su5525570899277871387at_nat @ A2 @ B2 )
% 2.86/3.10 = B2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.absorb2
% 2.86/3.10 thf(fact_3064_sup_Oabsorb2,axiom,
% 2.86/3.10 ! [A2: assn,B2: assn] :
% 2.86/3.10 ( ( ord_less_eq_assn @ A2 @ B2 )
% 2.86/3.10 => ( ( sup_sup_assn @ A2 @ B2 )
% 2.86/3.10 = B2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.absorb2
% 2.86/3.10 thf(fact_3065_sup_Oabsorb2,axiom,
% 2.86/3.10 ! [A2: filter_nat,B2: filter_nat] :
% 2.86/3.10 ( ( ord_le2510731241096832064er_nat @ A2 @ B2 )
% 2.86/3.10 => ( ( sup_sup_filter_nat @ A2 @ B2 )
% 2.86/3.10 = B2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.absorb2
% 2.86/3.10 thf(fact_3066_sup_Oabsorb2,axiom,
% 2.86/3.10 ! [A2: set_nat,B2: set_nat] :
% 2.86/3.10 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 2.86/3.10 => ( ( sup_sup_set_nat @ A2 @ B2 )
% 2.86/3.10 = B2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.absorb2
% 2.86/3.10 thf(fact_3067_sup_Oabsorb2,axiom,
% 2.86/3.10 ! [A2: nat,B2: nat] :
% 2.86/3.10 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.10 => ( ( sup_sup_nat @ A2 @ B2 )
% 2.86/3.10 = B2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.absorb2
% 2.86/3.10 thf(fact_3068_sup_Oabsorb2,axiom,
% 2.86/3.10 ! [A2: int,B2: int] :
% 2.86/3.10 ( ( ord_less_eq_int @ A2 @ B2 )
% 2.86/3.10 => ( ( sup_sup_int @ A2 @ B2 )
% 2.86/3.10 = B2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.absorb2
% 2.86/3.10 thf(fact_3069_sup__absorb1,axiom,
% 2.86/3.10 ! [Y: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( ord_le1268244103169919719at_nat @ Y @ X )
% 2.86/3.10 => ( ( sup_su5525570899277871387at_nat @ X @ Y )
% 2.86/3.10 = X ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_absorb1
% 2.86/3.10 thf(fact_3070_sup__absorb1,axiom,
% 2.86/3.10 ! [Y: assn,X: assn] :
% 2.86/3.10 ( ( ord_less_eq_assn @ Y @ X )
% 2.86/3.10 => ( ( sup_sup_assn @ X @ Y )
% 2.86/3.10 = X ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_absorb1
% 2.86/3.10 thf(fact_3071_sup__absorb1,axiom,
% 2.86/3.10 ! [Y: filter_nat,X: filter_nat] :
% 2.86/3.10 ( ( ord_le2510731241096832064er_nat @ Y @ X )
% 2.86/3.10 => ( ( sup_sup_filter_nat @ X @ Y )
% 2.86/3.10 = X ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_absorb1
% 2.86/3.10 thf(fact_3072_sup__absorb1,axiom,
% 2.86/3.10 ! [Y: set_nat,X: set_nat] :
% 2.86/3.10 ( ( ord_less_eq_set_nat @ Y @ X )
% 2.86/3.10 => ( ( sup_sup_set_nat @ X @ Y )
% 2.86/3.10 = X ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_absorb1
% 2.86/3.10 thf(fact_3073_sup__absorb1,axiom,
% 2.86/3.10 ! [Y: nat,X: nat] :
% 2.86/3.10 ( ( ord_less_eq_nat @ Y @ X )
% 2.86/3.10 => ( ( sup_sup_nat @ X @ Y )
% 2.86/3.10 = X ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_absorb1
% 2.86/3.10 thf(fact_3074_sup__absorb1,axiom,
% 2.86/3.10 ! [Y: int,X: int] :
% 2.86/3.10 ( ( ord_less_eq_int @ Y @ X )
% 2.86/3.10 => ( ( sup_sup_int @ X @ Y )
% 2.86/3.10 = X ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_absorb1
% 2.86/3.10 thf(fact_3075_sup__absorb2,axiom,
% 2.86/3.10 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( ord_le1268244103169919719at_nat @ X @ Y )
% 2.86/3.10 => ( ( sup_su5525570899277871387at_nat @ X @ Y )
% 2.86/3.10 = Y ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_absorb2
% 2.86/3.10 thf(fact_3076_sup__absorb2,axiom,
% 2.86/3.10 ! [X: assn,Y: assn] :
% 2.86/3.10 ( ( ord_less_eq_assn @ X @ Y )
% 2.86/3.10 => ( ( sup_sup_assn @ X @ Y )
% 2.86/3.10 = Y ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_absorb2
% 2.86/3.10 thf(fact_3077_sup__absorb2,axiom,
% 2.86/3.10 ! [X: filter_nat,Y: filter_nat] :
% 2.86/3.10 ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 2.86/3.10 => ( ( sup_sup_filter_nat @ X @ Y )
% 2.86/3.10 = Y ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_absorb2
% 2.86/3.10 thf(fact_3078_sup__absorb2,axiom,
% 2.86/3.10 ! [X: set_nat,Y: set_nat] :
% 2.86/3.10 ( ( ord_less_eq_set_nat @ X @ Y )
% 2.86/3.10 => ( ( sup_sup_set_nat @ X @ Y )
% 2.86/3.10 = Y ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_absorb2
% 2.86/3.10 thf(fact_3079_sup__absorb2,axiom,
% 2.86/3.10 ! [X: nat,Y: nat] :
% 2.86/3.10 ( ( ord_less_eq_nat @ X @ Y )
% 2.86/3.10 => ( ( sup_sup_nat @ X @ Y )
% 2.86/3.10 = Y ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_absorb2
% 2.86/3.10 thf(fact_3080_sup__absorb2,axiom,
% 2.86/3.10 ! [X: int,Y: int] :
% 2.86/3.10 ( ( ord_less_eq_int @ X @ Y )
% 2.86/3.10 => ( ( sup_sup_int @ X @ Y )
% 2.86/3.10 = Y ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_absorb2
% 2.86/3.10 thf(fact_3081_sup_OboundedE,axiom,
% 2.86/3.10 ! [B2: set_Pr4329608150637261639at_nat,C: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ B2 @ C ) @ A2 )
% 2.86/3.10 => ~ ( ( ord_le1268244103169919719at_nat @ B2 @ A2 )
% 2.86/3.10 => ~ ( ord_le1268244103169919719at_nat @ C @ A2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.boundedE
% 2.86/3.10 thf(fact_3082_sup_OboundedE,axiom,
% 2.86/3.10 ! [B2: assn,C: assn,A2: assn] :
% 2.86/3.10 ( ( ord_less_eq_assn @ ( sup_sup_assn @ B2 @ C ) @ A2 )
% 2.86/3.10 => ~ ( ( ord_less_eq_assn @ B2 @ A2 )
% 2.86/3.10 => ~ ( ord_less_eq_assn @ C @ A2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.boundedE
% 2.86/3.10 thf(fact_3083_sup_OboundedE,axiom,
% 2.86/3.10 ! [B2: filter_nat,C: filter_nat,A2: filter_nat] :
% 2.86/3.10 ( ( ord_le2510731241096832064er_nat @ ( sup_sup_filter_nat @ B2 @ C ) @ A2 )
% 2.86/3.10 => ~ ( ( ord_le2510731241096832064er_nat @ B2 @ A2 )
% 2.86/3.10 => ~ ( ord_le2510731241096832064er_nat @ C @ A2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.boundedE
% 2.86/3.10 thf(fact_3084_sup_OboundedE,axiom,
% 2.86/3.10 ! [B2: set_nat,C: set_nat,A2: set_nat] :
% 2.86/3.10 ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ B2 @ C ) @ A2 )
% 2.86/3.10 => ~ ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 2.86/3.10 => ~ ( ord_less_eq_set_nat @ C @ A2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.boundedE
% 2.86/3.10 thf(fact_3085_sup_OboundedE,axiom,
% 2.86/3.10 ! [B2: nat,C: nat,A2: nat] :
% 2.86/3.10 ( ( ord_less_eq_nat @ ( sup_sup_nat @ B2 @ C ) @ A2 )
% 2.86/3.10 => ~ ( ( ord_less_eq_nat @ B2 @ A2 )
% 2.86/3.10 => ~ ( ord_less_eq_nat @ C @ A2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.boundedE
% 2.86/3.10 thf(fact_3086_sup_OboundedE,axiom,
% 2.86/3.10 ! [B2: int,C: int,A2: int] :
% 2.86/3.10 ( ( ord_less_eq_int @ ( sup_sup_int @ B2 @ C ) @ A2 )
% 2.86/3.10 => ~ ( ( ord_less_eq_int @ B2 @ A2 )
% 2.86/3.10 => ~ ( ord_less_eq_int @ C @ A2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.boundedE
% 2.86/3.10 thf(fact_3087_sup_OboundedI,axiom,
% 2.86/3.10 ! [B2: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat,C: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( ord_le1268244103169919719at_nat @ B2 @ A2 )
% 2.86/3.10 => ( ( ord_le1268244103169919719at_nat @ C @ A2 )
% 2.86/3.10 => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ B2 @ C ) @ A2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.boundedI
% 2.86/3.10 thf(fact_3088_sup_OboundedI,axiom,
% 2.86/3.10 ! [B2: assn,A2: assn,C: assn] :
% 2.86/3.10 ( ( ord_less_eq_assn @ B2 @ A2 )
% 2.86/3.10 => ( ( ord_less_eq_assn @ C @ A2 )
% 2.86/3.10 => ( ord_less_eq_assn @ ( sup_sup_assn @ B2 @ C ) @ A2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.boundedI
% 2.86/3.10 thf(fact_3089_sup_OboundedI,axiom,
% 2.86/3.10 ! [B2: filter_nat,A2: filter_nat,C: filter_nat] :
% 2.86/3.10 ( ( ord_le2510731241096832064er_nat @ B2 @ A2 )
% 2.86/3.10 => ( ( ord_le2510731241096832064er_nat @ C @ A2 )
% 2.86/3.10 => ( ord_le2510731241096832064er_nat @ ( sup_sup_filter_nat @ B2 @ C ) @ A2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.boundedI
% 2.86/3.10 thf(fact_3090_sup_OboundedI,axiom,
% 2.86/3.10 ! [B2: set_nat,A2: set_nat,C: set_nat] :
% 2.86/3.10 ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 2.86/3.10 => ( ( ord_less_eq_set_nat @ C @ A2 )
% 2.86/3.10 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ B2 @ C ) @ A2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.boundedI
% 2.86/3.10 thf(fact_3091_sup_OboundedI,axiom,
% 2.86/3.10 ! [B2: nat,A2: nat,C: nat] :
% 2.86/3.10 ( ( ord_less_eq_nat @ B2 @ A2 )
% 2.86/3.10 => ( ( ord_less_eq_nat @ C @ A2 )
% 2.86/3.10 => ( ord_less_eq_nat @ ( sup_sup_nat @ B2 @ C ) @ A2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.boundedI
% 2.86/3.10 thf(fact_3092_sup_OboundedI,axiom,
% 2.86/3.10 ! [B2: int,A2: int,C: int] :
% 2.86/3.10 ( ( ord_less_eq_int @ B2 @ A2 )
% 2.86/3.10 => ( ( ord_less_eq_int @ C @ A2 )
% 2.86/3.10 => ( ord_less_eq_int @ ( sup_sup_int @ B2 @ C ) @ A2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.boundedI
% 2.86/3.10 thf(fact_3093_sup_Oorder__iff,axiom,
% 2.86/3.10 ( ord_le1268244103169919719at_nat
% 2.86/3.10 = ( ^ [B3: set_Pr4329608150637261639at_nat,A3: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( A3
% 2.86/3.10 = ( sup_su5525570899277871387at_nat @ A3 @ B3 ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.order_iff
% 2.86/3.10 thf(fact_3094_sup_Oorder__iff,axiom,
% 2.86/3.10 ( ord_less_eq_assn
% 2.86/3.10 = ( ^ [B3: assn,A3: assn] :
% 2.86/3.10 ( A3
% 2.86/3.10 = ( sup_sup_assn @ A3 @ B3 ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.order_iff
% 2.86/3.10 thf(fact_3095_sup_Oorder__iff,axiom,
% 2.86/3.10 ( ord_le2510731241096832064er_nat
% 2.86/3.10 = ( ^ [B3: filter_nat,A3: filter_nat] :
% 2.86/3.10 ( A3
% 2.86/3.10 = ( sup_sup_filter_nat @ A3 @ B3 ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.order_iff
% 2.86/3.10 thf(fact_3096_sup_Oorder__iff,axiom,
% 2.86/3.10 ( ord_less_eq_set_nat
% 2.86/3.10 = ( ^ [B3: set_nat,A3: set_nat] :
% 2.86/3.10 ( A3
% 2.86/3.10 = ( sup_sup_set_nat @ A3 @ B3 ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.order_iff
% 2.86/3.10 thf(fact_3097_sup_Oorder__iff,axiom,
% 2.86/3.10 ( ord_less_eq_nat
% 2.86/3.10 = ( ^ [B3: nat,A3: nat] :
% 2.86/3.10 ( A3
% 2.86/3.10 = ( sup_sup_nat @ A3 @ B3 ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.order_iff
% 2.86/3.10 thf(fact_3098_sup_Oorder__iff,axiom,
% 2.86/3.10 ( ord_less_eq_int
% 2.86/3.10 = ( ^ [B3: int,A3: int] :
% 2.86/3.10 ( A3
% 2.86/3.10 = ( sup_sup_int @ A3 @ B3 ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.order_iff
% 2.86/3.10 thf(fact_3099_sup_Ocobounded1,axiom,
% 2.86/3.10 ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ A2 @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.cobounded1
% 2.86/3.10 thf(fact_3100_sup_Ocobounded1,axiom,
% 2.86/3.10 ! [A2: assn,B2: assn] : ( ord_less_eq_assn @ A2 @ ( sup_sup_assn @ A2 @ B2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.cobounded1
% 2.86/3.10 thf(fact_3101_sup_Ocobounded1,axiom,
% 2.86/3.10 ! [A2: filter_nat,B2: filter_nat] : ( ord_le2510731241096832064er_nat @ A2 @ ( sup_sup_filter_nat @ A2 @ B2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.cobounded1
% 2.86/3.10 thf(fact_3102_sup_Ocobounded1,axiom,
% 2.86/3.10 ! [A2: set_nat,B2: set_nat] : ( ord_less_eq_set_nat @ A2 @ ( sup_sup_set_nat @ A2 @ B2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.cobounded1
% 2.86/3.10 thf(fact_3103_sup_Ocobounded1,axiom,
% 2.86/3.10 ! [A2: nat,B2: nat] : ( ord_less_eq_nat @ A2 @ ( sup_sup_nat @ A2 @ B2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.cobounded1
% 2.86/3.10 thf(fact_3104_sup_Ocobounded1,axiom,
% 2.86/3.10 ! [A2: int,B2: int] : ( ord_less_eq_int @ A2 @ ( sup_sup_int @ A2 @ B2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.cobounded1
% 2.86/3.10 thf(fact_3105_sup_Ocobounded2,axiom,
% 2.86/3.10 ! [B2: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ B2 @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.cobounded2
% 2.86/3.10 thf(fact_3106_sup_Ocobounded2,axiom,
% 2.86/3.10 ! [B2: assn,A2: assn] : ( ord_less_eq_assn @ B2 @ ( sup_sup_assn @ A2 @ B2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.cobounded2
% 2.86/3.10 thf(fact_3107_sup_Ocobounded2,axiom,
% 2.86/3.10 ! [B2: filter_nat,A2: filter_nat] : ( ord_le2510731241096832064er_nat @ B2 @ ( sup_sup_filter_nat @ A2 @ B2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.cobounded2
% 2.86/3.10 thf(fact_3108_sup_Ocobounded2,axiom,
% 2.86/3.10 ! [B2: set_nat,A2: set_nat] : ( ord_less_eq_set_nat @ B2 @ ( sup_sup_set_nat @ A2 @ B2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.cobounded2
% 2.86/3.10 thf(fact_3109_sup_Ocobounded2,axiom,
% 2.86/3.10 ! [B2: nat,A2: nat] : ( ord_less_eq_nat @ B2 @ ( sup_sup_nat @ A2 @ B2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.cobounded2
% 2.86/3.10 thf(fact_3110_sup_Ocobounded2,axiom,
% 2.86/3.10 ! [B2: int,A2: int] : ( ord_less_eq_int @ B2 @ ( sup_sup_int @ A2 @ B2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.cobounded2
% 2.86/3.10 thf(fact_3111_sup_Oabsorb__iff1,axiom,
% 2.86/3.10 ( ord_le1268244103169919719at_nat
% 2.86/3.10 = ( ^ [B3: set_Pr4329608150637261639at_nat,A3: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( sup_su5525570899277871387at_nat @ A3 @ B3 )
% 2.86/3.10 = A3 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.absorb_iff1
% 2.86/3.10 thf(fact_3112_sup_Oabsorb__iff1,axiom,
% 2.86/3.10 ( ord_less_eq_assn
% 2.86/3.10 = ( ^ [B3: assn,A3: assn] :
% 2.86/3.10 ( ( sup_sup_assn @ A3 @ B3 )
% 2.86/3.10 = A3 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.absorb_iff1
% 2.86/3.10 thf(fact_3113_sup_Oabsorb__iff1,axiom,
% 2.86/3.10 ( ord_le2510731241096832064er_nat
% 2.86/3.10 = ( ^ [B3: filter_nat,A3: filter_nat] :
% 2.86/3.10 ( ( sup_sup_filter_nat @ A3 @ B3 )
% 2.86/3.10 = A3 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.absorb_iff1
% 2.86/3.10 thf(fact_3114_sup_Oabsorb__iff1,axiom,
% 2.86/3.10 ( ord_less_eq_set_nat
% 2.86/3.10 = ( ^ [B3: set_nat,A3: set_nat] :
% 2.86/3.10 ( ( sup_sup_set_nat @ A3 @ B3 )
% 2.86/3.10 = A3 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.absorb_iff1
% 2.86/3.10 thf(fact_3115_sup_Oabsorb__iff1,axiom,
% 2.86/3.10 ( ord_less_eq_nat
% 2.86/3.10 = ( ^ [B3: nat,A3: nat] :
% 2.86/3.10 ( ( sup_sup_nat @ A3 @ B3 )
% 2.86/3.10 = A3 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.absorb_iff1
% 2.86/3.10 thf(fact_3116_sup_Oabsorb__iff1,axiom,
% 2.86/3.10 ( ord_less_eq_int
% 2.86/3.10 = ( ^ [B3: int,A3: int] :
% 2.86/3.10 ( ( sup_sup_int @ A3 @ B3 )
% 2.86/3.10 = A3 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.absorb_iff1
% 2.86/3.10 thf(fact_3117_sup_Oabsorb__iff2,axiom,
% 2.86/3.10 ( ord_le1268244103169919719at_nat
% 2.86/3.10 = ( ^ [A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( sup_su5525570899277871387at_nat @ A3 @ B3 )
% 2.86/3.10 = B3 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.absorb_iff2
% 2.86/3.10 thf(fact_3118_sup_Oabsorb__iff2,axiom,
% 2.86/3.10 ( ord_less_eq_assn
% 2.86/3.10 = ( ^ [A3: assn,B3: assn] :
% 2.86/3.10 ( ( sup_sup_assn @ A3 @ B3 )
% 2.86/3.10 = B3 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.absorb_iff2
% 2.86/3.10 thf(fact_3119_sup_Oabsorb__iff2,axiom,
% 2.86/3.10 ( ord_le2510731241096832064er_nat
% 2.86/3.10 = ( ^ [A3: filter_nat,B3: filter_nat] :
% 2.86/3.10 ( ( sup_sup_filter_nat @ A3 @ B3 )
% 2.86/3.10 = B3 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.absorb_iff2
% 2.86/3.10 thf(fact_3120_sup_Oabsorb__iff2,axiom,
% 2.86/3.10 ( ord_less_eq_set_nat
% 2.86/3.10 = ( ^ [A3: set_nat,B3: set_nat] :
% 2.86/3.10 ( ( sup_sup_set_nat @ A3 @ B3 )
% 2.86/3.10 = B3 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.absorb_iff2
% 2.86/3.10 thf(fact_3121_sup_Oabsorb__iff2,axiom,
% 2.86/3.10 ( ord_less_eq_nat
% 2.86/3.10 = ( ^ [A3: nat,B3: nat] :
% 2.86/3.10 ( ( sup_sup_nat @ A3 @ B3 )
% 2.86/3.10 = B3 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.absorb_iff2
% 2.86/3.10 thf(fact_3122_sup_Oabsorb__iff2,axiom,
% 2.86/3.10 ( ord_less_eq_int
% 2.86/3.10 = ( ^ [A3: int,B3: int] :
% 2.86/3.10 ( ( sup_sup_int @ A3 @ B3 )
% 2.86/3.10 = B3 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.absorb_iff2
% 2.86/3.10 thf(fact_3123_sup_OcoboundedI1,axiom,
% 2.86/3.10 ! [C: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( ord_le1268244103169919719at_nat @ C @ A2 )
% 2.86/3.10 => ( ord_le1268244103169919719at_nat @ C @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.coboundedI1
% 2.86/3.10 thf(fact_3124_sup_OcoboundedI1,axiom,
% 2.86/3.10 ! [C: assn,A2: assn,B2: assn] :
% 2.86/3.10 ( ( ord_less_eq_assn @ C @ A2 )
% 2.86/3.10 => ( ord_less_eq_assn @ C @ ( sup_sup_assn @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.coboundedI1
% 2.86/3.10 thf(fact_3125_sup_OcoboundedI1,axiom,
% 2.86/3.10 ! [C: filter_nat,A2: filter_nat,B2: filter_nat] :
% 2.86/3.10 ( ( ord_le2510731241096832064er_nat @ C @ A2 )
% 2.86/3.10 => ( ord_le2510731241096832064er_nat @ C @ ( sup_sup_filter_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.coboundedI1
% 2.86/3.10 thf(fact_3126_sup_OcoboundedI1,axiom,
% 2.86/3.10 ! [C: set_nat,A2: set_nat,B2: set_nat] :
% 2.86/3.10 ( ( ord_less_eq_set_nat @ C @ A2 )
% 2.86/3.10 => ( ord_less_eq_set_nat @ C @ ( sup_sup_set_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.coboundedI1
% 2.86/3.10 thf(fact_3127_sup_OcoboundedI1,axiom,
% 2.86/3.10 ! [C: nat,A2: nat,B2: nat] :
% 2.86/3.10 ( ( ord_less_eq_nat @ C @ A2 )
% 2.86/3.10 => ( ord_less_eq_nat @ C @ ( sup_sup_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.coboundedI1
% 2.86/3.10 thf(fact_3128_sup_OcoboundedI1,axiom,
% 2.86/3.10 ! [C: int,A2: int,B2: int] :
% 2.86/3.10 ( ( ord_less_eq_int @ C @ A2 )
% 2.86/3.10 => ( ord_less_eq_int @ C @ ( sup_sup_int @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.coboundedI1
% 2.86/3.10 thf(fact_3129_sup_OcoboundedI2,axiom,
% 2.86/3.10 ! [C: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( ord_le1268244103169919719at_nat @ C @ B2 )
% 2.86/3.10 => ( ord_le1268244103169919719at_nat @ C @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.coboundedI2
% 2.86/3.10 thf(fact_3130_sup_OcoboundedI2,axiom,
% 2.86/3.10 ! [C: assn,B2: assn,A2: assn] :
% 2.86/3.10 ( ( ord_less_eq_assn @ C @ B2 )
% 2.86/3.10 => ( ord_less_eq_assn @ C @ ( sup_sup_assn @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.coboundedI2
% 2.86/3.10 thf(fact_3131_sup_OcoboundedI2,axiom,
% 2.86/3.10 ! [C: filter_nat,B2: filter_nat,A2: filter_nat] :
% 2.86/3.10 ( ( ord_le2510731241096832064er_nat @ C @ B2 )
% 2.86/3.10 => ( ord_le2510731241096832064er_nat @ C @ ( sup_sup_filter_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.coboundedI2
% 2.86/3.10 thf(fact_3132_sup_OcoboundedI2,axiom,
% 2.86/3.10 ! [C: set_nat,B2: set_nat,A2: set_nat] :
% 2.86/3.10 ( ( ord_less_eq_set_nat @ C @ B2 )
% 2.86/3.10 => ( ord_less_eq_set_nat @ C @ ( sup_sup_set_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.coboundedI2
% 2.86/3.10 thf(fact_3133_sup_OcoboundedI2,axiom,
% 2.86/3.10 ! [C: nat,B2: nat,A2: nat] :
% 2.86/3.10 ( ( ord_less_eq_nat @ C @ B2 )
% 2.86/3.10 => ( ord_less_eq_nat @ C @ ( sup_sup_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.coboundedI2
% 2.86/3.10 thf(fact_3134_sup_OcoboundedI2,axiom,
% 2.86/3.10 ! [C: int,B2: int,A2: int] :
% 2.86/3.10 ( ( ord_less_eq_int @ C @ B2 )
% 2.86/3.10 => ( ord_less_eq_int @ C @ ( sup_sup_int @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.coboundedI2
% 2.86/3.10 thf(fact_3135_inf__min,axiom,
% 2.86/3.10 inf_inf_nat = ord_min_nat ).
% 2.86/3.10
% 2.86/3.10 % inf_min
% 2.86/3.10 thf(fact_3136_sup_Ostrict__coboundedI2,axiom,
% 2.86/3.10 ! [C: set_nat,B2: set_nat,A2: set_nat] :
% 2.86/3.10 ( ( ord_less_set_nat @ C @ B2 )
% 2.86/3.10 => ( ord_less_set_nat @ C @ ( sup_sup_set_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.strict_coboundedI2
% 2.86/3.10 thf(fact_3137_sup_Ostrict__coboundedI2,axiom,
% 2.86/3.10 ! [C: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( ord_le2604355607129572851at_nat @ C @ B2 )
% 2.86/3.10 => ( ord_le2604355607129572851at_nat @ C @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.strict_coboundedI2
% 2.86/3.10 thf(fact_3138_sup_Ostrict__coboundedI2,axiom,
% 2.86/3.10 ! [C: assn,B2: assn,A2: assn] :
% 2.86/3.10 ( ( ord_less_assn @ C @ B2 )
% 2.86/3.10 => ( ord_less_assn @ C @ ( sup_sup_assn @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.strict_coboundedI2
% 2.86/3.10 thf(fact_3139_sup_Ostrict__coboundedI2,axiom,
% 2.86/3.10 ! [C: nat,B2: nat,A2: nat] :
% 2.86/3.10 ( ( ord_less_nat @ C @ B2 )
% 2.86/3.10 => ( ord_less_nat @ C @ ( sup_sup_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.strict_coboundedI2
% 2.86/3.10 thf(fact_3140_sup_Ostrict__coboundedI2,axiom,
% 2.86/3.10 ! [C: int,B2: int,A2: int] :
% 2.86/3.10 ( ( ord_less_int @ C @ B2 )
% 2.86/3.10 => ( ord_less_int @ C @ ( sup_sup_int @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.strict_coboundedI2
% 2.86/3.10 thf(fact_3141_sup_Ostrict__coboundedI1,axiom,
% 2.86/3.10 ! [C: set_nat,A2: set_nat,B2: set_nat] :
% 2.86/3.10 ( ( ord_less_set_nat @ C @ A2 )
% 2.86/3.10 => ( ord_less_set_nat @ C @ ( sup_sup_set_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.strict_coboundedI1
% 2.86/3.10 thf(fact_3142_sup_Ostrict__coboundedI1,axiom,
% 2.86/3.10 ! [C: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( ord_le2604355607129572851at_nat @ C @ A2 )
% 2.86/3.10 => ( ord_le2604355607129572851at_nat @ C @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.strict_coboundedI1
% 2.86/3.10 thf(fact_3143_sup_Ostrict__coboundedI1,axiom,
% 2.86/3.10 ! [C: assn,A2: assn,B2: assn] :
% 2.86/3.10 ( ( ord_less_assn @ C @ A2 )
% 2.86/3.10 => ( ord_less_assn @ C @ ( sup_sup_assn @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.strict_coboundedI1
% 2.86/3.10 thf(fact_3144_sup_Ostrict__coboundedI1,axiom,
% 2.86/3.10 ! [C: nat,A2: nat,B2: nat] :
% 2.86/3.10 ( ( ord_less_nat @ C @ A2 )
% 2.86/3.10 => ( ord_less_nat @ C @ ( sup_sup_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.strict_coboundedI1
% 2.86/3.10 thf(fact_3145_sup_Ostrict__coboundedI1,axiom,
% 2.86/3.10 ! [C: int,A2: int,B2: int] :
% 2.86/3.10 ( ( ord_less_int @ C @ A2 )
% 2.86/3.10 => ( ord_less_int @ C @ ( sup_sup_int @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.strict_coboundedI1
% 2.86/3.10 thf(fact_3146_sup_Ostrict__order__iff,axiom,
% 2.86/3.10 ( ord_less_set_nat
% 2.86/3.10 = ( ^ [B3: set_nat,A3: set_nat] :
% 2.86/3.10 ( ( A3
% 2.86/3.10 = ( sup_sup_set_nat @ A3 @ B3 ) )
% 2.86/3.10 & ( A3 != B3 ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.strict_order_iff
% 2.86/3.10 thf(fact_3147_sup_Ostrict__order__iff,axiom,
% 2.86/3.10 ( ord_le2604355607129572851at_nat
% 2.86/3.10 = ( ^ [B3: set_Pr4329608150637261639at_nat,A3: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( A3
% 2.86/3.10 = ( sup_su5525570899277871387at_nat @ A3 @ B3 ) )
% 2.86/3.10 & ( A3 != B3 ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.strict_order_iff
% 2.86/3.10 thf(fact_3148_sup_Ostrict__order__iff,axiom,
% 2.86/3.10 ( ord_less_assn
% 2.86/3.10 = ( ^ [B3: assn,A3: assn] :
% 2.86/3.10 ( ( A3
% 2.86/3.10 = ( sup_sup_assn @ A3 @ B3 ) )
% 2.86/3.10 & ( A3 != B3 ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.strict_order_iff
% 2.86/3.10 thf(fact_3149_sup_Ostrict__order__iff,axiom,
% 2.86/3.10 ( ord_less_nat
% 2.86/3.10 = ( ^ [B3: nat,A3: nat] :
% 2.86/3.10 ( ( A3
% 2.86/3.10 = ( sup_sup_nat @ A3 @ B3 ) )
% 2.86/3.10 & ( A3 != B3 ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.strict_order_iff
% 2.86/3.10 thf(fact_3150_sup_Ostrict__order__iff,axiom,
% 2.86/3.10 ( ord_less_int
% 2.86/3.10 = ( ^ [B3: int,A3: int] :
% 2.86/3.10 ( ( A3
% 2.86/3.10 = ( sup_sup_int @ A3 @ B3 ) )
% 2.86/3.10 & ( A3 != B3 ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.strict_order_iff
% 2.86/3.10 thf(fact_3151_sup_Ostrict__boundedE,axiom,
% 2.86/3.10 ! [B2: set_nat,C: set_nat,A2: set_nat] :
% 2.86/3.10 ( ( ord_less_set_nat @ ( sup_sup_set_nat @ B2 @ C ) @ A2 )
% 2.86/3.10 => ~ ( ( ord_less_set_nat @ B2 @ A2 )
% 2.86/3.10 => ~ ( ord_less_set_nat @ C @ A2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.strict_boundedE
% 2.86/3.10 thf(fact_3152_sup_Ostrict__boundedE,axiom,
% 2.86/3.10 ! [B2: set_Pr4329608150637261639at_nat,C: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( ord_le2604355607129572851at_nat @ ( sup_su5525570899277871387at_nat @ B2 @ C ) @ A2 )
% 2.86/3.10 => ~ ( ( ord_le2604355607129572851at_nat @ B2 @ A2 )
% 2.86/3.10 => ~ ( ord_le2604355607129572851at_nat @ C @ A2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.strict_boundedE
% 2.86/3.10 thf(fact_3153_sup_Ostrict__boundedE,axiom,
% 2.86/3.10 ! [B2: assn,C: assn,A2: assn] :
% 2.86/3.10 ( ( ord_less_assn @ ( sup_sup_assn @ B2 @ C ) @ A2 )
% 2.86/3.10 => ~ ( ( ord_less_assn @ B2 @ A2 )
% 2.86/3.10 => ~ ( ord_less_assn @ C @ A2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.strict_boundedE
% 2.86/3.10 thf(fact_3154_sup_Ostrict__boundedE,axiom,
% 2.86/3.10 ! [B2: nat,C: nat,A2: nat] :
% 2.86/3.10 ( ( ord_less_nat @ ( sup_sup_nat @ B2 @ C ) @ A2 )
% 2.86/3.10 => ~ ( ( ord_less_nat @ B2 @ A2 )
% 2.86/3.10 => ~ ( ord_less_nat @ C @ A2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.strict_boundedE
% 2.86/3.10 thf(fact_3155_sup_Ostrict__boundedE,axiom,
% 2.86/3.10 ! [B2: int,C: int,A2: int] :
% 2.86/3.10 ( ( ord_less_int @ ( sup_sup_int @ B2 @ C ) @ A2 )
% 2.86/3.10 => ~ ( ( ord_less_int @ B2 @ A2 )
% 2.86/3.10 => ~ ( ord_less_int @ C @ A2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.strict_boundedE
% 2.86/3.10 thf(fact_3156_sup_Oabsorb4,axiom,
% 2.86/3.10 ! [A2: set_nat,B2: set_nat] :
% 2.86/3.10 ( ( ord_less_set_nat @ A2 @ B2 )
% 2.86/3.10 => ( ( sup_sup_set_nat @ A2 @ B2 )
% 2.86/3.10 = B2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.absorb4
% 2.86/3.10 thf(fact_3157_sup_Oabsorb4,axiom,
% 2.86/3.10 ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( ord_le2604355607129572851at_nat @ A2 @ B2 )
% 2.86/3.10 => ( ( sup_su5525570899277871387at_nat @ A2 @ B2 )
% 2.86/3.10 = B2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.absorb4
% 2.86/3.10 thf(fact_3158_sup_Oabsorb4,axiom,
% 2.86/3.10 ! [A2: assn,B2: assn] :
% 2.86/3.10 ( ( ord_less_assn @ A2 @ B2 )
% 2.86/3.10 => ( ( sup_sup_assn @ A2 @ B2 )
% 2.86/3.10 = B2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.absorb4
% 2.86/3.10 thf(fact_3159_sup_Oabsorb4,axiom,
% 2.86/3.10 ! [A2: nat,B2: nat] :
% 2.86/3.10 ( ( ord_less_nat @ A2 @ B2 )
% 2.86/3.10 => ( ( sup_sup_nat @ A2 @ B2 )
% 2.86/3.10 = B2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.absorb4
% 2.86/3.10 thf(fact_3160_sup_Oabsorb4,axiom,
% 2.86/3.10 ! [A2: int,B2: int] :
% 2.86/3.10 ( ( ord_less_int @ A2 @ B2 )
% 2.86/3.10 => ( ( sup_sup_int @ A2 @ B2 )
% 2.86/3.10 = B2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.absorb4
% 2.86/3.10 thf(fact_3161_sup_Oabsorb3,axiom,
% 2.86/3.10 ! [B2: set_nat,A2: set_nat] :
% 2.86/3.10 ( ( ord_less_set_nat @ B2 @ A2 )
% 2.86/3.10 => ( ( sup_sup_set_nat @ A2 @ B2 )
% 2.86/3.10 = A2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.absorb3
% 2.86/3.10 thf(fact_3162_sup_Oabsorb3,axiom,
% 2.86/3.10 ! [B2: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( ord_le2604355607129572851at_nat @ B2 @ A2 )
% 2.86/3.10 => ( ( sup_su5525570899277871387at_nat @ A2 @ B2 )
% 2.86/3.10 = A2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.absorb3
% 2.86/3.10 thf(fact_3163_sup_Oabsorb3,axiom,
% 2.86/3.10 ! [B2: assn,A2: assn] :
% 2.86/3.10 ( ( ord_less_assn @ B2 @ A2 )
% 2.86/3.10 => ( ( sup_sup_assn @ A2 @ B2 )
% 2.86/3.10 = A2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.absorb3
% 2.86/3.10 thf(fact_3164_sup_Oabsorb3,axiom,
% 2.86/3.10 ! [B2: nat,A2: nat] :
% 2.86/3.10 ( ( ord_less_nat @ B2 @ A2 )
% 2.86/3.10 => ( ( sup_sup_nat @ A2 @ B2 )
% 2.86/3.10 = A2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.absorb3
% 2.86/3.10 thf(fact_3165_sup_Oabsorb3,axiom,
% 2.86/3.10 ! [B2: int,A2: int] :
% 2.86/3.10 ( ( ord_less_int @ B2 @ A2 )
% 2.86/3.10 => ( ( sup_sup_int @ A2 @ B2 )
% 2.86/3.10 = A2 ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup.absorb3
% 2.86/3.10 thf(fact_3166_less__supI2,axiom,
% 2.86/3.10 ! [X: set_nat,B2: set_nat,A2: set_nat] :
% 2.86/3.10 ( ( ord_less_set_nat @ X @ B2 )
% 2.86/3.10 => ( ord_less_set_nat @ X @ ( sup_sup_set_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % less_supI2
% 2.86/3.10 thf(fact_3167_less__supI2,axiom,
% 2.86/3.10 ! [X: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( ord_le2604355607129572851at_nat @ X @ B2 )
% 2.86/3.10 => ( ord_le2604355607129572851at_nat @ X @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % less_supI2
% 2.86/3.10 thf(fact_3168_less__supI2,axiom,
% 2.86/3.10 ! [X: assn,B2: assn,A2: assn] :
% 2.86/3.10 ( ( ord_less_assn @ X @ B2 )
% 2.86/3.10 => ( ord_less_assn @ X @ ( sup_sup_assn @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % less_supI2
% 2.86/3.10 thf(fact_3169_less__supI2,axiom,
% 2.86/3.10 ! [X: nat,B2: nat,A2: nat] :
% 2.86/3.10 ( ( ord_less_nat @ X @ B2 )
% 2.86/3.10 => ( ord_less_nat @ X @ ( sup_sup_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % less_supI2
% 2.86/3.10 thf(fact_3170_less__supI2,axiom,
% 2.86/3.10 ! [X: int,B2: int,A2: int] :
% 2.86/3.10 ( ( ord_less_int @ X @ B2 )
% 2.86/3.10 => ( ord_less_int @ X @ ( sup_sup_int @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % less_supI2
% 2.86/3.10 thf(fact_3171_less__supI1,axiom,
% 2.86/3.10 ! [X: set_nat,A2: set_nat,B2: set_nat] :
% 2.86/3.10 ( ( ord_less_set_nat @ X @ A2 )
% 2.86/3.10 => ( ord_less_set_nat @ X @ ( sup_sup_set_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % less_supI1
% 2.86/3.10 thf(fact_3172_less__supI1,axiom,
% 2.86/3.10 ! [X: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( ord_le2604355607129572851at_nat @ X @ A2 )
% 2.86/3.10 => ( ord_le2604355607129572851at_nat @ X @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % less_supI1
% 2.86/3.10 thf(fact_3173_less__supI1,axiom,
% 2.86/3.10 ! [X: assn,A2: assn,B2: assn] :
% 2.86/3.10 ( ( ord_less_assn @ X @ A2 )
% 2.86/3.10 => ( ord_less_assn @ X @ ( sup_sup_assn @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % less_supI1
% 2.86/3.10 thf(fact_3174_less__supI1,axiom,
% 2.86/3.10 ! [X: nat,A2: nat,B2: nat] :
% 2.86/3.10 ( ( ord_less_nat @ X @ A2 )
% 2.86/3.10 => ( ord_less_nat @ X @ ( sup_sup_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % less_supI1
% 2.86/3.10 thf(fact_3175_less__supI1,axiom,
% 2.86/3.10 ! [X: int,A2: int,B2: int] :
% 2.86/3.10 ( ( ord_less_int @ X @ A2 )
% 2.86/3.10 => ( ord_less_int @ X @ ( sup_sup_int @ A2 @ B2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % less_supI1
% 2.86/3.10 thf(fact_3176_boolean__algebra_Odisj__zero__right,axiom,
% 2.86/3.10 ! [X: assn] :
% 2.86/3.10 ( ( sup_sup_assn @ X @ bot_bot_assn )
% 2.86/3.10 = X ) ).
% 2.86/3.10
% 2.86/3.10 % boolean_algebra.disj_zero_right
% 2.86/3.10 thf(fact_3177_boolean__algebra_Odisj__zero__right,axiom,
% 2.86/3.10 ! [X: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( sup_su5525570899277871387at_nat @ X @ bot_bo228742789529271731at_nat )
% 2.86/3.10 = X ) ).
% 2.86/3.10
% 2.86/3.10 % boolean_algebra.disj_zero_right
% 2.86/3.10 thf(fact_3178_boolean__algebra_Odisj__zero__right,axiom,
% 2.86/3.10 ! [X: set_Pr1261947904930325089at_nat] :
% 2.86/3.10 ( ( sup_su6327502436637775413at_nat @ X @ bot_bo2099793752762293965at_nat )
% 2.86/3.10 = X ) ).
% 2.86/3.10
% 2.86/3.10 % boolean_algebra.disj_zero_right
% 2.86/3.10 thf(fact_3179_boolean__algebra_Odisj__zero__right,axiom,
% 2.86/3.10 ! [X: set_o] :
% 2.86/3.10 ( ( sup_sup_set_o @ X @ bot_bot_set_o )
% 2.86/3.10 = X ) ).
% 2.86/3.10
% 2.86/3.10 % boolean_algebra.disj_zero_right
% 2.86/3.10 thf(fact_3180_boolean__algebra_Odisj__zero__right,axiom,
% 2.86/3.10 ! [X: set_nat] :
% 2.86/3.10 ( ( sup_sup_set_nat @ X @ bot_bot_set_nat )
% 2.86/3.10 = X ) ).
% 2.86/3.10
% 2.86/3.10 % boolean_algebra.disj_zero_right
% 2.86/3.10 thf(fact_3181_boolean__algebra_Odisj__zero__right,axiom,
% 2.86/3.10 ! [X: set_int] :
% 2.86/3.10 ( ( sup_sup_set_int @ X @ bot_bot_set_int )
% 2.86/3.10 = X ) ).
% 2.86/3.10
% 2.86/3.10 % boolean_algebra.disj_zero_right
% 2.86/3.10 thf(fact_3182_distrib__imp1,axiom,
% 2.86/3.10 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 2.86/3.10 ( ! [X3: set_Pr1261947904930325089at_nat,Y2: set_Pr1261947904930325089at_nat,Z4: set_Pr1261947904930325089at_nat] :
% 2.86/3.10 ( ( inf_in2572325071724192079at_nat @ X3 @ ( sup_su6327502436637775413at_nat @ Y2 @ Z4 ) )
% 2.86/3.10 = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ X3 @ Y2 ) @ ( inf_in2572325071724192079at_nat @ X3 @ Z4 ) ) )
% 2.86/3.10 => ( ( sup_su6327502436637775413at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) )
% 2.86/3.10 = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ X @ Y ) @ ( sup_su6327502436637775413at_nat @ X @ Z ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % distrib_imp1
% 2.86/3.10 thf(fact_3183_distrib__imp1,axiom,
% 2.86/3.10 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 2.86/3.10 ( ! [X3: set_nat,Y2: set_nat,Z4: set_nat] :
% 2.86/3.10 ( ( inf_inf_set_nat @ X3 @ ( sup_sup_set_nat @ Y2 @ Z4 ) )
% 2.86/3.10 = ( sup_sup_set_nat @ ( inf_inf_set_nat @ X3 @ Y2 ) @ ( inf_inf_set_nat @ X3 @ Z4 ) ) )
% 2.86/3.10 => ( ( sup_sup_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) )
% 2.86/3.10 = ( inf_inf_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ ( sup_sup_set_nat @ X @ Z ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % distrib_imp1
% 2.86/3.10 thf(fact_3184_distrib__imp1,axiom,
% 2.86/3.10 ! [X: assn,Y: assn,Z: assn] :
% 2.86/3.10 ( ! [X3: assn,Y2: assn,Z4: assn] :
% 2.86/3.10 ( ( inf_inf_assn @ X3 @ ( sup_sup_assn @ Y2 @ Z4 ) )
% 2.86/3.10 = ( sup_sup_assn @ ( inf_inf_assn @ X3 @ Y2 ) @ ( inf_inf_assn @ X3 @ Z4 ) ) )
% 2.86/3.10 => ( ( sup_sup_assn @ X @ ( inf_inf_assn @ Y @ Z ) )
% 2.86/3.10 = ( inf_inf_assn @ ( sup_sup_assn @ X @ Y ) @ ( sup_sup_assn @ X @ Z ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % distrib_imp1
% 2.86/3.10 thf(fact_3185_distrib__imp1,axiom,
% 2.86/3.10 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ! [X3: set_Pr4329608150637261639at_nat,Y2: set_Pr4329608150637261639at_nat,Z4: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( inf_in7913087082777306421at_nat @ X3 @ ( sup_su5525570899277871387at_nat @ Y2 @ Z4 ) )
% 2.86/3.10 = ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ X3 @ Y2 ) @ ( inf_in7913087082777306421at_nat @ X3 @ Z4 ) ) )
% 2.86/3.10 => ( ( sup_su5525570899277871387at_nat @ X @ ( inf_in7913087082777306421at_nat @ Y @ Z ) )
% 2.86/3.10 = ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) @ ( sup_su5525570899277871387at_nat @ X @ Z ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % distrib_imp1
% 2.86/3.10 thf(fact_3186_distrib__imp2,axiom,
% 2.86/3.10 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 2.86/3.10 ( ! [X3: set_Pr1261947904930325089at_nat,Y2: set_Pr1261947904930325089at_nat,Z4: set_Pr1261947904930325089at_nat] :
% 2.86/3.10 ( ( sup_su6327502436637775413at_nat @ X3 @ ( inf_in2572325071724192079at_nat @ Y2 @ Z4 ) )
% 2.86/3.10 = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ X3 @ Y2 ) @ ( sup_su6327502436637775413at_nat @ X3 @ Z4 ) ) )
% 2.86/3.10 => ( ( inf_in2572325071724192079at_nat @ X @ ( sup_su6327502436637775413at_nat @ Y @ Z ) )
% 2.86/3.10 = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ ( inf_in2572325071724192079at_nat @ X @ Z ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % distrib_imp2
% 2.86/3.10 thf(fact_3187_distrib__imp2,axiom,
% 2.86/3.10 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 2.86/3.10 ( ! [X3: set_nat,Y2: set_nat,Z4: set_nat] :
% 2.86/3.10 ( ( sup_sup_set_nat @ X3 @ ( inf_inf_set_nat @ Y2 @ Z4 ) )
% 2.86/3.10 = ( inf_inf_set_nat @ ( sup_sup_set_nat @ X3 @ Y2 ) @ ( sup_sup_set_nat @ X3 @ Z4 ) ) )
% 2.86/3.10 => ( ( inf_inf_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) )
% 2.86/3.10 = ( sup_sup_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ ( inf_inf_set_nat @ X @ Z ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % distrib_imp2
% 2.86/3.10 thf(fact_3188_distrib__imp2,axiom,
% 2.86/3.10 ! [X: assn,Y: assn,Z: assn] :
% 2.86/3.10 ( ! [X3: assn,Y2: assn,Z4: assn] :
% 2.86/3.10 ( ( sup_sup_assn @ X3 @ ( inf_inf_assn @ Y2 @ Z4 ) )
% 2.86/3.10 = ( inf_inf_assn @ ( sup_sup_assn @ X3 @ Y2 ) @ ( sup_sup_assn @ X3 @ Z4 ) ) )
% 2.86/3.10 => ( ( inf_inf_assn @ X @ ( sup_sup_assn @ Y @ Z ) )
% 2.86/3.10 = ( sup_sup_assn @ ( inf_inf_assn @ X @ Y ) @ ( inf_inf_assn @ X @ Z ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % distrib_imp2
% 2.86/3.10 thf(fact_3189_distrib__imp2,axiom,
% 2.86/3.10 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ! [X3: set_Pr4329608150637261639at_nat,Y2: set_Pr4329608150637261639at_nat,Z4: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( sup_su5525570899277871387at_nat @ X3 @ ( inf_in7913087082777306421at_nat @ Y2 @ Z4 ) )
% 2.86/3.10 = ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ X3 @ Y2 ) @ ( sup_su5525570899277871387at_nat @ X3 @ Z4 ) ) )
% 2.86/3.10 => ( ( inf_in7913087082777306421at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z ) )
% 2.86/3.10 = ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ X @ Y ) @ ( inf_in7913087082777306421at_nat @ X @ Z ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % distrib_imp2
% 2.86/3.10 thf(fact_3190_inf__sup__distrib1,axiom,
% 2.86/3.10 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 2.86/3.10 ( ( inf_in2572325071724192079at_nat @ X @ ( sup_su6327502436637775413at_nat @ Y @ Z ) )
% 2.86/3.10 = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ ( inf_in2572325071724192079at_nat @ X @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % inf_sup_distrib1
% 2.86/3.10 thf(fact_3191_inf__sup__distrib1,axiom,
% 2.86/3.10 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 2.86/3.10 ( ( inf_inf_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) )
% 2.86/3.10 = ( sup_sup_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ ( inf_inf_set_nat @ X @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % inf_sup_distrib1
% 2.86/3.10 thf(fact_3192_inf__sup__distrib1,axiom,
% 2.86/3.10 ! [X: assn,Y: assn,Z: assn] :
% 2.86/3.10 ( ( inf_inf_assn @ X @ ( sup_sup_assn @ Y @ Z ) )
% 2.86/3.10 = ( sup_sup_assn @ ( inf_inf_assn @ X @ Y ) @ ( inf_inf_assn @ X @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % inf_sup_distrib1
% 2.86/3.10 thf(fact_3193_inf__sup__distrib1,axiom,
% 2.86/3.10 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( inf_in7913087082777306421at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z ) )
% 2.86/3.10 = ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ X @ Y ) @ ( inf_in7913087082777306421at_nat @ X @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % inf_sup_distrib1
% 2.86/3.10 thf(fact_3194_inf__sup__distrib2,axiom,
% 2.86/3.10 ! [Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat] :
% 2.86/3.10 ( ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ Y @ Z ) @ X )
% 2.86/3.10 = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ Y @ X ) @ ( inf_in2572325071724192079at_nat @ Z @ X ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % inf_sup_distrib2
% 2.86/3.10 thf(fact_3195_inf__sup__distrib2,axiom,
% 2.86/3.10 ! [Y: set_nat,Z: set_nat,X: set_nat] :
% 2.86/3.10 ( ( inf_inf_set_nat @ ( sup_sup_set_nat @ Y @ Z ) @ X )
% 2.86/3.10 = ( sup_sup_set_nat @ ( inf_inf_set_nat @ Y @ X ) @ ( inf_inf_set_nat @ Z @ X ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % inf_sup_distrib2
% 2.86/3.10 thf(fact_3196_inf__sup__distrib2,axiom,
% 2.86/3.10 ! [Y: assn,Z: assn,X: assn] :
% 2.86/3.10 ( ( inf_inf_assn @ ( sup_sup_assn @ Y @ Z ) @ X )
% 2.86/3.10 = ( sup_sup_assn @ ( inf_inf_assn @ Y @ X ) @ ( inf_inf_assn @ Z @ X ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % inf_sup_distrib2
% 2.86/3.10 thf(fact_3197_inf__sup__distrib2,axiom,
% 2.86/3.10 ! [Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ Y @ Z ) @ X )
% 2.86/3.10 = ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ Y @ X ) @ ( inf_in7913087082777306421at_nat @ Z @ X ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % inf_sup_distrib2
% 2.86/3.10 thf(fact_3198_sup__inf__distrib1,axiom,
% 2.86/3.10 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 2.86/3.10 ( ( sup_su6327502436637775413at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) )
% 2.86/3.10 = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ X @ Y ) @ ( sup_su6327502436637775413at_nat @ X @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_inf_distrib1
% 2.86/3.10 thf(fact_3199_sup__inf__distrib1,axiom,
% 2.86/3.10 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 2.86/3.10 ( ( sup_sup_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) )
% 2.86/3.10 = ( inf_inf_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ ( sup_sup_set_nat @ X @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_inf_distrib1
% 2.86/3.10 thf(fact_3200_sup__inf__distrib1,axiom,
% 2.86/3.10 ! [X: assn,Y: assn,Z: assn] :
% 2.86/3.10 ( ( sup_sup_assn @ X @ ( inf_inf_assn @ Y @ Z ) )
% 2.86/3.10 = ( inf_inf_assn @ ( sup_sup_assn @ X @ Y ) @ ( sup_sup_assn @ X @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_inf_distrib1
% 2.86/3.10 thf(fact_3201_sup__inf__distrib1,axiom,
% 2.86/3.10 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( sup_su5525570899277871387at_nat @ X @ ( inf_in7913087082777306421at_nat @ Y @ Z ) )
% 2.86/3.10 = ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) @ ( sup_su5525570899277871387at_nat @ X @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_inf_distrib1
% 2.86/3.10 thf(fact_3202_sup__inf__distrib2,axiom,
% 2.86/3.10 ! [Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat] :
% 2.86/3.10 ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ Y @ Z ) @ X )
% 2.86/3.10 = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ Y @ X ) @ ( sup_su6327502436637775413at_nat @ Z @ X ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_inf_distrib2
% 2.86/3.10 thf(fact_3203_sup__inf__distrib2,axiom,
% 2.86/3.10 ! [Y: set_nat,Z: set_nat,X: set_nat] :
% 2.86/3.10 ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ Y @ Z ) @ X )
% 2.86/3.10 = ( inf_inf_set_nat @ ( sup_sup_set_nat @ Y @ X ) @ ( sup_sup_set_nat @ Z @ X ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_inf_distrib2
% 2.86/3.10 thf(fact_3204_sup__inf__distrib2,axiom,
% 2.86/3.10 ! [Y: assn,Z: assn,X: assn] :
% 2.86/3.10 ( ( sup_sup_assn @ ( inf_inf_assn @ Y @ Z ) @ X )
% 2.86/3.10 = ( inf_inf_assn @ ( sup_sup_assn @ Y @ X ) @ ( sup_sup_assn @ Z @ X ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_inf_distrib2
% 2.86/3.10 thf(fact_3205_sup__inf__distrib2,axiom,
% 2.86/3.10 ! [Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ Y @ Z ) @ X )
% 2.86/3.10 = ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ Y @ X ) @ ( sup_su5525570899277871387at_nat @ Z @ X ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sup_inf_distrib2
% 2.86/3.10 thf(fact_3206_Un__empty__left,axiom,
% 2.86/3.10 ! [B: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( sup_su5525570899277871387at_nat @ bot_bo228742789529271731at_nat @ B )
% 2.86/3.10 = B ) ).
% 2.86/3.10
% 2.86/3.10 % Un_empty_left
% 2.86/3.10 thf(fact_3207_Un__empty__left,axiom,
% 2.86/3.10 ! [B: set_Pr1261947904930325089at_nat] :
% 2.86/3.10 ( ( sup_su6327502436637775413at_nat @ bot_bo2099793752762293965at_nat @ B )
% 2.86/3.10 = B ) ).
% 2.86/3.10
% 2.86/3.10 % Un_empty_left
% 2.86/3.10 thf(fact_3208_Un__empty__left,axiom,
% 2.86/3.10 ! [B: set_o] :
% 2.86/3.10 ( ( sup_sup_set_o @ bot_bot_set_o @ B )
% 2.86/3.10 = B ) ).
% 2.86/3.10
% 2.86/3.10 % Un_empty_left
% 2.86/3.10 thf(fact_3209_Un__empty__left,axiom,
% 2.86/3.10 ! [B: set_nat] :
% 2.86/3.10 ( ( sup_sup_set_nat @ bot_bot_set_nat @ B )
% 2.86/3.10 = B ) ).
% 2.86/3.10
% 2.86/3.10 % Un_empty_left
% 2.86/3.10 thf(fact_3210_Un__empty__left,axiom,
% 2.86/3.10 ! [B: set_int] :
% 2.86/3.10 ( ( sup_sup_set_int @ bot_bot_set_int @ B )
% 2.86/3.10 = B ) ).
% 2.86/3.10
% 2.86/3.10 % Un_empty_left
% 2.86/3.10 thf(fact_3211_Un__empty__right,axiom,
% 2.86/3.10 ! [A: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( sup_su5525570899277871387at_nat @ A @ bot_bo228742789529271731at_nat )
% 2.86/3.10 = A ) ).
% 2.86/3.10
% 2.86/3.10 % Un_empty_right
% 2.86/3.10 thf(fact_3212_Un__empty__right,axiom,
% 2.86/3.10 ! [A: set_Pr1261947904930325089at_nat] :
% 2.86/3.10 ( ( sup_su6327502436637775413at_nat @ A @ bot_bo2099793752762293965at_nat )
% 2.86/3.10 = A ) ).
% 2.86/3.10
% 2.86/3.10 % Un_empty_right
% 2.86/3.10 thf(fact_3213_Un__empty__right,axiom,
% 2.86/3.10 ! [A: set_o] :
% 2.86/3.10 ( ( sup_sup_set_o @ A @ bot_bot_set_o )
% 2.86/3.10 = A ) ).
% 2.86/3.10
% 2.86/3.10 % Un_empty_right
% 2.86/3.10 thf(fact_3214_Un__empty__right,axiom,
% 2.86/3.10 ! [A: set_nat] :
% 2.86/3.10 ( ( sup_sup_set_nat @ A @ bot_bot_set_nat )
% 2.86/3.10 = A ) ).
% 2.86/3.10
% 2.86/3.10 % Un_empty_right
% 2.86/3.10 thf(fact_3215_Un__empty__right,axiom,
% 2.86/3.10 ! [A: set_int] :
% 2.86/3.10 ( ( sup_sup_set_int @ A @ bot_bot_set_int )
% 2.86/3.10 = A ) ).
% 2.86/3.10
% 2.86/3.10 % Un_empty_right
% 2.86/3.10 thf(fact_3216_foldl__un__empty__eq,axiom,
% 2.86/3.10 ! [I: set_Pr4329608150637261639at_nat,Ww: list_s4242580248156217677at_nat] :
% 2.86/3.10 ( ( foldl_4541198706405875041at_nat @ sup_su5525570899277871387at_nat @ I @ Ww )
% 2.86/3.10 = ( sup_su5525570899277871387at_nat @ I @ ( foldl_4541198706405875041at_nat @ sup_su5525570899277871387at_nat @ bot_bo228742789529271731at_nat @ Ww ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % foldl_un_empty_eq
% 2.86/3.10 thf(fact_3217_foldl__un__empty__eq,axiom,
% 2.86/3.10 ! [I: set_Pr1261947904930325089at_nat,Ww: list_s1210847774152347623at_nat] :
% 2.86/3.10 ( ( foldl_5307762784932486881at_nat @ sup_su6327502436637775413at_nat @ I @ Ww )
% 2.86/3.10 = ( sup_su6327502436637775413at_nat @ I @ ( foldl_5307762784932486881at_nat @ sup_su6327502436637775413at_nat @ bot_bo2099793752762293965at_nat @ Ww ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % foldl_un_empty_eq
% 2.86/3.10 thf(fact_3218_foldl__un__empty__eq,axiom,
% 2.86/3.10 ! [I: set_o,Ww: list_set_o] :
% 2.86/3.10 ( ( foldl_set_o_set_o @ sup_sup_set_o @ I @ Ww )
% 2.86/3.10 = ( sup_sup_set_o @ I @ ( foldl_set_o_set_o @ sup_sup_set_o @ bot_bot_set_o @ Ww ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % foldl_un_empty_eq
% 2.86/3.10 thf(fact_3219_foldl__un__empty__eq,axiom,
% 2.86/3.10 ! [I: set_nat,Ww: list_set_nat] :
% 2.86/3.10 ( ( foldl_4988731653086973103et_nat @ sup_sup_set_nat @ I @ Ww )
% 2.86/3.10 = ( sup_sup_set_nat @ I @ ( foldl_4988731653086973103et_nat @ sup_sup_set_nat @ bot_bot_set_nat @ Ww ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % foldl_un_empty_eq
% 2.86/3.10 thf(fact_3220_foldl__un__empty__eq,axiom,
% 2.86/3.10 ! [I: set_int,Ww: list_set_int] :
% 2.86/3.10 ( ( foldl_6819690284573351271et_int @ sup_sup_set_int @ I @ Ww )
% 2.86/3.10 = ( sup_sup_set_int @ I @ ( foldl_6819690284573351271et_int @ sup_sup_set_int @ bot_bot_set_int @ Ww ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % foldl_un_empty_eq
% 2.86/3.10 thf(fact_3221_Un__mono,axiom,
% 2.86/3.10 ! [A: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,D: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( ord_le1268244103169919719at_nat @ A @ C2 )
% 2.86/3.10 => ( ( ord_le1268244103169919719at_nat @ B @ D )
% 2.86/3.10 => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ A @ B ) @ ( sup_su5525570899277871387at_nat @ C2 @ D ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % Un_mono
% 2.86/3.10 thf(fact_3222_Un__mono,axiom,
% 2.86/3.10 ! [A: set_nat,C2: set_nat,B: set_nat,D: set_nat] :
% 2.86/3.10 ( ( ord_less_eq_set_nat @ A @ C2 )
% 2.86/3.10 => ( ( ord_less_eq_set_nat @ B @ D )
% 2.86/3.10 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A @ B ) @ ( sup_sup_set_nat @ C2 @ D ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % Un_mono
% 2.86/3.10 thf(fact_3223_Un__least,axiom,
% 2.86/3.10 ! [A: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( ord_le1268244103169919719at_nat @ A @ C2 )
% 2.86/3.10 => ( ( ord_le1268244103169919719at_nat @ B @ C2 )
% 2.86/3.10 => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ A @ B ) @ C2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % Un_least
% 2.86/3.10 thf(fact_3224_Un__least,axiom,
% 2.86/3.10 ! [A: set_nat,C2: set_nat,B: set_nat] :
% 2.86/3.10 ( ( ord_less_eq_set_nat @ A @ C2 )
% 2.86/3.10 => ( ( ord_less_eq_set_nat @ B @ C2 )
% 2.86/3.10 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A @ B ) @ C2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % Un_least
% 2.86/3.10 thf(fact_3225_Un__upper1,axiom,
% 2.86/3.10 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ A @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ).
% 2.86/3.10
% 2.86/3.10 % Un_upper1
% 2.86/3.10 thf(fact_3226_Un__upper1,axiom,
% 2.86/3.10 ! [A: set_nat,B: set_nat] : ( ord_less_eq_set_nat @ A @ ( sup_sup_set_nat @ A @ B ) ) ).
% 2.86/3.10
% 2.86/3.10 % Un_upper1
% 2.86/3.10 thf(fact_3227_Un__upper2,axiom,
% 2.86/3.10 ! [B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ B @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ).
% 2.86/3.10
% 2.86/3.10 % Un_upper2
% 2.86/3.10 thf(fact_3228_Un__upper2,axiom,
% 2.86/3.10 ! [B: set_nat,A: set_nat] : ( ord_less_eq_set_nat @ B @ ( sup_sup_set_nat @ A @ B ) ) ).
% 2.86/3.10
% 2.86/3.10 % Un_upper2
% 2.86/3.10 thf(fact_3229_Un__absorb1,axiom,
% 2.86/3.10 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( ord_le1268244103169919719at_nat @ A @ B )
% 2.86/3.10 => ( ( sup_su5525570899277871387at_nat @ A @ B )
% 2.86/3.10 = B ) ) ).
% 2.86/3.10
% 2.86/3.10 % Un_absorb1
% 2.86/3.10 thf(fact_3230_Un__absorb1,axiom,
% 2.86/3.10 ! [A: set_nat,B: set_nat] :
% 2.86/3.10 ( ( ord_less_eq_set_nat @ A @ B )
% 2.86/3.10 => ( ( sup_sup_set_nat @ A @ B )
% 2.86/3.10 = B ) ) ).
% 2.86/3.10
% 2.86/3.10 % Un_absorb1
% 2.86/3.10 thf(fact_3231_Un__absorb2,axiom,
% 2.86/3.10 ! [B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( ord_le1268244103169919719at_nat @ B @ A )
% 2.86/3.10 => ( ( sup_su5525570899277871387at_nat @ A @ B )
% 2.86/3.10 = A ) ) ).
% 2.86/3.10
% 2.86/3.10 % Un_absorb2
% 2.86/3.10 thf(fact_3232_Un__absorb2,axiom,
% 2.86/3.10 ! [B: set_nat,A: set_nat] :
% 2.86/3.10 ( ( ord_less_eq_set_nat @ B @ A )
% 2.86/3.10 => ( ( sup_sup_set_nat @ A @ B )
% 2.86/3.10 = A ) ) ).
% 2.86/3.10
% 2.86/3.10 % Un_absorb2
% 2.86/3.10 thf(fact_3233_subset__UnE,axiom,
% 2.86/3.10 ! [C2: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( ord_le1268244103169919719at_nat @ C2 @ ( sup_su5525570899277871387at_nat @ A @ B ) )
% 2.86/3.10 => ~ ! [A8: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( ord_le1268244103169919719at_nat @ A8 @ A )
% 2.86/3.10 => ! [B8: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( ord_le1268244103169919719at_nat @ B8 @ B )
% 2.86/3.10 => ( C2
% 2.86/3.10 != ( sup_su5525570899277871387at_nat @ A8 @ B8 ) ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % subset_UnE
% 2.86/3.10 thf(fact_3234_subset__UnE,axiom,
% 2.86/3.10 ! [C2: set_nat,A: set_nat,B: set_nat] :
% 2.86/3.10 ( ( ord_less_eq_set_nat @ C2 @ ( sup_sup_set_nat @ A @ B ) )
% 2.86/3.10 => ~ ! [A8: set_nat] :
% 2.86/3.10 ( ( ord_less_eq_set_nat @ A8 @ A )
% 2.86/3.10 => ! [B8: set_nat] :
% 2.86/3.10 ( ( ord_less_eq_set_nat @ B8 @ B )
% 2.86/3.10 => ( C2
% 2.86/3.10 != ( sup_sup_set_nat @ A8 @ B8 ) ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % subset_UnE
% 2.86/3.10 thf(fact_3235_subset__Un__eq,axiom,
% 2.86/3.10 ( ord_le1268244103169919719at_nat
% 2.86/3.10 = ( ^ [A5: set_Pr4329608150637261639at_nat,B7: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( sup_su5525570899277871387at_nat @ A5 @ B7 )
% 2.86/3.10 = B7 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % subset_Un_eq
% 2.86/3.10 thf(fact_3236_subset__Un__eq,axiom,
% 2.86/3.10 ( ord_less_eq_set_nat
% 2.86/3.10 = ( ^ [A5: set_nat,B7: set_nat] :
% 2.86/3.10 ( ( sup_sup_set_nat @ A5 @ B7 )
% 2.86/3.10 = B7 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % subset_Un_eq
% 2.86/3.10 thf(fact_3237_Un__Int__assoc__eq,axiom,
% 2.86/3.10 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 2.86/3.10 ( ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ C2 )
% 2.86/3.10 = ( inf_in2572325071724192079at_nat @ A @ ( sup_su6327502436637775413at_nat @ B @ C2 ) ) )
% 2.86/3.10 = ( ord_le3146513528884898305at_nat @ C2 @ A ) ) ).
% 2.86/3.10
% 2.86/3.10 % Un_Int_assoc_eq
% 2.86/3.10 thf(fact_3238_Un__Int__assoc__eq,axiom,
% 2.86/3.10 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ A @ B ) @ C2 )
% 2.86/3.10 = ( inf_in7913087082777306421at_nat @ A @ ( sup_su5525570899277871387at_nat @ B @ C2 ) ) )
% 2.86/3.10 = ( ord_le1268244103169919719at_nat @ C2 @ A ) ) ).
% 2.86/3.10
% 2.86/3.10 % Un_Int_assoc_eq
% 2.86/3.10 thf(fact_3239_Un__Int__assoc__eq,axiom,
% 2.86/3.10 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 2.86/3.10 ( ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ A @ B ) @ C2 )
% 2.86/3.10 = ( inf_inf_set_nat @ A @ ( sup_sup_set_nat @ B @ C2 ) ) )
% 2.86/3.10 = ( ord_less_eq_set_nat @ C2 @ A ) ) ).
% 2.86/3.10
% 2.86/3.10 % Un_Int_assoc_eq
% 2.86/3.10 thf(fact_3240_set__diff__diff__left,axiom,
% 2.86/3.10 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( minus_3314409938677909166at_nat @ ( minus_3314409938677909166at_nat @ A @ B ) @ C2 )
% 2.86/3.10 = ( minus_3314409938677909166at_nat @ A @ ( sup_su5525570899277871387at_nat @ B @ C2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % set_diff_diff_left
% 2.86/3.10 thf(fact_3241_set__diff__diff__left,axiom,
% 2.86/3.10 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 2.86/3.10 ( ( minus_minus_set_nat @ ( minus_minus_set_nat @ A @ B ) @ C2 )
% 2.86/3.10 = ( minus_minus_set_nat @ A @ ( sup_sup_set_nat @ B @ C2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % set_diff_diff_left
% 2.86/3.10 thf(fact_3242_Un__Diff,axiom,
% 2.86/3.10 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( minus_3314409938677909166at_nat @ ( sup_su5525570899277871387at_nat @ A @ B ) @ C2 )
% 2.86/3.10 = ( sup_su5525570899277871387at_nat @ ( minus_3314409938677909166at_nat @ A @ C2 ) @ ( minus_3314409938677909166at_nat @ B @ C2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % Un_Diff
% 2.86/3.10 thf(fact_3243_Un__Diff,axiom,
% 2.86/3.10 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 2.86/3.10 ( ( minus_minus_set_nat @ ( sup_sup_set_nat @ A @ B ) @ C2 )
% 2.86/3.10 = ( sup_sup_set_nat @ ( minus_minus_set_nat @ A @ C2 ) @ ( minus_minus_set_nat @ B @ C2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % Un_Diff
% 2.86/3.10 thf(fact_3244_Diff__Un,axiom,
% 2.86/3.10 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 2.86/3.10 ( ( minus_1356011639430497352at_nat @ A @ ( sup_su6327502436637775413at_nat @ B @ C2 ) )
% 2.86/3.10 = ( inf_in2572325071724192079at_nat @ ( minus_1356011639430497352at_nat @ A @ B ) @ ( minus_1356011639430497352at_nat @ A @ C2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % Diff_Un
% 2.86/3.10 thf(fact_3245_Diff__Un,axiom,
% 2.86/3.10 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( minus_3314409938677909166at_nat @ A @ ( sup_su5525570899277871387at_nat @ B @ C2 ) )
% 2.86/3.10 = ( inf_in7913087082777306421at_nat @ ( minus_3314409938677909166at_nat @ A @ B ) @ ( minus_3314409938677909166at_nat @ A @ C2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % Diff_Un
% 2.86/3.10 thf(fact_3246_Diff__Un,axiom,
% 2.86/3.10 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 2.86/3.10 ( ( minus_minus_set_nat @ A @ ( sup_sup_set_nat @ B @ C2 ) )
% 2.86/3.10 = ( inf_inf_set_nat @ ( minus_minus_set_nat @ A @ B ) @ ( minus_minus_set_nat @ A @ C2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % Diff_Un
% 2.86/3.10 thf(fact_3247_Diff__Int,axiom,
% 2.86/3.10 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 2.86/3.10 ( ( minus_1356011639430497352at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C2 ) )
% 2.86/3.10 = ( sup_su6327502436637775413at_nat @ ( minus_1356011639430497352at_nat @ A @ B ) @ ( minus_1356011639430497352at_nat @ A @ C2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % Diff_Int
% 2.86/3.10 thf(fact_3248_Diff__Int,axiom,
% 2.86/3.10 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( minus_3314409938677909166at_nat @ A @ ( inf_in7913087082777306421at_nat @ B @ C2 ) )
% 2.86/3.10 = ( sup_su5525570899277871387at_nat @ ( minus_3314409938677909166at_nat @ A @ B ) @ ( minus_3314409938677909166at_nat @ A @ C2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % Diff_Int
% 2.86/3.10 thf(fact_3249_Diff__Int,axiom,
% 2.86/3.10 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 2.86/3.10 ( ( minus_minus_set_nat @ A @ ( inf_inf_set_nat @ B @ C2 ) )
% 2.86/3.10 = ( sup_sup_set_nat @ ( minus_minus_set_nat @ A @ B ) @ ( minus_minus_set_nat @ A @ C2 ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % Diff_Int
% 2.86/3.10 thf(fact_3250_Int__Diff__Un,axiom,
% 2.86/3.10 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.10 ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ ( minus_1356011639430497352at_nat @ A @ B ) )
% 2.86/3.10 = A ) ).
% 2.86/3.10
% 2.86/3.10 % Int_Diff_Un
% 2.86/3.10 thf(fact_3251_Int__Diff__Un,axiom,
% 2.86/3.10 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ A @ B ) @ ( minus_3314409938677909166at_nat @ A @ B ) )
% 2.86/3.10 = A ) ).
% 2.86/3.10
% 2.86/3.10 % Int_Diff_Un
% 2.86/3.10 thf(fact_3252_Int__Diff__Un,axiom,
% 2.86/3.10 ! [A: set_nat,B: set_nat] :
% 2.86/3.10 ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ A @ B ) @ ( minus_minus_set_nat @ A @ B ) )
% 2.86/3.10 = A ) ).
% 2.86/3.10
% 2.86/3.10 % Int_Diff_Un
% 2.86/3.10 thf(fact_3253_Un__Diff__Int,axiom,
% 2.86/3.10 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.10 ( ( sup_su6327502436637775413at_nat @ ( minus_1356011639430497352at_nat @ A @ B ) @ ( inf_in2572325071724192079at_nat @ A @ B ) )
% 2.86/3.10 = A ) ).
% 2.86/3.10
% 2.86/3.10 % Un_Diff_Int
% 2.86/3.10 thf(fact_3254_Un__Diff__Int,axiom,
% 2.86/3.10 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( sup_su5525570899277871387at_nat @ ( minus_3314409938677909166at_nat @ A @ B ) @ ( inf_in7913087082777306421at_nat @ A @ B ) )
% 2.86/3.10 = A ) ).
% 2.86/3.10
% 2.86/3.10 % Un_Diff_Int
% 2.86/3.10 thf(fact_3255_Un__Diff__Int,axiom,
% 2.86/3.10 ! [A: set_nat,B: set_nat] :
% 2.86/3.10 ( ( sup_sup_set_nat @ ( minus_minus_set_nat @ A @ B ) @ ( inf_inf_set_nat @ A @ B ) )
% 2.86/3.10 = A ) ).
% 2.86/3.10
% 2.86/3.10 % Un_Diff_Int
% 2.86/3.10 thf(fact_3256_in__set__butlastD,axiom,
% 2.86/3.10 ! [X: produc3843707927480180839at_nat,Xs: list_P5464809261938338413at_nat] :
% 2.86/3.10 ( ( member8757157785044589968at_nat @ X @ ( set_Pr3765526544606949372at_nat @ ( butlas2561766218336428473at_nat @ Xs ) ) )
% 2.86/3.10 => ( member8757157785044589968at_nat @ X @ ( set_Pr3765526544606949372at_nat @ Xs ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % in_set_butlastD
% 2.86/3.10 thf(fact_3257_in__set__butlastD,axiom,
% 2.86/3.10 ! [X: product_prod_nat_nat,Xs: list_P6011104703257516679at_nat] :
% 2.86/3.10 ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ ( butlas5569151904373679443at_nat @ Xs ) ) )
% 2.86/3.10 => ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % in_set_butlastD
% 2.86/3.10 thf(fact_3258_in__set__butlastD,axiom,
% 2.86/3.10 ! [X: produc3658429121746597890et_nat > $o,Xs: list_P7985473006766602707_nat_o] :
% 2.86/3.10 ( ( member6576561426505652726_nat_o @ X @ ( set_Pr400311997697478754_nat_o @ ( butlas8287983287669047583_nat_o @ Xs ) ) )
% 2.86/3.10 => ( member6576561426505652726_nat_o @ X @ ( set_Pr400311997697478754_nat_o @ Xs ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % in_set_butlastD
% 2.86/3.10 thf(fact_3259_in__set__butlastD,axiom,
% 2.86/3.10 ! [X: int,Xs: list_int] :
% 2.86/3.10 ( ( member_int @ X @ ( set_int2 @ ( butlast_int @ Xs ) ) )
% 2.86/3.10 => ( member_int @ X @ ( set_int2 @ Xs ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % in_set_butlastD
% 2.86/3.10 thf(fact_3260_in__set__butlastD,axiom,
% 2.86/3.10 ! [X: nat,Xs: list_nat] :
% 2.86/3.10 ( ( member_nat @ X @ ( set_nat2 @ ( butlast_nat @ Xs ) ) )
% 2.86/3.10 => ( member_nat @ X @ ( set_nat2 @ Xs ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % in_set_butlastD
% 2.86/3.10 thf(fact_3261_in__set__butlastD,axiom,
% 2.86/3.10 ! [X: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn] :
% 2.86/3.10 ( ( member7957490590177025114n_assn @ X @ ( set_Pr1139785259514867910n_assn @ ( butlas3012047794866324995n_assn @ Xs ) ) )
% 2.86/3.10 => ( member7957490590177025114n_assn @ X @ ( set_Pr1139785259514867910n_assn @ Xs ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % in_set_butlastD
% 2.86/3.10 thf(fact_3262_distinct__butlast,axiom,
% 2.86/3.10 ! [Xs: list_int] :
% 2.86/3.10 ( ( distinct_int @ Xs )
% 2.86/3.10 => ( distinct_int @ ( butlast_int @ Xs ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % distinct_butlast
% 2.86/3.10 thf(fact_3263_distinct__butlast,axiom,
% 2.86/3.10 ! [Xs: list_nat] :
% 2.86/3.10 ( ( distinct_nat @ Xs )
% 2.86/3.10 => ( distinct_nat @ ( butlast_nat @ Xs ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % distinct_butlast
% 2.86/3.10 thf(fact_3264_butlast__update_H,axiom,
% 2.86/3.10 ! [L: list_nat,I: nat,X: nat] :
% 2.86/3.10 ( ( list_update_nat @ ( butlast_nat @ L ) @ I @ X )
% 2.86/3.10 = ( butlast_nat @ ( list_update_nat @ L @ I @ X ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % butlast_update'
% 2.86/3.10 thf(fact_3265_butlast__update_H,axiom,
% 2.86/3.10 ! [L: list_c,I: nat,X: c] :
% 2.86/3.10 ( ( list_update_c @ ( butlast_c @ L ) @ I @ X )
% 2.86/3.10 = ( butlast_c @ ( list_update_c @ L @ I @ X ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % butlast_update'
% 2.86/3.10 thf(fact_3266_butlast__update_H,axiom,
% 2.86/3.10 ! [L: list_d,I: nat,X: d] :
% 2.86/3.10 ( ( list_update_d @ ( butlast_d @ L ) @ I @ X )
% 2.86/3.10 = ( butlast_d @ ( list_update_d @ L @ I @ X ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % butlast_update'
% 2.86/3.10 thf(fact_3267_sorted__rev__iff__nth__mono,axiom,
% 2.86/3.10 ! [Xs: list_nat] :
% 2.86/3.10 ( ( sorted_wrt_nat @ ord_less_eq_nat @ ( rev_nat @ Xs ) )
% 2.86/3.10 = ( ! [I4: nat,J2: nat] :
% 2.86/3.10 ( ( ord_less_eq_nat @ I4 @ J2 )
% 2.86/3.10 => ( ( ord_less_nat @ J2 @ ( size_size_list_nat @ Xs ) )
% 2.86/3.10 => ( ord_less_eq_nat @ ( nth_nat @ Xs @ J2 ) @ ( nth_nat @ Xs @ I4 ) ) ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sorted_rev_iff_nth_mono
% 2.86/3.10 thf(fact_3268_sorted__rev__iff__nth__mono,axiom,
% 2.86/3.10 ! [Xs: list_int] :
% 2.86/3.10 ( ( sorted_wrt_int @ ord_less_eq_int @ ( rev_int @ Xs ) )
% 2.86/3.10 = ( ! [I4: nat,J2: nat] :
% 2.86/3.10 ( ( ord_less_eq_nat @ I4 @ J2 )
% 2.86/3.10 => ( ( ord_less_nat @ J2 @ ( size_size_list_int @ Xs ) )
% 2.86/3.10 => ( ord_less_eq_int @ ( nth_int @ Xs @ J2 ) @ ( nth_int @ Xs @ I4 ) ) ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sorted_rev_iff_nth_mono
% 2.86/3.10 thf(fact_3269_sorted__rev__nth__mono,axiom,
% 2.86/3.10 ! [Xs: list_nat,I: nat,J: nat] :
% 2.86/3.10 ( ( sorted_wrt_nat @ ord_less_eq_nat @ ( rev_nat @ Xs ) )
% 2.86/3.10 => ( ( ord_less_eq_nat @ I @ J )
% 2.86/3.10 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs ) )
% 2.86/3.10 => ( ord_less_eq_nat @ ( nth_nat @ Xs @ J ) @ ( nth_nat @ Xs @ I ) ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sorted_rev_nth_mono
% 2.86/3.10 thf(fact_3270_sorted__rev__nth__mono,axiom,
% 2.86/3.10 ! [Xs: list_int,I: nat,J: nat] :
% 2.86/3.10 ( ( sorted_wrt_int @ ord_less_eq_int @ ( rev_int @ Xs ) )
% 2.86/3.10 => ( ( ord_less_eq_nat @ I @ J )
% 2.86/3.10 => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs ) )
% 2.86/3.10 => ( ord_less_eq_int @ ( nth_int @ Xs @ J ) @ ( nth_int @ Xs @ I ) ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sorted_rev_nth_mono
% 2.86/3.10 thf(fact_3271_strict__sorted__imp__sorted,axiom,
% 2.86/3.10 ! [Xs: list_Code_integer] :
% 2.86/3.10 ( ( sorted710888440204495920nteger @ ord_le6747313008572928689nteger @ Xs )
% 2.86/3.10 => ( sorted710888440204495920nteger @ ord_le3102999989581377725nteger @ Xs ) ) ).
% 2.86/3.10
% 2.86/3.10 % strict_sorted_imp_sorted
% 2.86/3.10 thf(fact_3272_strict__sorted__imp__sorted,axiom,
% 2.86/3.10 ! [Xs: list_num] :
% 2.86/3.10 ( ( sorted_wrt_num @ ord_less_num @ Xs )
% 2.86/3.10 => ( sorted_wrt_num @ ord_less_eq_num @ Xs ) ) ).
% 2.86/3.10
% 2.86/3.10 % strict_sorted_imp_sorted
% 2.86/3.10 thf(fact_3273_strict__sorted__imp__sorted,axiom,
% 2.86/3.10 ! [Xs: list_nat] :
% 2.86/3.10 ( ( sorted_wrt_nat @ ord_less_nat @ Xs )
% 2.86/3.10 => ( sorted_wrt_nat @ ord_less_eq_nat @ Xs ) ) ).
% 2.86/3.10
% 2.86/3.10 % strict_sorted_imp_sorted
% 2.86/3.10 thf(fact_3274_strict__sorted__imp__sorted,axiom,
% 2.86/3.10 ! [Xs: list_int] :
% 2.86/3.10 ( ( sorted_wrt_int @ ord_less_int @ Xs )
% 2.86/3.10 => ( sorted_wrt_int @ ord_less_eq_int @ Xs ) ) ).
% 2.86/3.10
% 2.86/3.10 % strict_sorted_imp_sorted
% 2.86/3.10 thf(fact_3275_strict__sorted__equal,axiom,
% 2.86/3.10 ! [Xs: list_Code_integer,Ys: list_Code_integer] :
% 2.86/3.10 ( ( sorted710888440204495920nteger @ ord_le6747313008572928689nteger @ Xs )
% 2.86/3.10 => ( ( sorted710888440204495920nteger @ ord_le6747313008572928689nteger @ Ys )
% 2.86/3.10 => ( ( ( set_Code_integer2 @ Ys )
% 2.86/3.10 = ( set_Code_integer2 @ Xs ) )
% 2.86/3.10 => ( Ys = Xs ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % strict_sorted_equal
% 2.86/3.10 thf(fact_3276_strict__sorted__equal,axiom,
% 2.86/3.10 ! [Xs: list_num,Ys: list_num] :
% 2.86/3.10 ( ( sorted_wrt_num @ ord_less_num @ Xs )
% 2.86/3.10 => ( ( sorted_wrt_num @ ord_less_num @ Ys )
% 2.86/3.10 => ( ( ( set_num2 @ Ys )
% 2.86/3.10 = ( set_num2 @ Xs ) )
% 2.86/3.10 => ( Ys = Xs ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % strict_sorted_equal
% 2.86/3.10 thf(fact_3277_strict__sorted__equal,axiom,
% 2.86/3.10 ! [Xs: list_nat,Ys: list_nat] :
% 2.86/3.10 ( ( sorted_wrt_nat @ ord_less_nat @ Xs )
% 2.86/3.10 => ( ( sorted_wrt_nat @ ord_less_nat @ Ys )
% 2.86/3.10 => ( ( ( set_nat2 @ Ys )
% 2.86/3.10 = ( set_nat2 @ Xs ) )
% 2.86/3.10 => ( Ys = Xs ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % strict_sorted_equal
% 2.86/3.10 thf(fact_3278_strict__sorted__equal,axiom,
% 2.86/3.10 ! [Xs: list_int,Ys: list_int] :
% 2.86/3.10 ( ( sorted_wrt_int @ ord_less_int @ Xs )
% 2.86/3.10 => ( ( sorted_wrt_int @ ord_less_int @ Ys )
% 2.86/3.10 => ( ( ( set_int2 @ Ys )
% 2.86/3.10 = ( set_int2 @ Xs ) )
% 2.86/3.10 => ( Ys = Xs ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % strict_sorted_equal
% 2.86/3.10 thf(fact_3279_sorted__wrt01,axiom,
% 2.86/3.10 ! [Xs: list_c,P: c > c > $o] :
% 2.86/3.10 ( ( ord_less_eq_nat @ ( size_size_list_c @ Xs ) @ one_one_nat )
% 2.86/3.10 => ( sorted_wrt_c @ P @ Xs ) ) ).
% 2.86/3.10
% 2.86/3.10 % sorted_wrt01
% 2.86/3.10 thf(fact_3280_sorted__wrt01,axiom,
% 2.86/3.10 ! [Xs: list_d,P: d > d > $o] :
% 2.86/3.10 ( ( ord_less_eq_nat @ ( size_size_list_d @ Xs ) @ one_one_nat )
% 2.86/3.10 => ( sorted_wrt_d @ P @ Xs ) ) ).
% 2.86/3.10
% 2.86/3.10 % sorted_wrt01
% 2.86/3.10 thf(fact_3281_sorted__wrt01,axiom,
% 2.86/3.10 ! [Xs: list_nat,P: nat > nat > $o] :
% 2.86/3.10 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ one_one_nat )
% 2.86/3.10 => ( sorted_wrt_nat @ P @ Xs ) ) ).
% 2.86/3.10
% 2.86/3.10 % sorted_wrt01
% 2.86/3.10 thf(fact_3282_sorted__wrt01,axiom,
% 2.86/3.10 ! [Xs: list_int,P: int > int > $o] :
% 2.86/3.10 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ one_one_nat )
% 2.86/3.10 => ( sorted_wrt_int @ P @ Xs ) ) ).
% 2.86/3.10
% 2.86/3.10 % sorted_wrt01
% 2.86/3.10 thf(fact_3283_distrib__inf__le,axiom,
% 2.86/3.10 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ ( inf_in2572325071724192079at_nat @ X @ Z ) ) @ ( inf_in2572325071724192079at_nat @ X @ ( sup_su6327502436637775413at_nat @ Y @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % distrib_inf_le
% 2.86/3.10 thf(fact_3284_distrib__inf__le,axiom,
% 2.86/3.10 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ X @ Y ) @ ( inf_in7913087082777306421at_nat @ X @ Z ) ) @ ( inf_in7913087082777306421at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % distrib_inf_le
% 2.86/3.10 thf(fact_3285_distrib__inf__le,axiom,
% 2.86/3.10 ! [X: assn,Y: assn,Z: assn] : ( ord_less_eq_assn @ ( sup_sup_assn @ ( inf_inf_assn @ X @ Y ) @ ( inf_inf_assn @ X @ Z ) ) @ ( inf_inf_assn @ X @ ( sup_sup_assn @ Y @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % distrib_inf_le
% 2.86/3.10 thf(fact_3286_distrib__inf__le,axiom,
% 2.86/3.10 ! [X: filter_nat,Y: filter_nat,Z: filter_nat] : ( ord_le2510731241096832064er_nat @ ( sup_sup_filter_nat @ ( inf_inf_filter_nat @ X @ Y ) @ ( inf_inf_filter_nat @ X @ Z ) ) @ ( inf_inf_filter_nat @ X @ ( sup_sup_filter_nat @ Y @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % distrib_inf_le
% 2.86/3.10 thf(fact_3287_distrib__inf__le,axiom,
% 2.86/3.10 ! [X: set_nat,Y: set_nat,Z: set_nat] : ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ ( inf_inf_set_nat @ X @ Z ) ) @ ( inf_inf_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % distrib_inf_le
% 2.86/3.10 thf(fact_3288_distrib__inf__le,axiom,
% 2.86/3.10 ! [X: nat,Y: nat,Z: nat] : ( ord_less_eq_nat @ ( sup_sup_nat @ ( inf_inf_nat @ X @ Y ) @ ( inf_inf_nat @ X @ Z ) ) @ ( inf_inf_nat @ X @ ( sup_sup_nat @ Y @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % distrib_inf_le
% 2.86/3.10 thf(fact_3289_distrib__inf__le,axiom,
% 2.86/3.10 ! [X: int,Y: int,Z: int] : ( ord_less_eq_int @ ( sup_sup_int @ ( inf_inf_int @ X @ Y ) @ ( inf_inf_int @ X @ Z ) ) @ ( inf_inf_int @ X @ ( sup_sup_int @ Y @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % distrib_inf_le
% 2.86/3.10 thf(fact_3290_distrib__sup__le,axiom,
% 2.86/3.10 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( sup_su6327502436637775413at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) ) @ ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ X @ Y ) @ ( sup_su6327502436637775413at_nat @ X @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % distrib_sup_le
% 2.86/3.10 thf(fact_3291_distrib__sup__le,axiom,
% 2.86/3.10 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ X @ ( inf_in7913087082777306421at_nat @ Y @ Z ) ) @ ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) @ ( sup_su5525570899277871387at_nat @ X @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % distrib_sup_le
% 2.86/3.10 thf(fact_3292_distrib__sup__le,axiom,
% 2.86/3.10 ! [X: assn,Y: assn,Z: assn] : ( ord_less_eq_assn @ ( sup_sup_assn @ X @ ( inf_inf_assn @ Y @ Z ) ) @ ( inf_inf_assn @ ( sup_sup_assn @ X @ Y ) @ ( sup_sup_assn @ X @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % distrib_sup_le
% 2.86/3.10 thf(fact_3293_distrib__sup__le,axiom,
% 2.86/3.10 ! [X: filter_nat,Y: filter_nat,Z: filter_nat] : ( ord_le2510731241096832064er_nat @ ( sup_sup_filter_nat @ X @ ( inf_inf_filter_nat @ Y @ Z ) ) @ ( inf_inf_filter_nat @ ( sup_sup_filter_nat @ X @ Y ) @ ( sup_sup_filter_nat @ X @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % distrib_sup_le
% 2.86/3.10 thf(fact_3294_distrib__sup__le,axiom,
% 2.86/3.10 ! [X: set_nat,Y: set_nat,Z: set_nat] : ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) ) @ ( inf_inf_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ ( sup_sup_set_nat @ X @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % distrib_sup_le
% 2.86/3.10 thf(fact_3295_distrib__sup__le,axiom,
% 2.86/3.10 ! [X: nat,Y: nat,Z: nat] : ( ord_less_eq_nat @ ( sup_sup_nat @ X @ ( inf_inf_nat @ Y @ Z ) ) @ ( inf_inf_nat @ ( sup_sup_nat @ X @ Y ) @ ( sup_sup_nat @ X @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % distrib_sup_le
% 2.86/3.10 thf(fact_3296_distrib__sup__le,axiom,
% 2.86/3.10 ! [X: int,Y: int,Z: int] : ( ord_less_eq_int @ ( sup_sup_int @ X @ ( inf_inf_int @ Y @ Z ) ) @ ( inf_inf_int @ ( sup_sup_int @ X @ Y ) @ ( sup_sup_int @ X @ Z ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % distrib_sup_le
% 2.86/3.10 thf(fact_3297_sorted__remove1,axiom,
% 2.86/3.10 ! [Xs: list_nat,A2: nat] :
% 2.86/3.10 ( ( sorted_wrt_nat @ ord_less_eq_nat @ Xs )
% 2.86/3.10 => ( sorted_wrt_nat @ ord_less_eq_nat @ ( remove1_nat @ A2 @ Xs ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sorted_remove1
% 2.86/3.10 thf(fact_3298_sorted__remove1,axiom,
% 2.86/3.10 ! [Xs: list_int,A2: int] :
% 2.86/3.10 ( ( sorted_wrt_int @ ord_less_eq_int @ Xs )
% 2.86/3.10 => ( sorted_wrt_int @ ord_less_eq_int @ ( remove1_int @ A2 @ Xs ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % sorted_remove1
% 2.86/3.10 thf(fact_3299_insert__is__Un,axiom,
% 2.86/3.10 ( insert9069300056098147895at_nat
% 2.86/3.10 = ( ^ [A3: produc3843707927480180839at_nat] : ( sup_su5525570899277871387at_nat @ ( insert9069300056098147895at_nat @ A3 @ bot_bo228742789529271731at_nat ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % insert_is_Un
% 2.86/3.10 thf(fact_3300_insert__is__Un,axiom,
% 2.86/3.10 ( insert8211810215607154385at_nat
% 2.86/3.10 = ( ^ [A3: product_prod_nat_nat] : ( sup_su6327502436637775413at_nat @ ( insert8211810215607154385at_nat @ A3 @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % insert_is_Un
% 2.86/3.10 thf(fact_3301_insert__is__Un,axiom,
% 2.86/3.10 ( insert_o2
% 2.86/3.10 = ( ^ [A3: $o] : ( sup_sup_set_o @ ( insert_o2 @ A3 @ bot_bot_set_o ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % insert_is_Un
% 2.86/3.10 thf(fact_3302_insert__is__Un,axiom,
% 2.86/3.10 ( insert_nat2
% 2.86/3.10 = ( ^ [A3: nat] : ( sup_sup_set_nat @ ( insert_nat2 @ A3 @ bot_bot_set_nat ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % insert_is_Un
% 2.86/3.10 thf(fact_3303_insert__is__Un,axiom,
% 2.86/3.10 ( insert_int2
% 2.86/3.10 = ( ^ [A3: int] : ( sup_sup_set_int @ ( insert_int2 @ A3 @ bot_bot_set_int ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % insert_is_Un
% 2.86/3.10 thf(fact_3304_Un__singleton__iff,axiom,
% 2.86/3.10 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,X: produc3843707927480180839at_nat] :
% 2.86/3.10 ( ( ( sup_su5525570899277871387at_nat @ A @ B )
% 2.86/3.10 = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 2.86/3.10 = ( ( ( A = bot_bo228742789529271731at_nat )
% 2.86/3.10 & ( B
% 2.86/3.10 = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) )
% 2.86/3.10 | ( ( A
% 2.86/3.10 = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 2.86/3.10 & ( B = bot_bo228742789529271731at_nat ) )
% 2.86/3.10 | ( ( A
% 2.86/3.10 = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 2.86/3.10 & ( B
% 2.86/3.10 = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % Un_singleton_iff
% 2.86/3.10 thf(fact_3305_Un__singleton__iff,axiom,
% 2.86/3.10 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] :
% 2.86/3.10 ( ( ( sup_su6327502436637775413at_nat @ A @ B )
% 2.86/3.10 = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 2.86/3.10 = ( ( ( A = bot_bo2099793752762293965at_nat )
% 2.86/3.10 & ( B
% 2.86/3.10 = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) )
% 2.86/3.10 | ( ( A
% 2.86/3.10 = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 2.86/3.10 & ( B = bot_bo2099793752762293965at_nat ) )
% 2.86/3.10 | ( ( A
% 2.86/3.10 = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 2.86/3.10 & ( B
% 2.86/3.10 = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % Un_singleton_iff
% 2.86/3.10 thf(fact_3306_Un__singleton__iff,axiom,
% 2.86/3.10 ! [A: set_o,B: set_o,X: $o] :
% 2.86/3.10 ( ( ( sup_sup_set_o @ A @ B )
% 2.86/3.10 = ( insert_o2 @ X @ bot_bot_set_o ) )
% 2.86/3.10 = ( ( ( A = bot_bot_set_o )
% 2.86/3.10 & ( B
% 2.86/3.10 = ( insert_o2 @ X @ bot_bot_set_o ) ) )
% 2.86/3.10 | ( ( A
% 2.86/3.10 = ( insert_o2 @ X @ bot_bot_set_o ) )
% 2.86/3.10 & ( B = bot_bot_set_o ) )
% 2.86/3.10 | ( ( A
% 2.86/3.10 = ( insert_o2 @ X @ bot_bot_set_o ) )
% 2.86/3.10 & ( B
% 2.86/3.10 = ( insert_o2 @ X @ bot_bot_set_o ) ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % Un_singleton_iff
% 2.86/3.10 thf(fact_3307_Un__singleton__iff,axiom,
% 2.86/3.10 ! [A: set_nat,B: set_nat,X: nat] :
% 2.86/3.10 ( ( ( sup_sup_set_nat @ A @ B )
% 2.86/3.10 = ( insert_nat2 @ X @ bot_bot_set_nat ) )
% 2.86/3.10 = ( ( ( A = bot_bot_set_nat )
% 2.86/3.10 & ( B
% 2.86/3.10 = ( insert_nat2 @ X @ bot_bot_set_nat ) ) )
% 2.86/3.10 | ( ( A
% 2.86/3.10 = ( insert_nat2 @ X @ bot_bot_set_nat ) )
% 2.86/3.10 & ( B = bot_bot_set_nat ) )
% 2.86/3.10 | ( ( A
% 2.86/3.10 = ( insert_nat2 @ X @ bot_bot_set_nat ) )
% 2.86/3.10 & ( B
% 2.86/3.10 = ( insert_nat2 @ X @ bot_bot_set_nat ) ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % Un_singleton_iff
% 2.86/3.10 thf(fact_3308_Un__singleton__iff,axiom,
% 2.86/3.10 ! [A: set_int,B: set_int,X: int] :
% 2.86/3.10 ( ( ( sup_sup_set_int @ A @ B )
% 2.86/3.10 = ( insert_int2 @ X @ bot_bot_set_int ) )
% 2.86/3.10 = ( ( ( A = bot_bot_set_int )
% 2.86/3.10 & ( B
% 2.86/3.10 = ( insert_int2 @ X @ bot_bot_set_int ) ) )
% 2.86/3.10 | ( ( A
% 2.86/3.10 = ( insert_int2 @ X @ bot_bot_set_int ) )
% 2.86/3.10 & ( B = bot_bot_set_int ) )
% 2.86/3.10 | ( ( A
% 2.86/3.10 = ( insert_int2 @ X @ bot_bot_set_int ) )
% 2.86/3.10 & ( B
% 2.86/3.10 = ( insert_int2 @ X @ bot_bot_set_int ) ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % Un_singleton_iff
% 2.86/3.10 thf(fact_3309_singleton__Un__iff,axiom,
% 2.86/3.10 ! [X: produc3843707927480180839at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.10 ( ( ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat )
% 2.86/3.10 = ( sup_su5525570899277871387at_nat @ A @ B ) )
% 2.86/3.10 = ( ( ( A = bot_bo228742789529271731at_nat )
% 2.86/3.10 & ( B
% 2.86/3.10 = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) )
% 2.86/3.10 | ( ( A
% 2.86/3.10 = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 2.86/3.10 & ( B = bot_bo228742789529271731at_nat ) )
% 2.86/3.10 | ( ( A
% 2.86/3.10 = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 2.86/3.10 & ( B
% 2.86/3.10 = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % singleton_Un_iff
% 2.86/3.10 thf(fact_3310_singleton__Un__iff,axiom,
% 2.86/3.10 ! [X: product_prod_nat_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.86/3.10 ( ( ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat )
% 2.86/3.10 = ( sup_su6327502436637775413at_nat @ A @ B ) )
% 2.86/3.10 = ( ( ( A = bot_bo2099793752762293965at_nat )
% 2.86/3.10 & ( B
% 2.86/3.10 = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) )
% 2.86/3.10 | ( ( A
% 2.86/3.10 = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 2.86/3.10 & ( B = bot_bo2099793752762293965at_nat ) )
% 2.86/3.10 | ( ( A
% 2.86/3.10 = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 2.86/3.10 & ( B
% 2.86/3.10 = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ) ) ).
% 2.86/3.10
% 2.86/3.10 % singleton_Un_iff
% 2.86/3.10 thf(fact_3311_singleton__Un__iff,axiom,
% 2.86/3.10 ! [X: $o,A: set_o,B: set_o] :
% 2.86/3.10 ( ( ( insert_o2 @ X @ bot_bot_set_o )
% 2.86/3.10 = ( sup_sup_set_o @ A @ B ) )
% 2.86/3.10 = ( ( ( A = bot_bot_set_o )
% 2.86/3.10 & ( B
% 2.86/3.10 = ( insert_o2 @ X @ bot_bot_set_o ) ) )
% 2.86/3.10 | ( ( A
% 2.86/3.10 = ( insert_o2 @ X @ bot_bot_set_o ) )
% 2.86/3.11 & ( B = bot_bot_set_o ) )
% 2.86/3.11 | ( ( A
% 2.86/3.11 = ( insert_o2 @ X @ bot_bot_set_o ) )
% 2.86/3.11 & ( B
% 2.86/3.11 = ( insert_o2 @ X @ bot_bot_set_o ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % singleton_Un_iff
% 2.86/3.11 thf(fact_3312_singleton__Un__iff,axiom,
% 2.86/3.11 ! [X: nat,A: set_nat,B: set_nat] :
% 2.86/3.11 ( ( ( insert_nat2 @ X @ bot_bot_set_nat )
% 2.86/3.11 = ( sup_sup_set_nat @ A @ B ) )
% 2.86/3.11 = ( ( ( A = bot_bot_set_nat )
% 2.86/3.11 & ( B
% 2.86/3.11 = ( insert_nat2 @ X @ bot_bot_set_nat ) ) )
% 2.86/3.11 | ( ( A
% 2.86/3.11 = ( insert_nat2 @ X @ bot_bot_set_nat ) )
% 2.86/3.11 & ( B = bot_bot_set_nat ) )
% 2.86/3.11 | ( ( A
% 2.86/3.11 = ( insert_nat2 @ X @ bot_bot_set_nat ) )
% 2.86/3.11 & ( B
% 2.86/3.11 = ( insert_nat2 @ X @ bot_bot_set_nat ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % singleton_Un_iff
% 2.86/3.11 thf(fact_3313_singleton__Un__iff,axiom,
% 2.86/3.11 ! [X: int,A: set_int,B: set_int] :
% 2.86/3.11 ( ( ( insert_int2 @ X @ bot_bot_set_int )
% 2.86/3.11 = ( sup_sup_set_int @ A @ B ) )
% 2.86/3.11 = ( ( ( A = bot_bot_set_int )
% 2.86/3.11 & ( B
% 2.86/3.11 = ( insert_int2 @ X @ bot_bot_set_int ) ) )
% 2.86/3.11 | ( ( A
% 2.86/3.11 = ( insert_int2 @ X @ bot_bot_set_int ) )
% 2.86/3.11 & ( B = bot_bot_set_int ) )
% 2.86/3.11 | ( ( A
% 2.86/3.11 = ( insert_int2 @ X @ bot_bot_set_int ) )
% 2.86/3.11 & ( B
% 2.86/3.11 = ( insert_int2 @ X @ bot_bot_set_int ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % singleton_Un_iff
% 2.86/3.11 thf(fact_3314_Diff__partition,axiom,
% 2.86/3.11 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 2.86/3.11 ( ( ord_le1268244103169919719at_nat @ A @ B )
% 2.86/3.11 => ( ( sup_su5525570899277871387at_nat @ A @ ( minus_3314409938677909166at_nat @ B @ A ) )
% 2.86/3.11 = B ) ) ).
% 2.86/3.11
% 2.86/3.11 % Diff_partition
% 2.86/3.11 thf(fact_3315_Diff__partition,axiom,
% 2.86/3.11 ! [A: set_nat,B: set_nat] :
% 2.86/3.11 ( ( ord_less_eq_set_nat @ A @ B )
% 2.86/3.11 => ( ( sup_sup_set_nat @ A @ ( minus_minus_set_nat @ B @ A ) )
% 2.86/3.11 = B ) ) ).
% 2.86/3.11
% 2.86/3.11 % Diff_partition
% 2.86/3.11 thf(fact_3316_Diff__subset__conv,axiom,
% 2.86/3.11 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 2.86/3.11 ( ( ord_le1268244103169919719at_nat @ ( minus_3314409938677909166at_nat @ A @ B ) @ C2 )
% 2.86/3.11 = ( ord_le1268244103169919719at_nat @ A @ ( sup_su5525570899277871387at_nat @ B @ C2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % Diff_subset_conv
% 2.86/3.11 thf(fact_3317_Diff__subset__conv,axiom,
% 2.86/3.11 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 2.86/3.11 ( ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A @ B ) @ C2 )
% 2.86/3.11 = ( ord_less_eq_set_nat @ A @ ( sup_sup_set_nat @ B @ C2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % Diff_subset_conv
% 2.86/3.11 thf(fact_3318_strict__sorted__iff,axiom,
% 2.86/3.11 ! [L: list_Code_integer] :
% 2.86/3.11 ( ( sorted710888440204495920nteger @ ord_le6747313008572928689nteger @ L )
% 2.86/3.11 = ( ( sorted710888440204495920nteger @ ord_le3102999989581377725nteger @ L )
% 2.86/3.11 & ( distin1543349897113766820nteger @ L ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % strict_sorted_iff
% 2.86/3.11 thf(fact_3319_strict__sorted__iff,axiom,
% 2.86/3.11 ! [L: list_num] :
% 2.86/3.11 ( ( sorted_wrt_num @ ord_less_num @ L )
% 2.86/3.11 = ( ( sorted_wrt_num @ ord_less_eq_num @ L )
% 2.86/3.11 & ( distinct_num @ L ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % strict_sorted_iff
% 2.86/3.11 thf(fact_3320_strict__sorted__iff,axiom,
% 2.86/3.11 ! [L: list_nat] :
% 2.86/3.11 ( ( sorted_wrt_nat @ ord_less_nat @ L )
% 2.86/3.11 = ( ( sorted_wrt_nat @ ord_less_eq_nat @ L )
% 2.86/3.11 & ( distinct_nat @ L ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % strict_sorted_iff
% 2.86/3.11 thf(fact_3321_strict__sorted__iff,axiom,
% 2.86/3.11 ! [L: list_int] :
% 2.86/3.11 ( ( sorted_wrt_int @ ord_less_int @ L )
% 2.86/3.11 = ( ( sorted_wrt_int @ ord_less_eq_int @ L )
% 2.86/3.11 & ( distinct_int @ L ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % strict_sorted_iff
% 2.86/3.11 thf(fact_3322_sorted01,axiom,
% 2.86/3.11 ! [Xs: list_nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ one_one_nat )
% 2.86/3.11 => ( sorted_wrt_nat @ ord_less_eq_nat @ Xs ) ) ).
% 2.86/3.11
% 2.86/3.11 % sorted01
% 2.86/3.11 thf(fact_3323_sorted01,axiom,
% 2.86/3.11 ! [Xs: list_int] :
% 2.86/3.11 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ one_one_nat )
% 2.86/3.11 => ( sorted_wrt_int @ ord_less_eq_int @ Xs ) ) ).
% 2.86/3.11
% 2.86/3.11 % sorted01
% 2.86/3.11 thf(fact_3324_sorted__distinct__set__unique,axiom,
% 2.86/3.11 ! [Xs: list_nat,Ys: list_nat] :
% 2.86/3.11 ( ( sorted_wrt_nat @ ord_less_eq_nat @ Xs )
% 2.86/3.11 => ( ( distinct_nat @ Xs )
% 2.86/3.11 => ( ( sorted_wrt_nat @ ord_less_eq_nat @ Ys )
% 2.86/3.11 => ( ( distinct_nat @ Ys )
% 2.86/3.11 => ( ( ( set_nat2 @ Xs )
% 2.86/3.11 = ( set_nat2 @ Ys ) )
% 2.86/3.11 => ( Xs = Ys ) ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % sorted_distinct_set_unique
% 2.86/3.11 thf(fact_3325_sorted__distinct__set__unique,axiom,
% 2.86/3.11 ! [Xs: list_int,Ys: list_int] :
% 2.86/3.11 ( ( sorted_wrt_int @ ord_less_eq_int @ Xs )
% 2.86/3.11 => ( ( distinct_int @ Xs )
% 2.86/3.11 => ( ( sorted_wrt_int @ ord_less_eq_int @ Ys )
% 2.86/3.11 => ( ( distinct_int @ Ys )
% 2.86/3.11 => ( ( ( set_int2 @ Xs )
% 2.86/3.11 = ( set_int2 @ Ys ) )
% 2.86/3.11 => ( Xs = Ys ) ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % sorted_distinct_set_unique
% 2.86/3.11 thf(fact_3326_sorted__wrt__iff__nth__less,axiom,
% 2.86/3.11 ( sorted_wrt_c
% 2.86/3.11 = ( ^ [P2: c > c > $o,Xs3: list_c] :
% 2.86/3.11 ! [I4: nat,J2: nat] :
% 2.86/3.11 ( ( ord_less_nat @ I4 @ J2 )
% 2.86/3.11 => ( ( ord_less_nat @ J2 @ ( size_size_list_c @ Xs3 ) )
% 2.86/3.11 => ( P2 @ ( nth_c @ Xs3 @ I4 ) @ ( nth_c @ Xs3 @ J2 ) ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % sorted_wrt_iff_nth_less
% 2.86/3.11 thf(fact_3327_sorted__wrt__iff__nth__less,axiom,
% 2.86/3.11 ( sorted_wrt_d
% 2.86/3.11 = ( ^ [P2: d > d > $o,Xs3: list_d] :
% 2.86/3.11 ! [I4: nat,J2: nat] :
% 2.86/3.11 ( ( ord_less_nat @ I4 @ J2 )
% 2.86/3.11 => ( ( ord_less_nat @ J2 @ ( size_size_list_d @ Xs3 ) )
% 2.86/3.11 => ( P2 @ ( nth_d @ Xs3 @ I4 ) @ ( nth_d @ Xs3 @ J2 ) ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % sorted_wrt_iff_nth_less
% 2.86/3.11 thf(fact_3328_sorted__wrt__iff__nth__less,axiom,
% 2.86/3.11 ( sorted_wrt_nat
% 2.86/3.11 = ( ^ [P2: nat > nat > $o,Xs3: list_nat] :
% 2.86/3.11 ! [I4: nat,J2: nat] :
% 2.86/3.11 ( ( ord_less_nat @ I4 @ J2 )
% 2.86/3.11 => ( ( ord_less_nat @ J2 @ ( size_size_list_nat @ Xs3 ) )
% 2.86/3.11 => ( P2 @ ( nth_nat @ Xs3 @ I4 ) @ ( nth_nat @ Xs3 @ J2 ) ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % sorted_wrt_iff_nth_less
% 2.86/3.11 thf(fact_3329_sorted__wrt__iff__nth__less,axiom,
% 2.86/3.11 ( sorted_wrt_int
% 2.86/3.11 = ( ^ [P2: int > int > $o,Xs3: list_int] :
% 2.86/3.11 ! [I4: nat,J2: nat] :
% 2.86/3.11 ( ( ord_less_nat @ I4 @ J2 )
% 2.86/3.11 => ( ( ord_less_nat @ J2 @ ( size_size_list_int @ Xs3 ) )
% 2.86/3.11 => ( P2 @ ( nth_int @ Xs3 @ I4 ) @ ( nth_int @ Xs3 @ J2 ) ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % sorted_wrt_iff_nth_less
% 2.86/3.11 thf(fact_3330_sorted__wrt__nth__less,axiom,
% 2.86/3.11 ! [P: c > c > $o,Xs: list_c,I: nat,J: nat] :
% 2.86/3.11 ( ( sorted_wrt_c @ P @ Xs )
% 2.86/3.11 => ( ( ord_less_nat @ I @ J )
% 2.86/3.11 => ( ( ord_less_nat @ J @ ( size_size_list_c @ Xs ) )
% 2.86/3.11 => ( P @ ( nth_c @ Xs @ I ) @ ( nth_c @ Xs @ J ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % sorted_wrt_nth_less
% 2.86/3.11 thf(fact_3331_sorted__wrt__nth__less,axiom,
% 2.86/3.11 ! [P: d > d > $o,Xs: list_d,I: nat,J: nat] :
% 2.86/3.11 ( ( sorted_wrt_d @ P @ Xs )
% 2.86/3.11 => ( ( ord_less_nat @ I @ J )
% 2.86/3.11 => ( ( ord_less_nat @ J @ ( size_size_list_d @ Xs ) )
% 2.86/3.11 => ( P @ ( nth_d @ Xs @ I ) @ ( nth_d @ Xs @ J ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % sorted_wrt_nth_less
% 2.86/3.11 thf(fact_3332_sorted__wrt__nth__less,axiom,
% 2.86/3.11 ! [P: nat > nat > $o,Xs: list_nat,I: nat,J: nat] :
% 2.86/3.11 ( ( sorted_wrt_nat @ P @ Xs )
% 2.86/3.11 => ( ( ord_less_nat @ I @ J )
% 2.86/3.11 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs ) )
% 2.86/3.11 => ( P @ ( nth_nat @ Xs @ I ) @ ( nth_nat @ Xs @ J ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % sorted_wrt_nth_less
% 2.86/3.11 thf(fact_3333_sorted__wrt__nth__less,axiom,
% 2.86/3.11 ! [P: int > int > $o,Xs: list_int,I: nat,J: nat] :
% 2.86/3.11 ( ( sorted_wrt_int @ P @ Xs )
% 2.86/3.11 => ( ( ord_less_nat @ I @ J )
% 2.86/3.11 => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs ) )
% 2.86/3.11 => ( P @ ( nth_int @ Xs @ I ) @ ( nth_int @ Xs @ J ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % sorted_wrt_nth_less
% 2.86/3.11 thf(fact_3334_nth__butlast,axiom,
% 2.86/3.11 ! [N: nat,Xs: list_c] :
% 2.86/3.11 ( ( ord_less_nat @ N @ ( size_size_list_c @ ( butlast_c @ Xs ) ) )
% 2.86/3.11 => ( ( nth_c @ ( butlast_c @ Xs ) @ N )
% 2.86/3.11 = ( nth_c @ Xs @ N ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % nth_butlast
% 2.86/3.11 thf(fact_3335_nth__butlast,axiom,
% 2.86/3.11 ! [N: nat,Xs: list_d] :
% 2.86/3.11 ( ( ord_less_nat @ N @ ( size_size_list_d @ ( butlast_d @ Xs ) ) )
% 2.86/3.11 => ( ( nth_d @ ( butlast_d @ Xs ) @ N )
% 2.86/3.11 = ( nth_d @ Xs @ N ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % nth_butlast
% 2.86/3.11 thf(fact_3336_nth__butlast,axiom,
% 2.86/3.11 ! [N: nat,Xs: list_nat] :
% 2.86/3.11 ( ( ord_less_nat @ N @ ( size_size_list_nat @ ( butlast_nat @ Xs ) ) )
% 2.86/3.11 => ( ( nth_nat @ ( butlast_nat @ Xs ) @ N )
% 2.86/3.11 = ( nth_nat @ Xs @ N ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % nth_butlast
% 2.86/3.11 thf(fact_3337_nth__butlast,axiom,
% 2.86/3.11 ! [N: nat,Xs: list_int] :
% 2.86/3.11 ( ( ord_less_nat @ N @ ( size_size_list_int @ ( butlast_int @ Xs ) ) )
% 2.86/3.11 => ( ( nth_int @ ( butlast_int @ Xs ) @ N )
% 2.86/3.11 = ( nth_int @ Xs @ N ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % nth_butlast
% 2.86/3.11 thf(fact_3338_sorted__iff__nth__mono,axiom,
% 2.86/3.11 ! [Xs: list_nat] :
% 2.86/3.11 ( ( sorted_wrt_nat @ ord_less_eq_nat @ Xs )
% 2.86/3.11 = ( ! [I4: nat,J2: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ I4 @ J2 )
% 2.86/3.11 => ( ( ord_less_nat @ J2 @ ( size_size_list_nat @ Xs ) )
% 2.86/3.11 => ( ord_less_eq_nat @ ( nth_nat @ Xs @ I4 ) @ ( nth_nat @ Xs @ J2 ) ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % sorted_iff_nth_mono
% 2.86/3.11 thf(fact_3339_sorted__iff__nth__mono,axiom,
% 2.86/3.11 ! [Xs: list_int] :
% 2.86/3.11 ( ( sorted_wrt_int @ ord_less_eq_int @ Xs )
% 2.86/3.11 = ( ! [I4: nat,J2: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ I4 @ J2 )
% 2.86/3.11 => ( ( ord_less_nat @ J2 @ ( size_size_list_int @ Xs ) )
% 2.86/3.11 => ( ord_less_eq_int @ ( nth_int @ Xs @ I4 ) @ ( nth_int @ Xs @ J2 ) ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % sorted_iff_nth_mono
% 2.86/3.11 thf(fact_3340_sorted__nth__mono,axiom,
% 2.86/3.11 ! [Xs: list_nat,I: nat,J: nat] :
% 2.86/3.11 ( ( sorted_wrt_nat @ ord_less_eq_nat @ Xs )
% 2.86/3.11 => ( ( ord_less_eq_nat @ I @ J )
% 2.86/3.11 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs ) )
% 2.86/3.11 => ( ord_less_eq_nat @ ( nth_nat @ Xs @ I ) @ ( nth_nat @ Xs @ J ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % sorted_nth_mono
% 2.86/3.11 thf(fact_3341_sorted__nth__mono,axiom,
% 2.86/3.11 ! [Xs: list_int,I: nat,J: nat] :
% 2.86/3.11 ( ( sorted_wrt_int @ ord_less_eq_int @ Xs )
% 2.86/3.11 => ( ( ord_less_eq_nat @ I @ J )
% 2.86/3.11 => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs ) )
% 2.86/3.11 => ( ord_less_eq_int @ ( nth_int @ Xs @ I ) @ ( nth_int @ Xs @ J ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % sorted_nth_mono
% 2.86/3.11 thf(fact_3342_sorted__iff__nth__mono__less,axiom,
% 2.86/3.11 ! [Xs: list_nat] :
% 2.86/3.11 ( ( sorted_wrt_nat @ ord_less_eq_nat @ Xs )
% 2.86/3.11 = ( ! [I4: nat,J2: nat] :
% 2.86/3.11 ( ( ord_less_nat @ I4 @ J2 )
% 2.86/3.11 => ( ( ord_less_nat @ J2 @ ( size_size_list_nat @ Xs ) )
% 2.86/3.11 => ( ord_less_eq_nat @ ( nth_nat @ Xs @ I4 ) @ ( nth_nat @ Xs @ J2 ) ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % sorted_iff_nth_mono_less
% 2.86/3.11 thf(fact_3343_sorted__iff__nth__mono__less,axiom,
% 2.86/3.11 ! [Xs: list_int] :
% 2.86/3.11 ( ( sorted_wrt_int @ ord_less_eq_int @ Xs )
% 2.86/3.11 = ( ! [I4: nat,J2: nat] :
% 2.86/3.11 ( ( ord_less_nat @ I4 @ J2 )
% 2.86/3.11 => ( ( ord_less_nat @ J2 @ ( size_size_list_int @ Xs ) )
% 2.86/3.11 => ( ord_less_eq_int @ ( nth_int @ Xs @ I4 ) @ ( nth_int @ Xs @ J2 ) ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % sorted_iff_nth_mono_less
% 2.86/3.11 thf(fact_3344_mergesort__remdups__correct,axiom,
% 2.86/3.11 ! [L: list_nat] :
% 2.86/3.11 ( ( distinct_nat @ ( merges1656613366846331073ps_nat @ L ) )
% 2.86/3.11 & ( sorted_wrt_nat @ ord_less_eq_nat @ ( merges1656613366846331073ps_nat @ L ) )
% 2.86/3.11 & ( ( set_nat2 @ ( merges1656613366846331073ps_nat @ L ) )
% 2.86/3.11 = ( set_nat2 @ L ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % mergesort_remdups_correct
% 2.86/3.11 thf(fact_3345_mergesort__remdups__correct,axiom,
% 2.86/3.11 ! [L: list_int] :
% 2.86/3.11 ( ( distinct_int @ ( merges1654122896337280797ps_int @ L ) )
% 2.86/3.11 & ( sorted_wrt_int @ ord_less_eq_int @ ( merges1654122896337280797ps_int @ L ) )
% 2.86/3.11 & ( ( set_int2 @ ( merges1654122896337280797ps_int @ L ) )
% 2.86/3.11 = ( set_int2 @ L ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % mergesort_remdups_correct
% 2.86/3.11 thf(fact_3346_times__assn__raw_Osimps,axiom,
% 2.86/3.11 ! [P: produc3658429121746597890et_nat > $o,Q: produc3658429121746597890et_nat > $o,H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 2.86/3.11 ( ( times_assn_raw @ P @ Q @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 2.86/3.11 = ( ? [As1: set_nat,As22: set_nat] :
% 2.86/3.11 ( ( As2
% 2.86/3.11 = ( sup_sup_set_nat @ As1 @ As22 ) )
% 2.86/3.11 & ( ( inf_inf_set_nat @ As1 @ As22 )
% 2.86/3.11 = bot_bot_set_nat )
% 2.86/3.11 & ( P @ ( produc7507926704131184380et_nat @ H2 @ As1 ) )
% 2.86/3.11 & ( Q @ ( produc7507926704131184380et_nat @ H2 @ As22 ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % times_assn_raw.simps
% 2.86/3.11 thf(fact_3347_times__assn__raw_Oelims_I1_J,axiom,
% 2.86/3.11 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Y: $o] :
% 2.86/3.11 ( ( ( times_assn_raw @ X @ Xa @ Xb )
% 2.86/3.11 = Y )
% 2.86/3.11 => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.86/3.11 ( ( Xb
% 2.86/3.11 = ( produc7507926704131184380et_nat @ H @ As ) )
% 2.86/3.11 => ( Y
% 2.86/3.11 = ( ~ ? [As1: set_nat,As22: set_nat] :
% 2.86/3.11 ( ( As
% 2.86/3.11 = ( sup_sup_set_nat @ As1 @ As22 ) )
% 2.86/3.11 & ( ( inf_inf_set_nat @ As1 @ As22 )
% 2.86/3.11 = bot_bot_set_nat )
% 2.86/3.11 & ( X @ ( produc7507926704131184380et_nat @ H @ As1 ) )
% 2.86/3.11 & ( Xa @ ( produc7507926704131184380et_nat @ H @ As22 ) ) ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % times_assn_raw.elims(1)
% 2.86/3.11 thf(fact_3348_times__assn__raw_Oelims_I2_J,axiom,
% 2.86/3.11 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 2.86/3.11 ( ( times_assn_raw @ X @ Xa @ Xb )
% 2.86/3.11 => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.86/3.11 ( ( Xb
% 2.86/3.11 = ( produc7507926704131184380et_nat @ H @ As ) )
% 2.86/3.11 => ~ ? [As12: set_nat,As23: set_nat] :
% 2.86/3.11 ( ( As
% 2.86/3.11 = ( sup_sup_set_nat @ As12 @ As23 ) )
% 2.86/3.11 & ( ( inf_inf_set_nat @ As12 @ As23 )
% 2.86/3.11 = bot_bot_set_nat )
% 2.86/3.11 & ( X @ ( produc7507926704131184380et_nat @ H @ As12 ) )
% 2.86/3.11 & ( Xa @ ( produc7507926704131184380et_nat @ H @ As23 ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % times_assn_raw.elims(2)
% 2.86/3.11 thf(fact_3349_times__assn__raw_Oelims_I3_J,axiom,
% 2.86/3.11 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 2.86/3.11 ( ~ ( times_assn_raw @ X @ Xa @ Xb )
% 2.86/3.11 => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.86/3.11 ( ( Xb
% 2.86/3.11 = ( produc7507926704131184380et_nat @ H @ As ) )
% 2.86/3.11 => ? [As13: set_nat,As24: set_nat] :
% 2.86/3.11 ( ( As
% 2.86/3.11 = ( sup_sup_set_nat @ As13 @ As24 ) )
% 2.86/3.11 & ( ( inf_inf_set_nat @ As13 @ As24 )
% 2.86/3.11 = bot_bot_set_nat )
% 2.86/3.11 & ( X @ ( produc7507926704131184380et_nat @ H @ As13 ) )
% 2.86/3.11 & ( Xa @ ( produc7507926704131184380et_nat @ H @ As24 ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % times_assn_raw.elims(3)
% 2.86/3.11 thf(fact_3350_nat__descend__induct,axiom,
% 2.86/3.11 ! [N: nat,P: nat > $o,M2: nat] :
% 2.86/3.11 ( ! [K: nat] :
% 2.86/3.11 ( ( ord_less_nat @ N @ K )
% 2.86/3.11 => ( P @ K ) )
% 2.86/3.11 => ( ! [K: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ K @ N )
% 2.86/3.11 => ( ! [I6: nat] :
% 2.86/3.11 ( ( ord_less_nat @ K @ I6 )
% 2.86/3.11 => ( P @ I6 ) )
% 2.86/3.11 => ( P @ K ) ) )
% 2.86/3.11 => ( P @ M2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % nat_descend_induct
% 2.86/3.11 thf(fact_3351_merge__correct,axiom,
% 2.86/3.11 ! [L12: list_nat,L23: list_nat] :
% 2.86/3.11 ( ( ( distinct_nat @ L12 )
% 2.86/3.11 & ( sorted_wrt_nat @ ord_less_eq_nat @ L12 ) )
% 2.86/3.11 => ( ( ( distinct_nat @ L23 )
% 2.86/3.11 & ( sorted_wrt_nat @ ord_less_eq_nat @ L23 ) )
% 2.86/3.11 => ( ( distinct_nat @ ( merge_nat @ L12 @ L23 ) )
% 2.86/3.11 & ( sorted_wrt_nat @ ord_less_eq_nat @ ( merge_nat @ L12 @ L23 ) )
% 2.86/3.11 & ( ( set_nat2 @ ( merge_nat @ L12 @ L23 ) )
% 2.86/3.11 = ( sup_sup_set_nat @ ( set_nat2 @ L12 ) @ ( set_nat2 @ L23 ) ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % merge_correct
% 2.86/3.11 thf(fact_3352_merge__correct,axiom,
% 2.86/3.11 ! [L12: list_int,L23: list_int] :
% 2.86/3.11 ( ( ( distinct_int @ L12 )
% 2.86/3.11 & ( sorted_wrt_int @ ord_less_eq_int @ L12 ) )
% 2.86/3.11 => ( ( ( distinct_int @ L23 )
% 2.86/3.11 & ( sorted_wrt_int @ ord_less_eq_int @ L23 ) )
% 2.86/3.11 => ( ( distinct_int @ ( merge_int @ L12 @ L23 ) )
% 2.86/3.11 & ( sorted_wrt_int @ ord_less_eq_int @ ( merge_int @ L12 @ L23 ) )
% 2.86/3.11 & ( ( set_int2 @ ( merge_int @ L12 @ L23 ) )
% 2.86/3.11 = ( sup_sup_set_int @ ( set_int2 @ L12 ) @ ( set_int2 @ L23 ) ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % merge_correct
% 2.86/3.11 thf(fact_3353_slice__nth,axiom,
% 2.86/3.11 ! [From: nat,To: nat,Xs: list_c,I: nat] :
% 2.86/3.11 ( ( ord_less_nat @ From @ To )
% 2.86/3.11 => ( ( ord_less_eq_nat @ To @ ( size_size_list_c @ Xs ) )
% 2.86/3.11 => ( ( ord_less_nat @ I @ ( minus_minus_nat @ To @ From ) )
% 2.86/3.11 => ( ( nth_c @ ( slice_c @ From @ To @ Xs ) @ I )
% 2.86/3.11 = ( nth_c @ Xs @ ( plus_plus_nat @ From @ I ) ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % slice_nth
% 2.86/3.11 thf(fact_3354_slice__nth,axiom,
% 2.86/3.11 ! [From: nat,To: nat,Xs: list_d,I: nat] :
% 2.86/3.11 ( ( ord_less_nat @ From @ To )
% 2.86/3.11 => ( ( ord_less_eq_nat @ To @ ( size_size_list_d @ Xs ) )
% 2.86/3.11 => ( ( ord_less_nat @ I @ ( minus_minus_nat @ To @ From ) )
% 2.86/3.11 => ( ( nth_d @ ( slice_d @ From @ To @ Xs ) @ I )
% 2.86/3.11 = ( nth_d @ Xs @ ( plus_plus_nat @ From @ I ) ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % slice_nth
% 2.86/3.11 thf(fact_3355_slice__nth,axiom,
% 2.86/3.11 ! [From: nat,To: nat,Xs: list_nat,I: nat] :
% 2.86/3.11 ( ( ord_less_nat @ From @ To )
% 2.86/3.11 => ( ( ord_less_eq_nat @ To @ ( size_size_list_nat @ Xs ) )
% 2.86/3.11 => ( ( ord_less_nat @ I @ ( minus_minus_nat @ To @ From ) )
% 2.86/3.11 => ( ( nth_nat @ ( slice_nat @ From @ To @ Xs ) @ I )
% 2.86/3.11 = ( nth_nat @ Xs @ ( plus_plus_nat @ From @ I ) ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % slice_nth
% 2.86/3.11 thf(fact_3356_slice__nth,axiom,
% 2.86/3.11 ! [From: nat,To: nat,Xs: list_int,I: nat] :
% 2.86/3.11 ( ( ord_less_nat @ From @ To )
% 2.86/3.11 => ( ( ord_less_eq_nat @ To @ ( size_size_list_int @ Xs ) )
% 2.86/3.11 => ( ( ord_less_nat @ I @ ( minus_minus_nat @ To @ From ) )
% 2.86/3.11 => ( ( nth_int @ ( slice_int @ From @ To @ Xs ) @ I )
% 2.86/3.11 = ( nth_int @ Xs @ ( plus_plus_nat @ From @ I ) ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % slice_nth
% 2.86/3.11 thf(fact_3357_sorted__rev__iff__nth__Suc,axiom,
% 2.86/3.11 ! [Xs: list_nat] :
% 2.86/3.11 ( ( sorted_wrt_nat @ ord_less_eq_nat @ ( rev_nat @ Xs ) )
% 2.86/3.11 = ( ! [I4: nat] :
% 2.86/3.11 ( ( ord_less_nat @ ( suc @ I4 ) @ ( size_size_list_nat @ Xs ) )
% 2.86/3.11 => ( ord_less_eq_nat @ ( nth_nat @ Xs @ ( suc @ I4 ) ) @ ( nth_nat @ Xs @ I4 ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % sorted_rev_iff_nth_Suc
% 2.86/3.11 thf(fact_3358_sorted__rev__iff__nth__Suc,axiom,
% 2.86/3.11 ! [Xs: list_int] :
% 2.86/3.11 ( ( sorted_wrt_int @ ord_less_eq_int @ ( rev_int @ Xs ) )
% 2.86/3.11 = ( ! [I4: nat] :
% 2.86/3.11 ( ( ord_less_nat @ ( suc @ I4 ) @ ( size_size_list_int @ Xs ) )
% 2.86/3.11 => ( ord_less_eq_int @ ( nth_int @ Xs @ ( suc @ I4 ) ) @ ( nth_int @ Xs @ I4 ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % sorted_rev_iff_nth_Suc
% 2.86/3.11 thf(fact_3359_add__right__cancel,axiom,
% 2.86/3.11 ! [B2: multis2468970476368604999at_nat,A2: multis2468970476368604999at_nat,C: multis2468970476368604999at_nat] :
% 2.86/3.11 ( ( ( plus_p7104986032573967614at_nat @ B2 @ A2 )
% 2.86/3.11 = ( plus_p7104986032573967614at_nat @ C @ A2 ) )
% 2.86/3.11 = ( B2 = C ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_right_cancel
% 2.86/3.11 thf(fact_3360_add__right__cancel,axiom,
% 2.86/3.11 ! [B2: rat,A2: rat,C: rat] :
% 2.86/3.11 ( ( ( plus_plus_rat @ B2 @ A2 )
% 2.86/3.11 = ( plus_plus_rat @ C @ A2 ) )
% 2.86/3.11 = ( B2 = C ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_right_cancel
% 2.86/3.11 thf(fact_3361_add__right__cancel,axiom,
% 2.86/3.11 ! [B2: nat,A2: nat,C: nat] :
% 2.86/3.11 ( ( ( plus_plus_nat @ B2 @ A2 )
% 2.86/3.11 = ( plus_plus_nat @ C @ A2 ) )
% 2.86/3.11 = ( B2 = C ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_right_cancel
% 2.86/3.11 thf(fact_3362_add__right__cancel,axiom,
% 2.86/3.11 ! [B2: int,A2: int,C: int] :
% 2.86/3.11 ( ( ( plus_plus_int @ B2 @ A2 )
% 2.86/3.11 = ( plus_plus_int @ C @ A2 ) )
% 2.86/3.11 = ( B2 = C ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_right_cancel
% 2.86/3.11 thf(fact_3363_add__left__cancel,axiom,
% 2.86/3.11 ! [A2: multis2468970476368604999at_nat,B2: multis2468970476368604999at_nat,C: multis2468970476368604999at_nat] :
% 2.86/3.11 ( ( ( plus_p7104986032573967614at_nat @ A2 @ B2 )
% 2.86/3.11 = ( plus_p7104986032573967614at_nat @ A2 @ C ) )
% 2.86/3.11 = ( B2 = C ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_left_cancel
% 2.86/3.11 thf(fact_3364_add__left__cancel,axiom,
% 2.86/3.11 ! [A2: rat,B2: rat,C: rat] :
% 2.86/3.11 ( ( ( plus_plus_rat @ A2 @ B2 )
% 2.86/3.11 = ( plus_plus_rat @ A2 @ C ) )
% 2.86/3.11 = ( B2 = C ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_left_cancel
% 2.86/3.11 thf(fact_3365_add__left__cancel,axiom,
% 2.86/3.11 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.11 ( ( ( plus_plus_nat @ A2 @ B2 )
% 2.86/3.11 = ( plus_plus_nat @ A2 @ C ) )
% 2.86/3.11 = ( B2 = C ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_left_cancel
% 2.86/3.11 thf(fact_3366_add__left__cancel,axiom,
% 2.86/3.11 ! [A2: int,B2: int,C: int] :
% 2.86/3.11 ( ( ( plus_plus_int @ A2 @ B2 )
% 2.86/3.11 = ( plus_plus_int @ A2 @ C ) )
% 2.86/3.11 = ( B2 = C ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_left_cancel
% 2.86/3.11 thf(fact_3367_mod__or__dist,axiom,
% 2.86/3.11 ! [P: assn,Q: assn,H2: produc3658429121746597890et_nat] :
% 2.86/3.11 ( ( rep_assn @ ( sup_sup_assn @ P @ Q ) @ H2 )
% 2.86/3.11 = ( ( rep_assn @ P @ H2 )
% 2.86/3.11 | ( rep_assn @ Q @ H2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % mod_or_dist
% 2.86/3.11 thf(fact_3368_merge__pure__or,axiom,
% 2.86/3.11 ! [A2: $o,B2: $o] :
% 2.86/3.11 ( ( sup_sup_assn @ ( pure_assn @ A2 ) @ ( pure_assn @ B2 ) )
% 2.86/3.11 = ( pure_assn
% 2.86/3.11 @ ( A2
% 2.86/3.11 | B2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % merge_pure_or
% 2.86/3.11 thf(fact_3369_add__le__cancel__right,axiom,
% 2.86/3.11 ! [A2: rat,C: rat,B2: rat] :
% 2.86/3.11 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A2 @ C ) @ ( plus_plus_rat @ B2 @ C ) )
% 2.86/3.11 = ( ord_less_eq_rat @ A2 @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_le_cancel_right
% 2.86/3.11 thf(fact_3370_add__le__cancel__right,axiom,
% 2.86/3.11 ! [A2: nat,C: nat,B2: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ C ) @ ( plus_plus_nat @ B2 @ C ) )
% 2.86/3.11 = ( ord_less_eq_nat @ A2 @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_le_cancel_right
% 2.86/3.11 thf(fact_3371_add__le__cancel__right,axiom,
% 2.86/3.11 ! [A2: int,C: int,B2: int] :
% 2.86/3.11 ( ( ord_less_eq_int @ ( plus_plus_int @ A2 @ C ) @ ( plus_plus_int @ B2 @ C ) )
% 2.86/3.11 = ( ord_less_eq_int @ A2 @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_le_cancel_right
% 2.86/3.11 thf(fact_3372_add__le__cancel__left,axiom,
% 2.86/3.11 ! [C: rat,A2: rat,B2: rat] :
% 2.86/3.11 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A2 ) @ ( plus_plus_rat @ C @ B2 ) )
% 2.86/3.11 = ( ord_less_eq_rat @ A2 @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_le_cancel_left
% 2.86/3.11 thf(fact_3373_add__le__cancel__left,axiom,
% 2.86/3.11 ! [C: nat,A2: nat,B2: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A2 ) @ ( plus_plus_nat @ C @ B2 ) )
% 2.86/3.11 = ( ord_less_eq_nat @ A2 @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_le_cancel_left
% 2.86/3.11 thf(fact_3374_add__le__cancel__left,axiom,
% 2.86/3.11 ! [C: int,A2: int,B2: int] :
% 2.86/3.11 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A2 ) @ ( plus_plus_int @ C @ B2 ) )
% 2.86/3.11 = ( ord_less_eq_int @ A2 @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_le_cancel_left
% 2.86/3.11 thf(fact_3375_add__less__cancel__left,axiom,
% 2.86/3.11 ! [C: rat,A2: rat,B2: rat] :
% 2.86/3.11 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A2 ) @ ( plus_plus_rat @ C @ B2 ) )
% 2.86/3.11 = ( ord_less_rat @ A2 @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_less_cancel_left
% 2.86/3.11 thf(fact_3376_add__less__cancel__left,axiom,
% 2.86/3.11 ! [C: code_integer,A2: code_integer,B2: code_integer] :
% 2.86/3.11 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ C @ A2 ) @ ( plus_p5714425477246183910nteger @ C @ B2 ) )
% 2.86/3.11 = ( ord_le6747313008572928689nteger @ A2 @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_less_cancel_left
% 2.86/3.11 thf(fact_3377_add__less__cancel__left,axiom,
% 2.86/3.11 ! [C: nat,A2: nat,B2: nat] :
% 2.86/3.11 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A2 ) @ ( plus_plus_nat @ C @ B2 ) )
% 2.86/3.11 = ( ord_less_nat @ A2 @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_less_cancel_left
% 2.86/3.11 thf(fact_3378_add__less__cancel__left,axiom,
% 2.86/3.11 ! [C: int,A2: int,B2: int] :
% 2.86/3.11 ( ( ord_less_int @ ( plus_plus_int @ C @ A2 ) @ ( plus_plus_int @ C @ B2 ) )
% 2.86/3.11 = ( ord_less_int @ A2 @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_less_cancel_left
% 2.86/3.11 thf(fact_3379_add__less__cancel__right,axiom,
% 2.86/3.11 ! [A2: rat,C: rat,B2: rat] :
% 2.86/3.11 ( ( ord_less_rat @ ( plus_plus_rat @ A2 @ C ) @ ( plus_plus_rat @ B2 @ C ) )
% 2.86/3.11 = ( ord_less_rat @ A2 @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_less_cancel_right
% 2.86/3.11 thf(fact_3380_add__less__cancel__right,axiom,
% 2.86/3.11 ! [A2: code_integer,C: code_integer,B2: code_integer] :
% 2.86/3.11 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A2 @ C ) @ ( plus_p5714425477246183910nteger @ B2 @ C ) )
% 2.86/3.11 = ( ord_le6747313008572928689nteger @ A2 @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_less_cancel_right
% 2.86/3.11 thf(fact_3381_add__less__cancel__right,axiom,
% 2.86/3.11 ! [A2: nat,C: nat,B2: nat] :
% 2.86/3.11 ( ( ord_less_nat @ ( plus_plus_nat @ A2 @ C ) @ ( plus_plus_nat @ B2 @ C ) )
% 2.86/3.11 = ( ord_less_nat @ A2 @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_less_cancel_right
% 2.86/3.11 thf(fact_3382_add__less__cancel__right,axiom,
% 2.86/3.11 ! [A2: int,C: int,B2: int] :
% 2.86/3.11 ( ( ord_less_int @ ( plus_plus_int @ A2 @ C ) @ ( plus_plus_int @ B2 @ C ) )
% 2.86/3.11 = ( ord_less_int @ A2 @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_less_cancel_right
% 2.86/3.11 thf(fact_3383_add__diff__cancel,axiom,
% 2.86/3.11 ! [A2: rat,B2: rat] :
% 2.86/3.11 ( ( minus_minus_rat @ ( plus_plus_rat @ A2 @ B2 ) @ B2 )
% 2.86/3.11 = A2 ) ).
% 2.86/3.11
% 2.86/3.11 % add_diff_cancel
% 2.86/3.11 thf(fact_3384_add__diff__cancel,axiom,
% 2.86/3.11 ! [A2: int,B2: int] :
% 2.86/3.11 ( ( minus_minus_int @ ( plus_plus_int @ A2 @ B2 ) @ B2 )
% 2.86/3.11 = A2 ) ).
% 2.86/3.11
% 2.86/3.11 % add_diff_cancel
% 2.86/3.11 thf(fact_3385_diff__add__cancel,axiom,
% 2.86/3.11 ! [A2: rat,B2: rat] :
% 2.86/3.11 ( ( plus_plus_rat @ ( minus_minus_rat @ A2 @ B2 ) @ B2 )
% 2.86/3.11 = A2 ) ).
% 2.86/3.11
% 2.86/3.11 % diff_add_cancel
% 2.86/3.11 thf(fact_3386_diff__add__cancel,axiom,
% 2.86/3.11 ! [A2: int,B2: int] :
% 2.86/3.11 ( ( plus_plus_int @ ( minus_minus_int @ A2 @ B2 ) @ B2 )
% 2.86/3.11 = A2 ) ).
% 2.86/3.11
% 2.86/3.11 % diff_add_cancel
% 2.86/3.11 thf(fact_3387_add__diff__cancel__left,axiom,
% 2.86/3.11 ! [C: multis2468970476368604999at_nat,A2: multis2468970476368604999at_nat,B2: multis2468970476368604999at_nat] :
% 2.86/3.11 ( ( minus_4286766774447292334at_nat @ ( plus_p7104986032573967614at_nat @ C @ A2 ) @ ( plus_p7104986032573967614at_nat @ C @ B2 ) )
% 2.86/3.11 = ( minus_4286766774447292334at_nat @ A2 @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_diff_cancel_left
% 2.86/3.11 thf(fact_3388_add__diff__cancel__left,axiom,
% 2.86/3.11 ! [C: rat,A2: rat,B2: rat] :
% 2.86/3.11 ( ( minus_minus_rat @ ( plus_plus_rat @ C @ A2 ) @ ( plus_plus_rat @ C @ B2 ) )
% 2.86/3.11 = ( minus_minus_rat @ A2 @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_diff_cancel_left
% 2.86/3.11 thf(fact_3389_add__diff__cancel__left,axiom,
% 2.86/3.11 ! [C: nat,A2: nat,B2: nat] :
% 2.86/3.11 ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A2 ) @ ( plus_plus_nat @ C @ B2 ) )
% 2.86/3.11 = ( minus_minus_nat @ A2 @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_diff_cancel_left
% 2.86/3.11 thf(fact_3390_add__diff__cancel__left,axiom,
% 2.86/3.11 ! [C: int,A2: int,B2: int] :
% 2.86/3.11 ( ( minus_minus_int @ ( plus_plus_int @ C @ A2 ) @ ( plus_plus_int @ C @ B2 ) )
% 2.86/3.11 = ( minus_minus_int @ A2 @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_diff_cancel_left
% 2.86/3.11 thf(fact_3391_add__diff__cancel__left_H,axiom,
% 2.86/3.11 ! [A2: multis2468970476368604999at_nat,B2: multis2468970476368604999at_nat] :
% 2.86/3.11 ( ( minus_4286766774447292334at_nat @ ( plus_p7104986032573967614at_nat @ A2 @ B2 ) @ A2 )
% 2.86/3.11 = B2 ) ).
% 2.86/3.11
% 2.86/3.11 % add_diff_cancel_left'
% 2.86/3.11 thf(fact_3392_add__diff__cancel__left_H,axiom,
% 2.86/3.11 ! [A2: rat,B2: rat] :
% 2.86/3.11 ( ( minus_minus_rat @ ( plus_plus_rat @ A2 @ B2 ) @ A2 )
% 2.86/3.11 = B2 ) ).
% 2.86/3.11
% 2.86/3.11 % add_diff_cancel_left'
% 2.86/3.11 thf(fact_3393_add__diff__cancel__left_H,axiom,
% 2.86/3.11 ! [A2: nat,B2: nat] :
% 2.86/3.11 ( ( minus_minus_nat @ ( plus_plus_nat @ A2 @ B2 ) @ A2 )
% 2.86/3.11 = B2 ) ).
% 2.86/3.11
% 2.86/3.11 % add_diff_cancel_left'
% 2.86/3.11 thf(fact_3394_add__diff__cancel__left_H,axiom,
% 2.86/3.11 ! [A2: int,B2: int] :
% 2.86/3.11 ( ( minus_minus_int @ ( plus_plus_int @ A2 @ B2 ) @ A2 )
% 2.86/3.11 = B2 ) ).
% 2.86/3.11
% 2.86/3.11 % add_diff_cancel_left'
% 2.86/3.11 thf(fact_3395_add__diff__cancel__right,axiom,
% 2.86/3.11 ! [A2: multis2468970476368604999at_nat,C: multis2468970476368604999at_nat,B2: multis2468970476368604999at_nat] :
% 2.86/3.11 ( ( minus_4286766774447292334at_nat @ ( plus_p7104986032573967614at_nat @ A2 @ C ) @ ( plus_p7104986032573967614at_nat @ B2 @ C ) )
% 2.86/3.11 = ( minus_4286766774447292334at_nat @ A2 @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_diff_cancel_right
% 2.86/3.11 thf(fact_3396_add__diff__cancel__right,axiom,
% 2.86/3.11 ! [A2: rat,C: rat,B2: rat] :
% 2.86/3.11 ( ( minus_minus_rat @ ( plus_plus_rat @ A2 @ C ) @ ( plus_plus_rat @ B2 @ C ) )
% 2.86/3.11 = ( minus_minus_rat @ A2 @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_diff_cancel_right
% 2.86/3.11 thf(fact_3397_add__diff__cancel__right,axiom,
% 2.86/3.11 ! [A2: nat,C: nat,B2: nat] :
% 2.86/3.11 ( ( minus_minus_nat @ ( plus_plus_nat @ A2 @ C ) @ ( plus_plus_nat @ B2 @ C ) )
% 2.86/3.11 = ( minus_minus_nat @ A2 @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_diff_cancel_right
% 2.86/3.11 thf(fact_3398_add__diff__cancel__right,axiom,
% 2.86/3.11 ! [A2: int,C: int,B2: int] :
% 2.86/3.11 ( ( minus_minus_int @ ( plus_plus_int @ A2 @ C ) @ ( plus_plus_int @ B2 @ C ) )
% 2.86/3.11 = ( minus_minus_int @ A2 @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_diff_cancel_right
% 2.86/3.11 thf(fact_3399_add__diff__cancel__right_H,axiom,
% 2.86/3.11 ! [A2: multis2468970476368604999at_nat,B2: multis2468970476368604999at_nat] :
% 2.86/3.11 ( ( minus_4286766774447292334at_nat @ ( plus_p7104986032573967614at_nat @ A2 @ B2 ) @ B2 )
% 2.86/3.11 = A2 ) ).
% 2.86/3.11
% 2.86/3.11 % add_diff_cancel_right'
% 2.86/3.11 thf(fact_3400_add__diff__cancel__right_H,axiom,
% 2.86/3.11 ! [A2: rat,B2: rat] :
% 2.86/3.11 ( ( minus_minus_rat @ ( plus_plus_rat @ A2 @ B2 ) @ B2 )
% 2.86/3.11 = A2 ) ).
% 2.86/3.11
% 2.86/3.11 % add_diff_cancel_right'
% 2.86/3.11 thf(fact_3401_add__diff__cancel__right_H,axiom,
% 2.86/3.11 ! [A2: nat,B2: nat] :
% 2.86/3.11 ( ( minus_minus_nat @ ( plus_plus_nat @ A2 @ B2 ) @ B2 )
% 2.86/3.11 = A2 ) ).
% 2.86/3.11
% 2.86/3.11 % add_diff_cancel_right'
% 2.86/3.11 thf(fact_3402_add__diff__cancel__right_H,axiom,
% 2.86/3.11 ! [A2: int,B2: int] :
% 2.86/3.11 ( ( minus_minus_int @ ( plus_plus_int @ A2 @ B2 ) @ B2 )
% 2.86/3.11 = A2 ) ).
% 2.86/3.11
% 2.86/3.11 % add_diff_cancel_right'
% 2.86/3.11 thf(fact_3403_lessI,axiom,
% 2.86/3.11 ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 2.86/3.11
% 2.86/3.11 % lessI
% 2.86/3.11 thf(fact_3404_Suc__mono,axiom,
% 2.86/3.11 ! [M2: nat,N: nat] :
% 2.86/3.11 ( ( ord_less_nat @ M2 @ N )
% 2.86/3.11 => ( ord_less_nat @ ( suc @ M2 ) @ ( suc @ N ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % Suc_mono
% 2.86/3.11 thf(fact_3405_Suc__less__eq,axiom,
% 2.86/3.11 ! [M2: nat,N: nat] :
% 2.86/3.11 ( ( ord_less_nat @ ( suc @ M2 ) @ ( suc @ N ) )
% 2.86/3.11 = ( ord_less_nat @ M2 @ N ) ) ).
% 2.86/3.11
% 2.86/3.11 % Suc_less_eq
% 2.86/3.11 thf(fact_3406_nat__add__left__cancel__less,axiom,
% 2.86/3.11 ! [K3: nat,M2: nat,N: nat] :
% 2.86/3.11 ( ( ord_less_nat @ ( plus_plus_nat @ K3 @ M2 ) @ ( plus_plus_nat @ K3 @ N ) )
% 2.86/3.11 = ( ord_less_nat @ M2 @ N ) ) ).
% 2.86/3.11
% 2.86/3.11 % nat_add_left_cancel_less
% 2.86/3.11 thf(fact_3407_le__add__diff__inverse,axiom,
% 2.86/3.11 ! [B2: rat,A2: rat] :
% 2.86/3.11 ( ( ord_less_eq_rat @ B2 @ A2 )
% 2.86/3.11 => ( ( plus_plus_rat @ B2 @ ( minus_minus_rat @ A2 @ B2 ) )
% 2.86/3.11 = A2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % le_add_diff_inverse
% 2.86/3.11 thf(fact_3408_le__add__diff__inverse,axiom,
% 2.86/3.11 ! [B2: nat,A2: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ B2 @ A2 )
% 2.86/3.11 => ( ( plus_plus_nat @ B2 @ ( minus_minus_nat @ A2 @ B2 ) )
% 2.86/3.11 = A2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % le_add_diff_inverse
% 2.86/3.11 thf(fact_3409_le__add__diff__inverse,axiom,
% 2.86/3.11 ! [B2: int,A2: int] :
% 2.86/3.11 ( ( ord_less_eq_int @ B2 @ A2 )
% 2.86/3.11 => ( ( plus_plus_int @ B2 @ ( minus_minus_int @ A2 @ B2 ) )
% 2.86/3.11 = A2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % le_add_diff_inverse
% 2.86/3.11 thf(fact_3410_le__add__diff__inverse2,axiom,
% 2.86/3.11 ! [B2: rat,A2: rat] :
% 2.86/3.11 ( ( ord_less_eq_rat @ B2 @ A2 )
% 2.86/3.11 => ( ( plus_plus_rat @ ( minus_minus_rat @ A2 @ B2 ) @ B2 )
% 2.86/3.11 = A2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % le_add_diff_inverse2
% 2.86/3.11 thf(fact_3411_le__add__diff__inverse2,axiom,
% 2.86/3.11 ! [B2: nat,A2: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ B2 @ A2 )
% 2.86/3.11 => ( ( plus_plus_nat @ ( minus_minus_nat @ A2 @ B2 ) @ B2 )
% 2.86/3.11 = A2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % le_add_diff_inverse2
% 2.86/3.11 thf(fact_3412_le__add__diff__inverse2,axiom,
% 2.86/3.11 ! [B2: int,A2: int] :
% 2.86/3.11 ( ( ord_less_eq_int @ B2 @ A2 )
% 2.86/3.11 => ( ( plus_plus_int @ ( minus_minus_int @ A2 @ B2 ) @ B2 )
% 2.86/3.11 = A2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % le_add_diff_inverse2
% 2.86/3.11 thf(fact_3413_min__Suc__gt_I1_J,axiom,
% 2.86/3.11 ! [A2: nat,B2: nat] :
% 2.86/3.11 ( ( ord_less_nat @ A2 @ B2 )
% 2.86/3.11 => ( ( ord_min_nat @ ( suc @ A2 ) @ B2 )
% 2.86/3.11 = ( suc @ A2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % min_Suc_gt(1)
% 2.86/3.11 thf(fact_3414_min__Suc__gt_I2_J,axiom,
% 2.86/3.11 ! [A2: nat,B2: nat] :
% 2.86/3.11 ( ( ord_less_nat @ A2 @ B2 )
% 2.86/3.11 => ( ( ord_min_nat @ B2 @ ( suc @ A2 ) )
% 2.86/3.11 = ( suc @ A2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % min_Suc_gt(2)
% 2.86/3.11 thf(fact_3415_mod__h__bot__iff_I7_J,axiom,
% 2.86/3.11 ! [P: assn,Q: assn,H2: heap_e7401611519738050253t_unit] :
% 2.86/3.11 ( ( rep_assn @ ( sup_sup_assn @ P @ Q ) @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) )
% 2.86/3.11 = ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) )
% 2.86/3.11 | ( rep_assn @ Q @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % mod_h_bot_iff(7)
% 2.86/3.11 thf(fact_3416_Suc__diff,axiom,
% 2.86/3.11 ! [M2: nat,N: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ M2 @ N )
% 2.86/3.11 => ( ( ord_less_eq_nat @ one_one_nat @ M2 )
% 2.86/3.11 => ( ( suc @ ( minus_minus_nat @ N @ M2 ) )
% 2.86/3.11 = ( minus_minus_nat @ N @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % Suc_diff
% 2.86/3.11 thf(fact_3417_less__natE,axiom,
% 2.86/3.11 ! [M2: nat,N: nat] :
% 2.86/3.11 ( ( ord_less_nat @ M2 @ N )
% 2.86/3.11 => ~ ! [Q5: nat] :
% 2.86/3.11 ( N
% 2.86/3.11 != ( suc @ ( plus_plus_nat @ M2 @ Q5 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % less_natE
% 2.86/3.11 thf(fact_3418_less__add__Suc1,axiom,
% 2.86/3.11 ! [I: nat,M2: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ I @ M2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % less_add_Suc1
% 2.86/3.11 thf(fact_3419_less__add__Suc2,axiom,
% 2.86/3.11 ! [I: nat,M2: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ M2 @ I ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % less_add_Suc2
% 2.86/3.11 thf(fact_3420_less__iff__Suc__add,axiom,
% 2.86/3.11 ( ord_less_nat
% 2.86/3.11 = ( ^ [M: nat,N2: nat] :
% 2.86/3.11 ? [K4: nat] :
% 2.86/3.11 ( N2
% 2.86/3.11 = ( suc @ ( plus_plus_nat @ M @ K4 ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % less_iff_Suc_add
% 2.86/3.11 thf(fact_3421_less__imp__Suc__add,axiom,
% 2.86/3.11 ! [M2: nat,N: nat] :
% 2.86/3.11 ( ( ord_less_nat @ M2 @ N )
% 2.86/3.11 => ? [K: nat] :
% 2.86/3.11 ( N
% 2.86/3.11 = ( suc @ ( plus_plus_nat @ M2 @ K ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % less_imp_Suc_add
% 2.86/3.11 thf(fact_3422_add__right__imp__eq,axiom,
% 2.86/3.11 ! [B2: multis2468970476368604999at_nat,A2: multis2468970476368604999at_nat,C: multis2468970476368604999at_nat] :
% 2.86/3.11 ( ( ( plus_p7104986032573967614at_nat @ B2 @ A2 )
% 2.86/3.11 = ( plus_p7104986032573967614at_nat @ C @ A2 ) )
% 2.86/3.11 => ( B2 = C ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_right_imp_eq
% 2.86/3.11 thf(fact_3423_add__right__imp__eq,axiom,
% 2.86/3.11 ! [B2: rat,A2: rat,C: rat] :
% 2.86/3.11 ( ( ( plus_plus_rat @ B2 @ A2 )
% 2.86/3.11 = ( plus_plus_rat @ C @ A2 ) )
% 2.86/3.11 => ( B2 = C ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_right_imp_eq
% 2.86/3.11 thf(fact_3424_add__right__imp__eq,axiom,
% 2.86/3.11 ! [B2: nat,A2: nat,C: nat] :
% 2.86/3.11 ( ( ( plus_plus_nat @ B2 @ A2 )
% 2.86/3.11 = ( plus_plus_nat @ C @ A2 ) )
% 2.86/3.11 => ( B2 = C ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_right_imp_eq
% 2.86/3.11 thf(fact_3425_add__right__imp__eq,axiom,
% 2.86/3.11 ! [B2: int,A2: int,C: int] :
% 2.86/3.11 ( ( ( plus_plus_int @ B2 @ A2 )
% 2.86/3.11 = ( plus_plus_int @ C @ A2 ) )
% 2.86/3.11 => ( B2 = C ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_right_imp_eq
% 2.86/3.11 thf(fact_3426_add__left__imp__eq,axiom,
% 2.86/3.11 ! [A2: multis2468970476368604999at_nat,B2: multis2468970476368604999at_nat,C: multis2468970476368604999at_nat] :
% 2.86/3.11 ( ( ( plus_p7104986032573967614at_nat @ A2 @ B2 )
% 2.86/3.11 = ( plus_p7104986032573967614at_nat @ A2 @ C ) )
% 2.86/3.11 => ( B2 = C ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_left_imp_eq
% 2.86/3.11 thf(fact_3427_add__left__imp__eq,axiom,
% 2.86/3.11 ! [A2: rat,B2: rat,C: rat] :
% 2.86/3.11 ( ( ( plus_plus_rat @ A2 @ B2 )
% 2.86/3.11 = ( plus_plus_rat @ A2 @ C ) )
% 2.86/3.11 => ( B2 = C ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_left_imp_eq
% 2.86/3.11 thf(fact_3428_add__left__imp__eq,axiom,
% 2.86/3.11 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.11 ( ( ( plus_plus_nat @ A2 @ B2 )
% 2.86/3.11 = ( plus_plus_nat @ A2 @ C ) )
% 2.86/3.11 => ( B2 = C ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_left_imp_eq
% 2.86/3.11 thf(fact_3429_add__left__imp__eq,axiom,
% 2.86/3.11 ! [A2: int,B2: int,C: int] :
% 2.86/3.11 ( ( ( plus_plus_int @ A2 @ B2 )
% 2.86/3.11 = ( plus_plus_int @ A2 @ C ) )
% 2.86/3.11 => ( B2 = C ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_left_imp_eq
% 2.86/3.11 thf(fact_3430_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 2.86/3.11 ! [B2: multis2468970476368604999at_nat,A2: multis2468970476368604999at_nat,C: multis2468970476368604999at_nat] :
% 2.86/3.11 ( ( plus_p7104986032573967614at_nat @ B2 @ ( plus_p7104986032573967614at_nat @ A2 @ C ) )
% 2.86/3.11 = ( plus_p7104986032573967614at_nat @ A2 @ ( plus_p7104986032573967614at_nat @ B2 @ C ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % ab_semigroup_add_class.add.left_commute
% 2.86/3.11 thf(fact_3431_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 2.86/3.11 ! [B2: rat,A2: rat,C: rat] :
% 2.86/3.11 ( ( plus_plus_rat @ B2 @ ( plus_plus_rat @ A2 @ C ) )
% 2.86/3.11 = ( plus_plus_rat @ A2 @ ( plus_plus_rat @ B2 @ C ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % ab_semigroup_add_class.add.left_commute
% 2.86/3.11 thf(fact_3432_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 2.86/3.11 ! [B2: nat,A2: nat,C: nat] :
% 2.86/3.11 ( ( plus_plus_nat @ B2 @ ( plus_plus_nat @ A2 @ C ) )
% 2.86/3.11 = ( plus_plus_nat @ A2 @ ( plus_plus_nat @ B2 @ C ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % ab_semigroup_add_class.add.left_commute
% 2.86/3.11 thf(fact_3433_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 2.86/3.11 ! [B2: int,A2: int,C: int] :
% 2.86/3.11 ( ( plus_plus_int @ B2 @ ( plus_plus_int @ A2 @ C ) )
% 2.86/3.11 = ( plus_plus_int @ A2 @ ( plus_plus_int @ B2 @ C ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % ab_semigroup_add_class.add.left_commute
% 2.86/3.11 thf(fact_3434_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 2.86/3.11 ( plus_p7104986032573967614at_nat
% 2.86/3.11 = ( ^ [A3: multis2468970476368604999at_nat,B3: multis2468970476368604999at_nat] : ( plus_p7104986032573967614at_nat @ B3 @ A3 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % ab_semigroup_add_class.add.commute
% 2.86/3.11 thf(fact_3435_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 2.86/3.11 ( plus_plus_rat
% 2.86/3.11 = ( ^ [A3: rat,B3: rat] : ( plus_plus_rat @ B3 @ A3 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % ab_semigroup_add_class.add.commute
% 2.86/3.11 thf(fact_3436_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 2.86/3.11 ( plus_plus_nat
% 2.86/3.11 = ( ^ [A3: nat,B3: nat] : ( plus_plus_nat @ B3 @ A3 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % ab_semigroup_add_class.add.commute
% 2.86/3.11 thf(fact_3437_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 2.86/3.11 ( plus_plus_int
% 2.86/3.11 = ( ^ [A3: int,B3: int] : ( plus_plus_int @ B3 @ A3 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % ab_semigroup_add_class.add.commute
% 2.86/3.11 thf(fact_3438_add_Oright__cancel,axiom,
% 2.86/3.11 ! [B2: rat,A2: rat,C: rat] :
% 2.86/3.11 ( ( ( plus_plus_rat @ B2 @ A2 )
% 2.86/3.11 = ( plus_plus_rat @ C @ A2 ) )
% 2.86/3.11 = ( B2 = C ) ) ).
% 2.86/3.11
% 2.86/3.11 % add.right_cancel
% 2.86/3.11 thf(fact_3439_add_Oright__cancel,axiom,
% 2.86/3.11 ! [B2: int,A2: int,C: int] :
% 2.86/3.11 ( ( ( plus_plus_int @ B2 @ A2 )
% 2.86/3.11 = ( plus_plus_int @ C @ A2 ) )
% 2.86/3.11 = ( B2 = C ) ) ).
% 2.86/3.11
% 2.86/3.11 % add.right_cancel
% 2.86/3.11 thf(fact_3440_add_Oleft__cancel,axiom,
% 2.86/3.11 ! [A2: rat,B2: rat,C: rat] :
% 2.86/3.11 ( ( ( plus_plus_rat @ A2 @ B2 )
% 2.86/3.11 = ( plus_plus_rat @ A2 @ C ) )
% 2.86/3.11 = ( B2 = C ) ) ).
% 2.86/3.11
% 2.86/3.11 % add.left_cancel
% 2.86/3.11 thf(fact_3441_add_Oleft__cancel,axiom,
% 2.86/3.11 ! [A2: int,B2: int,C: int] :
% 2.86/3.11 ( ( ( plus_plus_int @ A2 @ B2 )
% 2.86/3.11 = ( plus_plus_int @ A2 @ C ) )
% 2.86/3.11 = ( B2 = C ) ) ).
% 2.86/3.11
% 2.86/3.11 % add.left_cancel
% 2.86/3.11 thf(fact_3442_add_Oassoc,axiom,
% 2.86/3.11 ! [A2: multis2468970476368604999at_nat,B2: multis2468970476368604999at_nat,C: multis2468970476368604999at_nat] :
% 2.86/3.11 ( ( plus_p7104986032573967614at_nat @ ( plus_p7104986032573967614at_nat @ A2 @ B2 ) @ C )
% 2.86/3.11 = ( plus_p7104986032573967614at_nat @ A2 @ ( plus_p7104986032573967614at_nat @ B2 @ C ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add.assoc
% 2.86/3.11 thf(fact_3443_add_Oassoc,axiom,
% 2.86/3.11 ! [A2: rat,B2: rat,C: rat] :
% 2.86/3.11 ( ( plus_plus_rat @ ( plus_plus_rat @ A2 @ B2 ) @ C )
% 2.86/3.11 = ( plus_plus_rat @ A2 @ ( plus_plus_rat @ B2 @ C ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add.assoc
% 2.86/3.11 thf(fact_3444_add_Oassoc,axiom,
% 2.86/3.11 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.11 ( ( plus_plus_nat @ ( plus_plus_nat @ A2 @ B2 ) @ C )
% 2.86/3.11 = ( plus_plus_nat @ A2 @ ( plus_plus_nat @ B2 @ C ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add.assoc
% 2.86/3.11 thf(fact_3445_add_Oassoc,axiom,
% 2.86/3.11 ! [A2: int,B2: int,C: int] :
% 2.86/3.11 ( ( plus_plus_int @ ( plus_plus_int @ A2 @ B2 ) @ C )
% 2.86/3.11 = ( plus_plus_int @ A2 @ ( plus_plus_int @ B2 @ C ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add.assoc
% 2.86/3.11 thf(fact_3446_group__cancel_Oadd2,axiom,
% 2.86/3.11 ! [B: multis2468970476368604999at_nat,K3: multis2468970476368604999at_nat,B2: multis2468970476368604999at_nat,A2: multis2468970476368604999at_nat] :
% 2.86/3.11 ( ( B
% 2.86/3.11 = ( plus_p7104986032573967614at_nat @ K3 @ B2 ) )
% 2.86/3.11 => ( ( plus_p7104986032573967614at_nat @ A2 @ B )
% 2.86/3.11 = ( plus_p7104986032573967614at_nat @ K3 @ ( plus_p7104986032573967614at_nat @ A2 @ B2 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % group_cancel.add2
% 2.86/3.11 thf(fact_3447_group__cancel_Oadd2,axiom,
% 2.86/3.11 ! [B: rat,K3: rat,B2: rat,A2: rat] :
% 2.86/3.11 ( ( B
% 2.86/3.11 = ( plus_plus_rat @ K3 @ B2 ) )
% 2.86/3.11 => ( ( plus_plus_rat @ A2 @ B )
% 2.86/3.11 = ( plus_plus_rat @ K3 @ ( plus_plus_rat @ A2 @ B2 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % group_cancel.add2
% 2.86/3.11 thf(fact_3448_group__cancel_Oadd2,axiom,
% 2.86/3.11 ! [B: nat,K3: nat,B2: nat,A2: nat] :
% 2.86/3.11 ( ( B
% 2.86/3.11 = ( plus_plus_nat @ K3 @ B2 ) )
% 2.86/3.11 => ( ( plus_plus_nat @ A2 @ B )
% 2.86/3.11 = ( plus_plus_nat @ K3 @ ( plus_plus_nat @ A2 @ B2 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % group_cancel.add2
% 2.86/3.11 thf(fact_3449_group__cancel_Oadd2,axiom,
% 2.86/3.11 ! [B: int,K3: int,B2: int,A2: int] :
% 2.86/3.11 ( ( B
% 2.86/3.11 = ( plus_plus_int @ K3 @ B2 ) )
% 2.86/3.11 => ( ( plus_plus_int @ A2 @ B )
% 2.86/3.11 = ( plus_plus_int @ K3 @ ( plus_plus_int @ A2 @ B2 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % group_cancel.add2
% 2.86/3.11 thf(fact_3450_group__cancel_Oadd1,axiom,
% 2.86/3.11 ! [A: multis2468970476368604999at_nat,K3: multis2468970476368604999at_nat,A2: multis2468970476368604999at_nat,B2: multis2468970476368604999at_nat] :
% 2.86/3.11 ( ( A
% 2.86/3.11 = ( plus_p7104986032573967614at_nat @ K3 @ A2 ) )
% 2.86/3.11 => ( ( plus_p7104986032573967614at_nat @ A @ B2 )
% 2.86/3.11 = ( plus_p7104986032573967614at_nat @ K3 @ ( plus_p7104986032573967614at_nat @ A2 @ B2 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % group_cancel.add1
% 2.86/3.11 thf(fact_3451_group__cancel_Oadd1,axiom,
% 2.86/3.11 ! [A: rat,K3: rat,A2: rat,B2: rat] :
% 2.86/3.11 ( ( A
% 2.86/3.11 = ( plus_plus_rat @ K3 @ A2 ) )
% 2.86/3.11 => ( ( plus_plus_rat @ A @ B2 )
% 2.86/3.11 = ( plus_plus_rat @ K3 @ ( plus_plus_rat @ A2 @ B2 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % group_cancel.add1
% 2.86/3.11 thf(fact_3452_group__cancel_Oadd1,axiom,
% 2.86/3.11 ! [A: nat,K3: nat,A2: nat,B2: nat] :
% 2.86/3.11 ( ( A
% 2.86/3.11 = ( plus_plus_nat @ K3 @ A2 ) )
% 2.86/3.11 => ( ( plus_plus_nat @ A @ B2 )
% 2.86/3.11 = ( plus_plus_nat @ K3 @ ( plus_plus_nat @ A2 @ B2 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % group_cancel.add1
% 2.86/3.11 thf(fact_3453_group__cancel_Oadd1,axiom,
% 2.86/3.11 ! [A: int,K3: int,A2: int,B2: int] :
% 2.86/3.11 ( ( A
% 2.86/3.11 = ( plus_plus_int @ K3 @ A2 ) )
% 2.86/3.11 => ( ( plus_plus_int @ A @ B2 )
% 2.86/3.11 = ( plus_plus_int @ K3 @ ( plus_plus_int @ A2 @ B2 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % group_cancel.add1
% 2.86/3.11 thf(fact_3454_add__mono__thms__linordered__semiring_I4_J,axiom,
% 2.86/3.11 ! [I: rat,J: rat,K3: rat,L: rat] :
% 2.86/3.11 ( ( ( I = J )
% 2.86/3.11 & ( K3 = L ) )
% 2.86/3.11 => ( ( plus_plus_rat @ I @ K3 )
% 2.86/3.11 = ( plus_plus_rat @ J @ L ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_mono_thms_linordered_semiring(4)
% 2.86/3.11 thf(fact_3455_add__mono__thms__linordered__semiring_I4_J,axiom,
% 2.86/3.11 ! [I: nat,J: nat,K3: nat,L: nat] :
% 2.86/3.11 ( ( ( I = J )
% 2.86/3.11 & ( K3 = L ) )
% 2.86/3.11 => ( ( plus_plus_nat @ I @ K3 )
% 2.86/3.11 = ( plus_plus_nat @ J @ L ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_mono_thms_linordered_semiring(4)
% 2.86/3.11 thf(fact_3456_add__mono__thms__linordered__semiring_I4_J,axiom,
% 2.86/3.11 ! [I: int,J: int,K3: int,L: int] :
% 2.86/3.11 ( ( ( I = J )
% 2.86/3.11 & ( K3 = L ) )
% 2.86/3.11 => ( ( plus_plus_int @ I @ K3 )
% 2.86/3.11 = ( plus_plus_int @ J @ L ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_mono_thms_linordered_semiring(4)
% 2.86/3.11 thf(fact_3457_add__le__imp__le__right,axiom,
% 2.86/3.11 ! [A2: rat,C: rat,B2: rat] :
% 2.86/3.11 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A2 @ C ) @ ( plus_plus_rat @ B2 @ C ) )
% 2.86/3.11 => ( ord_less_eq_rat @ A2 @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_le_imp_le_right
% 2.86/3.11 thf(fact_3458_add__le__imp__le__right,axiom,
% 2.86/3.11 ! [A2: nat,C: nat,B2: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ C ) @ ( plus_plus_nat @ B2 @ C ) )
% 2.86/3.11 => ( ord_less_eq_nat @ A2 @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_le_imp_le_right
% 2.86/3.11 thf(fact_3459_add__le__imp__le__right,axiom,
% 2.86/3.11 ! [A2: int,C: int,B2: int] :
% 2.86/3.11 ( ( ord_less_eq_int @ ( plus_plus_int @ A2 @ C ) @ ( plus_plus_int @ B2 @ C ) )
% 2.86/3.11 => ( ord_less_eq_int @ A2 @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_le_imp_le_right
% 2.86/3.11 thf(fact_3460_add__le__imp__le__left,axiom,
% 2.86/3.11 ! [C: rat,A2: rat,B2: rat] :
% 2.86/3.11 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A2 ) @ ( plus_plus_rat @ C @ B2 ) )
% 2.86/3.11 => ( ord_less_eq_rat @ A2 @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_le_imp_le_left
% 2.86/3.11 thf(fact_3461_add__le__imp__le__left,axiom,
% 2.86/3.11 ! [C: nat,A2: nat,B2: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A2 ) @ ( plus_plus_nat @ C @ B2 ) )
% 2.86/3.11 => ( ord_less_eq_nat @ A2 @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_le_imp_le_left
% 2.86/3.11 thf(fact_3462_add__le__imp__le__left,axiom,
% 2.86/3.11 ! [C: int,A2: int,B2: int] :
% 2.86/3.11 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A2 ) @ ( plus_plus_int @ C @ B2 ) )
% 2.86/3.11 => ( ord_less_eq_int @ A2 @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_le_imp_le_left
% 2.86/3.11 thf(fact_3463_le__iff__add,axiom,
% 2.86/3.11 ( ord_less_eq_nat
% 2.86/3.11 = ( ^ [A3: nat,B3: nat] :
% 2.86/3.11 ? [C5: nat] :
% 2.86/3.11 ( B3
% 2.86/3.11 = ( plus_plus_nat @ A3 @ C5 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % le_iff_add
% 2.86/3.11 thf(fact_3464_add__right__mono,axiom,
% 2.86/3.11 ! [A2: rat,B2: rat,C: rat] :
% 2.86/3.11 ( ( ord_less_eq_rat @ A2 @ B2 )
% 2.86/3.11 => ( ord_less_eq_rat @ ( plus_plus_rat @ A2 @ C ) @ ( plus_plus_rat @ B2 @ C ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_right_mono
% 2.86/3.11 thf(fact_3465_add__right__mono,axiom,
% 2.86/3.11 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.11 => ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ C ) @ ( plus_plus_nat @ B2 @ C ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_right_mono
% 2.86/3.11 thf(fact_3466_add__right__mono,axiom,
% 2.86/3.11 ! [A2: int,B2: int,C: int] :
% 2.86/3.11 ( ( ord_less_eq_int @ A2 @ B2 )
% 2.86/3.11 => ( ord_less_eq_int @ ( plus_plus_int @ A2 @ C ) @ ( plus_plus_int @ B2 @ C ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_right_mono
% 2.86/3.11 thf(fact_3467_less__eqE,axiom,
% 2.86/3.11 ! [A2: nat,B2: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.11 => ~ ! [C4: nat] :
% 2.86/3.11 ( B2
% 2.86/3.11 != ( plus_plus_nat @ A2 @ C4 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % less_eqE
% 2.86/3.11 thf(fact_3468_add__left__mono,axiom,
% 2.86/3.11 ! [A2: rat,B2: rat,C: rat] :
% 2.86/3.11 ( ( ord_less_eq_rat @ A2 @ B2 )
% 2.86/3.11 => ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A2 ) @ ( plus_plus_rat @ C @ B2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_left_mono
% 2.86/3.11 thf(fact_3469_add__left__mono,axiom,
% 2.86/3.11 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.11 => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A2 ) @ ( plus_plus_nat @ C @ B2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_left_mono
% 2.86/3.11 thf(fact_3470_add__left__mono,axiom,
% 2.86/3.11 ! [A2: int,B2: int,C: int] :
% 2.86/3.11 ( ( ord_less_eq_int @ A2 @ B2 )
% 2.86/3.11 => ( ord_less_eq_int @ ( plus_plus_int @ C @ A2 ) @ ( plus_plus_int @ C @ B2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_left_mono
% 2.86/3.11 thf(fact_3471_add__mono,axiom,
% 2.86/3.11 ! [A2: rat,B2: rat,C: rat,D2: rat] :
% 2.86/3.11 ( ( ord_less_eq_rat @ A2 @ B2 )
% 2.86/3.11 => ( ( ord_less_eq_rat @ C @ D2 )
% 2.86/3.11 => ( ord_less_eq_rat @ ( plus_plus_rat @ A2 @ C ) @ ( plus_plus_rat @ B2 @ D2 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_mono
% 2.86/3.11 thf(fact_3472_add__mono,axiom,
% 2.86/3.11 ! [A2: nat,B2: nat,C: nat,D2: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.11 => ( ( ord_less_eq_nat @ C @ D2 )
% 2.86/3.11 => ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ C ) @ ( plus_plus_nat @ B2 @ D2 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_mono
% 2.86/3.11 thf(fact_3473_add__mono,axiom,
% 2.86/3.11 ! [A2: int,B2: int,C: int,D2: int] :
% 2.86/3.11 ( ( ord_less_eq_int @ A2 @ B2 )
% 2.86/3.11 => ( ( ord_less_eq_int @ C @ D2 )
% 2.86/3.11 => ( ord_less_eq_int @ ( plus_plus_int @ A2 @ C ) @ ( plus_plus_int @ B2 @ D2 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_mono
% 2.86/3.11 thf(fact_3474_add__mono__thms__linordered__semiring_I1_J,axiom,
% 2.86/3.11 ! [I: rat,J: rat,K3: rat,L: rat] :
% 2.86/3.11 ( ( ( ord_less_eq_rat @ I @ J )
% 2.86/3.11 & ( ord_less_eq_rat @ K3 @ L ) )
% 2.86/3.11 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K3 ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_mono_thms_linordered_semiring(1)
% 2.86/3.11 thf(fact_3475_add__mono__thms__linordered__semiring_I1_J,axiom,
% 2.86/3.11 ! [I: nat,J: nat,K3: nat,L: nat] :
% 2.86/3.11 ( ( ( ord_less_eq_nat @ I @ J )
% 2.86/3.11 & ( ord_less_eq_nat @ K3 @ L ) )
% 2.86/3.11 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K3 ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_mono_thms_linordered_semiring(1)
% 2.86/3.11 thf(fact_3476_add__mono__thms__linordered__semiring_I1_J,axiom,
% 2.86/3.11 ! [I: int,J: int,K3: int,L: int] :
% 2.86/3.11 ( ( ( ord_less_eq_int @ I @ J )
% 2.86/3.11 & ( ord_less_eq_int @ K3 @ L ) )
% 2.86/3.11 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K3 ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_mono_thms_linordered_semiring(1)
% 2.86/3.11 thf(fact_3477_add__mono__thms__linordered__semiring_I2_J,axiom,
% 2.86/3.11 ! [I: rat,J: rat,K3: rat,L: rat] :
% 2.86/3.11 ( ( ( I = J )
% 2.86/3.11 & ( ord_less_eq_rat @ K3 @ L ) )
% 2.86/3.11 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K3 ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_mono_thms_linordered_semiring(2)
% 2.86/3.11 thf(fact_3478_add__mono__thms__linordered__semiring_I2_J,axiom,
% 2.86/3.11 ! [I: nat,J: nat,K3: nat,L: nat] :
% 2.86/3.11 ( ( ( I = J )
% 2.86/3.11 & ( ord_less_eq_nat @ K3 @ L ) )
% 2.86/3.11 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K3 ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_mono_thms_linordered_semiring(2)
% 2.86/3.11 thf(fact_3479_add__mono__thms__linordered__semiring_I2_J,axiom,
% 2.86/3.11 ! [I: int,J: int,K3: int,L: int] :
% 2.86/3.11 ( ( ( I = J )
% 2.86/3.11 & ( ord_less_eq_int @ K3 @ L ) )
% 2.86/3.11 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K3 ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_mono_thms_linordered_semiring(2)
% 2.86/3.11 thf(fact_3480_add__mono__thms__linordered__semiring_I3_J,axiom,
% 2.86/3.11 ! [I: rat,J: rat,K3: rat,L: rat] :
% 2.86/3.11 ( ( ( ord_less_eq_rat @ I @ J )
% 2.86/3.11 & ( K3 = L ) )
% 2.86/3.11 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K3 ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_mono_thms_linordered_semiring(3)
% 2.86/3.11 thf(fact_3481_add__mono__thms__linordered__semiring_I3_J,axiom,
% 2.86/3.11 ! [I: nat,J: nat,K3: nat,L: nat] :
% 2.86/3.11 ( ( ( ord_less_eq_nat @ I @ J )
% 2.86/3.11 & ( K3 = L ) )
% 2.86/3.11 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K3 ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_mono_thms_linordered_semiring(3)
% 2.86/3.11 thf(fact_3482_add__mono__thms__linordered__semiring_I3_J,axiom,
% 2.86/3.11 ! [I: int,J: int,K3: int,L: int] :
% 2.86/3.11 ( ( ( ord_less_eq_int @ I @ J )
% 2.86/3.11 & ( K3 = L ) )
% 2.86/3.11 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K3 ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_mono_thms_linordered_semiring(3)
% 2.86/3.11 thf(fact_3483_add__mono__thms__linordered__field_I5_J,axiom,
% 2.86/3.11 ! [I: rat,J: rat,K3: rat,L: rat] :
% 2.86/3.11 ( ( ( ord_less_rat @ I @ J )
% 2.86/3.11 & ( ord_less_rat @ K3 @ L ) )
% 2.86/3.11 => ( ord_less_rat @ ( plus_plus_rat @ I @ K3 ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_mono_thms_linordered_field(5)
% 2.86/3.11 thf(fact_3484_add__mono__thms__linordered__field_I5_J,axiom,
% 2.86/3.11 ! [I: code_integer,J: code_integer,K3: code_integer,L: code_integer] :
% 2.86/3.11 ( ( ( ord_le6747313008572928689nteger @ I @ J )
% 2.86/3.11 & ( ord_le6747313008572928689nteger @ K3 @ L ) )
% 2.86/3.11 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ I @ K3 ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_mono_thms_linordered_field(5)
% 2.86/3.11 thf(fact_3485_add__mono__thms__linordered__field_I5_J,axiom,
% 2.86/3.11 ! [I: nat,J: nat,K3: nat,L: nat] :
% 2.86/3.11 ( ( ( ord_less_nat @ I @ J )
% 2.86/3.11 & ( ord_less_nat @ K3 @ L ) )
% 2.86/3.11 => ( ord_less_nat @ ( plus_plus_nat @ I @ K3 ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_mono_thms_linordered_field(5)
% 2.86/3.11 thf(fact_3486_add__mono__thms__linordered__field_I5_J,axiom,
% 2.86/3.11 ! [I: int,J: int,K3: int,L: int] :
% 2.86/3.11 ( ( ( ord_less_int @ I @ J )
% 2.86/3.11 & ( ord_less_int @ K3 @ L ) )
% 2.86/3.11 => ( ord_less_int @ ( plus_plus_int @ I @ K3 ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_mono_thms_linordered_field(5)
% 2.86/3.11 thf(fact_3487_add__mono__thms__linordered__field_I2_J,axiom,
% 2.86/3.11 ! [I: rat,J: rat,K3: rat,L: rat] :
% 2.86/3.11 ( ( ( I = J )
% 2.86/3.11 & ( ord_less_rat @ K3 @ L ) )
% 2.86/3.11 => ( ord_less_rat @ ( plus_plus_rat @ I @ K3 ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_mono_thms_linordered_field(2)
% 2.86/3.11 thf(fact_3488_add__mono__thms__linordered__field_I2_J,axiom,
% 2.86/3.11 ! [I: code_integer,J: code_integer,K3: code_integer,L: code_integer] :
% 2.86/3.11 ( ( ( I = J )
% 2.86/3.11 & ( ord_le6747313008572928689nteger @ K3 @ L ) )
% 2.86/3.11 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ I @ K3 ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_mono_thms_linordered_field(2)
% 2.86/3.11 thf(fact_3489_add__mono__thms__linordered__field_I2_J,axiom,
% 2.86/3.11 ! [I: nat,J: nat,K3: nat,L: nat] :
% 2.86/3.11 ( ( ( I = J )
% 2.86/3.11 & ( ord_less_nat @ K3 @ L ) )
% 2.86/3.11 => ( ord_less_nat @ ( plus_plus_nat @ I @ K3 ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_mono_thms_linordered_field(2)
% 2.86/3.11 thf(fact_3490_add__mono__thms__linordered__field_I2_J,axiom,
% 2.86/3.11 ! [I: int,J: int,K3: int,L: int] :
% 2.86/3.11 ( ( ( I = J )
% 2.86/3.11 & ( ord_less_int @ K3 @ L ) )
% 2.86/3.11 => ( ord_less_int @ ( plus_plus_int @ I @ K3 ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_mono_thms_linordered_field(2)
% 2.86/3.11 thf(fact_3491_add__mono__thms__linordered__field_I1_J,axiom,
% 2.86/3.11 ! [I: rat,J: rat,K3: rat,L: rat] :
% 2.86/3.11 ( ( ( ord_less_rat @ I @ J )
% 2.86/3.11 & ( K3 = L ) )
% 2.86/3.11 => ( ord_less_rat @ ( plus_plus_rat @ I @ K3 ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_mono_thms_linordered_field(1)
% 2.86/3.11 thf(fact_3492_add__mono__thms__linordered__field_I1_J,axiom,
% 2.86/3.11 ! [I: code_integer,J: code_integer,K3: code_integer,L: code_integer] :
% 2.86/3.11 ( ( ( ord_le6747313008572928689nteger @ I @ J )
% 2.86/3.11 & ( K3 = L ) )
% 2.86/3.11 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ I @ K3 ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_mono_thms_linordered_field(1)
% 2.86/3.11 thf(fact_3493_add__mono__thms__linordered__field_I1_J,axiom,
% 2.86/3.11 ! [I: nat,J: nat,K3: nat,L: nat] :
% 2.86/3.11 ( ( ( ord_less_nat @ I @ J )
% 2.86/3.11 & ( K3 = L ) )
% 2.86/3.11 => ( ord_less_nat @ ( plus_plus_nat @ I @ K3 ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_mono_thms_linordered_field(1)
% 2.86/3.11 thf(fact_3494_add__mono__thms__linordered__field_I1_J,axiom,
% 2.86/3.11 ! [I: int,J: int,K3: int,L: int] :
% 2.86/3.11 ( ( ( ord_less_int @ I @ J )
% 2.86/3.11 & ( K3 = L ) )
% 2.86/3.11 => ( ord_less_int @ ( plus_plus_int @ I @ K3 ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_mono_thms_linordered_field(1)
% 2.86/3.11 thf(fact_3495_add__strict__mono,axiom,
% 2.86/3.11 ! [A2: rat,B2: rat,C: rat,D2: rat] :
% 2.86/3.11 ( ( ord_less_rat @ A2 @ B2 )
% 2.86/3.11 => ( ( ord_less_rat @ C @ D2 )
% 2.86/3.11 => ( ord_less_rat @ ( plus_plus_rat @ A2 @ C ) @ ( plus_plus_rat @ B2 @ D2 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_strict_mono
% 2.86/3.11 thf(fact_3496_add__strict__mono,axiom,
% 2.86/3.11 ! [A2: code_integer,B2: code_integer,C: code_integer,D2: code_integer] :
% 2.86/3.11 ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 2.86/3.11 => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 2.86/3.11 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A2 @ C ) @ ( plus_p5714425477246183910nteger @ B2 @ D2 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_strict_mono
% 2.86/3.11 thf(fact_3497_add__strict__mono,axiom,
% 2.86/3.11 ! [A2: nat,B2: nat,C: nat,D2: nat] :
% 2.86/3.11 ( ( ord_less_nat @ A2 @ B2 )
% 2.86/3.11 => ( ( ord_less_nat @ C @ D2 )
% 2.86/3.11 => ( ord_less_nat @ ( plus_plus_nat @ A2 @ C ) @ ( plus_plus_nat @ B2 @ D2 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_strict_mono
% 2.86/3.11 thf(fact_3498_add__strict__mono,axiom,
% 2.86/3.11 ! [A2: int,B2: int,C: int,D2: int] :
% 2.86/3.11 ( ( ord_less_int @ A2 @ B2 )
% 2.86/3.11 => ( ( ord_less_int @ C @ D2 )
% 2.86/3.11 => ( ord_less_int @ ( plus_plus_int @ A2 @ C ) @ ( plus_plus_int @ B2 @ D2 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_strict_mono
% 2.86/3.11 thf(fact_3499_add__strict__left__mono,axiom,
% 2.86/3.11 ! [A2: rat,B2: rat,C: rat] :
% 2.86/3.11 ( ( ord_less_rat @ A2 @ B2 )
% 2.86/3.11 => ( ord_less_rat @ ( plus_plus_rat @ C @ A2 ) @ ( plus_plus_rat @ C @ B2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_strict_left_mono
% 2.86/3.11 thf(fact_3500_add__strict__left__mono,axiom,
% 2.86/3.11 ! [A2: code_integer,B2: code_integer,C: code_integer] :
% 2.86/3.11 ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 2.86/3.11 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ C @ A2 ) @ ( plus_p5714425477246183910nteger @ C @ B2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_strict_left_mono
% 2.86/3.11 thf(fact_3501_add__strict__left__mono,axiom,
% 2.86/3.11 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.11 ( ( ord_less_nat @ A2 @ B2 )
% 2.86/3.11 => ( ord_less_nat @ ( plus_plus_nat @ C @ A2 ) @ ( plus_plus_nat @ C @ B2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_strict_left_mono
% 2.86/3.11 thf(fact_3502_add__strict__left__mono,axiom,
% 2.86/3.11 ! [A2: int,B2: int,C: int] :
% 2.86/3.11 ( ( ord_less_int @ A2 @ B2 )
% 2.86/3.11 => ( ord_less_int @ ( plus_plus_int @ C @ A2 ) @ ( plus_plus_int @ C @ B2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_strict_left_mono
% 2.86/3.11 thf(fact_3503_add__strict__right__mono,axiom,
% 2.86/3.11 ! [A2: rat,B2: rat,C: rat] :
% 2.86/3.11 ( ( ord_less_rat @ A2 @ B2 )
% 2.86/3.11 => ( ord_less_rat @ ( plus_plus_rat @ A2 @ C ) @ ( plus_plus_rat @ B2 @ C ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_strict_right_mono
% 2.86/3.11 thf(fact_3504_add__strict__right__mono,axiom,
% 2.86/3.11 ! [A2: code_integer,B2: code_integer,C: code_integer] :
% 2.86/3.11 ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 2.86/3.11 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A2 @ C ) @ ( plus_p5714425477246183910nteger @ B2 @ C ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_strict_right_mono
% 2.86/3.11 thf(fact_3505_add__strict__right__mono,axiom,
% 2.86/3.11 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.11 ( ( ord_less_nat @ A2 @ B2 )
% 2.86/3.11 => ( ord_less_nat @ ( plus_plus_nat @ A2 @ C ) @ ( plus_plus_nat @ B2 @ C ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_strict_right_mono
% 2.86/3.11 thf(fact_3506_add__strict__right__mono,axiom,
% 2.86/3.11 ! [A2: int,B2: int,C: int] :
% 2.86/3.11 ( ( ord_less_int @ A2 @ B2 )
% 2.86/3.11 => ( ord_less_int @ ( plus_plus_int @ A2 @ C ) @ ( plus_plus_int @ B2 @ C ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_strict_right_mono
% 2.86/3.11 thf(fact_3507_add__less__imp__less__left,axiom,
% 2.86/3.11 ! [C: rat,A2: rat,B2: rat] :
% 2.86/3.11 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A2 ) @ ( plus_plus_rat @ C @ B2 ) )
% 2.86/3.11 => ( ord_less_rat @ A2 @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_less_imp_less_left
% 2.86/3.11 thf(fact_3508_add__less__imp__less__left,axiom,
% 2.86/3.11 ! [C: code_integer,A2: code_integer,B2: code_integer] :
% 2.86/3.11 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ C @ A2 ) @ ( plus_p5714425477246183910nteger @ C @ B2 ) )
% 2.86/3.11 => ( ord_le6747313008572928689nteger @ A2 @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_less_imp_less_left
% 2.86/3.11 thf(fact_3509_add__less__imp__less__left,axiom,
% 2.86/3.11 ! [C: nat,A2: nat,B2: nat] :
% 2.86/3.11 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A2 ) @ ( plus_plus_nat @ C @ B2 ) )
% 2.86/3.11 => ( ord_less_nat @ A2 @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_less_imp_less_left
% 2.86/3.11 thf(fact_3510_add__less__imp__less__left,axiom,
% 2.86/3.11 ! [C: int,A2: int,B2: int] :
% 2.86/3.11 ( ( ord_less_int @ ( plus_plus_int @ C @ A2 ) @ ( plus_plus_int @ C @ B2 ) )
% 2.86/3.11 => ( ord_less_int @ A2 @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_less_imp_less_left
% 2.86/3.11 thf(fact_3511_add__less__imp__less__right,axiom,
% 2.86/3.11 ! [A2: rat,C: rat,B2: rat] :
% 2.86/3.11 ( ( ord_less_rat @ ( plus_plus_rat @ A2 @ C ) @ ( plus_plus_rat @ B2 @ C ) )
% 2.86/3.11 => ( ord_less_rat @ A2 @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_less_imp_less_right
% 2.86/3.11 thf(fact_3512_add__less__imp__less__right,axiom,
% 2.86/3.11 ! [A2: code_integer,C: code_integer,B2: code_integer] :
% 2.86/3.11 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A2 @ C ) @ ( plus_p5714425477246183910nteger @ B2 @ C ) )
% 2.86/3.11 => ( ord_le6747313008572928689nteger @ A2 @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_less_imp_less_right
% 2.86/3.11 thf(fact_3513_add__less__imp__less__right,axiom,
% 2.86/3.11 ! [A2: nat,C: nat,B2: nat] :
% 2.86/3.11 ( ( ord_less_nat @ ( plus_plus_nat @ A2 @ C ) @ ( plus_plus_nat @ B2 @ C ) )
% 2.86/3.11 => ( ord_less_nat @ A2 @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_less_imp_less_right
% 2.86/3.11 thf(fact_3514_add__less__imp__less__right,axiom,
% 2.86/3.11 ! [A2: int,C: int,B2: int] :
% 2.86/3.11 ( ( ord_less_int @ ( plus_plus_int @ A2 @ C ) @ ( plus_plus_int @ B2 @ C ) )
% 2.86/3.11 => ( ord_less_int @ A2 @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_less_imp_less_right
% 2.86/3.11 thf(fact_3515_ring__class_Oring__distribs_I2_J,axiom,
% 2.86/3.11 ! [A2: code_integer,B2: code_integer,C: code_integer] :
% 2.86/3.11 ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A2 @ B2 ) @ C )
% 2.86/3.11 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ ( times_3573771949741848930nteger @ B2 @ C ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % ring_class.ring_distribs(2)
% 2.86/3.11 thf(fact_3516_ring__class_Oring__distribs_I2_J,axiom,
% 2.86/3.11 ! [A2: rat,B2: rat,C: rat] :
% 2.86/3.11 ( ( times_times_rat @ ( plus_plus_rat @ A2 @ B2 ) @ C )
% 2.86/3.11 = ( plus_plus_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B2 @ C ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % ring_class.ring_distribs(2)
% 2.86/3.11 thf(fact_3517_ring__class_Oring__distribs_I2_J,axiom,
% 2.86/3.11 ! [A2: int,B2: int,C: int] :
% 2.86/3.11 ( ( times_times_int @ ( plus_plus_int @ A2 @ B2 ) @ C )
% 2.86/3.11 = ( plus_plus_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B2 @ C ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % ring_class.ring_distribs(2)
% 2.86/3.11 thf(fact_3518_ring__class_Oring__distribs_I1_J,axiom,
% 2.86/3.11 ! [A2: code_integer,B2: code_integer,C: code_integer] :
% 2.86/3.11 ( ( times_3573771949741848930nteger @ A2 @ ( plus_p5714425477246183910nteger @ B2 @ C ) )
% 2.86/3.11 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A2 @ B2 ) @ ( times_3573771949741848930nteger @ A2 @ C ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % ring_class.ring_distribs(1)
% 2.86/3.11 thf(fact_3519_ring__class_Oring__distribs_I1_J,axiom,
% 2.86/3.11 ! [A2: rat,B2: rat,C: rat] :
% 2.86/3.11 ( ( times_times_rat @ A2 @ ( plus_plus_rat @ B2 @ C ) )
% 2.86/3.11 = ( plus_plus_rat @ ( times_times_rat @ A2 @ B2 ) @ ( times_times_rat @ A2 @ C ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % ring_class.ring_distribs(1)
% 2.86/3.11 thf(fact_3520_ring__class_Oring__distribs_I1_J,axiom,
% 2.86/3.11 ! [A2: int,B2: int,C: int] :
% 2.86/3.11 ( ( times_times_int @ A2 @ ( plus_plus_int @ B2 @ C ) )
% 2.86/3.11 = ( plus_plus_int @ ( times_times_int @ A2 @ B2 ) @ ( times_times_int @ A2 @ C ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % ring_class.ring_distribs(1)
% 2.86/3.11 thf(fact_3521_comm__semiring__class_Odistrib,axiom,
% 2.86/3.11 ! [A2: code_integer,B2: code_integer,C: code_integer] :
% 2.86/3.11 ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A2 @ B2 ) @ C )
% 2.86/3.11 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ ( times_3573771949741848930nteger @ B2 @ C ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % comm_semiring_class.distrib
% 2.86/3.11 thf(fact_3522_comm__semiring__class_Odistrib,axiom,
% 2.86/3.11 ! [A2: rat,B2: rat,C: rat] :
% 2.86/3.11 ( ( times_times_rat @ ( plus_plus_rat @ A2 @ B2 ) @ C )
% 2.86/3.11 = ( plus_plus_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B2 @ C ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % comm_semiring_class.distrib
% 2.86/3.11 thf(fact_3523_comm__semiring__class_Odistrib,axiom,
% 2.86/3.11 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.11 ( ( times_times_nat @ ( plus_plus_nat @ A2 @ B2 ) @ C )
% 2.86/3.11 = ( plus_plus_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B2 @ C ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % comm_semiring_class.distrib
% 2.86/3.11 thf(fact_3524_comm__semiring__class_Odistrib,axiom,
% 2.86/3.11 ! [A2: int,B2: int,C: int] :
% 2.86/3.11 ( ( times_times_int @ ( plus_plus_int @ A2 @ B2 ) @ C )
% 2.86/3.11 = ( plus_plus_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B2 @ C ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % comm_semiring_class.distrib
% 2.86/3.11 thf(fact_3525_distrib__left,axiom,
% 2.86/3.11 ! [A2: code_integer,B2: code_integer,C: code_integer] :
% 2.86/3.11 ( ( times_3573771949741848930nteger @ A2 @ ( plus_p5714425477246183910nteger @ B2 @ C ) )
% 2.86/3.11 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A2 @ B2 ) @ ( times_3573771949741848930nteger @ A2 @ C ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % distrib_left
% 2.86/3.11 thf(fact_3526_distrib__left,axiom,
% 2.86/3.11 ! [A2: rat,B2: rat,C: rat] :
% 2.86/3.11 ( ( times_times_rat @ A2 @ ( plus_plus_rat @ B2 @ C ) )
% 2.86/3.11 = ( plus_plus_rat @ ( times_times_rat @ A2 @ B2 ) @ ( times_times_rat @ A2 @ C ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % distrib_left
% 2.86/3.11 thf(fact_3527_distrib__left,axiom,
% 2.86/3.11 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.11 ( ( times_times_nat @ A2 @ ( plus_plus_nat @ B2 @ C ) )
% 2.86/3.11 = ( plus_plus_nat @ ( times_times_nat @ A2 @ B2 ) @ ( times_times_nat @ A2 @ C ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % distrib_left
% 2.86/3.11 thf(fact_3528_distrib__left,axiom,
% 2.86/3.11 ! [A2: int,B2: int,C: int] :
% 2.86/3.11 ( ( times_times_int @ A2 @ ( plus_plus_int @ B2 @ C ) )
% 2.86/3.11 = ( plus_plus_int @ ( times_times_int @ A2 @ B2 ) @ ( times_times_int @ A2 @ C ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % distrib_left
% 2.86/3.11 thf(fact_3529_distrib__right,axiom,
% 2.86/3.11 ! [A2: code_integer,B2: code_integer,C: code_integer] :
% 2.86/3.11 ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A2 @ B2 ) @ C )
% 2.86/3.11 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ ( times_3573771949741848930nteger @ B2 @ C ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % distrib_right
% 2.86/3.11 thf(fact_3530_distrib__right,axiom,
% 2.86/3.11 ! [A2: rat,B2: rat,C: rat] :
% 2.86/3.11 ( ( times_times_rat @ ( plus_plus_rat @ A2 @ B2 ) @ C )
% 2.86/3.11 = ( plus_plus_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B2 @ C ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % distrib_right
% 2.86/3.11 thf(fact_3531_distrib__right,axiom,
% 2.86/3.11 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.11 ( ( times_times_nat @ ( plus_plus_nat @ A2 @ B2 ) @ C )
% 2.86/3.11 = ( plus_plus_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B2 @ C ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % distrib_right
% 2.86/3.11 thf(fact_3532_distrib__right,axiom,
% 2.86/3.11 ! [A2: int,B2: int,C: int] :
% 2.86/3.11 ( ( times_times_int @ ( plus_plus_int @ A2 @ B2 ) @ C )
% 2.86/3.11 = ( plus_plus_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B2 @ C ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % distrib_right
% 2.86/3.11 thf(fact_3533_combine__common__factor,axiom,
% 2.86/3.11 ! [A2: code_integer,E: code_integer,B2: code_integer,C: code_integer] :
% 2.86/3.11 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A2 @ E ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B2 @ E ) @ C ) )
% 2.86/3.11 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A2 @ B2 ) @ E ) @ C ) ) ).
% 2.86/3.11
% 2.86/3.11 % combine_common_factor
% 2.86/3.11 thf(fact_3534_combine__common__factor,axiom,
% 2.86/3.11 ! [A2: rat,E: rat,B2: rat,C: rat] :
% 2.86/3.11 ( ( plus_plus_rat @ ( times_times_rat @ A2 @ E ) @ ( plus_plus_rat @ ( times_times_rat @ B2 @ E ) @ C ) )
% 2.86/3.11 = ( plus_plus_rat @ ( times_times_rat @ ( plus_plus_rat @ A2 @ B2 ) @ E ) @ C ) ) ).
% 2.86/3.11
% 2.86/3.11 % combine_common_factor
% 2.86/3.11 thf(fact_3535_combine__common__factor,axiom,
% 2.86/3.11 ! [A2: nat,E: nat,B2: nat,C: nat] :
% 2.86/3.11 ( ( plus_plus_nat @ ( times_times_nat @ A2 @ E ) @ ( plus_plus_nat @ ( times_times_nat @ B2 @ E ) @ C ) )
% 2.86/3.11 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A2 @ B2 ) @ E ) @ C ) ) ).
% 2.86/3.11
% 2.86/3.11 % combine_common_factor
% 2.86/3.11 thf(fact_3536_combine__common__factor,axiom,
% 2.86/3.11 ! [A2: int,E: int,B2: int,C: int] :
% 2.86/3.11 ( ( plus_plus_int @ ( times_times_int @ A2 @ E ) @ ( plus_plus_int @ ( times_times_int @ B2 @ E ) @ C ) )
% 2.86/3.11 = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A2 @ B2 ) @ E ) @ C ) ) ).
% 2.86/3.11
% 2.86/3.11 % combine_common_factor
% 2.86/3.11 thf(fact_3537_group__cancel_Osub1,axiom,
% 2.86/3.11 ! [A: rat,K3: rat,A2: rat,B2: rat] :
% 2.86/3.11 ( ( A
% 2.86/3.11 = ( plus_plus_rat @ K3 @ A2 ) )
% 2.86/3.11 => ( ( minus_minus_rat @ A @ B2 )
% 2.86/3.11 = ( plus_plus_rat @ K3 @ ( minus_minus_rat @ A2 @ B2 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % group_cancel.sub1
% 2.86/3.11 thf(fact_3538_group__cancel_Osub1,axiom,
% 2.86/3.11 ! [A: int,K3: int,A2: int,B2: int] :
% 2.86/3.11 ( ( A
% 2.86/3.11 = ( plus_plus_int @ K3 @ A2 ) )
% 2.86/3.11 => ( ( minus_minus_int @ A @ B2 )
% 2.86/3.11 = ( plus_plus_int @ K3 @ ( minus_minus_int @ A2 @ B2 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % group_cancel.sub1
% 2.86/3.11 thf(fact_3539_diff__eq__eq,axiom,
% 2.86/3.11 ! [A2: rat,B2: rat,C: rat] :
% 2.86/3.11 ( ( ( minus_minus_rat @ A2 @ B2 )
% 2.86/3.11 = C )
% 2.86/3.11 = ( A2
% 2.86/3.11 = ( plus_plus_rat @ C @ B2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % diff_eq_eq
% 2.86/3.11 thf(fact_3540_diff__eq__eq,axiom,
% 2.86/3.11 ! [A2: int,B2: int,C: int] :
% 2.86/3.11 ( ( ( minus_minus_int @ A2 @ B2 )
% 2.86/3.11 = C )
% 2.86/3.11 = ( A2
% 2.86/3.11 = ( plus_plus_int @ C @ B2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % diff_eq_eq
% 2.86/3.11 thf(fact_3541_eq__diff__eq,axiom,
% 2.86/3.11 ! [A2: rat,C: rat,B2: rat] :
% 2.86/3.11 ( ( A2
% 2.86/3.11 = ( minus_minus_rat @ C @ B2 ) )
% 2.86/3.11 = ( ( plus_plus_rat @ A2 @ B2 )
% 2.86/3.11 = C ) ) ).
% 2.86/3.11
% 2.86/3.11 % eq_diff_eq
% 2.86/3.11 thf(fact_3542_eq__diff__eq,axiom,
% 2.86/3.11 ! [A2: int,C: int,B2: int] :
% 2.86/3.11 ( ( A2
% 2.86/3.11 = ( minus_minus_int @ C @ B2 ) )
% 2.86/3.11 = ( ( plus_plus_int @ A2 @ B2 )
% 2.86/3.11 = C ) ) ).
% 2.86/3.11
% 2.86/3.11 % eq_diff_eq
% 2.86/3.11 thf(fact_3543_add__diff__eq,axiom,
% 2.86/3.11 ! [A2: rat,B2: rat,C: rat] :
% 2.86/3.11 ( ( plus_plus_rat @ A2 @ ( minus_minus_rat @ B2 @ C ) )
% 2.86/3.11 = ( minus_minus_rat @ ( plus_plus_rat @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_diff_eq
% 2.86/3.11 thf(fact_3544_add__diff__eq,axiom,
% 2.86/3.11 ! [A2: int,B2: int,C: int] :
% 2.86/3.11 ( ( plus_plus_int @ A2 @ ( minus_minus_int @ B2 @ C ) )
% 2.86/3.11 = ( minus_minus_int @ ( plus_plus_int @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_diff_eq
% 2.86/3.11 thf(fact_3545_diff__diff__eq2,axiom,
% 2.86/3.11 ! [A2: rat,B2: rat,C: rat] :
% 2.86/3.11 ( ( minus_minus_rat @ A2 @ ( minus_minus_rat @ B2 @ C ) )
% 2.86/3.11 = ( minus_minus_rat @ ( plus_plus_rat @ A2 @ C ) @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % diff_diff_eq2
% 2.86/3.11 thf(fact_3546_diff__diff__eq2,axiom,
% 2.86/3.11 ! [A2: int,B2: int,C: int] :
% 2.86/3.11 ( ( minus_minus_int @ A2 @ ( minus_minus_int @ B2 @ C ) )
% 2.86/3.11 = ( minus_minus_int @ ( plus_plus_int @ A2 @ C ) @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % diff_diff_eq2
% 2.86/3.11 thf(fact_3547_diff__add__eq,axiom,
% 2.86/3.11 ! [A2: rat,B2: rat,C: rat] :
% 2.86/3.11 ( ( plus_plus_rat @ ( minus_minus_rat @ A2 @ B2 ) @ C )
% 2.86/3.11 = ( minus_minus_rat @ ( plus_plus_rat @ A2 @ C ) @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % diff_add_eq
% 2.86/3.11 thf(fact_3548_diff__add__eq,axiom,
% 2.86/3.11 ! [A2: int,B2: int,C: int] :
% 2.86/3.11 ( ( plus_plus_int @ ( minus_minus_int @ A2 @ B2 ) @ C )
% 2.86/3.11 = ( minus_minus_int @ ( plus_plus_int @ A2 @ C ) @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % diff_add_eq
% 2.86/3.11 thf(fact_3549_diff__add__eq__diff__diff__swap,axiom,
% 2.86/3.11 ! [A2: rat,B2: rat,C: rat] :
% 2.86/3.11 ( ( minus_minus_rat @ A2 @ ( plus_plus_rat @ B2 @ C ) )
% 2.86/3.11 = ( minus_minus_rat @ ( minus_minus_rat @ A2 @ C ) @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % diff_add_eq_diff_diff_swap
% 2.86/3.11 thf(fact_3550_diff__add__eq__diff__diff__swap,axiom,
% 2.86/3.11 ! [A2: int,B2: int,C: int] :
% 2.86/3.11 ( ( minus_minus_int @ A2 @ ( plus_plus_int @ B2 @ C ) )
% 2.86/3.11 = ( minus_minus_int @ ( minus_minus_int @ A2 @ C ) @ B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % diff_add_eq_diff_diff_swap
% 2.86/3.11 thf(fact_3551_add__implies__diff,axiom,
% 2.86/3.11 ! [C: multis2468970476368604999at_nat,B2: multis2468970476368604999at_nat,A2: multis2468970476368604999at_nat] :
% 2.86/3.11 ( ( ( plus_p7104986032573967614at_nat @ C @ B2 )
% 2.86/3.11 = A2 )
% 2.86/3.11 => ( C
% 2.86/3.11 = ( minus_4286766774447292334at_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_implies_diff
% 2.86/3.11 thf(fact_3552_add__implies__diff,axiom,
% 2.86/3.11 ! [C: rat,B2: rat,A2: rat] :
% 2.86/3.11 ( ( ( plus_plus_rat @ C @ B2 )
% 2.86/3.11 = A2 )
% 2.86/3.11 => ( C
% 2.86/3.11 = ( minus_minus_rat @ A2 @ B2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_implies_diff
% 2.86/3.11 thf(fact_3553_add__implies__diff,axiom,
% 2.86/3.11 ! [C: nat,B2: nat,A2: nat] :
% 2.86/3.11 ( ( ( plus_plus_nat @ C @ B2 )
% 2.86/3.11 = A2 )
% 2.86/3.11 => ( C
% 2.86/3.11 = ( minus_minus_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_implies_diff
% 2.86/3.11 thf(fact_3554_add__implies__diff,axiom,
% 2.86/3.11 ! [C: int,B2: int,A2: int] :
% 2.86/3.11 ( ( ( plus_plus_int @ C @ B2 )
% 2.86/3.11 = A2 )
% 2.86/3.11 => ( C
% 2.86/3.11 = ( minus_minus_int @ A2 @ B2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_implies_diff
% 2.86/3.11 thf(fact_3555_diff__diff__eq,axiom,
% 2.86/3.11 ! [A2: multis2468970476368604999at_nat,B2: multis2468970476368604999at_nat,C: multis2468970476368604999at_nat] :
% 2.86/3.11 ( ( minus_4286766774447292334at_nat @ ( minus_4286766774447292334at_nat @ A2 @ B2 ) @ C )
% 2.86/3.11 = ( minus_4286766774447292334at_nat @ A2 @ ( plus_p7104986032573967614at_nat @ B2 @ C ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % diff_diff_eq
% 2.86/3.11 thf(fact_3556_diff__diff__eq,axiom,
% 2.86/3.11 ! [A2: rat,B2: rat,C: rat] :
% 2.86/3.11 ( ( minus_minus_rat @ ( minus_minus_rat @ A2 @ B2 ) @ C )
% 2.86/3.11 = ( minus_minus_rat @ A2 @ ( plus_plus_rat @ B2 @ C ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % diff_diff_eq
% 2.86/3.11 thf(fact_3557_diff__diff__eq,axiom,
% 2.86/3.11 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.11 ( ( minus_minus_nat @ ( minus_minus_nat @ A2 @ B2 ) @ C )
% 2.86/3.11 = ( minus_minus_nat @ A2 @ ( plus_plus_nat @ B2 @ C ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % diff_diff_eq
% 2.86/3.11 thf(fact_3558_diff__diff__eq,axiom,
% 2.86/3.11 ! [A2: int,B2: int,C: int] :
% 2.86/3.11 ( ( minus_minus_int @ ( minus_minus_int @ A2 @ B2 ) @ C )
% 2.86/3.11 = ( minus_minus_int @ A2 @ ( plus_plus_int @ B2 @ C ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % diff_diff_eq
% 2.86/3.11 thf(fact_3559_star__or__dist1,axiom,
% 2.86/3.11 ! [A: assn,B: assn,C2: assn] :
% 2.86/3.11 ( ( times_times_assn @ ( sup_sup_assn @ A @ B ) @ C2 )
% 2.86/3.11 = ( sup_sup_assn @ ( times_times_assn @ A @ C2 ) @ ( times_times_assn @ B @ C2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % star_or_dist1
% 2.86/3.11 thf(fact_3560_star__or__dist2,axiom,
% 2.86/3.11 ! [C2: assn,A: assn,B: assn] :
% 2.86/3.11 ( ( times_times_assn @ C2 @ ( sup_sup_assn @ A @ B ) )
% 2.86/3.11 = ( sup_sup_assn @ ( times_times_assn @ C2 @ A ) @ ( times_times_assn @ C2 @ B ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % star_or_dist2
% 2.86/3.11 thf(fact_3561_Nat_OlessE,axiom,
% 2.86/3.11 ! [I: nat,K3: nat] :
% 2.86/3.11 ( ( ord_less_nat @ I @ K3 )
% 2.86/3.11 => ( ( K3
% 2.86/3.11 != ( suc @ I ) )
% 2.86/3.11 => ~ ! [J3: nat] :
% 2.86/3.11 ( ( ord_less_nat @ I @ J3 )
% 2.86/3.11 => ( K3
% 2.86/3.11 != ( suc @ J3 ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % Nat.lessE
% 2.86/3.11 thf(fact_3562_Suc__lessD,axiom,
% 2.86/3.11 ! [M2: nat,N: nat] :
% 2.86/3.11 ( ( ord_less_nat @ ( suc @ M2 ) @ N )
% 2.86/3.11 => ( ord_less_nat @ M2 @ N ) ) ).
% 2.86/3.11
% 2.86/3.11 % Suc_lessD
% 2.86/3.11 thf(fact_3563_Suc__lessE,axiom,
% 2.86/3.11 ! [I: nat,K3: nat] :
% 2.86/3.11 ( ( ord_less_nat @ ( suc @ I ) @ K3 )
% 2.86/3.11 => ~ ! [J3: nat] :
% 2.86/3.11 ( ( ord_less_nat @ I @ J3 )
% 2.86/3.11 => ( K3
% 2.86/3.11 != ( suc @ J3 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % Suc_lessE
% 2.86/3.11 thf(fact_3564_Suc__lessI,axiom,
% 2.86/3.11 ! [M2: nat,N: nat] :
% 2.86/3.11 ( ( ord_less_nat @ M2 @ N )
% 2.86/3.11 => ( ( ( suc @ M2 )
% 2.86/3.11 != N )
% 2.86/3.11 => ( ord_less_nat @ ( suc @ M2 ) @ N ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % Suc_lessI
% 2.86/3.11 thf(fact_3565_less__SucE,axiom,
% 2.86/3.11 ! [M2: nat,N: nat] :
% 2.86/3.11 ( ( ord_less_nat @ M2 @ ( suc @ N ) )
% 2.86/3.11 => ( ~ ( ord_less_nat @ M2 @ N )
% 2.86/3.11 => ( M2 = N ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % less_SucE
% 2.86/3.11 thf(fact_3566_less__SucI,axiom,
% 2.86/3.11 ! [M2: nat,N: nat] :
% 2.86/3.11 ( ( ord_less_nat @ M2 @ N )
% 2.86/3.11 => ( ord_less_nat @ M2 @ ( suc @ N ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % less_SucI
% 2.86/3.11 thf(fact_3567_Ex__less__Suc,axiom,
% 2.86/3.11 ! [N: nat,P: nat > $o] :
% 2.86/3.11 ( ( ? [I4: nat] :
% 2.86/3.11 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 2.86/3.11 & ( P @ I4 ) ) )
% 2.86/3.11 = ( ( P @ N )
% 2.86/3.11 | ? [I4: nat] :
% 2.86/3.11 ( ( ord_less_nat @ I4 @ N )
% 2.86/3.11 & ( P @ I4 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % Ex_less_Suc
% 2.86/3.11 thf(fact_3568_less__Suc__eq,axiom,
% 2.86/3.11 ! [M2: nat,N: nat] :
% 2.86/3.11 ( ( ord_less_nat @ M2 @ ( suc @ N ) )
% 2.86/3.11 = ( ( ord_less_nat @ M2 @ N )
% 2.86/3.11 | ( M2 = N ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % less_Suc_eq
% 2.86/3.11 thf(fact_3569_not__less__eq,axiom,
% 2.86/3.11 ! [M2: nat,N: nat] :
% 2.86/3.11 ( ( ~ ( ord_less_nat @ M2 @ N ) )
% 2.86/3.11 = ( ord_less_nat @ N @ ( suc @ M2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % not_less_eq
% 2.86/3.11 thf(fact_3570_All__less__Suc,axiom,
% 2.86/3.11 ! [N: nat,P: nat > $o] :
% 2.86/3.11 ( ( ! [I4: nat] :
% 2.86/3.11 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 2.86/3.11 => ( P @ I4 ) ) )
% 2.86/3.11 = ( ( P @ N )
% 2.86/3.11 & ! [I4: nat] :
% 2.86/3.11 ( ( ord_less_nat @ I4 @ N )
% 2.86/3.11 => ( P @ I4 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % All_less_Suc
% 2.86/3.11 thf(fact_3571_Suc__less__eq2,axiom,
% 2.86/3.11 ! [N: nat,M2: nat] :
% 2.86/3.11 ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 2.86/3.11 = ( ? [M4: nat] :
% 2.86/3.11 ( ( M2
% 2.86/3.11 = ( suc @ M4 ) )
% 2.86/3.11 & ( ord_less_nat @ N @ M4 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % Suc_less_eq2
% 2.86/3.11 thf(fact_3572_less__antisym,axiom,
% 2.86/3.11 ! [N: nat,M2: nat] :
% 2.86/3.11 ( ~ ( ord_less_nat @ N @ M2 )
% 2.86/3.11 => ( ( ord_less_nat @ N @ ( suc @ M2 ) )
% 2.86/3.11 => ( M2 = N ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % less_antisym
% 2.86/3.11 thf(fact_3573_Suc__less__SucD,axiom,
% 2.86/3.11 ! [M2: nat,N: nat] :
% 2.86/3.11 ( ( ord_less_nat @ ( suc @ M2 ) @ ( suc @ N ) )
% 2.86/3.11 => ( ord_less_nat @ M2 @ N ) ) ).
% 2.86/3.11
% 2.86/3.11 % Suc_less_SucD
% 2.86/3.11 thf(fact_3574_less__trans__Suc,axiom,
% 2.86/3.11 ! [I: nat,J: nat,K3: nat] :
% 2.86/3.11 ( ( ord_less_nat @ I @ J )
% 2.86/3.11 => ( ( ord_less_nat @ J @ K3 )
% 2.86/3.11 => ( ord_less_nat @ ( suc @ I ) @ K3 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % less_trans_Suc
% 2.86/3.11 thf(fact_3575_less__Suc__induct,axiom,
% 2.86/3.11 ! [I: nat,J: nat,P: nat > nat > $o] :
% 2.86/3.11 ( ( ord_less_nat @ I @ J )
% 2.86/3.11 => ( ! [I5: nat] : ( P @ I5 @ ( suc @ I5 ) )
% 2.86/3.11 => ( ! [I5: nat,J3: nat,K: nat] :
% 2.86/3.11 ( ( ord_less_nat @ I5 @ J3 )
% 2.86/3.11 => ( ( ord_less_nat @ J3 @ K )
% 2.86/3.11 => ( ( P @ I5 @ J3 )
% 2.86/3.11 => ( ( P @ J3 @ K )
% 2.86/3.11 => ( P @ I5 @ K ) ) ) ) )
% 2.86/3.11 => ( P @ I @ J ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % less_Suc_induct
% 2.86/3.11 thf(fact_3576_strict__inc__induct,axiom,
% 2.86/3.11 ! [I: nat,J: nat,P: nat > $o] :
% 2.86/3.11 ( ( ord_less_nat @ I @ J )
% 2.86/3.11 => ( ! [I5: nat] :
% 2.86/3.11 ( ( J
% 2.86/3.11 = ( suc @ I5 ) )
% 2.86/3.11 => ( P @ I5 ) )
% 2.86/3.11 => ( ! [I5: nat] :
% 2.86/3.11 ( ( ord_less_nat @ I5 @ J )
% 2.86/3.11 => ( ( P @ ( suc @ I5 ) )
% 2.86/3.11 => ( P @ I5 ) ) )
% 2.86/3.11 => ( P @ I ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % strict_inc_induct
% 2.86/3.11 thf(fact_3577_not__less__less__Suc__eq,axiom,
% 2.86/3.11 ! [N: nat,M2: nat] :
% 2.86/3.11 ( ~ ( ord_less_nat @ N @ M2 )
% 2.86/3.11 => ( ( ord_less_nat @ N @ ( suc @ M2 ) )
% 2.86/3.11 = ( N = M2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % not_less_less_Suc_eq
% 2.86/3.11 thf(fact_3578_add__lessD1,axiom,
% 2.86/3.11 ! [I: nat,J: nat,K3: nat] :
% 2.86/3.11 ( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K3 )
% 2.86/3.11 => ( ord_less_nat @ I @ K3 ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_lessD1
% 2.86/3.11 thf(fact_3579_add__less__mono,axiom,
% 2.86/3.11 ! [I: nat,J: nat,K3: nat,L: nat] :
% 2.86/3.11 ( ( ord_less_nat @ I @ J )
% 2.86/3.11 => ( ( ord_less_nat @ K3 @ L )
% 2.86/3.11 => ( ord_less_nat @ ( plus_plus_nat @ I @ K3 ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_less_mono
% 2.86/3.11 thf(fact_3580_not__add__less1,axiom,
% 2.86/3.11 ! [I: nat,J: nat] :
% 2.86/3.11 ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% 2.86/3.11
% 2.86/3.11 % not_add_less1
% 2.86/3.11 thf(fact_3581_not__add__less2,axiom,
% 2.86/3.11 ! [J: nat,I: nat] :
% 2.86/3.11 ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% 2.86/3.11
% 2.86/3.11 % not_add_less2
% 2.86/3.11 thf(fact_3582_add__less__mono1,axiom,
% 2.86/3.11 ! [I: nat,J: nat,K3: nat] :
% 2.86/3.11 ( ( ord_less_nat @ I @ J )
% 2.86/3.11 => ( ord_less_nat @ ( plus_plus_nat @ I @ K3 ) @ ( plus_plus_nat @ J @ K3 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_less_mono1
% 2.86/3.11 thf(fact_3583_trans__less__add1,axiom,
% 2.86/3.11 ! [I: nat,J: nat,M2: nat] :
% 2.86/3.11 ( ( ord_less_nat @ I @ J )
% 2.86/3.11 => ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % trans_less_add1
% 2.86/3.11 thf(fact_3584_trans__less__add2,axiom,
% 2.86/3.11 ! [I: nat,J: nat,M2: nat] :
% 2.86/3.11 ( ( ord_less_nat @ I @ J )
% 2.86/3.11 => ( ord_less_nat @ I @ ( plus_plus_nat @ M2 @ J ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % trans_less_add2
% 2.86/3.11 thf(fact_3585_less__add__eq__less,axiom,
% 2.86/3.11 ! [K3: nat,L: nat,M2: nat,N: nat] :
% 2.86/3.11 ( ( ord_less_nat @ K3 @ L )
% 2.86/3.11 => ( ( ( plus_plus_nat @ M2 @ L )
% 2.86/3.11 = ( plus_plus_nat @ K3 @ N ) )
% 2.86/3.11 => ( ord_less_nat @ M2 @ N ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % less_add_eq_less
% 2.86/3.11 thf(fact_3586_ent__disjI2__direct,axiom,
% 2.86/3.11 ! [B: assn,A: assn] : ( entails @ B @ ( sup_sup_assn @ A @ B ) ) ).
% 2.86/3.11
% 2.86/3.11 % ent_disjI2_direct
% 2.86/3.11 thf(fact_3587_ent__disjI1__direct,axiom,
% 2.86/3.11 ! [A: assn,B: assn] : ( entails @ A @ ( sup_sup_assn @ A @ B ) ) ).
% 2.86/3.11
% 2.86/3.11 % ent_disjI1_direct
% 2.86/3.11 thf(fact_3588_ent__disjI2_H,axiom,
% 2.86/3.11 ! [A: assn,C2: assn,B: assn] :
% 2.86/3.11 ( ( entails @ A @ C2 )
% 2.86/3.11 => ( entails @ A @ ( sup_sup_assn @ B @ C2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % ent_disjI2'
% 2.86/3.11 thf(fact_3589_ent__disjI1_H,axiom,
% 2.86/3.11 ! [A: assn,B: assn,C2: assn] :
% 2.86/3.11 ( ( entails @ A @ B )
% 2.86/3.11 => ( entails @ A @ ( sup_sup_assn @ B @ C2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % ent_disjI1'
% 2.86/3.11 thf(fact_3590_ent__disjI2,axiom,
% 2.86/3.11 ! [P: assn,Q: assn,R: assn] :
% 2.86/3.11 ( ( entails @ ( sup_sup_assn @ P @ Q ) @ R )
% 2.86/3.11 => ( entails @ Q @ R ) ) ).
% 2.86/3.11
% 2.86/3.11 % ent_disjI2
% 2.86/3.11 thf(fact_3591_ent__disjI1,axiom,
% 2.86/3.11 ! [P: assn,Q: assn,R: assn] :
% 2.86/3.11 ( ( entails @ ( sup_sup_assn @ P @ Q ) @ R )
% 2.86/3.11 => ( entails @ P @ R ) ) ).
% 2.86/3.11
% 2.86/3.11 % ent_disjI1
% 2.86/3.11 thf(fact_3592_ent__disjE,axiom,
% 2.86/3.11 ! [A: assn,C2: assn,B: assn] :
% 2.86/3.11 ( ( entails @ A @ C2 )
% 2.86/3.11 => ( ( entails @ B @ C2 )
% 2.86/3.11 => ( entails @ ( sup_sup_assn @ A @ B ) @ C2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % ent_disjE
% 2.86/3.11 thf(fact_3593_min__add__distrib__right,axiom,
% 2.86/3.11 ! [X: rat,Y: rat,Z: rat] :
% 2.86/3.11 ( ( plus_plus_rat @ X @ ( ord_min_rat @ Y @ Z ) )
% 2.86/3.11 = ( ord_min_rat @ ( plus_plus_rat @ X @ Y ) @ ( plus_plus_rat @ X @ Z ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % min_add_distrib_right
% 2.86/3.11 thf(fact_3594_min__add__distrib__right,axiom,
% 2.86/3.11 ! [X: int,Y: int,Z: int] :
% 2.86/3.11 ( ( plus_plus_int @ X @ ( ord_min_int @ Y @ Z ) )
% 2.86/3.11 = ( ord_min_int @ ( plus_plus_int @ X @ Y ) @ ( plus_plus_int @ X @ Z ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % min_add_distrib_right
% 2.86/3.11 thf(fact_3595_min__add__distrib__right,axiom,
% 2.86/3.11 ! [X: nat,Y: nat,Z: nat] :
% 2.86/3.11 ( ( plus_plus_nat @ X @ ( ord_min_nat @ Y @ Z ) )
% 2.86/3.11 = ( ord_min_nat @ ( plus_plus_nat @ X @ Y ) @ ( plus_plus_nat @ X @ Z ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % min_add_distrib_right
% 2.86/3.11 thf(fact_3596_min__add__distrib__left,axiom,
% 2.86/3.11 ! [X: rat,Y: rat,Z: rat] :
% 2.86/3.11 ( ( plus_plus_rat @ ( ord_min_rat @ X @ Y ) @ Z )
% 2.86/3.11 = ( ord_min_rat @ ( plus_plus_rat @ X @ Z ) @ ( plus_plus_rat @ Y @ Z ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % min_add_distrib_left
% 2.86/3.11 thf(fact_3597_min__add__distrib__left,axiom,
% 2.86/3.11 ! [X: int,Y: int,Z: int] :
% 2.86/3.11 ( ( plus_plus_int @ ( ord_min_int @ X @ Y ) @ Z )
% 2.86/3.11 = ( ord_min_int @ ( plus_plus_int @ X @ Z ) @ ( plus_plus_int @ Y @ Z ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % min_add_distrib_left
% 2.86/3.11 thf(fact_3598_min__add__distrib__left,axiom,
% 2.86/3.11 ! [X: nat,Y: nat,Z: nat] :
% 2.86/3.11 ( ( plus_plus_nat @ ( ord_min_nat @ X @ Y ) @ Z )
% 2.86/3.11 = ( ord_min_nat @ ( plus_plus_nat @ X @ Z ) @ ( plus_plus_nat @ Y @ Z ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % min_add_distrib_left
% 2.86/3.11 thf(fact_3599_entt__disjE,axiom,
% 2.86/3.11 ! [A: assn,M5: assn,B: assn] :
% 2.86/3.11 ( ( entailst @ A @ M5 )
% 2.86/3.11 => ( ( entailst @ B @ M5 )
% 2.86/3.11 => ( entailst @ ( sup_sup_assn @ A @ B ) @ M5 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % entt_disjE
% 2.86/3.11 thf(fact_3600_entt__disjD1,axiom,
% 2.86/3.11 ! [A: assn,B: assn,C2: assn] :
% 2.86/3.11 ( ( entailst @ ( sup_sup_assn @ A @ B ) @ C2 )
% 2.86/3.11 => ( entailst @ A @ C2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % entt_disjD1
% 2.86/3.11 thf(fact_3601_entt__disjD2,axiom,
% 2.86/3.11 ! [A: assn,B: assn,C2: assn] :
% 2.86/3.11 ( ( entailst @ ( sup_sup_assn @ A @ B ) @ C2 )
% 2.86/3.11 => ( entailst @ B @ C2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % entt_disjD2
% 2.86/3.11 thf(fact_3602_entt__disjI1_H,axiom,
% 2.86/3.11 ! [A: assn,B: assn,C2: assn] :
% 2.86/3.11 ( ( entailst @ A @ B )
% 2.86/3.11 => ( entailst @ A @ ( sup_sup_assn @ B @ C2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % entt_disjI1'
% 2.86/3.11 thf(fact_3603_entt__disjI2_H,axiom,
% 2.86/3.11 ! [A: assn,C2: assn,B: assn] :
% 2.86/3.11 ( ( entailst @ A @ C2 )
% 2.86/3.11 => ( entailst @ A @ ( sup_sup_assn @ B @ C2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % entt_disjI2'
% 2.86/3.11 thf(fact_3604_entt__disjI1__direct,axiom,
% 2.86/3.11 ! [A: assn,B: assn] : ( entailst @ A @ ( sup_sup_assn @ A @ B ) ) ).
% 2.86/3.11
% 2.86/3.11 % entt_disjI1_direct
% 2.86/3.11 thf(fact_3605_entt__disjI2__direct,axiom,
% 2.86/3.11 ! [B: assn,A: assn] : ( entailst @ B @ ( sup_sup_assn @ A @ B ) ) ).
% 2.86/3.11
% 2.86/3.11 % entt_disjI2_direct
% 2.86/3.11 thf(fact_3606_norm__assertion__simps_I6_J,axiom,
% 2.86/3.11 ! [X: assn] :
% 2.86/3.11 ( ( sup_sup_assn @ X @ bot_bot_assn )
% 2.86/3.11 = X ) ).
% 2.86/3.11
% 2.86/3.11 % norm_assertion_simps(6)
% 2.86/3.11 thf(fact_3607_norm__assertion__simps_I5_J,axiom,
% 2.86/3.11 ! [X: assn] :
% 2.86/3.11 ( ( sup_sup_assn @ bot_bot_assn @ X )
% 2.86/3.11 = X ) ).
% 2.86/3.11
% 2.86/3.11 % norm_assertion_simps(5)
% 2.86/3.11 thf(fact_3608_add__mono__thms__linordered__field_I4_J,axiom,
% 2.86/3.11 ! [I: rat,J: rat,K3: rat,L: rat] :
% 2.86/3.11 ( ( ( ord_less_eq_rat @ I @ J )
% 2.86/3.11 & ( ord_less_rat @ K3 @ L ) )
% 2.86/3.11 => ( ord_less_rat @ ( plus_plus_rat @ I @ K3 ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_mono_thms_linordered_field(4)
% 2.86/3.11 thf(fact_3609_add__mono__thms__linordered__field_I4_J,axiom,
% 2.86/3.11 ! [I: code_integer,J: code_integer,K3: code_integer,L: code_integer] :
% 2.86/3.11 ( ( ( ord_le3102999989581377725nteger @ I @ J )
% 2.86/3.11 & ( ord_le6747313008572928689nteger @ K3 @ L ) )
% 2.86/3.11 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ I @ K3 ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_mono_thms_linordered_field(4)
% 2.86/3.11 thf(fact_3610_add__mono__thms__linordered__field_I4_J,axiom,
% 2.86/3.11 ! [I: nat,J: nat,K3: nat,L: nat] :
% 2.86/3.11 ( ( ( ord_less_eq_nat @ I @ J )
% 2.86/3.11 & ( ord_less_nat @ K3 @ L ) )
% 2.86/3.11 => ( ord_less_nat @ ( plus_plus_nat @ I @ K3 ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_mono_thms_linordered_field(4)
% 2.86/3.11 thf(fact_3611_add__mono__thms__linordered__field_I4_J,axiom,
% 2.86/3.11 ! [I: int,J: int,K3: int,L: int] :
% 2.86/3.11 ( ( ( ord_less_eq_int @ I @ J )
% 2.86/3.11 & ( ord_less_int @ K3 @ L ) )
% 2.86/3.11 => ( ord_less_int @ ( plus_plus_int @ I @ K3 ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_mono_thms_linordered_field(4)
% 2.86/3.11 thf(fact_3612_add__mono__thms__linordered__field_I3_J,axiom,
% 2.86/3.11 ! [I: rat,J: rat,K3: rat,L: rat] :
% 2.86/3.11 ( ( ( ord_less_rat @ I @ J )
% 2.86/3.11 & ( ord_less_eq_rat @ K3 @ L ) )
% 2.86/3.11 => ( ord_less_rat @ ( plus_plus_rat @ I @ K3 ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_mono_thms_linordered_field(3)
% 2.86/3.11 thf(fact_3613_add__mono__thms__linordered__field_I3_J,axiom,
% 2.86/3.11 ! [I: code_integer,J: code_integer,K3: code_integer,L: code_integer] :
% 2.86/3.11 ( ( ( ord_le6747313008572928689nteger @ I @ J )
% 2.86/3.11 & ( ord_le3102999989581377725nteger @ K3 @ L ) )
% 2.86/3.11 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ I @ K3 ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_mono_thms_linordered_field(3)
% 2.86/3.11 thf(fact_3614_add__mono__thms__linordered__field_I3_J,axiom,
% 2.86/3.11 ! [I: nat,J: nat,K3: nat,L: nat] :
% 2.86/3.11 ( ( ( ord_less_nat @ I @ J )
% 2.86/3.11 & ( ord_less_eq_nat @ K3 @ L ) )
% 2.86/3.11 => ( ord_less_nat @ ( plus_plus_nat @ I @ K3 ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_mono_thms_linordered_field(3)
% 2.86/3.11 thf(fact_3615_add__mono__thms__linordered__field_I3_J,axiom,
% 2.86/3.11 ! [I: int,J: int,K3: int,L: int] :
% 2.86/3.11 ( ( ( ord_less_int @ I @ J )
% 2.86/3.11 & ( ord_less_eq_int @ K3 @ L ) )
% 2.86/3.11 => ( ord_less_int @ ( plus_plus_int @ I @ K3 ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_mono_thms_linordered_field(3)
% 2.86/3.11 thf(fact_3616_add__le__less__mono,axiom,
% 2.86/3.11 ! [A2: rat,B2: rat,C: rat,D2: rat] :
% 2.86/3.11 ( ( ord_less_eq_rat @ A2 @ B2 )
% 2.86/3.11 => ( ( ord_less_rat @ C @ D2 )
% 2.86/3.11 => ( ord_less_rat @ ( plus_plus_rat @ A2 @ C ) @ ( plus_plus_rat @ B2 @ D2 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_le_less_mono
% 2.86/3.11 thf(fact_3617_add__le__less__mono,axiom,
% 2.86/3.11 ! [A2: code_integer,B2: code_integer,C: code_integer,D2: code_integer] :
% 2.86/3.11 ( ( ord_le3102999989581377725nteger @ A2 @ B2 )
% 2.86/3.11 => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 2.86/3.11 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A2 @ C ) @ ( plus_p5714425477246183910nteger @ B2 @ D2 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_le_less_mono
% 2.86/3.11 thf(fact_3618_add__le__less__mono,axiom,
% 2.86/3.11 ! [A2: nat,B2: nat,C: nat,D2: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.11 => ( ( ord_less_nat @ C @ D2 )
% 2.86/3.11 => ( ord_less_nat @ ( plus_plus_nat @ A2 @ C ) @ ( plus_plus_nat @ B2 @ D2 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_le_less_mono
% 2.86/3.11 thf(fact_3619_add__le__less__mono,axiom,
% 2.86/3.11 ! [A2: int,B2: int,C: int,D2: int] :
% 2.86/3.11 ( ( ord_less_eq_int @ A2 @ B2 )
% 2.86/3.11 => ( ( ord_less_int @ C @ D2 )
% 2.86/3.11 => ( ord_less_int @ ( plus_plus_int @ A2 @ C ) @ ( plus_plus_int @ B2 @ D2 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_le_less_mono
% 2.86/3.11 thf(fact_3620_add__less__le__mono,axiom,
% 2.86/3.11 ! [A2: rat,B2: rat,C: rat,D2: rat] :
% 2.86/3.11 ( ( ord_less_rat @ A2 @ B2 )
% 2.86/3.11 => ( ( ord_less_eq_rat @ C @ D2 )
% 2.86/3.11 => ( ord_less_rat @ ( plus_plus_rat @ A2 @ C ) @ ( plus_plus_rat @ B2 @ D2 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_less_le_mono
% 2.86/3.11 thf(fact_3621_add__less__le__mono,axiom,
% 2.86/3.11 ! [A2: code_integer,B2: code_integer,C: code_integer,D2: code_integer] :
% 2.86/3.11 ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 2.86/3.11 => ( ( ord_le3102999989581377725nteger @ C @ D2 )
% 2.86/3.11 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A2 @ C ) @ ( plus_p5714425477246183910nteger @ B2 @ D2 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_less_le_mono
% 2.86/3.11 thf(fact_3622_add__less__le__mono,axiom,
% 2.86/3.11 ! [A2: nat,B2: nat,C: nat,D2: nat] :
% 2.86/3.11 ( ( ord_less_nat @ A2 @ B2 )
% 2.86/3.11 => ( ( ord_less_eq_nat @ C @ D2 )
% 2.86/3.11 => ( ord_less_nat @ ( plus_plus_nat @ A2 @ C ) @ ( plus_plus_nat @ B2 @ D2 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_less_le_mono
% 2.86/3.11 thf(fact_3623_add__less__le__mono,axiom,
% 2.86/3.11 ! [A2: int,B2: int,C: int,D2: int] :
% 2.86/3.11 ( ( ord_less_int @ A2 @ B2 )
% 2.86/3.11 => ( ( ord_less_eq_int @ C @ D2 )
% 2.86/3.11 => ( ord_less_int @ ( plus_plus_int @ A2 @ C ) @ ( plus_plus_int @ B2 @ D2 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_less_le_mono
% 2.86/3.11 thf(fact_3624_diff__le__eq,axiom,
% 2.86/3.11 ! [A2: rat,B2: rat,C: rat] :
% 2.86/3.11 ( ( ord_less_eq_rat @ ( minus_minus_rat @ A2 @ B2 ) @ C )
% 2.86/3.11 = ( ord_less_eq_rat @ A2 @ ( plus_plus_rat @ C @ B2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % diff_le_eq
% 2.86/3.11 thf(fact_3625_diff__le__eq,axiom,
% 2.86/3.11 ! [A2: int,B2: int,C: int] :
% 2.86/3.11 ( ( ord_less_eq_int @ ( minus_minus_int @ A2 @ B2 ) @ C )
% 2.86/3.11 = ( ord_less_eq_int @ A2 @ ( plus_plus_int @ C @ B2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % diff_le_eq
% 2.86/3.11 thf(fact_3626_le__diff__eq,axiom,
% 2.86/3.11 ! [A2: rat,C: rat,B2: rat] :
% 2.86/3.11 ( ( ord_less_eq_rat @ A2 @ ( minus_minus_rat @ C @ B2 ) )
% 2.86/3.11 = ( ord_less_eq_rat @ ( plus_plus_rat @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.11
% 2.86/3.11 % le_diff_eq
% 2.86/3.11 thf(fact_3627_le__diff__eq,axiom,
% 2.86/3.11 ! [A2: int,C: int,B2: int] :
% 2.86/3.11 ( ( ord_less_eq_int @ A2 @ ( minus_minus_int @ C @ B2 ) )
% 2.86/3.11 = ( ord_less_eq_int @ ( plus_plus_int @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.11
% 2.86/3.11 % le_diff_eq
% 2.86/3.11 thf(fact_3628_add__le__imp__le__diff,axiom,
% 2.86/3.11 ! [I: rat,K3: rat,N: rat] :
% 2.86/3.11 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K3 ) @ N )
% 2.86/3.11 => ( ord_less_eq_rat @ I @ ( minus_minus_rat @ N @ K3 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_le_imp_le_diff
% 2.86/3.11 thf(fact_3629_add__le__imp__le__diff,axiom,
% 2.86/3.11 ! [I: nat,K3: nat,N: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K3 ) @ N )
% 2.86/3.11 => ( ord_less_eq_nat @ I @ ( minus_minus_nat @ N @ K3 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_le_imp_le_diff
% 2.86/3.11 thf(fact_3630_add__le__imp__le__diff,axiom,
% 2.86/3.11 ! [I: int,K3: int,N: int] :
% 2.86/3.11 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K3 ) @ N )
% 2.86/3.11 => ( ord_less_eq_int @ I @ ( minus_minus_int @ N @ K3 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_le_imp_le_diff
% 2.86/3.11 thf(fact_3631_ordered__cancel__comm__monoid__diff__class_Odiff__add,axiom,
% 2.86/3.11 ! [A2: nat,B2: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.11 => ( ( plus_plus_nat @ ( minus_minus_nat @ B2 @ A2 ) @ A2 )
% 2.86/3.11 = B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % ordered_cancel_comm_monoid_diff_class.diff_add
% 2.86/3.11 thf(fact_3632_add__le__add__imp__diff__le,axiom,
% 2.86/3.11 ! [I: rat,K3: rat,N: rat,J: rat] :
% 2.86/3.11 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K3 ) @ N )
% 2.86/3.11 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K3 ) )
% 2.86/3.11 => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K3 ) @ N )
% 2.86/3.11 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K3 ) )
% 2.86/3.11 => ( ord_less_eq_rat @ ( minus_minus_rat @ N @ K3 ) @ J ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_le_add_imp_diff_le
% 2.86/3.11 thf(fact_3633_add__le__add__imp__diff__le,axiom,
% 2.86/3.11 ! [I: nat,K3: nat,N: nat,J: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K3 ) @ N )
% 2.86/3.11 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K3 ) )
% 2.86/3.11 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K3 ) @ N )
% 2.86/3.11 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K3 ) )
% 2.86/3.11 => ( ord_less_eq_nat @ ( minus_minus_nat @ N @ K3 ) @ J ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_le_add_imp_diff_le
% 2.86/3.11 thf(fact_3634_add__le__add__imp__diff__le,axiom,
% 2.86/3.11 ! [I: int,K3: int,N: int,J: int] :
% 2.86/3.11 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K3 ) @ N )
% 2.86/3.11 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K3 ) )
% 2.86/3.11 => ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K3 ) @ N )
% 2.86/3.11 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K3 ) )
% 2.86/3.11 => ( ord_less_eq_int @ ( minus_minus_int @ N @ K3 ) @ J ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_le_add_imp_diff_le
% 2.86/3.11 thf(fact_3635_le__add__diff,axiom,
% 2.86/3.11 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.11 => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B2 @ C ) @ A2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % le_add_diff
% 2.86/3.11 thf(fact_3636_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 2.86/3.11 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.11 => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B2 @ A2 ) )
% 2.86/3.11 = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A2 ) @ B2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
% 2.86/3.11 thf(fact_3637_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 2.86/3.11 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.11 => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B2 @ A2 ) )
% 2.86/3.11 = ( minus_minus_nat @ ( plus_plus_nat @ C @ B2 ) @ A2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
% 2.86/3.11 thf(fact_3638_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 2.86/3.11 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.11 => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B2 ) @ A2 )
% 2.86/3.11 = ( plus_plus_nat @ C @ ( minus_minus_nat @ B2 @ A2 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
% 2.86/3.11 thf(fact_3639_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 2.86/3.11 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.11 => ( ( plus_plus_nat @ ( minus_minus_nat @ B2 @ A2 ) @ C )
% 2.86/3.11 = ( minus_minus_nat @ ( plus_plus_nat @ B2 @ C ) @ A2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
% 2.86/3.11 thf(fact_3640_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 2.86/3.11 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.11 => ( ( minus_minus_nat @ ( plus_plus_nat @ B2 @ C ) @ A2 )
% 2.86/3.11 = ( plus_plus_nat @ ( minus_minus_nat @ B2 @ A2 ) @ C ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 2.86/3.11 thf(fact_3641_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 2.86/3.11 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.11 => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B2 @ A2 ) )
% 2.86/3.11 = ( minus_minus_nat @ ( plus_plus_nat @ C @ A2 ) @ B2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 2.86/3.11 thf(fact_3642_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 2.86/3.11 ! [A2: nat,B2: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.11 => ( ( plus_plus_nat @ A2 @ ( minus_minus_nat @ B2 @ A2 ) )
% 2.86/3.11 = B2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 2.86/3.11 thf(fact_3643_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 2.86/3.11 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.11 => ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.11 => ( ( ( minus_minus_nat @ B2 @ A2 )
% 2.86/3.11 = C )
% 2.86/3.11 = ( B2
% 2.86/3.11 = ( plus_plus_nat @ C @ A2 ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 2.86/3.11 thf(fact_3644_less__add__one,axiom,
% 2.86/3.11 ! [A2: rat] : ( ord_less_rat @ A2 @ ( plus_plus_rat @ A2 @ one_one_rat ) ) ).
% 2.86/3.11
% 2.86/3.11 % less_add_one
% 2.86/3.11 thf(fact_3645_less__add__one,axiom,
% 2.86/3.11 ! [A2: code_integer] : ( ord_le6747313008572928689nteger @ A2 @ ( plus_p5714425477246183910nteger @ A2 @ one_one_Code_integer ) ) ).
% 2.86/3.11
% 2.86/3.11 % less_add_one
% 2.86/3.11 thf(fact_3646_less__add__one,axiom,
% 2.86/3.11 ! [A2: nat] : ( ord_less_nat @ A2 @ ( plus_plus_nat @ A2 @ one_one_nat ) ) ).
% 2.86/3.11
% 2.86/3.11 % less_add_one
% 2.86/3.11 thf(fact_3647_less__add__one,axiom,
% 2.86/3.11 ! [A2: int] : ( ord_less_int @ A2 @ ( plus_plus_int @ A2 @ one_one_int ) ) ).
% 2.86/3.11
% 2.86/3.11 % less_add_one
% 2.86/3.11 thf(fact_3648_add__mono1,axiom,
% 2.86/3.11 ! [A2: rat,B2: rat] :
% 2.86/3.11 ( ( ord_less_rat @ A2 @ B2 )
% 2.86/3.11 => ( ord_less_rat @ ( plus_plus_rat @ A2 @ one_one_rat ) @ ( plus_plus_rat @ B2 @ one_one_rat ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_mono1
% 2.86/3.11 thf(fact_3649_add__mono1,axiom,
% 2.86/3.11 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.11 ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 2.86/3.11 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A2 @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ B2 @ one_one_Code_integer ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_mono1
% 2.86/3.11 thf(fact_3650_add__mono1,axiom,
% 2.86/3.11 ! [A2: nat,B2: nat] :
% 2.86/3.11 ( ( ord_less_nat @ A2 @ B2 )
% 2.86/3.11 => ( ord_less_nat @ ( plus_plus_nat @ A2 @ one_one_nat ) @ ( plus_plus_nat @ B2 @ one_one_nat ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_mono1
% 2.86/3.11 thf(fact_3651_add__mono1,axiom,
% 2.86/3.11 ! [A2: int,B2: int] :
% 2.86/3.11 ( ( ord_less_int @ A2 @ B2 )
% 2.86/3.11 => ( ord_less_int @ ( plus_plus_int @ A2 @ one_one_int ) @ ( plus_plus_int @ B2 @ one_one_int ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_mono1
% 2.86/3.11 thf(fact_3652_diff__less__eq,axiom,
% 2.86/3.11 ! [A2: rat,B2: rat,C: rat] :
% 2.86/3.11 ( ( ord_less_rat @ ( minus_minus_rat @ A2 @ B2 ) @ C )
% 2.86/3.11 = ( ord_less_rat @ A2 @ ( plus_plus_rat @ C @ B2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % diff_less_eq
% 2.86/3.11 thf(fact_3653_diff__less__eq,axiom,
% 2.86/3.11 ! [A2: code_integer,B2: code_integer,C: code_integer] :
% 2.86/3.11 ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A2 @ B2 ) @ C )
% 2.86/3.11 = ( ord_le6747313008572928689nteger @ A2 @ ( plus_p5714425477246183910nteger @ C @ B2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % diff_less_eq
% 2.86/3.11 thf(fact_3654_diff__less__eq,axiom,
% 2.86/3.11 ! [A2: int,B2: int,C: int] :
% 2.86/3.11 ( ( ord_less_int @ ( minus_minus_int @ A2 @ B2 ) @ C )
% 2.86/3.11 = ( ord_less_int @ A2 @ ( plus_plus_int @ C @ B2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % diff_less_eq
% 2.86/3.11 thf(fact_3655_less__diff__eq,axiom,
% 2.86/3.11 ! [A2: rat,C: rat,B2: rat] :
% 2.86/3.11 ( ( ord_less_rat @ A2 @ ( minus_minus_rat @ C @ B2 ) )
% 2.86/3.11 = ( ord_less_rat @ ( plus_plus_rat @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.11
% 2.86/3.11 % less_diff_eq
% 2.86/3.11 thf(fact_3656_less__diff__eq,axiom,
% 2.86/3.11 ! [A2: code_integer,C: code_integer,B2: code_integer] :
% 2.86/3.11 ( ( ord_le6747313008572928689nteger @ A2 @ ( minus_8373710615458151222nteger @ C @ B2 ) )
% 2.86/3.11 = ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.11
% 2.86/3.11 % less_diff_eq
% 2.86/3.11 thf(fact_3657_less__diff__eq,axiom,
% 2.86/3.11 ! [A2: int,C: int,B2: int] :
% 2.86/3.11 ( ( ord_less_int @ A2 @ ( minus_minus_int @ C @ B2 ) )
% 2.86/3.11 = ( ord_less_int @ ( plus_plus_int @ A2 @ B2 ) @ C ) ) ).
% 2.86/3.11
% 2.86/3.11 % less_diff_eq
% 2.86/3.11 thf(fact_3658_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 2.86/3.11 ! [A2: rat,B2: rat] :
% 2.86/3.11 ( ~ ( ord_less_rat @ A2 @ B2 )
% 2.86/3.11 => ( ( plus_plus_rat @ B2 @ ( minus_minus_rat @ A2 @ B2 ) )
% 2.86/3.11 = A2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % linordered_semidom_class.add_diff_inverse
% 2.86/3.11 thf(fact_3659_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 2.86/3.11 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.11 ( ~ ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 2.86/3.11 => ( ( plus_p5714425477246183910nteger @ B2 @ ( minus_8373710615458151222nteger @ A2 @ B2 ) )
% 2.86/3.11 = A2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % linordered_semidom_class.add_diff_inverse
% 2.86/3.11 thf(fact_3660_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 2.86/3.11 ! [A2: nat,B2: nat] :
% 2.86/3.11 ( ~ ( ord_less_nat @ A2 @ B2 )
% 2.86/3.11 => ( ( plus_plus_nat @ B2 @ ( minus_minus_nat @ A2 @ B2 ) )
% 2.86/3.11 = A2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % linordered_semidom_class.add_diff_inverse
% 2.86/3.11 thf(fact_3661_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 2.86/3.11 ! [A2: int,B2: int] :
% 2.86/3.11 ( ~ ( ord_less_int @ A2 @ B2 )
% 2.86/3.11 => ( ( plus_plus_int @ B2 @ ( minus_minus_int @ A2 @ B2 ) )
% 2.86/3.11 = A2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % linordered_semidom_class.add_diff_inverse
% 2.86/3.11 thf(fact_3662_square__diff__square__factored,axiom,
% 2.86/3.11 ! [X: code_integer,Y: code_integer] :
% 2.86/3.11 ( ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) )
% 2.86/3.11 = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ X @ Y ) @ ( minus_8373710615458151222nteger @ X @ Y ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % square_diff_square_factored
% 2.86/3.11 thf(fact_3663_square__diff__square__factored,axiom,
% 2.86/3.11 ! [X: rat,Y: rat] :
% 2.86/3.11 ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 2.86/3.11 = ( times_times_rat @ ( plus_plus_rat @ X @ Y ) @ ( minus_minus_rat @ X @ Y ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % square_diff_square_factored
% 2.86/3.11 thf(fact_3664_square__diff__square__factored,axiom,
% 2.86/3.11 ! [X: int,Y: int] :
% 2.86/3.11 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 2.86/3.11 = ( times_times_int @ ( plus_plus_int @ X @ Y ) @ ( minus_minus_int @ X @ Y ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % square_diff_square_factored
% 2.86/3.11 thf(fact_3665_eq__add__iff2,axiom,
% 2.86/3.11 ! [A2: code_integer,E: code_integer,C: code_integer,B2: code_integer,D2: code_integer] :
% 2.86/3.11 ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A2 @ E ) @ C )
% 2.86/3.11 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B2 @ E ) @ D2 ) )
% 2.86/3.11 = ( C
% 2.86/3.11 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ B2 @ A2 ) @ E ) @ D2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % eq_add_iff2
% 2.86/3.11 thf(fact_3666_eq__add__iff2,axiom,
% 2.86/3.11 ! [A2: rat,E: rat,C: rat,B2: rat,D2: rat] :
% 2.86/3.11 ( ( ( plus_plus_rat @ ( times_times_rat @ A2 @ E ) @ C )
% 2.86/3.11 = ( plus_plus_rat @ ( times_times_rat @ B2 @ E ) @ D2 ) )
% 2.86/3.11 = ( C
% 2.86/3.11 = ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B2 @ A2 ) @ E ) @ D2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % eq_add_iff2
% 2.86/3.11 thf(fact_3667_eq__add__iff2,axiom,
% 2.86/3.11 ! [A2: int,E: int,C: int,B2: int,D2: int] :
% 2.86/3.11 ( ( ( plus_plus_int @ ( times_times_int @ A2 @ E ) @ C )
% 2.86/3.11 = ( plus_plus_int @ ( times_times_int @ B2 @ E ) @ D2 ) )
% 2.86/3.11 = ( C
% 2.86/3.11 = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B2 @ A2 ) @ E ) @ D2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % eq_add_iff2
% 2.86/3.11 thf(fact_3668_eq__add__iff1,axiom,
% 2.86/3.11 ! [A2: code_integer,E: code_integer,C: code_integer,B2: code_integer,D2: code_integer] :
% 2.86/3.11 ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A2 @ E ) @ C )
% 2.86/3.11 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B2 @ E ) @ D2 ) )
% 2.86/3.11 = ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A2 @ B2 ) @ E ) @ C )
% 2.86/3.11 = D2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % eq_add_iff1
% 2.86/3.11 thf(fact_3669_eq__add__iff1,axiom,
% 2.86/3.11 ! [A2: rat,E: rat,C: rat,B2: rat,D2: rat] :
% 2.86/3.11 ( ( ( plus_plus_rat @ ( times_times_rat @ A2 @ E ) @ C )
% 2.86/3.11 = ( plus_plus_rat @ ( times_times_rat @ B2 @ E ) @ D2 ) )
% 2.86/3.11 = ( ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A2 @ B2 ) @ E ) @ C )
% 2.86/3.11 = D2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % eq_add_iff1
% 2.86/3.11 thf(fact_3670_eq__add__iff1,axiom,
% 2.86/3.11 ! [A2: int,E: int,C: int,B2: int,D2: int] :
% 2.86/3.11 ( ( ( plus_plus_int @ ( times_times_int @ A2 @ E ) @ C )
% 2.86/3.11 = ( plus_plus_int @ ( times_times_int @ B2 @ E ) @ D2 ) )
% 2.86/3.11 = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A2 @ B2 ) @ E ) @ C )
% 2.86/3.11 = D2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % eq_add_iff1
% 2.86/3.11 thf(fact_3671_lift__Suc__mono__less,axiom,
% 2.86/3.11 ! [F4: nat > code_integer,N: nat,N6: nat] :
% 2.86/3.11 ( ! [N5: nat] : ( ord_le6747313008572928689nteger @ ( F4 @ N5 ) @ ( F4 @ ( suc @ N5 ) ) )
% 2.86/3.11 => ( ( ord_less_nat @ N @ N6 )
% 2.86/3.11 => ( ord_le6747313008572928689nteger @ ( F4 @ N ) @ ( F4 @ N6 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % lift_Suc_mono_less
% 2.86/3.11 thf(fact_3672_lift__Suc__mono__less,axiom,
% 2.86/3.11 ! [F4: nat > assn,N: nat,N6: nat] :
% 2.86/3.11 ( ! [N5: nat] : ( ord_less_assn @ ( F4 @ N5 ) @ ( F4 @ ( suc @ N5 ) ) )
% 2.86/3.11 => ( ( ord_less_nat @ N @ N6 )
% 2.86/3.11 => ( ord_less_assn @ ( F4 @ N ) @ ( F4 @ N6 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % lift_Suc_mono_less
% 2.86/3.11 thf(fact_3673_lift__Suc__mono__less,axiom,
% 2.86/3.11 ! [F4: nat > num,N: nat,N6: nat] :
% 2.86/3.11 ( ! [N5: nat] : ( ord_less_num @ ( F4 @ N5 ) @ ( F4 @ ( suc @ N5 ) ) )
% 2.86/3.11 => ( ( ord_less_nat @ N @ N6 )
% 2.86/3.11 => ( ord_less_num @ ( F4 @ N ) @ ( F4 @ N6 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % lift_Suc_mono_less
% 2.86/3.11 thf(fact_3674_lift__Suc__mono__less,axiom,
% 2.86/3.11 ! [F4: nat > nat,N: nat,N6: nat] :
% 2.86/3.11 ( ! [N5: nat] : ( ord_less_nat @ ( F4 @ N5 ) @ ( F4 @ ( suc @ N5 ) ) )
% 2.86/3.11 => ( ( ord_less_nat @ N @ N6 )
% 2.86/3.11 => ( ord_less_nat @ ( F4 @ N ) @ ( F4 @ N6 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % lift_Suc_mono_less
% 2.86/3.11 thf(fact_3675_lift__Suc__mono__less,axiom,
% 2.86/3.11 ! [F4: nat > int,N: nat,N6: nat] :
% 2.86/3.11 ( ! [N5: nat] : ( ord_less_int @ ( F4 @ N5 ) @ ( F4 @ ( suc @ N5 ) ) )
% 2.86/3.11 => ( ( ord_less_nat @ N @ N6 )
% 2.86/3.11 => ( ord_less_int @ ( F4 @ N ) @ ( F4 @ N6 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % lift_Suc_mono_less
% 2.86/3.11 thf(fact_3676_lift__Suc__mono__less__iff,axiom,
% 2.86/3.11 ! [F4: nat > code_integer,N: nat,M2: nat] :
% 2.86/3.11 ( ! [N5: nat] : ( ord_le6747313008572928689nteger @ ( F4 @ N5 ) @ ( F4 @ ( suc @ N5 ) ) )
% 2.86/3.11 => ( ( ord_le6747313008572928689nteger @ ( F4 @ N ) @ ( F4 @ M2 ) )
% 2.86/3.11 = ( ord_less_nat @ N @ M2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % lift_Suc_mono_less_iff
% 2.86/3.11 thf(fact_3677_lift__Suc__mono__less__iff,axiom,
% 2.86/3.11 ! [F4: nat > assn,N: nat,M2: nat] :
% 2.86/3.11 ( ! [N5: nat] : ( ord_less_assn @ ( F4 @ N5 ) @ ( F4 @ ( suc @ N5 ) ) )
% 2.86/3.11 => ( ( ord_less_assn @ ( F4 @ N ) @ ( F4 @ M2 ) )
% 2.86/3.11 = ( ord_less_nat @ N @ M2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % lift_Suc_mono_less_iff
% 2.86/3.11 thf(fact_3678_lift__Suc__mono__less__iff,axiom,
% 2.86/3.11 ! [F4: nat > num,N: nat,M2: nat] :
% 2.86/3.11 ( ! [N5: nat] : ( ord_less_num @ ( F4 @ N5 ) @ ( F4 @ ( suc @ N5 ) ) )
% 2.86/3.11 => ( ( ord_less_num @ ( F4 @ N ) @ ( F4 @ M2 ) )
% 2.86/3.11 = ( ord_less_nat @ N @ M2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % lift_Suc_mono_less_iff
% 2.86/3.11 thf(fact_3679_lift__Suc__mono__less__iff,axiom,
% 2.86/3.11 ! [F4: nat > nat,N: nat,M2: nat] :
% 2.86/3.11 ( ! [N5: nat] : ( ord_less_nat @ ( F4 @ N5 ) @ ( F4 @ ( suc @ N5 ) ) )
% 2.86/3.11 => ( ( ord_less_nat @ ( F4 @ N ) @ ( F4 @ M2 ) )
% 2.86/3.11 = ( ord_less_nat @ N @ M2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % lift_Suc_mono_less_iff
% 2.86/3.11 thf(fact_3680_lift__Suc__mono__less__iff,axiom,
% 2.86/3.11 ! [F4: nat > int,N: nat,M2: nat] :
% 2.86/3.11 ( ! [N5: nat] : ( ord_less_int @ ( F4 @ N5 ) @ ( F4 @ ( suc @ N5 ) ) )
% 2.86/3.11 => ( ( ord_less_int @ ( F4 @ N ) @ ( F4 @ M2 ) )
% 2.86/3.11 = ( ord_less_nat @ N @ M2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % lift_Suc_mono_less_iff
% 2.86/3.11 thf(fact_3681_Suc__leI,axiom,
% 2.86/3.11 ! [M2: nat,N: nat] :
% 2.86/3.11 ( ( ord_less_nat @ M2 @ N )
% 2.86/3.11 => ( ord_less_eq_nat @ ( suc @ M2 ) @ N ) ) ).
% 2.86/3.11
% 2.86/3.11 % Suc_leI
% 2.86/3.11 thf(fact_3682_Suc__le__eq,axiom,
% 2.86/3.11 ! [M2: nat,N: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N )
% 2.86/3.11 = ( ord_less_nat @ M2 @ N ) ) ).
% 2.86/3.11
% 2.86/3.11 % Suc_le_eq
% 2.86/3.11 thf(fact_3683_dec__induct,axiom,
% 2.86/3.11 ! [I: nat,J: nat,P: nat > $o] :
% 2.86/3.11 ( ( ord_less_eq_nat @ I @ J )
% 2.86/3.11 => ( ( P @ I )
% 2.86/3.11 => ( ! [N5: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ I @ N5 )
% 2.86/3.11 => ( ( ord_less_nat @ N5 @ J )
% 2.86/3.11 => ( ( P @ N5 )
% 2.86/3.11 => ( P @ ( suc @ N5 ) ) ) ) )
% 2.86/3.11 => ( P @ J ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % dec_induct
% 2.86/3.11 thf(fact_3684_inc__induct,axiom,
% 2.86/3.11 ! [I: nat,J: nat,P: nat > $o] :
% 2.86/3.11 ( ( ord_less_eq_nat @ I @ J )
% 2.86/3.11 => ( ( P @ J )
% 2.86/3.11 => ( ! [N5: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ I @ N5 )
% 2.86/3.11 => ( ( ord_less_nat @ N5 @ J )
% 2.86/3.11 => ( ( P @ ( suc @ N5 ) )
% 2.86/3.11 => ( P @ N5 ) ) ) )
% 2.86/3.11 => ( P @ I ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % inc_induct
% 2.86/3.11 thf(fact_3685_Suc__le__lessD,axiom,
% 2.86/3.11 ! [M2: nat,N: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N )
% 2.86/3.11 => ( ord_less_nat @ M2 @ N ) ) ).
% 2.86/3.11
% 2.86/3.11 % Suc_le_lessD
% 2.86/3.11 thf(fact_3686_le__less__Suc__eq,axiom,
% 2.86/3.11 ! [M2: nat,N: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ M2 @ N )
% 2.86/3.11 => ( ( ord_less_nat @ N @ ( suc @ M2 ) )
% 2.86/3.11 = ( N = M2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % le_less_Suc_eq
% 2.86/3.11 thf(fact_3687_less__Suc__eq__le,axiom,
% 2.86/3.11 ! [M2: nat,N: nat] :
% 2.86/3.11 ( ( ord_less_nat @ M2 @ ( suc @ N ) )
% 2.86/3.11 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 2.86/3.11
% 2.86/3.11 % less_Suc_eq_le
% 2.86/3.11 thf(fact_3688_less__eq__Suc__le,axiom,
% 2.86/3.11 ( ord_less_nat
% 2.86/3.11 = ( ^ [N2: nat] : ( ord_less_eq_nat @ ( suc @ N2 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % less_eq_Suc_le
% 2.86/3.11 thf(fact_3689_le__imp__less__Suc,axiom,
% 2.86/3.11 ! [M2: nat,N: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ M2 @ N )
% 2.86/3.11 => ( ord_less_nat @ M2 @ ( suc @ N ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % le_imp_less_Suc
% 2.86/3.11 thf(fact_3690_nat__in__between__eq_I1_J,axiom,
% 2.86/3.11 ! [A2: nat,B2: nat] :
% 2.86/3.11 ( ( ( ord_less_nat @ A2 @ B2 )
% 2.86/3.11 & ( ord_less_eq_nat @ B2 @ ( suc @ A2 ) ) )
% 2.86/3.11 = ( B2
% 2.86/3.11 = ( suc @ A2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % nat_in_between_eq(1)
% 2.86/3.11 thf(fact_3691_nat__in__between__eq_I2_J,axiom,
% 2.86/3.11 ! [A2: nat,B2: nat] :
% 2.86/3.11 ( ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.11 & ( ord_less_nat @ B2 @ ( suc @ A2 ) ) )
% 2.86/3.11 = ( B2 = A2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % nat_in_between_eq(2)
% 2.86/3.11 thf(fact_3692_Suc__diff__Suc,axiom,
% 2.86/3.11 ! [N: nat,M2: nat] :
% 2.86/3.11 ( ( ord_less_nat @ N @ M2 )
% 2.86/3.11 => ( ( suc @ ( minus_minus_nat @ M2 @ ( suc @ N ) ) )
% 2.86/3.11 = ( minus_minus_nat @ M2 @ N ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % Suc_diff_Suc
% 2.86/3.11 thf(fact_3693_diff__less__Suc,axiom,
% 2.86/3.11 ! [M2: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M2 @ N ) @ ( suc @ M2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % diff_less_Suc
% 2.86/3.11 thf(fact_3694_mono__nat__linear__lb,axiom,
% 2.86/3.11 ! [F4: nat > nat,M2: nat,K3: nat] :
% 2.86/3.11 ( ! [M6: nat,N5: nat] :
% 2.86/3.11 ( ( ord_less_nat @ M6 @ N5 )
% 2.86/3.11 => ( ord_less_nat @ ( F4 @ M6 ) @ ( F4 @ N5 ) ) )
% 2.86/3.11 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F4 @ M2 ) @ K3 ) @ ( F4 @ ( plus_plus_nat @ M2 @ K3 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % mono_nat_linear_lb
% 2.86/3.11 thf(fact_3695_Suc__mult__less__cancel1,axiom,
% 2.86/3.11 ! [K3: nat,M2: nat,N: nat] :
% 2.86/3.11 ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K3 ) @ M2 ) @ ( times_times_nat @ ( suc @ K3 ) @ N ) )
% 2.86/3.11 = ( ord_less_nat @ M2 @ N ) ) ).
% 2.86/3.11
% 2.86/3.11 % Suc_mult_less_cancel1
% 2.86/3.11 thf(fact_3696_less__diff__conv,axiom,
% 2.86/3.11 ! [I: nat,J: nat,K3: nat] :
% 2.86/3.11 ( ( ord_less_nat @ I @ ( minus_minus_nat @ J @ K3 ) )
% 2.86/3.11 = ( ord_less_nat @ ( plus_plus_nat @ I @ K3 ) @ J ) ) ).
% 2.86/3.11
% 2.86/3.11 % less_diff_conv
% 2.86/3.11 thf(fact_3697_add__diff__inverse__nat,axiom,
% 2.86/3.11 ! [M2: nat,N: nat] :
% 2.86/3.11 ( ~ ( ord_less_nat @ M2 @ N )
% 2.86/3.11 => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M2 @ N ) )
% 2.86/3.11 = M2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % add_diff_inverse_nat
% 2.86/3.11 thf(fact_3698_mlex__bound,axiom,
% 2.86/3.11 ! [A2: nat,A: nat,B2: nat,N7: nat] :
% 2.86/3.11 ( ( ord_less_nat @ A2 @ A )
% 2.86/3.11 => ( ( ord_less_nat @ B2 @ N7 )
% 2.86/3.11 => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ A2 @ N7 ) @ B2 ) @ ( times_times_nat @ A @ N7 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % mlex_bound
% 2.86/3.11 thf(fact_3699_mlex__fst__decrI,axiom,
% 2.86/3.11 ! [A2: nat,A7: nat,B2: nat,N7: nat,B6: nat] :
% 2.86/3.11 ( ( ord_less_nat @ A2 @ A7 )
% 2.86/3.11 => ( ( ord_less_nat @ B2 @ N7 )
% 2.86/3.11 => ( ( ord_less_nat @ B6 @ N7 )
% 2.86/3.11 => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ A2 @ N7 ) @ B2 ) @ ( plus_plus_nat @ ( times_times_nat @ A7 @ N7 ) @ B6 ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % mlex_fst_decrI
% 2.86/3.11 thf(fact_3700_mlex__snd__decrI,axiom,
% 2.86/3.11 ! [A2: nat,A7: nat,B2: nat,B6: nat,N7: nat] :
% 2.86/3.11 ( ( A2 = A7 )
% 2.86/3.11 => ( ( ord_less_nat @ B2 @ B6 )
% 2.86/3.11 => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ A2 @ N7 ) @ B2 ) @ ( plus_plus_nat @ ( times_times_nat @ A7 @ N7 ) @ B6 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % mlex_snd_decrI
% 2.86/3.11 thf(fact_3701_mlex__leI,axiom,
% 2.86/3.11 ! [A2: nat,A7: nat,B2: nat,B6: nat,N7: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ A2 @ A7 )
% 2.86/3.11 => ( ( ord_less_eq_nat @ B2 @ B6 )
% 2.86/3.11 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ A2 @ N7 ) @ B2 ) @ ( plus_plus_nat @ ( times_times_nat @ A7 @ N7 ) @ B6 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % mlex_leI
% 2.86/3.11 thf(fact_3702_le__add__iff2,axiom,
% 2.86/3.11 ! [A2: code_integer,E: code_integer,C: code_integer,B2: code_integer,D2: code_integer] :
% 2.86/3.11 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A2 @ E ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B2 @ E ) @ D2 ) )
% 2.86/3.11 = ( ord_le3102999989581377725nteger @ C @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ B2 @ A2 ) @ E ) @ D2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % le_add_iff2
% 2.86/3.11 thf(fact_3703_le__add__iff2,axiom,
% 2.86/3.11 ! [A2: rat,E: rat,C: rat,B2: rat,D2: rat] :
% 2.86/3.11 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A2 @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B2 @ E ) @ D2 ) )
% 2.86/3.11 = ( ord_less_eq_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B2 @ A2 ) @ E ) @ D2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % le_add_iff2
% 2.86/3.11 thf(fact_3704_le__add__iff2,axiom,
% 2.86/3.11 ! [A2: int,E: int,C: int,B2: int,D2: int] :
% 2.86/3.11 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A2 @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B2 @ E ) @ D2 ) )
% 2.86/3.11 = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B2 @ A2 ) @ E ) @ D2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % le_add_iff2
% 2.86/3.11 thf(fact_3705_le__add__iff1,axiom,
% 2.86/3.11 ! [A2: code_integer,E: code_integer,C: code_integer,B2: code_integer,D2: code_integer] :
% 2.86/3.11 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A2 @ E ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B2 @ E ) @ D2 ) )
% 2.86/3.11 = ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A2 @ B2 ) @ E ) @ C ) @ D2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % le_add_iff1
% 2.86/3.11 thf(fact_3706_le__add__iff1,axiom,
% 2.86/3.11 ! [A2: rat,E: rat,C: rat,B2: rat,D2: rat] :
% 2.86/3.11 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A2 @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B2 @ E ) @ D2 ) )
% 2.86/3.11 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A2 @ B2 ) @ E ) @ C ) @ D2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % le_add_iff1
% 2.86/3.11 thf(fact_3707_le__add__iff1,axiom,
% 2.86/3.11 ! [A2: int,E: int,C: int,B2: int,D2: int] :
% 2.86/3.11 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A2 @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B2 @ E ) @ D2 ) )
% 2.86/3.11 = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A2 @ B2 ) @ E ) @ C ) @ D2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % le_add_iff1
% 2.86/3.11 thf(fact_3708_less__add__iff2,axiom,
% 2.86/3.11 ! [A2: rat,E: rat,C: rat,B2: rat,D2: rat] :
% 2.86/3.11 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A2 @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B2 @ E ) @ D2 ) )
% 2.86/3.11 = ( ord_less_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B2 @ A2 ) @ E ) @ D2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % less_add_iff2
% 2.86/3.11 thf(fact_3709_less__add__iff2,axiom,
% 2.86/3.11 ! [A2: code_integer,E: code_integer,C: code_integer,B2: code_integer,D2: code_integer] :
% 2.86/3.11 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A2 @ E ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B2 @ E ) @ D2 ) )
% 2.86/3.11 = ( ord_le6747313008572928689nteger @ C @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ B2 @ A2 ) @ E ) @ D2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % less_add_iff2
% 2.86/3.11 thf(fact_3710_less__add__iff2,axiom,
% 2.86/3.11 ! [A2: int,E: int,C: int,B2: int,D2: int] :
% 2.86/3.11 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A2 @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B2 @ E ) @ D2 ) )
% 2.86/3.11 = ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B2 @ A2 ) @ E ) @ D2 ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % less_add_iff2
% 2.86/3.11 thf(fact_3711_less__add__iff1,axiom,
% 2.86/3.11 ! [A2: rat,E: rat,C: rat,B2: rat,D2: rat] :
% 2.86/3.11 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A2 @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B2 @ E ) @ D2 ) )
% 2.86/3.11 = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A2 @ B2 ) @ E ) @ C ) @ D2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % less_add_iff1
% 2.86/3.11 thf(fact_3712_less__add__iff1,axiom,
% 2.86/3.11 ! [A2: code_integer,E: code_integer,C: code_integer,B2: code_integer,D2: code_integer] :
% 2.86/3.11 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A2 @ E ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B2 @ E ) @ D2 ) )
% 2.86/3.11 = ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A2 @ B2 ) @ E ) @ C ) @ D2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % less_add_iff1
% 2.86/3.11 thf(fact_3713_less__add__iff1,axiom,
% 2.86/3.11 ! [A2: int,E: int,C: int,B2: int,D2: int] :
% 2.86/3.11 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A2 @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B2 @ E ) @ D2 ) )
% 2.86/3.11 = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A2 @ B2 ) @ E ) @ C ) @ D2 ) ) ).
% 2.86/3.11
% 2.86/3.11 % less_add_iff1
% 2.86/3.11 thf(fact_3714_square__diff__one__factored,axiom,
% 2.86/3.11 ! [X: code_integer] :
% 2.86/3.11 ( ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ X @ X ) @ one_one_Code_integer )
% 2.86/3.11 = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ X @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ X @ one_one_Code_integer ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % square_diff_one_factored
% 2.86/3.11 thf(fact_3715_square__diff__one__factored,axiom,
% 2.86/3.11 ! [X: rat] :
% 2.86/3.11 ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ one_one_rat )
% 2.86/3.11 = ( times_times_rat @ ( plus_plus_rat @ X @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % square_diff_one_factored
% 2.86/3.11 thf(fact_3716_square__diff__one__factored,axiom,
% 2.86/3.11 ! [X: int] :
% 2.86/3.11 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ one_one_int )
% 2.86/3.11 = ( times_times_int @ ( plus_plus_int @ X @ one_one_int ) @ ( minus_minus_int @ X @ one_one_int ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % square_diff_one_factored
% 2.86/3.11 thf(fact_3717_less__diff__conv2,axiom,
% 2.86/3.11 ! [K3: nat,J: nat,I: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ K3 @ J )
% 2.86/3.11 => ( ( ord_less_nat @ ( minus_minus_nat @ J @ K3 ) @ I )
% 2.86/3.11 = ( ord_less_nat @ J @ ( plus_plus_nat @ I @ K3 ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % less_diff_conv2
% 2.86/3.11 thf(fact_3718_Suc__n__minus__m__eq,axiom,
% 2.86/3.11 ! [M2: nat,N: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ M2 @ N )
% 2.86/3.11 => ( ( ord_less_nat @ one_one_nat @ M2 )
% 2.86/3.11 => ( ( suc @ ( minus_minus_nat @ N @ M2 ) )
% 2.86/3.11 = ( minus_minus_nat @ N @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % Suc_n_minus_m_eq
% 2.86/3.11 thf(fact_3719_sorted__iff__nth__Suc,axiom,
% 2.86/3.11 ! [Xs: list_nat] :
% 2.86/3.11 ( ( sorted_wrt_nat @ ord_less_eq_nat @ Xs )
% 2.86/3.11 = ( ! [I4: nat] :
% 2.86/3.11 ( ( ord_less_nat @ ( suc @ I4 ) @ ( size_size_list_nat @ Xs ) )
% 2.86/3.11 => ( ord_less_eq_nat @ ( nth_nat @ Xs @ I4 ) @ ( nth_nat @ Xs @ ( suc @ I4 ) ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % sorted_iff_nth_Suc
% 2.86/3.11 thf(fact_3720_sorted__iff__nth__Suc,axiom,
% 2.86/3.11 ! [Xs: list_int] :
% 2.86/3.11 ( ( sorted_wrt_int @ ord_less_eq_int @ Xs )
% 2.86/3.11 = ( ! [I4: nat] :
% 2.86/3.11 ( ( ord_less_nat @ ( suc @ I4 ) @ ( size_size_list_int @ Xs ) )
% 2.86/3.11 => ( ord_less_eq_int @ ( nth_int @ Xs @ I4 ) @ ( nth_int @ Xs @ ( suc @ I4 ) ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % sorted_iff_nth_Suc
% 2.86/3.11 thf(fact_3721_rev__nth,axiom,
% 2.86/3.11 ! [N: nat,Xs: list_c] :
% 2.86/3.11 ( ( ord_less_nat @ N @ ( size_size_list_c @ Xs ) )
% 2.86/3.11 => ( ( nth_c @ ( rev_c @ Xs ) @ N )
% 2.86/3.11 = ( nth_c @ Xs @ ( minus_minus_nat @ ( size_size_list_c @ Xs ) @ ( suc @ N ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % rev_nth
% 2.86/3.11 thf(fact_3722_rev__nth,axiom,
% 2.86/3.11 ! [N: nat,Xs: list_d] :
% 2.86/3.11 ( ( ord_less_nat @ N @ ( size_size_list_d @ Xs ) )
% 2.86/3.11 => ( ( nth_d @ ( rev_d @ Xs ) @ N )
% 2.86/3.11 = ( nth_d @ Xs @ ( minus_minus_nat @ ( size_size_list_d @ Xs ) @ ( suc @ N ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % rev_nth
% 2.86/3.11 thf(fact_3723_rev__nth,axiom,
% 2.86/3.11 ! [N: nat,Xs: list_nat] :
% 2.86/3.11 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 2.86/3.11 => ( ( nth_nat @ ( rev_nat @ Xs ) @ N )
% 2.86/3.11 = ( nth_nat @ Xs @ ( minus_minus_nat @ ( size_size_list_nat @ Xs ) @ ( suc @ N ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % rev_nth
% 2.86/3.11 thf(fact_3724_rev__nth,axiom,
% 2.86/3.11 ! [N: nat,Xs: list_int] :
% 2.86/3.11 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 2.86/3.11 => ( ( nth_int @ ( rev_int @ Xs ) @ N )
% 2.86/3.11 = ( nth_int @ Xs @ ( minus_minus_nat @ ( size_size_list_int @ Xs ) @ ( suc @ N ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % rev_nth
% 2.86/3.11 thf(fact_3725_nat__less__add__iff1,axiom,
% 2.86/3.11 ! [J: nat,I: nat,U: nat,M2: nat,N: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ J @ I )
% 2.86/3.11 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 2.86/3.11 = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M2 ) @ N ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % nat_less_add_iff1
% 2.86/3.11 thf(fact_3726_nat__less__add__iff2,axiom,
% 2.86/3.11 ! [I: nat,J: nat,U: nat,M2: nat,N: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ I @ J )
% 2.86/3.11 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 2.86/3.11 = ( ord_less_nat @ M2 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % nat_less_add_iff2
% 2.86/3.11 thf(fact_3727_discrete,axiom,
% 2.86/3.11 ( ord_le6747313008572928689nteger
% 2.86/3.11 = ( ^ [A3: code_integer] : ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A3 @ one_one_Code_integer ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % discrete
% 2.86/3.11 thf(fact_3728_discrete,axiom,
% 2.86/3.11 ( ord_less_nat
% 2.86/3.11 = ( ^ [A3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A3 @ one_one_nat ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % discrete
% 2.86/3.11 thf(fact_3729_discrete,axiom,
% 2.86/3.11 ( ord_less_int
% 2.86/3.11 = ( ^ [A3: int] : ( ord_less_eq_int @ ( plus_plus_int @ A3 @ one_one_int ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % discrete
% 2.86/3.11 thf(fact_3730_sorted__in__between,axiom,
% 2.86/3.11 ! [I: nat,J: nat,L: list_Code_integer,X: code_integer] :
% 2.86/3.11 ( ( ord_less_eq_nat @ zero_zero_nat @ I )
% 2.86/3.11 => ( ( ord_less_nat @ I @ J )
% 2.86/3.11 => ( ( ord_less_nat @ J @ ( size_s3445333598471063425nteger @ L ) )
% 2.86/3.11 => ( ( sorted710888440204495920nteger @ ord_le3102999989581377725nteger @ L )
% 2.86/3.11 => ( ( ord_le3102999989581377725nteger @ ( nth_Code_integer @ L @ I ) @ X )
% 2.86/3.11 => ( ( ord_le6747313008572928689nteger @ X @ ( nth_Code_integer @ L @ J ) )
% 2.86/3.11 => ~ ! [K: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ I @ K )
% 2.86/3.11 => ( ( ord_less_nat @ K @ J )
% 2.86/3.11 => ( ( ord_le3102999989581377725nteger @ ( nth_Code_integer @ L @ K ) @ X )
% 2.86/3.11 => ~ ( ord_le6747313008572928689nteger @ X @ ( nth_Code_integer @ L @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % sorted_in_between
% 2.86/3.11 thf(fact_3731_sorted__in__between,axiom,
% 2.86/3.11 ! [I: nat,J: nat,L: list_num,X: num] :
% 2.86/3.11 ( ( ord_less_eq_nat @ zero_zero_nat @ I )
% 2.86/3.11 => ( ( ord_less_nat @ I @ J )
% 2.86/3.11 => ( ( ord_less_nat @ J @ ( size_size_list_num @ L ) )
% 2.86/3.11 => ( ( sorted_wrt_num @ ord_less_eq_num @ L )
% 2.86/3.11 => ( ( ord_less_eq_num @ ( nth_num @ L @ I ) @ X )
% 2.86/3.11 => ( ( ord_less_num @ X @ ( nth_num @ L @ J ) )
% 2.86/3.11 => ~ ! [K: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ I @ K )
% 2.86/3.11 => ( ( ord_less_nat @ K @ J )
% 2.86/3.11 => ( ( ord_less_eq_num @ ( nth_num @ L @ K ) @ X )
% 2.86/3.11 => ~ ( ord_less_num @ X @ ( nth_num @ L @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % sorted_in_between
% 2.86/3.11 thf(fact_3732_sorted__in__between,axiom,
% 2.86/3.11 ! [I: nat,J: nat,L: list_nat,X: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ zero_zero_nat @ I )
% 2.86/3.11 => ( ( ord_less_nat @ I @ J )
% 2.86/3.11 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ L ) )
% 2.86/3.11 => ( ( sorted_wrt_nat @ ord_less_eq_nat @ L )
% 2.86/3.11 => ( ( ord_less_eq_nat @ ( nth_nat @ L @ I ) @ X )
% 2.86/3.11 => ( ( ord_less_nat @ X @ ( nth_nat @ L @ J ) )
% 2.86/3.11 => ~ ! [K: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ I @ K )
% 2.86/3.11 => ( ( ord_less_nat @ K @ J )
% 2.86/3.11 => ( ( ord_less_eq_nat @ ( nth_nat @ L @ K ) @ X )
% 2.86/3.11 => ~ ( ord_less_nat @ X @ ( nth_nat @ L @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % sorted_in_between
% 2.86/3.11 thf(fact_3733_sorted__in__between,axiom,
% 2.86/3.11 ! [I: nat,J: nat,L: list_int,X: int] :
% 2.86/3.11 ( ( ord_less_eq_nat @ zero_zero_nat @ I )
% 2.86/3.11 => ( ( ord_less_nat @ I @ J )
% 2.86/3.11 => ( ( ord_less_nat @ J @ ( size_size_list_int @ L ) )
% 2.86/3.11 => ( ( sorted_wrt_int @ ord_less_eq_int @ L )
% 2.86/3.11 => ( ( ord_less_eq_int @ ( nth_int @ L @ I ) @ X )
% 2.86/3.11 => ( ( ord_less_int @ X @ ( nth_int @ L @ J ) )
% 2.86/3.11 => ~ ! [K: nat] :
% 2.86/3.11 ( ( ord_less_eq_nat @ I @ K )
% 2.86/3.11 => ( ( ord_less_nat @ K @ J )
% 2.86/3.11 => ( ( ord_less_eq_int @ ( nth_int @ L @ K ) @ X )
% 2.86/3.11 => ~ ( ord_less_int @ X @ ( nth_int @ L @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % sorted_in_between
% 2.86/3.11 thf(fact_3734_crossproduct__eq,axiom,
% 2.86/3.11 ! [W: code_integer,Y: code_integer,X: code_integer,Z: code_integer] :
% 2.86/3.11 ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ W @ Y ) @ ( times_3573771949741848930nteger @ X @ Z ) )
% 2.86/3.11 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ W @ Z ) @ ( times_3573771949741848930nteger @ X @ Y ) ) )
% 2.86/3.11 = ( ( W = X )
% 2.86/3.11 | ( Y = Z ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % crossproduct_eq
% 2.86/3.11 thf(fact_3735_crossproduct__eq,axiom,
% 2.86/3.11 ! [W: rat,Y: rat,X: rat,Z: rat] :
% 2.86/3.11 ( ( ( plus_plus_rat @ ( times_times_rat @ W @ Y ) @ ( times_times_rat @ X @ Z ) )
% 2.86/3.11 = ( plus_plus_rat @ ( times_times_rat @ W @ Z ) @ ( times_times_rat @ X @ Y ) ) )
% 2.86/3.11 = ( ( W = X )
% 2.86/3.11 | ( Y = Z ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % crossproduct_eq
% 2.86/3.11 thf(fact_3736_crossproduct__eq,axiom,
% 2.86/3.11 ! [W: nat,Y: nat,X: nat,Z: nat] :
% 2.86/3.11 ( ( ( plus_plus_nat @ ( times_times_nat @ W @ Y ) @ ( times_times_nat @ X @ Z ) )
% 2.86/3.11 = ( plus_plus_nat @ ( times_times_nat @ W @ Z ) @ ( times_times_nat @ X @ Y ) ) )
% 2.86/3.11 = ( ( W = X )
% 2.86/3.11 | ( Y = Z ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % crossproduct_eq
% 2.86/3.11 thf(fact_3737_crossproduct__eq,axiom,
% 2.86/3.11 ! [W: int,Y: int,X: int,Z: int] :
% 2.86/3.11 ( ( ( plus_plus_int @ ( times_times_int @ W @ Y ) @ ( times_times_int @ X @ Z ) )
% 2.86/3.11 = ( plus_plus_int @ ( times_times_int @ W @ Z ) @ ( times_times_int @ X @ Y ) ) )
% 2.86/3.11 = ( ( W = X )
% 2.86/3.11 | ( Y = Z ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % crossproduct_eq
% 2.86/3.11 thf(fact_3738_crossproduct__noteq,axiom,
% 2.86/3.11 ! [A2: code_integer,B2: code_integer,C: code_integer,D2: code_integer] :
% 2.86/3.11 ( ( ( A2 != B2 )
% 2.86/3.11 & ( C != D2 ) )
% 2.86/3.11 = ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ ( times_3573771949741848930nteger @ B2 @ D2 ) )
% 2.86/3.11 != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A2 @ D2 ) @ ( times_3573771949741848930nteger @ B2 @ C ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % crossproduct_noteq
% 2.86/3.11 thf(fact_3739_crossproduct__noteq,axiom,
% 2.86/3.11 ! [A2: rat,B2: rat,C: rat,D2: rat] :
% 2.86/3.11 ( ( ( A2 != B2 )
% 2.86/3.11 & ( C != D2 ) )
% 2.86/3.11 = ( ( plus_plus_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B2 @ D2 ) )
% 2.86/3.11 != ( plus_plus_rat @ ( times_times_rat @ A2 @ D2 ) @ ( times_times_rat @ B2 @ C ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % crossproduct_noteq
% 2.86/3.11 thf(fact_3740_crossproduct__noteq,axiom,
% 2.86/3.11 ! [A2: nat,B2: nat,C: nat,D2: nat] :
% 2.86/3.11 ( ( ( A2 != B2 )
% 2.86/3.11 & ( C != D2 ) )
% 2.86/3.11 = ( ( plus_plus_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B2 @ D2 ) )
% 2.86/3.11 != ( plus_plus_nat @ ( times_times_nat @ A2 @ D2 ) @ ( times_times_nat @ B2 @ C ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % crossproduct_noteq
% 2.86/3.11 thf(fact_3741_crossproduct__noteq,axiom,
% 2.86/3.11 ! [A2: int,B2: int,C: int,D2: int] :
% 2.86/3.11 ( ( ( A2 != B2 )
% 2.86/3.11 & ( C != D2 ) )
% 2.86/3.11 = ( ( plus_plus_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B2 @ D2 ) )
% 2.86/3.11 != ( plus_plus_int @ ( times_times_int @ A2 @ D2 ) @ ( times_times_int @ B2 @ C ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % crossproduct_noteq
% 2.86/3.11 thf(fact_3742_nth__step__trancl,axiom,
% 2.86/3.11 ! [Xs: list_s1210847774152347623at_nat,R: set_Pr4329608150637261639at_nat,N: nat,M2: nat] :
% 2.86/3.11 ( ! [N5: nat] :
% 2.86/3.11 ( ( ord_less_nat @ N5 @ ( minus_minus_nat @ ( size_s8736152011456118867at_nat @ Xs ) @ one_one_nat ) )
% 2.86/3.11 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( nth_se5679702624988424552at_nat @ Xs @ ( suc @ N5 ) ) @ ( nth_se5679702624988424552at_nat @ Xs @ N5 ) ) @ R ) )
% 2.86/3.11 => ( ( ord_less_nat @ N @ ( size_s8736152011456118867at_nat @ Xs ) )
% 2.86/3.11 => ( ( ord_less_nat @ M2 @ N )
% 2.86/3.11 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( nth_se5679702624988424552at_nat @ Xs @ N ) @ ( nth_se5679702624988424552at_nat @ Xs @ M2 ) ) @ ( transi2703068831062848130at_nat @ R ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % nth_step_trancl
% 2.86/3.11 thf(fact_3743_nth__step__trancl,axiom,
% 2.86/3.11 ! [Xs: list_c,R: set_Product_prod_c_c,N: nat,M2: nat] :
% 2.86/3.11 ( ! [N5: nat] :
% 2.86/3.11 ( ( ord_less_nat @ N5 @ ( minus_minus_nat @ ( size_size_list_c @ Xs ) @ one_one_nat ) )
% 2.86/3.11 => ( member5074992359041316560od_c_c @ ( product_Pair_c_c @ ( nth_c @ Xs @ ( suc @ N5 ) ) @ ( nth_c @ Xs @ N5 ) ) @ R ) )
% 2.86/3.11 => ( ( ord_less_nat @ N @ ( size_size_list_c @ Xs ) )
% 2.86/3.11 => ( ( ord_less_nat @ M2 @ N )
% 2.86/3.11 => ( member5074992359041316560od_c_c @ ( product_Pair_c_c @ ( nth_c @ Xs @ N ) @ ( nth_c @ Xs @ M2 ) ) @ ( transitive_trancl_c @ R ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % nth_step_trancl
% 2.86/3.11 thf(fact_3744_nth__step__trancl,axiom,
% 2.86/3.11 ! [Xs: list_d,R: set_Product_prod_d_d,N: nat,M2: nat] :
% 2.86/3.11 ( ! [N5: nat] :
% 2.86/3.11 ( ( ord_less_nat @ N5 @ ( minus_minus_nat @ ( size_size_list_d @ Xs ) @ one_one_nat ) )
% 2.86/3.11 => ( member2287536781371869328od_d_d @ ( product_Pair_d_d @ ( nth_d @ Xs @ ( suc @ N5 ) ) @ ( nth_d @ Xs @ N5 ) ) @ R ) )
% 2.86/3.11 => ( ( ord_less_nat @ N @ ( size_size_list_d @ Xs ) )
% 2.86/3.11 => ( ( ord_less_nat @ M2 @ N )
% 2.86/3.11 => ( member2287536781371869328od_d_d @ ( product_Pair_d_d @ ( nth_d @ Xs @ N ) @ ( nth_d @ Xs @ M2 ) ) @ ( transitive_trancl_d @ R ) ) ) ) ) ).
% 2.86/3.11
% 2.86/3.11 % nth_step_trancl
% 2.86/3.11 thf(fact_3745_nth__step__trancl,axiom,
% 2.86/3.11 ! [Xs: list_int,R: set_Pr958786334691620121nt_int,N: nat,M2: nat] :
% 2.86/3.11 ( ! [N5: nat] :
% 2.86/3.11 ( ( ord_less_nat @ N5 @ ( minus_minus_nat @ ( size_size_list_int @ Xs ) @ one_one_nat ) )
% 2.86/3.11 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( nth_int @ Xs @ ( suc @ N5 ) ) @ ( nth_int @ Xs @ N5 ) ) @ R ) )
% 2.86/3.12 => ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 2.86/3.12 => ( ( ord_less_nat @ M2 @ N )
% 2.86/3.12 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( nth_int @ Xs @ N ) @ ( nth_int @ Xs @ M2 ) ) @ ( transi6261509568448316235cl_int @ R ) ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % nth_step_trancl
% 2.86/3.12 thf(fact_3746_nth__step__trancl,axiom,
% 2.86/3.12 ! [Xs: list_nat,R: set_Pr1261947904930325089at_nat,N: nat,M2: nat] :
% 2.86/3.12 ( ! [N5: nat] :
% 2.86/3.12 ( ( ord_less_nat @ N5 @ ( minus_minus_nat @ ( size_size_list_nat @ Xs ) @ one_one_nat ) )
% 2.86/3.12 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( nth_nat @ Xs @ ( suc @ N5 ) ) @ ( nth_nat @ Xs @ N5 ) ) @ R ) )
% 2.86/3.12 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 2.86/3.12 => ( ( ord_less_nat @ M2 @ N )
% 2.86/3.12 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( nth_nat @ Xs @ N ) @ ( nth_nat @ Xs @ M2 ) ) @ ( transi6264000038957366511cl_nat @ R ) ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % nth_step_trancl
% 2.86/3.12 thf(fact_3747_dbl__dec__def,axiom,
% 2.86/3.12 ( neg_nu7757733837767384882nteger
% 2.86/3.12 = ( ^ [X2: code_integer] : ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ X2 @ X2 ) @ one_one_Code_integer ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % dbl_dec_def
% 2.86/3.12 thf(fact_3748_dbl__dec__def,axiom,
% 2.86/3.12 ( neg_nu3179335615603231917ec_rat
% 2.86/3.12 = ( ^ [X2: rat] : ( minus_minus_rat @ ( plus_plus_rat @ X2 @ X2 ) @ one_one_rat ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % dbl_dec_def
% 2.86/3.12 thf(fact_3749_dbl__dec__def,axiom,
% 2.86/3.12 ( neg_nu3811975205180677377ec_int
% 2.86/3.12 = ( ^ [X2: int] : ( minus_minus_int @ ( plus_plus_int @ X2 @ X2 ) @ one_one_int ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % dbl_dec_def
% 2.86/3.12 thf(fact_3750_le__zero__eq,axiom,
% 2.86/3.12 ! [N: nat] :
% 2.86/3.12 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 2.86/3.12 = ( N = zero_zero_nat ) ) ).
% 2.86/3.12
% 2.86/3.12 % le_zero_eq
% 2.86/3.12 thf(fact_3751_not__gr__zero,axiom,
% 2.86/3.12 ! [N: nat] :
% 2.86/3.12 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 2.86/3.12 = ( N = zero_zero_nat ) ) ).
% 2.86/3.12
% 2.86/3.12 % not_gr_zero
% 2.86/3.12 thf(fact_3752_add_Oright__neutral,axiom,
% 2.86/3.12 ! [A2: code_integer] :
% 2.86/3.12 ( ( plus_p5714425477246183910nteger @ A2 @ zero_z3403309356797280102nteger )
% 2.86/3.12 = A2 ) ).
% 2.86/3.12
% 2.86/3.12 % add.right_neutral
% 2.86/3.12 thf(fact_3753_add_Oright__neutral,axiom,
% 2.86/3.12 ! [A2: multis2468970476368604999at_nat] :
% 2.86/3.12 ( ( plus_p7104986032573967614at_nat @ A2 @ zero_z1048942125864253310at_nat )
% 2.86/3.12 = A2 ) ).
% 2.86/3.12
% 2.86/3.12 % add.right_neutral
% 2.86/3.12 thf(fact_3754_add_Oright__neutral,axiom,
% 2.86/3.12 ! [A2: rat] :
% 2.86/3.12 ( ( plus_plus_rat @ A2 @ zero_zero_rat )
% 2.86/3.12 = A2 ) ).
% 2.86/3.12
% 2.86/3.12 % add.right_neutral
% 2.86/3.12 thf(fact_3755_add_Oright__neutral,axiom,
% 2.86/3.12 ! [A2: nat] :
% 2.86/3.12 ( ( plus_plus_nat @ A2 @ zero_zero_nat )
% 2.86/3.12 = A2 ) ).
% 2.86/3.12
% 2.86/3.12 % add.right_neutral
% 2.86/3.12 thf(fact_3756_add_Oright__neutral,axiom,
% 2.86/3.12 ! [A2: int] :
% 2.86/3.12 ( ( plus_plus_int @ A2 @ zero_zero_int )
% 2.86/3.12 = A2 ) ).
% 2.86/3.12
% 2.86/3.12 % add.right_neutral
% 2.86/3.12 thf(fact_3757_double__zero__sym,axiom,
% 2.86/3.12 ! [A2: code_integer] :
% 2.86/3.12 ( ( zero_z3403309356797280102nteger
% 2.86/3.12 = ( plus_p5714425477246183910nteger @ A2 @ A2 ) )
% 2.86/3.12 = ( A2 = zero_z3403309356797280102nteger ) ) ).
% 2.86/3.12
% 2.86/3.12 % double_zero_sym
% 2.86/3.12 thf(fact_3758_double__zero__sym,axiom,
% 2.86/3.12 ! [A2: rat] :
% 2.86/3.12 ( ( zero_zero_rat
% 2.86/3.12 = ( plus_plus_rat @ A2 @ A2 ) )
% 2.86/3.12 = ( A2 = zero_zero_rat ) ) ).
% 2.86/3.12
% 2.86/3.12 % double_zero_sym
% 2.86/3.12 thf(fact_3759_double__zero__sym,axiom,
% 2.86/3.12 ! [A2: int] :
% 2.86/3.12 ( ( zero_zero_int
% 2.86/3.12 = ( plus_plus_int @ A2 @ A2 ) )
% 2.86/3.12 = ( A2 = zero_zero_int ) ) ).
% 2.86/3.12
% 2.86/3.12 % double_zero_sym
% 2.86/3.12 thf(fact_3760_add__cancel__left__left,axiom,
% 2.86/3.12 ! [B2: code_integer,A2: code_integer] :
% 2.86/3.12 ( ( ( plus_p5714425477246183910nteger @ B2 @ A2 )
% 2.86/3.12 = A2 )
% 2.86/3.12 = ( B2 = zero_z3403309356797280102nteger ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_cancel_left_left
% 2.86/3.12 thf(fact_3761_add__cancel__left__left,axiom,
% 2.86/3.12 ! [B2: multis2468970476368604999at_nat,A2: multis2468970476368604999at_nat] :
% 2.86/3.12 ( ( ( plus_p7104986032573967614at_nat @ B2 @ A2 )
% 2.86/3.12 = A2 )
% 2.86/3.12 = ( B2 = zero_z1048942125864253310at_nat ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_cancel_left_left
% 2.86/3.12 thf(fact_3762_add__cancel__left__left,axiom,
% 2.86/3.12 ! [B2: rat,A2: rat] :
% 2.86/3.12 ( ( ( plus_plus_rat @ B2 @ A2 )
% 2.86/3.12 = A2 )
% 2.86/3.12 = ( B2 = zero_zero_rat ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_cancel_left_left
% 2.86/3.12 thf(fact_3763_add__cancel__left__left,axiom,
% 2.86/3.12 ! [B2: nat,A2: nat] :
% 2.86/3.12 ( ( ( plus_plus_nat @ B2 @ A2 )
% 2.86/3.12 = A2 )
% 2.86/3.12 = ( B2 = zero_zero_nat ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_cancel_left_left
% 2.86/3.12 thf(fact_3764_add__cancel__left__left,axiom,
% 2.86/3.12 ! [B2: int,A2: int] :
% 2.86/3.12 ( ( ( plus_plus_int @ B2 @ A2 )
% 2.86/3.12 = A2 )
% 2.86/3.12 = ( B2 = zero_zero_int ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_cancel_left_left
% 2.86/3.12 thf(fact_3765_add__cancel__left__right,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ( plus_p5714425477246183910nteger @ A2 @ B2 )
% 2.86/3.12 = A2 )
% 2.86/3.12 = ( B2 = zero_z3403309356797280102nteger ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_cancel_left_right
% 2.86/3.12 thf(fact_3766_add__cancel__left__right,axiom,
% 2.86/3.12 ! [A2: multis2468970476368604999at_nat,B2: multis2468970476368604999at_nat] :
% 2.86/3.12 ( ( ( plus_p7104986032573967614at_nat @ A2 @ B2 )
% 2.86/3.12 = A2 )
% 2.86/3.12 = ( B2 = zero_z1048942125864253310at_nat ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_cancel_left_right
% 2.86/3.12 thf(fact_3767_add__cancel__left__right,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat] :
% 2.86/3.12 ( ( ( plus_plus_rat @ A2 @ B2 )
% 2.86/3.12 = A2 )
% 2.86/3.12 = ( B2 = zero_zero_rat ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_cancel_left_right
% 2.86/3.12 thf(fact_3768_add__cancel__left__right,axiom,
% 2.86/3.12 ! [A2: nat,B2: nat] :
% 2.86/3.12 ( ( ( plus_plus_nat @ A2 @ B2 )
% 2.86/3.12 = A2 )
% 2.86/3.12 = ( B2 = zero_zero_nat ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_cancel_left_right
% 2.86/3.12 thf(fact_3769_add__cancel__left__right,axiom,
% 2.86/3.12 ! [A2: int,B2: int] :
% 2.86/3.12 ( ( ( plus_plus_int @ A2 @ B2 )
% 2.86/3.12 = A2 )
% 2.86/3.12 = ( B2 = zero_zero_int ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_cancel_left_right
% 2.86/3.12 thf(fact_3770_add__cancel__right__left,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( A2
% 2.86/3.12 = ( plus_p5714425477246183910nteger @ B2 @ A2 ) )
% 2.86/3.12 = ( B2 = zero_z3403309356797280102nteger ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_cancel_right_left
% 2.86/3.12 thf(fact_3771_add__cancel__right__left,axiom,
% 2.86/3.12 ! [A2: multis2468970476368604999at_nat,B2: multis2468970476368604999at_nat] :
% 2.86/3.12 ( ( A2
% 2.86/3.12 = ( plus_p7104986032573967614at_nat @ B2 @ A2 ) )
% 2.86/3.12 = ( B2 = zero_z1048942125864253310at_nat ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_cancel_right_left
% 2.86/3.12 thf(fact_3772_add__cancel__right__left,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat] :
% 2.86/3.12 ( ( A2
% 2.86/3.12 = ( plus_plus_rat @ B2 @ A2 ) )
% 2.86/3.12 = ( B2 = zero_zero_rat ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_cancel_right_left
% 2.86/3.12 thf(fact_3773_add__cancel__right__left,axiom,
% 2.86/3.12 ! [A2: nat,B2: nat] :
% 2.86/3.12 ( ( A2
% 2.86/3.12 = ( plus_plus_nat @ B2 @ A2 ) )
% 2.86/3.12 = ( B2 = zero_zero_nat ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_cancel_right_left
% 2.86/3.12 thf(fact_3774_add__cancel__right__left,axiom,
% 2.86/3.12 ! [A2: int,B2: int] :
% 2.86/3.12 ( ( A2
% 2.86/3.12 = ( plus_plus_int @ B2 @ A2 ) )
% 2.86/3.12 = ( B2 = zero_zero_int ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_cancel_right_left
% 2.86/3.12 thf(fact_3775_add__cancel__right__right,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( A2
% 2.86/3.12 = ( plus_p5714425477246183910nteger @ A2 @ B2 ) )
% 2.86/3.12 = ( B2 = zero_z3403309356797280102nteger ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_cancel_right_right
% 2.86/3.12 thf(fact_3776_add__cancel__right__right,axiom,
% 2.86/3.12 ! [A2: multis2468970476368604999at_nat,B2: multis2468970476368604999at_nat] :
% 2.86/3.12 ( ( A2
% 2.86/3.12 = ( plus_p7104986032573967614at_nat @ A2 @ B2 ) )
% 2.86/3.12 = ( B2 = zero_z1048942125864253310at_nat ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_cancel_right_right
% 2.86/3.12 thf(fact_3777_add__cancel__right__right,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat] :
% 2.86/3.12 ( ( A2
% 2.86/3.12 = ( plus_plus_rat @ A2 @ B2 ) )
% 2.86/3.12 = ( B2 = zero_zero_rat ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_cancel_right_right
% 2.86/3.12 thf(fact_3778_add__cancel__right__right,axiom,
% 2.86/3.12 ! [A2: nat,B2: nat] :
% 2.86/3.12 ( ( A2
% 2.86/3.12 = ( plus_plus_nat @ A2 @ B2 ) )
% 2.86/3.12 = ( B2 = zero_zero_nat ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_cancel_right_right
% 2.86/3.12 thf(fact_3779_add__cancel__right__right,axiom,
% 2.86/3.12 ! [A2: int,B2: int] :
% 2.86/3.12 ( ( A2
% 2.86/3.12 = ( plus_plus_int @ A2 @ B2 ) )
% 2.86/3.12 = ( B2 = zero_zero_int ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_cancel_right_right
% 2.86/3.12 thf(fact_3780_add__eq__0__iff__both__eq__0,axiom,
% 2.86/3.12 ! [X: nat,Y: nat] :
% 2.86/3.12 ( ( ( plus_plus_nat @ X @ Y )
% 2.86/3.12 = zero_zero_nat )
% 2.86/3.12 = ( ( X = zero_zero_nat )
% 2.86/3.12 & ( Y = zero_zero_nat ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_eq_0_iff_both_eq_0
% 2.86/3.12 thf(fact_3781_zero__eq__add__iff__both__eq__0,axiom,
% 2.86/3.12 ! [X: nat,Y: nat] :
% 2.86/3.12 ( ( zero_zero_nat
% 2.86/3.12 = ( plus_plus_nat @ X @ Y ) )
% 2.86/3.12 = ( ( X = zero_zero_nat )
% 2.86/3.12 & ( Y = zero_zero_nat ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % zero_eq_add_iff_both_eq_0
% 2.86/3.12 thf(fact_3782_add__0,axiom,
% 2.86/3.12 ! [A2: code_integer] :
% 2.86/3.12 ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ A2 )
% 2.86/3.12 = A2 ) ).
% 2.86/3.12
% 2.86/3.12 % add_0
% 2.86/3.12 thf(fact_3783_add__0,axiom,
% 2.86/3.12 ! [A2: multis2468970476368604999at_nat] :
% 2.86/3.12 ( ( plus_p7104986032573967614at_nat @ zero_z1048942125864253310at_nat @ A2 )
% 2.86/3.12 = A2 ) ).
% 2.86/3.12
% 2.86/3.12 % add_0
% 2.86/3.12 thf(fact_3784_add__0,axiom,
% 2.86/3.12 ! [A2: rat] :
% 2.86/3.12 ( ( plus_plus_rat @ zero_zero_rat @ A2 )
% 2.86/3.12 = A2 ) ).
% 2.86/3.12
% 2.86/3.12 % add_0
% 2.86/3.12 thf(fact_3785_add__0,axiom,
% 2.86/3.12 ! [A2: nat] :
% 2.86/3.12 ( ( plus_plus_nat @ zero_zero_nat @ A2 )
% 2.86/3.12 = A2 ) ).
% 2.86/3.12
% 2.86/3.12 % add_0
% 2.86/3.12 thf(fact_3786_add__0,axiom,
% 2.86/3.12 ! [A2: int] :
% 2.86/3.12 ( ( plus_plus_int @ zero_zero_int @ A2 )
% 2.86/3.12 = A2 ) ).
% 2.86/3.12
% 2.86/3.12 % add_0
% 2.86/3.12 thf(fact_3787_mult__cancel__right,axiom,
% 2.86/3.12 ! [A2: code_integer,C: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ( times_3573771949741848930nteger @ A2 @ C )
% 2.86/3.12 = ( times_3573771949741848930nteger @ B2 @ C ) )
% 2.86/3.12 = ( ( C = zero_z3403309356797280102nteger )
% 2.86/3.12 | ( A2 = B2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_cancel_right
% 2.86/3.12 thf(fact_3788_mult__cancel__right,axiom,
% 2.86/3.12 ! [A2: rat,C: rat,B2: rat] :
% 2.86/3.12 ( ( ( times_times_rat @ A2 @ C )
% 2.86/3.12 = ( times_times_rat @ B2 @ C ) )
% 2.86/3.12 = ( ( C = zero_zero_rat )
% 2.86/3.12 | ( A2 = B2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_cancel_right
% 2.86/3.12 thf(fact_3789_mult__cancel__right,axiom,
% 2.86/3.12 ! [A2: nat,C: nat,B2: nat] :
% 2.86/3.12 ( ( ( times_times_nat @ A2 @ C )
% 2.86/3.12 = ( times_times_nat @ B2 @ C ) )
% 2.86/3.12 = ( ( C = zero_zero_nat )
% 2.86/3.12 | ( A2 = B2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_cancel_right
% 2.86/3.12 thf(fact_3790_mult__cancel__right,axiom,
% 2.86/3.12 ! [A2: int,C: int,B2: int] :
% 2.86/3.12 ( ( ( times_times_int @ A2 @ C )
% 2.86/3.12 = ( times_times_int @ B2 @ C ) )
% 2.86/3.12 = ( ( C = zero_zero_int )
% 2.86/3.12 | ( A2 = B2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_cancel_right
% 2.86/3.12 thf(fact_3791_mult__cancel__left,axiom,
% 2.86/3.12 ! [C: code_integer,A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ( times_3573771949741848930nteger @ C @ A2 )
% 2.86/3.12 = ( times_3573771949741848930nteger @ C @ B2 ) )
% 2.86/3.12 = ( ( C = zero_z3403309356797280102nteger )
% 2.86/3.12 | ( A2 = B2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_cancel_left
% 2.86/3.12 thf(fact_3792_mult__cancel__left,axiom,
% 2.86/3.12 ! [C: rat,A2: rat,B2: rat] :
% 2.86/3.12 ( ( ( times_times_rat @ C @ A2 )
% 2.86/3.12 = ( times_times_rat @ C @ B2 ) )
% 2.86/3.12 = ( ( C = zero_zero_rat )
% 2.86/3.12 | ( A2 = B2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_cancel_left
% 2.86/3.12 thf(fact_3793_mult__cancel__left,axiom,
% 2.86/3.12 ! [C: nat,A2: nat,B2: nat] :
% 2.86/3.12 ( ( ( times_times_nat @ C @ A2 )
% 2.86/3.12 = ( times_times_nat @ C @ B2 ) )
% 2.86/3.12 = ( ( C = zero_zero_nat )
% 2.86/3.12 | ( A2 = B2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_cancel_left
% 2.86/3.12 thf(fact_3794_mult__cancel__left,axiom,
% 2.86/3.12 ! [C: int,A2: int,B2: int] :
% 2.86/3.12 ( ( ( times_times_int @ C @ A2 )
% 2.86/3.12 = ( times_times_int @ C @ B2 ) )
% 2.86/3.12 = ( ( C = zero_zero_int )
% 2.86/3.12 | ( A2 = B2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_cancel_left
% 2.86/3.12 thf(fact_3795_mult__eq__0__iff,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ( times_3573771949741848930nteger @ A2 @ B2 )
% 2.86/3.12 = zero_z3403309356797280102nteger )
% 2.86/3.12 = ( ( A2 = zero_z3403309356797280102nteger )
% 2.86/3.12 | ( B2 = zero_z3403309356797280102nteger ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_eq_0_iff
% 2.86/3.12 thf(fact_3796_mult__eq__0__iff,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat] :
% 2.86/3.12 ( ( ( times_times_rat @ A2 @ B2 )
% 2.86/3.12 = zero_zero_rat )
% 2.86/3.12 = ( ( A2 = zero_zero_rat )
% 2.86/3.12 | ( B2 = zero_zero_rat ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_eq_0_iff
% 2.86/3.12 thf(fact_3797_mult__eq__0__iff,axiom,
% 2.86/3.12 ! [A2: nat,B2: nat] :
% 2.86/3.12 ( ( ( times_times_nat @ A2 @ B2 )
% 2.86/3.12 = zero_zero_nat )
% 2.86/3.12 = ( ( A2 = zero_zero_nat )
% 2.86/3.12 | ( B2 = zero_zero_nat ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_eq_0_iff
% 2.86/3.12 thf(fact_3798_mult__eq__0__iff,axiom,
% 2.86/3.12 ! [A2: int,B2: int] :
% 2.86/3.12 ( ( ( times_times_int @ A2 @ B2 )
% 2.86/3.12 = zero_zero_int )
% 2.86/3.12 = ( ( A2 = zero_zero_int )
% 2.86/3.12 | ( B2 = zero_zero_int ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_eq_0_iff
% 2.86/3.12 thf(fact_3799_mult__zero__right,axiom,
% 2.86/3.12 ! [A2: code_integer] :
% 2.86/3.12 ( ( times_3573771949741848930nteger @ A2 @ zero_z3403309356797280102nteger )
% 2.86/3.12 = zero_z3403309356797280102nteger ) ).
% 2.86/3.12
% 2.86/3.12 % mult_zero_right
% 2.86/3.12 thf(fact_3800_mult__zero__right,axiom,
% 2.86/3.12 ! [A2: rat] :
% 2.86/3.12 ( ( times_times_rat @ A2 @ zero_zero_rat )
% 2.86/3.12 = zero_zero_rat ) ).
% 2.86/3.12
% 2.86/3.12 % mult_zero_right
% 2.86/3.12 thf(fact_3801_mult__zero__right,axiom,
% 2.86/3.12 ! [A2: nat] :
% 2.86/3.12 ( ( times_times_nat @ A2 @ zero_zero_nat )
% 2.86/3.12 = zero_zero_nat ) ).
% 2.86/3.12
% 2.86/3.12 % mult_zero_right
% 2.86/3.12 thf(fact_3802_mult__zero__right,axiom,
% 2.86/3.12 ! [A2: int] :
% 2.86/3.12 ( ( times_times_int @ A2 @ zero_zero_int )
% 2.86/3.12 = zero_zero_int ) ).
% 2.86/3.12
% 2.86/3.12 % mult_zero_right
% 2.86/3.12 thf(fact_3803_mult__zero__left,axiom,
% 2.86/3.12 ! [A2: code_integer] :
% 2.86/3.12 ( ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger @ A2 )
% 2.86/3.12 = zero_z3403309356797280102nteger ) ).
% 2.86/3.12
% 2.86/3.12 % mult_zero_left
% 2.86/3.12 thf(fact_3804_mult__zero__left,axiom,
% 2.86/3.12 ! [A2: rat] :
% 2.86/3.12 ( ( times_times_rat @ zero_zero_rat @ A2 )
% 2.86/3.12 = zero_zero_rat ) ).
% 2.86/3.12
% 2.86/3.12 % mult_zero_left
% 2.86/3.12 thf(fact_3805_mult__zero__left,axiom,
% 2.86/3.12 ! [A2: nat] :
% 2.86/3.12 ( ( times_times_nat @ zero_zero_nat @ A2 )
% 2.86/3.12 = zero_zero_nat ) ).
% 2.86/3.12
% 2.86/3.12 % mult_zero_left
% 2.86/3.12 thf(fact_3806_mult__zero__left,axiom,
% 2.86/3.12 ! [A2: int] :
% 2.86/3.12 ( ( times_times_int @ zero_zero_int @ A2 )
% 2.86/3.12 = zero_zero_int ) ).
% 2.86/3.12
% 2.86/3.12 % mult_zero_left
% 2.86/3.12 thf(fact_3807_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 2.86/3.12 ! [A2: code_integer] :
% 2.86/3.12 ( ( minus_8373710615458151222nteger @ A2 @ A2 )
% 2.86/3.12 = zero_z3403309356797280102nteger ) ).
% 2.86/3.12
% 2.86/3.12 % cancel_comm_monoid_add_class.diff_cancel
% 2.86/3.12 thf(fact_3808_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 2.86/3.12 ! [A2: multis2468970476368604999at_nat] :
% 2.86/3.12 ( ( minus_4286766774447292334at_nat @ A2 @ A2 )
% 2.86/3.12 = zero_z1048942125864253310at_nat ) ).
% 2.86/3.12
% 2.86/3.12 % cancel_comm_monoid_add_class.diff_cancel
% 2.86/3.12 thf(fact_3809_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 2.86/3.12 ! [A2: rat] :
% 2.86/3.12 ( ( minus_minus_rat @ A2 @ A2 )
% 2.86/3.12 = zero_zero_rat ) ).
% 2.86/3.12
% 2.86/3.12 % cancel_comm_monoid_add_class.diff_cancel
% 2.86/3.12 thf(fact_3810_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 2.86/3.12 ! [A2: nat] :
% 2.86/3.12 ( ( minus_minus_nat @ A2 @ A2 )
% 2.86/3.12 = zero_zero_nat ) ).
% 2.86/3.12
% 2.86/3.12 % cancel_comm_monoid_add_class.diff_cancel
% 2.86/3.12 thf(fact_3811_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 2.86/3.12 ! [A2: int] :
% 2.86/3.12 ( ( minus_minus_int @ A2 @ A2 )
% 2.86/3.12 = zero_zero_int ) ).
% 2.86/3.12
% 2.86/3.12 % cancel_comm_monoid_add_class.diff_cancel
% 2.86/3.12 thf(fact_3812_diff__zero,axiom,
% 2.86/3.12 ! [A2: code_integer] :
% 2.86/3.12 ( ( minus_8373710615458151222nteger @ A2 @ zero_z3403309356797280102nteger )
% 2.86/3.12 = A2 ) ).
% 2.86/3.12
% 2.86/3.12 % diff_zero
% 2.86/3.12 thf(fact_3813_diff__zero,axiom,
% 2.86/3.12 ! [A2: multis2468970476368604999at_nat] :
% 2.86/3.12 ( ( minus_4286766774447292334at_nat @ A2 @ zero_z1048942125864253310at_nat )
% 2.86/3.12 = A2 ) ).
% 2.86/3.12
% 2.86/3.12 % diff_zero
% 2.86/3.12 thf(fact_3814_diff__zero,axiom,
% 2.86/3.12 ! [A2: rat] :
% 2.86/3.12 ( ( minus_minus_rat @ A2 @ zero_zero_rat )
% 2.86/3.12 = A2 ) ).
% 2.86/3.12
% 2.86/3.12 % diff_zero
% 2.86/3.12 thf(fact_3815_diff__zero,axiom,
% 2.86/3.12 ! [A2: nat] :
% 2.86/3.12 ( ( minus_minus_nat @ A2 @ zero_zero_nat )
% 2.86/3.12 = A2 ) ).
% 2.86/3.12
% 2.86/3.12 % diff_zero
% 2.86/3.12 thf(fact_3816_diff__zero,axiom,
% 2.86/3.12 ! [A2: int] :
% 2.86/3.12 ( ( minus_minus_int @ A2 @ zero_zero_int )
% 2.86/3.12 = A2 ) ).
% 2.86/3.12
% 2.86/3.12 % diff_zero
% 2.86/3.12 thf(fact_3817_zero__diff,axiom,
% 2.86/3.12 ! [A2: multis2468970476368604999at_nat] :
% 2.86/3.12 ( ( minus_4286766774447292334at_nat @ zero_z1048942125864253310at_nat @ A2 )
% 2.86/3.12 = zero_z1048942125864253310at_nat ) ).
% 2.86/3.12
% 2.86/3.12 % zero_diff
% 2.86/3.12 thf(fact_3818_zero__diff,axiom,
% 2.86/3.12 ! [A2: nat] :
% 2.86/3.12 ( ( minus_minus_nat @ zero_zero_nat @ A2 )
% 2.86/3.12 = zero_zero_nat ) ).
% 2.86/3.12
% 2.86/3.12 % zero_diff
% 2.86/3.12 thf(fact_3819_diff__0__right,axiom,
% 2.86/3.12 ! [A2: code_integer] :
% 2.86/3.12 ( ( minus_8373710615458151222nteger @ A2 @ zero_z3403309356797280102nteger )
% 2.86/3.12 = A2 ) ).
% 2.86/3.12
% 2.86/3.12 % diff_0_right
% 2.86/3.12 thf(fact_3820_diff__0__right,axiom,
% 2.86/3.12 ! [A2: rat] :
% 2.86/3.12 ( ( minus_minus_rat @ A2 @ zero_zero_rat )
% 2.86/3.12 = A2 ) ).
% 2.86/3.12
% 2.86/3.12 % diff_0_right
% 2.86/3.12 thf(fact_3821_diff__0__right,axiom,
% 2.86/3.12 ! [A2: int] :
% 2.86/3.12 ( ( minus_minus_int @ A2 @ zero_zero_int )
% 2.86/3.12 = A2 ) ).
% 2.86/3.12
% 2.86/3.12 % diff_0_right
% 2.86/3.12 thf(fact_3822_diff__self,axiom,
% 2.86/3.12 ! [A2: code_integer] :
% 2.86/3.12 ( ( minus_8373710615458151222nteger @ A2 @ A2 )
% 2.86/3.12 = zero_z3403309356797280102nteger ) ).
% 2.86/3.12
% 2.86/3.12 % diff_self
% 2.86/3.12 thf(fact_3823_diff__self,axiom,
% 2.86/3.12 ! [A2: rat] :
% 2.86/3.12 ( ( minus_minus_rat @ A2 @ A2 )
% 2.86/3.12 = zero_zero_rat ) ).
% 2.86/3.12
% 2.86/3.12 % diff_self
% 2.86/3.12 thf(fact_3824_diff__self,axiom,
% 2.86/3.12 ! [A2: int] :
% 2.86/3.12 ( ( minus_minus_int @ A2 @ A2 )
% 2.86/3.12 = zero_zero_int ) ).
% 2.86/3.12
% 2.86/3.12 % diff_self
% 2.86/3.12 thf(fact_3825_less__nat__zero__code,axiom,
% 2.86/3.12 ! [N: nat] :
% 2.86/3.12 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 2.86/3.12
% 2.86/3.12 % less_nat_zero_code
% 2.86/3.12 thf(fact_3826_neq0__conv,axiom,
% 2.86/3.12 ! [N: nat] :
% 2.86/3.12 ( ( N != zero_zero_nat )
% 2.86/3.12 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 2.86/3.12
% 2.86/3.12 % neq0_conv
% 2.86/3.12 thf(fact_3827_bot__nat__0_Onot__eq__extremum,axiom,
% 2.86/3.12 ! [A2: nat] :
% 2.86/3.12 ( ( A2 != zero_zero_nat )
% 2.86/3.12 = ( ord_less_nat @ zero_zero_nat @ A2 ) ) ).
% 2.86/3.12
% 2.86/3.12 % bot_nat_0.not_eq_extremum
% 2.86/3.12 thf(fact_3828_trancl__single,axiom,
% 2.86/3.12 ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 2.86/3.12 ( ( transi2703068831062848130at_nat @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ A2 @ B2 ) @ bot_bo228742789529271731at_nat ) )
% 2.86/3.12 = ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ A2 @ B2 ) @ bot_bo228742789529271731at_nat ) ) ).
% 2.86/3.12
% 2.86/3.12 % trancl_single
% 2.86/3.12 thf(fact_3829_trancl__single,axiom,
% 2.86/3.12 ! [A2: nat,B2: nat] :
% 2.86/3.12 ( ( transi6264000038957366511cl_nat @ ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ A2 @ B2 ) @ bot_bo2099793752762293965at_nat ) )
% 2.86/3.12 = ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ A2 @ B2 ) @ bot_bo2099793752762293965at_nat ) ) ).
% 2.86/3.12
% 2.86/3.12 % trancl_single
% 2.86/3.12 thf(fact_3830_add__le__same__cancel1,axiom,
% 2.86/3.12 ! [B2: code_integer,A2: code_integer] :
% 2.86/3.12 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ B2 @ A2 ) @ B2 )
% 2.86/3.12 = ( ord_le3102999989581377725nteger @ A2 @ zero_z3403309356797280102nteger ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_le_same_cancel1
% 2.86/3.12 thf(fact_3831_add__le__same__cancel1,axiom,
% 2.86/3.12 ! [B2: rat,A2: rat] :
% 2.86/3.12 ( ( ord_less_eq_rat @ ( plus_plus_rat @ B2 @ A2 ) @ B2 )
% 2.86/3.12 = ( ord_less_eq_rat @ A2 @ zero_zero_rat ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_le_same_cancel1
% 2.86/3.12 thf(fact_3832_add__le__same__cancel1,axiom,
% 2.86/3.12 ! [B2: nat,A2: nat] :
% 2.86/3.12 ( ( ord_less_eq_nat @ ( plus_plus_nat @ B2 @ A2 ) @ B2 )
% 2.86/3.12 = ( ord_less_eq_nat @ A2 @ zero_zero_nat ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_le_same_cancel1
% 2.86/3.12 thf(fact_3833_add__le__same__cancel1,axiom,
% 2.86/3.12 ! [B2: int,A2: int] :
% 2.86/3.12 ( ( ord_less_eq_int @ ( plus_plus_int @ B2 @ A2 ) @ B2 )
% 2.86/3.12 = ( ord_less_eq_int @ A2 @ zero_zero_int ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_le_same_cancel1
% 2.86/3.12 thf(fact_3834_add__le__same__cancel2,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A2 @ B2 ) @ B2 )
% 2.86/3.12 = ( ord_le3102999989581377725nteger @ A2 @ zero_z3403309356797280102nteger ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_le_same_cancel2
% 2.86/3.12 thf(fact_3835_add__le__same__cancel2,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat] :
% 2.86/3.12 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A2 @ B2 ) @ B2 )
% 2.86/3.12 = ( ord_less_eq_rat @ A2 @ zero_zero_rat ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_le_same_cancel2
% 2.86/3.12 thf(fact_3836_add__le__same__cancel2,axiom,
% 2.86/3.12 ! [A2: nat,B2: nat] :
% 2.86/3.12 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ B2 ) @ B2 )
% 2.86/3.12 = ( ord_less_eq_nat @ A2 @ zero_zero_nat ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_le_same_cancel2
% 2.86/3.12 thf(fact_3837_add__le__same__cancel2,axiom,
% 2.86/3.12 ! [A2: int,B2: int] :
% 2.86/3.12 ( ( ord_less_eq_int @ ( plus_plus_int @ A2 @ B2 ) @ B2 )
% 2.86/3.12 = ( ord_less_eq_int @ A2 @ zero_zero_int ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_le_same_cancel2
% 2.86/3.12 thf(fact_3838_le__add__same__cancel1,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ord_le3102999989581377725nteger @ A2 @ ( plus_p5714425477246183910nteger @ A2 @ B2 ) )
% 2.86/3.12 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B2 ) ) ).
% 2.86/3.12
% 2.86/3.12 % le_add_same_cancel1
% 2.86/3.12 thf(fact_3839_le__add__same__cancel1,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat] :
% 2.86/3.12 ( ( ord_less_eq_rat @ A2 @ ( plus_plus_rat @ A2 @ B2 ) )
% 2.86/3.12 = ( ord_less_eq_rat @ zero_zero_rat @ B2 ) ) ).
% 2.86/3.12
% 2.86/3.12 % le_add_same_cancel1
% 2.86/3.12 thf(fact_3840_le__add__same__cancel1,axiom,
% 2.86/3.12 ! [A2: nat,B2: nat] :
% 2.86/3.12 ( ( ord_less_eq_nat @ A2 @ ( plus_plus_nat @ A2 @ B2 ) )
% 2.86/3.12 = ( ord_less_eq_nat @ zero_zero_nat @ B2 ) ) ).
% 2.86/3.12
% 2.86/3.12 % le_add_same_cancel1
% 2.86/3.12 thf(fact_3841_le__add__same__cancel1,axiom,
% 2.86/3.12 ! [A2: int,B2: int] :
% 2.86/3.12 ( ( ord_less_eq_int @ A2 @ ( plus_plus_int @ A2 @ B2 ) )
% 2.86/3.12 = ( ord_less_eq_int @ zero_zero_int @ B2 ) ) ).
% 2.86/3.12
% 2.86/3.12 % le_add_same_cancel1
% 2.86/3.12 thf(fact_3842_le__add__same__cancel2,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ord_le3102999989581377725nteger @ A2 @ ( plus_p5714425477246183910nteger @ B2 @ A2 ) )
% 2.86/3.12 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B2 ) ) ).
% 2.86/3.12
% 2.86/3.12 % le_add_same_cancel2
% 2.86/3.12 thf(fact_3843_le__add__same__cancel2,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat] :
% 2.86/3.12 ( ( ord_less_eq_rat @ A2 @ ( plus_plus_rat @ B2 @ A2 ) )
% 2.86/3.12 = ( ord_less_eq_rat @ zero_zero_rat @ B2 ) ) ).
% 2.86/3.12
% 2.86/3.12 % le_add_same_cancel2
% 2.86/3.12 thf(fact_3844_le__add__same__cancel2,axiom,
% 2.86/3.12 ! [A2: nat,B2: nat] :
% 2.86/3.12 ( ( ord_less_eq_nat @ A2 @ ( plus_plus_nat @ B2 @ A2 ) )
% 2.86/3.12 = ( ord_less_eq_nat @ zero_zero_nat @ B2 ) ) ).
% 2.86/3.12
% 2.86/3.12 % le_add_same_cancel2
% 2.86/3.12 thf(fact_3845_le__add__same__cancel2,axiom,
% 2.86/3.12 ! [A2: int,B2: int] :
% 2.86/3.12 ( ( ord_less_eq_int @ A2 @ ( plus_plus_int @ B2 @ A2 ) )
% 2.86/3.12 = ( ord_less_eq_int @ zero_zero_int @ B2 ) ) ).
% 2.86/3.12
% 2.86/3.12 % le_add_same_cancel2
% 2.86/3.12 thf(fact_3846_double__add__le__zero__iff__single__add__le__zero,axiom,
% 2.86/3.12 ! [A2: code_integer] :
% 2.86/3.12 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A2 @ A2 ) @ zero_z3403309356797280102nteger )
% 2.86/3.12 = ( ord_le3102999989581377725nteger @ A2 @ zero_z3403309356797280102nteger ) ) ).
% 2.86/3.12
% 2.86/3.12 % double_add_le_zero_iff_single_add_le_zero
% 2.86/3.12 thf(fact_3847_double__add__le__zero__iff__single__add__le__zero,axiom,
% 2.86/3.12 ! [A2: rat] :
% 2.86/3.12 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A2 @ A2 ) @ zero_zero_rat )
% 2.86/3.12 = ( ord_less_eq_rat @ A2 @ zero_zero_rat ) ) ).
% 2.86/3.12
% 2.86/3.12 % double_add_le_zero_iff_single_add_le_zero
% 2.86/3.12 thf(fact_3848_double__add__le__zero__iff__single__add__le__zero,axiom,
% 2.86/3.12 ! [A2: int] :
% 2.86/3.12 ( ( ord_less_eq_int @ ( plus_plus_int @ A2 @ A2 ) @ zero_zero_int )
% 2.86/3.12 = ( ord_less_eq_int @ A2 @ zero_zero_int ) ) ).
% 2.86/3.12
% 2.86/3.12 % double_add_le_zero_iff_single_add_le_zero
% 2.86/3.12 thf(fact_3849_zero__le__double__add__iff__zero__le__single__add,axiom,
% 2.86/3.12 ! [A2: code_integer] :
% 2.86/3.12 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A2 @ A2 ) )
% 2.86/3.12 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 ) ) ).
% 2.86/3.12
% 2.86/3.12 % zero_le_double_add_iff_zero_le_single_add
% 2.86/3.12 thf(fact_3850_zero__le__double__add__iff__zero__le__single__add,axiom,
% 2.86/3.12 ! [A2: rat] :
% 2.86/3.12 ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A2 @ A2 ) )
% 2.86/3.12 = ( ord_less_eq_rat @ zero_zero_rat @ A2 ) ) ).
% 2.86/3.12
% 2.86/3.12 % zero_le_double_add_iff_zero_le_single_add
% 2.86/3.12 thf(fact_3851_zero__le__double__add__iff__zero__le__single__add,axiom,
% 2.86/3.12 ! [A2: int] :
% 2.86/3.12 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A2 @ A2 ) )
% 2.86/3.12 = ( ord_less_eq_int @ zero_zero_int @ A2 ) ) ).
% 2.86/3.12
% 2.86/3.12 % zero_le_double_add_iff_zero_le_single_add
% 2.86/3.12 thf(fact_3852_diff__ge__0__iff__ge,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ A2 @ B2 ) )
% 2.86/3.12 = ( ord_le3102999989581377725nteger @ B2 @ A2 ) ) ).
% 2.86/3.12
% 2.86/3.12 % diff_ge_0_iff_ge
% 2.86/3.12 thf(fact_3853_diff__ge__0__iff__ge,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat] :
% 2.86/3.12 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A2 @ B2 ) )
% 2.86/3.12 = ( ord_less_eq_rat @ B2 @ A2 ) ) ).
% 2.86/3.12
% 2.86/3.12 % diff_ge_0_iff_ge
% 2.86/3.12 thf(fact_3854_diff__ge__0__iff__ge,axiom,
% 2.86/3.12 ! [A2: int,B2: int] :
% 2.86/3.12 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A2 @ B2 ) )
% 2.86/3.12 = ( ord_less_eq_int @ B2 @ A2 ) ) ).
% 2.86/3.12
% 2.86/3.12 % diff_ge_0_iff_ge
% 2.86/3.12 thf(fact_3855_zero__comp__diff__simps_I1_J,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ A2 @ B2 ) )
% 2.86/3.12 = ( ord_le3102999989581377725nteger @ B2 @ A2 ) ) ).
% 2.86/3.12
% 2.86/3.12 % zero_comp_diff_simps(1)
% 2.86/3.12 thf(fact_3856_zero__comp__diff__simps_I1_J,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat] :
% 2.86/3.12 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A2 @ B2 ) )
% 2.86/3.12 = ( ord_less_eq_rat @ B2 @ A2 ) ) ).
% 2.86/3.12
% 2.86/3.12 % zero_comp_diff_simps(1)
% 2.86/3.12 thf(fact_3857_zero__comp__diff__simps_I1_J,axiom,
% 2.86/3.12 ! [A2: int,B2: int] :
% 2.86/3.12 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A2 @ B2 ) )
% 2.86/3.12 = ( ord_less_eq_int @ B2 @ A2 ) ) ).
% 2.86/3.12
% 2.86/3.12 % zero_comp_diff_simps(1)
% 2.86/3.12 thf(fact_3858_zero__less__double__add__iff__zero__less__single__add,axiom,
% 2.86/3.12 ! [A2: rat] :
% 2.86/3.12 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A2 @ A2 ) )
% 2.86/3.12 = ( ord_less_rat @ zero_zero_rat @ A2 ) ) ).
% 2.86/3.12
% 2.86/3.12 % zero_less_double_add_iff_zero_less_single_add
% 2.86/3.12 thf(fact_3859_zero__less__double__add__iff__zero__less__single__add,axiom,
% 2.86/3.12 ! [A2: code_integer] :
% 2.86/3.12 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A2 @ A2 ) )
% 2.86/3.12 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 ) ) ).
% 2.86/3.12
% 2.86/3.12 % zero_less_double_add_iff_zero_less_single_add
% 2.86/3.12 thf(fact_3860_zero__less__double__add__iff__zero__less__single__add,axiom,
% 2.86/3.12 ! [A2: int] :
% 2.86/3.12 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A2 @ A2 ) )
% 2.86/3.12 = ( ord_less_int @ zero_zero_int @ A2 ) ) ).
% 2.86/3.12
% 2.86/3.12 % zero_less_double_add_iff_zero_less_single_add
% 2.86/3.12 thf(fact_3861_double__add__less__zero__iff__single__add__less__zero,axiom,
% 2.86/3.12 ! [A2: rat] :
% 2.86/3.12 ( ( ord_less_rat @ ( plus_plus_rat @ A2 @ A2 ) @ zero_zero_rat )
% 2.86/3.12 = ( ord_less_rat @ A2 @ zero_zero_rat ) ) ).
% 2.86/3.12
% 2.86/3.12 % double_add_less_zero_iff_single_add_less_zero
% 2.86/3.12 thf(fact_3862_double__add__less__zero__iff__single__add__less__zero,axiom,
% 2.86/3.12 ! [A2: code_integer] :
% 2.86/3.12 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A2 @ A2 ) @ zero_z3403309356797280102nteger )
% 2.86/3.12 = ( ord_le6747313008572928689nteger @ A2 @ zero_z3403309356797280102nteger ) ) ).
% 2.86/3.12
% 2.86/3.12 % double_add_less_zero_iff_single_add_less_zero
% 2.86/3.12 thf(fact_3863_double__add__less__zero__iff__single__add__less__zero,axiom,
% 2.86/3.12 ! [A2: int] :
% 2.86/3.12 ( ( ord_less_int @ ( plus_plus_int @ A2 @ A2 ) @ zero_zero_int )
% 2.86/3.12 = ( ord_less_int @ A2 @ zero_zero_int ) ) ).
% 2.86/3.12
% 2.86/3.12 % double_add_less_zero_iff_single_add_less_zero
% 2.86/3.12 thf(fact_3864_less__add__same__cancel2,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat] :
% 2.86/3.12 ( ( ord_less_rat @ A2 @ ( plus_plus_rat @ B2 @ A2 ) )
% 2.86/3.12 = ( ord_less_rat @ zero_zero_rat @ B2 ) ) ).
% 2.86/3.12
% 2.86/3.12 % less_add_same_cancel2
% 2.86/3.12 thf(fact_3865_less__add__same__cancel2,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ord_le6747313008572928689nteger @ A2 @ ( plus_p5714425477246183910nteger @ B2 @ A2 ) )
% 2.86/3.12 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B2 ) ) ).
% 2.86/3.12
% 2.86/3.12 % less_add_same_cancel2
% 2.86/3.12 thf(fact_3866_less__add__same__cancel2,axiom,
% 2.86/3.12 ! [A2: nat,B2: nat] :
% 2.86/3.12 ( ( ord_less_nat @ A2 @ ( plus_plus_nat @ B2 @ A2 ) )
% 2.86/3.12 = ( ord_less_nat @ zero_zero_nat @ B2 ) ) ).
% 2.86/3.12
% 2.86/3.12 % less_add_same_cancel2
% 2.86/3.12 thf(fact_3867_less__add__same__cancel2,axiom,
% 2.86/3.12 ! [A2: int,B2: int] :
% 2.86/3.12 ( ( ord_less_int @ A2 @ ( plus_plus_int @ B2 @ A2 ) )
% 2.86/3.12 = ( ord_less_int @ zero_zero_int @ B2 ) ) ).
% 2.86/3.12
% 2.86/3.12 % less_add_same_cancel2
% 2.86/3.12 thf(fact_3868_less__add__same__cancel1,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat] :
% 2.86/3.12 ( ( ord_less_rat @ A2 @ ( plus_plus_rat @ A2 @ B2 ) )
% 2.86/3.12 = ( ord_less_rat @ zero_zero_rat @ B2 ) ) ).
% 2.86/3.12
% 2.86/3.12 % less_add_same_cancel1
% 2.86/3.12 thf(fact_3869_less__add__same__cancel1,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ord_le6747313008572928689nteger @ A2 @ ( plus_p5714425477246183910nteger @ A2 @ B2 ) )
% 2.86/3.12 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B2 ) ) ).
% 2.86/3.12
% 2.86/3.12 % less_add_same_cancel1
% 2.86/3.12 thf(fact_3870_less__add__same__cancel1,axiom,
% 2.86/3.12 ! [A2: nat,B2: nat] :
% 2.86/3.12 ( ( ord_less_nat @ A2 @ ( plus_plus_nat @ A2 @ B2 ) )
% 2.86/3.12 = ( ord_less_nat @ zero_zero_nat @ B2 ) ) ).
% 2.86/3.12
% 2.86/3.12 % less_add_same_cancel1
% 2.86/3.12 thf(fact_3871_less__add__same__cancel1,axiom,
% 2.86/3.12 ! [A2: int,B2: int] :
% 2.86/3.12 ( ( ord_less_int @ A2 @ ( plus_plus_int @ A2 @ B2 ) )
% 2.86/3.12 = ( ord_less_int @ zero_zero_int @ B2 ) ) ).
% 2.86/3.12
% 2.86/3.12 % less_add_same_cancel1
% 2.86/3.12 thf(fact_3872_add__less__same__cancel2,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat] :
% 2.86/3.12 ( ( ord_less_rat @ ( plus_plus_rat @ A2 @ B2 ) @ B2 )
% 2.86/3.12 = ( ord_less_rat @ A2 @ zero_zero_rat ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_less_same_cancel2
% 2.86/3.12 thf(fact_3873_add__less__same__cancel2,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A2 @ B2 ) @ B2 )
% 2.86/3.12 = ( ord_le6747313008572928689nteger @ A2 @ zero_z3403309356797280102nteger ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_less_same_cancel2
% 2.86/3.12 thf(fact_3874_add__less__same__cancel2,axiom,
% 2.86/3.12 ! [A2: nat,B2: nat] :
% 2.86/3.12 ( ( ord_less_nat @ ( plus_plus_nat @ A2 @ B2 ) @ B2 )
% 2.86/3.12 = ( ord_less_nat @ A2 @ zero_zero_nat ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_less_same_cancel2
% 2.86/3.12 thf(fact_3875_add__less__same__cancel2,axiom,
% 2.86/3.12 ! [A2: int,B2: int] :
% 2.86/3.12 ( ( ord_less_int @ ( plus_plus_int @ A2 @ B2 ) @ B2 )
% 2.86/3.12 = ( ord_less_int @ A2 @ zero_zero_int ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_less_same_cancel2
% 2.86/3.12 thf(fact_3876_add__less__same__cancel1,axiom,
% 2.86/3.12 ! [B2: rat,A2: rat] :
% 2.86/3.12 ( ( ord_less_rat @ ( plus_plus_rat @ B2 @ A2 ) @ B2 )
% 2.86/3.12 = ( ord_less_rat @ A2 @ zero_zero_rat ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_less_same_cancel1
% 2.86/3.12 thf(fact_3877_add__less__same__cancel1,axiom,
% 2.86/3.12 ! [B2: code_integer,A2: code_integer] :
% 2.86/3.12 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ B2 @ A2 ) @ B2 )
% 2.86/3.12 = ( ord_le6747313008572928689nteger @ A2 @ zero_z3403309356797280102nteger ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_less_same_cancel1
% 2.86/3.12 thf(fact_3878_add__less__same__cancel1,axiom,
% 2.86/3.12 ! [B2: nat,A2: nat] :
% 2.86/3.12 ( ( ord_less_nat @ ( plus_plus_nat @ B2 @ A2 ) @ B2 )
% 2.86/3.12 = ( ord_less_nat @ A2 @ zero_zero_nat ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_less_same_cancel1
% 2.86/3.12 thf(fact_3879_add__less__same__cancel1,axiom,
% 2.86/3.12 ! [B2: int,A2: int] :
% 2.86/3.12 ( ( ord_less_int @ ( plus_plus_int @ B2 @ A2 ) @ B2 )
% 2.86/3.12 = ( ord_less_int @ A2 @ zero_zero_int ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_less_same_cancel1
% 2.86/3.12 thf(fact_3880_diff__gt__0__iff__gt,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat] :
% 2.86/3.12 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A2 @ B2 ) )
% 2.86/3.12 = ( ord_less_rat @ B2 @ A2 ) ) ).
% 2.86/3.12
% 2.86/3.12 % diff_gt_0_iff_gt
% 2.86/3.12 thf(fact_3881_diff__gt__0__iff__gt,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ A2 @ B2 ) )
% 2.86/3.12 = ( ord_le6747313008572928689nteger @ B2 @ A2 ) ) ).
% 2.86/3.12
% 2.86/3.12 % diff_gt_0_iff_gt
% 2.86/3.12 thf(fact_3882_diff__gt__0__iff__gt,axiom,
% 2.86/3.12 ! [A2: int,B2: int] :
% 2.86/3.12 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A2 @ B2 ) )
% 2.86/3.12 = ( ord_less_int @ B2 @ A2 ) ) ).
% 2.86/3.12
% 2.86/3.12 % diff_gt_0_iff_gt
% 2.86/3.12 thf(fact_3883_zero__comp__diff__simps_I2_J,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat] :
% 2.86/3.12 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A2 @ B2 ) )
% 2.86/3.12 = ( ord_less_rat @ B2 @ A2 ) ) ).
% 2.86/3.12
% 2.86/3.12 % zero_comp_diff_simps(2)
% 2.86/3.12 thf(fact_3884_zero__comp__diff__simps_I2_J,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ A2 @ B2 ) )
% 2.86/3.12 = ( ord_le6747313008572928689nteger @ B2 @ A2 ) ) ).
% 2.86/3.12
% 2.86/3.12 % zero_comp_diff_simps(2)
% 2.86/3.12 thf(fact_3885_zero__comp__diff__simps_I2_J,axiom,
% 2.86/3.12 ! [A2: int,B2: int] :
% 2.86/3.12 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A2 @ B2 ) )
% 2.86/3.12 = ( ord_less_int @ B2 @ A2 ) ) ).
% 2.86/3.12
% 2.86/3.12 % zero_comp_diff_simps(2)
% 2.86/3.12 thf(fact_3886_mult__cancel__left1,axiom,
% 2.86/3.12 ! [C: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( C
% 2.86/3.12 = ( times_3573771949741848930nteger @ C @ B2 ) )
% 2.86/3.12 = ( ( C = zero_z3403309356797280102nteger )
% 2.86/3.12 | ( B2 = one_one_Code_integer ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_cancel_left1
% 2.86/3.12 thf(fact_3887_mult__cancel__left1,axiom,
% 2.86/3.12 ! [C: rat,B2: rat] :
% 2.86/3.12 ( ( C
% 2.86/3.12 = ( times_times_rat @ C @ B2 ) )
% 2.86/3.12 = ( ( C = zero_zero_rat )
% 2.86/3.12 | ( B2 = one_one_rat ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_cancel_left1
% 2.86/3.12 thf(fact_3888_mult__cancel__left1,axiom,
% 2.86/3.12 ! [C: int,B2: int] :
% 2.86/3.12 ( ( C
% 2.86/3.12 = ( times_times_int @ C @ B2 ) )
% 2.86/3.12 = ( ( C = zero_zero_int )
% 2.86/3.12 | ( B2 = one_one_int ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_cancel_left1
% 2.86/3.12 thf(fact_3889_mult__cancel__left2,axiom,
% 2.86/3.12 ! [C: code_integer,A2: code_integer] :
% 2.86/3.12 ( ( ( times_3573771949741848930nteger @ C @ A2 )
% 2.86/3.12 = C )
% 2.86/3.12 = ( ( C = zero_z3403309356797280102nteger )
% 2.86/3.12 | ( A2 = one_one_Code_integer ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_cancel_left2
% 2.86/3.12 thf(fact_3890_mult__cancel__left2,axiom,
% 2.86/3.12 ! [C: rat,A2: rat] :
% 2.86/3.12 ( ( ( times_times_rat @ C @ A2 )
% 2.86/3.12 = C )
% 2.86/3.12 = ( ( C = zero_zero_rat )
% 2.86/3.12 | ( A2 = one_one_rat ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_cancel_left2
% 2.86/3.12 thf(fact_3891_mult__cancel__left2,axiom,
% 2.86/3.12 ! [C: int,A2: int] :
% 2.86/3.12 ( ( ( times_times_int @ C @ A2 )
% 2.86/3.12 = C )
% 2.86/3.12 = ( ( C = zero_zero_int )
% 2.86/3.12 | ( A2 = one_one_int ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_cancel_left2
% 2.86/3.12 thf(fact_3892_mult__cancel__right1,axiom,
% 2.86/3.12 ! [C: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( C
% 2.86/3.12 = ( times_3573771949741848930nteger @ B2 @ C ) )
% 2.86/3.12 = ( ( C = zero_z3403309356797280102nteger )
% 2.86/3.12 | ( B2 = one_one_Code_integer ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_cancel_right1
% 2.86/3.12 thf(fact_3893_mult__cancel__right1,axiom,
% 2.86/3.12 ! [C: rat,B2: rat] :
% 2.86/3.12 ( ( C
% 2.86/3.12 = ( times_times_rat @ B2 @ C ) )
% 2.86/3.12 = ( ( C = zero_zero_rat )
% 2.86/3.12 | ( B2 = one_one_rat ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_cancel_right1
% 2.86/3.12 thf(fact_3894_mult__cancel__right1,axiom,
% 2.86/3.12 ! [C: int,B2: int] :
% 2.86/3.12 ( ( C
% 2.86/3.12 = ( times_times_int @ B2 @ C ) )
% 2.86/3.12 = ( ( C = zero_zero_int )
% 2.86/3.12 | ( B2 = one_one_int ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_cancel_right1
% 2.86/3.12 thf(fact_3895_mult__cancel__right2,axiom,
% 2.86/3.12 ! [A2: code_integer,C: code_integer] :
% 2.86/3.12 ( ( ( times_3573771949741848930nteger @ A2 @ C )
% 2.86/3.12 = C )
% 2.86/3.12 = ( ( C = zero_z3403309356797280102nteger )
% 2.86/3.12 | ( A2 = one_one_Code_integer ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_cancel_right2
% 2.86/3.12 thf(fact_3896_mult__cancel__right2,axiom,
% 2.86/3.12 ! [A2: rat,C: rat] :
% 2.86/3.12 ( ( ( times_times_rat @ A2 @ C )
% 2.86/3.12 = C )
% 2.86/3.12 = ( ( C = zero_zero_rat )
% 2.86/3.12 | ( A2 = one_one_rat ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_cancel_right2
% 2.86/3.12 thf(fact_3897_mult__cancel__right2,axiom,
% 2.86/3.12 ! [A2: int,C: int] :
% 2.86/3.12 ( ( ( times_times_int @ A2 @ C )
% 2.86/3.12 = C )
% 2.86/3.12 = ( ( C = zero_zero_int )
% 2.86/3.12 | ( A2 = one_one_int ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_cancel_right2
% 2.86/3.12 thf(fact_3898_diff__add__zero,axiom,
% 2.86/3.12 ! [A2: multis2468970476368604999at_nat,B2: multis2468970476368604999at_nat] :
% 2.86/3.12 ( ( minus_4286766774447292334at_nat @ A2 @ ( plus_p7104986032573967614at_nat @ A2 @ B2 ) )
% 2.86/3.12 = zero_z1048942125864253310at_nat ) ).
% 2.86/3.12
% 2.86/3.12 % diff_add_zero
% 2.86/3.12 thf(fact_3899_diff__add__zero,axiom,
% 2.86/3.12 ! [A2: nat,B2: nat] :
% 2.86/3.12 ( ( minus_minus_nat @ A2 @ ( plus_plus_nat @ A2 @ B2 ) )
% 2.86/3.12 = zero_zero_nat ) ).
% 2.86/3.12
% 2.86/3.12 % diff_add_zero
% 2.86/3.12 thf(fact_3900_diff__numeral__special_I9_J,axiom,
% 2.86/3.12 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ one_one_Code_integer )
% 2.86/3.12 = zero_z3403309356797280102nteger ) ).
% 2.86/3.12
% 2.86/3.12 % diff_numeral_special(9)
% 2.86/3.12 thf(fact_3901_diff__numeral__special_I9_J,axiom,
% 2.86/3.12 ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 2.86/3.12 = zero_zero_rat ) ).
% 2.86/3.12
% 2.86/3.12 % diff_numeral_special(9)
% 2.86/3.12 thf(fact_3902_diff__numeral__special_I9_J,axiom,
% 2.86/3.12 ( ( minus_minus_int @ one_one_int @ one_one_int )
% 2.86/3.12 = zero_zero_int ) ).
% 2.86/3.12
% 2.86/3.12 % diff_numeral_special(9)
% 2.86/3.12 thf(fact_3903_less__Suc0,axiom,
% 2.86/3.12 ! [N: nat] :
% 2.86/3.12 ( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
% 2.86/3.12 = ( N = zero_zero_nat ) ) ).
% 2.86/3.12
% 2.86/3.12 % less_Suc0
% 2.86/3.12 thf(fact_3904_zero__less__Suc,axiom,
% 2.86/3.12 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 2.86/3.12
% 2.86/3.12 % zero_less_Suc
% 2.86/3.12 thf(fact_3905_add__gr__0,axiom,
% 2.86/3.12 ! [M2: nat,N: nat] :
% 2.86/3.12 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M2 @ N ) )
% 2.86/3.12 = ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 2.86/3.12 | ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_gr_0
% 2.86/3.12 thf(fact_3906_zero__less__diff,axiom,
% 2.86/3.12 ! [N: nat,M2: nat] :
% 2.86/3.12 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M2 ) )
% 2.86/3.12 = ( ord_less_nat @ M2 @ N ) ) ).
% 2.86/3.12
% 2.86/3.12 % zero_less_diff
% 2.86/3.12 thf(fact_3907_nat__mult__less__cancel__disj,axiom,
% 2.86/3.12 ! [K3: nat,M2: nat,N: nat] :
% 2.86/3.12 ( ( ord_less_nat @ ( times_times_nat @ K3 @ M2 ) @ ( times_times_nat @ K3 @ N ) )
% 2.86/3.12 = ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 2.86/3.12 & ( ord_less_nat @ M2 @ N ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % nat_mult_less_cancel_disj
% 2.86/3.12 thf(fact_3908_mult__less__cancel2,axiom,
% 2.86/3.12 ! [M2: nat,K3: nat,N: nat] :
% 2.86/3.12 ( ( ord_less_nat @ ( times_times_nat @ M2 @ K3 ) @ ( times_times_nat @ N @ K3 ) )
% 2.86/3.12 = ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 2.86/3.12 & ( ord_less_nat @ M2 @ N ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_less_cancel2
% 2.86/3.12 thf(fact_3909_nat__0__less__mult__iff,axiom,
% 2.86/3.12 ! [M2: nat,N: nat] :
% 2.86/3.12 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M2 @ N ) )
% 2.86/3.12 = ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 2.86/3.12 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % nat_0_less_mult_iff
% 2.86/3.12 thf(fact_3910_less__one,axiom,
% 2.86/3.12 ! [N: nat] :
% 2.86/3.12 ( ( ord_less_nat @ N @ one_one_nat )
% 2.86/3.12 = ( N = zero_zero_nat ) ) ).
% 2.86/3.12
% 2.86/3.12 % less_one
% 2.86/3.12 thf(fact_3911_slice__complete,axiom,
% 2.86/3.12 ! [Xs: list_c] :
% 2.86/3.12 ( ( slice_c @ zero_zero_nat @ ( size_size_list_c @ Xs ) @ Xs )
% 2.86/3.12 = Xs ) ).
% 2.86/3.12
% 2.86/3.12 % slice_complete
% 2.86/3.12 thf(fact_3912_slice__complete,axiom,
% 2.86/3.12 ! [Xs: list_d] :
% 2.86/3.12 ( ( slice_d @ zero_zero_nat @ ( size_size_list_d @ Xs ) @ Xs )
% 2.86/3.12 = Xs ) ).
% 2.86/3.12
% 2.86/3.12 % slice_complete
% 2.86/3.12 thf(fact_3913_slice__complete,axiom,
% 2.86/3.12 ! [Xs: list_nat] :
% 2.86/3.12 ( ( slice_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs ) @ Xs )
% 2.86/3.12 = Xs ) ).
% 2.86/3.12
% 2.86/3.12 % slice_complete
% 2.86/3.12 thf(fact_3914_slice__complete,axiom,
% 2.86/3.12 ! [Xs: list_int] :
% 2.86/3.12 ( ( slice_int @ zero_zero_nat @ ( size_size_list_int @ Xs ) @ Xs )
% 2.86/3.12 = Xs ) ).
% 2.86/3.12
% 2.86/3.12 % slice_complete
% 2.86/3.12 thf(fact_3915_Suc__pred,axiom,
% 2.86/3.12 ! [N: nat] :
% 2.86/3.12 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.12 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 2.86/3.12 = N ) ) ).
% 2.86/3.12
% 2.86/3.12 % Suc_pred
% 2.86/3.12 thf(fact_3916_nat__mult__le__cancel__disj,axiom,
% 2.86/3.12 ! [K3: nat,M2: nat,N: nat] :
% 2.86/3.12 ( ( ord_less_eq_nat @ ( times_times_nat @ K3 @ M2 ) @ ( times_times_nat @ K3 @ N ) )
% 2.86/3.12 = ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 2.86/3.12 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % nat_mult_le_cancel_disj
% 2.86/3.12 thf(fact_3917_mult__le__cancel2,axiom,
% 2.86/3.12 ! [M2: nat,K3: nat,N: nat] :
% 2.86/3.12 ( ( ord_less_eq_nat @ ( times_times_nat @ M2 @ K3 ) @ ( times_times_nat @ N @ K3 ) )
% 2.86/3.12 = ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 2.86/3.12 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_le_cancel2
% 2.86/3.12 thf(fact_3918_Suc__diff__1,axiom,
% 2.86/3.12 ! [N: nat] :
% 2.86/3.12 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.12 => ( ( suc @ ( minus_minus_nat @ N @ one_one_nat ) )
% 2.86/3.12 = N ) ) ).
% 2.86/3.12
% 2.86/3.12 % Suc_diff_1
% 2.86/3.12 thf(fact_3919_assn__aci_I8_J,axiom,
% 2.86/3.12 ! [X: assn,Y: assn] :
% 2.86/3.12 ( ( sup_sup_assn @ X @ ( sup_sup_assn @ X @ Y ) )
% 2.86/3.12 = ( sup_sup_assn @ X @ Y ) ) ).
% 2.86/3.12
% 2.86/3.12 % assn_aci(8)
% 2.86/3.12 thf(fact_3920_assn__aci_I7_J,axiom,
% 2.86/3.12 ! [X: assn,Y: assn,Z: assn] :
% 2.86/3.12 ( ( sup_sup_assn @ X @ ( sup_sup_assn @ Y @ Z ) )
% 2.86/3.12 = ( sup_sup_assn @ Y @ ( sup_sup_assn @ X @ Z ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % assn_aci(7)
% 2.86/3.12 thf(fact_3921_assn__aci_I5_J,axiom,
% 2.86/3.12 ( sup_sup_assn
% 2.86/3.12 = ( ^ [X2: assn,Y5: assn] : ( sup_sup_assn @ Y5 @ X2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % assn_aci(5)
% 2.86/3.12 thf(fact_3922_norm__assertion__simps_I32_J,axiom,
% 2.86/3.12 ! [X: assn] :
% 2.86/3.12 ( ( sup_sup_assn @ X @ X )
% 2.86/3.12 = X ) ).
% 2.86/3.12
% 2.86/3.12 % norm_assertion_simps(32)
% 2.86/3.12 thf(fact_3923_norm__assertion__simps_I15_J,axiom,
% 2.86/3.12 ! [X: assn,Y: assn,Z: assn] :
% 2.86/3.12 ( ( sup_sup_assn @ ( sup_sup_assn @ X @ Y ) @ Z )
% 2.86/3.12 = ( sup_sup_assn @ X @ ( sup_sup_assn @ Y @ Z ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % norm_assertion_simps(15)
% 2.86/3.12 thf(fact_3924_zero__reorient,axiom,
% 2.86/3.12 ! [X: code_integer] :
% 2.86/3.12 ( ( zero_z3403309356797280102nteger = X )
% 2.86/3.12 = ( X = zero_z3403309356797280102nteger ) ) ).
% 2.86/3.12
% 2.86/3.12 % zero_reorient
% 2.86/3.12 thf(fact_3925_zero__reorient,axiom,
% 2.86/3.12 ! [X: multis2468970476368604999at_nat] :
% 2.86/3.12 ( ( zero_z1048942125864253310at_nat = X )
% 2.86/3.12 = ( X = zero_z1048942125864253310at_nat ) ) ).
% 2.86/3.12
% 2.86/3.12 % zero_reorient
% 2.86/3.12 thf(fact_3926_zero__reorient,axiom,
% 2.86/3.12 ! [X: rat] :
% 2.86/3.12 ( ( zero_zero_rat = X )
% 2.86/3.12 = ( X = zero_zero_rat ) ) ).
% 2.86/3.12
% 2.86/3.12 % zero_reorient
% 2.86/3.12 thf(fact_3927_zero__reorient,axiom,
% 2.86/3.12 ! [X: nat] :
% 2.86/3.12 ( ( zero_zero_nat = X )
% 2.86/3.12 = ( X = zero_zero_nat ) ) ).
% 2.86/3.12
% 2.86/3.12 % zero_reorient
% 2.86/3.12 thf(fact_3928_zero__reorient,axiom,
% 2.86/3.12 ! [X: int] :
% 2.86/3.12 ( ( zero_zero_int = X )
% 2.86/3.12 = ( X = zero_zero_int ) ) ).
% 2.86/3.12
% 2.86/3.12 % zero_reorient
% 2.86/3.12 thf(fact_3929_trancl__mono__mp,axiom,
% 2.86/3.12 ! [U2: set_Pr4329608150637261639at_nat,V: set_Pr4329608150637261639at_nat,X: produc3843707927480180839at_nat] :
% 2.86/3.12 ( ( ord_le1268244103169919719at_nat @ U2 @ V )
% 2.86/3.12 => ( ( member8757157785044589968at_nat @ X @ ( transi2703068831062848130at_nat @ U2 ) )
% 2.86/3.12 => ( member8757157785044589968at_nat @ X @ ( transi2703068831062848130at_nat @ V ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % trancl_mono_mp
% 2.86/3.12 thf(fact_3930_trancl__mono__mp,axiom,
% 2.86/3.12 ! [U2: set_Pr1261947904930325089at_nat,V: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] :
% 2.86/3.12 ( ( ord_le3146513528884898305at_nat @ U2 @ V )
% 2.86/3.12 => ( ( member8440522571783428010at_nat @ X @ ( transi6264000038957366511cl_nat @ U2 ) )
% 2.86/3.12 => ( member8440522571783428010at_nat @ X @ ( transi6264000038957366511cl_nat @ V ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % trancl_mono_mp
% 2.86/3.12 thf(fact_3931_trancl__sub,axiom,
% 2.86/3.12 ! [R: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ R @ ( transi6264000038957366511cl_nat @ R ) ) ).
% 2.86/3.12
% 2.86/3.12 % trancl_sub
% 2.86/3.12 thf(fact_3932_trancl__sub__insert__trancl,axiom,
% 2.86/3.12 ! [R: set_Pr4329608150637261639at_nat,X: produc3843707927480180839at_nat] : ( ord_le1268244103169919719at_nat @ ( transi2703068831062848130at_nat @ R ) @ ( transi2703068831062848130at_nat @ ( insert9069300056098147895at_nat @ X @ R ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % trancl_sub_insert_trancl
% 2.86/3.12 thf(fact_3933_trancl__sub__insert__trancl,axiom,
% 2.86/3.12 ! [R: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] : ( ord_le3146513528884898305at_nat @ ( transi6264000038957366511cl_nat @ R ) @ ( transi6264000038957366511cl_nat @ ( insert8211810215607154385at_nat @ X @ R ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % trancl_sub_insert_trancl
% 2.86/3.12 thf(fact_3934_zero__le,axiom,
% 2.86/3.12 ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% 2.86/3.12
% 2.86/3.12 % zero_le
% 2.86/3.12 thf(fact_3935_zero__less__iff__neq__zero,axiom,
% 2.86/3.12 ! [N: nat] :
% 2.86/3.12 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.12 = ( N != zero_zero_nat ) ) ).
% 2.86/3.12
% 2.86/3.12 % zero_less_iff_neq_zero
% 2.86/3.12 thf(fact_3936_gr__implies__not__zero,axiom,
% 2.86/3.12 ! [M2: nat,N: nat] :
% 2.86/3.12 ( ( ord_less_nat @ M2 @ N )
% 2.86/3.12 => ( N != zero_zero_nat ) ) ).
% 2.86/3.12
% 2.86/3.12 % gr_implies_not_zero
% 2.86/3.12 thf(fact_3937_not__less__zero,axiom,
% 2.86/3.12 ! [N: nat] :
% 2.86/3.12 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 2.86/3.12
% 2.86/3.12 % not_less_zero
% 2.86/3.12 thf(fact_3938_gr__zeroI,axiom,
% 2.86/3.12 ! [N: nat] :
% 2.86/3.12 ( ( N != zero_zero_nat )
% 2.86/3.12 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 2.86/3.12
% 2.86/3.12 % gr_zeroI
% 2.86/3.12 thf(fact_3939_less__numeral__extra_I3_J,axiom,
% 2.86/3.12 ~ ( ord_less_rat @ zero_zero_rat @ zero_zero_rat ) ).
% 2.86/3.12
% 2.86/3.12 % less_numeral_extra(3)
% 2.86/3.12 thf(fact_3940_less__numeral__extra_I3_J,axiom,
% 2.86/3.12 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ).
% 2.86/3.12
% 2.86/3.12 % less_numeral_extra(3)
% 2.86/3.12 thf(fact_3941_less__numeral__extra_I3_J,axiom,
% 2.86/3.12 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 2.86/3.12
% 2.86/3.12 % less_numeral_extra(3)
% 2.86/3.12 thf(fact_3942_less__numeral__extra_I3_J,axiom,
% 2.86/3.12 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 2.86/3.12
% 2.86/3.12 % less_numeral_extra(3)
% 2.86/3.12 thf(fact_3943_comm__monoid__add__class_Oadd__0,axiom,
% 2.86/3.12 ! [A2: code_integer] :
% 2.86/3.12 ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ A2 )
% 2.86/3.12 = A2 ) ).
% 2.86/3.12
% 2.86/3.12 % comm_monoid_add_class.add_0
% 2.86/3.12 thf(fact_3944_comm__monoid__add__class_Oadd__0,axiom,
% 2.86/3.12 ! [A2: multis2468970476368604999at_nat] :
% 2.86/3.12 ( ( plus_p7104986032573967614at_nat @ zero_z1048942125864253310at_nat @ A2 )
% 2.86/3.12 = A2 ) ).
% 2.86/3.12
% 2.86/3.12 % comm_monoid_add_class.add_0
% 2.86/3.12 thf(fact_3945_comm__monoid__add__class_Oadd__0,axiom,
% 2.86/3.12 ! [A2: rat] :
% 2.86/3.12 ( ( plus_plus_rat @ zero_zero_rat @ A2 )
% 2.86/3.12 = A2 ) ).
% 2.86/3.12
% 2.86/3.12 % comm_monoid_add_class.add_0
% 2.86/3.12 thf(fact_3946_comm__monoid__add__class_Oadd__0,axiom,
% 2.86/3.12 ! [A2: nat] :
% 2.86/3.12 ( ( plus_plus_nat @ zero_zero_nat @ A2 )
% 2.86/3.12 = A2 ) ).
% 2.86/3.12
% 2.86/3.12 % comm_monoid_add_class.add_0
% 2.86/3.12 thf(fact_3947_comm__monoid__add__class_Oadd__0,axiom,
% 2.86/3.12 ! [A2: int] :
% 2.86/3.12 ( ( plus_plus_int @ zero_zero_int @ A2 )
% 2.86/3.12 = A2 ) ).
% 2.86/3.12
% 2.86/3.12 % comm_monoid_add_class.add_0
% 2.86/3.12 thf(fact_3948_add_Ocomm__neutral,axiom,
% 2.86/3.12 ! [A2: code_integer] :
% 2.86/3.12 ( ( plus_p5714425477246183910nteger @ A2 @ zero_z3403309356797280102nteger )
% 2.86/3.12 = A2 ) ).
% 2.86/3.12
% 2.86/3.12 % add.comm_neutral
% 2.86/3.12 thf(fact_3949_add_Ocomm__neutral,axiom,
% 2.86/3.12 ! [A2: multis2468970476368604999at_nat] :
% 2.86/3.12 ( ( plus_p7104986032573967614at_nat @ A2 @ zero_z1048942125864253310at_nat )
% 2.86/3.12 = A2 ) ).
% 2.86/3.12
% 2.86/3.12 % add.comm_neutral
% 2.86/3.12 thf(fact_3950_add_Ocomm__neutral,axiom,
% 2.86/3.12 ! [A2: rat] :
% 2.86/3.12 ( ( plus_plus_rat @ A2 @ zero_zero_rat )
% 2.86/3.12 = A2 ) ).
% 2.86/3.12
% 2.86/3.12 % add.comm_neutral
% 2.86/3.12 thf(fact_3951_add_Ocomm__neutral,axiom,
% 2.86/3.12 ! [A2: nat] :
% 2.86/3.12 ( ( plus_plus_nat @ A2 @ zero_zero_nat )
% 2.86/3.12 = A2 ) ).
% 2.86/3.12
% 2.86/3.12 % add.comm_neutral
% 2.86/3.12 thf(fact_3952_add_Ocomm__neutral,axiom,
% 2.86/3.12 ! [A2: int] :
% 2.86/3.12 ( ( plus_plus_int @ A2 @ zero_zero_int )
% 2.86/3.12 = A2 ) ).
% 2.86/3.12
% 2.86/3.12 % add.comm_neutral
% 2.86/3.12 thf(fact_3953_add_Ogroup__left__neutral,axiom,
% 2.86/3.12 ! [A2: code_integer] :
% 2.86/3.12 ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ A2 )
% 2.86/3.12 = A2 ) ).
% 2.86/3.12
% 2.86/3.12 % add.group_left_neutral
% 2.86/3.12 thf(fact_3954_add_Ogroup__left__neutral,axiom,
% 2.86/3.12 ! [A2: rat] :
% 2.86/3.12 ( ( plus_plus_rat @ zero_zero_rat @ A2 )
% 2.86/3.12 = A2 ) ).
% 2.86/3.12
% 2.86/3.12 % add.group_left_neutral
% 2.86/3.12 thf(fact_3955_add_Ogroup__left__neutral,axiom,
% 2.86/3.12 ! [A2: int] :
% 2.86/3.12 ( ( plus_plus_int @ zero_zero_int @ A2 )
% 2.86/3.12 = A2 ) ).
% 2.86/3.12
% 2.86/3.12 % add.group_left_neutral
% 2.86/3.12 thf(fact_3956_mult__right__cancel,axiom,
% 2.86/3.12 ! [C: code_integer,A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( C != zero_z3403309356797280102nteger )
% 2.86/3.12 => ( ( ( times_3573771949741848930nteger @ A2 @ C )
% 2.86/3.12 = ( times_3573771949741848930nteger @ B2 @ C ) )
% 2.86/3.12 = ( A2 = B2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_right_cancel
% 2.86/3.12 thf(fact_3957_mult__right__cancel,axiom,
% 2.86/3.12 ! [C: rat,A2: rat,B2: rat] :
% 2.86/3.12 ( ( C != zero_zero_rat )
% 2.86/3.12 => ( ( ( times_times_rat @ A2 @ C )
% 2.86/3.12 = ( times_times_rat @ B2 @ C ) )
% 2.86/3.12 = ( A2 = B2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_right_cancel
% 2.86/3.12 thf(fact_3958_mult__right__cancel,axiom,
% 2.86/3.12 ! [C: nat,A2: nat,B2: nat] :
% 2.86/3.12 ( ( C != zero_zero_nat )
% 2.86/3.12 => ( ( ( times_times_nat @ A2 @ C )
% 2.86/3.12 = ( times_times_nat @ B2 @ C ) )
% 2.86/3.12 = ( A2 = B2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_right_cancel
% 2.86/3.12 thf(fact_3959_mult__right__cancel,axiom,
% 2.86/3.12 ! [C: int,A2: int,B2: int] :
% 2.86/3.12 ( ( C != zero_zero_int )
% 2.86/3.12 => ( ( ( times_times_int @ A2 @ C )
% 2.86/3.12 = ( times_times_int @ B2 @ C ) )
% 2.86/3.12 = ( A2 = B2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_right_cancel
% 2.86/3.12 thf(fact_3960_mult__left__cancel,axiom,
% 2.86/3.12 ! [C: code_integer,A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( C != zero_z3403309356797280102nteger )
% 2.86/3.12 => ( ( ( times_3573771949741848930nteger @ C @ A2 )
% 2.86/3.12 = ( times_3573771949741848930nteger @ C @ B2 ) )
% 2.86/3.12 = ( A2 = B2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_left_cancel
% 2.86/3.12 thf(fact_3961_mult__left__cancel,axiom,
% 2.86/3.12 ! [C: rat,A2: rat,B2: rat] :
% 2.86/3.12 ( ( C != zero_zero_rat )
% 2.86/3.12 => ( ( ( times_times_rat @ C @ A2 )
% 2.86/3.12 = ( times_times_rat @ C @ B2 ) )
% 2.86/3.12 = ( A2 = B2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_left_cancel
% 2.86/3.12 thf(fact_3962_mult__left__cancel,axiom,
% 2.86/3.12 ! [C: nat,A2: nat,B2: nat] :
% 2.86/3.12 ( ( C != zero_zero_nat )
% 2.86/3.12 => ( ( ( times_times_nat @ C @ A2 )
% 2.86/3.12 = ( times_times_nat @ C @ B2 ) )
% 2.86/3.12 = ( A2 = B2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_left_cancel
% 2.86/3.12 thf(fact_3963_mult__left__cancel,axiom,
% 2.86/3.12 ! [C: int,A2: int,B2: int] :
% 2.86/3.12 ( ( C != zero_zero_int )
% 2.86/3.12 => ( ( ( times_times_int @ C @ A2 )
% 2.86/3.12 = ( times_times_int @ C @ B2 ) )
% 2.86/3.12 = ( A2 = B2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_left_cancel
% 2.86/3.12 thf(fact_3964_no__zero__divisors,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( A2 != zero_z3403309356797280102nteger )
% 2.86/3.12 => ( ( B2 != zero_z3403309356797280102nteger )
% 2.86/3.12 => ( ( times_3573771949741848930nteger @ A2 @ B2 )
% 2.86/3.12 != zero_z3403309356797280102nteger ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % no_zero_divisors
% 2.86/3.12 thf(fact_3965_no__zero__divisors,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat] :
% 2.86/3.12 ( ( A2 != zero_zero_rat )
% 2.86/3.12 => ( ( B2 != zero_zero_rat )
% 2.86/3.12 => ( ( times_times_rat @ A2 @ B2 )
% 2.86/3.12 != zero_zero_rat ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % no_zero_divisors
% 2.86/3.12 thf(fact_3966_no__zero__divisors,axiom,
% 2.86/3.12 ! [A2: nat,B2: nat] :
% 2.86/3.12 ( ( A2 != zero_zero_nat )
% 2.86/3.12 => ( ( B2 != zero_zero_nat )
% 2.86/3.12 => ( ( times_times_nat @ A2 @ B2 )
% 2.86/3.12 != zero_zero_nat ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % no_zero_divisors
% 2.86/3.12 thf(fact_3967_no__zero__divisors,axiom,
% 2.86/3.12 ! [A2: int,B2: int] :
% 2.86/3.12 ( ( A2 != zero_zero_int )
% 2.86/3.12 => ( ( B2 != zero_zero_int )
% 2.86/3.12 => ( ( times_times_int @ A2 @ B2 )
% 2.86/3.12 != zero_zero_int ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % no_zero_divisors
% 2.86/3.12 thf(fact_3968_divisors__zero,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ( times_3573771949741848930nteger @ A2 @ B2 )
% 2.86/3.12 = zero_z3403309356797280102nteger )
% 2.86/3.12 => ( ( A2 = zero_z3403309356797280102nteger )
% 2.86/3.12 | ( B2 = zero_z3403309356797280102nteger ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % divisors_zero
% 2.86/3.12 thf(fact_3969_divisors__zero,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat] :
% 2.86/3.12 ( ( ( times_times_rat @ A2 @ B2 )
% 2.86/3.12 = zero_zero_rat )
% 2.86/3.12 => ( ( A2 = zero_zero_rat )
% 2.86/3.12 | ( B2 = zero_zero_rat ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % divisors_zero
% 2.86/3.12 thf(fact_3970_divisors__zero,axiom,
% 2.86/3.12 ! [A2: nat,B2: nat] :
% 2.86/3.12 ( ( ( times_times_nat @ A2 @ B2 )
% 2.86/3.12 = zero_zero_nat )
% 2.86/3.12 => ( ( A2 = zero_zero_nat )
% 2.86/3.12 | ( B2 = zero_zero_nat ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % divisors_zero
% 2.86/3.12 thf(fact_3971_divisors__zero,axiom,
% 2.86/3.12 ! [A2: int,B2: int] :
% 2.86/3.12 ( ( ( times_times_int @ A2 @ B2 )
% 2.86/3.12 = zero_zero_int )
% 2.86/3.12 => ( ( A2 = zero_zero_int )
% 2.86/3.12 | ( B2 = zero_zero_int ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % divisors_zero
% 2.86/3.12 thf(fact_3972_mult__not__zero,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ( times_3573771949741848930nteger @ A2 @ B2 )
% 2.86/3.12 != zero_z3403309356797280102nteger )
% 2.86/3.12 => ( ( A2 != zero_z3403309356797280102nteger )
% 2.86/3.12 & ( B2 != zero_z3403309356797280102nteger ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_not_zero
% 2.86/3.12 thf(fact_3973_mult__not__zero,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat] :
% 2.86/3.12 ( ( ( times_times_rat @ A2 @ B2 )
% 2.86/3.12 != zero_zero_rat )
% 2.86/3.12 => ( ( A2 != zero_zero_rat )
% 2.86/3.12 & ( B2 != zero_zero_rat ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_not_zero
% 2.86/3.12 thf(fact_3974_mult__not__zero,axiom,
% 2.86/3.12 ! [A2: nat,B2: nat] :
% 2.86/3.12 ( ( ( times_times_nat @ A2 @ B2 )
% 2.86/3.12 != zero_zero_nat )
% 2.86/3.12 => ( ( A2 != zero_zero_nat )
% 2.86/3.12 & ( B2 != zero_zero_nat ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_not_zero
% 2.86/3.12 thf(fact_3975_mult__not__zero,axiom,
% 2.86/3.12 ! [A2: int,B2: int] :
% 2.86/3.12 ( ( ( times_times_int @ A2 @ B2 )
% 2.86/3.12 != zero_zero_int )
% 2.86/3.12 => ( ( A2 != zero_zero_int )
% 2.86/3.12 & ( B2 != zero_zero_int ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_not_zero
% 2.86/3.12 thf(fact_3976_zero__neq__one,axiom,
% 2.86/3.12 zero_z3403309356797280102nteger != one_one_Code_integer ).
% 2.86/3.12
% 2.86/3.12 % zero_neq_one
% 2.86/3.12 thf(fact_3977_zero__neq__one,axiom,
% 2.86/3.12 zero_zero_rat != one_one_rat ).
% 2.86/3.12
% 2.86/3.12 % zero_neq_one
% 2.86/3.12 thf(fact_3978_zero__neq__one,axiom,
% 2.86/3.12 zero_zero_nat != one_one_nat ).
% 2.86/3.12
% 2.86/3.12 % zero_neq_one
% 2.86/3.12 thf(fact_3979_zero__neq__one,axiom,
% 2.86/3.12 zero_zero_int != one_one_int ).
% 2.86/3.12
% 2.86/3.12 % zero_neq_one
% 2.86/3.12 thf(fact_3980_eq__iff__diff__eq__0,axiom,
% 2.86/3.12 ( ( ^ [Y4: code_integer,Z2: code_integer] : ( Y4 = Z2 ) )
% 2.86/3.12 = ( ^ [A3: code_integer,B3: code_integer] :
% 2.86/3.12 ( ( minus_8373710615458151222nteger @ A3 @ B3 )
% 2.86/3.12 = zero_z3403309356797280102nteger ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % eq_iff_diff_eq_0
% 2.86/3.12 thf(fact_3981_eq__iff__diff__eq__0,axiom,
% 2.86/3.12 ( ( ^ [Y4: rat,Z2: rat] : ( Y4 = Z2 ) )
% 2.86/3.12 = ( ^ [A3: rat,B3: rat] :
% 2.86/3.12 ( ( minus_minus_rat @ A3 @ B3 )
% 2.86/3.12 = zero_zero_rat ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % eq_iff_diff_eq_0
% 2.86/3.12 thf(fact_3982_eq__iff__diff__eq__0,axiom,
% 2.86/3.12 ( ( ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 2.86/3.12 = ( ^ [A3: int,B3: int] :
% 2.86/3.12 ( ( minus_minus_int @ A3 @ B3 )
% 2.86/3.12 = zero_zero_int ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % eq_iff_diff_eq_0
% 2.86/3.12 thf(fact_3983_infinite__descent0,axiom,
% 2.86/3.12 ! [P: nat > $o,N: nat] :
% 2.86/3.12 ( ( P @ zero_zero_nat )
% 2.86/3.12 => ( ! [N5: nat] :
% 2.86/3.12 ( ( ord_less_nat @ zero_zero_nat @ N5 )
% 2.86/3.12 => ( ~ ( P @ N5 )
% 2.86/3.12 => ? [M3: nat] :
% 2.86/3.12 ( ( ord_less_nat @ M3 @ N5 )
% 2.86/3.12 & ~ ( P @ M3 ) ) ) )
% 2.86/3.12 => ( P @ N ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % infinite_descent0
% 2.86/3.12 thf(fact_3984_gr__implies__not0,axiom,
% 2.86/3.12 ! [M2: nat,N: nat] :
% 2.86/3.12 ( ( ord_less_nat @ M2 @ N )
% 2.86/3.12 => ( N != zero_zero_nat ) ) ).
% 2.86/3.12
% 2.86/3.12 % gr_implies_not0
% 2.86/3.12 thf(fact_3985_less__zeroE,axiom,
% 2.86/3.12 ! [N: nat] :
% 2.86/3.12 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 2.86/3.12
% 2.86/3.12 % less_zeroE
% 2.86/3.12 thf(fact_3986_not__less0,axiom,
% 2.86/3.12 ! [N: nat] :
% 2.86/3.12 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 2.86/3.12
% 2.86/3.12 % not_less0
% 2.86/3.12 thf(fact_3987_not__gr0,axiom,
% 2.86/3.12 ! [N: nat] :
% 2.86/3.12 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 2.86/3.12 = ( N = zero_zero_nat ) ) ).
% 2.86/3.12
% 2.86/3.12 % not_gr0
% 2.86/3.12 thf(fact_3988_gr0I,axiom,
% 2.86/3.12 ! [N: nat] :
% 2.86/3.12 ( ( N != zero_zero_nat )
% 2.86/3.12 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 2.86/3.12
% 2.86/3.12 % gr0I
% 2.86/3.12 thf(fact_3989_bot__nat__0_Oextremum__strict,axiom,
% 2.86/3.12 ! [A2: nat] :
% 2.86/3.12 ~ ( ord_less_nat @ A2 @ zero_zero_nat ) ).
% 2.86/3.12
% 2.86/3.12 % bot_nat_0.extremum_strict
% 2.86/3.12 thf(fact_3990_add__scale__eq__noteq,axiom,
% 2.86/3.12 ! [R2: code_integer,A2: code_integer,B2: code_integer,C: code_integer,D2: code_integer] :
% 2.86/3.12 ( ( R2 != zero_z3403309356797280102nteger )
% 2.86/3.12 => ( ( ( A2 = B2 )
% 2.86/3.12 & ( C != D2 ) )
% 2.86/3.12 => ( ( plus_p5714425477246183910nteger @ A2 @ ( times_3573771949741848930nteger @ R2 @ C ) )
% 2.86/3.12 != ( plus_p5714425477246183910nteger @ B2 @ ( times_3573771949741848930nteger @ R2 @ D2 ) ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_scale_eq_noteq
% 2.86/3.12 thf(fact_3991_add__scale__eq__noteq,axiom,
% 2.86/3.12 ! [R2: rat,A2: rat,B2: rat,C: rat,D2: rat] :
% 2.86/3.12 ( ( R2 != zero_zero_rat )
% 2.86/3.12 => ( ( ( A2 = B2 )
% 2.86/3.12 & ( C != D2 ) )
% 2.86/3.12 => ( ( plus_plus_rat @ A2 @ ( times_times_rat @ R2 @ C ) )
% 2.86/3.12 != ( plus_plus_rat @ B2 @ ( times_times_rat @ R2 @ D2 ) ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_scale_eq_noteq
% 2.86/3.12 thf(fact_3992_add__scale__eq__noteq,axiom,
% 2.86/3.12 ! [R2: nat,A2: nat,B2: nat,C: nat,D2: nat] :
% 2.86/3.12 ( ( R2 != zero_zero_nat )
% 2.86/3.12 => ( ( ( A2 = B2 )
% 2.86/3.12 & ( C != D2 ) )
% 2.86/3.12 => ( ( plus_plus_nat @ A2 @ ( times_times_nat @ R2 @ C ) )
% 2.86/3.12 != ( plus_plus_nat @ B2 @ ( times_times_nat @ R2 @ D2 ) ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_scale_eq_noteq
% 2.86/3.12 thf(fact_3993_add__scale__eq__noteq,axiom,
% 2.86/3.12 ! [R2: int,A2: int,B2: int,C: int,D2: int] :
% 2.86/3.12 ( ( R2 != zero_zero_int )
% 2.86/3.12 => ( ( ( A2 = B2 )
% 2.86/3.12 & ( C != D2 ) )
% 2.86/3.12 => ( ( plus_plus_int @ A2 @ ( times_times_int @ R2 @ C ) )
% 2.86/3.12 != ( plus_plus_int @ B2 @ ( times_times_int @ R2 @ D2 ) ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_scale_eq_noteq
% 2.86/3.12 thf(fact_3994_nat__mult__eq__cancel1,axiom,
% 2.86/3.12 ! [K3: nat,M2: nat,N: nat] :
% 2.86/3.12 ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 2.86/3.12 => ( ( ( times_times_nat @ K3 @ M2 )
% 2.86/3.12 = ( times_times_nat @ K3 @ N ) )
% 2.86/3.12 = ( M2 = N ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % nat_mult_eq_cancel1
% 2.86/3.12 thf(fact_3995_nat__mult__less__cancel1,axiom,
% 2.86/3.12 ! [K3: nat,M2: nat,N: nat] :
% 2.86/3.12 ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 2.86/3.12 => ( ( ord_less_nat @ ( times_times_nat @ K3 @ M2 ) @ ( times_times_nat @ K3 @ N ) )
% 2.86/3.12 = ( ord_less_nat @ M2 @ N ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % nat_mult_less_cancel1
% 2.86/3.12 thf(fact_3996_add__nonpos__eq__0__iff,axiom,
% 2.86/3.12 ! [X: code_integer,Y: code_integer] :
% 2.86/3.12 ( ( ord_le3102999989581377725nteger @ X @ zero_z3403309356797280102nteger )
% 2.86/3.12 => ( ( ord_le3102999989581377725nteger @ Y @ zero_z3403309356797280102nteger )
% 2.86/3.12 => ( ( ( plus_p5714425477246183910nteger @ X @ Y )
% 2.86/3.12 = zero_z3403309356797280102nteger )
% 2.86/3.12 = ( ( X = zero_z3403309356797280102nteger )
% 2.86/3.12 & ( Y = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_nonpos_eq_0_iff
% 2.86/3.12 thf(fact_3997_add__nonpos__eq__0__iff,axiom,
% 2.86/3.12 ! [X: rat,Y: rat] :
% 2.86/3.12 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 2.86/3.12 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 2.86/3.12 => ( ( ( plus_plus_rat @ X @ Y )
% 2.86/3.12 = zero_zero_rat )
% 2.86/3.12 = ( ( X = zero_zero_rat )
% 2.86/3.12 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_nonpos_eq_0_iff
% 2.86/3.12 thf(fact_3998_add__nonpos__eq__0__iff,axiom,
% 2.86/3.12 ! [X: nat,Y: nat] :
% 2.86/3.12 ( ( ord_less_eq_nat @ X @ zero_zero_nat )
% 2.86/3.12 => ( ( ord_less_eq_nat @ Y @ zero_zero_nat )
% 2.86/3.12 => ( ( ( plus_plus_nat @ X @ Y )
% 2.86/3.12 = zero_zero_nat )
% 2.86/3.12 = ( ( X = zero_zero_nat )
% 2.86/3.12 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_nonpos_eq_0_iff
% 2.86/3.12 thf(fact_3999_add__nonpos__eq__0__iff,axiom,
% 2.86/3.12 ! [X: int,Y: int] :
% 2.86/3.12 ( ( ord_less_eq_int @ X @ zero_zero_int )
% 2.86/3.12 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 2.86/3.12 => ( ( ( plus_plus_int @ X @ Y )
% 2.86/3.12 = zero_zero_int )
% 2.86/3.12 = ( ( X = zero_zero_int )
% 2.86/3.12 & ( Y = zero_zero_int ) ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_nonpos_eq_0_iff
% 2.86/3.12 thf(fact_4000_add__nonneg__eq__0__iff,axiom,
% 2.86/3.12 ! [X: code_integer,Y: code_integer] :
% 2.86/3.12 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 2.86/3.12 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 2.86/3.12 => ( ( ( plus_p5714425477246183910nteger @ X @ Y )
% 2.86/3.12 = zero_z3403309356797280102nteger )
% 2.86/3.12 = ( ( X = zero_z3403309356797280102nteger )
% 2.86/3.12 & ( Y = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_nonneg_eq_0_iff
% 2.86/3.12 thf(fact_4001_add__nonneg__eq__0__iff,axiom,
% 2.86/3.12 ! [X: rat,Y: rat] :
% 2.86/3.12 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 2.86/3.12 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 2.86/3.12 => ( ( ( plus_plus_rat @ X @ Y )
% 2.86/3.12 = zero_zero_rat )
% 2.86/3.12 = ( ( X = zero_zero_rat )
% 2.86/3.12 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_nonneg_eq_0_iff
% 2.86/3.12 thf(fact_4002_add__nonneg__eq__0__iff,axiom,
% 2.86/3.12 ! [X: nat,Y: nat] :
% 2.86/3.12 ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 2.86/3.12 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 2.86/3.12 => ( ( ( plus_plus_nat @ X @ Y )
% 2.86/3.12 = zero_zero_nat )
% 2.86/3.12 = ( ( X = zero_zero_nat )
% 2.86/3.12 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_nonneg_eq_0_iff
% 2.86/3.12 thf(fact_4003_add__nonneg__eq__0__iff,axiom,
% 2.86/3.12 ! [X: int,Y: int] :
% 2.86/3.12 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 2.86/3.12 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 2.86/3.12 => ( ( ( plus_plus_int @ X @ Y )
% 2.86/3.12 = zero_zero_int )
% 2.86/3.12 = ( ( X = zero_zero_int )
% 2.86/3.12 & ( Y = zero_zero_int ) ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_nonneg_eq_0_iff
% 2.86/3.12 thf(fact_4004_add__nonpos__nonpos,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ord_le3102999989581377725nteger @ A2 @ zero_z3403309356797280102nteger )
% 2.86/3.12 => ( ( ord_le3102999989581377725nteger @ B2 @ zero_z3403309356797280102nteger )
% 2.86/3.12 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A2 @ B2 ) @ zero_z3403309356797280102nteger ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_nonpos_nonpos
% 2.86/3.12 thf(fact_4005_add__nonpos__nonpos,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat] :
% 2.86/3.12 ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 2.86/3.12 => ( ( ord_less_eq_rat @ B2 @ zero_zero_rat )
% 2.86/3.12 => ( ord_less_eq_rat @ ( plus_plus_rat @ A2 @ B2 ) @ zero_zero_rat ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_nonpos_nonpos
% 2.86/3.12 thf(fact_4006_add__nonpos__nonpos,axiom,
% 2.86/3.12 ! [A2: nat,B2: nat] :
% 2.86/3.12 ( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
% 2.86/3.12 => ( ( ord_less_eq_nat @ B2 @ zero_zero_nat )
% 2.86/3.12 => ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ B2 ) @ zero_zero_nat ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_nonpos_nonpos
% 2.86/3.12 thf(fact_4007_add__nonpos__nonpos,axiom,
% 2.86/3.12 ! [A2: int,B2: int] :
% 2.86/3.12 ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 2.86/3.12 => ( ( ord_less_eq_int @ B2 @ zero_zero_int )
% 2.86/3.12 => ( ord_less_eq_int @ ( plus_plus_int @ A2 @ B2 ) @ zero_zero_int ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_nonpos_nonpos
% 2.86/3.12 thf(fact_4008_add__nonneg__nonneg,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 2.86/3.12 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B2 )
% 2.86/3.12 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A2 @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_nonneg_nonneg
% 2.86/3.12 thf(fact_4009_add__nonneg__nonneg,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat] :
% 2.86/3.12 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 2.86/3.12 => ( ( ord_less_eq_rat @ zero_zero_rat @ B2 )
% 2.86/3.12 => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A2 @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_nonneg_nonneg
% 2.86/3.12 thf(fact_4010_add__nonneg__nonneg,axiom,
% 2.86/3.12 ! [A2: nat,B2: nat] :
% 2.86/3.12 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 2.86/3.12 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 2.86/3.12 => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A2 @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_nonneg_nonneg
% 2.86/3.12 thf(fact_4011_add__nonneg__nonneg,axiom,
% 2.86/3.12 ! [A2: int,B2: int] :
% 2.86/3.12 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 2.86/3.12 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 2.86/3.12 => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A2 @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_nonneg_nonneg
% 2.86/3.12 thf(fact_4012_add__increasing2,axiom,
% 2.86/3.12 ! [C: code_integer,B2: code_integer,A2: code_integer] :
% 2.86/3.12 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 2.86/3.12 => ( ( ord_le3102999989581377725nteger @ B2 @ A2 )
% 2.86/3.12 => ( ord_le3102999989581377725nteger @ B2 @ ( plus_p5714425477246183910nteger @ A2 @ C ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_increasing2
% 2.86/3.12 thf(fact_4013_add__increasing2,axiom,
% 2.86/3.12 ! [C: rat,B2: rat,A2: rat] :
% 2.86/3.12 ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 2.86/3.12 => ( ( ord_less_eq_rat @ B2 @ A2 )
% 2.86/3.12 => ( ord_less_eq_rat @ B2 @ ( plus_plus_rat @ A2 @ C ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_increasing2
% 2.86/3.12 thf(fact_4014_add__increasing2,axiom,
% 2.86/3.12 ! [C: nat,B2: nat,A2: nat] :
% 2.86/3.12 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 2.86/3.12 => ( ( ord_less_eq_nat @ B2 @ A2 )
% 2.86/3.12 => ( ord_less_eq_nat @ B2 @ ( plus_plus_nat @ A2 @ C ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_increasing2
% 2.86/3.12 thf(fact_4015_add__increasing2,axiom,
% 2.86/3.12 ! [C: int,B2: int,A2: int] :
% 2.86/3.12 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 2.86/3.12 => ( ( ord_less_eq_int @ B2 @ A2 )
% 2.86/3.12 => ( ord_less_eq_int @ B2 @ ( plus_plus_int @ A2 @ C ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_increasing2
% 2.86/3.12 thf(fact_4016_add__decreasing2,axiom,
% 2.86/3.12 ! [C: code_integer,A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 2.86/3.12 => ( ( ord_le3102999989581377725nteger @ A2 @ B2 )
% 2.86/3.12 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A2 @ C ) @ B2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_decreasing2
% 2.86/3.12 thf(fact_4017_add__decreasing2,axiom,
% 2.86/3.12 ! [C: rat,A2: rat,B2: rat] :
% 2.86/3.12 ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 2.86/3.12 => ( ( ord_less_eq_rat @ A2 @ B2 )
% 2.86/3.12 => ( ord_less_eq_rat @ ( plus_plus_rat @ A2 @ C ) @ B2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_decreasing2
% 2.86/3.12 thf(fact_4018_add__decreasing2,axiom,
% 2.86/3.12 ! [C: nat,A2: nat,B2: nat] :
% 2.86/3.12 ( ( ord_less_eq_nat @ C @ zero_zero_nat )
% 2.86/3.12 => ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.12 => ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ C ) @ B2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_decreasing2
% 2.86/3.12 thf(fact_4019_add__decreasing2,axiom,
% 2.86/3.12 ! [C: int,A2: int,B2: int] :
% 2.86/3.12 ( ( ord_less_eq_int @ C @ zero_zero_int )
% 2.86/3.12 => ( ( ord_less_eq_int @ A2 @ B2 )
% 2.86/3.12 => ( ord_less_eq_int @ ( plus_plus_int @ A2 @ C ) @ B2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_decreasing2
% 2.86/3.12 thf(fact_4020_add__increasing,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer,C: code_integer] :
% 2.86/3.12 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 2.86/3.12 => ( ( ord_le3102999989581377725nteger @ B2 @ C )
% 2.86/3.12 => ( ord_le3102999989581377725nteger @ B2 @ ( plus_p5714425477246183910nteger @ A2 @ C ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_increasing
% 2.86/3.12 thf(fact_4021_add__increasing,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat,C: rat] :
% 2.86/3.12 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 2.86/3.12 => ( ( ord_less_eq_rat @ B2 @ C )
% 2.86/3.12 => ( ord_less_eq_rat @ B2 @ ( plus_plus_rat @ A2 @ C ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_increasing
% 2.86/3.12 thf(fact_4022_add__increasing,axiom,
% 2.86/3.12 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.12 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 2.86/3.12 => ( ( ord_less_eq_nat @ B2 @ C )
% 2.86/3.12 => ( ord_less_eq_nat @ B2 @ ( plus_plus_nat @ A2 @ C ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_increasing
% 2.86/3.12 thf(fact_4023_add__increasing,axiom,
% 2.86/3.12 ! [A2: int,B2: int,C: int] :
% 2.86/3.12 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 2.86/3.12 => ( ( ord_less_eq_int @ B2 @ C )
% 2.86/3.12 => ( ord_less_eq_int @ B2 @ ( plus_plus_int @ A2 @ C ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_increasing
% 2.86/3.12 thf(fact_4024_add__decreasing,axiom,
% 2.86/3.12 ! [A2: code_integer,C: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ord_le3102999989581377725nteger @ A2 @ zero_z3403309356797280102nteger )
% 2.86/3.12 => ( ( ord_le3102999989581377725nteger @ C @ B2 )
% 2.86/3.12 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A2 @ C ) @ B2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_decreasing
% 2.86/3.12 thf(fact_4025_add__decreasing,axiom,
% 2.86/3.12 ! [A2: rat,C: rat,B2: rat] :
% 2.86/3.12 ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 2.86/3.12 => ( ( ord_less_eq_rat @ C @ B2 )
% 2.86/3.12 => ( ord_less_eq_rat @ ( plus_plus_rat @ A2 @ C ) @ B2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_decreasing
% 2.86/3.12 thf(fact_4026_add__decreasing,axiom,
% 2.86/3.12 ! [A2: nat,C: nat,B2: nat] :
% 2.86/3.12 ( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
% 2.86/3.12 => ( ( ord_less_eq_nat @ C @ B2 )
% 2.86/3.12 => ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ C ) @ B2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_decreasing
% 2.86/3.12 thf(fact_4027_add__decreasing,axiom,
% 2.86/3.12 ! [A2: int,C: int,B2: int] :
% 2.86/3.12 ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 2.86/3.12 => ( ( ord_less_eq_int @ C @ B2 )
% 2.86/3.12 => ( ord_less_eq_int @ ( plus_plus_int @ A2 @ C ) @ B2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_decreasing
% 2.86/3.12 thf(fact_4028_mult__mono,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer,C: code_integer,D2: code_integer] :
% 2.86/3.12 ( ( ord_le3102999989581377725nteger @ A2 @ B2 )
% 2.86/3.12 => ( ( ord_le3102999989581377725nteger @ C @ D2 )
% 2.86/3.12 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B2 )
% 2.86/3.12 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 2.86/3.12 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ ( times_3573771949741848930nteger @ B2 @ D2 ) ) ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_mono
% 2.86/3.12 thf(fact_4029_mult__mono,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat,C: rat,D2: rat] :
% 2.86/3.12 ( ( ord_less_eq_rat @ A2 @ B2 )
% 2.86/3.12 => ( ( ord_less_eq_rat @ C @ D2 )
% 2.86/3.12 => ( ( ord_less_eq_rat @ zero_zero_rat @ B2 )
% 2.86/3.12 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 2.86/3.12 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B2 @ D2 ) ) ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_mono
% 2.86/3.12 thf(fact_4030_mult__mono,axiom,
% 2.86/3.12 ! [A2: nat,B2: nat,C: nat,D2: nat] :
% 2.86/3.12 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.12 => ( ( ord_less_eq_nat @ C @ D2 )
% 2.86/3.12 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 2.86/3.12 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 2.86/3.12 => ( ord_less_eq_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B2 @ D2 ) ) ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_mono
% 2.86/3.12 thf(fact_4031_mult__mono,axiom,
% 2.86/3.12 ! [A2: int,B2: int,C: int,D2: int] :
% 2.86/3.12 ( ( ord_less_eq_int @ A2 @ B2 )
% 2.86/3.12 => ( ( ord_less_eq_int @ C @ D2 )
% 2.86/3.12 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 2.86/3.12 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 2.86/3.12 => ( ord_less_eq_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B2 @ D2 ) ) ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_mono
% 2.86/3.12 thf(fact_4032_mult__mono_H,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer,C: code_integer,D2: code_integer] :
% 2.86/3.12 ( ( ord_le3102999989581377725nteger @ A2 @ B2 )
% 2.86/3.12 => ( ( ord_le3102999989581377725nteger @ C @ D2 )
% 2.86/3.12 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 2.86/3.12 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 2.86/3.12 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ ( times_3573771949741848930nteger @ B2 @ D2 ) ) ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_mono'
% 2.86/3.12 thf(fact_4033_mult__mono_H,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat,C: rat,D2: rat] :
% 2.86/3.12 ( ( ord_less_eq_rat @ A2 @ B2 )
% 2.86/3.12 => ( ( ord_less_eq_rat @ C @ D2 )
% 2.86/3.12 => ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 2.86/3.12 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 2.86/3.12 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B2 @ D2 ) ) ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_mono'
% 2.86/3.12 thf(fact_4034_mult__mono_H,axiom,
% 2.86/3.12 ! [A2: nat,B2: nat,C: nat,D2: nat] :
% 2.86/3.12 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.12 => ( ( ord_less_eq_nat @ C @ D2 )
% 2.86/3.12 => ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 2.86/3.12 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 2.86/3.12 => ( ord_less_eq_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B2 @ D2 ) ) ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_mono'
% 2.86/3.12 thf(fact_4035_mult__mono_H,axiom,
% 2.86/3.12 ! [A2: int,B2: int,C: int,D2: int] :
% 2.86/3.12 ( ( ord_less_eq_int @ A2 @ B2 )
% 2.86/3.12 => ( ( ord_less_eq_int @ C @ D2 )
% 2.86/3.12 => ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 2.86/3.12 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 2.86/3.12 => ( ord_less_eq_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B2 @ D2 ) ) ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_mono'
% 2.86/3.12 thf(fact_4036_zero__le__square,axiom,
% 2.86/3.12 ! [A2: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A2 @ A2 ) ) ).
% 2.86/3.12
% 2.86/3.12 % zero_le_square
% 2.86/3.12 thf(fact_4037_zero__le__square,axiom,
% 2.86/3.12 ! [A2: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ A2 ) ) ).
% 2.86/3.12
% 2.86/3.12 % zero_le_square
% 2.86/3.12 thf(fact_4038_zero__le__square,axiom,
% 2.86/3.12 ! [A2: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A2 @ A2 ) ) ).
% 2.86/3.12
% 2.86/3.12 % zero_le_square
% 2.86/3.12 thf(fact_4039_split__mult__pos__le,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 2.86/3.12 & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B2 ) )
% 2.86/3.12 | ( ( ord_le3102999989581377725nteger @ A2 @ zero_z3403309356797280102nteger )
% 2.86/3.12 & ( ord_le3102999989581377725nteger @ B2 @ zero_z3403309356797280102nteger ) ) )
% 2.86/3.12 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A2 @ B2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % split_mult_pos_le
% 2.86/3.12 thf(fact_4040_split__mult__pos__le,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat] :
% 2.86/3.12 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 2.86/3.12 & ( ord_less_eq_rat @ zero_zero_rat @ B2 ) )
% 2.86/3.12 | ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 2.86/3.12 & ( ord_less_eq_rat @ B2 @ zero_zero_rat ) ) )
% 2.86/3.12 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ B2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % split_mult_pos_le
% 2.86/3.12 thf(fact_4041_split__mult__pos__le,axiom,
% 2.86/3.12 ! [A2: int,B2: int] :
% 2.86/3.12 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 2.86/3.12 & ( ord_less_eq_int @ zero_zero_int @ B2 ) )
% 2.86/3.12 | ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 2.86/3.12 & ( ord_less_eq_int @ B2 @ zero_zero_int ) ) )
% 2.86/3.12 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A2 @ B2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % split_mult_pos_le
% 2.86/3.12 thf(fact_4042_mult__left__mono__neg,axiom,
% 2.86/3.12 ! [B2: code_integer,A2: code_integer,C: code_integer] :
% 2.86/3.12 ( ( ord_le3102999989581377725nteger @ B2 @ A2 )
% 2.86/3.12 => ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 2.86/3.12 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A2 ) @ ( times_3573771949741848930nteger @ C @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_left_mono_neg
% 2.86/3.12 thf(fact_4043_mult__left__mono__neg,axiom,
% 2.86/3.12 ! [B2: rat,A2: rat,C: rat] :
% 2.86/3.12 ( ( ord_less_eq_rat @ B2 @ A2 )
% 2.86/3.12 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 2.86/3.12 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_left_mono_neg
% 2.86/3.12 thf(fact_4044_mult__left__mono__neg,axiom,
% 2.86/3.12 ! [B2: int,A2: int,C: int] :
% 2.86/3.12 ( ( ord_less_eq_int @ B2 @ A2 )
% 2.86/3.12 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 2.86/3.12 => ( ord_less_eq_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_left_mono_neg
% 2.86/3.12 thf(fact_4045_mult__nonpos__nonpos,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ord_le3102999989581377725nteger @ A2 @ zero_z3403309356797280102nteger )
% 2.86/3.12 => ( ( ord_le3102999989581377725nteger @ B2 @ zero_z3403309356797280102nteger )
% 2.86/3.12 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A2 @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_nonpos_nonpos
% 2.86/3.12 thf(fact_4046_mult__nonpos__nonpos,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat] :
% 2.86/3.12 ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 2.86/3.12 => ( ( ord_less_eq_rat @ B2 @ zero_zero_rat )
% 2.86/3.12 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_nonpos_nonpos
% 2.86/3.12 thf(fact_4047_mult__nonpos__nonpos,axiom,
% 2.86/3.12 ! [A2: int,B2: int] :
% 2.86/3.12 ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 2.86/3.12 => ( ( ord_less_eq_int @ B2 @ zero_zero_int )
% 2.86/3.12 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A2 @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_nonpos_nonpos
% 2.86/3.12 thf(fact_4048_mult__left__mono,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer,C: code_integer] :
% 2.86/3.12 ( ( ord_le3102999989581377725nteger @ A2 @ B2 )
% 2.86/3.12 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 2.86/3.12 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A2 ) @ ( times_3573771949741848930nteger @ C @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_left_mono
% 2.86/3.12 thf(fact_4049_mult__left__mono,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat,C: rat] :
% 2.86/3.12 ( ( ord_less_eq_rat @ A2 @ B2 )
% 2.86/3.12 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 2.86/3.12 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_left_mono
% 2.86/3.12 thf(fact_4050_mult__left__mono,axiom,
% 2.86/3.12 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.12 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.12 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 2.86/3.12 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A2 ) @ ( times_times_nat @ C @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_left_mono
% 2.86/3.12 thf(fact_4051_mult__left__mono,axiom,
% 2.86/3.12 ! [A2: int,B2: int,C: int] :
% 2.86/3.12 ( ( ord_less_eq_int @ A2 @ B2 )
% 2.86/3.12 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 2.86/3.12 => ( ord_less_eq_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_left_mono
% 2.86/3.12 thf(fact_4052_mult__right__mono__neg,axiom,
% 2.86/3.12 ! [B2: code_integer,A2: code_integer,C: code_integer] :
% 2.86/3.12 ( ( ord_le3102999989581377725nteger @ B2 @ A2 )
% 2.86/3.12 => ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 2.86/3.12 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ ( times_3573771949741848930nteger @ B2 @ C ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_right_mono_neg
% 2.86/3.12 thf(fact_4053_mult__right__mono__neg,axiom,
% 2.86/3.12 ! [B2: rat,A2: rat,C: rat] :
% 2.86/3.12 ( ( ord_less_eq_rat @ B2 @ A2 )
% 2.86/3.12 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 2.86/3.12 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B2 @ C ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_right_mono_neg
% 2.86/3.12 thf(fact_4054_mult__right__mono__neg,axiom,
% 2.86/3.12 ! [B2: int,A2: int,C: int] :
% 2.86/3.12 ( ( ord_less_eq_int @ B2 @ A2 )
% 2.86/3.12 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 2.86/3.12 => ( ord_less_eq_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B2 @ C ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_right_mono_neg
% 2.86/3.12 thf(fact_4055_mult__right__mono,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer,C: code_integer] :
% 2.86/3.12 ( ( ord_le3102999989581377725nteger @ A2 @ B2 )
% 2.86/3.12 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 2.86/3.12 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ ( times_3573771949741848930nteger @ B2 @ C ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_right_mono
% 2.86/3.12 thf(fact_4056_mult__right__mono,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat,C: rat] :
% 2.86/3.12 ( ( ord_less_eq_rat @ A2 @ B2 )
% 2.86/3.12 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 2.86/3.12 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B2 @ C ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_right_mono
% 2.86/3.12 thf(fact_4057_mult__right__mono,axiom,
% 2.86/3.12 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.12 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.12 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 2.86/3.12 => ( ord_less_eq_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B2 @ C ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_right_mono
% 2.86/3.12 thf(fact_4058_mult__right__mono,axiom,
% 2.86/3.12 ! [A2: int,B2: int,C: int] :
% 2.86/3.12 ( ( ord_less_eq_int @ A2 @ B2 )
% 2.86/3.12 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 2.86/3.12 => ( ord_less_eq_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B2 @ C ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_right_mono
% 2.86/3.12 thf(fact_4059_mult__le__0__iff,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A2 @ B2 ) @ zero_z3403309356797280102nteger )
% 2.86/3.12 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 2.86/3.12 & ( ord_le3102999989581377725nteger @ B2 @ zero_z3403309356797280102nteger ) )
% 2.86/3.12 | ( ( ord_le3102999989581377725nteger @ A2 @ zero_z3403309356797280102nteger )
% 2.86/3.12 & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_le_0_iff
% 2.86/3.12 thf(fact_4060_mult__le__0__iff,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat] :
% 2.86/3.12 ( ( ord_less_eq_rat @ ( times_times_rat @ A2 @ B2 ) @ zero_zero_rat )
% 2.86/3.12 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 2.86/3.12 & ( ord_less_eq_rat @ B2 @ zero_zero_rat ) )
% 2.86/3.12 | ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 2.86/3.12 & ( ord_less_eq_rat @ zero_zero_rat @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_le_0_iff
% 2.86/3.12 thf(fact_4061_mult__le__0__iff,axiom,
% 2.86/3.12 ! [A2: int,B2: int] :
% 2.86/3.12 ( ( ord_less_eq_int @ ( times_times_int @ A2 @ B2 ) @ zero_zero_int )
% 2.86/3.12 = ( ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 2.86/3.12 & ( ord_less_eq_int @ B2 @ zero_zero_int ) )
% 2.86/3.12 | ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 2.86/3.12 & ( ord_less_eq_int @ zero_zero_int @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_le_0_iff
% 2.86/3.12 thf(fact_4062_split__mult__neg__le,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 2.86/3.12 & ( ord_le3102999989581377725nteger @ B2 @ zero_z3403309356797280102nteger ) )
% 2.86/3.12 | ( ( ord_le3102999989581377725nteger @ A2 @ zero_z3403309356797280102nteger )
% 2.86/3.12 & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B2 ) ) )
% 2.86/3.12 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A2 @ B2 ) @ zero_z3403309356797280102nteger ) ) ).
% 2.86/3.12
% 2.86/3.12 % split_mult_neg_le
% 2.86/3.12 thf(fact_4063_split__mult__neg__le,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat] :
% 2.86/3.12 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 2.86/3.12 & ( ord_less_eq_rat @ B2 @ zero_zero_rat ) )
% 2.86/3.12 | ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 2.86/3.12 & ( ord_less_eq_rat @ zero_zero_rat @ B2 ) ) )
% 2.86/3.12 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ B2 ) @ zero_zero_rat ) ) ).
% 2.86/3.12
% 2.86/3.12 % split_mult_neg_le
% 2.86/3.12 thf(fact_4064_split__mult__neg__le,axiom,
% 2.86/3.12 ! [A2: nat,B2: nat] :
% 2.86/3.12 ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 2.86/3.12 & ( ord_less_eq_nat @ B2 @ zero_zero_nat ) )
% 2.86/3.12 | ( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
% 2.86/3.12 & ( ord_less_eq_nat @ zero_zero_nat @ B2 ) ) )
% 2.86/3.12 => ( ord_less_eq_nat @ ( times_times_nat @ A2 @ B2 ) @ zero_zero_nat ) ) ).
% 2.86/3.12
% 2.86/3.12 % split_mult_neg_le
% 2.86/3.12 thf(fact_4065_split__mult__neg__le,axiom,
% 2.86/3.12 ! [A2: int,B2: int] :
% 2.86/3.12 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 2.86/3.12 & ( ord_less_eq_int @ B2 @ zero_zero_int ) )
% 2.86/3.12 | ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 2.86/3.12 & ( ord_less_eq_int @ zero_zero_int @ B2 ) ) )
% 2.86/3.12 => ( ord_less_eq_int @ ( times_times_int @ A2 @ B2 ) @ zero_zero_int ) ) ).
% 2.86/3.12
% 2.86/3.12 % split_mult_neg_le
% 2.86/3.12 thf(fact_4066_mult__nonneg__nonneg,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 2.86/3.12 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B2 )
% 2.86/3.12 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A2 @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_nonneg_nonneg
% 2.86/3.12 thf(fact_4067_mult__nonneg__nonneg,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat] :
% 2.86/3.12 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 2.86/3.12 => ( ( ord_less_eq_rat @ zero_zero_rat @ B2 )
% 2.86/3.12 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_nonneg_nonneg
% 2.86/3.12 thf(fact_4068_mult__nonneg__nonneg,axiom,
% 2.86/3.12 ! [A2: nat,B2: nat] :
% 2.86/3.12 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 2.86/3.12 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 2.86/3.12 => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A2 @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_nonneg_nonneg
% 2.86/3.12 thf(fact_4069_mult__nonneg__nonneg,axiom,
% 2.86/3.12 ! [A2: int,B2: int] :
% 2.86/3.12 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 2.86/3.12 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 2.86/3.12 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A2 @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_nonneg_nonneg
% 2.86/3.12 thf(fact_4070_mult__nonneg__nonpos,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 2.86/3.12 => ( ( ord_le3102999989581377725nteger @ B2 @ zero_z3403309356797280102nteger )
% 2.86/3.12 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A2 @ B2 ) @ zero_z3403309356797280102nteger ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_nonneg_nonpos
% 2.86/3.12 thf(fact_4071_mult__nonneg__nonpos,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat] :
% 2.86/3.12 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 2.86/3.12 => ( ( ord_less_eq_rat @ B2 @ zero_zero_rat )
% 2.86/3.12 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ B2 ) @ zero_zero_rat ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_nonneg_nonpos
% 2.86/3.12 thf(fact_4072_mult__nonneg__nonpos,axiom,
% 2.86/3.12 ! [A2: nat,B2: nat] :
% 2.86/3.12 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 2.86/3.12 => ( ( ord_less_eq_nat @ B2 @ zero_zero_nat )
% 2.86/3.12 => ( ord_less_eq_nat @ ( times_times_nat @ A2 @ B2 ) @ zero_zero_nat ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_nonneg_nonpos
% 2.86/3.12 thf(fact_4073_mult__nonneg__nonpos,axiom,
% 2.86/3.12 ! [A2: int,B2: int] :
% 2.86/3.12 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 2.86/3.12 => ( ( ord_less_eq_int @ B2 @ zero_zero_int )
% 2.86/3.12 => ( ord_less_eq_int @ ( times_times_int @ A2 @ B2 ) @ zero_zero_int ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_nonneg_nonpos
% 2.86/3.12 thf(fact_4074_mult__nonpos__nonneg,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ord_le3102999989581377725nteger @ A2 @ zero_z3403309356797280102nteger )
% 2.86/3.12 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B2 )
% 2.86/3.12 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A2 @ B2 ) @ zero_z3403309356797280102nteger ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_nonpos_nonneg
% 2.86/3.12 thf(fact_4075_mult__nonpos__nonneg,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat] :
% 2.86/3.12 ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 2.86/3.12 => ( ( ord_less_eq_rat @ zero_zero_rat @ B2 )
% 2.86/3.12 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ B2 ) @ zero_zero_rat ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_nonpos_nonneg
% 2.86/3.12 thf(fact_4076_mult__nonpos__nonneg,axiom,
% 2.86/3.12 ! [A2: nat,B2: nat] :
% 2.86/3.12 ( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
% 2.86/3.12 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 2.86/3.12 => ( ord_less_eq_nat @ ( times_times_nat @ A2 @ B2 ) @ zero_zero_nat ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_nonpos_nonneg
% 2.86/3.12 thf(fact_4077_mult__nonpos__nonneg,axiom,
% 2.86/3.12 ! [A2: int,B2: int] :
% 2.86/3.12 ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 2.86/3.12 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 2.86/3.12 => ( ord_less_eq_int @ ( times_times_int @ A2 @ B2 ) @ zero_zero_int ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_nonpos_nonneg
% 2.86/3.12 thf(fact_4078_mult__nonneg__nonpos2,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 2.86/3.12 => ( ( ord_le3102999989581377725nteger @ B2 @ zero_z3403309356797280102nteger )
% 2.86/3.12 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ B2 @ A2 ) @ zero_z3403309356797280102nteger ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_nonneg_nonpos2
% 2.86/3.12 thf(fact_4079_mult__nonneg__nonpos2,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat] :
% 2.86/3.12 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 2.86/3.12 => ( ( ord_less_eq_rat @ B2 @ zero_zero_rat )
% 2.86/3.12 => ( ord_less_eq_rat @ ( times_times_rat @ B2 @ A2 ) @ zero_zero_rat ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_nonneg_nonpos2
% 2.86/3.12 thf(fact_4080_mult__nonneg__nonpos2,axiom,
% 2.86/3.12 ! [A2: nat,B2: nat] :
% 2.86/3.12 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 2.86/3.12 => ( ( ord_less_eq_nat @ B2 @ zero_zero_nat )
% 2.86/3.12 => ( ord_less_eq_nat @ ( times_times_nat @ B2 @ A2 ) @ zero_zero_nat ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_nonneg_nonpos2
% 2.86/3.12 thf(fact_4081_mult__nonneg__nonpos2,axiom,
% 2.86/3.12 ! [A2: int,B2: int] :
% 2.86/3.12 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 2.86/3.12 => ( ( ord_less_eq_int @ B2 @ zero_zero_int )
% 2.86/3.12 => ( ord_less_eq_int @ ( times_times_int @ B2 @ A2 ) @ zero_zero_int ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_nonneg_nonpos2
% 2.86/3.12 thf(fact_4082_zero__le__mult__iff,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A2 @ B2 ) )
% 2.86/3.12 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 2.86/3.12 & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B2 ) )
% 2.86/3.12 | ( ( ord_le3102999989581377725nteger @ A2 @ zero_z3403309356797280102nteger )
% 2.86/3.12 & ( ord_le3102999989581377725nteger @ B2 @ zero_z3403309356797280102nteger ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % zero_le_mult_iff
% 2.86/3.12 thf(fact_4083_zero__le__mult__iff,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat] :
% 2.86/3.12 ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ B2 ) )
% 2.86/3.12 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 2.86/3.12 & ( ord_less_eq_rat @ zero_zero_rat @ B2 ) )
% 2.86/3.12 | ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 2.86/3.12 & ( ord_less_eq_rat @ B2 @ zero_zero_rat ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % zero_le_mult_iff
% 2.86/3.12 thf(fact_4084_zero__le__mult__iff,axiom,
% 2.86/3.12 ! [A2: int,B2: int] :
% 2.86/3.12 ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A2 @ B2 ) )
% 2.86/3.12 = ( ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 2.86/3.12 & ( ord_less_eq_int @ zero_zero_int @ B2 ) )
% 2.86/3.12 | ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 2.86/3.12 & ( ord_less_eq_int @ B2 @ zero_zero_int ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % zero_le_mult_iff
% 2.86/3.12 thf(fact_4085_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer,C: code_integer] :
% 2.86/3.12 ( ( ord_le3102999989581377725nteger @ A2 @ B2 )
% 2.86/3.12 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 2.86/3.12 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A2 ) @ ( times_3573771949741848930nteger @ C @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % ordered_comm_semiring_class.comm_mult_left_mono
% 2.86/3.12 thf(fact_4086_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat,C: rat] :
% 2.86/3.12 ( ( ord_less_eq_rat @ A2 @ B2 )
% 2.86/3.12 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 2.86/3.12 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % ordered_comm_semiring_class.comm_mult_left_mono
% 2.86/3.12 thf(fact_4087_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 2.86/3.12 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.12 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.12 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 2.86/3.12 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A2 ) @ ( times_times_nat @ C @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % ordered_comm_semiring_class.comm_mult_left_mono
% 2.86/3.12 thf(fact_4088_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 2.86/3.12 ! [A2: int,B2: int,C: int] :
% 2.86/3.12 ( ( ord_less_eq_int @ A2 @ B2 )
% 2.86/3.12 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 2.86/3.12 => ( ord_less_eq_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % ordered_comm_semiring_class.comm_mult_left_mono
% 2.86/3.12 thf(fact_4089_zero__less__one__class_Ozero__le__one,axiom,
% 2.86/3.12 ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 2.86/3.12
% 2.86/3.12 % zero_less_one_class.zero_le_one
% 2.86/3.12 thf(fact_4090_zero__less__one__class_Ozero__le__one,axiom,
% 2.86/3.12 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 2.86/3.12
% 2.86/3.12 % zero_less_one_class.zero_le_one
% 2.86/3.12 thf(fact_4091_zero__less__one__class_Ozero__le__one,axiom,
% 2.86/3.12 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 2.86/3.12
% 2.86/3.12 % zero_less_one_class.zero_le_one
% 2.86/3.12 thf(fact_4092_zero__less__one__class_Ozero__le__one,axiom,
% 2.86/3.12 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 2.86/3.12
% 2.86/3.12 % zero_less_one_class.zero_le_one
% 2.86/3.12 thf(fact_4093_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 2.86/3.12 ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 2.86/3.12
% 2.86/3.12 % linordered_nonzero_semiring_class.zero_le_one
% 2.86/3.12 thf(fact_4094_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 2.86/3.12 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 2.86/3.12
% 2.86/3.12 % linordered_nonzero_semiring_class.zero_le_one
% 2.86/3.12 thf(fact_4095_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 2.86/3.12 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 2.86/3.12
% 2.86/3.12 % linordered_nonzero_semiring_class.zero_le_one
% 2.86/3.12 thf(fact_4096_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 2.86/3.12 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 2.86/3.12
% 2.86/3.12 % linordered_nonzero_semiring_class.zero_le_one
% 2.86/3.12 thf(fact_4097_not__one__le__zero,axiom,
% 2.86/3.12 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ).
% 2.86/3.12
% 2.86/3.12 % not_one_le_zero
% 2.86/3.12 thf(fact_4098_not__one__le__zero,axiom,
% 2.86/3.12 ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 2.86/3.12
% 2.86/3.12 % not_one_le_zero
% 2.86/3.12 thf(fact_4099_not__one__le__zero,axiom,
% 2.86/3.12 ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 2.86/3.12
% 2.86/3.12 % not_one_le_zero
% 2.86/3.12 thf(fact_4100_not__one__le__zero,axiom,
% 2.86/3.12 ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 2.86/3.12
% 2.86/3.12 % not_one_le_zero
% 2.86/3.12 thf(fact_4101_le__iff__diff__le__0,axiom,
% 2.86/3.12 ( ord_le3102999989581377725nteger
% 2.86/3.12 = ( ^ [A3: code_integer,B3: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A3 @ B3 ) @ zero_z3403309356797280102nteger ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % le_iff_diff_le_0
% 2.86/3.12 thf(fact_4102_le__iff__diff__le__0,axiom,
% 2.86/3.12 ( ord_less_eq_rat
% 2.86/3.12 = ( ^ [A3: rat,B3: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A3 @ B3 ) @ zero_zero_rat ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % le_iff_diff_le_0
% 2.86/3.12 thf(fact_4103_le__iff__diff__le__0,axiom,
% 2.86/3.12 ( ord_less_eq_int
% 2.86/3.12 = ( ^ [A3: int,B3: int] : ( ord_less_eq_int @ ( minus_minus_int @ A3 @ B3 ) @ zero_zero_int ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % le_iff_diff_le_0
% 2.86/3.12 thf(fact_4104_add__less__zeroD,axiom,
% 2.86/3.12 ! [X: rat,Y: rat] :
% 2.86/3.12 ( ( ord_less_rat @ ( plus_plus_rat @ X @ Y ) @ zero_zero_rat )
% 2.86/3.12 => ( ( ord_less_rat @ X @ zero_zero_rat )
% 2.86/3.12 | ( ord_less_rat @ Y @ zero_zero_rat ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_less_zeroD
% 2.86/3.12 thf(fact_4105_add__less__zeroD,axiom,
% 2.86/3.12 ! [X: code_integer,Y: code_integer] :
% 2.86/3.12 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ X @ Y ) @ zero_z3403309356797280102nteger )
% 2.86/3.12 => ( ( ord_le6747313008572928689nteger @ X @ zero_z3403309356797280102nteger )
% 2.86/3.12 | ( ord_le6747313008572928689nteger @ Y @ zero_z3403309356797280102nteger ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_less_zeroD
% 2.86/3.12 thf(fact_4106_add__less__zeroD,axiom,
% 2.86/3.12 ! [X: int,Y: int] :
% 2.86/3.12 ( ( ord_less_int @ ( plus_plus_int @ X @ Y ) @ zero_zero_int )
% 2.86/3.12 => ( ( ord_less_int @ X @ zero_zero_int )
% 2.86/3.12 | ( ord_less_int @ Y @ zero_zero_int ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_less_zeroD
% 2.86/3.12 thf(fact_4107_add__neg__neg,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat] :
% 2.86/3.12 ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 2.86/3.12 => ( ( ord_less_rat @ B2 @ zero_zero_rat )
% 2.86/3.12 => ( ord_less_rat @ ( plus_plus_rat @ A2 @ B2 ) @ zero_zero_rat ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_neg_neg
% 2.86/3.12 thf(fact_4108_add__neg__neg,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ord_le6747313008572928689nteger @ A2 @ zero_z3403309356797280102nteger )
% 2.86/3.12 => ( ( ord_le6747313008572928689nteger @ B2 @ zero_z3403309356797280102nteger )
% 2.86/3.12 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A2 @ B2 ) @ zero_z3403309356797280102nteger ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_neg_neg
% 2.86/3.12 thf(fact_4109_add__neg__neg,axiom,
% 2.86/3.12 ! [A2: nat,B2: nat] :
% 2.86/3.12 ( ( ord_less_nat @ A2 @ zero_zero_nat )
% 2.86/3.12 => ( ( ord_less_nat @ B2 @ zero_zero_nat )
% 2.86/3.12 => ( ord_less_nat @ ( plus_plus_nat @ A2 @ B2 ) @ zero_zero_nat ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_neg_neg
% 2.86/3.12 thf(fact_4110_add__neg__neg,axiom,
% 2.86/3.12 ! [A2: int,B2: int] :
% 2.86/3.12 ( ( ord_less_int @ A2 @ zero_zero_int )
% 2.86/3.12 => ( ( ord_less_int @ B2 @ zero_zero_int )
% 2.86/3.12 => ( ord_less_int @ ( plus_plus_int @ A2 @ B2 ) @ zero_zero_int ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_neg_neg
% 2.86/3.12 thf(fact_4111_add__pos__pos,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat] :
% 2.86/3.12 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 2.86/3.12 => ( ( ord_less_rat @ zero_zero_rat @ B2 )
% 2.86/3.12 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A2 @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_pos_pos
% 2.86/3.12 thf(fact_4112_add__pos__pos,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 )
% 2.86/3.12 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B2 )
% 2.86/3.12 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A2 @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_pos_pos
% 2.86/3.12 thf(fact_4113_add__pos__pos,axiom,
% 2.86/3.12 ! [A2: nat,B2: nat] :
% 2.86/3.12 ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 2.86/3.12 => ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 2.86/3.12 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A2 @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_pos_pos
% 2.86/3.12 thf(fact_4114_add__pos__pos,axiom,
% 2.86/3.12 ! [A2: int,B2: int] :
% 2.86/3.12 ( ( ord_less_int @ zero_zero_int @ A2 )
% 2.86/3.12 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 2.86/3.12 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A2 @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % add_pos_pos
% 2.86/3.12 thf(fact_4115_canonically__ordered__monoid__add__class_OlessE,axiom,
% 2.86/3.12 ! [A2: nat,B2: nat] :
% 2.86/3.12 ( ( ord_less_nat @ A2 @ B2 )
% 2.86/3.12 => ~ ! [C4: nat] :
% 2.86/3.12 ( ( B2
% 2.86/3.12 = ( plus_plus_nat @ A2 @ C4 ) )
% 2.86/3.12 => ( C4 = zero_zero_nat ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % canonically_ordered_monoid_add_class.lessE
% 2.86/3.12 thf(fact_4116_pos__add__strict,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat,C: rat] :
% 2.86/3.12 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 2.86/3.12 => ( ( ord_less_rat @ B2 @ C )
% 2.86/3.12 => ( ord_less_rat @ B2 @ ( plus_plus_rat @ A2 @ C ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % pos_add_strict
% 2.86/3.12 thf(fact_4117_pos__add__strict,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer,C: code_integer] :
% 2.86/3.12 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 )
% 2.86/3.12 => ( ( ord_le6747313008572928689nteger @ B2 @ C )
% 2.86/3.12 => ( ord_le6747313008572928689nteger @ B2 @ ( plus_p5714425477246183910nteger @ A2 @ C ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % pos_add_strict
% 2.86/3.12 thf(fact_4118_pos__add__strict,axiom,
% 2.86/3.12 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.12 ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 2.86/3.12 => ( ( ord_less_nat @ B2 @ C )
% 2.86/3.12 => ( ord_less_nat @ B2 @ ( plus_plus_nat @ A2 @ C ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % pos_add_strict
% 2.86/3.12 thf(fact_4119_pos__add__strict,axiom,
% 2.86/3.12 ! [A2: int,B2: int,C: int] :
% 2.86/3.12 ( ( ord_less_int @ zero_zero_int @ A2 )
% 2.86/3.12 => ( ( ord_less_int @ B2 @ C )
% 2.86/3.12 => ( ord_less_int @ B2 @ ( plus_plus_int @ A2 @ C ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % pos_add_strict
% 2.86/3.12 thf(fact_4120_mult__neg__neg,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat] :
% 2.86/3.12 ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 2.86/3.12 => ( ( ord_less_rat @ B2 @ zero_zero_rat )
% 2.86/3.12 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_neg_neg
% 2.86/3.12 thf(fact_4121_mult__neg__neg,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ord_le6747313008572928689nteger @ A2 @ zero_z3403309356797280102nteger )
% 2.86/3.12 => ( ( ord_le6747313008572928689nteger @ B2 @ zero_z3403309356797280102nteger )
% 2.86/3.12 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A2 @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_neg_neg
% 2.86/3.12 thf(fact_4122_mult__neg__neg,axiom,
% 2.86/3.12 ! [A2: int,B2: int] :
% 2.86/3.12 ( ( ord_less_int @ A2 @ zero_zero_int )
% 2.86/3.12 => ( ( ord_less_int @ B2 @ zero_zero_int )
% 2.86/3.12 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A2 @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_neg_neg
% 2.86/3.12 thf(fact_4123_not__square__less__zero,axiom,
% 2.86/3.12 ! [A2: rat] :
% 2.86/3.12 ~ ( ord_less_rat @ ( times_times_rat @ A2 @ A2 ) @ zero_zero_rat ) ).
% 2.86/3.12
% 2.86/3.12 % not_square_less_zero
% 2.86/3.12 thf(fact_4124_not__square__less__zero,axiom,
% 2.86/3.12 ! [A2: code_integer] :
% 2.86/3.12 ~ ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A2 @ A2 ) @ zero_z3403309356797280102nteger ) ).
% 2.86/3.12
% 2.86/3.12 % not_square_less_zero
% 2.86/3.12 thf(fact_4125_not__square__less__zero,axiom,
% 2.86/3.12 ! [A2: int] :
% 2.86/3.12 ~ ( ord_less_int @ ( times_times_int @ A2 @ A2 ) @ zero_zero_int ) ).
% 2.86/3.12
% 2.86/3.12 % not_square_less_zero
% 2.86/3.12 thf(fact_4126_mult__less__0__iff,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat] :
% 2.86/3.12 ( ( ord_less_rat @ ( times_times_rat @ A2 @ B2 ) @ zero_zero_rat )
% 2.86/3.12 = ( ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 2.86/3.12 & ( ord_less_rat @ B2 @ zero_zero_rat ) )
% 2.86/3.12 | ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 2.86/3.12 & ( ord_less_rat @ zero_zero_rat @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_less_0_iff
% 2.86/3.12 thf(fact_4127_mult__less__0__iff,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A2 @ B2 ) @ zero_z3403309356797280102nteger )
% 2.86/3.12 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 )
% 2.86/3.12 & ( ord_le6747313008572928689nteger @ B2 @ zero_z3403309356797280102nteger ) )
% 2.86/3.12 | ( ( ord_le6747313008572928689nteger @ A2 @ zero_z3403309356797280102nteger )
% 2.86/3.12 & ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_less_0_iff
% 2.86/3.12 thf(fact_4128_mult__less__0__iff,axiom,
% 2.86/3.12 ! [A2: int,B2: int] :
% 2.86/3.12 ( ( ord_less_int @ ( times_times_int @ A2 @ B2 ) @ zero_zero_int )
% 2.86/3.12 = ( ( ( ord_less_int @ zero_zero_int @ A2 )
% 2.86/3.12 & ( ord_less_int @ B2 @ zero_zero_int ) )
% 2.86/3.12 | ( ( ord_less_int @ A2 @ zero_zero_int )
% 2.86/3.12 & ( ord_less_int @ zero_zero_int @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_less_0_iff
% 2.86/3.12 thf(fact_4129_mult__neg__pos,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat] :
% 2.86/3.12 ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 2.86/3.12 => ( ( ord_less_rat @ zero_zero_rat @ B2 )
% 2.86/3.12 => ( ord_less_rat @ ( times_times_rat @ A2 @ B2 ) @ zero_zero_rat ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_neg_pos
% 2.86/3.12 thf(fact_4130_mult__neg__pos,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ord_le6747313008572928689nteger @ A2 @ zero_z3403309356797280102nteger )
% 2.86/3.12 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B2 )
% 2.86/3.12 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A2 @ B2 ) @ zero_z3403309356797280102nteger ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_neg_pos
% 2.86/3.12 thf(fact_4131_mult__neg__pos,axiom,
% 2.86/3.12 ! [A2: nat,B2: nat] :
% 2.86/3.12 ( ( ord_less_nat @ A2 @ zero_zero_nat )
% 2.86/3.12 => ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 2.86/3.12 => ( ord_less_nat @ ( times_times_nat @ A2 @ B2 ) @ zero_zero_nat ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_neg_pos
% 2.86/3.12 thf(fact_4132_mult__neg__pos,axiom,
% 2.86/3.12 ! [A2: int,B2: int] :
% 2.86/3.12 ( ( ord_less_int @ A2 @ zero_zero_int )
% 2.86/3.12 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 2.86/3.12 => ( ord_less_int @ ( times_times_int @ A2 @ B2 ) @ zero_zero_int ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_neg_pos
% 2.86/3.12 thf(fact_4133_mult__pos__neg,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat] :
% 2.86/3.12 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 2.86/3.12 => ( ( ord_less_rat @ B2 @ zero_zero_rat )
% 2.86/3.12 => ( ord_less_rat @ ( times_times_rat @ A2 @ B2 ) @ zero_zero_rat ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_pos_neg
% 2.86/3.12 thf(fact_4134_mult__pos__neg,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 )
% 2.86/3.12 => ( ( ord_le6747313008572928689nteger @ B2 @ zero_z3403309356797280102nteger )
% 2.86/3.12 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A2 @ B2 ) @ zero_z3403309356797280102nteger ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_pos_neg
% 2.86/3.12 thf(fact_4135_mult__pos__neg,axiom,
% 2.86/3.12 ! [A2: nat,B2: nat] :
% 2.86/3.12 ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 2.86/3.12 => ( ( ord_less_nat @ B2 @ zero_zero_nat )
% 2.86/3.12 => ( ord_less_nat @ ( times_times_nat @ A2 @ B2 ) @ zero_zero_nat ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_pos_neg
% 2.86/3.12 thf(fact_4136_mult__pos__neg,axiom,
% 2.86/3.12 ! [A2: int,B2: int] :
% 2.86/3.12 ( ( ord_less_int @ zero_zero_int @ A2 )
% 2.86/3.12 => ( ( ord_less_int @ B2 @ zero_zero_int )
% 2.86/3.12 => ( ord_less_int @ ( times_times_int @ A2 @ B2 ) @ zero_zero_int ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_pos_neg
% 2.86/3.12 thf(fact_4137_mult__pos__pos,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat] :
% 2.86/3.12 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 2.86/3.12 => ( ( ord_less_rat @ zero_zero_rat @ B2 )
% 2.86/3.12 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_pos_pos
% 2.86/3.12 thf(fact_4138_mult__pos__pos,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 )
% 2.86/3.12 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B2 )
% 2.86/3.12 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A2 @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_pos_pos
% 2.86/3.12 thf(fact_4139_mult__pos__pos,axiom,
% 2.86/3.12 ! [A2: nat,B2: nat] :
% 2.86/3.12 ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 2.86/3.12 => ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 2.86/3.12 => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A2 @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_pos_pos
% 2.86/3.12 thf(fact_4140_mult__pos__pos,axiom,
% 2.86/3.12 ! [A2: int,B2: int] :
% 2.86/3.12 ( ( ord_less_int @ zero_zero_int @ A2 )
% 2.86/3.12 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 2.86/3.12 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A2 @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_pos_pos
% 2.86/3.12 thf(fact_4141_mult__pos__neg2,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat] :
% 2.86/3.12 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 2.86/3.12 => ( ( ord_less_rat @ B2 @ zero_zero_rat )
% 2.86/3.12 => ( ord_less_rat @ ( times_times_rat @ B2 @ A2 ) @ zero_zero_rat ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_pos_neg2
% 2.86/3.12 thf(fact_4142_mult__pos__neg2,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 )
% 2.86/3.12 => ( ( ord_le6747313008572928689nteger @ B2 @ zero_z3403309356797280102nteger )
% 2.86/3.12 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ B2 @ A2 ) @ zero_z3403309356797280102nteger ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_pos_neg2
% 2.86/3.12 thf(fact_4143_mult__pos__neg2,axiom,
% 2.86/3.12 ! [A2: nat,B2: nat] :
% 2.86/3.12 ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 2.86/3.12 => ( ( ord_less_nat @ B2 @ zero_zero_nat )
% 2.86/3.12 => ( ord_less_nat @ ( times_times_nat @ B2 @ A2 ) @ zero_zero_nat ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_pos_neg2
% 2.86/3.12 thf(fact_4144_mult__pos__neg2,axiom,
% 2.86/3.12 ! [A2: int,B2: int] :
% 2.86/3.12 ( ( ord_less_int @ zero_zero_int @ A2 )
% 2.86/3.12 => ( ( ord_less_int @ B2 @ zero_zero_int )
% 2.86/3.12 => ( ord_less_int @ ( times_times_int @ B2 @ A2 ) @ zero_zero_int ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_pos_neg2
% 2.86/3.12 thf(fact_4145_zero__less__mult__iff,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat] :
% 2.86/3.12 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ B2 ) )
% 2.86/3.12 = ( ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 2.86/3.12 & ( ord_less_rat @ zero_zero_rat @ B2 ) )
% 2.86/3.12 | ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 2.86/3.12 & ( ord_less_rat @ B2 @ zero_zero_rat ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % zero_less_mult_iff
% 2.86/3.12 thf(fact_4146_zero__less__mult__iff,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A2 @ B2 ) )
% 2.86/3.12 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 )
% 2.86/3.12 & ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B2 ) )
% 2.86/3.12 | ( ( ord_le6747313008572928689nteger @ A2 @ zero_z3403309356797280102nteger )
% 2.86/3.12 & ( ord_le6747313008572928689nteger @ B2 @ zero_z3403309356797280102nteger ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % zero_less_mult_iff
% 2.86/3.12 thf(fact_4147_zero__less__mult__iff,axiom,
% 2.86/3.12 ! [A2: int,B2: int] :
% 2.86/3.12 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A2 @ B2 ) )
% 2.86/3.12 = ( ( ( ord_less_int @ zero_zero_int @ A2 )
% 2.86/3.12 & ( ord_less_int @ zero_zero_int @ B2 ) )
% 2.86/3.12 | ( ( ord_less_int @ A2 @ zero_zero_int )
% 2.86/3.12 & ( ord_less_int @ B2 @ zero_zero_int ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % zero_less_mult_iff
% 2.86/3.12 thf(fact_4148_zero__less__mult__pos,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat] :
% 2.86/3.12 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ B2 ) )
% 2.86/3.12 => ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 2.86/3.12 => ( ord_less_rat @ zero_zero_rat @ B2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % zero_less_mult_pos
% 2.86/3.12 thf(fact_4149_zero__less__mult__pos,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A2 @ B2 ) )
% 2.86/3.12 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 )
% 2.86/3.12 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % zero_less_mult_pos
% 2.86/3.12 thf(fact_4150_zero__less__mult__pos,axiom,
% 2.86/3.12 ! [A2: nat,B2: nat] :
% 2.86/3.12 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A2 @ B2 ) )
% 2.86/3.12 => ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 2.86/3.12 => ( ord_less_nat @ zero_zero_nat @ B2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % zero_less_mult_pos
% 2.86/3.12 thf(fact_4151_zero__less__mult__pos,axiom,
% 2.86/3.12 ! [A2: int,B2: int] :
% 2.86/3.12 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A2 @ B2 ) )
% 2.86/3.12 => ( ( ord_less_int @ zero_zero_int @ A2 )
% 2.86/3.12 => ( ord_less_int @ zero_zero_int @ B2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % zero_less_mult_pos
% 2.86/3.12 thf(fact_4152_zero__less__mult__pos2,axiom,
% 2.86/3.12 ! [B2: rat,A2: rat] :
% 2.86/3.12 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B2 @ A2 ) )
% 2.86/3.12 => ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 2.86/3.12 => ( ord_less_rat @ zero_zero_rat @ B2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % zero_less_mult_pos2
% 2.86/3.12 thf(fact_4153_zero__less__mult__pos2,axiom,
% 2.86/3.12 ! [B2: code_integer,A2: code_integer] :
% 2.86/3.12 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ B2 @ A2 ) )
% 2.86/3.12 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 )
% 2.86/3.12 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % zero_less_mult_pos2
% 2.86/3.12 thf(fact_4154_zero__less__mult__pos2,axiom,
% 2.86/3.12 ! [B2: nat,A2: nat] :
% 2.86/3.12 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B2 @ A2 ) )
% 2.86/3.12 => ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 2.86/3.12 => ( ord_less_nat @ zero_zero_nat @ B2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % zero_less_mult_pos2
% 2.86/3.12 thf(fact_4155_zero__less__mult__pos2,axiom,
% 2.86/3.12 ! [B2: int,A2: int] :
% 2.86/3.12 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B2 @ A2 ) )
% 2.86/3.12 => ( ( ord_less_int @ zero_zero_int @ A2 )
% 2.86/3.12 => ( ord_less_int @ zero_zero_int @ B2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % zero_less_mult_pos2
% 2.86/3.12 thf(fact_4156_mult__less__cancel__left__neg,axiom,
% 2.86/3.12 ! [C: rat,A2: rat,B2: rat] :
% 2.86/3.12 ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.86/3.12 => ( ( ord_less_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B2 ) )
% 2.86/3.12 = ( ord_less_rat @ B2 @ A2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_less_cancel_left_neg
% 2.86/3.12 thf(fact_4157_mult__less__cancel__left__neg,axiom,
% 2.86/3.12 ! [C: code_integer,A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 2.86/3.12 => ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A2 ) @ ( times_3573771949741848930nteger @ C @ B2 ) )
% 2.86/3.12 = ( ord_le6747313008572928689nteger @ B2 @ A2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_less_cancel_left_neg
% 2.86/3.12 thf(fact_4158_mult__less__cancel__left__neg,axiom,
% 2.86/3.12 ! [C: int,A2: int,B2: int] :
% 2.86/3.12 ( ( ord_less_int @ C @ zero_zero_int )
% 2.86/3.12 => ( ( ord_less_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B2 ) )
% 2.86/3.12 = ( ord_less_int @ B2 @ A2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_less_cancel_left_neg
% 2.86/3.12 thf(fact_4159_mult__less__cancel__left__pos,axiom,
% 2.86/3.12 ! [C: rat,A2: rat,B2: rat] :
% 2.86/3.12 ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.86/3.12 => ( ( ord_less_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B2 ) )
% 2.86/3.12 = ( ord_less_rat @ A2 @ B2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_less_cancel_left_pos
% 2.86/3.12 thf(fact_4160_mult__less__cancel__left__pos,axiom,
% 2.86/3.12 ! [C: code_integer,A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 2.86/3.12 => ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A2 ) @ ( times_3573771949741848930nteger @ C @ B2 ) )
% 2.86/3.12 = ( ord_le6747313008572928689nteger @ A2 @ B2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_less_cancel_left_pos
% 2.86/3.12 thf(fact_4161_mult__less__cancel__left__pos,axiom,
% 2.86/3.12 ! [C: int,A2: int,B2: int] :
% 2.86/3.12 ( ( ord_less_int @ zero_zero_int @ C )
% 2.86/3.12 => ( ( ord_less_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B2 ) )
% 2.86/3.12 = ( ord_less_int @ A2 @ B2 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_less_cancel_left_pos
% 2.86/3.12 thf(fact_4162_mult__strict__left__mono__neg,axiom,
% 2.86/3.12 ! [B2: rat,A2: rat,C: rat] :
% 2.86/3.12 ( ( ord_less_rat @ B2 @ A2 )
% 2.86/3.12 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.86/3.12 => ( ord_less_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_strict_left_mono_neg
% 2.86/3.12 thf(fact_4163_mult__strict__left__mono__neg,axiom,
% 2.86/3.12 ! [B2: code_integer,A2: code_integer,C: code_integer] :
% 2.86/3.12 ( ( ord_le6747313008572928689nteger @ B2 @ A2 )
% 2.86/3.12 => ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 2.86/3.12 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A2 ) @ ( times_3573771949741848930nteger @ C @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_strict_left_mono_neg
% 2.86/3.12 thf(fact_4164_mult__strict__left__mono__neg,axiom,
% 2.86/3.12 ! [B2: int,A2: int,C: int] :
% 2.86/3.12 ( ( ord_less_int @ B2 @ A2 )
% 2.86/3.12 => ( ( ord_less_int @ C @ zero_zero_int )
% 2.86/3.12 => ( ord_less_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_strict_left_mono_neg
% 2.86/3.12 thf(fact_4165_mult__strict__left__mono,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat,C: rat] :
% 2.86/3.12 ( ( ord_less_rat @ A2 @ B2 )
% 2.86/3.12 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.86/3.12 => ( ord_less_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_strict_left_mono
% 2.86/3.12 thf(fact_4166_mult__strict__left__mono,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer,C: code_integer] :
% 2.86/3.12 ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 2.86/3.12 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 2.86/3.12 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A2 ) @ ( times_3573771949741848930nteger @ C @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_strict_left_mono
% 2.86/3.12 thf(fact_4167_mult__strict__left__mono,axiom,
% 2.86/3.12 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.12 ( ( ord_less_nat @ A2 @ B2 )
% 2.86/3.12 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 2.86/3.12 => ( ord_less_nat @ ( times_times_nat @ C @ A2 ) @ ( times_times_nat @ C @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_strict_left_mono
% 2.86/3.12 thf(fact_4168_mult__strict__left__mono,axiom,
% 2.86/3.12 ! [A2: int,B2: int,C: int] :
% 2.86/3.12 ( ( ord_less_int @ A2 @ B2 )
% 2.86/3.12 => ( ( ord_less_int @ zero_zero_int @ C )
% 2.86/3.12 => ( ord_less_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_strict_left_mono
% 2.86/3.12 thf(fact_4169_mult__less__cancel__left__disj,axiom,
% 2.86/3.12 ! [C: rat,A2: rat,B2: rat] :
% 2.86/3.12 ( ( ord_less_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B2 ) )
% 2.86/3.12 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.86/3.12 & ( ord_less_rat @ A2 @ B2 ) )
% 2.86/3.12 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.86/3.12 & ( ord_less_rat @ B2 @ A2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_less_cancel_left_disj
% 2.86/3.12 thf(fact_4170_mult__less__cancel__left__disj,axiom,
% 2.86/3.12 ! [C: code_integer,A2: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A2 ) @ ( times_3573771949741848930nteger @ C @ B2 ) )
% 2.86/3.12 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 2.86/3.12 & ( ord_le6747313008572928689nteger @ A2 @ B2 ) )
% 2.86/3.12 | ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 2.86/3.12 & ( ord_le6747313008572928689nteger @ B2 @ A2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_less_cancel_left_disj
% 2.86/3.12 thf(fact_4171_mult__less__cancel__left__disj,axiom,
% 2.86/3.12 ! [C: int,A2: int,B2: int] :
% 2.86/3.12 ( ( ord_less_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B2 ) )
% 2.86/3.12 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 2.86/3.12 & ( ord_less_int @ A2 @ B2 ) )
% 2.86/3.12 | ( ( ord_less_int @ C @ zero_zero_int )
% 2.86/3.12 & ( ord_less_int @ B2 @ A2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_less_cancel_left_disj
% 2.86/3.12 thf(fact_4172_mult__strict__right__mono__neg,axiom,
% 2.86/3.12 ! [B2: rat,A2: rat,C: rat] :
% 2.86/3.12 ( ( ord_less_rat @ B2 @ A2 )
% 2.86/3.12 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.86/3.12 => ( ord_less_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B2 @ C ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_strict_right_mono_neg
% 2.86/3.12 thf(fact_4173_mult__strict__right__mono__neg,axiom,
% 2.86/3.12 ! [B2: code_integer,A2: code_integer,C: code_integer] :
% 2.86/3.12 ( ( ord_le6747313008572928689nteger @ B2 @ A2 )
% 2.86/3.12 => ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 2.86/3.12 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ ( times_3573771949741848930nteger @ B2 @ C ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_strict_right_mono_neg
% 2.86/3.12 thf(fact_4174_mult__strict__right__mono__neg,axiom,
% 2.86/3.12 ! [B2: int,A2: int,C: int] :
% 2.86/3.12 ( ( ord_less_int @ B2 @ A2 )
% 2.86/3.12 => ( ( ord_less_int @ C @ zero_zero_int )
% 2.86/3.12 => ( ord_less_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B2 @ C ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_strict_right_mono_neg
% 2.86/3.12 thf(fact_4175_mult__strict__right__mono,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat,C: rat] :
% 2.86/3.12 ( ( ord_less_rat @ A2 @ B2 )
% 2.86/3.12 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.86/3.12 => ( ord_less_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B2 @ C ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_strict_right_mono
% 2.86/3.12 thf(fact_4176_mult__strict__right__mono,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer,C: code_integer] :
% 2.86/3.12 ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 2.86/3.12 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 2.86/3.12 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ ( times_3573771949741848930nteger @ B2 @ C ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_strict_right_mono
% 2.86/3.12 thf(fact_4177_mult__strict__right__mono,axiom,
% 2.86/3.12 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.12 ( ( ord_less_nat @ A2 @ B2 )
% 2.86/3.12 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 2.86/3.12 => ( ord_less_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B2 @ C ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_strict_right_mono
% 2.86/3.12 thf(fact_4178_mult__strict__right__mono,axiom,
% 2.86/3.12 ! [A2: int,B2: int,C: int] :
% 2.86/3.12 ( ( ord_less_int @ A2 @ B2 )
% 2.86/3.12 => ( ( ord_less_int @ zero_zero_int @ C )
% 2.86/3.12 => ( ord_less_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B2 @ C ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_strict_right_mono
% 2.86/3.12 thf(fact_4179_mult__less__cancel__right__disj,axiom,
% 2.86/3.12 ! [A2: rat,C: rat,B2: rat] :
% 2.86/3.12 ( ( ord_less_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B2 @ C ) )
% 2.86/3.12 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.86/3.12 & ( ord_less_rat @ A2 @ B2 ) )
% 2.86/3.12 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.86/3.12 & ( ord_less_rat @ B2 @ A2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_less_cancel_right_disj
% 2.86/3.12 thf(fact_4180_mult__less__cancel__right__disj,axiom,
% 2.86/3.12 ! [A2: code_integer,C: code_integer,B2: code_integer] :
% 2.86/3.12 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ ( times_3573771949741848930nteger @ B2 @ C ) )
% 2.86/3.12 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 2.86/3.12 & ( ord_le6747313008572928689nteger @ A2 @ B2 ) )
% 2.86/3.12 | ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 2.86/3.12 & ( ord_le6747313008572928689nteger @ B2 @ A2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_less_cancel_right_disj
% 2.86/3.12 thf(fact_4181_mult__less__cancel__right__disj,axiom,
% 2.86/3.12 ! [A2: int,C: int,B2: int] :
% 2.86/3.12 ( ( ord_less_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B2 @ C ) )
% 2.86/3.12 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 2.86/3.12 & ( ord_less_int @ A2 @ B2 ) )
% 2.86/3.12 | ( ( ord_less_int @ C @ zero_zero_int )
% 2.86/3.12 & ( ord_less_int @ B2 @ A2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % mult_less_cancel_right_disj
% 2.86/3.12 thf(fact_4182_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 2.86/3.12 ! [A2: rat,B2: rat,C: rat] :
% 2.86/3.12 ( ( ord_less_rat @ A2 @ B2 )
% 2.86/3.12 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.86/3.12 => ( ord_less_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 2.86/3.12 thf(fact_4183_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 2.86/3.12 ! [A2: code_integer,B2: code_integer,C: code_integer] :
% 2.86/3.12 ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 2.86/3.12 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 2.86/3.12 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A2 ) @ ( times_3573771949741848930nteger @ C @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 2.86/3.12 thf(fact_4184_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 2.86/3.12 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.12 ( ( ord_less_nat @ A2 @ B2 )
% 2.86/3.12 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 2.86/3.12 => ( ord_less_nat @ ( times_times_nat @ C @ A2 ) @ ( times_times_nat @ C @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 2.86/3.12 thf(fact_4185_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 2.86/3.12 ! [A2: int,B2: int,C: int] :
% 2.86/3.12 ( ( ord_less_int @ A2 @ B2 )
% 2.86/3.12 => ( ( ord_less_int @ zero_zero_int @ C )
% 2.86/3.12 => ( ord_less_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B2 ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 2.86/3.12 thf(fact_4186_not__one__less__zero,axiom,
% 2.86/3.12 ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 2.86/3.12
% 2.86/3.12 % not_one_less_zero
% 2.86/3.12 thf(fact_4187_not__one__less__zero,axiom,
% 2.86/3.12 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ).
% 2.86/3.12
% 2.86/3.12 % not_one_less_zero
% 2.86/3.12 thf(fact_4188_not__one__less__zero,axiom,
% 2.86/3.12 ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 2.86/3.12
% 2.86/3.12 % not_one_less_zero
% 2.86/3.12 thf(fact_4189_not__one__less__zero,axiom,
% 2.86/3.12 ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 2.86/3.12
% 2.86/3.12 % not_one_less_zero
% 2.86/3.12 thf(fact_4190_zero__less__one,axiom,
% 2.86/3.12 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 2.86/3.12
% 2.86/3.12 % zero_less_one
% 2.86/3.12 thf(fact_4191_zero__less__one,axiom,
% 2.86/3.12 ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 2.86/3.12
% 2.86/3.12 % zero_less_one
% 2.86/3.12 thf(fact_4192_zero__less__one,axiom,
% 2.86/3.12 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 2.86/3.12
% 2.86/3.12 % zero_less_one
% 2.86/3.12 thf(fact_4193_zero__less__one,axiom,
% 2.86/3.12 ord_less_int @ zero_zero_int @ one_one_int ).
% 2.86/3.12
% 2.86/3.12 % zero_less_one
% 2.86/3.12 thf(fact_4194_less__numeral__extra_I1_J,axiom,
% 2.86/3.12 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 2.86/3.12
% 2.86/3.12 % less_numeral_extra(1)
% 2.86/3.12 thf(fact_4195_less__numeral__extra_I1_J,axiom,
% 2.86/3.12 ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 2.86/3.12
% 2.86/3.12 % less_numeral_extra(1)
% 2.86/3.12 thf(fact_4196_less__numeral__extra_I1_J,axiom,
% 2.86/3.12 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 2.86/3.12
% 2.86/3.12 % less_numeral_extra(1)
% 2.86/3.12 thf(fact_4197_less__numeral__extra_I1_J,axiom,
% 2.86/3.12 ord_less_int @ zero_zero_int @ one_one_int ).
% 2.86/3.12
% 2.86/3.12 % less_numeral_extra(1)
% 2.86/3.12 thf(fact_4198_less__iff__diff__less__0,axiom,
% 2.86/3.12 ( ord_less_rat
% 2.86/3.12 = ( ^ [A3: rat,B3: rat] : ( ord_less_rat @ ( minus_minus_rat @ A3 @ B3 ) @ zero_zero_rat ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % less_iff_diff_less_0
% 2.86/3.12 thf(fact_4199_less__iff__diff__less__0,axiom,
% 2.86/3.12 ( ord_le6747313008572928689nteger
% 2.86/3.12 = ( ^ [A3: code_integer,B3: code_integer] : ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A3 @ B3 ) @ zero_z3403309356797280102nteger ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % less_iff_diff_less_0
% 2.86/3.12 thf(fact_4200_less__iff__diff__less__0,axiom,
% 2.86/3.12 ( ord_less_int
% 2.86/3.12 = ( ^ [A3: int,B3: int] : ( ord_less_int @ ( minus_minus_int @ A3 @ B3 ) @ zero_zero_int ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % less_iff_diff_less_0
% 2.86/3.12 thf(fact_4201_nat__mult__le__cancel1,axiom,
% 2.86/3.12 ! [K3: nat,M2: nat,N: nat] :
% 2.86/3.12 ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 2.86/3.12 => ( ( ord_less_eq_nat @ ( times_times_nat @ K3 @ M2 ) @ ( times_times_nat @ K3 @ N ) )
% 2.86/3.12 = ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % nat_mult_le_cancel1
% 2.86/3.12 thf(fact_4202_Ex__less__Suc2,axiom,
% 2.86/3.12 ! [N: nat,P: nat > $o] :
% 2.86/3.12 ( ( ? [I4: nat] :
% 2.86/3.12 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 2.86/3.12 & ( P @ I4 ) ) )
% 2.86/3.12 = ( ( P @ zero_zero_nat )
% 2.86/3.12 | ? [I4: nat] :
% 2.86/3.12 ( ( ord_less_nat @ I4 @ N )
% 2.86/3.12 & ( P @ ( suc @ I4 ) ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % Ex_less_Suc2
% 2.86/3.12 thf(fact_4203_gr0__conv__Suc,axiom,
% 2.86/3.12 ! [N: nat] :
% 2.86/3.12 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.12 = ( ? [M: nat] :
% 2.86/3.12 ( N
% 2.86/3.12 = ( suc @ M ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % gr0_conv_Suc
% 2.86/3.12 thf(fact_4204_All__less__Suc2,axiom,
% 2.86/3.12 ! [N: nat,P: nat > $o] :
% 2.86/3.12 ( ( ! [I4: nat] :
% 2.86/3.12 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 2.86/3.12 => ( P @ I4 ) ) )
% 2.86/3.12 = ( ( P @ zero_zero_nat )
% 2.86/3.12 & ! [I4: nat] :
% 2.86/3.12 ( ( ord_less_nat @ I4 @ N )
% 2.86/3.12 => ( P @ ( suc @ I4 ) ) ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % All_less_Suc2
% 2.86/3.12 thf(fact_4205_gr0__implies__Suc,axiom,
% 2.86/3.12 ! [N: nat] :
% 2.86/3.12 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.12 => ? [M6: nat] :
% 2.86/3.12 ( N
% 2.86/3.12 = ( suc @ M6 ) ) ) ).
% 2.86/3.12
% 2.86/3.12 % gr0_implies_Suc
% 2.86/3.12 thf(fact_4206_less__Suc__eq__0__disj,axiom,
% 2.86/3.12 ! [M2: nat,N: nat] :
% 2.86/3.12 ( ( ord_less_nat @ M2 @ ( suc @ N ) )
% 2.86/3.12 = ( ( M2 = zero_zero_nat )
% 2.86/3.12 | ? [J2: nat] :
% 2.86/3.12 ( ( M2
% 2.86/3.13 = ( suc @ J2 ) )
% 2.86/3.13 & ( ord_less_nat @ J2 @ N ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % less_Suc_eq_0_disj
% 2.86/3.13 thf(fact_4207_nat__compl__induct,axiom,
% 2.86/3.13 ! [P: nat > $o,N: nat] :
% 2.86/3.13 ( ( P @ zero_zero_nat )
% 2.86/3.13 => ( ! [N5: nat] :
% 2.86/3.13 ( ! [Nn: nat] :
% 2.86/3.13 ( ( ord_less_eq_nat @ Nn @ N5 )
% 2.86/3.13 => ( P @ Nn ) )
% 2.86/3.13 => ( P @ ( suc @ N5 ) ) )
% 2.86/3.13 => ( P @ N ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % nat_compl_induct
% 2.86/3.13 thf(fact_4208_nat__compl__induct_H,axiom,
% 2.86/3.13 ! [P: nat > $o,N: nat] :
% 2.86/3.13 ( ( P @ zero_zero_nat )
% 2.86/3.13 => ( ! [N5: nat] :
% 2.86/3.13 ( ! [Nn: nat] :
% 2.86/3.13 ( ( ord_less_eq_nat @ Nn @ N5 )
% 2.86/3.13 => ( P @ Nn ) )
% 2.86/3.13 => ( P @ ( suc @ N5 ) ) )
% 2.86/3.13 => ( P @ N ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % nat_compl_induct'
% 2.86/3.13 thf(fact_4209_ex__least__nat__le,axiom,
% 2.86/3.13 ! [P: nat > $o,N: nat] :
% 2.86/3.13 ( ( P @ N )
% 2.86/3.13 => ( ~ ( P @ zero_zero_nat )
% 2.86/3.13 => ? [K: nat] :
% 2.86/3.13 ( ( ord_less_eq_nat @ K @ N )
% 2.86/3.13 & ! [I6: nat] :
% 2.86/3.13 ( ( ord_less_nat @ I6 @ K )
% 2.86/3.13 => ~ ( P @ I6 ) )
% 2.86/3.13 & ( P @ K ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % ex_least_nat_le
% 2.86/3.13 thf(fact_4210_less__imp__add__positive,axiom,
% 2.86/3.13 ! [I: nat,J: nat] :
% 2.86/3.13 ( ( ord_less_nat @ I @ J )
% 2.86/3.13 => ? [K: nat] :
% 2.86/3.13 ( ( ord_less_nat @ zero_zero_nat @ K )
% 2.86/3.13 & ( ( plus_plus_nat @ I @ K )
% 2.86/3.13 = J ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % less_imp_add_positive
% 2.86/3.13 thf(fact_4211_Suc__to__right,axiom,
% 2.86/3.13 ! [N: nat,M2: nat] :
% 2.86/3.13 ( ( ( suc @ N )
% 2.86/3.13 = M2 )
% 2.86/3.13 => ( N
% 2.86/3.13 = ( minus_minus_nat @ M2 @ ( suc @ zero_zero_nat ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % Suc_to_right
% 2.86/3.13 thf(fact_4212_diff__less,axiom,
% 2.86/3.13 ! [N: nat,M2: nat] :
% 2.86/3.13 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.13 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 2.86/3.13 => ( ord_less_nat @ ( minus_minus_nat @ M2 @ N ) @ M2 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % diff_less
% 2.86/3.13 thf(fact_4213_mult__less__mono1,axiom,
% 2.86/3.13 ! [I: nat,J: nat,K3: nat] :
% 2.86/3.13 ( ( ord_less_nat @ I @ J )
% 2.86/3.13 => ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 2.86/3.13 => ( ord_less_nat @ ( times_times_nat @ I @ K3 ) @ ( times_times_nat @ J @ K3 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_less_mono1
% 2.86/3.13 thf(fact_4214_mult__less__mono2,axiom,
% 2.86/3.13 ! [I: nat,J: nat,K3: nat] :
% 2.86/3.13 ( ( ord_less_nat @ I @ J )
% 2.86/3.13 => ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 2.86/3.13 => ( ord_less_nat @ ( times_times_nat @ K3 @ I ) @ ( times_times_nat @ K3 @ J ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_less_mono2
% 2.86/3.13 thf(fact_4215_nat__geq__1__eq__neqz,axiom,
% 2.86/3.13 ! [X: nat] :
% 2.86/3.13 ( ( ord_less_eq_nat @ one_one_nat @ X )
% 2.86/3.13 = ( X != zero_zero_nat ) ) ).
% 2.86/3.13
% 2.86/3.13 % nat_geq_1_eq_neqz
% 2.86/3.13 thf(fact_4216_add__neg__nonpos,axiom,
% 2.86/3.13 ! [A2: rat,B2: rat] :
% 2.86/3.13 ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 2.86/3.13 => ( ( ord_less_eq_rat @ B2 @ zero_zero_rat )
% 2.86/3.13 => ( ord_less_rat @ ( plus_plus_rat @ A2 @ B2 ) @ zero_zero_rat ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % add_neg_nonpos
% 2.86/3.13 thf(fact_4217_add__neg__nonpos,axiom,
% 2.86/3.13 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.13 ( ( ord_le6747313008572928689nteger @ A2 @ zero_z3403309356797280102nteger )
% 2.86/3.13 => ( ( ord_le3102999989581377725nteger @ B2 @ zero_z3403309356797280102nteger )
% 2.86/3.13 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A2 @ B2 ) @ zero_z3403309356797280102nteger ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % add_neg_nonpos
% 2.86/3.13 thf(fact_4218_add__neg__nonpos,axiom,
% 2.86/3.13 ! [A2: nat,B2: nat] :
% 2.86/3.13 ( ( ord_less_nat @ A2 @ zero_zero_nat )
% 2.86/3.13 => ( ( ord_less_eq_nat @ B2 @ zero_zero_nat )
% 2.86/3.13 => ( ord_less_nat @ ( plus_plus_nat @ A2 @ B2 ) @ zero_zero_nat ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % add_neg_nonpos
% 2.86/3.13 thf(fact_4219_add__neg__nonpos,axiom,
% 2.86/3.13 ! [A2: int,B2: int] :
% 2.86/3.13 ( ( ord_less_int @ A2 @ zero_zero_int )
% 2.86/3.13 => ( ( ord_less_eq_int @ B2 @ zero_zero_int )
% 2.86/3.13 => ( ord_less_int @ ( plus_plus_int @ A2 @ B2 ) @ zero_zero_int ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % add_neg_nonpos
% 2.86/3.13 thf(fact_4220_add__nonneg__pos,axiom,
% 2.86/3.13 ! [A2: rat,B2: rat] :
% 2.86/3.13 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 2.86/3.13 => ( ( ord_less_rat @ zero_zero_rat @ B2 )
% 2.86/3.13 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A2 @ B2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % add_nonneg_pos
% 2.86/3.13 thf(fact_4221_add__nonneg__pos,axiom,
% 2.86/3.13 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.13 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 2.86/3.13 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B2 )
% 2.86/3.13 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A2 @ B2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % add_nonneg_pos
% 2.86/3.13 thf(fact_4222_add__nonneg__pos,axiom,
% 2.86/3.13 ! [A2: nat,B2: nat] :
% 2.86/3.13 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 2.86/3.13 => ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 2.86/3.13 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A2 @ B2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % add_nonneg_pos
% 2.86/3.13 thf(fact_4223_add__nonneg__pos,axiom,
% 2.86/3.13 ! [A2: int,B2: int] :
% 2.86/3.13 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 2.86/3.13 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 2.86/3.13 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A2 @ B2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % add_nonneg_pos
% 2.86/3.13 thf(fact_4224_add__nonpos__neg,axiom,
% 2.86/3.13 ! [A2: rat,B2: rat] :
% 2.86/3.13 ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 2.86/3.13 => ( ( ord_less_rat @ B2 @ zero_zero_rat )
% 2.86/3.13 => ( ord_less_rat @ ( plus_plus_rat @ A2 @ B2 ) @ zero_zero_rat ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % add_nonpos_neg
% 2.86/3.13 thf(fact_4225_add__nonpos__neg,axiom,
% 2.86/3.13 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.13 ( ( ord_le3102999989581377725nteger @ A2 @ zero_z3403309356797280102nteger )
% 2.86/3.13 => ( ( ord_le6747313008572928689nteger @ B2 @ zero_z3403309356797280102nteger )
% 2.86/3.13 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A2 @ B2 ) @ zero_z3403309356797280102nteger ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % add_nonpos_neg
% 2.86/3.13 thf(fact_4226_add__nonpos__neg,axiom,
% 2.86/3.13 ! [A2: nat,B2: nat] :
% 2.86/3.13 ( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
% 2.86/3.13 => ( ( ord_less_nat @ B2 @ zero_zero_nat )
% 2.86/3.13 => ( ord_less_nat @ ( plus_plus_nat @ A2 @ B2 ) @ zero_zero_nat ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % add_nonpos_neg
% 2.86/3.13 thf(fact_4227_add__nonpos__neg,axiom,
% 2.86/3.13 ! [A2: int,B2: int] :
% 2.86/3.13 ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 2.86/3.13 => ( ( ord_less_int @ B2 @ zero_zero_int )
% 2.86/3.13 => ( ord_less_int @ ( plus_plus_int @ A2 @ B2 ) @ zero_zero_int ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % add_nonpos_neg
% 2.86/3.13 thf(fact_4228_add__pos__nonneg,axiom,
% 2.86/3.13 ! [A2: rat,B2: rat] :
% 2.86/3.13 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 2.86/3.13 => ( ( ord_less_eq_rat @ zero_zero_rat @ B2 )
% 2.86/3.13 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A2 @ B2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % add_pos_nonneg
% 2.86/3.13 thf(fact_4229_add__pos__nonneg,axiom,
% 2.86/3.13 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.13 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 )
% 2.86/3.13 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B2 )
% 2.86/3.13 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A2 @ B2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % add_pos_nonneg
% 2.86/3.13 thf(fact_4230_add__pos__nonneg,axiom,
% 2.86/3.13 ! [A2: nat,B2: nat] :
% 2.86/3.13 ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 2.86/3.13 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 2.86/3.13 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A2 @ B2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % add_pos_nonneg
% 2.86/3.13 thf(fact_4231_add__pos__nonneg,axiom,
% 2.86/3.13 ! [A2: int,B2: int] :
% 2.86/3.13 ( ( ord_less_int @ zero_zero_int @ A2 )
% 2.86/3.13 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 2.86/3.13 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A2 @ B2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % add_pos_nonneg
% 2.86/3.13 thf(fact_4232_add__strict__increasing,axiom,
% 2.86/3.13 ! [A2: rat,B2: rat,C: rat] :
% 2.86/3.13 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 2.86/3.13 => ( ( ord_less_eq_rat @ B2 @ C )
% 2.86/3.13 => ( ord_less_rat @ B2 @ ( plus_plus_rat @ A2 @ C ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % add_strict_increasing
% 2.86/3.13 thf(fact_4233_add__strict__increasing,axiom,
% 2.86/3.13 ! [A2: code_integer,B2: code_integer,C: code_integer] :
% 2.86/3.13 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 )
% 2.86/3.13 => ( ( ord_le3102999989581377725nteger @ B2 @ C )
% 2.86/3.13 => ( ord_le6747313008572928689nteger @ B2 @ ( plus_p5714425477246183910nteger @ A2 @ C ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % add_strict_increasing
% 2.86/3.13 thf(fact_4234_add__strict__increasing,axiom,
% 2.86/3.13 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.13 ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 2.86/3.13 => ( ( ord_less_eq_nat @ B2 @ C )
% 2.86/3.13 => ( ord_less_nat @ B2 @ ( plus_plus_nat @ A2 @ C ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % add_strict_increasing
% 2.86/3.13 thf(fact_4235_add__strict__increasing,axiom,
% 2.86/3.13 ! [A2: int,B2: int,C: int] :
% 2.86/3.13 ( ( ord_less_int @ zero_zero_int @ A2 )
% 2.86/3.13 => ( ( ord_less_eq_int @ B2 @ C )
% 2.86/3.13 => ( ord_less_int @ B2 @ ( plus_plus_int @ A2 @ C ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % add_strict_increasing
% 2.86/3.13 thf(fact_4236_add__strict__increasing2,axiom,
% 2.86/3.13 ! [A2: rat,B2: rat,C: rat] :
% 2.86/3.13 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 2.86/3.13 => ( ( ord_less_rat @ B2 @ C )
% 2.86/3.13 => ( ord_less_rat @ B2 @ ( plus_plus_rat @ A2 @ C ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % add_strict_increasing2
% 2.86/3.13 thf(fact_4237_add__strict__increasing2,axiom,
% 2.86/3.13 ! [A2: code_integer,B2: code_integer,C: code_integer] :
% 2.86/3.13 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 2.86/3.13 => ( ( ord_le6747313008572928689nteger @ B2 @ C )
% 2.86/3.13 => ( ord_le6747313008572928689nteger @ B2 @ ( plus_p5714425477246183910nteger @ A2 @ C ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % add_strict_increasing2
% 2.86/3.13 thf(fact_4238_add__strict__increasing2,axiom,
% 2.86/3.13 ! [A2: nat,B2: nat,C: nat] :
% 2.86/3.13 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 2.86/3.13 => ( ( ord_less_nat @ B2 @ C )
% 2.86/3.13 => ( ord_less_nat @ B2 @ ( plus_plus_nat @ A2 @ C ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % add_strict_increasing2
% 2.86/3.13 thf(fact_4239_add__strict__increasing2,axiom,
% 2.86/3.13 ! [A2: int,B2: int,C: int] :
% 2.86/3.13 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 2.86/3.13 => ( ( ord_less_int @ B2 @ C )
% 2.86/3.13 => ( ord_less_int @ B2 @ ( plus_plus_int @ A2 @ C ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % add_strict_increasing2
% 2.86/3.13 thf(fact_4240_mult__le__cancel__left,axiom,
% 2.86/3.13 ! [C: rat,A2: rat,B2: rat] :
% 2.86/3.13 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B2 ) )
% 2.86/3.13 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.86/3.13 => ( ord_less_eq_rat @ A2 @ B2 ) )
% 2.86/3.13 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.86/3.13 => ( ord_less_eq_rat @ B2 @ A2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_le_cancel_left
% 2.86/3.13 thf(fact_4241_mult__le__cancel__left,axiom,
% 2.86/3.13 ! [C: code_integer,A2: code_integer,B2: code_integer] :
% 2.86/3.13 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A2 ) @ ( times_3573771949741848930nteger @ C @ B2 ) )
% 2.86/3.13 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 2.86/3.13 => ( ord_le3102999989581377725nteger @ A2 @ B2 ) )
% 2.86/3.13 & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 2.86/3.13 => ( ord_le3102999989581377725nteger @ B2 @ A2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_le_cancel_left
% 2.86/3.13 thf(fact_4242_mult__le__cancel__left,axiom,
% 2.86/3.13 ! [C: int,A2: int,B2: int] :
% 2.86/3.13 ( ( ord_less_eq_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B2 ) )
% 2.86/3.13 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 2.86/3.13 => ( ord_less_eq_int @ A2 @ B2 ) )
% 2.86/3.13 & ( ( ord_less_int @ C @ zero_zero_int )
% 2.86/3.13 => ( ord_less_eq_int @ B2 @ A2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_le_cancel_left
% 2.86/3.13 thf(fact_4243_mult__le__cancel__right,axiom,
% 2.86/3.13 ! [A2: rat,C: rat,B2: rat] :
% 2.86/3.13 ( ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B2 @ C ) )
% 2.86/3.13 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.86/3.13 => ( ord_less_eq_rat @ A2 @ B2 ) )
% 2.86/3.13 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.86/3.13 => ( ord_less_eq_rat @ B2 @ A2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_le_cancel_right
% 2.86/3.13 thf(fact_4244_mult__le__cancel__right,axiom,
% 2.86/3.13 ! [A2: code_integer,C: code_integer,B2: code_integer] :
% 2.86/3.13 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ ( times_3573771949741848930nteger @ B2 @ C ) )
% 2.86/3.13 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 2.86/3.13 => ( ord_le3102999989581377725nteger @ A2 @ B2 ) )
% 2.86/3.13 & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 2.86/3.13 => ( ord_le3102999989581377725nteger @ B2 @ A2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_le_cancel_right
% 2.86/3.13 thf(fact_4245_mult__le__cancel__right,axiom,
% 2.86/3.13 ! [A2: int,C: int,B2: int] :
% 2.86/3.13 ( ( ord_less_eq_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B2 @ C ) )
% 2.86/3.13 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 2.86/3.13 => ( ord_less_eq_int @ A2 @ B2 ) )
% 2.86/3.13 & ( ( ord_less_int @ C @ zero_zero_int )
% 2.86/3.13 => ( ord_less_eq_int @ B2 @ A2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_le_cancel_right
% 2.86/3.13 thf(fact_4246_mult__left__less__imp__less,axiom,
% 2.86/3.13 ! [C: rat,A2: rat,B2: rat] :
% 2.86/3.13 ( ( ord_less_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B2 ) )
% 2.86/3.13 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 2.86/3.13 => ( ord_less_rat @ A2 @ B2 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_left_less_imp_less
% 2.86/3.13 thf(fact_4247_mult__left__less__imp__less,axiom,
% 2.86/3.13 ! [C: code_integer,A2: code_integer,B2: code_integer] :
% 2.86/3.13 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A2 ) @ ( times_3573771949741848930nteger @ C @ B2 ) )
% 2.86/3.13 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 2.86/3.13 => ( ord_le6747313008572928689nteger @ A2 @ B2 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_left_less_imp_less
% 2.86/3.13 thf(fact_4248_mult__left__less__imp__less,axiom,
% 2.86/3.13 ! [C: nat,A2: nat,B2: nat] :
% 2.86/3.13 ( ( ord_less_nat @ ( times_times_nat @ C @ A2 ) @ ( times_times_nat @ C @ B2 ) )
% 2.86/3.13 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 2.86/3.13 => ( ord_less_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_left_less_imp_less
% 2.86/3.13 thf(fact_4249_mult__left__less__imp__less,axiom,
% 2.86/3.13 ! [C: int,A2: int,B2: int] :
% 2.86/3.13 ( ( ord_less_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B2 ) )
% 2.86/3.13 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 2.86/3.13 => ( ord_less_int @ A2 @ B2 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_left_less_imp_less
% 2.86/3.13 thf(fact_4250_mult__strict__mono,axiom,
% 2.86/3.13 ! [A2: rat,B2: rat,C: rat,D2: rat] :
% 2.86/3.13 ( ( ord_less_rat @ A2 @ B2 )
% 2.86/3.13 => ( ( ord_less_rat @ C @ D2 )
% 2.86/3.13 => ( ( ord_less_rat @ zero_zero_rat @ B2 )
% 2.86/3.13 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 2.86/3.13 => ( ord_less_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B2 @ D2 ) ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_strict_mono
% 2.86/3.13 thf(fact_4251_mult__strict__mono,axiom,
% 2.86/3.13 ! [A2: code_integer,B2: code_integer,C: code_integer,D2: code_integer] :
% 2.86/3.13 ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 2.86/3.13 => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 2.86/3.13 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B2 )
% 2.86/3.13 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 2.86/3.13 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ ( times_3573771949741848930nteger @ B2 @ D2 ) ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_strict_mono
% 2.86/3.13 thf(fact_4252_mult__strict__mono,axiom,
% 2.86/3.13 ! [A2: nat,B2: nat,C: nat,D2: nat] :
% 2.86/3.13 ( ( ord_less_nat @ A2 @ B2 )
% 2.86/3.13 => ( ( ord_less_nat @ C @ D2 )
% 2.86/3.13 => ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 2.86/3.13 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 2.86/3.13 => ( ord_less_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B2 @ D2 ) ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_strict_mono
% 2.86/3.13 thf(fact_4253_mult__strict__mono,axiom,
% 2.86/3.13 ! [A2: int,B2: int,C: int,D2: int] :
% 2.86/3.13 ( ( ord_less_int @ A2 @ B2 )
% 2.86/3.13 => ( ( ord_less_int @ C @ D2 )
% 2.86/3.13 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 2.86/3.13 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 2.86/3.13 => ( ord_less_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B2 @ D2 ) ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_strict_mono
% 2.86/3.13 thf(fact_4254_mult__less__cancel__left,axiom,
% 2.86/3.13 ! [C: rat,A2: rat,B2: rat] :
% 2.86/3.13 ( ( ord_less_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B2 ) )
% 2.86/3.13 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 2.86/3.13 => ( ord_less_rat @ A2 @ B2 ) )
% 2.86/3.13 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 2.86/3.13 => ( ord_less_rat @ B2 @ A2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_less_cancel_left
% 2.86/3.13 thf(fact_4255_mult__less__cancel__left,axiom,
% 2.86/3.13 ! [C: code_integer,A2: code_integer,B2: code_integer] :
% 2.86/3.13 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A2 ) @ ( times_3573771949741848930nteger @ C @ B2 ) )
% 2.86/3.13 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 2.86/3.13 => ( ord_le6747313008572928689nteger @ A2 @ B2 ) )
% 2.86/3.13 & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 2.86/3.13 => ( ord_le6747313008572928689nteger @ B2 @ A2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_less_cancel_left
% 2.86/3.13 thf(fact_4256_mult__less__cancel__left,axiom,
% 2.86/3.13 ! [C: int,A2: int,B2: int] :
% 2.86/3.13 ( ( ord_less_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B2 ) )
% 2.86/3.13 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 2.86/3.13 => ( ord_less_int @ A2 @ B2 ) )
% 2.86/3.13 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 2.86/3.13 => ( ord_less_int @ B2 @ A2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_less_cancel_left
% 2.86/3.13 thf(fact_4257_mult__right__less__imp__less,axiom,
% 2.86/3.13 ! [A2: rat,C: rat,B2: rat] :
% 2.86/3.13 ( ( ord_less_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B2 @ C ) )
% 2.86/3.13 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 2.86/3.13 => ( ord_less_rat @ A2 @ B2 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_right_less_imp_less
% 2.86/3.13 thf(fact_4258_mult__right__less__imp__less,axiom,
% 2.86/3.13 ! [A2: code_integer,C: code_integer,B2: code_integer] :
% 2.86/3.13 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ ( times_3573771949741848930nteger @ B2 @ C ) )
% 2.86/3.13 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 2.86/3.13 => ( ord_le6747313008572928689nteger @ A2 @ B2 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_right_less_imp_less
% 2.86/3.13 thf(fact_4259_mult__right__less__imp__less,axiom,
% 2.86/3.13 ! [A2: nat,C: nat,B2: nat] :
% 2.86/3.13 ( ( ord_less_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B2 @ C ) )
% 2.86/3.13 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 2.86/3.13 => ( ord_less_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_right_less_imp_less
% 2.86/3.13 thf(fact_4260_mult__right__less__imp__less,axiom,
% 2.86/3.13 ! [A2: int,C: int,B2: int] :
% 2.86/3.13 ( ( ord_less_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B2 @ C ) )
% 2.86/3.13 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 2.86/3.13 => ( ord_less_int @ A2 @ B2 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_right_less_imp_less
% 2.86/3.13 thf(fact_4261_mult__strict__mono_H,axiom,
% 2.86/3.13 ! [A2: rat,B2: rat,C: rat,D2: rat] :
% 2.86/3.13 ( ( ord_less_rat @ A2 @ B2 )
% 2.86/3.13 => ( ( ord_less_rat @ C @ D2 )
% 2.86/3.13 => ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 2.86/3.13 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 2.86/3.13 => ( ord_less_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B2 @ D2 ) ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_strict_mono'
% 2.86/3.13 thf(fact_4262_mult__strict__mono_H,axiom,
% 2.86/3.13 ! [A2: code_integer,B2: code_integer,C: code_integer,D2: code_integer] :
% 2.86/3.13 ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 2.86/3.13 => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 2.86/3.13 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 2.86/3.13 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 2.86/3.13 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ ( times_3573771949741848930nteger @ B2 @ D2 ) ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_strict_mono'
% 2.86/3.13 thf(fact_4263_mult__strict__mono_H,axiom,
% 2.86/3.13 ! [A2: nat,B2: nat,C: nat,D2: nat] :
% 2.86/3.13 ( ( ord_less_nat @ A2 @ B2 )
% 2.86/3.13 => ( ( ord_less_nat @ C @ D2 )
% 2.86/3.13 => ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 2.86/3.13 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 2.86/3.13 => ( ord_less_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B2 @ D2 ) ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_strict_mono'
% 2.86/3.13 thf(fact_4264_mult__strict__mono_H,axiom,
% 2.86/3.13 ! [A2: int,B2: int,C: int,D2: int] :
% 2.86/3.13 ( ( ord_less_int @ A2 @ B2 )
% 2.86/3.13 => ( ( ord_less_int @ C @ D2 )
% 2.86/3.13 => ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 2.86/3.13 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 2.86/3.13 => ( ord_less_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B2 @ D2 ) ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_strict_mono'
% 2.86/3.13 thf(fact_4265_mult__less__cancel__right,axiom,
% 2.86/3.13 ! [A2: rat,C: rat,B2: rat] :
% 2.86/3.13 ( ( ord_less_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B2 @ C ) )
% 2.86/3.13 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 2.86/3.13 => ( ord_less_rat @ A2 @ B2 ) )
% 2.86/3.13 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 2.86/3.13 => ( ord_less_rat @ B2 @ A2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_less_cancel_right
% 2.86/3.13 thf(fact_4266_mult__less__cancel__right,axiom,
% 2.86/3.13 ! [A2: code_integer,C: code_integer,B2: code_integer] :
% 2.86/3.13 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ ( times_3573771949741848930nteger @ B2 @ C ) )
% 2.86/3.13 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 2.86/3.13 => ( ord_le6747313008572928689nteger @ A2 @ B2 ) )
% 2.86/3.13 & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 2.86/3.13 => ( ord_le6747313008572928689nteger @ B2 @ A2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_less_cancel_right
% 2.86/3.13 thf(fact_4267_mult__less__cancel__right,axiom,
% 2.86/3.13 ! [A2: int,C: int,B2: int] :
% 2.86/3.13 ( ( ord_less_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B2 @ C ) )
% 2.86/3.13 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 2.86/3.13 => ( ord_less_int @ A2 @ B2 ) )
% 2.86/3.13 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 2.86/3.13 => ( ord_less_int @ B2 @ A2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_less_cancel_right
% 2.86/3.13 thf(fact_4268_mult__le__cancel__left__neg,axiom,
% 2.86/3.13 ! [C: rat,A2: rat,B2: rat] :
% 2.86/3.13 ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.86/3.13 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B2 ) )
% 2.86/3.13 = ( ord_less_eq_rat @ B2 @ A2 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_le_cancel_left_neg
% 2.86/3.13 thf(fact_4269_mult__le__cancel__left__neg,axiom,
% 2.86/3.13 ! [C: code_integer,A2: code_integer,B2: code_integer] :
% 2.86/3.13 ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 2.86/3.13 => ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A2 ) @ ( times_3573771949741848930nteger @ C @ B2 ) )
% 2.86/3.13 = ( ord_le3102999989581377725nteger @ B2 @ A2 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_le_cancel_left_neg
% 2.86/3.13 thf(fact_4270_mult__le__cancel__left__neg,axiom,
% 2.86/3.13 ! [C: int,A2: int,B2: int] :
% 2.86/3.13 ( ( ord_less_int @ C @ zero_zero_int )
% 2.86/3.13 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B2 ) )
% 2.86/3.13 = ( ord_less_eq_int @ B2 @ A2 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_le_cancel_left_neg
% 2.86/3.13 thf(fact_4271_mult__le__cancel__left__pos,axiom,
% 2.86/3.13 ! [C: rat,A2: rat,B2: rat] :
% 2.86/3.13 ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.86/3.13 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B2 ) )
% 2.86/3.13 = ( ord_less_eq_rat @ A2 @ B2 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_le_cancel_left_pos
% 2.86/3.13 thf(fact_4272_mult__le__cancel__left__pos,axiom,
% 2.86/3.13 ! [C: code_integer,A2: code_integer,B2: code_integer] :
% 2.86/3.13 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 2.86/3.13 => ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A2 ) @ ( times_3573771949741848930nteger @ C @ B2 ) )
% 2.86/3.13 = ( ord_le3102999989581377725nteger @ A2 @ B2 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_le_cancel_left_pos
% 2.86/3.13 thf(fact_4273_mult__le__cancel__left__pos,axiom,
% 2.86/3.13 ! [C: int,A2: int,B2: int] :
% 2.86/3.13 ( ( ord_less_int @ zero_zero_int @ C )
% 2.86/3.13 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B2 ) )
% 2.86/3.13 = ( ord_less_eq_int @ A2 @ B2 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_le_cancel_left_pos
% 2.86/3.13 thf(fact_4274_mult__left__le__imp__le,axiom,
% 2.86/3.13 ! [C: rat,A2: rat,B2: rat] :
% 2.86/3.13 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B2 ) )
% 2.86/3.13 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.86/3.13 => ( ord_less_eq_rat @ A2 @ B2 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_left_le_imp_le
% 2.86/3.13 thf(fact_4275_mult__left__le__imp__le,axiom,
% 2.86/3.13 ! [C: code_integer,A2: code_integer,B2: code_integer] :
% 2.86/3.13 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A2 ) @ ( times_3573771949741848930nteger @ C @ B2 ) )
% 2.86/3.13 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 2.86/3.13 => ( ord_le3102999989581377725nteger @ A2 @ B2 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_left_le_imp_le
% 2.86/3.13 thf(fact_4276_mult__left__le__imp__le,axiom,
% 2.86/3.13 ! [C: nat,A2: nat,B2: nat] :
% 2.86/3.13 ( ( ord_less_eq_nat @ ( times_times_nat @ C @ A2 ) @ ( times_times_nat @ C @ B2 ) )
% 2.86/3.13 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 2.86/3.13 => ( ord_less_eq_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_left_le_imp_le
% 2.86/3.13 thf(fact_4277_mult__left__le__imp__le,axiom,
% 2.86/3.13 ! [C: int,A2: int,B2: int] :
% 2.86/3.13 ( ( ord_less_eq_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B2 ) )
% 2.86/3.13 => ( ( ord_less_int @ zero_zero_int @ C )
% 2.86/3.13 => ( ord_less_eq_int @ A2 @ B2 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_left_le_imp_le
% 2.86/3.13 thf(fact_4278_mult__right__le__imp__le,axiom,
% 2.86/3.13 ! [A2: rat,C: rat,B2: rat] :
% 2.86/3.13 ( ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B2 @ C ) )
% 2.86/3.13 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.86/3.13 => ( ord_less_eq_rat @ A2 @ B2 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_right_le_imp_le
% 2.86/3.13 thf(fact_4279_mult__right__le__imp__le,axiom,
% 2.86/3.13 ! [A2: code_integer,C: code_integer,B2: code_integer] :
% 2.86/3.13 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ ( times_3573771949741848930nteger @ B2 @ C ) )
% 2.86/3.13 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 2.86/3.13 => ( ord_le3102999989581377725nteger @ A2 @ B2 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_right_le_imp_le
% 2.86/3.13 thf(fact_4280_mult__right__le__imp__le,axiom,
% 2.86/3.13 ! [A2: nat,C: nat,B2: nat] :
% 2.86/3.13 ( ( ord_less_eq_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B2 @ C ) )
% 2.86/3.13 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 2.86/3.13 => ( ord_less_eq_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_right_le_imp_le
% 2.86/3.13 thf(fact_4281_mult__right__le__imp__le,axiom,
% 2.86/3.13 ! [A2: int,C: int,B2: int] :
% 2.86/3.13 ( ( ord_less_eq_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B2 @ C ) )
% 2.86/3.13 => ( ( ord_less_int @ zero_zero_int @ C )
% 2.86/3.13 => ( ord_less_eq_int @ A2 @ B2 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_right_le_imp_le
% 2.86/3.13 thf(fact_4282_mult__le__less__imp__less,axiom,
% 2.86/3.13 ! [A2: rat,B2: rat,C: rat,D2: rat] :
% 2.86/3.13 ( ( ord_less_eq_rat @ A2 @ B2 )
% 2.86/3.13 => ( ( ord_less_rat @ C @ D2 )
% 2.86/3.13 => ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 2.86/3.13 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 2.86/3.13 => ( ord_less_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B2 @ D2 ) ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_le_less_imp_less
% 2.86/3.13 thf(fact_4283_mult__le__less__imp__less,axiom,
% 2.86/3.13 ! [A2: code_integer,B2: code_integer,C: code_integer,D2: code_integer] :
% 2.86/3.13 ( ( ord_le3102999989581377725nteger @ A2 @ B2 )
% 2.86/3.13 => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 2.86/3.13 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 )
% 2.86/3.13 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 2.86/3.13 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ ( times_3573771949741848930nteger @ B2 @ D2 ) ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_le_less_imp_less
% 2.86/3.13 thf(fact_4284_mult__le__less__imp__less,axiom,
% 2.86/3.13 ! [A2: nat,B2: nat,C: nat,D2: nat] :
% 2.86/3.13 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.13 => ( ( ord_less_nat @ C @ D2 )
% 2.86/3.13 => ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 2.86/3.13 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 2.86/3.13 => ( ord_less_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B2 @ D2 ) ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_le_less_imp_less
% 2.86/3.13 thf(fact_4285_mult__le__less__imp__less,axiom,
% 2.86/3.13 ! [A2: int,B2: int,C: int,D2: int] :
% 2.86/3.13 ( ( ord_less_eq_int @ A2 @ B2 )
% 2.86/3.13 => ( ( ord_less_int @ C @ D2 )
% 2.86/3.13 => ( ( ord_less_int @ zero_zero_int @ A2 )
% 2.86/3.13 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 2.86/3.13 => ( ord_less_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B2 @ D2 ) ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_le_less_imp_less
% 2.86/3.13 thf(fact_4286_mult__less__le__imp__less,axiom,
% 2.86/3.13 ! [A2: rat,B2: rat,C: rat,D2: rat] :
% 2.86/3.13 ( ( ord_less_rat @ A2 @ B2 )
% 2.86/3.13 => ( ( ord_less_eq_rat @ C @ D2 )
% 2.86/3.13 => ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 2.86/3.13 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.86/3.13 => ( ord_less_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B2 @ D2 ) ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_less_le_imp_less
% 2.86/3.13 thf(fact_4287_mult__less__le__imp__less,axiom,
% 2.86/3.13 ! [A2: code_integer,B2: code_integer,C: code_integer,D2: code_integer] :
% 2.86/3.13 ( ( ord_le6747313008572928689nteger @ A2 @ B2 )
% 2.86/3.13 => ( ( ord_le3102999989581377725nteger @ C @ D2 )
% 2.86/3.13 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 2.86/3.13 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 2.86/3.13 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ ( times_3573771949741848930nteger @ B2 @ D2 ) ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_less_le_imp_less
% 2.86/3.13 thf(fact_4288_mult__less__le__imp__less,axiom,
% 2.86/3.13 ! [A2: nat,B2: nat,C: nat,D2: nat] :
% 2.86/3.13 ( ( ord_less_nat @ A2 @ B2 )
% 2.86/3.13 => ( ( ord_less_eq_nat @ C @ D2 )
% 2.86/3.13 => ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 2.86/3.13 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 2.86/3.13 => ( ord_less_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B2 @ D2 ) ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_less_le_imp_less
% 2.86/3.13 thf(fact_4289_mult__less__le__imp__less,axiom,
% 2.86/3.13 ! [A2: int,B2: int,C: int,D2: int] :
% 2.86/3.13 ( ( ord_less_int @ A2 @ B2 )
% 2.86/3.13 => ( ( ord_less_eq_int @ C @ D2 )
% 2.86/3.13 => ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 2.86/3.13 => ( ( ord_less_int @ zero_zero_int @ C )
% 2.86/3.13 => ( ord_less_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B2 @ D2 ) ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_less_le_imp_less
% 2.86/3.13 thf(fact_4290_sum__squares__ge__zero,axiom,
% 2.86/3.13 ! [X: code_integer,Y: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % sum_squares_ge_zero
% 2.86/3.13 thf(fact_4291_sum__squares__ge__zero,axiom,
% 2.86/3.13 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % sum_squares_ge_zero
% 2.86/3.13 thf(fact_4292_sum__squares__ge__zero,axiom,
% 2.86/3.13 ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % sum_squares_ge_zero
% 2.86/3.13 thf(fact_4293_mult__left__le,axiom,
% 2.86/3.13 ! [C: code_integer,A2: code_integer] :
% 2.86/3.13 ( ( ord_le3102999989581377725nteger @ C @ one_one_Code_integer )
% 2.86/3.13 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 2.86/3.13 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ A2 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_left_le
% 2.86/3.13 thf(fact_4294_mult__left__le,axiom,
% 2.86/3.13 ! [C: rat,A2: rat] :
% 2.86/3.13 ( ( ord_less_eq_rat @ C @ one_one_rat )
% 2.86/3.13 => ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 2.86/3.13 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C ) @ A2 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_left_le
% 2.86/3.13 thf(fact_4295_mult__left__le,axiom,
% 2.86/3.13 ! [C: nat,A2: nat] :
% 2.86/3.13 ( ( ord_less_eq_nat @ C @ one_one_nat )
% 2.86/3.13 => ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 2.86/3.13 => ( ord_less_eq_nat @ ( times_times_nat @ A2 @ C ) @ A2 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_left_le
% 2.86/3.13 thf(fact_4296_mult__left__le,axiom,
% 2.86/3.13 ! [C: int,A2: int] :
% 2.86/3.13 ( ( ord_less_eq_int @ C @ one_one_int )
% 2.86/3.13 => ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 2.86/3.13 => ( ord_less_eq_int @ ( times_times_int @ A2 @ C ) @ A2 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_left_le
% 2.86/3.13 thf(fact_4297_mult__le__one,axiom,
% 2.86/3.13 ! [A2: code_integer,B2: code_integer] :
% 2.86/3.13 ( ( ord_le3102999989581377725nteger @ A2 @ one_one_Code_integer )
% 2.86/3.13 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B2 )
% 2.86/3.13 => ( ( ord_le3102999989581377725nteger @ B2 @ one_one_Code_integer )
% 2.86/3.13 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A2 @ B2 ) @ one_one_Code_integer ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_le_one
% 2.86/3.13 thf(fact_4298_mult__le__one,axiom,
% 2.86/3.13 ! [A2: rat,B2: rat] :
% 2.86/3.13 ( ( ord_less_eq_rat @ A2 @ one_one_rat )
% 2.86/3.13 => ( ( ord_less_eq_rat @ zero_zero_rat @ B2 )
% 2.86/3.13 => ( ( ord_less_eq_rat @ B2 @ one_one_rat )
% 2.86/3.13 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ B2 ) @ one_one_rat ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_le_one
% 2.86/3.13 thf(fact_4299_mult__le__one,axiom,
% 2.86/3.13 ! [A2: nat,B2: nat] :
% 2.86/3.13 ( ( ord_less_eq_nat @ A2 @ one_one_nat )
% 2.86/3.13 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 2.86/3.13 => ( ( ord_less_eq_nat @ B2 @ one_one_nat )
% 2.86/3.13 => ( ord_less_eq_nat @ ( times_times_nat @ A2 @ B2 ) @ one_one_nat ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_le_one
% 2.86/3.13 thf(fact_4300_mult__le__one,axiom,
% 2.86/3.13 ! [A2: int,B2: int] :
% 2.86/3.13 ( ( ord_less_eq_int @ A2 @ one_one_int )
% 2.86/3.13 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 2.86/3.13 => ( ( ord_less_eq_int @ B2 @ one_one_int )
% 2.86/3.13 => ( ord_less_eq_int @ ( times_times_int @ A2 @ B2 ) @ one_one_int ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_le_one
% 2.86/3.13 thf(fact_4301_mult__right__le__one__le,axiom,
% 2.86/3.13 ! [X: code_integer,Y: code_integer] :
% 2.86/3.13 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 2.86/3.13 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 2.86/3.13 => ( ( ord_le3102999989581377725nteger @ Y @ one_one_Code_integer )
% 2.86/3.13 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ X @ Y ) @ X ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_right_le_one_le
% 2.86/3.13 thf(fact_4302_mult__right__le__one__le,axiom,
% 2.86/3.13 ! [X: rat,Y: rat] :
% 2.86/3.13 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 2.86/3.13 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 2.86/3.13 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 2.86/3.13 => ( ord_less_eq_rat @ ( times_times_rat @ X @ Y ) @ X ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_right_le_one_le
% 2.86/3.13 thf(fact_4303_mult__right__le__one__le,axiom,
% 2.86/3.13 ! [X: int,Y: int] :
% 2.86/3.13 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 2.86/3.13 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 2.86/3.13 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 2.86/3.13 => ( ord_less_eq_int @ ( times_times_int @ X @ Y ) @ X ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_right_le_one_le
% 2.86/3.13 thf(fact_4304_mult__left__le__one__le,axiom,
% 2.86/3.13 ! [X: code_integer,Y: code_integer] :
% 2.86/3.13 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 2.86/3.13 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 2.86/3.13 => ( ( ord_le3102999989581377725nteger @ Y @ one_one_Code_integer )
% 2.86/3.13 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ Y @ X ) @ X ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_left_le_one_le
% 2.86/3.13 thf(fact_4305_mult__left__le__one__le,axiom,
% 2.86/3.13 ! [X: rat,Y: rat] :
% 2.86/3.13 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 2.86/3.13 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 2.86/3.13 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 2.86/3.13 => ( ord_less_eq_rat @ ( times_times_rat @ Y @ X ) @ X ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_left_le_one_le
% 2.86/3.13 thf(fact_4306_mult__left__le__one__le,axiom,
% 2.86/3.13 ! [X: int,Y: int] :
% 2.86/3.13 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 2.86/3.13 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 2.86/3.13 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 2.86/3.13 => ( ord_less_eq_int @ ( times_times_int @ Y @ X ) @ X ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_left_le_one_le
% 2.86/3.13 thf(fact_4307_not__sum__squares__lt__zero,axiom,
% 2.86/3.13 ! [X: rat,Y: rat] :
% 2.86/3.13 ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat ) ).
% 2.86/3.13
% 2.86/3.13 % not_sum_squares_lt_zero
% 2.86/3.13 thf(fact_4308_not__sum__squares__lt__zero,axiom,
% 2.86/3.13 ! [X: code_integer,Y: code_integer] :
% 2.86/3.13 ~ ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) @ zero_z3403309356797280102nteger ) ).
% 2.86/3.13
% 2.86/3.13 % not_sum_squares_lt_zero
% 2.86/3.13 thf(fact_4309_not__sum__squares__lt__zero,axiom,
% 2.86/3.13 ! [X: int,Y: int] :
% 2.86/3.13 ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int ) ).
% 2.86/3.13
% 2.86/3.13 % not_sum_squares_lt_zero
% 2.86/3.13 thf(fact_4310_zero__less__two,axiom,
% 2.86/3.13 ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 2.86/3.13
% 2.86/3.13 % zero_less_two
% 2.86/3.13 thf(fact_4311_zero__less__two,axiom,
% 2.86/3.13 ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ one_one_Code_integer ) ).
% 2.86/3.13
% 2.86/3.13 % zero_less_two
% 2.86/3.13 thf(fact_4312_zero__less__two,axiom,
% 2.86/3.13 ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 2.86/3.13
% 2.86/3.13 % zero_less_two
% 2.86/3.13 thf(fact_4313_zero__less__two,axiom,
% 2.86/3.13 ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 2.86/3.13
% 2.86/3.13 % zero_less_two
% 2.86/3.13 thf(fact_4314_ex__least__nat__less,axiom,
% 2.86/3.13 ! [P: nat > $o,N: nat] :
% 2.86/3.13 ( ( P @ N )
% 2.86/3.13 => ( ~ ( P @ zero_zero_nat )
% 2.86/3.13 => ? [K: nat] :
% 2.86/3.13 ( ( ord_less_nat @ K @ N )
% 2.86/3.13 & ! [I6: nat] :
% 2.86/3.13 ( ( ord_less_eq_nat @ I6 @ K )
% 2.86/3.13 => ~ ( P @ I6 ) )
% 2.86/3.13 & ( P @ ( suc @ K ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % ex_least_nat_less
% 2.86/3.13 thf(fact_4315_length__pos__if__in__set,axiom,
% 2.86/3.13 ! [X: produc3843707927480180839at_nat,Xs: list_P5464809261938338413at_nat] :
% 2.86/3.13 ( ( member8757157785044589968at_nat @ X @ ( set_Pr3765526544606949372at_nat @ Xs ) )
% 2.86/3.13 => ( ord_less_nat @ zero_zero_nat @ ( size_s1588839187904960729at_nat @ Xs ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % length_pos_if_in_set
% 2.86/3.13 thf(fact_4316_length__pos__if__in__set,axiom,
% 2.86/3.13 ! [X: product_prod_nat_nat,Xs: list_P6011104703257516679at_nat] :
% 2.86/3.13 ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 2.86/3.13 => ( ord_less_nat @ zero_zero_nat @ ( size_s5460976970255530739at_nat @ Xs ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % length_pos_if_in_set
% 2.86/3.13 thf(fact_4317_length__pos__if__in__set,axiom,
% 2.86/3.13 ! [X: produc3658429121746597890et_nat > $o,Xs: list_P7985473006766602707_nat_o] :
% 2.86/3.13 ( ( member6576561426505652726_nat_o @ X @ ( set_Pr400311997697478754_nat_o @ Xs ) )
% 2.86/3.13 => ( ord_less_nat @ zero_zero_nat @ ( size_s8908918004648414271_nat_o @ Xs ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % length_pos_if_in_set
% 2.86/3.13 thf(fact_4318_length__pos__if__in__set,axiom,
% 2.86/3.13 ! [X: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn] :
% 2.86/3.13 ( ( member7957490590177025114n_assn @ X @ ( set_Pr1139785259514867910n_assn @ Xs ) )
% 2.86/3.13 => ( ord_less_nat @ zero_zero_nat @ ( size_s6829681357464350627n_assn @ Xs ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % length_pos_if_in_set
% 2.86/3.13 thf(fact_4319_length__pos__if__in__set,axiom,
% 2.86/3.13 ! [X: c,Xs: list_c] :
% 2.86/3.13 ( ( member_c @ X @ ( set_c2 @ Xs ) )
% 2.86/3.13 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_c @ Xs ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % length_pos_if_in_set
% 2.86/3.13 thf(fact_4320_length__pos__if__in__set,axiom,
% 2.86/3.13 ! [X: d,Xs: list_d] :
% 2.86/3.13 ( ( member_d @ X @ ( set_d2 @ Xs ) )
% 2.86/3.13 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_d @ Xs ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % length_pos_if_in_set
% 2.86/3.13 thf(fact_4321_length__pos__if__in__set,axiom,
% 2.86/3.13 ! [X: nat,Xs: list_nat] :
% 2.86/3.13 ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 2.86/3.13 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % length_pos_if_in_set
% 2.86/3.13 thf(fact_4322_length__pos__if__in__set,axiom,
% 2.86/3.13 ! [X: int,Xs: list_int] :
% 2.86/3.13 ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 2.86/3.13 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % length_pos_if_in_set
% 2.86/3.13 thf(fact_4323_diff__Suc__less,axiom,
% 2.86/3.13 ! [N: nat,I: nat] :
% 2.86/3.13 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.13 => ( ord_less_nat @ ( minus_minus_nat @ N @ ( suc @ I ) ) @ N ) ) ).
% 2.86/3.13
% 2.86/3.13 % diff_Suc_less
% 2.86/3.13 thf(fact_4324_n__less__n__mult__m,axiom,
% 2.86/3.13 ! [N: nat,M2: nat] :
% 2.86/3.13 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.13 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M2 )
% 2.86/3.13 => ( ord_less_nat @ N @ ( times_times_nat @ N @ M2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % n_less_n_mult_m
% 2.86/3.13 thf(fact_4325_n__less__m__mult__n,axiom,
% 2.86/3.13 ! [N: nat,M2: nat] :
% 2.86/3.13 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.13 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M2 )
% 2.86/3.13 => ( ord_less_nat @ N @ ( times_times_nat @ M2 @ N ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % n_less_m_mult_n
% 2.86/3.13 thf(fact_4326_one__less__mult,axiom,
% 2.86/3.13 ! [N: nat,M2: nat] :
% 2.86/3.13 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 2.86/3.13 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M2 )
% 2.86/3.13 => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M2 @ N ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % one_less_mult
% 2.86/3.13 thf(fact_4327_nat__induct__non__zero,axiom,
% 2.86/3.13 ! [N: nat,P: nat > $o] :
% 2.86/3.13 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.13 => ( ( P @ one_one_nat )
% 2.86/3.13 => ( ! [N5: nat] :
% 2.86/3.13 ( ( ord_less_nat @ zero_zero_nat @ N5 )
% 2.86/3.13 => ( ( P @ N5 )
% 2.86/3.13 => ( P @ ( suc @ N5 ) ) ) )
% 2.86/3.13 => ( P @ N ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % nat_induct_non_zero
% 2.86/3.13 thf(fact_4328_nat__diff__split,axiom,
% 2.86/3.13 ! [P: nat > $o,A2: nat,B2: nat] :
% 2.86/3.13 ( ( P @ ( minus_minus_nat @ A2 @ B2 ) )
% 2.86/3.13 = ( ( ( ord_less_nat @ A2 @ B2 )
% 2.86/3.13 => ( P @ zero_zero_nat ) )
% 2.86/3.13 & ! [D5: nat] :
% 2.86/3.13 ( ( A2
% 2.86/3.13 = ( plus_plus_nat @ B2 @ D5 ) )
% 2.86/3.13 => ( P @ D5 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % nat_diff_split
% 2.86/3.13 thf(fact_4329_nat__diff__split__asm,axiom,
% 2.86/3.13 ! [P: nat > $o,A2: nat,B2: nat] :
% 2.86/3.13 ( ( P @ ( minus_minus_nat @ A2 @ B2 ) )
% 2.86/3.13 = ( ~ ( ( ( ord_less_nat @ A2 @ B2 )
% 2.86/3.13 & ~ ( P @ zero_zero_nat ) )
% 2.86/3.13 | ? [D5: nat] :
% 2.86/3.13 ( ( A2
% 2.86/3.13 = ( plus_plus_nat @ B2 @ D5 ) )
% 2.86/3.13 & ~ ( P @ D5 ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % nat_diff_split_asm
% 2.86/3.13 thf(fact_4330_mult__le__cancel__left1,axiom,
% 2.86/3.13 ! [C: rat,B2: rat] :
% 2.86/3.13 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ C @ B2 ) )
% 2.86/3.13 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.86/3.13 => ( ord_less_eq_rat @ one_one_rat @ B2 ) )
% 2.86/3.13 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.86/3.13 => ( ord_less_eq_rat @ B2 @ one_one_rat ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_le_cancel_left1
% 2.86/3.13 thf(fact_4331_mult__le__cancel__left1,axiom,
% 2.86/3.13 ! [C: code_integer,B2: code_integer] :
% 2.86/3.13 ( ( ord_le3102999989581377725nteger @ C @ ( times_3573771949741848930nteger @ C @ B2 ) )
% 2.86/3.13 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 2.86/3.13 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ B2 ) )
% 2.86/3.13 & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 2.86/3.13 => ( ord_le3102999989581377725nteger @ B2 @ one_one_Code_integer ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_le_cancel_left1
% 2.86/3.13 thf(fact_4332_mult__le__cancel__left1,axiom,
% 2.86/3.13 ! [C: int,B2: int] :
% 2.86/3.13 ( ( ord_less_eq_int @ C @ ( times_times_int @ C @ B2 ) )
% 2.86/3.13 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 2.86/3.13 => ( ord_less_eq_int @ one_one_int @ B2 ) )
% 2.86/3.13 & ( ( ord_less_int @ C @ zero_zero_int )
% 2.86/3.13 => ( ord_less_eq_int @ B2 @ one_one_int ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_le_cancel_left1
% 2.86/3.13 thf(fact_4333_mult__le__cancel__left2,axiom,
% 2.86/3.13 ! [C: rat,A2: rat] :
% 2.86/3.13 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A2 ) @ C )
% 2.86/3.13 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.86/3.13 => ( ord_less_eq_rat @ A2 @ one_one_rat ) )
% 2.86/3.13 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.86/3.13 => ( ord_less_eq_rat @ one_one_rat @ A2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_le_cancel_left2
% 2.86/3.13 thf(fact_4334_mult__le__cancel__left2,axiom,
% 2.86/3.13 ! [C: code_integer,A2: code_integer] :
% 2.86/3.13 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A2 ) @ C )
% 2.86/3.13 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 2.86/3.13 => ( ord_le3102999989581377725nteger @ A2 @ one_one_Code_integer ) )
% 2.86/3.13 & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 2.86/3.13 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_le_cancel_left2
% 2.86/3.13 thf(fact_4335_mult__le__cancel__left2,axiom,
% 2.86/3.13 ! [C: int,A2: int] :
% 2.86/3.13 ( ( ord_less_eq_int @ ( times_times_int @ C @ A2 ) @ C )
% 2.86/3.13 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 2.86/3.13 => ( ord_less_eq_int @ A2 @ one_one_int ) )
% 2.86/3.13 & ( ( ord_less_int @ C @ zero_zero_int )
% 2.86/3.13 => ( ord_less_eq_int @ one_one_int @ A2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_le_cancel_left2
% 2.86/3.13 thf(fact_4336_mult__le__cancel__right1,axiom,
% 2.86/3.13 ! [C: rat,B2: rat] :
% 2.86/3.13 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ B2 @ C ) )
% 2.86/3.13 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.86/3.13 => ( ord_less_eq_rat @ one_one_rat @ B2 ) )
% 2.86/3.13 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.86/3.13 => ( ord_less_eq_rat @ B2 @ one_one_rat ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_le_cancel_right1
% 2.86/3.13 thf(fact_4337_mult__le__cancel__right1,axiom,
% 2.86/3.13 ! [C: code_integer,B2: code_integer] :
% 2.86/3.13 ( ( ord_le3102999989581377725nteger @ C @ ( times_3573771949741848930nteger @ B2 @ C ) )
% 2.86/3.13 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 2.86/3.13 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ B2 ) )
% 2.86/3.13 & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 2.86/3.13 => ( ord_le3102999989581377725nteger @ B2 @ one_one_Code_integer ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_le_cancel_right1
% 2.86/3.13 thf(fact_4338_mult__le__cancel__right1,axiom,
% 2.86/3.13 ! [C: int,B2: int] :
% 2.86/3.13 ( ( ord_less_eq_int @ C @ ( times_times_int @ B2 @ C ) )
% 2.86/3.13 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 2.86/3.13 => ( ord_less_eq_int @ one_one_int @ B2 ) )
% 2.86/3.13 & ( ( ord_less_int @ C @ zero_zero_int )
% 2.86/3.13 => ( ord_less_eq_int @ B2 @ one_one_int ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_le_cancel_right1
% 2.86/3.13 thf(fact_4339_mult__le__cancel__right2,axiom,
% 2.86/3.13 ! [A2: rat,C: rat] :
% 2.86/3.13 ( ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C ) @ C )
% 2.86/3.13 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.86/3.13 => ( ord_less_eq_rat @ A2 @ one_one_rat ) )
% 2.86/3.13 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.86/3.13 => ( ord_less_eq_rat @ one_one_rat @ A2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_le_cancel_right2
% 2.86/3.13 thf(fact_4340_mult__le__cancel__right2,axiom,
% 2.86/3.13 ! [A2: code_integer,C: code_integer] :
% 2.86/3.13 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ C )
% 2.86/3.13 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 2.86/3.13 => ( ord_le3102999989581377725nteger @ A2 @ one_one_Code_integer ) )
% 2.86/3.13 & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 2.86/3.13 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_le_cancel_right2
% 2.86/3.13 thf(fact_4341_mult__le__cancel__right2,axiom,
% 2.86/3.13 ! [A2: int,C: int] :
% 2.86/3.13 ( ( ord_less_eq_int @ ( times_times_int @ A2 @ C ) @ C )
% 2.86/3.13 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 2.86/3.13 => ( ord_less_eq_int @ A2 @ one_one_int ) )
% 2.86/3.13 & ( ( ord_less_int @ C @ zero_zero_int )
% 2.86/3.13 => ( ord_less_eq_int @ one_one_int @ A2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_le_cancel_right2
% 2.86/3.13 thf(fact_4342_mult__less__cancel__left1,axiom,
% 2.86/3.13 ! [C: rat,B2: rat] :
% 2.86/3.13 ( ( ord_less_rat @ C @ ( times_times_rat @ C @ B2 ) )
% 2.86/3.13 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 2.86/3.13 => ( ord_less_rat @ one_one_rat @ B2 ) )
% 2.86/3.13 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 2.86/3.13 => ( ord_less_rat @ B2 @ one_one_rat ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_less_cancel_left1
% 2.86/3.13 thf(fact_4343_mult__less__cancel__left1,axiom,
% 2.86/3.13 ! [C: code_integer,B2: code_integer] :
% 2.86/3.13 ( ( ord_le6747313008572928689nteger @ C @ ( times_3573771949741848930nteger @ C @ B2 ) )
% 2.86/3.13 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 2.86/3.13 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B2 ) )
% 2.86/3.13 & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 2.86/3.13 => ( ord_le6747313008572928689nteger @ B2 @ one_one_Code_integer ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_less_cancel_left1
% 2.86/3.13 thf(fact_4344_mult__less__cancel__left1,axiom,
% 2.86/3.13 ! [C: int,B2: int] :
% 2.86/3.13 ( ( ord_less_int @ C @ ( times_times_int @ C @ B2 ) )
% 2.86/3.13 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 2.86/3.13 => ( ord_less_int @ one_one_int @ B2 ) )
% 2.86/3.13 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 2.86/3.13 => ( ord_less_int @ B2 @ one_one_int ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_less_cancel_left1
% 2.86/3.13 thf(fact_4345_mult__less__cancel__left2,axiom,
% 2.86/3.13 ! [C: rat,A2: rat] :
% 2.86/3.13 ( ( ord_less_rat @ ( times_times_rat @ C @ A2 ) @ C )
% 2.86/3.13 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 2.86/3.13 => ( ord_less_rat @ A2 @ one_one_rat ) )
% 2.86/3.13 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 2.86/3.13 => ( ord_less_rat @ one_one_rat @ A2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_less_cancel_left2
% 2.86/3.13 thf(fact_4346_mult__less__cancel__left2,axiom,
% 2.86/3.13 ! [C: code_integer,A2: code_integer] :
% 2.86/3.13 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A2 ) @ C )
% 2.86/3.13 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 2.86/3.13 => ( ord_le6747313008572928689nteger @ A2 @ one_one_Code_integer ) )
% 2.86/3.13 & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 2.86/3.13 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_less_cancel_left2
% 2.86/3.13 thf(fact_4347_mult__less__cancel__left2,axiom,
% 2.86/3.13 ! [C: int,A2: int] :
% 2.86/3.13 ( ( ord_less_int @ ( times_times_int @ C @ A2 ) @ C )
% 2.86/3.13 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 2.86/3.13 => ( ord_less_int @ A2 @ one_one_int ) )
% 2.86/3.13 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 2.86/3.13 => ( ord_less_int @ one_one_int @ A2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_less_cancel_left2
% 2.86/3.13 thf(fact_4348_mult__less__cancel__right1,axiom,
% 2.86/3.13 ! [C: rat,B2: rat] :
% 2.86/3.13 ( ( ord_less_rat @ C @ ( times_times_rat @ B2 @ C ) )
% 2.86/3.13 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 2.86/3.13 => ( ord_less_rat @ one_one_rat @ B2 ) )
% 2.86/3.13 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 2.86/3.13 => ( ord_less_rat @ B2 @ one_one_rat ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_less_cancel_right1
% 2.86/3.13 thf(fact_4349_mult__less__cancel__right1,axiom,
% 2.86/3.13 ! [C: code_integer,B2: code_integer] :
% 2.86/3.13 ( ( ord_le6747313008572928689nteger @ C @ ( times_3573771949741848930nteger @ B2 @ C ) )
% 2.86/3.13 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 2.86/3.13 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B2 ) )
% 2.86/3.13 & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 2.86/3.13 => ( ord_le6747313008572928689nteger @ B2 @ one_one_Code_integer ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_less_cancel_right1
% 2.86/3.13 thf(fact_4350_mult__less__cancel__right1,axiom,
% 2.86/3.13 ! [C: int,B2: int] :
% 2.86/3.13 ( ( ord_less_int @ C @ ( times_times_int @ B2 @ C ) )
% 2.86/3.13 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 2.86/3.13 => ( ord_less_int @ one_one_int @ B2 ) )
% 2.86/3.13 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 2.86/3.13 => ( ord_less_int @ B2 @ one_one_int ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_less_cancel_right1
% 2.86/3.13 thf(fact_4351_mult__less__cancel__right2,axiom,
% 2.86/3.13 ! [A2: rat,C: rat] :
% 2.86/3.13 ( ( ord_less_rat @ ( times_times_rat @ A2 @ C ) @ C )
% 2.86/3.13 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 2.86/3.13 => ( ord_less_rat @ A2 @ one_one_rat ) )
% 2.86/3.13 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 2.86/3.13 => ( ord_less_rat @ one_one_rat @ A2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_less_cancel_right2
% 2.86/3.13 thf(fact_4352_mult__less__cancel__right2,axiom,
% 2.86/3.13 ! [A2: code_integer,C: code_integer] :
% 2.86/3.13 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ C )
% 2.86/3.13 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 2.86/3.13 => ( ord_le6747313008572928689nteger @ A2 @ one_one_Code_integer ) )
% 2.86/3.13 & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 2.86/3.13 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_less_cancel_right2
% 2.86/3.13 thf(fact_4353_mult__less__cancel__right2,axiom,
% 2.86/3.13 ! [A2: int,C: int] :
% 2.86/3.13 ( ( ord_less_int @ ( times_times_int @ A2 @ C ) @ C )
% 2.86/3.13 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 2.86/3.13 => ( ord_less_int @ A2 @ one_one_int ) )
% 2.86/3.13 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 2.86/3.13 => ( ord_less_int @ one_one_int @ A2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_less_cancel_right2
% 2.86/3.13 thf(fact_4354_convex__bound__le,axiom,
% 2.86/3.13 ! [X: code_integer,A2: code_integer,Y: code_integer,U: code_integer,V2: code_integer] :
% 2.86/3.13 ( ( ord_le3102999989581377725nteger @ X @ A2 )
% 2.86/3.13 => ( ( ord_le3102999989581377725nteger @ Y @ A2 )
% 2.86/3.13 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ U )
% 2.86/3.13 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ V2 )
% 2.86/3.13 => ( ( ( plus_p5714425477246183910nteger @ U @ V2 )
% 2.86/3.13 = one_one_Code_integer )
% 2.86/3.13 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ U @ X ) @ ( times_3573771949741848930nteger @ V2 @ Y ) ) @ A2 ) ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % convex_bound_le
% 2.86/3.13 thf(fact_4355_convex__bound__le,axiom,
% 2.86/3.13 ! [X: rat,A2: rat,Y: rat,U: rat,V2: rat] :
% 2.86/3.13 ( ( ord_less_eq_rat @ X @ A2 )
% 2.86/3.13 => ( ( ord_less_eq_rat @ Y @ A2 )
% 2.86/3.13 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 2.86/3.13 => ( ( ord_less_eq_rat @ zero_zero_rat @ V2 )
% 2.86/3.13 => ( ( ( plus_plus_rat @ U @ V2 )
% 2.86/3.13 = one_one_rat )
% 2.86/3.13 => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V2 @ Y ) ) @ A2 ) ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % convex_bound_le
% 2.86/3.13 thf(fact_4356_convex__bound__le,axiom,
% 2.86/3.13 ! [X: int,A2: int,Y: int,U: int,V2: int] :
% 2.86/3.13 ( ( ord_less_eq_int @ X @ A2 )
% 2.86/3.13 => ( ( ord_less_eq_int @ Y @ A2 )
% 2.86/3.13 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 2.86/3.13 => ( ( ord_less_eq_int @ zero_zero_int @ V2 )
% 2.86/3.13 => ( ( ( plus_plus_int @ U @ V2 )
% 2.86/3.13 = one_one_int )
% 2.86/3.13 => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V2 @ Y ) ) @ A2 ) ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % convex_bound_le
% 2.86/3.13 thf(fact_4357_nz__le__conv__less,axiom,
% 2.86/3.13 ! [K3: nat,M2: nat] :
% 2.86/3.13 ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 2.86/3.13 => ( ( ord_less_eq_nat @ K3 @ M2 )
% 2.86/3.13 => ( ord_less_nat @ ( minus_minus_nat @ K3 @ ( suc @ zero_zero_nat ) ) @ M2 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % nz_le_conv_less
% 2.86/3.13 thf(fact_4358_Suc__pred_H,axiom,
% 2.86/3.13 ! [N: nat] :
% 2.86/3.13 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.13 => ( N
% 2.86/3.13 = ( suc @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % Suc_pred'
% 2.86/3.13 thf(fact_4359_Suc__diff__eq__diff__pred,axiom,
% 2.86/3.13 ! [N: nat,M2: nat] :
% 2.86/3.13 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.13 => ( ( minus_minus_nat @ ( suc @ M2 ) @ N )
% 2.86/3.13 = ( minus_minus_nat @ M2 @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % Suc_diff_eq_diff_pred
% 2.86/3.13 thf(fact_4360_convex__bound__lt,axiom,
% 2.86/3.13 ! [X: rat,A2: rat,Y: rat,U: rat,V2: rat] :
% 2.86/3.13 ( ( ord_less_rat @ X @ A2 )
% 2.86/3.13 => ( ( ord_less_rat @ Y @ A2 )
% 2.86/3.13 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 2.86/3.13 => ( ( ord_less_eq_rat @ zero_zero_rat @ V2 )
% 2.86/3.13 => ( ( ( plus_plus_rat @ U @ V2 )
% 2.86/3.13 = one_one_rat )
% 2.86/3.13 => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V2 @ Y ) ) @ A2 ) ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % convex_bound_lt
% 2.86/3.13 thf(fact_4361_convex__bound__lt,axiom,
% 2.86/3.13 ! [X: code_integer,A2: code_integer,Y: code_integer,U: code_integer,V2: code_integer] :
% 2.86/3.13 ( ( ord_le6747313008572928689nteger @ X @ A2 )
% 2.86/3.13 => ( ( ord_le6747313008572928689nteger @ Y @ A2 )
% 2.86/3.13 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ U )
% 2.86/3.13 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ V2 )
% 2.86/3.13 => ( ( ( plus_p5714425477246183910nteger @ U @ V2 )
% 2.86/3.13 = one_one_Code_integer )
% 2.86/3.13 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ U @ X ) @ ( times_3573771949741848930nteger @ V2 @ Y ) ) @ A2 ) ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % convex_bound_lt
% 2.86/3.13 thf(fact_4362_convex__bound__lt,axiom,
% 2.86/3.13 ! [X: int,A2: int,Y: int,U: int,V2: int] :
% 2.86/3.13 ( ( ord_less_int @ X @ A2 )
% 2.86/3.13 => ( ( ord_less_int @ Y @ A2 )
% 2.86/3.13 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 2.86/3.13 => ( ( ord_less_eq_int @ zero_zero_int @ V2 )
% 2.86/3.13 => ( ( ( plus_plus_int @ U @ V2 )
% 2.86/3.13 = one_one_int )
% 2.86/3.13 => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V2 @ Y ) ) @ A2 ) ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % convex_bound_lt
% 2.86/3.13 thf(fact_4363_field__le__mult__one__interval,axiom,
% 2.86/3.13 ! [X: rat,Y: rat] :
% 2.86/3.13 ( ! [Z4: rat] :
% 2.86/3.13 ( ( ord_less_rat @ zero_zero_rat @ Z4 )
% 2.86/3.13 => ( ( ord_less_rat @ Z4 @ one_one_rat )
% 2.86/3.13 => ( ord_less_eq_rat @ ( times_times_rat @ Z4 @ X ) @ Y ) ) )
% 2.86/3.13 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 2.86/3.13
% 2.86/3.13 % field_le_mult_one_interval
% 2.86/3.13 thf(fact_4364_sum__squares__gt__zero__iff,axiom,
% 2.86/3.13 ! [X: rat,Y: rat] :
% 2.86/3.13 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) )
% 2.86/3.13 = ( ( X != zero_zero_rat )
% 2.86/3.13 | ( Y != zero_zero_rat ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % sum_squares_gt_zero_iff
% 2.86/3.13 thf(fact_4365_sum__squares__gt__zero__iff,axiom,
% 2.86/3.13 ! [X: code_integer,Y: code_integer] :
% 2.86/3.13 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) )
% 2.86/3.13 = ( ( X != zero_z3403309356797280102nteger )
% 2.86/3.13 | ( Y != zero_z3403309356797280102nteger ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % sum_squares_gt_zero_iff
% 2.86/3.13 thf(fact_4366_sum__squares__gt__zero__iff,axiom,
% 2.86/3.13 ! [X: int,Y: int] :
% 2.86/3.13 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) )
% 2.86/3.13 = ( ( X != zero_zero_int )
% 2.86/3.13 | ( Y != zero_zero_int ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % sum_squares_gt_zero_iff
% 2.86/3.13 thf(fact_4367_sum__squares__le__zero__iff,axiom,
% 2.86/3.13 ! [X: code_integer,Y: code_integer] :
% 2.86/3.13 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) @ zero_z3403309356797280102nteger )
% 2.86/3.13 = ( ( X = zero_z3403309356797280102nteger )
% 2.86/3.13 & ( Y = zero_z3403309356797280102nteger ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % sum_squares_le_zero_iff
% 2.86/3.13 thf(fact_4368_sum__squares__le__zero__iff,axiom,
% 2.86/3.13 ! [X: rat,Y: rat] :
% 2.86/3.13 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat )
% 2.86/3.13 = ( ( X = zero_zero_rat )
% 2.86/3.13 & ( Y = zero_zero_rat ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % sum_squares_le_zero_iff
% 2.86/3.13 thf(fact_4369_sum__squares__le__zero__iff,axiom,
% 2.86/3.13 ! [X: int,Y: int] :
% 2.86/3.13 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int )
% 2.86/3.13 = ( ( X = zero_zero_int )
% 2.86/3.13 & ( Y = zero_zero_int ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % sum_squares_le_zero_iff
% 2.86/3.13 thf(fact_4370_mult__le__cancel__iff1,axiom,
% 2.86/3.13 ! [Z: rat,X: rat,Y: rat] :
% 2.86/3.13 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 2.86/3.13 => ( ( ord_less_eq_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 2.86/3.13 = ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_le_cancel_iff1
% 2.86/3.13 thf(fact_4371_mult__le__cancel__iff1,axiom,
% 2.86/3.13 ! [Z: code_integer,X: code_integer,Y: code_integer] :
% 2.86/3.13 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ Z )
% 2.86/3.13 => ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ X @ Z ) @ ( times_3573771949741848930nteger @ Y @ Z ) )
% 2.86/3.13 = ( ord_le3102999989581377725nteger @ X @ Y ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_le_cancel_iff1
% 2.86/3.13 thf(fact_4372_mult__le__cancel__iff1,axiom,
% 2.86/3.13 ! [Z: int,X: int,Y: int] :
% 2.86/3.13 ( ( ord_less_int @ zero_zero_int @ Z )
% 2.86/3.13 => ( ( ord_less_eq_int @ ( times_times_int @ X @ Z ) @ ( times_times_int @ Y @ Z ) )
% 2.86/3.13 = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_le_cancel_iff1
% 2.86/3.13 thf(fact_4373_mult__le__cancel__iff2,axiom,
% 2.86/3.13 ! [Z: rat,X: rat,Y: rat] :
% 2.86/3.13 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 2.86/3.13 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ X ) @ ( times_times_rat @ Z @ Y ) )
% 2.86/3.13 = ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_le_cancel_iff2
% 2.86/3.13 thf(fact_4374_mult__le__cancel__iff2,axiom,
% 2.86/3.13 ! [Z: code_integer,X: code_integer,Y: code_integer] :
% 2.86/3.13 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ Z )
% 2.86/3.13 => ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ Z @ X ) @ ( times_3573771949741848930nteger @ Z @ Y ) )
% 2.86/3.13 = ( ord_le3102999989581377725nteger @ X @ Y ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_le_cancel_iff2
% 2.86/3.13 thf(fact_4375_mult__le__cancel__iff2,axiom,
% 2.86/3.13 ! [Z: int,X: int,Y: int] :
% 2.86/3.13 ( ( ord_less_int @ zero_zero_int @ Z )
% 2.86/3.13 => ( ( ord_less_eq_int @ ( times_times_int @ Z @ X ) @ ( times_times_int @ Z @ Y ) )
% 2.86/3.13 = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_le_cancel_iff2
% 2.86/3.13 thf(fact_4376_field__le__epsilon,axiom,
% 2.86/3.13 ! [X: rat,Y: rat] :
% 2.86/3.13 ( ! [E2: rat] :
% 2.86/3.13 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 2.86/3.13 => ( ord_less_eq_rat @ X @ ( plus_plus_rat @ Y @ E2 ) ) )
% 2.86/3.13 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 2.86/3.13
% 2.86/3.13 % field_le_epsilon
% 2.86/3.13 thf(fact_4377_divides__aux__eq,axiom,
% 2.86/3.13 ! [Q6: code_integer,R2: code_integer] :
% 2.86/3.13 ( ( unique5706413561485394159nteger @ ( produc1086072967326762835nteger @ Q6 @ R2 ) )
% 2.86/3.13 = ( R2 = zero_z3403309356797280102nteger ) ) ).
% 2.86/3.13
% 2.86/3.13 % divides_aux_eq
% 2.86/3.13 thf(fact_4378_divides__aux__eq,axiom,
% 2.86/3.13 ! [Q6: nat,R2: nat] :
% 2.86/3.13 ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q6 @ R2 ) )
% 2.86/3.13 = ( R2 = zero_zero_nat ) ) ).
% 2.86/3.13
% 2.86/3.13 % divides_aux_eq
% 2.86/3.13 thf(fact_4379_divides__aux__eq,axiom,
% 2.86/3.13 ! [Q6: int,R2: int] :
% 2.86/3.13 ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q6 @ R2 ) )
% 2.86/3.13 = ( R2 = zero_zero_int ) ) ).
% 2.86/3.13
% 2.86/3.13 % divides_aux_eq
% 2.86/3.13 thf(fact_4380_sum__squares__eq__zero__iff,axiom,
% 2.86/3.13 ! [X: code_integer,Y: code_integer] :
% 2.86/3.13 ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) )
% 2.86/3.13 = zero_z3403309356797280102nteger )
% 2.86/3.13 = ( ( X = zero_z3403309356797280102nteger )
% 2.86/3.13 & ( Y = zero_z3403309356797280102nteger ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % sum_squares_eq_zero_iff
% 2.86/3.13 thf(fact_4381_sum__squares__eq__zero__iff,axiom,
% 2.86/3.13 ! [X: rat,Y: rat] :
% 2.86/3.13 ( ( ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 2.86/3.13 = zero_zero_rat )
% 2.86/3.13 = ( ( X = zero_zero_rat )
% 2.86/3.13 & ( Y = zero_zero_rat ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % sum_squares_eq_zero_iff
% 2.86/3.13 thf(fact_4382_sum__squares__eq__zero__iff,axiom,
% 2.86/3.13 ! [X: int,Y: int] :
% 2.86/3.13 ( ( ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 2.86/3.13 = zero_zero_int )
% 2.86/3.13 = ( ( X = zero_zero_int )
% 2.86/3.13 & ( Y = zero_zero_int ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % sum_squares_eq_zero_iff
% 2.86/3.13 thf(fact_4383_mult__less__iff1,axiom,
% 2.86/3.13 ! [Z: rat,X: rat,Y: rat] :
% 2.86/3.13 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 2.86/3.13 => ( ( ord_less_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 2.86/3.13 = ( ord_less_rat @ X @ Y ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_less_iff1
% 2.86/3.13 thf(fact_4384_mult__less__iff1,axiom,
% 2.86/3.13 ! [Z: code_integer,X: code_integer,Y: code_integer] :
% 2.86/3.13 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ Z )
% 2.86/3.13 => ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ X @ Z ) @ ( times_3573771949741848930nteger @ Y @ Z ) )
% 2.86/3.13 = ( ord_le6747313008572928689nteger @ X @ Y ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_less_iff1
% 2.86/3.13 thf(fact_4385_mult__less__iff1,axiom,
% 2.86/3.13 ! [Z: int,X: int,Y: int] :
% 2.86/3.13 ( ( ord_less_int @ zero_zero_int @ Z )
% 2.86/3.13 => ( ( ord_less_int @ ( times_times_int @ X @ Z ) @ ( times_times_int @ Y @ Z ) )
% 2.86/3.13 = ( ord_less_int @ X @ Y ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % mult_less_iff1
% 2.86/3.13 thf(fact_4386_converse__trancl__induct,axiom,
% 2.86/3.13 ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,R2: set_Pr4329608150637261639at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 2.86/3.13 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A2 @ B2 ) @ ( transi2703068831062848130at_nat @ R2 ) )
% 2.86/3.13 => ( ! [Y2: set_Pr1261947904930325089at_nat] :
% 2.86/3.13 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y2 @ B2 ) @ R2 )
% 2.86/3.13 => ( P @ Y2 ) )
% 2.86/3.13 => ( ! [Y2: set_Pr1261947904930325089at_nat,Z4: set_Pr1261947904930325089at_nat] :
% 2.86/3.13 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y2 @ Z4 ) @ R2 )
% 2.86/3.13 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Z4 @ B2 ) @ ( transi2703068831062848130at_nat @ R2 ) )
% 2.86/3.13 => ( ( P @ Z4 )
% 2.86/3.13 => ( P @ Y2 ) ) ) )
% 2.86/3.13 => ( P @ A2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % converse_trancl_induct
% 2.86/3.13 thf(fact_4387_converse__trancl__induct,axiom,
% 2.86/3.13 ! [A2: nat,B2: nat,R2: set_Pr1261947904930325089at_nat,P: nat > $o] :
% 2.86/3.13 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B2 ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 2.86/3.13 => ( ! [Y2: nat] :
% 2.86/3.13 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y2 @ B2 ) @ R2 )
% 2.86/3.13 => ( P @ Y2 ) )
% 2.86/3.13 => ( ! [Y2: nat,Z4: nat] :
% 2.86/3.13 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y2 @ Z4 ) @ R2 )
% 2.86/3.13 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Z4 @ B2 ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 2.86/3.13 => ( ( P @ Z4 )
% 2.86/3.13 => ( P @ Y2 ) ) ) )
% 2.86/3.13 => ( P @ A2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % converse_trancl_induct
% 2.86/3.13 thf(fact_4388_trancl__trans__induct,axiom,
% 2.86/3.13 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,R2: set_Pr4329608150637261639at_nat,P: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o] :
% 2.86/3.13 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( transi2703068831062848130at_nat @ R2 ) )
% 2.86/3.13 => ( ! [X3: set_Pr1261947904930325089at_nat,Y2: set_Pr1261947904930325089at_nat] :
% 2.86/3.13 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y2 ) @ R2 )
% 2.86/3.13 => ( P @ X3 @ Y2 ) )
% 2.86/3.13 => ( ! [X3: set_Pr1261947904930325089at_nat,Y2: set_Pr1261947904930325089at_nat,Z4: set_Pr1261947904930325089at_nat] :
% 2.86/3.13 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y2 ) @ ( transi2703068831062848130at_nat @ R2 ) )
% 2.86/3.13 => ( ( P @ X3 @ Y2 )
% 2.86/3.13 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y2 @ Z4 ) @ ( transi2703068831062848130at_nat @ R2 ) )
% 2.86/3.13 => ( ( P @ Y2 @ Z4 )
% 2.86/3.13 => ( P @ X3 @ Z4 ) ) ) ) )
% 2.86/3.13 => ( P @ X @ Y ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % trancl_trans_induct
% 2.86/3.13 thf(fact_4389_trancl__trans__induct,axiom,
% 2.86/3.13 ! [X: nat,Y: nat,R2: set_Pr1261947904930325089at_nat,P: nat > nat > $o] :
% 2.86/3.13 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 2.86/3.13 => ( ! [X3: nat,Y2: nat] :
% 2.86/3.13 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y2 ) @ R2 )
% 2.86/3.13 => ( P @ X3 @ Y2 ) )
% 2.86/3.13 => ( ! [X3: nat,Y2: nat,Z4: nat] :
% 2.86/3.13 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y2 ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 2.86/3.13 => ( ( P @ X3 @ Y2 )
% 2.86/3.13 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y2 @ Z4 ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 2.86/3.13 => ( ( P @ Y2 @ Z4 )
% 2.86/3.13 => ( P @ X3 @ Z4 ) ) ) ) )
% 2.86/3.13 => ( P @ X @ Y ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % trancl_trans_induct
% 2.86/3.13 thf(fact_4390_trancl__into__trancl2,axiom,
% 2.86/3.13 ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,R2: set_Pr4329608150637261639at_nat,C: set_Pr1261947904930325089at_nat] :
% 2.86/3.13 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A2 @ B2 ) @ R2 )
% 2.86/3.13 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ B2 @ C ) @ ( transi2703068831062848130at_nat @ R2 ) )
% 2.86/3.13 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A2 @ C ) @ ( transi2703068831062848130at_nat @ R2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % trancl_into_trancl2
% 2.86/3.13 thf(fact_4391_trancl__into__trancl2,axiom,
% 2.86/3.13 ! [A2: nat,B2: nat,R2: set_Pr1261947904930325089at_nat,C: nat] :
% 2.86/3.13 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B2 ) @ R2 )
% 2.86/3.13 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B2 @ C ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 2.86/3.13 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ C ) @ ( transi6264000038957366511cl_nat @ R2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % trancl_into_trancl2
% 2.86/3.13 thf(fact_4392_Transitive__Closure_Otrancl__into__trancl,axiom,
% 2.86/3.13 ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,R2: set_Pr4329608150637261639at_nat,C: set_Pr1261947904930325089at_nat] :
% 2.86/3.13 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A2 @ B2 ) @ ( transi2703068831062848130at_nat @ R2 ) )
% 2.86/3.13 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ B2 @ C ) @ R2 )
% 2.86/3.13 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A2 @ C ) @ ( transi2703068831062848130at_nat @ R2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % Transitive_Closure.trancl_into_trancl
% 2.86/3.13 thf(fact_4393_Transitive__Closure_Otrancl__into__trancl,axiom,
% 2.86/3.13 ! [A2: nat,B2: nat,R2: set_Pr1261947904930325089at_nat,C: nat] :
% 2.86/3.13 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B2 ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 2.86/3.13 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B2 @ C ) @ R2 )
% 2.86/3.13 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ C ) @ ( transi6264000038957366511cl_nat @ R2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % Transitive_Closure.trancl_into_trancl
% 2.86/3.13 thf(fact_4394_irrefl__trancl__rD,axiom,
% 2.86/3.13 ! [R2: set_Pr4329608150637261639at_nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 2.86/3.13 ( ! [X3: set_Pr1261947904930325089at_nat] :
% 2.86/3.13 ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ X3 ) @ ( transi2703068831062848130at_nat @ R2 ) )
% 2.86/3.13 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ R2 )
% 2.86/3.13 => ( X != Y ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % irrefl_trancl_rD
% 2.86/3.13 thf(fact_4395_irrefl__trancl__rD,axiom,
% 2.86/3.13 ! [R2: set_Pr1261947904930325089at_nat,X: nat,Y: nat] :
% 2.86/3.13 ( ! [X3: nat] :
% 2.86/3.13 ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ X3 ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 2.86/3.13 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R2 )
% 2.86/3.13 => ( X != Y ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % irrefl_trancl_rD
% 2.86/3.13 thf(fact_4396_converse__tranclE,axiom,
% 2.86/3.13 ! [X: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat,R2: set_Pr4329608150637261639at_nat] :
% 2.86/3.13 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Z ) @ ( transi2703068831062848130at_nat @ R2 ) )
% 2.86/3.13 => ( ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Z ) @ R2 )
% 2.86/3.13 => ~ ! [Y2: set_Pr1261947904930325089at_nat] :
% 2.86/3.13 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y2 ) @ R2 )
% 2.86/3.13 => ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y2 @ Z ) @ ( transi2703068831062848130at_nat @ R2 ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % converse_tranclE
% 2.86/3.13 thf(fact_4397_converse__tranclE,axiom,
% 2.86/3.13 ! [X: nat,Z: nat,R2: set_Pr1261947904930325089at_nat] :
% 2.86/3.13 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Z ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 2.86/3.13 => ( ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Z ) @ R2 )
% 2.86/3.13 => ~ ! [Y2: nat] :
% 2.86/3.13 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y2 ) @ R2 )
% 2.86/3.13 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y2 @ Z ) @ ( transi6264000038957366511cl_nat @ R2 ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % converse_tranclE
% 2.86/3.13 thf(fact_4398_r__r__into__trancl,axiom,
% 2.86/3.13 ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,R: set_Pr4329608150637261639at_nat,C: set_Pr1261947904930325089at_nat] :
% 2.86/3.13 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A2 @ B2 ) @ R )
% 2.86/3.13 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ B2 @ C ) @ R )
% 2.86/3.13 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A2 @ C ) @ ( transi2703068831062848130at_nat @ R ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % r_r_into_trancl
% 2.86/3.13 thf(fact_4399_r__r__into__trancl,axiom,
% 2.86/3.13 ! [A2: nat,B2: nat,R: set_Pr1261947904930325089at_nat,C: nat] :
% 2.86/3.13 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B2 ) @ R )
% 2.86/3.13 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B2 @ C ) @ R )
% 2.86/3.13 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ C ) @ ( transi6264000038957366511cl_nat @ R ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % r_r_into_trancl
% 2.86/3.13 thf(fact_4400_trancl__induct,axiom,
% 2.86/3.13 ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,R2: set_Pr4329608150637261639at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 2.86/3.13 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A2 @ B2 ) @ ( transi2703068831062848130at_nat @ R2 ) )
% 2.86/3.13 => ( ! [Y2: set_Pr1261947904930325089at_nat] :
% 2.86/3.13 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A2 @ Y2 ) @ R2 )
% 2.86/3.13 => ( P @ Y2 ) )
% 2.86/3.13 => ( ! [Y2: set_Pr1261947904930325089at_nat,Z4: set_Pr1261947904930325089at_nat] :
% 2.86/3.13 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A2 @ Y2 ) @ ( transi2703068831062848130at_nat @ R2 ) )
% 2.86/3.13 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y2 @ Z4 ) @ R2 )
% 2.86/3.13 => ( ( P @ Y2 )
% 2.86/3.13 => ( P @ Z4 ) ) ) )
% 2.86/3.13 => ( P @ B2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % trancl_induct
% 2.86/3.13 thf(fact_4401_trancl__induct,axiom,
% 2.86/3.13 ! [A2: nat,B2: nat,R2: set_Pr1261947904930325089at_nat,P: nat > $o] :
% 2.86/3.13 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B2 ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 2.86/3.13 => ( ! [Y2: nat] :
% 2.86/3.13 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ Y2 ) @ R2 )
% 2.86/3.13 => ( P @ Y2 ) )
% 2.86/3.13 => ( ! [Y2: nat,Z4: nat] :
% 2.86/3.13 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ Y2 ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 2.86/3.13 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y2 @ Z4 ) @ R2 )
% 2.86/3.13 => ( ( P @ Y2 )
% 2.86/3.13 => ( P @ Z4 ) ) ) )
% 2.86/3.13 => ( P @ B2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % trancl_induct
% 2.86/3.13 thf(fact_4402_trancl__induct2,axiom,
% 2.86/3.13 ! [Ax: produc6241069584506657477e_term > option6357759511663192854e_term,Ay: produc8923325533196201883nteger,Bx: produc6241069584506657477e_term > option6357759511663192854e_term,By: produc8923325533196201883nteger,R2: set_Pr1722956316086891245nteger,P: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o] :
% 2.86/3.13 ( ( member2446009503569356342nteger @ ( produc7954516348491987909nteger @ ( produc8603105652947943368nteger @ Ax @ Ay ) @ ( produc8603105652947943368nteger @ Bx @ By ) ) @ ( transi6228740973808232501nteger @ R2 ) )
% 2.86/3.13 => ( ! [A4: produc6241069584506657477e_term > option6357759511663192854e_term,B4: produc8923325533196201883nteger] :
% 2.86/3.13 ( ( member2446009503569356342nteger @ ( produc7954516348491987909nteger @ ( produc8603105652947943368nteger @ Ax @ Ay ) @ ( produc8603105652947943368nteger @ A4 @ B4 ) ) @ R2 )
% 2.86/3.13 => ( P @ A4 @ B4 ) )
% 2.86/3.13 => ( ! [A4: produc6241069584506657477e_term > option6357759511663192854e_term,B4: produc8923325533196201883nteger,Aa: produc6241069584506657477e_term > option6357759511663192854e_term,Ba: produc8923325533196201883nteger] :
% 2.86/3.13 ( ( member2446009503569356342nteger @ ( produc7954516348491987909nteger @ ( produc8603105652947943368nteger @ Ax @ Ay ) @ ( produc8603105652947943368nteger @ A4 @ B4 ) ) @ ( transi6228740973808232501nteger @ R2 ) )
% 2.86/3.13 => ( ( member2446009503569356342nteger @ ( produc7954516348491987909nteger @ ( produc8603105652947943368nteger @ A4 @ B4 ) @ ( produc8603105652947943368nteger @ Aa @ Ba ) ) @ R2 )
% 2.86/3.13 => ( ( P @ A4 @ B4 )
% 2.86/3.13 => ( P @ Aa @ Ba ) ) ) )
% 2.86/3.13 => ( P @ Bx @ By ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % trancl_induct2
% 2.86/3.13 thf(fact_4403_trancl__induct2,axiom,
% 2.86/3.13 ! [Ax: produc3658429121746597890et_nat > $o,Ay: produc3658429121746597890et_nat,Bx: produc3658429121746597890et_nat > $o,By: produc3658429121746597890et_nat,R2: set_Pr7928877670098842301et_nat,P: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o] :
% 2.86/3.13 ( ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ ( produc5001842942810119800et_nat @ Ax @ Ay ) @ ( produc5001842942810119800et_nat @ Bx @ By ) ) @ ( transi3145040225084697757et_nat @ R2 ) )
% 2.86/3.13 => ( ! [A4: produc3658429121746597890et_nat > $o,B4: produc3658429121746597890et_nat] :
% 2.86/3.13 ( ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ ( produc5001842942810119800et_nat @ Ax @ Ay ) @ ( produc5001842942810119800et_nat @ A4 @ B4 ) ) @ R2 )
% 2.86/3.13 => ( P @ A4 @ B4 ) )
% 2.86/3.13 => ( ! [A4: produc3658429121746597890et_nat > $o,B4: produc3658429121746597890et_nat,Aa: produc3658429121746597890et_nat > $o,Ba: produc3658429121746597890et_nat] :
% 2.86/3.13 ( ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ ( produc5001842942810119800et_nat @ Ax @ Ay ) @ ( produc5001842942810119800et_nat @ A4 @ B4 ) ) @ ( transi3145040225084697757et_nat @ R2 ) )
% 2.86/3.13 => ( ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ ( produc5001842942810119800et_nat @ A4 @ B4 ) @ ( produc5001842942810119800et_nat @ Aa @ Ba ) ) @ R2 )
% 2.86/3.13 => ( ( P @ A4 @ B4 )
% 2.86/3.13 => ( P @ Aa @ Ba ) ) ) )
% 2.86/3.13 => ( P @ Bx @ By ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % trancl_induct2
% 2.86/3.13 thf(fact_4404_trancl__induct2,axiom,
% 2.86/3.13 ! [Ax: produc3658429121746597890et_nat > $o,Ay: produc3925858234332021118et_nat,Bx: produc3658429121746597890et_nat > $o,By: produc3925858234332021118et_nat,R2: set_Pr3444600963470892981et_nat,P: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o] :
% 2.86/3.13 ( ( member6341495586645257982et_nat @ ( produc1940133919992309389et_nat @ ( produc2245416461498447860et_nat @ Ax @ Ay ) @ ( produc2245416461498447860et_nat @ Bx @ By ) ) @ ( transi5221092739591632921et_nat @ R2 ) )
% 2.86/3.13 => ( ! [A4: produc3658429121746597890et_nat > $o,B4: produc3925858234332021118et_nat] :
% 2.86/3.13 ( ( member6341495586645257982et_nat @ ( produc1940133919992309389et_nat @ ( produc2245416461498447860et_nat @ Ax @ Ay ) @ ( produc2245416461498447860et_nat @ A4 @ B4 ) ) @ R2 )
% 2.86/3.13 => ( P @ A4 @ B4 ) )
% 2.86/3.13 => ( ! [A4: produc3658429121746597890et_nat > $o,B4: produc3925858234332021118et_nat,Aa: produc3658429121746597890et_nat > $o,Ba: produc3925858234332021118et_nat] :
% 2.86/3.13 ( ( member6341495586645257982et_nat @ ( produc1940133919992309389et_nat @ ( produc2245416461498447860et_nat @ Ax @ Ay ) @ ( produc2245416461498447860et_nat @ A4 @ B4 ) ) @ ( transi5221092739591632921et_nat @ R2 ) )
% 2.86/3.13 => ( ( member6341495586645257982et_nat @ ( produc1940133919992309389et_nat @ ( produc2245416461498447860et_nat @ A4 @ B4 ) @ ( produc2245416461498447860et_nat @ Aa @ Ba ) ) @ R2 )
% 2.86/3.13 => ( ( P @ A4 @ B4 )
% 2.86/3.13 => ( P @ Aa @ Ba ) ) ) )
% 2.86/3.13 => ( P @ Bx @ By ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % trancl_induct2
% 2.86/3.13 thf(fact_4405_trancl__induct2,axiom,
% 2.86/3.13 ! [Ax: produc8551481072490612790e_term > option6357759511663192854e_term,Ay: product_prod_int_int,Bx: produc8551481072490612790e_term > option6357759511663192854e_term,By: product_prod_int_int,R2: set_Pr4708930517165415495nt_int,P: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o] :
% 2.86/3.13 ( ( member6582457606847315088nt_int @ ( produc7601053194514725023nt_int @ ( produc5700946648718959541nt_int @ Ax @ Ay ) @ ( produc5700946648718959541nt_int @ Bx @ By ) ) @ ( transi7434818091516421410nt_int @ R2 ) )
% 2.86/3.13 => ( ! [A4: produc8551481072490612790e_term > option6357759511663192854e_term,B4: product_prod_int_int] :
% 2.86/3.13 ( ( member6582457606847315088nt_int @ ( produc7601053194514725023nt_int @ ( produc5700946648718959541nt_int @ Ax @ Ay ) @ ( produc5700946648718959541nt_int @ A4 @ B4 ) ) @ R2 )
% 2.86/3.13 => ( P @ A4 @ B4 ) )
% 2.86/3.13 => ( ! [A4: produc8551481072490612790e_term > option6357759511663192854e_term,B4: product_prod_int_int,Aa: produc8551481072490612790e_term > option6357759511663192854e_term,Ba: product_prod_int_int] :
% 2.86/3.13 ( ( member6582457606847315088nt_int @ ( produc7601053194514725023nt_int @ ( produc5700946648718959541nt_int @ Ax @ Ay ) @ ( produc5700946648718959541nt_int @ A4 @ B4 ) ) @ ( transi7434818091516421410nt_int @ R2 ) )
% 2.86/3.13 => ( ( member6582457606847315088nt_int @ ( produc7601053194514725023nt_int @ ( produc5700946648718959541nt_int @ A4 @ B4 ) @ ( produc5700946648718959541nt_int @ Aa @ Ba ) ) @ R2 )
% 2.86/3.13 => ( ( P @ A4 @ B4 )
% 2.86/3.13 => ( P @ Aa @ Ba ) ) ) )
% 2.86/3.13 => ( P @ Bx @ By ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % trancl_induct2
% 2.86/3.13 thf(fact_4406_trancl__induct2,axiom,
% 2.86/3.13 ! [Ax: int > option6357759511663192854e_term,Ay: product_prod_int_int,Bx: int > option6357759511663192854e_term,By: product_prod_int_int,R2: set_Pr8634505666381077339nt_int,P: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o] :
% 2.86/3.13 ( ( member4085533954029916580nt_int @ ( produc8406175334058502835nt_int @ ( produc4305682042979456191nt_int @ Ax @ Ay ) @ ( produc4305682042979456191nt_int @ Bx @ By ) ) @ ( transi4533545184864474924nt_int @ R2 ) )
% 2.86/3.13 => ( ! [A4: int > option6357759511663192854e_term,B4: product_prod_int_int] :
% 2.86/3.13 ( ( member4085533954029916580nt_int @ ( produc8406175334058502835nt_int @ ( produc4305682042979456191nt_int @ Ax @ Ay ) @ ( produc4305682042979456191nt_int @ A4 @ B4 ) ) @ R2 )
% 2.86/3.13 => ( P @ A4 @ B4 ) )
% 2.86/3.13 => ( ! [A4: int > option6357759511663192854e_term,B4: product_prod_int_int,Aa: int > option6357759511663192854e_term,Ba: product_prod_int_int] :
% 2.86/3.13 ( ( member4085533954029916580nt_int @ ( produc8406175334058502835nt_int @ ( produc4305682042979456191nt_int @ Ax @ Ay ) @ ( produc4305682042979456191nt_int @ A4 @ B4 ) ) @ ( transi4533545184864474924nt_int @ R2 ) )
% 2.86/3.13 => ( ( member4085533954029916580nt_int @ ( produc8406175334058502835nt_int @ ( produc4305682042979456191nt_int @ A4 @ B4 ) @ ( produc4305682042979456191nt_int @ Aa @ Ba ) ) @ R2 )
% 2.86/3.13 => ( ( P @ A4 @ B4 )
% 2.86/3.13 => ( P @ Aa @ Ba ) ) ) )
% 2.86/3.13 => ( P @ Bx @ By ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % trancl_induct2
% 2.86/3.13 thf(fact_4407_trancl_Ocases,axiom,
% 2.86/3.13 ! [A1: set_Pr1261947904930325089at_nat,A22: set_Pr1261947904930325089at_nat,R2: set_Pr4329608150637261639at_nat] :
% 2.86/3.13 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A1 @ A22 ) @ ( transi2703068831062848130at_nat @ R2 ) )
% 2.86/3.13 => ( ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A1 @ A22 ) @ R2 )
% 2.86/3.13 => ~ ! [B4: set_Pr1261947904930325089at_nat] :
% 2.86/3.13 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A1 @ B4 ) @ ( transi2703068831062848130at_nat @ R2 ) )
% 2.86/3.13 => ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ B4 @ A22 ) @ R2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % trancl.cases
% 2.86/3.13 thf(fact_4408_trancl_Ocases,axiom,
% 2.86/3.13 ! [A1: nat,A22: nat,R2: set_Pr1261947904930325089at_nat] :
% 2.86/3.13 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A1 @ A22 ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 2.86/3.13 => ( ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A1 @ A22 ) @ R2 )
% 2.86/3.13 => ~ ! [B4: nat] :
% 2.86/3.13 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A1 @ B4 ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 2.86/3.13 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B4 @ A22 ) @ R2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % trancl.cases
% 2.86/3.13 thf(fact_4409_trancl_Osimps,axiom,
% 2.86/3.13 ! [A1: set_Pr1261947904930325089at_nat,A22: set_Pr1261947904930325089at_nat,R2: set_Pr4329608150637261639at_nat] :
% 2.86/3.13 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A1 @ A22 ) @ ( transi2703068831062848130at_nat @ R2 ) )
% 2.86/3.13 = ( ? [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.86/3.13 ( ( A1 = A3 )
% 2.86/3.13 & ( A22 = B3 )
% 2.86/3.13 & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A3 @ B3 ) @ R2 ) )
% 2.86/3.13 | ? [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,C5: set_Pr1261947904930325089at_nat] :
% 2.86/3.13 ( ( A1 = A3 )
% 2.86/3.13 & ( A22 = C5 )
% 2.86/3.13 & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A3 @ B3 ) @ ( transi2703068831062848130at_nat @ R2 ) )
% 2.86/3.13 & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ B3 @ C5 ) @ R2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % trancl.simps
% 2.86/3.13 thf(fact_4410_trancl_Osimps,axiom,
% 2.86/3.13 ! [A1: nat,A22: nat,R2: set_Pr1261947904930325089at_nat] :
% 2.86/3.13 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A1 @ A22 ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 2.86/3.13 = ( ? [A3: nat,B3: nat] :
% 2.86/3.13 ( ( A1 = A3 )
% 2.86/3.13 & ( A22 = B3 )
% 2.86/3.13 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A3 @ B3 ) @ R2 ) )
% 2.86/3.13 | ? [A3: nat,B3: nat,C5: nat] :
% 2.86/3.13 ( ( A1 = A3 )
% 2.86/3.13 & ( A22 = C5 )
% 2.86/3.13 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A3 @ B3 ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 2.86/3.13 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B3 @ C5 ) @ R2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % trancl.simps
% 2.86/3.13 thf(fact_4411_trancl_Or__into__trancl,axiom,
% 2.86/3.13 ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,R2: set_Pr4329608150637261639at_nat] :
% 2.86/3.13 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A2 @ B2 ) @ R2 )
% 2.86/3.13 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A2 @ B2 ) @ ( transi2703068831062848130at_nat @ R2 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % trancl.r_into_trancl
% 2.86/3.13 thf(fact_4412_trancl_Or__into__trancl,axiom,
% 2.86/3.13 ! [A2: nat,B2: nat,R2: set_Pr1261947904930325089at_nat] :
% 2.86/3.13 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B2 ) @ R2 )
% 2.86/3.13 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B2 ) @ ( transi6264000038957366511cl_nat @ R2 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % trancl.r_into_trancl
% 2.86/3.13 thf(fact_4413_tranclE,axiom,
% 2.86/3.13 ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,R2: set_Pr4329608150637261639at_nat] :
% 2.86/3.13 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A2 @ B2 ) @ ( transi2703068831062848130at_nat @ R2 ) )
% 2.86/3.13 => ( ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A2 @ B2 ) @ R2 )
% 2.86/3.13 => ~ ! [C4: set_Pr1261947904930325089at_nat] :
% 2.86/3.13 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A2 @ C4 ) @ ( transi2703068831062848130at_nat @ R2 ) )
% 2.86/3.13 => ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ C4 @ B2 ) @ R2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % tranclE
% 2.86/3.13 thf(fact_4414_tranclE,axiom,
% 2.86/3.13 ! [A2: nat,B2: nat,R2: set_Pr1261947904930325089at_nat] :
% 2.86/3.13 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B2 ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 2.86/3.13 => ( ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B2 ) @ R2 )
% 2.86/3.13 => ~ ! [C4: nat] :
% 2.86/3.13 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ C4 ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 2.86/3.13 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ C4 @ B2 ) @ R2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % tranclE
% 2.86/3.13 thf(fact_4415_trancl__trans,axiom,
% 2.86/3.13 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,R2: set_Pr4329608150637261639at_nat,Z: set_Pr1261947904930325089at_nat] :
% 2.86/3.13 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( transi2703068831062848130at_nat @ R2 ) )
% 2.86/3.13 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y @ Z ) @ ( transi2703068831062848130at_nat @ R2 ) )
% 2.86/3.13 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Z ) @ ( transi2703068831062848130at_nat @ R2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % trancl_trans
% 2.86/3.13 thf(fact_4416_trancl__trans,axiom,
% 2.86/3.13 ! [X: nat,Y: nat,R2: set_Pr1261947904930325089at_nat,Z: nat] :
% 2.86/3.13 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 2.86/3.13 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y @ Z ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 2.86/3.13 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Z ) @ ( transi6264000038957366511cl_nat @ R2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % trancl_trans
% 2.86/3.13 thf(fact_4417_nonempty__has__size,axiom,
% 2.86/3.13 ! [S: multis2468970476368604999at_nat] :
% 2.86/3.13 ( ( S != zero_z1048942125864253310at_nat )
% 2.86/3.13 = ( ord_less_nat @ zero_zero_nat @ ( size_s8510653225128441779at_nat @ S ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % nonempty_has_size
% 2.86/3.13 thf(fact_4418_bijective__Empty,axiom,
% 2.86/3.13 biject3388518990857851981at_nat @ bot_bo228742789529271731at_nat ).
% 2.86/3.13
% 2.86/3.13 % bijective_Empty
% 2.86/3.13 thf(fact_4419_bijective__Empty,axiom,
% 2.86/3.13 bijective_nat_nat @ bot_bo2099793752762293965at_nat ).
% 2.86/3.13
% 2.86/3.13 % bijective_Empty
% 2.86/3.13 thf(fact_4420_total__on__singleton,axiom,
% 2.86/3.13 ! [X: set_Pr1261947904930325089at_nat] : ( total_7212417256332265445at_nat @ ( insert9200635055090092081at_nat @ X @ bot_bo3083307316010499117at_nat ) @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ X @ X ) @ bot_bo228742789529271731at_nat ) ) ).
% 2.86/3.13
% 2.86/3.13 % total_on_singleton
% 2.86/3.13 thf(fact_4421_total__on__singleton,axiom,
% 2.86/3.13 ! [X: produc3843707927480180839at_nat] : ( total_1513685709984341995at_nat @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) @ ( insert398606708087465655at_nat @ ( produc2335810615602371415at_nat @ X @ X ) @ bot_bo7193250159860175667at_nat ) ) ).
% 2.86/3.13
% 2.86/3.13 % total_on_singleton
% 2.86/3.13 thf(fact_4422_total__on__singleton,axiom,
% 2.86/3.13 ! [X: product_prod_nat_nat] : ( total_3592101749530773125at_nat @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) @ ( insert5050368324300391991at_nat @ ( produc6161850002892822231at_nat @ X @ X ) @ bot_bo5327735625951526323at_nat ) ) ).
% 2.86/3.13
% 2.86/3.13 % total_on_singleton
% 2.86/3.13 thf(fact_4423_total__on__singleton,axiom,
% 2.86/3.13 ! [X: $o] : ( total_on_o @ ( insert_o2 @ X @ bot_bot_set_o ) @ ( insert6201435330877294327od_o_o @ ( product_Pair_o_o @ X @ X ) @ bot_bo7073875226086086771od_o_o ) ) ).
% 2.86/3.13
% 2.86/3.13 % total_on_singleton
% 2.86/3.13 thf(fact_4424_total__on__singleton,axiom,
% 2.86/3.13 ! [X: nat] : ( total_on_nat @ ( insert_nat2 @ X @ bot_bot_set_nat ) @ ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ X @ X ) @ bot_bo2099793752762293965at_nat ) ) ).
% 2.86/3.13
% 2.86/3.13 % total_on_singleton
% 2.86/3.13 thf(fact_4425_total__on__singleton,axiom,
% 2.86/3.13 ! [X: int] : ( total_on_int @ ( insert_int2 @ X @ bot_bot_set_int ) @ ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ X @ X ) @ bot_bo1796632182523588997nt_int ) ) ).
% 2.86/3.13
% 2.86/3.13 % total_on_singleton
% 2.86/3.13 thf(fact_4426_nth__Cons__pos,axiom,
% 2.86/3.13 ! [N: nat,X: int,Xs: list_int] :
% 2.86/3.13 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.13 => ( ( nth_int @ ( cons_int @ X @ Xs ) @ N )
% 2.86/3.13 = ( nth_int @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % nth_Cons_pos
% 2.86/3.13 thf(fact_4427_nth__Cons__pos,axiom,
% 2.86/3.13 ! [N: nat,X: nat,Xs: list_nat] :
% 2.86/3.13 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.13 => ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ N )
% 2.86/3.13 = ( nth_nat @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % nth_Cons_pos
% 2.86/3.13 thf(fact_4428_nth__Cons__pos,axiom,
% 2.86/3.13 ! [N: nat,X: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn] :
% 2.86/3.13 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.13 => ( ( nth_Pr1769885009046257848n_assn @ ( cons_P2971678138204555879n_assn @ X @ Xs ) @ N )
% 2.86/3.13 = ( nth_Pr1769885009046257848n_assn @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % nth_Cons_pos
% 2.86/3.13 thf(fact_4429_Field__insert,axiom,
% 2.86/3.13 ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,R2: set_Pr4329608150637261639at_nat] :
% 2.86/3.13 ( ( field_3145993188331922222at_nat @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ A2 @ B2 ) @ R2 ) )
% 2.86/3.13 = ( sup_su3642409539654194069at_nat @ ( insert9200635055090092081at_nat @ A2 @ ( insert9200635055090092081at_nat @ B2 @ bot_bo3083307316010499117at_nat ) ) @ ( field_3145993188331922222at_nat @ R2 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % Field_insert
% 2.86/3.13 thf(fact_4430_Field__insert,axiom,
% 2.86/3.13 ! [A2: produc3843707927480180839at_nat,B2: produc3843707927480180839at_nat,R2: set_Pr5564308138774400199at_nat] :
% 2.86/3.13 ( ( field_2862844103579723188at_nat @ ( insert398606708087465655at_nat @ ( produc2335810615602371415at_nat @ A2 @ B2 ) @ R2 ) )
% 2.86/3.13 = ( sup_su5525570899277871387at_nat @ ( insert9069300056098147895at_nat @ A2 @ ( insert9069300056098147895at_nat @ B2 @ bot_bo228742789529271731at_nat ) ) @ ( field_2862844103579723188at_nat @ R2 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % Field_insert
% 2.86/3.13 thf(fact_4431_Field__insert,axiom,
% 2.86/3.13 ! [A2: product_prod_nat_nat,B2: product_prod_nat_nat,R2: set_Pr8693737435421807431at_nat] :
% 2.86/3.13 ( ( field_4706345496283612622at_nat @ ( insert5050368324300391991at_nat @ ( produc6161850002892822231at_nat @ A2 @ B2 ) @ R2 ) )
% 2.86/3.13 = ( sup_su6327502436637775413at_nat @ ( insert8211810215607154385at_nat @ A2 @ ( insert8211810215607154385at_nat @ B2 @ bot_bo2099793752762293965at_nat ) ) @ ( field_4706345496283612622at_nat @ R2 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % Field_insert
% 2.86/3.13 thf(fact_4432_Field__insert,axiom,
% 2.86/3.13 ! [A2: $o,B2: $o,R2: set_Product_prod_o_o] :
% 2.86/3.13 ( ( field_o @ ( insert6201435330877294327od_o_o @ ( product_Pair_o_o @ A2 @ B2 ) @ R2 ) )
% 2.86/3.13 = ( sup_sup_set_o @ ( insert_o2 @ A2 @ ( insert_o2 @ B2 @ bot_bot_set_o ) ) @ ( field_o @ R2 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % Field_insert
% 2.86/3.13 thf(fact_4433_Field__insert,axiom,
% 2.86/3.13 ! [A2: nat,B2: nat,R2: set_Pr1261947904930325089at_nat] :
% 2.86/3.13 ( ( field_nat @ ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ A2 @ B2 ) @ R2 ) )
% 2.86/3.13 = ( sup_sup_set_nat @ ( insert_nat2 @ A2 @ ( insert_nat2 @ B2 @ bot_bot_set_nat ) ) @ ( field_nat @ R2 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % Field_insert
% 2.86/3.13 thf(fact_4434_Field__insert,axiom,
% 2.86/3.13 ! [A2: int,B2: int,R2: set_Pr958786334691620121nt_int] :
% 2.86/3.13 ( ( field_int @ ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ A2 @ B2 ) @ R2 ) )
% 2.86/3.13 = ( sup_sup_set_int @ ( insert_int2 @ A2 @ ( insert_int2 @ B2 @ bot_bot_set_int ) ) @ ( field_int @ R2 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % Field_insert
% 2.86/3.13 thf(fact_4435_nth__enumerate__eq,axiom,
% 2.86/3.13 ! [M2: nat,Xs: list_c,N: nat] :
% 2.86/3.13 ( ( ord_less_nat @ M2 @ ( size_size_list_c @ Xs ) )
% 2.86/3.13 => ( ( nth_Pr2476257089995772766_nat_c @ ( enumerate_c @ N @ Xs ) @ M2 )
% 2.86/3.13 = ( product_Pair_nat_c @ ( plus_plus_nat @ N @ M2 ) @ ( nth_c @ Xs @ M2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % nth_enumerate_eq
% 2.86/3.13 thf(fact_4436_nth__enumerate__eq,axiom,
% 2.86/3.13 ! [M2: nat,Xs: list_d,N: nat] :
% 2.86/3.13 ( ( ord_less_nat @ M2 @ ( size_size_list_d @ Xs ) )
% 2.86/3.13 => ( ( nth_Pr2476257094299001567_nat_d @ ( enumerate_d @ N @ Xs ) @ M2 )
% 2.86/3.13 = ( product_Pair_nat_d @ ( plus_plus_nat @ N @ M2 ) @ ( nth_d @ Xs @ M2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % nth_enumerate_eq
% 2.86/3.13 thf(fact_4437_nth__enumerate__eq,axiom,
% 2.86/3.13 ! [M2: nat,Xs: list_nat,N: nat] :
% 2.86/3.13 ( ( ord_less_nat @ M2 @ ( size_size_list_nat @ Xs ) )
% 2.86/3.13 => ( ( nth_Pr7617993195940197384at_nat @ ( enumerate_nat @ N @ Xs ) @ M2 )
% 2.86/3.13 = ( product_Pair_nat_nat @ ( plus_plus_nat @ N @ M2 ) @ ( nth_nat @ Xs @ M2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % nth_enumerate_eq
% 2.86/3.13 thf(fact_4438_nth__enumerate__eq,axiom,
% 2.86/3.13 ! [M2: nat,Xs: list_int,N: nat] :
% 2.86/3.13 ( ( ord_less_nat @ M2 @ ( size_size_list_int @ Xs ) )
% 2.86/3.13 => ( ( nth_Pr3440142176431000676at_int @ ( enumerate_int @ N @ Xs ) @ M2 )
% 2.86/3.13 = ( product_Pair_nat_int @ ( plus_plus_nat @ N @ M2 ) @ ( nth_int @ Xs @ M2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % nth_enumerate_eq
% 2.86/3.13 thf(fact_4439_times__assn__raw_Opelims_I3_J,axiom,
% 2.86/3.13 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 2.86/3.13 ( ~ ( times_assn_raw @ X @ Xa @ Xb )
% 2.86/3.13 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 2.86/3.13 => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.86/3.13 ( ( Xb
% 2.86/3.13 = ( produc7507926704131184380et_nat @ H @ As ) )
% 2.86/3.13 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H @ As ) ) ) )
% 2.86/3.13 => ? [As13: set_nat,As24: set_nat] :
% 2.86/3.13 ( ( As
% 2.86/3.13 = ( sup_sup_set_nat @ As13 @ As24 ) )
% 2.86/3.13 & ( ( inf_inf_set_nat @ As13 @ As24 )
% 2.86/3.13 = bot_bot_set_nat )
% 2.86/3.13 & ( X @ ( produc7507926704131184380et_nat @ H @ As13 ) )
% 2.86/3.13 & ( Xa @ ( produc7507926704131184380et_nat @ H @ As24 ) ) ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % times_assn_raw.pelims(3)
% 2.86/3.13 thf(fact_4440_times__assn__raw_Opelims_I2_J,axiom,
% 2.86/3.13 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 2.86/3.13 ( ( times_assn_raw @ X @ Xa @ Xb )
% 2.86/3.13 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 2.86/3.13 => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.86/3.13 ( ( Xb
% 2.86/3.13 = ( produc7507926704131184380et_nat @ H @ As ) )
% 2.86/3.13 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H @ As ) ) ) )
% 2.86/3.13 => ~ ? [As12: set_nat,As23: set_nat] :
% 2.86/3.13 ( ( As
% 2.86/3.13 = ( sup_sup_set_nat @ As12 @ As23 ) )
% 2.86/3.13 & ( ( inf_inf_set_nat @ As12 @ As23 )
% 2.86/3.13 = bot_bot_set_nat )
% 2.86/3.13 & ( X @ ( produc7507926704131184380et_nat @ H @ As12 ) )
% 2.86/3.13 & ( Xa @ ( produc7507926704131184380et_nat @ H @ As23 ) ) ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % times_assn_raw.pelims(2)
% 2.86/3.13 thf(fact_4441_list_Oinject,axiom,
% 2.86/3.13 ! [X21: int,X222: list_int,Y21: int,Y222: list_int] :
% 2.86/3.13 ( ( ( cons_int @ X21 @ X222 )
% 2.86/3.13 = ( cons_int @ Y21 @ Y222 ) )
% 2.86/3.13 = ( ( X21 = Y21 )
% 2.86/3.13 & ( X222 = Y222 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % list.inject
% 2.86/3.13 thf(fact_4442_list_Oinject,axiom,
% 2.86/3.13 ! [X21: nat,X222: list_nat,Y21: nat,Y222: list_nat] :
% 2.86/3.13 ( ( ( cons_nat @ X21 @ X222 )
% 2.86/3.13 = ( cons_nat @ Y21 @ Y222 ) )
% 2.86/3.13 = ( ( X21 = Y21 )
% 2.86/3.13 & ( X222 = Y222 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % list.inject
% 2.86/3.13 thf(fact_4443_list_Oinject,axiom,
% 2.86/3.13 ! [X21: produc6575502325842934193n_assn,X222: list_P8527749157015355191n_assn,Y21: produc6575502325842934193n_assn,Y222: list_P8527749157015355191n_assn] :
% 2.86/3.13 ( ( ( cons_P2971678138204555879n_assn @ X21 @ X222 )
% 2.86/3.13 = ( cons_P2971678138204555879n_assn @ Y21 @ Y222 ) )
% 2.86/3.13 = ( ( X21 = Y21 )
% 2.86/3.13 & ( X222 = Y222 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % list.inject
% 2.86/3.13 thf(fact_4444_Field__Un,axiom,
% 2.86/3.13 ! [R2: set_Product_prod_o_o,S3: set_Product_prod_o_o] :
% 2.86/3.13 ( ( field_o @ ( sup_su5769328420594410459od_o_o @ R2 @ S3 ) )
% 2.86/3.13 = ( sup_sup_set_o @ ( field_o @ R2 ) @ ( field_o @ S3 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % Field_Un
% 2.86/3.13 thf(fact_4445_Field__Un,axiom,
% 2.86/3.13 ! [R2: set_Pr1261947904930325089at_nat,S3: set_Pr1261947904930325089at_nat] :
% 2.86/3.13 ( ( field_nat @ ( sup_su6327502436637775413at_nat @ R2 @ S3 ) )
% 2.86/3.13 = ( sup_sup_set_nat @ ( field_nat @ R2 ) @ ( field_nat @ S3 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % Field_Un
% 2.86/3.13 thf(fact_4446_Field__Un,axiom,
% 2.86/3.13 ! [R2: set_Pr5564308138774400199at_nat,S3: set_Pr5564308138774400199at_nat] :
% 2.86/3.13 ( ( field_2862844103579723188at_nat @ ( sup_su6664651903789602459at_nat @ R2 @ S3 ) )
% 2.86/3.13 = ( sup_su5525570899277871387at_nat @ ( field_2862844103579723188at_nat @ R2 ) @ ( field_2862844103579723188at_nat @ S3 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % Field_Un
% 2.86/3.13 thf(fact_4447_Field__Un,axiom,
% 2.86/3.13 ! [R2: set_Pr4329608150637261639at_nat,S3: set_Pr4329608150637261639at_nat] :
% 2.86/3.13 ( ( field_3145993188331922222at_nat @ ( sup_su5525570899277871387at_nat @ R2 @ S3 ) )
% 2.86/3.13 = ( sup_su3642409539654194069at_nat @ ( field_3145993188331922222at_nat @ R2 ) @ ( field_3145993188331922222at_nat @ S3 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % Field_Un
% 2.86/3.13 thf(fact_4448_list__ex__simps_I1_J,axiom,
% 2.86/3.13 ! [P: int > $o,X: int,Xs: list_int] :
% 2.86/3.13 ( ( list_ex_int @ P @ ( cons_int @ X @ Xs ) )
% 2.86/3.13 = ( ( P @ X )
% 2.86/3.13 | ( list_ex_int @ P @ Xs ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % list_ex_simps(1)
% 2.86/3.13 thf(fact_4449_list__ex__simps_I1_J,axiom,
% 2.86/3.13 ! [P: nat > $o,X: nat,Xs: list_nat] :
% 2.86/3.13 ( ( list_ex_nat @ P @ ( cons_nat @ X @ Xs ) )
% 2.86/3.13 = ( ( P @ X )
% 2.86/3.13 | ( list_ex_nat @ P @ Xs ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % list_ex_simps(1)
% 2.86/3.13 thf(fact_4450_list__ex__simps_I1_J,axiom,
% 2.86/3.13 ! [P: produc6575502325842934193n_assn > $o,X: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn] :
% 2.86/3.13 ( ( list_e1087220904399170805n_assn @ P @ ( cons_P2971678138204555879n_assn @ X @ Xs ) )
% 2.86/3.13 = ( ( P @ X )
% 2.86/3.13 | ( list_e1087220904399170805n_assn @ P @ Xs ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % list_ex_simps(1)
% 2.86/3.13 thf(fact_4451_length__enumerate,axiom,
% 2.86/3.13 ! [N: nat,Xs: list_c] :
% 2.86/3.13 ( ( size_s385972143775086793_nat_c @ ( enumerate_c @ N @ Xs ) )
% 2.86/3.13 = ( size_size_list_c @ Xs ) ) ).
% 2.86/3.13
% 2.86/3.13 % length_enumerate
% 2.86/3.13 thf(fact_4452_length__enumerate,axiom,
% 2.86/3.13 ! [N: nat,Xs: list_d] :
% 2.86/3.13 ( ( size_s457006183821432778_nat_d @ ( enumerate_d @ N @ Xs ) )
% 2.86/3.13 = ( size_size_list_d @ Xs ) ) ).
% 2.86/3.13
% 2.86/3.13 % length_enumerate
% 2.86/3.13 thf(fact_4453_length__enumerate,axiom,
% 2.86/3.13 ! [N: nat,Xs: list_nat] :
% 2.86/3.13 ( ( size_s5460976970255530739at_nat @ ( enumerate_nat @ N @ Xs ) )
% 2.86/3.13 = ( size_size_list_nat @ Xs ) ) ).
% 2.86/3.13
% 2.86/3.13 % length_enumerate
% 2.86/3.13 thf(fact_4454_length__enumerate,axiom,
% 2.86/3.13 ! [N: nat,Xs: list_int] :
% 2.86/3.13 ( ( size_s2970893825323803983at_int @ ( enumerate_int @ N @ Xs ) )
% 2.86/3.13 = ( size_size_list_int @ Xs ) ) ).
% 2.86/3.13
% 2.86/3.13 % length_enumerate
% 2.86/3.13 thf(fact_4455_list_Osimps_I15_J,axiom,
% 2.86/3.13 ! [X21: product_prod_nat_nat,X222: list_P6011104703257516679at_nat] :
% 2.86/3.13 ( ( set_Pr5648618587558075414at_nat @ ( cons_P6512896166579812791at_nat @ X21 @ X222 ) )
% 2.86/3.13 = ( insert8211810215607154385at_nat @ X21 @ ( set_Pr5648618587558075414at_nat @ X222 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % list.simps(15)
% 2.86/3.13 thf(fact_4456_list_Osimps_I15_J,axiom,
% 2.86/3.13 ! [X21: produc3843707927480180839at_nat,X222: list_P5464809261938338413at_nat] :
% 2.86/3.13 ( ( set_Pr3765526544606949372at_nat @ ( cons_P3940603068885512221at_nat @ X21 @ X222 ) )
% 2.86/3.13 = ( insert9069300056098147895at_nat @ X21 @ ( set_Pr3765526544606949372at_nat @ X222 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % list.simps(15)
% 2.86/3.13 thf(fact_4457_list_Osimps_I15_J,axiom,
% 2.86/3.13 ! [X21: $o,X222: list_o] :
% 2.86/3.13 ( ( set_o2 @ ( cons_o @ X21 @ X222 ) )
% 2.86/3.13 = ( insert_o2 @ X21 @ ( set_o2 @ X222 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % list.simps(15)
% 2.86/3.13 thf(fact_4458_list_Osimps_I15_J,axiom,
% 2.86/3.13 ! [X21: int,X222: list_int] :
% 2.86/3.13 ( ( set_int2 @ ( cons_int @ X21 @ X222 ) )
% 2.86/3.13 = ( insert_int2 @ X21 @ ( set_int2 @ X222 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % list.simps(15)
% 2.86/3.13 thf(fact_4459_list_Osimps_I15_J,axiom,
% 2.86/3.13 ! [X21: nat,X222: list_nat] :
% 2.86/3.13 ( ( set_nat2 @ ( cons_nat @ X21 @ X222 ) )
% 2.86/3.13 = ( insert_nat2 @ X21 @ ( set_nat2 @ X222 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % list.simps(15)
% 2.86/3.13 thf(fact_4460_list_Osimps_I15_J,axiom,
% 2.86/3.13 ! [X21: produc6575502325842934193n_assn,X222: list_P8527749157015355191n_assn] :
% 2.86/3.13 ( ( set_Pr1139785259514867910n_assn @ ( cons_P2971678138204555879n_assn @ X21 @ X222 ) )
% 2.86/3.13 = ( insert5290817439147925377n_assn @ X21 @ ( set_Pr1139785259514867910n_assn @ X222 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % list.simps(15)
% 2.86/3.13 thf(fact_4461_nth__Cons__0,axiom,
% 2.86/3.13 ! [X: int,Xs: list_int] :
% 2.86/3.13 ( ( nth_int @ ( cons_int @ X @ Xs ) @ zero_zero_nat )
% 2.86/3.13 = X ) ).
% 2.86/3.13
% 2.86/3.13 % nth_Cons_0
% 2.86/3.13 thf(fact_4462_nth__Cons__0,axiom,
% 2.86/3.13 ! [X: nat,Xs: list_nat] :
% 2.86/3.13 ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ zero_zero_nat )
% 2.86/3.13 = X ) ).
% 2.86/3.13
% 2.86/3.13 % nth_Cons_0
% 2.86/3.13 thf(fact_4463_nth__Cons__0,axiom,
% 2.86/3.13 ! [X: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn] :
% 2.86/3.13 ( ( nth_Pr1769885009046257848n_assn @ ( cons_P2971678138204555879n_assn @ X @ Xs ) @ zero_zero_nat )
% 2.86/3.13 = X ) ).
% 2.86/3.13
% 2.86/3.13 % nth_Cons_0
% 2.86/3.13 thf(fact_4464_nth__Cons__Suc,axiom,
% 2.86/3.13 ! [X: int,Xs: list_int,N: nat] :
% 2.86/3.13 ( ( nth_int @ ( cons_int @ X @ Xs ) @ ( suc @ N ) )
% 2.86/3.13 = ( nth_int @ Xs @ N ) ) ).
% 2.86/3.13
% 2.86/3.13 % nth_Cons_Suc
% 2.86/3.13 thf(fact_4465_nth__Cons__Suc,axiom,
% 2.86/3.13 ! [X: nat,Xs: list_nat,N: nat] :
% 2.86/3.13 ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ ( suc @ N ) )
% 2.86/3.13 = ( nth_nat @ Xs @ N ) ) ).
% 2.86/3.13
% 2.86/3.13 % nth_Cons_Suc
% 2.86/3.13 thf(fact_4466_nth__Cons__Suc,axiom,
% 2.86/3.13 ! [X: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn,N: nat] :
% 2.86/3.13 ( ( nth_Pr1769885009046257848n_assn @ ( cons_P2971678138204555879n_assn @ X @ Xs ) @ ( suc @ N ) )
% 2.86/3.13 = ( nth_Pr1769885009046257848n_assn @ Xs @ N ) ) ).
% 2.86/3.13
% 2.86/3.13 % nth_Cons_Suc
% 2.86/3.13 thf(fact_4467_zip__Cons__Cons,axiom,
% 2.86/3.13 ! [X: assn,Xs: list_assn,Y: assn,Ys: list_assn] :
% 2.86/3.13 ( ( zip_assn_assn @ ( cons_assn @ X @ Xs ) @ ( cons_assn @ Y @ Ys ) )
% 2.86/3.13 = ( cons_P2971678138204555879n_assn @ ( produc118845697133431529n_assn @ X @ Y ) @ ( zip_assn_assn @ Xs @ Ys ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % zip_Cons_Cons
% 2.86/3.13 thf(fact_4468_zip__Cons__Cons,axiom,
% 2.86/3.13 ! [X: int,Xs: list_int,Y: int,Ys: list_int] :
% 2.86/3.13 ( ( zip_int_int @ ( cons_int @ X @ Xs ) @ ( cons_int @ Y @ Ys ) )
% 2.86/3.13 = ( cons_P3334398858971670639nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( zip_int_int @ Xs @ Ys ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % zip_Cons_Cons
% 2.86/3.13 thf(fact_4469_zip__Cons__Cons,axiom,
% 2.86/3.13 ! [X: int,Xs: list_int,Y: nat,Ys: list_nat] :
% 2.86/3.13 ( ( zip_int_nat @ ( cons_int @ X @ Xs ) @ ( cons_nat @ Y @ Ys ) )
% 2.86/3.13 = ( cons_P7512249878480867347nt_nat @ ( product_Pair_int_nat @ X @ Y ) @ ( zip_int_nat @ Xs @ Ys ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % zip_Cons_Cons
% 2.86/3.13 thf(fact_4470_zip__Cons__Cons,axiom,
% 2.86/3.13 ! [X: nat,Xs: list_nat,Y: int,Ys: list_int] :
% 2.86/3.13 ( ( zip_nat_int @ ( cons_nat @ X @ Xs ) @ ( cons_int @ Y @ Ys ) )
% 2.86/3.13 = ( cons_P2335045147070616083at_int @ ( product_Pair_nat_int @ X @ Y ) @ ( zip_nat_int @ Xs @ Ys ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % zip_Cons_Cons
% 2.86/3.13 thf(fact_4471_zip__Cons__Cons,axiom,
% 2.86/3.13 ! [X: nat,Xs: list_nat,Y: nat,Ys: list_nat] :
% 2.86/3.13 ( ( zip_nat_nat @ ( cons_nat @ X @ Xs ) @ ( cons_nat @ Y @ Ys ) )
% 2.86/3.13 = ( cons_P6512896166579812791at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( zip_nat_nat @ Xs @ Ys ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % zip_Cons_Cons
% 2.86/3.13 thf(fact_4472_zip__Cons__Cons,axiom,
% 2.86/3.13 ! [X: int,Xs: list_int,Y: produc6575502325842934193n_assn,Ys: list_P8527749157015355191n_assn] :
% 2.86/3.13 ( ( zip_in7098856637274830732n_assn @ ( cons_int @ X @ Xs ) @ ( cons_P2971678138204555879n_assn @ Y @ Ys ) )
% 2.86/3.13 = ( cons_P8828502514829229636n_assn @ ( produc3313821056773121708n_assn @ X @ Y ) @ ( zip_in7098856637274830732n_assn @ Xs @ Ys ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % zip_Cons_Cons
% 2.86/3.13 thf(fact_4473_zip__Cons__Cons,axiom,
% 2.86/3.13 ! [X: nat,Xs: list_nat,Y: produc6575502325842934193n_assn,Ys: list_P8527749157015355191n_assn] :
% 2.86/3.13 ( ( zip_na5338819973521719528n_assn @ ( cons_nat @ X @ Xs ) @ ( cons_P2971678138204555879n_assn @ Y @ Ys ) )
% 2.86/3.13 = ( cons_P7068465851076118432n_assn @ ( produc1553784393020010504n_assn @ X @ Y ) @ ( zip_na5338819973521719528n_assn @ Xs @ Ys ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % zip_Cons_Cons
% 2.86/3.13 thf(fact_4474_zip__Cons__Cons,axiom,
% 2.86/3.13 ! [X: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn,Y: int,Ys: list_int] :
% 2.86/3.13 ( ( zip_Pr1015554993053626726sn_int @ ( cons_P2971678138204555879n_assn @ X @ Xs ) @ ( cons_int @ Y @ Ys ) )
% 2.86/3.13 = ( cons_P5155970366129889750sn_int @ ( produc6453891449406693510sn_int @ X @ Y ) @ ( zip_Pr1015554993053626726sn_int @ Xs @ Ys ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % zip_Cons_Cons
% 2.86/3.13 thf(fact_4475_zip__Cons__Cons,axiom,
% 2.86/3.13 ! [X: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn,Y: nat,Ys: list_nat] :
% 2.86/3.13 ( ( zip_Pr1018045463562677002sn_nat @ ( cons_P2971678138204555879n_assn @ X @ Xs ) @ ( cons_nat @ Y @ Ys ) )
% 2.86/3.13 = ( cons_P110449348784310650sn_nat @ ( produc6456381919915743786sn_nat @ X @ Y ) @ ( zip_Pr1018045463562677002sn_nat @ Xs @ Ys ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % zip_Cons_Cons
% 2.86/3.13 thf(fact_4476_zip__Cons__Cons,axiom,
% 2.86/3.13 ! [X: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn,Y: produc6575502325842934193n_assn,Ys: list_P8527749157015355191n_assn] :
% 2.86/3.13 ( ( zip_Pr8806919808394484215n_assn @ ( cons_P2971678138204555879n_assn @ X @ Xs ) @ ( cons_P2971678138204555879n_assn @ Y @ Ys ) )
% 2.86/3.13 = ( cons_P9150528168557782045n_assn @ ( produc6128706242671166167n_assn @ X @ Y ) @ ( zip_Pr8806919808394484215n_assn @ Xs @ Ys ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % zip_Cons_Cons
% 2.86/3.13 thf(fact_4477_Field__empty,axiom,
% 2.86/3.13 ( ( field_2862844103579723188at_nat @ bot_bo7193250159860175667at_nat )
% 2.86/3.13 = bot_bo228742789529271731at_nat ) ).
% 2.86/3.13
% 2.86/3.13 % Field_empty
% 2.86/3.13 thf(fact_4478_Field__empty,axiom,
% 2.86/3.13 ( ( field_4706345496283612622at_nat @ bot_bo5327735625951526323at_nat )
% 2.86/3.13 = bot_bo2099793752762293965at_nat ) ).
% 2.86/3.13
% 2.86/3.13 % Field_empty
% 2.86/3.13 thf(fact_4479_Field__empty,axiom,
% 2.86/3.13 ( ( field_o @ bot_bo7073875226086086771od_o_o )
% 2.86/3.13 = bot_bot_set_o ) ).
% 2.86/3.13
% 2.86/3.13 % Field_empty
% 2.86/3.13 thf(fact_4480_Field__empty,axiom,
% 2.86/3.13 ( ( field_int @ bot_bo1796632182523588997nt_int )
% 2.86/3.13 = bot_bot_set_int ) ).
% 2.86/3.13
% 2.86/3.13 % Field_empty
% 2.86/3.13 thf(fact_4481_Field__empty,axiom,
% 2.86/3.13 ( ( field_3145993188331922222at_nat @ bot_bo228742789529271731at_nat )
% 2.86/3.13 = bot_bo3083307316010499117at_nat ) ).
% 2.86/3.13
% 2.86/3.13 % Field_empty
% 2.86/3.13 thf(fact_4482_Field__empty,axiom,
% 2.86/3.13 ( ( field_nat @ bot_bo2099793752762293965at_nat )
% 2.86/3.13 = bot_bot_set_nat ) ).
% 2.86/3.13
% 2.86/3.13 % Field_empty
% 2.86/3.13 thf(fact_4483_not__in__set__insert,axiom,
% 2.86/3.13 ! [X: produc3843707927480180839at_nat,Xs: list_P5464809261938338413at_nat] :
% 2.86/3.13 ( ~ ( member8757157785044589968at_nat @ X @ ( set_Pr3765526544606949372at_nat @ Xs ) )
% 2.86/3.13 => ( ( insert4149901806602606979at_nat @ X @ Xs )
% 2.86/3.13 = ( cons_P3940603068885512221at_nat @ X @ Xs ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % not_in_set_insert
% 2.86/3.13 thf(fact_4484_not__in__set__insert,axiom,
% 2.86/3.13 ! [X: product_prod_nat_nat,Xs: list_P6011104703257516679at_nat] :
% 2.86/3.13 ( ~ ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 2.86/3.13 => ( ( insert8944034826898310173at_nat @ X @ Xs )
% 2.86/3.13 = ( cons_P6512896166579812791at_nat @ X @ Xs ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % not_in_set_insert
% 2.86/3.13 thf(fact_4485_not__in__set__insert,axiom,
% 2.86/3.13 ! [X: produc3658429121746597890et_nat > $o,Xs: list_P7985473006766602707_nat_o] :
% 2.86/3.13 ( ~ ( member6576561426505652726_nat_o @ X @ ( set_Pr400311997697478754_nat_o @ Xs ) )
% 2.86/3.13 => ( ( insert8021100735160035049_nat_o @ X @ Xs )
% 2.86/3.13 = ( cons_P6219271836124797827_nat_o @ X @ Xs ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % not_in_set_insert
% 2.86/3.13 thf(fact_4486_not__in__set__insert,axiom,
% 2.86/3.13 ! [X: int,Xs: list_int] :
% 2.86/3.13 ( ~ ( member_int @ X @ ( set_int2 @ Xs ) )
% 2.86/3.13 => ( ( insert_int @ X @ Xs )
% 2.86/3.13 = ( cons_int @ X @ Xs ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % not_in_set_insert
% 2.86/3.13 thf(fact_4487_not__in__set__insert,axiom,
% 2.86/3.13 ! [X: nat,Xs: list_nat] :
% 2.86/3.13 ( ~ ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 2.86/3.13 => ( ( insert_nat @ X @ Xs )
% 2.86/3.13 = ( cons_nat @ X @ Xs ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % not_in_set_insert
% 2.86/3.13 thf(fact_4488_not__in__set__insert,axiom,
% 2.86/3.13 ! [X: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn] :
% 2.86/3.13 ( ~ ( member7957490590177025114n_assn @ X @ ( set_Pr1139785259514867910n_assn @ Xs ) )
% 2.86/3.13 => ( ( insert3246601298802261197n_assn @ X @ Xs )
% 2.86/3.13 = ( cons_P2971678138204555879n_assn @ X @ Xs ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % not_in_set_insert
% 2.86/3.13 thf(fact_4489_Cons__listrel1__Cons,axiom,
% 2.86/3.13 ! [X: set_Pr1261947904930325089at_nat,Xs: list_s1210847774152347623at_nat,Y: set_Pr1261947904930325089at_nat,Ys: list_s1210847774152347623at_nat,R2: set_Pr4329608150637261639at_nat] :
% 2.86/3.13 ( ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ ( cons_s6881495754146722583at_nat @ X @ Xs ) @ ( cons_s6881495754146722583at_nat @ Y @ Ys ) ) @ ( listre8180072825634266816at_nat @ R2 ) )
% 2.86/3.13 = ( ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ R2 )
% 2.86/3.13 & ( Xs = Ys ) )
% 2.86/3.13 | ( ( X = Y )
% 2.86/3.13 & ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ Xs @ Ys ) @ ( listre8180072825634266816at_nat @ R2 ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % Cons_listrel1_Cons
% 2.86/3.13 thf(fact_4490_Cons__listrel1__Cons,axiom,
% 2.86/3.13 ! [X: int,Xs: list_int,Y: int,Ys: list_int,R2: set_Pr958786334691620121nt_int] :
% 2.86/3.13 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ ( cons_int @ X @ Xs ) @ ( cons_int @ Y @ Ys ) ) @ ( listrel1_int @ R2 ) )
% 2.86/3.13 = ( ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R2 )
% 2.86/3.13 & ( Xs = Ys ) )
% 2.86/3.13 | ( ( X = Y )
% 2.86/3.13 & ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs @ Ys ) @ ( listrel1_int @ R2 ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % Cons_listrel1_Cons
% 2.86/3.13 thf(fact_4491_Cons__listrel1__Cons,axiom,
% 2.86/3.13 ! [X: nat,Xs: list_nat,Y: nat,Ys: list_nat,R2: set_Pr1261947904930325089at_nat] :
% 2.86/3.13 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ ( cons_nat @ X @ Xs ) @ ( cons_nat @ Y @ Ys ) ) @ ( listrel1_nat @ R2 ) )
% 2.86/3.13 = ( ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R2 )
% 2.86/3.13 & ( Xs = Ys ) )
% 2.86/3.13 | ( ( X = Y )
% 2.86/3.13 & ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs @ Ys ) @ ( listrel1_nat @ R2 ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % Cons_listrel1_Cons
% 2.86/3.13 thf(fact_4492_Cons__listrel1__Cons,axiom,
% 2.86/3.13 ! [X: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn,Y: produc6575502325842934193n_assn,Ys: list_P8527749157015355191n_assn,R2: set_Pr8116311503512020807n_assn] :
% 2.86/3.13 ( ( member3994142547374651152n_assn @ ( produc3014731801419794263n_assn @ ( cons_P2971678138204555879n_assn @ X @ Xs ) @ ( cons_P2971678138204555879n_assn @ Y @ Ys ) ) @ ( listre4270255209692100112n_assn @ R2 ) )
% 2.86/3.13 = ( ( ( member4743710847862083984n_assn @ ( produc6128706242671166167n_assn @ X @ Y ) @ R2 )
% 2.86/3.13 & ( Xs = Ys ) )
% 2.86/3.13 | ( ( X = Y )
% 2.86/3.13 & ( member3994142547374651152n_assn @ ( produc3014731801419794263n_assn @ Xs @ Ys ) @ ( listre4270255209692100112n_assn @ R2 ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % Cons_listrel1_Cons
% 2.86/3.13 thf(fact_4493_enumerate__simps_I2_J,axiom,
% 2.86/3.13 ! [N: nat,X: int,Xs: list_int] :
% 2.86/3.13 ( ( enumerate_int @ N @ ( cons_int @ X @ Xs ) )
% 2.86/3.13 = ( cons_P2335045147070616083at_int @ ( product_Pair_nat_int @ N @ X ) @ ( enumerate_int @ ( suc @ N ) @ Xs ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % enumerate_simps(2)
% 2.86/3.13 thf(fact_4494_enumerate__simps_I2_J,axiom,
% 2.86/3.13 ! [N: nat,X: nat,Xs: list_nat] :
% 2.86/3.13 ( ( enumerate_nat @ N @ ( cons_nat @ X @ Xs ) )
% 2.86/3.13 = ( cons_P6512896166579812791at_nat @ ( product_Pair_nat_nat @ N @ X ) @ ( enumerate_nat @ ( suc @ N ) @ Xs ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % enumerate_simps(2)
% 2.86/3.13 thf(fact_4495_enumerate__simps_I2_J,axiom,
% 2.86/3.13 ! [N: nat,X: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn] :
% 2.86/3.13 ( ( enumer9200277086812776726n_assn @ N @ ( cons_P2971678138204555879n_assn @ X @ Xs ) )
% 2.86/3.13 = ( cons_P7068465851076118432n_assn @ ( produc1553784393020010504n_assn @ N @ X ) @ ( enumer9200277086812776726n_assn @ ( suc @ N ) @ Xs ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % enumerate_simps(2)
% 2.86/3.13 thf(fact_4496_not__Cons__self2,axiom,
% 2.86/3.13 ! [X: int,Xs: list_int] :
% 2.86/3.13 ( ( cons_int @ X @ Xs )
% 2.86/3.13 != Xs ) ).
% 2.86/3.13
% 2.86/3.13 % not_Cons_self2
% 2.86/3.13 thf(fact_4497_not__Cons__self2,axiom,
% 2.86/3.13 ! [X: nat,Xs: list_nat] :
% 2.86/3.13 ( ( cons_nat @ X @ Xs )
% 2.86/3.13 != Xs ) ).
% 2.86/3.13
% 2.86/3.13 % not_Cons_self2
% 2.86/3.13 thf(fact_4498_not__Cons__self2,axiom,
% 2.86/3.13 ! [X: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn] :
% 2.86/3.13 ( ( cons_P2971678138204555879n_assn @ X @ Xs )
% 2.86/3.13 != Xs ) ).
% 2.86/3.13
% 2.86/3.13 % not_Cons_self2
% 2.86/3.13 thf(fact_4499_list__tail__coinc,axiom,
% 2.86/3.13 ! [N1: int,R1: list_int,N22: int,R22: list_int] :
% 2.86/3.13 ( ( ( cons_int @ N1 @ R1 )
% 2.86/3.13 = ( cons_int @ N22 @ R22 ) )
% 2.86/3.13 => ( ( N1 = N22 )
% 2.86/3.13 & ( R1 = R22 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % list_tail_coinc
% 2.86/3.13 thf(fact_4500_list__tail__coinc,axiom,
% 2.86/3.13 ! [N1: nat,R1: list_nat,N22: nat,R22: list_nat] :
% 2.86/3.13 ( ( ( cons_nat @ N1 @ R1 )
% 2.86/3.13 = ( cons_nat @ N22 @ R22 ) )
% 2.86/3.13 => ( ( N1 = N22 )
% 2.86/3.13 & ( R1 = R22 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % list_tail_coinc
% 2.86/3.13 thf(fact_4501_list__tail__coinc,axiom,
% 2.86/3.13 ! [N1: produc6575502325842934193n_assn,R1: list_P8527749157015355191n_assn,N22: produc6575502325842934193n_assn,R22: list_P8527749157015355191n_assn] :
% 2.86/3.13 ( ( ( cons_P2971678138204555879n_assn @ N1 @ R1 )
% 2.86/3.13 = ( cons_P2971678138204555879n_assn @ N22 @ R22 ) )
% 2.86/3.13 => ( ( N1 = N22 )
% 2.86/3.13 & ( R1 = R22 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % list_tail_coinc
% 2.86/3.13 thf(fact_4502_union__diff__assoc,axiom,
% 2.86/3.13 ! [C2: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat,A: multis2468970476368604999at_nat] :
% 2.86/3.13 ( ( ( minus_4286766774447292334at_nat @ C2 @ B )
% 2.86/3.13 = zero_z1048942125864253310at_nat )
% 2.86/3.13 => ( ( minus_4286766774447292334at_nat @ ( plus_p7104986032573967614at_nat @ A @ B ) @ C2 )
% 2.86/3.13 = ( plus_p7104986032573967614at_nat @ A @ ( minus_4286766774447292334at_nat @ B @ C2 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % union_diff_assoc
% 2.86/3.13 thf(fact_4503_zip__eq__ConsE,axiom,
% 2.86/3.13 ! [Xs: list_int,Ys: list_int,Xy: product_prod_int_int,Xys: list_P5707943133018811711nt_int] :
% 2.86/3.13 ( ( ( zip_int_int @ Xs @ Ys )
% 2.86/3.13 = ( cons_P3334398858971670639nt_int @ Xy @ Xys ) )
% 2.86/3.13 => ~ ! [X3: int,Xs5: list_int] :
% 2.86/3.13 ( ( Xs
% 2.86/3.13 = ( cons_int @ X3 @ Xs5 ) )
% 2.86/3.13 => ! [Y2: int,Ys4: list_int] :
% 2.86/3.13 ( ( Ys
% 2.86/3.13 = ( cons_int @ Y2 @ Ys4 ) )
% 2.86/3.13 => ( ( Xy
% 2.86/3.13 = ( product_Pair_int_int @ X3 @ Y2 ) )
% 2.86/3.13 => ( Xys
% 2.86/3.13 != ( zip_int_int @ Xs5 @ Ys4 ) ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % zip_eq_ConsE
% 2.86/3.13 thf(fact_4504_zip__eq__ConsE,axiom,
% 2.86/3.13 ! [Xs: list_int,Ys: list_nat,Xy: product_prod_int_nat,Xys: list_P8198026277950538467nt_nat] :
% 2.86/3.13 ( ( ( zip_int_nat @ Xs @ Ys )
% 2.86/3.13 = ( cons_P7512249878480867347nt_nat @ Xy @ Xys ) )
% 2.86/3.13 => ~ ! [X3: int,Xs5: list_int] :
% 2.86/3.13 ( ( Xs
% 2.86/3.13 = ( cons_int @ X3 @ Xs5 ) )
% 2.86/3.13 => ! [Y2: nat,Ys4: list_nat] :
% 2.86/3.13 ( ( Ys
% 2.86/3.13 = ( cons_nat @ Y2 @ Ys4 ) )
% 2.86/3.13 => ( ( Xy
% 2.86/3.13 = ( product_Pair_int_nat @ X3 @ Y2 ) )
% 2.86/3.13 => ( Xys
% 2.86/3.13 != ( zip_int_nat @ Xs5 @ Ys4 ) ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % zip_eq_ConsE
% 2.86/3.13 thf(fact_4505_zip__eq__ConsE,axiom,
% 2.86/3.13 ! [Xs: list_nat,Ys: list_int,Xy: product_prod_nat_int,Xys: list_P3521021558325789923at_int] :
% 2.86/3.13 ( ( ( zip_nat_int @ Xs @ Ys )
% 2.86/3.13 = ( cons_P2335045147070616083at_int @ Xy @ Xys ) )
% 2.86/3.13 => ~ ! [X3: nat,Xs5: list_nat] :
% 2.86/3.13 ( ( Xs
% 2.86/3.13 = ( cons_nat @ X3 @ Xs5 ) )
% 2.86/3.13 => ! [Y2: int,Ys4: list_int] :
% 2.86/3.13 ( ( Ys
% 2.86/3.13 = ( cons_int @ Y2 @ Ys4 ) )
% 2.86/3.13 => ( ( Xy
% 2.86/3.13 = ( product_Pair_nat_int @ X3 @ Y2 ) )
% 2.86/3.13 => ( Xys
% 2.86/3.13 != ( zip_nat_int @ Xs5 @ Ys4 ) ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % zip_eq_ConsE
% 2.86/3.13 thf(fact_4506_zip__eq__ConsE,axiom,
% 2.86/3.13 ! [Xs: list_nat,Ys: list_nat,Xy: product_prod_nat_nat,Xys: list_P6011104703257516679at_nat] :
% 2.86/3.13 ( ( ( zip_nat_nat @ Xs @ Ys )
% 2.86/3.13 = ( cons_P6512896166579812791at_nat @ Xy @ Xys ) )
% 2.86/3.13 => ~ ! [X3: nat,Xs5: list_nat] :
% 2.86/3.13 ( ( Xs
% 2.86/3.13 = ( cons_nat @ X3 @ Xs5 ) )
% 2.86/3.13 => ! [Y2: nat,Ys4: list_nat] :
% 2.86/3.13 ( ( Ys
% 2.86/3.13 = ( cons_nat @ Y2 @ Ys4 ) )
% 2.86/3.13 => ( ( Xy
% 2.86/3.13 = ( product_Pair_nat_nat @ X3 @ Y2 ) )
% 2.86/3.13 => ( Xys
% 2.86/3.13 != ( zip_nat_nat @ Xs5 @ Ys4 ) ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % zip_eq_ConsE
% 2.86/3.13 thf(fact_4507_zip__eq__ConsE,axiom,
% 2.86/3.13 ! [Xs: list_assn,Ys: list_assn,Xy: produc6575502325842934193n_assn,Xys: list_P8527749157015355191n_assn] :
% 2.86/3.13 ( ( ( zip_assn_assn @ Xs @ Ys )
% 2.86/3.13 = ( cons_P2971678138204555879n_assn @ Xy @ Xys ) )
% 2.86/3.13 => ~ ! [X3: assn,Xs5: list_assn] :
% 2.86/3.13 ( ( Xs
% 2.86/3.13 = ( cons_assn @ X3 @ Xs5 ) )
% 2.86/3.13 => ! [Y2: assn,Ys4: list_assn] :
% 2.86/3.13 ( ( Ys
% 2.86/3.13 = ( cons_assn @ Y2 @ Ys4 ) )
% 2.86/3.13 => ( ( Xy
% 2.86/3.13 = ( produc118845697133431529n_assn @ X3 @ Y2 ) )
% 2.86/3.13 => ( Xys
% 2.86/3.13 != ( zip_assn_assn @ Xs5 @ Ys4 ) ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % zip_eq_ConsE
% 2.86/3.13 thf(fact_4508_zip__eq__ConsE,axiom,
% 2.86/3.13 ! [Xs: list_int,Ys: list_P8527749157015355191n_assn,Xy: produc3167338625816234618n_assn,Xys: list_P1495281457390866698n_assn] :
% 2.86/3.13 ( ( ( zip_in7098856637274830732n_assn @ Xs @ Ys )
% 2.86/3.13 = ( cons_P8828502514829229636n_assn @ Xy @ Xys ) )
% 2.86/3.13 => ~ ! [X3: int,Xs5: list_int] :
% 2.86/3.13 ( ( Xs
% 2.86/3.13 = ( cons_int @ X3 @ Xs5 ) )
% 2.86/3.13 => ! [Y2: produc6575502325842934193n_assn,Ys4: list_P8527749157015355191n_assn] :
% 2.86/3.13 ( ( Ys
% 2.86/3.13 = ( cons_P2971678138204555879n_assn @ Y2 @ Ys4 ) )
% 2.86/3.13 => ( ( Xy
% 2.86/3.13 = ( produc3313821056773121708n_assn @ X3 @ Y2 ) )
% 2.86/3.13 => ( Xys
% 2.86/3.13 != ( zip_in7098856637274830732n_assn @ Xs5 @ Ys4 ) ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % zip_eq_ConsE
% 2.86/3.13 thf(fact_4509_zip__eq__ConsE,axiom,
% 2.86/3.13 ! [Xs: list_nat,Ys: list_P8527749157015355191n_assn,Xy: produc1407301962063123414n_assn,Xys: list_P7711101519850957926n_assn] :
% 2.86/3.13 ( ( ( zip_na5338819973521719528n_assn @ Xs @ Ys )
% 2.86/3.13 = ( cons_P7068465851076118432n_assn @ Xy @ Xys ) )
% 2.86/3.13 => ~ ! [X3: nat,Xs5: list_nat] :
% 2.86/3.13 ( ( Xs
% 2.86/3.13 = ( cons_nat @ X3 @ Xs5 ) )
% 2.86/3.13 => ! [Y2: produc6575502325842934193n_assn,Ys4: list_P8527749157015355191n_assn] :
% 2.86/3.13 ( ( Ys
% 2.86/3.13 = ( cons_P2971678138204555879n_assn @ Y2 @ Ys4 ) )
% 2.86/3.13 => ( ( Xy
% 2.86/3.13 = ( produc1553784393020010504n_assn @ X3 @ Y2 ) )
% 2.86/3.13 => ( Xys
% 2.86/3.13 != ( zip_na5338819973521719528n_assn @ Xs5 @ Ys4 ) ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % zip_eq_ConsE
% 2.86/3.13 thf(fact_4510_zip__eq__ConsE,axiom,
% 2.86/3.13 ! [Xs: list_P8527749157015355191n_assn,Ys: list_int,Xy: produc8718178513971670540sn_int,Xys: list_P421884338359569308sn_int] :
% 2.86/3.13 ( ( ( zip_Pr1015554993053626726sn_int @ Xs @ Ys )
% 2.86/3.13 = ( cons_P5155970366129889750sn_int @ Xy @ Xys ) )
% 2.86/3.13 => ~ ! [X3: produc6575502325842934193n_assn,Xs5: list_P8527749157015355191n_assn] :
% 2.86/3.13 ( ( Xs
% 2.86/3.13 = ( cons_P2971678138204555879n_assn @ X3 @ Xs5 ) )
% 2.86/3.13 => ! [Y2: int,Ys4: list_int] :
% 2.86/3.13 ( ( Ys
% 2.86/3.13 = ( cons_int @ Y2 @ Ys4 ) )
% 2.86/3.13 => ( ( Xy
% 2.86/3.13 = ( produc6453891449406693510sn_int @ X3 @ Y2 ) )
% 2.86/3.13 => ( Xys
% 2.86/3.13 != ( zip_Pr1015554993053626726sn_int @ Xs5 @ Ys4 ) ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % zip_eq_ConsE
% 2.86/3.13 thf(fact_4511_zip__eq__ConsE,axiom,
% 2.86/3.13 ! [Xs: list_P8527749157015355191n_assn,Ys: list_nat,Xy: produc3672657496626091440sn_nat,Xys: list_P2911967483291296064sn_nat] :
% 2.86/3.13 ( ( ( zip_Pr1018045463562677002sn_nat @ Xs @ Ys )
% 2.86/3.13 = ( cons_P110449348784310650sn_nat @ Xy @ Xys ) )
% 2.86/3.13 => ~ ! [X3: produc6575502325842934193n_assn,Xs5: list_P8527749157015355191n_assn] :
% 2.86/3.13 ( ( Xs
% 2.86/3.13 = ( cons_P2971678138204555879n_assn @ X3 @ Xs5 ) )
% 2.86/3.13 => ! [Y2: nat,Ys4: list_nat] :
% 2.86/3.13 ( ( Ys
% 2.86/3.13 = ( cons_nat @ Y2 @ Ys4 ) )
% 2.86/3.13 => ( ( Xy
% 2.86/3.13 = ( produc6456381919915743786sn_nat @ X3 @ Y2 ) )
% 2.86/3.13 => ( Xys
% 2.86/3.13 != ( zip_Pr1018045463562677002sn_nat @ Xs5 @ Ys4 ) ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % zip_eq_ConsE
% 2.86/3.13 thf(fact_4512_zip__eq__ConsE,axiom,
% 2.86/3.13 ! [Xs: list_P8527749157015355191n_assn,Ys: list_P8527749157015355191n_assn,Xy: produc9053633027152450663n_assn,Xys: list_P28140577958321773n_assn] :
% 2.86/3.13 ( ( ( zip_Pr8806919808394484215n_assn @ Xs @ Ys )
% 2.86/3.13 = ( cons_P9150528168557782045n_assn @ Xy @ Xys ) )
% 2.86/3.13 => ~ ! [X3: produc6575502325842934193n_assn,Xs5: list_P8527749157015355191n_assn] :
% 2.86/3.13 ( ( Xs
% 2.86/3.13 = ( cons_P2971678138204555879n_assn @ X3 @ Xs5 ) )
% 2.86/3.13 => ! [Y2: produc6575502325842934193n_assn,Ys4: list_P8527749157015355191n_assn] :
% 2.86/3.13 ( ( Ys
% 2.86/3.13 = ( cons_P2971678138204555879n_assn @ Y2 @ Ys4 ) )
% 2.86/3.13 => ( ( Xy
% 2.86/3.13 = ( produc6128706242671166167n_assn @ X3 @ Y2 ) )
% 2.86/3.13 => ( Xys
% 2.86/3.13 != ( zip_Pr8806919808394484215n_assn @ Xs5 @ Ys4 ) ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % zip_eq_ConsE
% 2.86/3.13 thf(fact_4513_FieldI1,axiom,
% 2.86/3.13 ! [I: produc3843707927480180839at_nat,J: produc3843707927480180839at_nat,R: set_Pr5564308138774400199at_nat] :
% 2.86/3.13 ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ I @ J ) @ R )
% 2.86/3.13 => ( member8757157785044589968at_nat @ I @ ( field_2862844103579723188at_nat @ R ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % FieldI1
% 2.86/3.13 thf(fact_4514_FieldI1,axiom,
% 2.86/3.13 ! [I: product_prod_nat_nat,J: product_prod_nat_nat,R: set_Pr8693737435421807431at_nat] :
% 2.86/3.13 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ I @ J ) @ R )
% 2.86/3.13 => ( member8440522571783428010at_nat @ I @ ( field_4706345496283612622at_nat @ R ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % FieldI1
% 2.86/3.13 thf(fact_4515_FieldI1,axiom,
% 2.86/3.13 ! [I: int,J: int,R: set_Pr958786334691620121nt_int] :
% 2.86/3.13 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ I @ J ) @ R )
% 2.86/3.13 => ( member_int @ I @ ( field_int @ R ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % FieldI1
% 2.86/3.13 thf(fact_4516_FieldI1,axiom,
% 2.86/3.13 ! [I: produc3658429121746597890et_nat > $o,J: produc3658429121746597890et_nat > $o,R: set_Pr2161125870931222855_nat_o] :
% 2.86/3.13 ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ I @ J ) @ R )
% 2.86/3.13 => ( member6576561426505652726_nat_o @ I @ ( field_81821745747897882_nat_o @ R ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % FieldI1
% 2.86/3.13 thf(fact_4517_FieldI1,axiom,
% 2.86/3.13 ! [I: set_Pr1261947904930325089at_nat,J: set_Pr1261947904930325089at_nat,R: set_Pr4329608150637261639at_nat] :
% 2.86/3.13 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ I @ J ) @ R )
% 2.86/3.13 => ( member2643936169264416010at_nat @ I @ ( field_3145993188331922222at_nat @ R ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % FieldI1
% 2.86/3.13 thf(fact_4518_FieldI1,axiom,
% 2.86/3.13 ! [I: nat,J: nat,R: set_Pr1261947904930325089at_nat] :
% 2.86/3.13 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ I @ J ) @ R )
% 2.86/3.13 => ( member_nat @ I @ ( field_nat @ R ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % FieldI1
% 2.86/3.13 thf(fact_4519_FieldI1,axiom,
% 2.86/3.13 ! [I: $o,J: $o,R: set_Product_prod_o_o] :
% 2.86/3.13 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ I @ J ) @ R )
% 2.86/3.13 => ( member_o @ I @ ( field_o @ R ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % FieldI1
% 2.86/3.13 thf(fact_4520_FieldI2,axiom,
% 2.86/3.13 ! [I: produc3843707927480180839at_nat,J: produc3843707927480180839at_nat,R: set_Pr5564308138774400199at_nat] :
% 2.86/3.13 ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ I @ J ) @ R )
% 2.86/3.13 => ( member8757157785044589968at_nat @ J @ ( field_2862844103579723188at_nat @ R ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % FieldI2
% 2.86/3.13 thf(fact_4521_FieldI2,axiom,
% 2.86/3.13 ! [I: product_prod_nat_nat,J: product_prod_nat_nat,R: set_Pr8693737435421807431at_nat] :
% 2.86/3.13 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ I @ J ) @ R )
% 2.86/3.13 => ( member8440522571783428010at_nat @ J @ ( field_4706345496283612622at_nat @ R ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % FieldI2
% 2.86/3.13 thf(fact_4522_FieldI2,axiom,
% 2.86/3.13 ! [I: int,J: int,R: set_Pr958786334691620121nt_int] :
% 2.86/3.13 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ I @ J ) @ R )
% 2.86/3.13 => ( member_int @ J @ ( field_int @ R ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % FieldI2
% 2.86/3.13 thf(fact_4523_FieldI2,axiom,
% 2.86/3.13 ! [I: produc3658429121746597890et_nat > $o,J: produc3658429121746597890et_nat > $o,R: set_Pr2161125870931222855_nat_o] :
% 2.86/3.13 ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ I @ J ) @ R )
% 2.86/3.13 => ( member6576561426505652726_nat_o @ J @ ( field_81821745747897882_nat_o @ R ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % FieldI2
% 2.86/3.13 thf(fact_4524_FieldI2,axiom,
% 2.86/3.13 ! [I: set_Pr1261947904930325089at_nat,J: set_Pr1261947904930325089at_nat,R: set_Pr4329608150637261639at_nat] :
% 2.86/3.13 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ I @ J ) @ R )
% 2.86/3.13 => ( member2643936169264416010at_nat @ J @ ( field_3145993188331922222at_nat @ R ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % FieldI2
% 2.86/3.13 thf(fact_4525_FieldI2,axiom,
% 2.86/3.13 ! [I: nat,J: nat,R: set_Pr1261947904930325089at_nat] :
% 2.86/3.13 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ I @ J ) @ R )
% 2.86/3.13 => ( member_nat @ J @ ( field_nat @ R ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % FieldI2
% 2.86/3.13 thf(fact_4526_FieldI2,axiom,
% 2.86/3.13 ! [I: $o,J: $o,R: set_Product_prod_o_o] :
% 2.86/3.13 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ I @ J ) @ R )
% 2.86/3.13 => ( member_o @ J @ ( field_o @ R ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % FieldI2
% 2.86/3.13 thf(fact_4527_set__ConsD,axiom,
% 2.86/3.13 ! [Y: produc3843707927480180839at_nat,X: produc3843707927480180839at_nat,Xs: list_P5464809261938338413at_nat] :
% 2.86/3.13 ( ( member8757157785044589968at_nat @ Y @ ( set_Pr3765526544606949372at_nat @ ( cons_P3940603068885512221at_nat @ X @ Xs ) ) )
% 2.86/3.13 => ( ( Y = X )
% 2.86/3.13 | ( member8757157785044589968at_nat @ Y @ ( set_Pr3765526544606949372at_nat @ Xs ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % set_ConsD
% 2.86/3.13 thf(fact_4528_set__ConsD,axiom,
% 2.86/3.13 ! [Y: product_prod_nat_nat,X: product_prod_nat_nat,Xs: list_P6011104703257516679at_nat] :
% 2.86/3.13 ( ( member8440522571783428010at_nat @ Y @ ( set_Pr5648618587558075414at_nat @ ( cons_P6512896166579812791at_nat @ X @ Xs ) ) )
% 2.86/3.13 => ( ( Y = X )
% 2.86/3.13 | ( member8440522571783428010at_nat @ Y @ ( set_Pr5648618587558075414at_nat @ Xs ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % set_ConsD
% 2.86/3.13 thf(fact_4529_set__ConsD,axiom,
% 2.86/3.13 ! [Y: produc3658429121746597890et_nat > $o,X: produc3658429121746597890et_nat > $o,Xs: list_P7985473006766602707_nat_o] :
% 2.86/3.13 ( ( member6576561426505652726_nat_o @ Y @ ( set_Pr400311997697478754_nat_o @ ( cons_P6219271836124797827_nat_o @ X @ Xs ) ) )
% 2.86/3.13 => ( ( Y = X )
% 2.86/3.13 | ( member6576561426505652726_nat_o @ Y @ ( set_Pr400311997697478754_nat_o @ Xs ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % set_ConsD
% 2.86/3.13 thf(fact_4530_set__ConsD,axiom,
% 2.86/3.13 ! [Y: int,X: int,Xs: list_int] :
% 2.86/3.13 ( ( member_int @ Y @ ( set_int2 @ ( cons_int @ X @ Xs ) ) )
% 2.86/3.13 => ( ( Y = X )
% 2.86/3.13 | ( member_int @ Y @ ( set_int2 @ Xs ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % set_ConsD
% 2.86/3.13 thf(fact_4531_set__ConsD,axiom,
% 2.86/3.13 ! [Y: nat,X: nat,Xs: list_nat] :
% 2.86/3.13 ( ( member_nat @ Y @ ( set_nat2 @ ( cons_nat @ X @ Xs ) ) )
% 2.86/3.13 => ( ( Y = X )
% 2.86/3.13 | ( member_nat @ Y @ ( set_nat2 @ Xs ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % set_ConsD
% 2.86/3.13 thf(fact_4532_set__ConsD,axiom,
% 2.86/3.13 ! [Y: produc6575502325842934193n_assn,X: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn] :
% 2.86/3.13 ( ( member7957490590177025114n_assn @ Y @ ( set_Pr1139785259514867910n_assn @ ( cons_P2971678138204555879n_assn @ X @ Xs ) ) )
% 2.86/3.13 => ( ( Y = X )
% 2.86/3.13 | ( member7957490590177025114n_assn @ Y @ ( set_Pr1139785259514867910n_assn @ Xs ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % set_ConsD
% 2.86/3.13 thf(fact_4533_list_Oset__cases,axiom,
% 2.86/3.13 ! [E: produc3843707927480180839at_nat,A2: list_P5464809261938338413at_nat] :
% 2.86/3.13 ( ( member8757157785044589968at_nat @ E @ ( set_Pr3765526544606949372at_nat @ A2 ) )
% 2.86/3.13 => ( ! [Z22: list_P5464809261938338413at_nat] :
% 2.86/3.13 ( A2
% 2.86/3.13 != ( cons_P3940603068885512221at_nat @ E @ Z22 ) )
% 2.86/3.13 => ~ ! [Z1: produc3843707927480180839at_nat,Z22: list_P5464809261938338413at_nat] :
% 2.86/3.13 ( ( A2
% 2.86/3.13 = ( cons_P3940603068885512221at_nat @ Z1 @ Z22 ) )
% 2.86/3.13 => ~ ( member8757157785044589968at_nat @ E @ ( set_Pr3765526544606949372at_nat @ Z22 ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % list.set_cases
% 2.86/3.13 thf(fact_4534_list_Oset__cases,axiom,
% 2.86/3.13 ! [E: product_prod_nat_nat,A2: list_P6011104703257516679at_nat] :
% 2.86/3.13 ( ( member8440522571783428010at_nat @ E @ ( set_Pr5648618587558075414at_nat @ A2 ) )
% 2.86/3.13 => ( ! [Z22: list_P6011104703257516679at_nat] :
% 2.86/3.13 ( A2
% 2.86/3.13 != ( cons_P6512896166579812791at_nat @ E @ Z22 ) )
% 2.86/3.13 => ~ ! [Z1: product_prod_nat_nat,Z22: list_P6011104703257516679at_nat] :
% 2.86/3.13 ( ( A2
% 2.86/3.13 = ( cons_P6512896166579812791at_nat @ Z1 @ Z22 ) )
% 2.86/3.13 => ~ ( member8440522571783428010at_nat @ E @ ( set_Pr5648618587558075414at_nat @ Z22 ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % list.set_cases
% 2.86/3.13 thf(fact_4535_list_Oset__cases,axiom,
% 2.86/3.13 ! [E: produc3658429121746597890et_nat > $o,A2: list_P7985473006766602707_nat_o] :
% 2.86/3.13 ( ( member6576561426505652726_nat_o @ E @ ( set_Pr400311997697478754_nat_o @ A2 ) )
% 2.86/3.13 => ( ! [Z22: list_P7985473006766602707_nat_o] :
% 2.86/3.13 ( A2
% 2.86/3.13 != ( cons_P6219271836124797827_nat_o @ E @ Z22 ) )
% 2.86/3.13 => ~ ! [Z1: produc3658429121746597890et_nat > $o,Z22: list_P7985473006766602707_nat_o] :
% 2.86/3.13 ( ( A2
% 2.86/3.13 = ( cons_P6219271836124797827_nat_o @ Z1 @ Z22 ) )
% 2.86/3.13 => ~ ( member6576561426505652726_nat_o @ E @ ( set_Pr400311997697478754_nat_o @ Z22 ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % list.set_cases
% 2.86/3.13 thf(fact_4536_list_Oset__cases,axiom,
% 2.86/3.13 ! [E: int,A2: list_int] :
% 2.86/3.13 ( ( member_int @ E @ ( set_int2 @ A2 ) )
% 2.86/3.13 => ( ! [Z22: list_int] :
% 2.86/3.13 ( A2
% 2.86/3.13 != ( cons_int @ E @ Z22 ) )
% 2.86/3.13 => ~ ! [Z1: int,Z22: list_int] :
% 2.86/3.13 ( ( A2
% 2.86/3.13 = ( cons_int @ Z1 @ Z22 ) )
% 2.86/3.13 => ~ ( member_int @ E @ ( set_int2 @ Z22 ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % list.set_cases
% 2.86/3.13 thf(fact_4537_list_Oset__cases,axiom,
% 2.86/3.13 ! [E: nat,A2: list_nat] :
% 2.86/3.13 ( ( member_nat @ E @ ( set_nat2 @ A2 ) )
% 2.86/3.13 => ( ! [Z22: list_nat] :
% 2.86/3.13 ( A2
% 2.86/3.13 != ( cons_nat @ E @ Z22 ) )
% 2.86/3.13 => ~ ! [Z1: nat,Z22: list_nat] :
% 2.86/3.13 ( ( A2
% 2.86/3.13 = ( cons_nat @ Z1 @ Z22 ) )
% 2.86/3.13 => ~ ( member_nat @ E @ ( set_nat2 @ Z22 ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % list.set_cases
% 2.86/3.13 thf(fact_4538_list_Oset__cases,axiom,
% 2.86/3.13 ! [E: produc6575502325842934193n_assn,A2: list_P8527749157015355191n_assn] :
% 2.86/3.13 ( ( member7957490590177025114n_assn @ E @ ( set_Pr1139785259514867910n_assn @ A2 ) )
% 2.86/3.13 => ( ! [Z22: list_P8527749157015355191n_assn] :
% 2.86/3.13 ( A2
% 2.86/3.13 != ( cons_P2971678138204555879n_assn @ E @ Z22 ) )
% 2.86/3.13 => ~ ! [Z1: produc6575502325842934193n_assn,Z22: list_P8527749157015355191n_assn] :
% 2.86/3.13 ( ( A2
% 2.86/3.13 = ( cons_P2971678138204555879n_assn @ Z1 @ Z22 ) )
% 2.86/3.13 => ~ ( member7957490590177025114n_assn @ E @ ( set_Pr1139785259514867910n_assn @ Z22 ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % list.set_cases
% 2.86/3.13 thf(fact_4539_list_Oset__intros_I1_J,axiom,
% 2.86/3.13 ! [X21: produc3843707927480180839at_nat,X222: list_P5464809261938338413at_nat] : ( member8757157785044589968at_nat @ X21 @ ( set_Pr3765526544606949372at_nat @ ( cons_P3940603068885512221at_nat @ X21 @ X222 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % list.set_intros(1)
% 2.86/3.13 thf(fact_4540_list_Oset__intros_I1_J,axiom,
% 2.86/3.13 ! [X21: product_prod_nat_nat,X222: list_P6011104703257516679at_nat] : ( member8440522571783428010at_nat @ X21 @ ( set_Pr5648618587558075414at_nat @ ( cons_P6512896166579812791at_nat @ X21 @ X222 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % list.set_intros(1)
% 2.86/3.13 thf(fact_4541_list_Oset__intros_I1_J,axiom,
% 2.86/3.13 ! [X21: produc3658429121746597890et_nat > $o,X222: list_P7985473006766602707_nat_o] : ( member6576561426505652726_nat_o @ X21 @ ( set_Pr400311997697478754_nat_o @ ( cons_P6219271836124797827_nat_o @ X21 @ X222 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % list.set_intros(1)
% 2.86/3.13 thf(fact_4542_list_Oset__intros_I1_J,axiom,
% 2.86/3.13 ! [X21: int,X222: list_int] : ( member_int @ X21 @ ( set_int2 @ ( cons_int @ X21 @ X222 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % list.set_intros(1)
% 2.86/3.13 thf(fact_4543_list_Oset__intros_I1_J,axiom,
% 2.86/3.13 ! [X21: nat,X222: list_nat] : ( member_nat @ X21 @ ( set_nat2 @ ( cons_nat @ X21 @ X222 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % list.set_intros(1)
% 2.86/3.13 thf(fact_4544_list_Oset__intros_I1_J,axiom,
% 2.86/3.13 ! [X21: produc6575502325842934193n_assn,X222: list_P8527749157015355191n_assn] : ( member7957490590177025114n_assn @ X21 @ ( set_Pr1139785259514867910n_assn @ ( cons_P2971678138204555879n_assn @ X21 @ X222 ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % list.set_intros(1)
% 2.86/3.13 thf(fact_4545_list_Oset__intros_I2_J,axiom,
% 2.86/3.13 ! [Y: produc3843707927480180839at_nat,X222: list_P5464809261938338413at_nat,X21: produc3843707927480180839at_nat] :
% 2.86/3.13 ( ( member8757157785044589968at_nat @ Y @ ( set_Pr3765526544606949372at_nat @ X222 ) )
% 2.86/3.13 => ( member8757157785044589968at_nat @ Y @ ( set_Pr3765526544606949372at_nat @ ( cons_P3940603068885512221at_nat @ X21 @ X222 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % list.set_intros(2)
% 2.86/3.13 thf(fact_4546_list_Oset__intros_I2_J,axiom,
% 2.86/3.13 ! [Y: product_prod_nat_nat,X222: list_P6011104703257516679at_nat,X21: product_prod_nat_nat] :
% 2.86/3.13 ( ( member8440522571783428010at_nat @ Y @ ( set_Pr5648618587558075414at_nat @ X222 ) )
% 2.86/3.13 => ( member8440522571783428010at_nat @ Y @ ( set_Pr5648618587558075414at_nat @ ( cons_P6512896166579812791at_nat @ X21 @ X222 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % list.set_intros(2)
% 2.86/3.13 thf(fact_4547_list_Oset__intros_I2_J,axiom,
% 2.86/3.13 ! [Y: produc3658429121746597890et_nat > $o,X222: list_P7985473006766602707_nat_o,X21: produc3658429121746597890et_nat > $o] :
% 2.86/3.13 ( ( member6576561426505652726_nat_o @ Y @ ( set_Pr400311997697478754_nat_o @ X222 ) )
% 2.86/3.13 => ( member6576561426505652726_nat_o @ Y @ ( set_Pr400311997697478754_nat_o @ ( cons_P6219271836124797827_nat_o @ X21 @ X222 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % list.set_intros(2)
% 2.86/3.13 thf(fact_4548_list_Oset__intros_I2_J,axiom,
% 2.86/3.13 ! [Y: int,X222: list_int,X21: int] :
% 2.86/3.13 ( ( member_int @ Y @ ( set_int2 @ X222 ) )
% 2.86/3.13 => ( member_int @ Y @ ( set_int2 @ ( cons_int @ X21 @ X222 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % list.set_intros(2)
% 2.86/3.13 thf(fact_4549_list_Oset__intros_I2_J,axiom,
% 2.86/3.13 ! [Y: nat,X222: list_nat,X21: nat] :
% 2.86/3.13 ( ( member_nat @ Y @ ( set_nat2 @ X222 ) )
% 2.86/3.13 => ( member_nat @ Y @ ( set_nat2 @ ( cons_nat @ X21 @ X222 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % list.set_intros(2)
% 2.86/3.13 thf(fact_4550_list_Oset__intros_I2_J,axiom,
% 2.86/3.13 ! [Y: produc6575502325842934193n_assn,X222: list_P8527749157015355191n_assn,X21: produc6575502325842934193n_assn] :
% 2.86/3.13 ( ( member7957490590177025114n_assn @ Y @ ( set_Pr1139785259514867910n_assn @ X222 ) )
% 2.86/3.13 => ( member7957490590177025114n_assn @ Y @ ( set_Pr1139785259514867910n_assn @ ( cons_P2971678138204555879n_assn @ X21 @ X222 ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % list.set_intros(2)
% 2.86/3.13 thf(fact_4551_distinct__length__2__or__more,axiom,
% 2.86/3.13 ! [A2: int,B2: int,Xs: list_int] :
% 2.86/3.13 ( ( distinct_int @ ( cons_int @ A2 @ ( cons_int @ B2 @ Xs ) ) )
% 2.86/3.13 = ( ( A2 != B2 )
% 2.86/3.13 & ( distinct_int @ ( cons_int @ A2 @ Xs ) )
% 2.86/3.13 & ( distinct_int @ ( cons_int @ B2 @ Xs ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % distinct_length_2_or_more
% 2.86/3.13 thf(fact_4552_distinct__length__2__or__more,axiom,
% 2.86/3.13 ! [A2: nat,B2: nat,Xs: list_nat] :
% 2.86/3.13 ( ( distinct_nat @ ( cons_nat @ A2 @ ( cons_nat @ B2 @ Xs ) ) )
% 2.86/3.13 = ( ( A2 != B2 )
% 2.86/3.13 & ( distinct_nat @ ( cons_nat @ A2 @ Xs ) )
% 2.86/3.13 & ( distinct_nat @ ( cons_nat @ B2 @ Xs ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % distinct_length_2_or_more
% 2.86/3.13 thf(fact_4553_distinct__length__2__or__more,axiom,
% 2.86/3.13 ! [A2: produc6575502325842934193n_assn,B2: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn] :
% 2.86/3.13 ( ( distin4809818325527169450n_assn @ ( cons_P2971678138204555879n_assn @ A2 @ ( cons_P2971678138204555879n_assn @ B2 @ Xs ) ) )
% 2.86/3.13 = ( ( A2 != B2 )
% 2.86/3.13 & ( distin4809818325527169450n_assn @ ( cons_P2971678138204555879n_assn @ A2 @ Xs ) )
% 2.86/3.13 & ( distin4809818325527169450n_assn @ ( cons_P2971678138204555879n_assn @ B2 @ Xs ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % distinct_length_2_or_more
% 2.86/3.13 thf(fact_4554_remove1_Osimps_I2_J,axiom,
% 2.86/3.13 ! [X: int,Y: int,Xs: list_int] :
% 2.86/3.13 ( ( ( X = Y )
% 2.86/3.13 => ( ( remove1_int @ X @ ( cons_int @ Y @ Xs ) )
% 2.86/3.13 = Xs ) )
% 2.86/3.13 & ( ( X != Y )
% 2.86/3.13 => ( ( remove1_int @ X @ ( cons_int @ Y @ Xs ) )
% 2.86/3.13 = ( cons_int @ Y @ ( remove1_int @ X @ Xs ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % remove1.simps(2)
% 2.86/3.13 thf(fact_4555_remove1_Osimps_I2_J,axiom,
% 2.86/3.13 ! [X: nat,Y: nat,Xs: list_nat] :
% 2.86/3.13 ( ( ( X = Y )
% 2.86/3.13 => ( ( remove1_nat @ X @ ( cons_nat @ Y @ Xs ) )
% 2.86/3.13 = Xs ) )
% 2.86/3.13 & ( ( X != Y )
% 2.86/3.13 => ( ( remove1_nat @ X @ ( cons_nat @ Y @ Xs ) )
% 2.86/3.13 = ( cons_nat @ Y @ ( remove1_nat @ X @ Xs ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % remove1.simps(2)
% 2.86/3.13 thf(fact_4556_remove1_Osimps_I2_J,axiom,
% 2.86/3.13 ! [X: produc6575502325842934193n_assn,Y: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn] :
% 2.86/3.13 ( ( ( X = Y )
% 2.86/3.13 => ( ( remove1670527618125605709n_assn @ X @ ( cons_P2971678138204555879n_assn @ Y @ Xs ) )
% 2.86/3.13 = Xs ) )
% 2.86/3.13 & ( ( X != Y )
% 2.86/3.13 => ( ( remove1670527618125605709n_assn @ X @ ( cons_P2971678138204555879n_assn @ Y @ Xs ) )
% 2.86/3.13 = ( cons_P2971678138204555879n_assn @ Y @ ( remove1670527618125605709n_assn @ X @ Xs ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % remove1.simps(2)
% 2.86/3.13 thf(fact_4557_total__onI,axiom,
% 2.86/3.13 ! [A: set_se7855581050983116737at_nat,R2: set_Pr4329608150637261639at_nat] :
% 2.86/3.13 ( ! [X3: set_Pr1261947904930325089at_nat,Y2: set_Pr1261947904930325089at_nat] :
% 2.86/3.13 ( ( member2643936169264416010at_nat @ X3 @ A )
% 2.86/3.13 => ( ( member2643936169264416010at_nat @ Y2 @ A )
% 2.86/3.13 => ( ( X3 != Y2 )
% 2.86/3.13 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y2 ) @ R2 )
% 2.86/3.13 | ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y2 @ X3 ) @ R2 ) ) ) ) )
% 2.86/3.13 => ( total_7212417256332265445at_nat @ A @ R2 ) ) ).
% 2.86/3.13
% 2.86/3.13 % total_onI
% 2.86/3.13 thf(fact_4558_total__onI,axiom,
% 2.86/3.13 ! [A: set_Pr4329608150637261639at_nat,R2: set_Pr5564308138774400199at_nat] :
% 2.86/3.13 ( ! [X3: produc3843707927480180839at_nat,Y2: produc3843707927480180839at_nat] :
% 2.86/3.13 ( ( member8757157785044589968at_nat @ X3 @ A )
% 2.86/3.13 => ( ( member8757157785044589968at_nat @ Y2 @ A )
% 2.86/3.13 => ( ( X3 != Y2 )
% 2.86/3.13 => ( ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ X3 @ Y2 ) @ R2 )
% 2.86/3.13 | ( member6009668390874684176at_nat @ ( produc2335810615602371415at_nat @ Y2 @ X3 ) @ R2 ) ) ) ) )
% 2.86/3.13 => ( total_1513685709984341995at_nat @ A @ R2 ) ) ).
% 2.86/3.13
% 2.86/3.13 % total_onI
% 2.86/3.13 thf(fact_4559_total__onI,axiom,
% 2.86/3.13 ! [A: set_Pr1261947904930325089at_nat,R2: set_Pr8693737435421807431at_nat] :
% 2.86/3.13 ( ! [X3: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 2.86/3.13 ( ( member8440522571783428010at_nat @ X3 @ A )
% 2.86/3.13 => ( ( member8440522571783428010at_nat @ Y2 @ A )
% 2.86/3.13 => ( ( X3 != Y2 )
% 2.86/3.13 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X3 @ Y2 ) @ R2 )
% 2.86/3.13 | ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ Y2 @ X3 ) @ R2 ) ) ) ) )
% 2.86/3.13 => ( total_3592101749530773125at_nat @ A @ R2 ) ) ).
% 2.86/3.13
% 2.86/3.13 % total_onI
% 2.86/3.13 thf(fact_4560_total__onI,axiom,
% 2.86/3.13 ! [A: set_nat,R2: set_Pr1261947904930325089at_nat] :
% 2.86/3.13 ( ! [X3: nat,Y2: nat] :
% 2.86/3.13 ( ( member_nat @ X3 @ A )
% 2.86/3.13 => ( ( member_nat @ Y2 @ A )
% 2.86/3.13 => ( ( X3 != Y2 )
% 2.86/3.13 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y2 ) @ R2 )
% 2.86/3.13 | ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y2 @ X3 ) @ R2 ) ) ) ) )
% 2.86/3.13 => ( total_on_nat @ A @ R2 ) ) ).
% 2.86/3.13
% 2.86/3.13 % total_onI
% 2.86/3.13 thf(fact_4561_total__onI,axiom,
% 2.86/3.13 ! [A: set_int,R2: set_Pr958786334691620121nt_int] :
% 2.86/3.13 ( ! [X3: int,Y2: int] :
% 2.86/3.13 ( ( member_int @ X3 @ A )
% 2.86/3.13 => ( ( member_int @ Y2 @ A )
% 2.86/3.13 => ( ( X3 != Y2 )
% 2.86/3.13 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y2 ) @ R2 )
% 2.86/3.13 | ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y2 @ X3 ) @ R2 ) ) ) ) )
% 2.86/3.13 => ( total_on_int @ A @ R2 ) ) ).
% 2.86/3.13
% 2.86/3.13 % total_onI
% 2.86/3.13 thf(fact_4562_total__onI,axiom,
% 2.86/3.13 ! [A: set_Pr4532377907799695533_nat_o,R2: set_Pr2161125870931222855_nat_o] :
% 2.86/3.13 ( ! [X3: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat > $o] :
% 2.86/3.13 ( ( member6576561426505652726_nat_o @ X3 @ A )
% 2.86/3.13 => ( ( member6576561426505652726_nat_o @ Y2 @ A )
% 2.86/3.13 => ( ( X3 != Y2 )
% 2.86/3.13 => ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ X3 @ Y2 ) @ R2 )
% 2.86/3.13 | ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ Y2 @ X3 ) @ R2 ) ) ) ) )
% 2.86/3.13 => ( total_7429123086324524369_nat_o @ A @ R2 ) ) ).
% 2.86/3.13
% 2.86/3.13 % total_onI
% 2.86/3.13 thf(fact_4563_total__on__def,axiom,
% 2.86/3.13 ( total_7212417256332265445at_nat
% 2.86/3.13 = ( ^ [A5: set_se7855581050983116737at_nat,R4: set_Pr4329608150637261639at_nat] :
% 2.86/3.13 ! [X2: set_Pr1261947904930325089at_nat] :
% 2.86/3.13 ( ( member2643936169264416010at_nat @ X2 @ A5 )
% 2.86/3.13 => ! [Y5: set_Pr1261947904930325089at_nat] :
% 2.86/3.13 ( ( member2643936169264416010at_nat @ Y5 @ A5 )
% 2.86/3.13 => ( ( X2 != Y5 )
% 2.86/3.13 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y5 ) @ R4 )
% 2.86/3.13 | ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y5 @ X2 ) @ R4 ) ) ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % total_on_def
% 2.86/3.13 thf(fact_4564_total__on__def,axiom,
% 2.86/3.13 ( total_on_nat
% 2.86/3.13 = ( ^ [A5: set_nat,R4: set_Pr1261947904930325089at_nat] :
% 2.86/3.13 ! [X2: nat] :
% 2.86/3.13 ( ( member_nat @ X2 @ A5 )
% 2.86/3.13 => ! [Y5: nat] :
% 2.86/3.13 ( ( member_nat @ Y5 @ A5 )
% 2.86/3.13 => ( ( X2 != Y5 )
% 2.86/3.13 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y5 ) @ R4 )
% 2.86/3.13 | ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y5 @ X2 ) @ R4 ) ) ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % total_on_def
% 2.86/3.13 thf(fact_4565_total__on__empty,axiom,
% 2.86/3.13 ! [R2: set_Pr5564308138774400199at_nat] : ( total_1513685709984341995at_nat @ bot_bo228742789529271731at_nat @ R2 ) ).
% 2.86/3.13
% 2.86/3.13 % total_on_empty
% 2.86/3.13 thf(fact_4566_total__on__empty,axiom,
% 2.86/3.13 ! [R2: set_Pr8693737435421807431at_nat] : ( total_3592101749530773125at_nat @ bot_bo2099793752762293965at_nat @ R2 ) ).
% 2.86/3.13
% 2.86/3.13 % total_on_empty
% 2.86/3.13 thf(fact_4567_total__on__empty,axiom,
% 2.86/3.13 ! [R2: set_Product_prod_o_o] : ( total_on_o @ bot_bot_set_o @ R2 ) ).
% 2.86/3.13
% 2.86/3.13 % total_on_empty
% 2.86/3.13 thf(fact_4568_total__on__empty,axiom,
% 2.86/3.13 ! [R2: set_Pr1261947904930325089at_nat] : ( total_on_nat @ bot_bot_set_nat @ R2 ) ).
% 2.86/3.13
% 2.86/3.13 % total_on_empty
% 2.86/3.13 thf(fact_4569_total__on__empty,axiom,
% 2.86/3.13 ! [R2: set_Pr958786334691620121nt_int] : ( total_on_int @ bot_bot_set_int @ R2 ) ).
% 2.86/3.13
% 2.86/3.13 % total_on_empty
% 2.86/3.13 thf(fact_4570_removeAll_Osimps_I2_J,axiom,
% 2.86/3.13 ! [X: int,Y: int,Xs: list_int] :
% 2.86/3.13 ( ( ( X = Y )
% 2.86/3.13 => ( ( removeAll_int @ X @ ( cons_int @ Y @ Xs ) )
% 2.86/3.13 = ( removeAll_int @ X @ Xs ) ) )
% 2.86/3.13 & ( ( X != Y )
% 2.86/3.13 => ( ( removeAll_int @ X @ ( cons_int @ Y @ Xs ) )
% 2.86/3.13 = ( cons_int @ Y @ ( removeAll_int @ X @ Xs ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % removeAll.simps(2)
% 2.86/3.13 thf(fact_4571_removeAll_Osimps_I2_J,axiom,
% 2.86/3.13 ! [X: nat,Y: nat,Xs: list_nat] :
% 2.86/3.13 ( ( ( X = Y )
% 2.86/3.13 => ( ( removeAll_nat @ X @ ( cons_nat @ Y @ Xs ) )
% 2.86/3.13 = ( removeAll_nat @ X @ Xs ) ) )
% 2.86/3.13 & ( ( X != Y )
% 2.86/3.13 => ( ( removeAll_nat @ X @ ( cons_nat @ Y @ Xs ) )
% 2.86/3.13 = ( cons_nat @ Y @ ( removeAll_nat @ X @ Xs ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % removeAll.simps(2)
% 2.86/3.13 thf(fact_4572_removeAll_Osimps_I2_J,axiom,
% 2.86/3.13 ! [X: produc6575502325842934193n_assn,Y: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn] :
% 2.86/3.13 ( ( ( X = Y )
% 2.86/3.13 => ( ( remove1763081955827946941n_assn @ X @ ( cons_P2971678138204555879n_assn @ Y @ Xs ) )
% 2.86/3.13 = ( remove1763081955827946941n_assn @ X @ Xs ) ) )
% 2.86/3.13 & ( ( X != Y )
% 2.86/3.13 => ( ( remove1763081955827946941n_assn @ X @ ( cons_P2971678138204555879n_assn @ Y @ Xs ) )
% 2.86/3.13 = ( cons_P2971678138204555879n_assn @ Y @ ( remove1763081955827946941n_assn @ X @ Xs ) ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % removeAll.simps(2)
% 2.86/3.13 thf(fact_4573_zipf_Osimps_I2_J,axiom,
% 2.86/3.13 ! [F4: int > int > int,A2: int,As2: list_int,B2: int,Bs: list_int] :
% 2.86/3.13 ( ( zipf_int_int_int @ F4 @ ( cons_int @ A2 @ As2 ) @ ( cons_int @ B2 @ Bs ) )
% 2.86/3.13 = ( cons_int @ ( F4 @ A2 @ B2 ) @ ( zipf_int_int_int @ F4 @ As2 @ Bs ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % zipf.simps(2)
% 2.86/3.13 thf(fact_4574_zipf_Osimps_I2_J,axiom,
% 2.86/3.13 ! [F4: int > int > nat,A2: int,As2: list_int,B2: int,Bs: list_int] :
% 2.86/3.13 ( ( zipf_int_int_nat @ F4 @ ( cons_int @ A2 @ As2 ) @ ( cons_int @ B2 @ Bs ) )
% 2.86/3.13 = ( cons_nat @ ( F4 @ A2 @ B2 ) @ ( zipf_int_int_nat @ F4 @ As2 @ Bs ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % zipf.simps(2)
% 2.86/3.13 thf(fact_4575_zipf_Osimps_I2_J,axiom,
% 2.86/3.13 ! [F4: int > nat > int,A2: int,As2: list_int,B2: nat,Bs: list_nat] :
% 2.86/3.13 ( ( zipf_int_nat_int @ F4 @ ( cons_int @ A2 @ As2 ) @ ( cons_nat @ B2 @ Bs ) )
% 2.86/3.13 = ( cons_int @ ( F4 @ A2 @ B2 ) @ ( zipf_int_nat_int @ F4 @ As2 @ Bs ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % zipf.simps(2)
% 2.86/3.13 thf(fact_4576_zipf_Osimps_I2_J,axiom,
% 2.86/3.13 ! [F4: int > nat > nat,A2: int,As2: list_int,B2: nat,Bs: list_nat] :
% 2.86/3.13 ( ( zipf_int_nat_nat @ F4 @ ( cons_int @ A2 @ As2 ) @ ( cons_nat @ B2 @ Bs ) )
% 2.86/3.13 = ( cons_nat @ ( F4 @ A2 @ B2 ) @ ( zipf_int_nat_nat @ F4 @ As2 @ Bs ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % zipf.simps(2)
% 2.86/3.13 thf(fact_4577_zipf_Osimps_I2_J,axiom,
% 2.86/3.13 ! [F4: nat > int > int,A2: nat,As2: list_nat,B2: int,Bs: list_int] :
% 2.86/3.13 ( ( zipf_nat_int_int @ F4 @ ( cons_nat @ A2 @ As2 ) @ ( cons_int @ B2 @ Bs ) )
% 2.86/3.13 = ( cons_int @ ( F4 @ A2 @ B2 ) @ ( zipf_nat_int_int @ F4 @ As2 @ Bs ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % zipf.simps(2)
% 2.86/3.13 thf(fact_4578_zipf_Osimps_I2_J,axiom,
% 2.86/3.13 ! [F4: nat > int > nat,A2: nat,As2: list_nat,B2: int,Bs: list_int] :
% 2.86/3.13 ( ( zipf_nat_int_nat @ F4 @ ( cons_nat @ A2 @ As2 ) @ ( cons_int @ B2 @ Bs ) )
% 2.86/3.13 = ( cons_nat @ ( F4 @ A2 @ B2 ) @ ( zipf_nat_int_nat @ F4 @ As2 @ Bs ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % zipf.simps(2)
% 2.86/3.13 thf(fact_4579_zipf_Osimps_I2_J,axiom,
% 2.86/3.13 ! [F4: nat > nat > int,A2: nat,As2: list_nat,B2: nat,Bs: list_nat] :
% 2.86/3.13 ( ( zipf_nat_nat_int @ F4 @ ( cons_nat @ A2 @ As2 ) @ ( cons_nat @ B2 @ Bs ) )
% 2.86/3.13 = ( cons_int @ ( F4 @ A2 @ B2 ) @ ( zipf_nat_nat_int @ F4 @ As2 @ Bs ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % zipf.simps(2)
% 2.86/3.13 thf(fact_4580_zipf_Osimps_I2_J,axiom,
% 2.86/3.13 ! [F4: nat > nat > nat,A2: nat,As2: list_nat,B2: nat,Bs: list_nat] :
% 2.86/3.13 ( ( zipf_nat_nat_nat @ F4 @ ( cons_nat @ A2 @ As2 ) @ ( cons_nat @ B2 @ Bs ) )
% 2.86/3.13 = ( cons_nat @ ( F4 @ A2 @ B2 ) @ ( zipf_nat_nat_nat @ F4 @ As2 @ Bs ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % zipf.simps(2)
% 2.86/3.13 thf(fact_4581_zipf_Osimps_I2_J,axiom,
% 2.86/3.13 ! [F4: int > int > produc6575502325842934193n_assn,A2: int,As2: list_int,B2: int,Bs: list_int] :
% 2.86/3.13 ( ( zipf_i7756021159461276697n_assn @ F4 @ ( cons_int @ A2 @ As2 ) @ ( cons_int @ B2 @ Bs ) )
% 2.86/3.13 = ( cons_P2971678138204555879n_assn @ ( F4 @ A2 @ B2 ) @ ( zipf_i7756021159461276697n_assn @ F4 @ As2 @ Bs ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % zipf.simps(2)
% 2.86/3.13 thf(fact_4582_zipf_Osimps_I2_J,axiom,
% 2.86/3.13 ! [F4: int > nat > produc6575502325842934193n_assn,A2: int,As2: list_int,B2: nat,Bs: list_nat] :
% 2.86/3.13 ( ( zipf_i5995984495708165493n_assn @ F4 @ ( cons_int @ A2 @ As2 ) @ ( cons_nat @ B2 @ Bs ) )
% 2.86/3.13 = ( cons_P2971678138204555879n_assn @ ( F4 @ A2 @ B2 ) @ ( zipf_i5995984495708165493n_assn @ F4 @ As2 @ Bs ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % zipf.simps(2)
% 2.86/3.13 thf(fact_4583_null__rec_I1_J,axiom,
% 2.86/3.13 ! [X: int,Xs: list_int] :
% 2.86/3.13 ~ ( null_int @ ( cons_int @ X @ Xs ) ) ).
% 2.86/3.13
% 2.86/3.13 % null_rec(1)
% 2.86/3.13 thf(fact_4584_null__rec_I1_J,axiom,
% 2.86/3.13 ! [X: nat,Xs: list_nat] :
% 2.86/3.13 ~ ( null_nat @ ( cons_nat @ X @ Xs ) ) ).
% 2.86/3.13
% 2.86/3.13 % null_rec(1)
% 2.86/3.13 thf(fact_4585_null__rec_I1_J,axiom,
% 2.86/3.13 ! [X: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn] :
% 2.86/3.13 ~ ( null_P7596217980778516671n_assn @ ( cons_P2971678138204555879n_assn @ X @ Xs ) ) ).
% 2.86/3.13
% 2.86/3.13 % null_rec(1)
% 2.86/3.13 thf(fact_4586_length__Suc__conv,axiom,
% 2.86/3.13 ! [Xs: list_P8527749157015355191n_assn,N: nat] :
% 2.86/3.13 ( ( ( size_s6829681357464350627n_assn @ Xs )
% 2.86/3.13 = ( suc @ N ) )
% 2.86/3.13 = ( ? [Y5: produc6575502325842934193n_assn,Ys3: list_P8527749157015355191n_assn] :
% 2.86/3.13 ( ( Xs
% 2.86/3.13 = ( cons_P2971678138204555879n_assn @ Y5 @ Ys3 ) )
% 2.86/3.13 & ( ( size_s6829681357464350627n_assn @ Ys3 )
% 2.86/3.13 = N ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % length_Suc_conv
% 2.86/3.13 thf(fact_4587_length__Suc__conv,axiom,
% 2.86/3.13 ! [Xs: list_c,N: nat] :
% 2.86/3.13 ( ( ( size_size_list_c @ Xs )
% 2.86/3.13 = ( suc @ N ) )
% 2.86/3.13 = ( ? [Y5: c,Ys3: list_c] :
% 2.86/3.13 ( ( Xs
% 2.86/3.13 = ( cons_c @ Y5 @ Ys3 ) )
% 2.86/3.13 & ( ( size_size_list_c @ Ys3 )
% 2.86/3.13 = N ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % length_Suc_conv
% 2.86/3.13 thf(fact_4588_length__Suc__conv,axiom,
% 2.86/3.13 ! [Xs: list_d,N: nat] :
% 2.86/3.13 ( ( ( size_size_list_d @ Xs )
% 2.86/3.13 = ( suc @ N ) )
% 2.86/3.13 = ( ? [Y5: d,Ys3: list_d] :
% 2.86/3.13 ( ( Xs
% 2.86/3.13 = ( cons_d @ Y5 @ Ys3 ) )
% 2.86/3.13 & ( ( size_size_list_d @ Ys3 )
% 2.86/3.13 = N ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % length_Suc_conv
% 2.86/3.13 thf(fact_4589_length__Suc__conv,axiom,
% 2.86/3.13 ! [Xs: list_nat,N: nat] :
% 2.86/3.13 ( ( ( size_size_list_nat @ Xs )
% 2.86/3.13 = ( suc @ N ) )
% 2.86/3.13 = ( ? [Y5: nat,Ys3: list_nat] :
% 2.86/3.13 ( ( Xs
% 2.86/3.13 = ( cons_nat @ Y5 @ Ys3 ) )
% 2.86/3.13 & ( ( size_size_list_nat @ Ys3 )
% 2.86/3.13 = N ) ) ) ) ).
% 2.86/3.13
% 2.86/3.13 % length_Suc_conv
% 2.86/3.13 thf(fact_4590_length__Suc__conv,axiom,
% 2.86/3.13 ! [Xs: list_int,N: nat] :
% 2.86/3.13 ( ( ( size_size_list_int @ Xs )
% 2.86/3.13 = ( suc @ N ) )
% 2.86/3.13 = ( ? [Y5: int,Ys3: list_int] :
% 2.86/3.13 ( ( Xs
% 2.86/3.13 = ( cons_int @ Y5 @ Ys3 ) )
% 2.86/3.13 & ( ( size_size_list_int @ Ys3 )
% 2.86/3.14 = N ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % length_Suc_conv
% 2.86/3.14 thf(fact_4591_Suc__length__conv,axiom,
% 2.86/3.14 ! [N: nat,Xs: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( ( suc @ N )
% 2.86/3.14 = ( size_s6829681357464350627n_assn @ Xs ) )
% 2.86/3.14 = ( ? [Y5: produc6575502325842934193n_assn,Ys3: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( Xs
% 2.86/3.14 = ( cons_P2971678138204555879n_assn @ Y5 @ Ys3 ) )
% 2.86/3.14 & ( ( size_s6829681357464350627n_assn @ Ys3 )
% 2.86/3.14 = N ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % Suc_length_conv
% 2.86/3.14 thf(fact_4592_Suc__length__conv,axiom,
% 2.86/3.14 ! [N: nat,Xs: list_c] :
% 2.86/3.14 ( ( ( suc @ N )
% 2.86/3.14 = ( size_size_list_c @ Xs ) )
% 2.86/3.14 = ( ? [Y5: c,Ys3: list_c] :
% 2.86/3.14 ( ( Xs
% 2.86/3.14 = ( cons_c @ Y5 @ Ys3 ) )
% 2.86/3.14 & ( ( size_size_list_c @ Ys3 )
% 2.86/3.14 = N ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % Suc_length_conv
% 2.86/3.14 thf(fact_4593_Suc__length__conv,axiom,
% 2.86/3.14 ! [N: nat,Xs: list_d] :
% 2.86/3.14 ( ( ( suc @ N )
% 2.86/3.14 = ( size_size_list_d @ Xs ) )
% 2.86/3.14 = ( ? [Y5: d,Ys3: list_d] :
% 2.86/3.14 ( ( Xs
% 2.86/3.14 = ( cons_d @ Y5 @ Ys3 ) )
% 2.86/3.14 & ( ( size_size_list_d @ Ys3 )
% 2.86/3.14 = N ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % Suc_length_conv
% 2.86/3.14 thf(fact_4594_Suc__length__conv,axiom,
% 2.86/3.14 ! [N: nat,Xs: list_nat] :
% 2.86/3.14 ( ( ( suc @ N )
% 2.86/3.14 = ( size_size_list_nat @ Xs ) )
% 2.86/3.14 = ( ? [Y5: nat,Ys3: list_nat] :
% 2.86/3.14 ( ( Xs
% 2.86/3.14 = ( cons_nat @ Y5 @ Ys3 ) )
% 2.86/3.14 & ( ( size_size_list_nat @ Ys3 )
% 2.86/3.14 = N ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % Suc_length_conv
% 2.86/3.14 thf(fact_4595_Suc__length__conv,axiom,
% 2.86/3.14 ! [N: nat,Xs: list_int] :
% 2.86/3.14 ( ( ( suc @ N )
% 2.86/3.14 = ( size_size_list_int @ Xs ) )
% 2.86/3.14 = ( ? [Y5: int,Ys3: list_int] :
% 2.86/3.14 ( ( Xs
% 2.86/3.14 = ( cons_int @ Y5 @ Ys3 ) )
% 2.86/3.14 & ( ( size_size_list_int @ Ys3 )
% 2.86/3.14 = N ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % Suc_length_conv
% 2.86/3.14 thf(fact_4596_set__subset__Cons,axiom,
% 2.86/3.14 ! [Xs: list_int,X: int] : ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ ( set_int2 @ ( cons_int @ X @ Xs ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % set_subset_Cons
% 2.86/3.14 thf(fact_4597_set__subset__Cons,axiom,
% 2.86/3.14 ! [Xs: list_P8527749157015355191n_assn,X: produc6575502325842934193n_assn] : ( ord_le171416862856029873n_assn @ ( set_Pr1139785259514867910n_assn @ Xs ) @ ( set_Pr1139785259514867910n_assn @ ( cons_P2971678138204555879n_assn @ X @ Xs ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % set_subset_Cons
% 2.86/3.14 thf(fact_4598_set__subset__Cons,axiom,
% 2.86/3.14 ! [Xs: list_nat,X: nat] : ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ ( set_nat2 @ ( cons_nat @ X @ Xs ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % set_subset_Cons
% 2.86/3.14 thf(fact_4599_mono__Field,axiom,
% 2.86/3.14 ! [R2: set_Product_prod_o_o,S3: set_Product_prod_o_o] :
% 2.86/3.14 ( ( ord_le192195778054999463od_o_o @ R2 @ S3 )
% 2.86/3.14 => ( ord_less_eq_set_o @ ( field_o @ R2 ) @ ( field_o @ S3 ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % mono_Field
% 2.86/3.14 thf(fact_4600_mono__Field,axiom,
% 2.86/3.14 ! [R2: set_Pr1261947904930325089at_nat,S3: set_Pr1261947904930325089at_nat] :
% 2.86/3.14 ( ( ord_le3146513528884898305at_nat @ R2 @ S3 )
% 2.86/3.14 => ( ord_less_eq_set_nat @ ( field_nat @ R2 ) @ ( field_nat @ S3 ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % mono_Field
% 2.86/3.14 thf(fact_4601_impossible__Cons,axiom,
% 2.86/3.14 ! [Xs: list_P8527749157015355191n_assn,Ys: list_P8527749157015355191n_assn,X: produc6575502325842934193n_assn] :
% 2.86/3.14 ( ( ord_less_eq_nat @ ( size_s6829681357464350627n_assn @ Xs ) @ ( size_s6829681357464350627n_assn @ Ys ) )
% 2.86/3.14 => ( Xs
% 2.86/3.14 != ( cons_P2971678138204555879n_assn @ X @ Ys ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % impossible_Cons
% 2.86/3.14 thf(fact_4602_impossible__Cons,axiom,
% 2.86/3.14 ! [Xs: list_c,Ys: list_c,X: c] :
% 2.86/3.14 ( ( ord_less_eq_nat @ ( size_size_list_c @ Xs ) @ ( size_size_list_c @ Ys ) )
% 2.86/3.14 => ( Xs
% 2.86/3.14 != ( cons_c @ X @ Ys ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % impossible_Cons
% 2.86/3.14 thf(fact_4603_impossible__Cons,axiom,
% 2.86/3.14 ! [Xs: list_d,Ys: list_d,X: d] :
% 2.86/3.14 ( ( ord_less_eq_nat @ ( size_size_list_d @ Xs ) @ ( size_size_list_d @ Ys ) )
% 2.86/3.14 => ( Xs
% 2.86/3.14 != ( cons_d @ X @ Ys ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % impossible_Cons
% 2.86/3.14 thf(fact_4604_impossible__Cons,axiom,
% 2.86/3.14 ! [Xs: list_nat,Ys: list_nat,X: nat] :
% 2.86/3.14 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_nat @ Ys ) )
% 2.86/3.14 => ( Xs
% 2.86/3.14 != ( cons_nat @ X @ Ys ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % impossible_Cons
% 2.86/3.14 thf(fact_4605_impossible__Cons,axiom,
% 2.86/3.14 ! [Xs: list_int,Ys: list_int,X: int] :
% 2.86/3.14 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ ( size_size_list_int @ Ys ) )
% 2.86/3.14 => ( Xs
% 2.86/3.14 != ( cons_int @ X @ Ys ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % impossible_Cons
% 2.86/3.14 thf(fact_4606_sorted2,axiom,
% 2.86/3.14 ! [X: nat,Y: nat,Zs: list_nat] :
% 2.86/3.14 ( ( sorted_wrt_nat @ ord_less_eq_nat @ ( cons_nat @ X @ ( cons_nat @ Y @ Zs ) ) )
% 2.86/3.14 = ( ( ord_less_eq_nat @ X @ Y )
% 2.86/3.14 & ( sorted_wrt_nat @ ord_less_eq_nat @ ( cons_nat @ Y @ Zs ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % sorted2
% 2.86/3.14 thf(fact_4607_sorted2,axiom,
% 2.86/3.14 ! [X: int,Y: int,Zs: list_int] :
% 2.86/3.14 ( ( sorted_wrt_int @ ord_less_eq_int @ ( cons_int @ X @ ( cons_int @ Y @ Zs ) ) )
% 2.86/3.14 = ( ( ord_less_eq_int @ X @ Y )
% 2.86/3.14 & ( sorted_wrt_int @ ord_less_eq_int @ ( cons_int @ Y @ Zs ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % sorted2
% 2.86/3.14 thf(fact_4608_distinct_Osimps_I2_J,axiom,
% 2.86/3.14 ! [X: produc3843707927480180839at_nat,Xs: list_P5464809261938338413at_nat] :
% 2.86/3.14 ( ( distin5355857245021852384at_nat @ ( cons_P3940603068885512221at_nat @ X @ Xs ) )
% 2.86/3.14 = ( ~ ( member8757157785044589968at_nat @ X @ ( set_Pr3765526544606949372at_nat @ Xs ) )
% 2.86/3.14 & ( distin5355857245021852384at_nat @ Xs ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % distinct.simps(2)
% 2.86/3.14 thf(fact_4609_distinct_Osimps_I2_J,axiom,
% 2.86/3.14 ! [X: product_prod_nat_nat,Xs: list_P6011104703257516679at_nat] :
% 2.86/3.14 ( ( distin6923225563576452346at_nat @ ( cons_P6512896166579812791at_nat @ X @ Xs ) )
% 2.86/3.14 = ( ~ ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 2.86/3.14 & ( distin6923225563576452346at_nat @ Xs ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % distinct.simps(2)
% 2.86/3.14 thf(fact_4610_distinct_Osimps_I2_J,axiom,
% 2.86/3.14 ! [X: produc3658429121746597890et_nat > $o,Xs: list_P7985473006766602707_nat_o] :
% 2.86/3.14 ( ( distin299582740263731014_nat_o @ ( cons_P6219271836124797827_nat_o @ X @ Xs ) )
% 2.86/3.14 = ( ~ ( member6576561426505652726_nat_o @ X @ ( set_Pr400311997697478754_nat_o @ Xs ) )
% 2.86/3.14 & ( distin299582740263731014_nat_o @ Xs ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % distinct.simps(2)
% 2.86/3.14 thf(fact_4611_distinct_Osimps_I2_J,axiom,
% 2.86/3.14 ! [X: int,Xs: list_int] :
% 2.86/3.14 ( ( distinct_int @ ( cons_int @ X @ Xs ) )
% 2.86/3.14 = ( ~ ( member_int @ X @ ( set_int2 @ Xs ) )
% 2.86/3.14 & ( distinct_int @ Xs ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % distinct.simps(2)
% 2.86/3.14 thf(fact_4612_distinct_Osimps_I2_J,axiom,
% 2.86/3.14 ! [X: nat,Xs: list_nat] :
% 2.86/3.14 ( ( distinct_nat @ ( cons_nat @ X @ Xs ) )
% 2.86/3.14 = ( ~ ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 2.86/3.14 & ( distinct_nat @ Xs ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % distinct.simps(2)
% 2.86/3.14 thf(fact_4613_distinct_Osimps_I2_J,axiom,
% 2.86/3.14 ! [X: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( distin4809818325527169450n_assn @ ( cons_P2971678138204555879n_assn @ X @ Xs ) )
% 2.86/3.14 = ( ~ ( member7957490590177025114n_assn @ X @ ( set_Pr1139785259514867910n_assn @ Xs ) )
% 2.86/3.14 & ( distin4809818325527169450n_assn @ Xs ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % distinct.simps(2)
% 2.86/3.14 thf(fact_4614_list__update__code_I2_J,axiom,
% 2.86/3.14 ! [X: int,Xs: list_int,Y: int] :
% 2.86/3.14 ( ( list_update_int @ ( cons_int @ X @ Xs ) @ zero_zero_nat @ Y )
% 2.86/3.14 = ( cons_int @ Y @ Xs ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_update_code(2)
% 2.86/3.14 thf(fact_4615_list__update__code_I2_J,axiom,
% 2.86/3.14 ! [X: nat,Xs: list_nat,Y: nat] :
% 2.86/3.14 ( ( list_update_nat @ ( cons_nat @ X @ Xs ) @ zero_zero_nat @ Y )
% 2.86/3.14 = ( cons_nat @ Y @ Xs ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_update_code(2)
% 2.86/3.14 thf(fact_4616_list__update__code_I2_J,axiom,
% 2.86/3.14 ! [X: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn,Y: produc6575502325842934193n_assn] :
% 2.86/3.14 ( ( list_u4534839942911652127n_assn @ ( cons_P2971678138204555879n_assn @ X @ Xs ) @ zero_zero_nat @ Y )
% 2.86/3.14 = ( cons_P2971678138204555879n_assn @ Y @ Xs ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_update_code(2)
% 2.86/3.14 thf(fact_4617_list__update__code_I2_J,axiom,
% 2.86/3.14 ! [X: c,Xs: list_c,Y: c] :
% 2.86/3.14 ( ( list_update_c @ ( cons_c @ X @ Xs ) @ zero_zero_nat @ Y )
% 2.86/3.14 = ( cons_c @ Y @ Xs ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_update_code(2)
% 2.86/3.14 thf(fact_4618_list__update__code_I2_J,axiom,
% 2.86/3.14 ! [X: d,Xs: list_d,Y: d] :
% 2.86/3.14 ( ( list_update_d @ ( cons_d @ X @ Xs ) @ zero_zero_nat @ Y )
% 2.86/3.14 = ( cons_d @ Y @ Xs ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_update_code(2)
% 2.86/3.14 thf(fact_4619_list__update__code_I3_J,axiom,
% 2.86/3.14 ! [X: int,Xs: list_int,I: nat,Y: int] :
% 2.86/3.14 ( ( list_update_int @ ( cons_int @ X @ Xs ) @ ( suc @ I ) @ Y )
% 2.86/3.14 = ( cons_int @ X @ ( list_update_int @ Xs @ I @ Y ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_update_code(3)
% 2.86/3.14 thf(fact_4620_list__update__code_I3_J,axiom,
% 2.86/3.14 ! [X: nat,Xs: list_nat,I: nat,Y: nat] :
% 2.86/3.14 ( ( list_update_nat @ ( cons_nat @ X @ Xs ) @ ( suc @ I ) @ Y )
% 2.86/3.14 = ( cons_nat @ X @ ( list_update_nat @ Xs @ I @ Y ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_update_code(3)
% 2.86/3.14 thf(fact_4621_list__update__code_I3_J,axiom,
% 2.86/3.14 ! [X: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn,I: nat,Y: produc6575502325842934193n_assn] :
% 2.86/3.14 ( ( list_u4534839942911652127n_assn @ ( cons_P2971678138204555879n_assn @ X @ Xs ) @ ( suc @ I ) @ Y )
% 2.86/3.14 = ( cons_P2971678138204555879n_assn @ X @ ( list_u4534839942911652127n_assn @ Xs @ I @ Y ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_update_code(3)
% 2.86/3.14 thf(fact_4622_list__update__code_I3_J,axiom,
% 2.86/3.14 ! [X: c,Xs: list_c,I: nat,Y: c] :
% 2.86/3.14 ( ( list_update_c @ ( cons_c @ X @ Xs ) @ ( suc @ I ) @ Y )
% 2.86/3.14 = ( cons_c @ X @ ( list_update_c @ Xs @ I @ Y ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_update_code(3)
% 2.86/3.14 thf(fact_4623_list__update__code_I3_J,axiom,
% 2.86/3.14 ! [X: d,Xs: list_d,I: nat,Y: d] :
% 2.86/3.14 ( ( list_update_d @ ( cons_d @ X @ Xs ) @ ( suc @ I ) @ Y )
% 2.86/3.14 = ( cons_d @ X @ ( list_update_d @ Xs @ I @ Y ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_update_code(3)
% 2.86/3.14 thf(fact_4624_listrel1I2,axiom,
% 2.86/3.14 ! [Xs: list_int,Ys: list_int,R2: set_Pr958786334691620121nt_int,X: int] :
% 2.86/3.14 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs @ Ys ) @ ( listrel1_int @ R2 ) )
% 2.86/3.14 => ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ ( cons_int @ X @ Xs ) @ ( cons_int @ X @ Ys ) ) @ ( listrel1_int @ R2 ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % listrel1I2
% 2.86/3.14 thf(fact_4625_listrel1I2,axiom,
% 2.86/3.14 ! [Xs: list_nat,Ys: list_nat,R2: set_Pr1261947904930325089at_nat,X: nat] :
% 2.86/3.14 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs @ Ys ) @ ( listrel1_nat @ R2 ) )
% 2.86/3.14 => ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ ( cons_nat @ X @ Xs ) @ ( cons_nat @ X @ Ys ) ) @ ( listrel1_nat @ R2 ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % listrel1I2
% 2.86/3.14 thf(fact_4626_listrel1I2,axiom,
% 2.86/3.14 ! [Xs: list_P8527749157015355191n_assn,Ys: list_P8527749157015355191n_assn,R2: set_Pr8116311503512020807n_assn,X: produc6575502325842934193n_assn] :
% 2.86/3.14 ( ( member3994142547374651152n_assn @ ( produc3014731801419794263n_assn @ Xs @ Ys ) @ ( listre4270255209692100112n_assn @ R2 ) )
% 2.86/3.14 => ( member3994142547374651152n_assn @ ( produc3014731801419794263n_assn @ ( cons_P2971678138204555879n_assn @ X @ Xs ) @ ( cons_P2971678138204555879n_assn @ X @ Ys ) ) @ ( listre4270255209692100112n_assn @ R2 ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % listrel1I2
% 2.86/3.14 thf(fact_4627_merge_Osimps_I3_J,axiom,
% 2.86/3.14 ! [X1: code_integer,X22: code_integer,L12: list_Code_integer,L23: list_Code_integer] :
% 2.86/3.14 ( ( ( ord_le6747313008572928689nteger @ X1 @ X22 )
% 2.86/3.14 => ( ( merge_Code_integer @ ( cons_Code_integer @ X1 @ L12 ) @ ( cons_Code_integer @ X22 @ L23 ) )
% 2.86/3.14 = ( cons_Code_integer @ X1 @ ( merge_Code_integer @ L12 @ ( cons_Code_integer @ X22 @ L23 ) ) ) ) )
% 2.86/3.14 & ( ~ ( ord_le6747313008572928689nteger @ X1 @ X22 )
% 2.86/3.14 => ( ( ( X1 = X22 )
% 2.86/3.14 => ( ( merge_Code_integer @ ( cons_Code_integer @ X1 @ L12 ) @ ( cons_Code_integer @ X22 @ L23 ) )
% 2.86/3.14 = ( cons_Code_integer @ X1 @ ( merge_Code_integer @ L12 @ L23 ) ) ) )
% 2.86/3.14 & ( ( X1 != X22 )
% 2.86/3.14 => ( ( merge_Code_integer @ ( cons_Code_integer @ X1 @ L12 ) @ ( cons_Code_integer @ X22 @ L23 ) )
% 2.86/3.14 = ( cons_Code_integer @ X22 @ ( merge_Code_integer @ ( cons_Code_integer @ X1 @ L12 ) @ L23 ) ) ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % merge.simps(3)
% 2.86/3.14 thf(fact_4628_merge_Osimps_I3_J,axiom,
% 2.86/3.14 ! [X1: num,X22: num,L12: list_num,L23: list_num] :
% 2.86/3.14 ( ( ( ord_less_num @ X1 @ X22 )
% 2.86/3.14 => ( ( merge_num @ ( cons_num @ X1 @ L12 ) @ ( cons_num @ X22 @ L23 ) )
% 2.86/3.14 = ( cons_num @ X1 @ ( merge_num @ L12 @ ( cons_num @ X22 @ L23 ) ) ) ) )
% 2.86/3.14 & ( ~ ( ord_less_num @ X1 @ X22 )
% 2.86/3.14 => ( ( ( X1 = X22 )
% 2.86/3.14 => ( ( merge_num @ ( cons_num @ X1 @ L12 ) @ ( cons_num @ X22 @ L23 ) )
% 2.86/3.14 = ( cons_num @ X1 @ ( merge_num @ L12 @ L23 ) ) ) )
% 2.86/3.14 & ( ( X1 != X22 )
% 2.86/3.14 => ( ( merge_num @ ( cons_num @ X1 @ L12 ) @ ( cons_num @ X22 @ L23 ) )
% 2.86/3.14 = ( cons_num @ X22 @ ( merge_num @ ( cons_num @ X1 @ L12 ) @ L23 ) ) ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % merge.simps(3)
% 2.86/3.14 thf(fact_4629_merge_Osimps_I3_J,axiom,
% 2.86/3.14 ! [X1: nat,X22: nat,L12: list_nat,L23: list_nat] :
% 2.86/3.14 ( ( ( ord_less_nat @ X1 @ X22 )
% 2.86/3.14 => ( ( merge_nat @ ( cons_nat @ X1 @ L12 ) @ ( cons_nat @ X22 @ L23 ) )
% 2.86/3.14 = ( cons_nat @ X1 @ ( merge_nat @ L12 @ ( cons_nat @ X22 @ L23 ) ) ) ) )
% 2.86/3.14 & ( ~ ( ord_less_nat @ X1 @ X22 )
% 2.86/3.14 => ( ( ( X1 = X22 )
% 2.86/3.14 => ( ( merge_nat @ ( cons_nat @ X1 @ L12 ) @ ( cons_nat @ X22 @ L23 ) )
% 2.86/3.14 = ( cons_nat @ X1 @ ( merge_nat @ L12 @ L23 ) ) ) )
% 2.86/3.14 & ( ( X1 != X22 )
% 2.86/3.14 => ( ( merge_nat @ ( cons_nat @ X1 @ L12 ) @ ( cons_nat @ X22 @ L23 ) )
% 2.86/3.14 = ( cons_nat @ X22 @ ( merge_nat @ ( cons_nat @ X1 @ L12 ) @ L23 ) ) ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % merge.simps(3)
% 2.86/3.14 thf(fact_4630_merge_Osimps_I3_J,axiom,
% 2.86/3.14 ! [X1: int,X22: int,L12: list_int,L23: list_int] :
% 2.86/3.14 ( ( ( ord_less_int @ X1 @ X22 )
% 2.86/3.14 => ( ( merge_int @ ( cons_int @ X1 @ L12 ) @ ( cons_int @ X22 @ L23 ) )
% 2.86/3.14 = ( cons_int @ X1 @ ( merge_int @ L12 @ ( cons_int @ X22 @ L23 ) ) ) ) )
% 2.86/3.14 & ( ~ ( ord_less_int @ X1 @ X22 )
% 2.86/3.14 => ( ( ( X1 = X22 )
% 2.86/3.14 => ( ( merge_int @ ( cons_int @ X1 @ L12 ) @ ( cons_int @ X22 @ L23 ) )
% 2.86/3.14 = ( cons_int @ X1 @ ( merge_int @ L12 @ L23 ) ) ) )
% 2.86/3.14 & ( ( X1 != X22 )
% 2.86/3.14 => ( ( merge_int @ ( cons_int @ X1 @ L12 ) @ ( cons_int @ X22 @ L23 ) )
% 2.86/3.14 = ( cons_int @ X22 @ ( merge_int @ ( cons_int @ X1 @ L12 ) @ L23 ) ) ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % merge.simps(3)
% 2.86/3.14 thf(fact_4631_list__assn_Osimps_I2_J,axiom,
% 2.86/3.14 ! [P: int > int > assn,A2: int,As2: list_int,C: int,Cs: list_int] :
% 2.86/3.14 ( ( vEBT_L74593716426352029nt_int @ P @ ( cons_int @ A2 @ As2 ) @ ( cons_int @ C @ Cs ) )
% 2.86/3.14 = ( times_times_assn @ ( P @ A2 @ C ) @ ( vEBT_L74593716426352029nt_int @ P @ As2 @ Cs ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn.simps(2)
% 2.86/3.14 thf(fact_4632_list__assn_Osimps_I2_J,axiom,
% 2.86/3.14 ! [P: int > nat > assn,A2: int,As2: list_int,C: nat,Cs: list_nat] :
% 2.86/3.14 ( ( vEBT_L77084186935402305nt_nat @ P @ ( cons_int @ A2 @ As2 ) @ ( cons_nat @ C @ Cs ) )
% 2.86/3.14 = ( times_times_assn @ ( P @ A2 @ C ) @ ( vEBT_L77084186935402305nt_nat @ P @ As2 @ Cs ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn.simps(2)
% 2.86/3.14 thf(fact_4633_list__assn_Osimps_I2_J,axiom,
% 2.86/3.14 ! [P: int > produc6575502325842934193n_assn > assn,A2: int,As2: list_int,C: produc6575502325842934193n_assn,Cs: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( vEBT_L1620274777744359680n_assn @ P @ ( cons_int @ A2 @ As2 ) @ ( cons_P2971678138204555879n_assn @ C @ Cs ) )
% 2.86/3.14 = ( times_times_assn @ ( P @ A2 @ C ) @ ( vEBT_L1620274777744359680n_assn @ P @ As2 @ Cs ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn.simps(2)
% 2.86/3.14 thf(fact_4634_list__assn_Osimps_I2_J,axiom,
% 2.86/3.14 ! [P: nat > int > assn,A2: nat,As2: list_nat,C: int,Cs: list_int] :
% 2.86/3.14 ( ( vEBT_L8298612041380073281at_int @ P @ ( cons_nat @ A2 @ As2 ) @ ( cons_int @ C @ Cs ) )
% 2.86/3.14 = ( times_times_assn @ ( P @ A2 @ C ) @ ( vEBT_L8298612041380073281at_int @ P @ As2 @ Cs ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn.simps(2)
% 2.86/3.14 thf(fact_4635_list__assn_Osimps_I2_J,axiom,
% 2.86/3.14 ! [P: nat > nat > assn,A2: nat,As2: list_nat,C: nat,Cs: list_nat] :
% 2.86/3.14 ( ( vEBT_L8301102511889123557at_nat @ P @ ( cons_nat @ A2 @ As2 ) @ ( cons_nat @ C @ Cs ) )
% 2.86/3.14 = ( times_times_assn @ ( P @ A2 @ C ) @ ( vEBT_L8301102511889123557at_nat @ P @ As2 @ Cs ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn.simps(2)
% 2.86/3.14 thf(fact_4636_list__assn_Osimps_I2_J,axiom,
% 2.86/3.14 ! [P: nat > produc6575502325842934193n_assn > assn,A2: nat,As2: list_nat,C: produc6575502325842934193n_assn,Cs: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( vEBT_L9083610150846024284n_assn @ P @ ( cons_nat @ A2 @ As2 ) @ ( cons_P2971678138204555879n_assn @ C @ Cs ) )
% 2.86/3.14 = ( times_times_assn @ ( P @ A2 @ C ) @ ( vEBT_L9083610150846024284n_assn @ P @ As2 @ Cs ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn.simps(2)
% 2.86/3.14 thf(fact_4637_list__assn_Osimps_I2_J,axiom,
% 2.86/3.14 ! [P: produc6575502325842934193n_assn > int > assn,A2: produc6575502325842934193n_assn,As2: list_P8527749157015355191n_assn,C: int,Cs: list_int] :
% 2.86/3.14 ( ( vEBT_L4760345170377931482sn_int @ P @ ( cons_P2971678138204555879n_assn @ A2 @ As2 ) @ ( cons_int @ C @ Cs ) )
% 2.86/3.14 = ( times_times_assn @ ( P @ A2 @ C ) @ ( vEBT_L4760345170377931482sn_int @ P @ As2 @ Cs ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn.simps(2)
% 2.86/3.14 thf(fact_4638_list__assn_Osimps_I2_J,axiom,
% 2.86/3.14 ! [P: produc6575502325842934193n_assn > nat > assn,A2: produc6575502325842934193n_assn,As2: list_P8527749157015355191n_assn,C: nat,Cs: list_nat] :
% 2.86/3.14 ( ( vEBT_L4762835640886981758sn_nat @ P @ ( cons_P2971678138204555879n_assn @ A2 @ As2 ) @ ( cons_nat @ C @ Cs ) )
% 2.86/3.14 = ( times_times_assn @ ( P @ A2 @ C ) @ ( vEBT_L4762835640886981758sn_nat @ P @ As2 @ Cs ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn.simps(2)
% 2.86/3.14 thf(fact_4639_list__assn_Osimps_I2_J,axiom,
% 2.86/3.14 ! [P: produc6575502325842934193n_assn > produc6575502325842934193n_assn > assn,A2: produc6575502325842934193n_assn,As2: list_P8527749157015355191n_assn,C: produc6575502325842934193n_assn,Cs: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( vEBT_L3108143461992071043n_assn @ P @ ( cons_P2971678138204555879n_assn @ A2 @ As2 ) @ ( cons_P2971678138204555879n_assn @ C @ Cs ) )
% 2.86/3.14 = ( times_times_assn @ ( P @ A2 @ C ) @ ( vEBT_L3108143461992071043n_assn @ P @ As2 @ Cs ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn.simps(2)
% 2.86/3.14 thf(fact_4640_list__assn__simps_I2_J,axiom,
% 2.86/3.14 ! [P: int > int > assn,A2: int,As2: list_int,C: int,Cs: list_int] :
% 2.86/3.14 ( ( vEBT_L74593716426352029nt_int @ P @ ( cons_int @ A2 @ As2 ) @ ( cons_int @ C @ Cs ) )
% 2.86/3.14 = ( times_times_assn @ ( P @ A2 @ C ) @ ( vEBT_L74593716426352029nt_int @ P @ As2 @ Cs ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn_simps(2)
% 2.86/3.14 thf(fact_4641_list__assn__simps_I2_J,axiom,
% 2.86/3.14 ! [P: int > nat > assn,A2: int,As2: list_int,C: nat,Cs: list_nat] :
% 2.86/3.14 ( ( vEBT_L77084186935402305nt_nat @ P @ ( cons_int @ A2 @ As2 ) @ ( cons_nat @ C @ Cs ) )
% 2.86/3.14 = ( times_times_assn @ ( P @ A2 @ C ) @ ( vEBT_L77084186935402305nt_nat @ P @ As2 @ Cs ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn_simps(2)
% 2.86/3.14 thf(fact_4642_list__assn__simps_I2_J,axiom,
% 2.86/3.14 ! [P: int > produc6575502325842934193n_assn > assn,A2: int,As2: list_int,C: produc6575502325842934193n_assn,Cs: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( vEBT_L1620274777744359680n_assn @ P @ ( cons_int @ A2 @ As2 ) @ ( cons_P2971678138204555879n_assn @ C @ Cs ) )
% 2.86/3.14 = ( times_times_assn @ ( P @ A2 @ C ) @ ( vEBT_L1620274777744359680n_assn @ P @ As2 @ Cs ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn_simps(2)
% 2.86/3.14 thf(fact_4643_list__assn__simps_I2_J,axiom,
% 2.86/3.14 ! [P: nat > int > assn,A2: nat,As2: list_nat,C: int,Cs: list_int] :
% 2.86/3.14 ( ( vEBT_L8298612041380073281at_int @ P @ ( cons_nat @ A2 @ As2 ) @ ( cons_int @ C @ Cs ) )
% 2.86/3.14 = ( times_times_assn @ ( P @ A2 @ C ) @ ( vEBT_L8298612041380073281at_int @ P @ As2 @ Cs ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn_simps(2)
% 2.86/3.14 thf(fact_4644_list__assn__simps_I2_J,axiom,
% 2.86/3.14 ! [P: nat > nat > assn,A2: nat,As2: list_nat,C: nat,Cs: list_nat] :
% 2.86/3.14 ( ( vEBT_L8301102511889123557at_nat @ P @ ( cons_nat @ A2 @ As2 ) @ ( cons_nat @ C @ Cs ) )
% 2.86/3.14 = ( times_times_assn @ ( P @ A2 @ C ) @ ( vEBT_L8301102511889123557at_nat @ P @ As2 @ Cs ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn_simps(2)
% 2.86/3.14 thf(fact_4645_list__assn__simps_I2_J,axiom,
% 2.86/3.14 ! [P: nat > produc6575502325842934193n_assn > assn,A2: nat,As2: list_nat,C: produc6575502325842934193n_assn,Cs: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( vEBT_L9083610150846024284n_assn @ P @ ( cons_nat @ A2 @ As2 ) @ ( cons_P2971678138204555879n_assn @ C @ Cs ) )
% 2.86/3.14 = ( times_times_assn @ ( P @ A2 @ C ) @ ( vEBT_L9083610150846024284n_assn @ P @ As2 @ Cs ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn_simps(2)
% 2.86/3.14 thf(fact_4646_list__assn__simps_I2_J,axiom,
% 2.86/3.14 ! [P: produc6575502325842934193n_assn > int > assn,A2: produc6575502325842934193n_assn,As2: list_P8527749157015355191n_assn,C: int,Cs: list_int] :
% 2.86/3.14 ( ( vEBT_L4760345170377931482sn_int @ P @ ( cons_P2971678138204555879n_assn @ A2 @ As2 ) @ ( cons_int @ C @ Cs ) )
% 2.86/3.14 = ( times_times_assn @ ( P @ A2 @ C ) @ ( vEBT_L4760345170377931482sn_int @ P @ As2 @ Cs ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn_simps(2)
% 2.86/3.14 thf(fact_4647_list__assn__simps_I2_J,axiom,
% 2.86/3.14 ! [P: produc6575502325842934193n_assn > nat > assn,A2: produc6575502325842934193n_assn,As2: list_P8527749157015355191n_assn,C: nat,Cs: list_nat] :
% 2.86/3.14 ( ( vEBT_L4762835640886981758sn_nat @ P @ ( cons_P2971678138204555879n_assn @ A2 @ As2 ) @ ( cons_nat @ C @ Cs ) )
% 2.86/3.14 = ( times_times_assn @ ( P @ A2 @ C ) @ ( vEBT_L4762835640886981758sn_nat @ P @ As2 @ Cs ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn_simps(2)
% 2.86/3.14 thf(fact_4648_list__assn__simps_I2_J,axiom,
% 2.86/3.14 ! [P: produc6575502325842934193n_assn > produc6575502325842934193n_assn > assn,A2: produc6575502325842934193n_assn,As2: list_P8527749157015355191n_assn,C: produc6575502325842934193n_assn,Cs: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( vEBT_L3108143461992071043n_assn @ P @ ( cons_P2971678138204555879n_assn @ A2 @ As2 ) @ ( cons_P2971678138204555879n_assn @ C @ Cs ) )
% 2.86/3.14 = ( times_times_assn @ ( P @ A2 @ C ) @ ( vEBT_L3108143461992071043n_assn @ P @ As2 @ Cs ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn_simps(2)
% 2.86/3.14 thf(fact_4649_List_Oinsert__def,axiom,
% 2.86/3.14 ( insert4149901806602606979at_nat
% 2.86/3.14 = ( ^ [X2: produc3843707927480180839at_nat,Xs3: list_P5464809261938338413at_nat] : ( if_lis7508161100780771379at_nat @ ( member8757157785044589968at_nat @ X2 @ ( set_Pr3765526544606949372at_nat @ Xs3 ) ) @ Xs3 @ ( cons_P3940603068885512221at_nat @ X2 @ Xs3 ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % List.insert_def
% 2.86/3.14 thf(fact_4650_List_Oinsert__def,axiom,
% 2.86/3.14 ( insert8944034826898310173at_nat
% 2.86/3.14 = ( ^ [X2: product_prod_nat_nat,Xs3: list_P6011104703257516679at_nat] : ( if_lis9186351972506106189at_nat @ ( member8440522571783428010at_nat @ X2 @ ( set_Pr5648618587558075414at_nat @ Xs3 ) ) @ Xs3 @ ( cons_P6512896166579812791at_nat @ X2 @ Xs3 ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % List.insert_def
% 2.86/3.14 thf(fact_4651_List_Oinsert__def,axiom,
% 2.86/3.14 ( insert8021100735160035049_nat_o
% 2.86/3.14 = ( ^ [X2: produc3658429121746597890et_nat > $o,Xs3: list_P7985473006766602707_nat_o] : ( if_lis2904118647880296857_nat_o @ ( member6576561426505652726_nat_o @ X2 @ ( set_Pr400311997697478754_nat_o @ Xs3 ) ) @ Xs3 @ ( cons_P6219271836124797827_nat_o @ X2 @ Xs3 ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % List.insert_def
% 2.86/3.14 thf(fact_4652_List_Oinsert__def,axiom,
% 2.86/3.14 ( insert_int
% 2.86/3.14 = ( ^ [X2: int,Xs3: list_int] : ( if_list_int @ ( member_int @ X2 @ ( set_int2 @ Xs3 ) ) @ Xs3 @ ( cons_int @ X2 @ Xs3 ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % List.insert_def
% 2.86/3.14 thf(fact_4653_List_Oinsert__def,axiom,
% 2.86/3.14 ( insert_nat
% 2.86/3.14 = ( ^ [X2: nat,Xs3: list_nat] : ( if_list_nat @ ( member_nat @ X2 @ ( set_nat2 @ Xs3 ) ) @ Xs3 @ ( cons_nat @ X2 @ Xs3 ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % List.insert_def
% 2.86/3.14 thf(fact_4654_List_Oinsert__def,axiom,
% 2.86/3.14 ( insert3246601298802261197n_assn
% 2.86/3.14 = ( ^ [X2: produc6575502325842934193n_assn,Xs3: list_P8527749157015355191n_assn] : ( if_lis7173127979115136509n_assn @ ( member7957490590177025114n_assn @ X2 @ ( set_Pr1139785259514867910n_assn @ Xs3 ) ) @ Xs3 @ ( cons_P2971678138204555879n_assn @ X2 @ Xs3 ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % List.insert_def
% 2.86/3.14 thf(fact_4655_Suc__le__length__iff,axiom,
% 2.86/3.14 ! [N: nat,Xs: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_s6829681357464350627n_assn @ Xs ) )
% 2.86/3.14 = ( ? [X2: produc6575502325842934193n_assn,Ys3: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( Xs
% 2.86/3.14 = ( cons_P2971678138204555879n_assn @ X2 @ Ys3 ) )
% 2.86/3.14 & ( ord_less_eq_nat @ N @ ( size_s6829681357464350627n_assn @ Ys3 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % Suc_le_length_iff
% 2.86/3.14 thf(fact_4656_Suc__le__length__iff,axiom,
% 2.86/3.14 ! [N: nat,Xs: list_c] :
% 2.86/3.14 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_size_list_c @ Xs ) )
% 2.86/3.14 = ( ? [X2: c,Ys3: list_c] :
% 2.86/3.14 ( ( Xs
% 2.86/3.14 = ( cons_c @ X2 @ Ys3 ) )
% 2.86/3.14 & ( ord_less_eq_nat @ N @ ( size_size_list_c @ Ys3 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % Suc_le_length_iff
% 2.86/3.14 thf(fact_4657_Suc__le__length__iff,axiom,
% 2.86/3.14 ! [N: nat,Xs: list_d] :
% 2.86/3.14 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_size_list_d @ Xs ) )
% 2.86/3.14 = ( ? [X2: d,Ys3: list_d] :
% 2.86/3.14 ( ( Xs
% 2.86/3.14 = ( cons_d @ X2 @ Ys3 ) )
% 2.86/3.14 & ( ord_less_eq_nat @ N @ ( size_size_list_d @ Ys3 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % Suc_le_length_iff
% 2.86/3.14 thf(fact_4658_Suc__le__length__iff,axiom,
% 2.86/3.14 ! [N: nat,Xs: list_nat] :
% 2.86/3.14 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_size_list_nat @ Xs ) )
% 2.86/3.14 = ( ? [X2: nat,Ys3: list_nat] :
% 2.86/3.14 ( ( Xs
% 2.86/3.14 = ( cons_nat @ X2 @ Ys3 ) )
% 2.86/3.14 & ( ord_less_eq_nat @ N @ ( size_size_list_nat @ Ys3 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % Suc_le_length_iff
% 2.86/3.14 thf(fact_4659_Suc__le__length__iff,axiom,
% 2.86/3.14 ! [N: nat,Xs: list_int] :
% 2.86/3.14 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_size_list_int @ Xs ) )
% 2.86/3.14 = ( ? [X2: int,Ys3: list_int] :
% 2.86/3.14 ( ( Xs
% 2.86/3.14 = ( cons_int @ X2 @ Ys3 ) )
% 2.86/3.14 & ( ord_less_eq_nat @ N @ ( size_size_list_int @ Ys3 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % Suc_le_length_iff
% 2.86/3.14 thf(fact_4660_sorted__simps_I2_J,axiom,
% 2.86/3.14 ! [X: nat,Ys: list_nat] :
% 2.86/3.14 ( ( sorted_wrt_nat @ ord_less_eq_nat @ ( cons_nat @ X @ Ys ) )
% 2.86/3.14 = ( ! [X2: nat] :
% 2.86/3.14 ( ( member_nat @ X2 @ ( set_nat2 @ Ys ) )
% 2.86/3.14 => ( ord_less_eq_nat @ X @ X2 ) )
% 2.86/3.14 & ( sorted_wrt_nat @ ord_less_eq_nat @ Ys ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % sorted_simps(2)
% 2.86/3.14 thf(fact_4661_sorted__simps_I2_J,axiom,
% 2.86/3.14 ! [X: int,Ys: list_int] :
% 2.86/3.14 ( ( sorted_wrt_int @ ord_less_eq_int @ ( cons_int @ X @ Ys ) )
% 2.86/3.14 = ( ! [X2: int] :
% 2.86/3.14 ( ( member_int @ X2 @ ( set_int2 @ Ys ) )
% 2.86/3.14 => ( ord_less_eq_int @ X @ X2 ) )
% 2.86/3.14 & ( sorted_wrt_int @ ord_less_eq_int @ Ys ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % sorted_simps(2)
% 2.86/3.14 thf(fact_4662_strict__sorted__simps_I2_J,axiom,
% 2.86/3.14 ! [X: code_integer,Ys: list_Code_integer] :
% 2.86/3.14 ( ( sorted710888440204495920nteger @ ord_le6747313008572928689nteger @ ( cons_Code_integer @ X @ Ys ) )
% 2.86/3.14 = ( ! [X2: code_integer] :
% 2.86/3.14 ( ( member_Code_integer @ X2 @ ( set_Code_integer2 @ Ys ) )
% 2.86/3.14 => ( ord_le6747313008572928689nteger @ X @ X2 ) )
% 2.86/3.14 & ( sorted710888440204495920nteger @ ord_le6747313008572928689nteger @ Ys ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % strict_sorted_simps(2)
% 2.86/3.14 thf(fact_4663_strict__sorted__simps_I2_J,axiom,
% 2.86/3.14 ! [X: num,Ys: list_num] :
% 2.86/3.14 ( ( sorted_wrt_num @ ord_less_num @ ( cons_num @ X @ Ys ) )
% 2.86/3.14 = ( ! [X2: num] :
% 2.86/3.14 ( ( member_num @ X2 @ ( set_num2 @ Ys ) )
% 2.86/3.14 => ( ord_less_num @ X @ X2 ) )
% 2.86/3.14 & ( sorted_wrt_num @ ord_less_num @ Ys ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % strict_sorted_simps(2)
% 2.86/3.14 thf(fact_4664_strict__sorted__simps_I2_J,axiom,
% 2.86/3.14 ! [X: nat,Ys: list_nat] :
% 2.86/3.14 ( ( sorted_wrt_nat @ ord_less_nat @ ( cons_nat @ X @ Ys ) )
% 2.86/3.14 = ( ! [X2: nat] :
% 2.86/3.14 ( ( member_nat @ X2 @ ( set_nat2 @ Ys ) )
% 2.86/3.14 => ( ord_less_nat @ X @ X2 ) )
% 2.86/3.14 & ( sorted_wrt_nat @ ord_less_nat @ Ys ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % strict_sorted_simps(2)
% 2.86/3.14 thf(fact_4665_strict__sorted__simps_I2_J,axiom,
% 2.86/3.14 ! [X: int,Ys: list_int] :
% 2.86/3.14 ( ( sorted_wrt_int @ ord_less_int @ ( cons_int @ X @ Ys ) )
% 2.86/3.14 = ( ! [X2: int] :
% 2.86/3.14 ( ( member_int @ X2 @ ( set_int2 @ Ys ) )
% 2.86/3.14 => ( ord_less_int @ X @ X2 ) )
% 2.86/3.14 & ( sorted_wrt_int @ ord_less_int @ Ys ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % strict_sorted_simps(2)
% 2.86/3.14 thf(fact_4666_bijective__def,axiom,
% 2.86/3.14 ( biject3388518990857851981at_nat
% 2.86/3.14 = ( ^ [R3: set_Pr4329608150637261639at_nat] :
% 2.86/3.14 ( ! [X2: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat,Z5: set_Pr1261947904930325089at_nat] :
% 2.86/3.14 ( ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X2 @ Y5 ) @ R3 )
% 2.86/3.14 & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X2 @ Z5 ) @ R3 ) )
% 2.86/3.14 => ( Y5 = Z5 ) )
% 2.86/3.14 & ! [X2: set_Pr1261947904930325089at_nat,Y5: set_Pr1261947904930325089at_nat,Z5: set_Pr1261947904930325089at_nat] :
% 2.86/3.14 ( ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X2 @ Z5 ) @ R3 )
% 2.86/3.14 & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y5 @ Z5 ) @ R3 ) )
% 2.86/3.14 => ( X2 = Y5 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % bijective_def
% 2.86/3.14 thf(fact_4667_bijective__def,axiom,
% 2.86/3.14 ( bijective_nat_nat
% 2.86/3.14 = ( ^ [R3: set_Pr1261947904930325089at_nat] :
% 2.86/3.14 ( ! [X2: nat,Y5: nat,Z5: nat] :
% 2.86/3.14 ( ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y5 ) @ R3 )
% 2.86/3.14 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Z5 ) @ R3 ) )
% 2.86/3.14 => ( Y5 = Z5 ) )
% 2.86/3.14 & ! [X2: nat,Y5: nat,Z5: nat] :
% 2.86/3.14 ( ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Z5 ) @ R3 )
% 2.86/3.14 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y5 @ Z5 ) @ R3 ) )
% 2.86/3.14 => ( X2 = Y5 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % bijective_def
% 2.86/3.14 thf(fact_4668_bijective__def,axiom,
% 2.86/3.14 ( biject9051520373387432658nteger
% 2.86/3.14 = ( ^ [R3: set_Pr1281608226676607948nteger] :
% 2.86/3.14 ( ! [X2: produc6241069584506657477e_term > option6357759511663192854e_term,Y5: produc8923325533196201883nteger,Z5: produc8923325533196201883nteger] :
% 2.86/3.14 ( ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X2 @ Y5 ) @ R3 )
% 2.86/3.14 & ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X2 @ Z5 ) @ R3 ) )
% 2.86/3.14 => ( Y5 = Z5 ) )
% 2.86/3.14 & ! [X2: produc6241069584506657477e_term > option6357759511663192854e_term,Y5: produc6241069584506657477e_term > option6357759511663192854e_term,Z5: produc8923325533196201883nteger] :
% 2.86/3.14 ( ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X2 @ Z5 ) @ R3 )
% 2.86/3.14 & ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ Y5 @ Z5 ) @ R3 ) )
% 2.86/3.14 => ( X2 = Y5 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % bijective_def
% 2.86/3.14 thf(fact_4669_bijective__def,axiom,
% 2.86/3.14 ( biject2615096655818420098et_nat
% 2.86/3.14 = ( ^ [R3: set_Pr3286484037609594932et_nat] :
% 2.86/3.14 ( ! [X2: produc3658429121746597890et_nat > $o,Y5: produc3658429121746597890et_nat,Z5: produc3658429121746597890et_nat] :
% 2.86/3.14 ( ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X2 @ Y5 ) @ R3 )
% 2.86/3.14 & ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X2 @ Z5 ) @ R3 ) )
% 2.86/3.14 => ( Y5 = Z5 ) )
% 2.86/3.14 & ! [X2: produc3658429121746597890et_nat > $o,Y5: produc3658429121746597890et_nat > $o,Z5: produc3658429121746597890et_nat] :
% 2.86/3.14 ( ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X2 @ Z5 ) @ R3 )
% 2.86/3.14 & ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ Y5 @ Z5 ) @ R3 ) )
% 2.86/3.14 => ( X2 = Y5 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % bijective_def
% 2.86/3.14 thf(fact_4670_bijective__def,axiom,
% 2.86/3.14 ( biject1468766312547416318et_nat
% 2.86/3.14 = ( ^ [R3: set_Pr8536935166611901872et_nat] :
% 2.86/3.14 ( ! [X2: produc3658429121746597890et_nat > $o,Y5: produc3925858234332021118et_nat,Z5: produc3925858234332021118et_nat] :
% 2.86/3.14 ( ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X2 @ Y5 ) @ R3 )
% 2.86/3.14 & ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X2 @ Z5 ) @ R3 ) )
% 2.86/3.14 => ( Y5 = Z5 ) )
% 2.86/3.14 & ! [X2: produc3658429121746597890et_nat > $o,Y5: produc3658429121746597890et_nat > $o,Z5: produc3925858234332021118et_nat] :
% 2.86/3.14 ( ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X2 @ Z5 ) @ R3 )
% 2.86/3.14 & ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ Y5 @ Z5 ) @ R3 ) )
% 2.86/3.14 => ( X2 = Y5 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % bijective_def
% 2.86/3.14 thf(fact_4671_bijective__def,axiom,
% 2.86/3.14 ( biject383251550997737151nt_int
% 2.86/3.14 = ( ^ [R3: set_Pr9222295170931077689nt_int] :
% 2.86/3.14 ( ! [X2: produc8551481072490612790e_term > option6357759511663192854e_term,Y5: product_prod_int_int,Z5: product_prod_int_int] :
% 2.86/3.14 ( ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X2 @ Y5 ) @ R3 )
% 2.86/3.14 & ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X2 @ Z5 ) @ R3 ) )
% 2.86/3.14 => ( Y5 = Z5 ) )
% 2.86/3.14 & ! [X2: produc8551481072490612790e_term > option6357759511663192854e_term,Y5: produc8551481072490612790e_term > option6357759511663192854e_term,Z5: product_prod_int_int] :
% 2.86/3.14 ( ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X2 @ Z5 ) @ R3 )
% 2.86/3.14 & ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ Y5 @ Z5 ) @ R3 ) )
% 2.86/3.14 => ( X2 = Y5 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % bijective_def
% 2.86/3.14 thf(fact_4672_bijective__def,axiom,
% 2.86/3.14 ( biject576505603616484041nt_int
% 2.86/3.14 = ( ^ [R3: set_Pr1872883991513573699nt_int] :
% 2.86/3.14 ( ! [X2: int > option6357759511663192854e_term,Y5: product_prod_int_int,Z5: product_prod_int_int] :
% 2.86/3.14 ( ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X2 @ Y5 ) @ R3 )
% 2.86/3.14 & ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X2 @ Z5 ) @ R3 ) )
% 2.86/3.14 => ( Y5 = Z5 ) )
% 2.86/3.14 & ! [X2: int > option6357759511663192854e_term,Y5: int > option6357759511663192854e_term,Z5: product_prod_int_int] :
% 2.86/3.14 ( ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X2 @ Z5 ) @ R3 )
% 2.86/3.14 & ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ Y5 @ Z5 ) @ R3 ) )
% 2.86/3.14 => ( X2 = Y5 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % bijective_def
% 2.86/3.14 thf(fact_4673_Cons__listrel1E2,axiom,
% 2.86/3.14 ! [Xs: list_s1210847774152347623at_nat,Y: set_Pr1261947904930325089at_nat,Ys: list_s1210847774152347623at_nat,R2: set_Pr4329608150637261639at_nat] :
% 2.86/3.14 ( ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ Xs @ ( cons_s6881495754146722583at_nat @ Y @ Ys ) ) @ ( listre8180072825634266816at_nat @ R2 ) )
% 2.86/3.14 => ( ! [X3: set_Pr1261947904930325089at_nat] :
% 2.86/3.14 ( ( Xs
% 2.86/3.14 = ( cons_s6881495754146722583at_nat @ X3 @ Ys ) )
% 2.86/3.14 => ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y ) @ R2 ) )
% 2.86/3.14 => ~ ! [Zs2: list_s1210847774152347623at_nat] :
% 2.86/3.14 ( ( Xs
% 2.86/3.14 = ( cons_s6881495754146722583at_nat @ Y @ Zs2 ) )
% 2.86/3.14 => ~ ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ Zs2 @ Ys ) @ ( listre8180072825634266816at_nat @ R2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % Cons_listrel1E2
% 2.86/3.14 thf(fact_4674_Cons__listrel1E2,axiom,
% 2.86/3.14 ! [Xs: list_int,Y: int,Ys: list_int,R2: set_Pr958786334691620121nt_int] :
% 2.86/3.14 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs @ ( cons_int @ Y @ Ys ) ) @ ( listrel1_int @ R2 ) )
% 2.86/3.14 => ( ! [X3: int] :
% 2.86/3.14 ( ( Xs
% 2.86/3.14 = ( cons_int @ X3 @ Ys ) )
% 2.86/3.14 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y ) @ R2 ) )
% 2.86/3.14 => ~ ! [Zs2: list_int] :
% 2.86/3.14 ( ( Xs
% 2.86/3.14 = ( cons_int @ Y @ Zs2 ) )
% 2.86/3.14 => ~ ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Zs2 @ Ys ) @ ( listrel1_int @ R2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % Cons_listrel1E2
% 2.86/3.14 thf(fact_4675_Cons__listrel1E2,axiom,
% 2.86/3.14 ! [Xs: list_nat,Y: nat,Ys: list_nat,R2: set_Pr1261947904930325089at_nat] :
% 2.86/3.14 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs @ ( cons_nat @ Y @ Ys ) ) @ ( listrel1_nat @ R2 ) )
% 2.86/3.14 => ( ! [X3: nat] :
% 2.86/3.14 ( ( Xs
% 2.86/3.14 = ( cons_nat @ X3 @ Ys ) )
% 2.86/3.14 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y ) @ R2 ) )
% 2.86/3.14 => ~ ! [Zs2: list_nat] :
% 2.86/3.14 ( ( Xs
% 2.86/3.14 = ( cons_nat @ Y @ Zs2 ) )
% 2.86/3.14 => ~ ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Zs2 @ Ys ) @ ( listrel1_nat @ R2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % Cons_listrel1E2
% 2.86/3.14 thf(fact_4676_Cons__listrel1E2,axiom,
% 2.86/3.14 ! [Xs: list_P8527749157015355191n_assn,Y: produc6575502325842934193n_assn,Ys: list_P8527749157015355191n_assn,R2: set_Pr8116311503512020807n_assn] :
% 2.86/3.14 ( ( member3994142547374651152n_assn @ ( produc3014731801419794263n_assn @ Xs @ ( cons_P2971678138204555879n_assn @ Y @ Ys ) ) @ ( listre4270255209692100112n_assn @ R2 ) )
% 2.86/3.14 => ( ! [X3: produc6575502325842934193n_assn] :
% 2.86/3.14 ( ( Xs
% 2.86/3.14 = ( cons_P2971678138204555879n_assn @ X3 @ Ys ) )
% 2.86/3.14 => ~ ( member4743710847862083984n_assn @ ( produc6128706242671166167n_assn @ X3 @ Y ) @ R2 ) )
% 2.86/3.14 => ~ ! [Zs2: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( Xs
% 2.86/3.14 = ( cons_P2971678138204555879n_assn @ Y @ Zs2 ) )
% 2.86/3.14 => ~ ( member3994142547374651152n_assn @ ( produc3014731801419794263n_assn @ Zs2 @ Ys ) @ ( listre4270255209692100112n_assn @ R2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % Cons_listrel1E2
% 2.86/3.14 thf(fact_4677_Cons__listrel1E1,axiom,
% 2.86/3.14 ! [X: set_Pr1261947904930325089at_nat,Xs: list_s1210847774152347623at_nat,Ys: list_s1210847774152347623at_nat,R2: set_Pr4329608150637261639at_nat] :
% 2.86/3.14 ( ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ ( cons_s6881495754146722583at_nat @ X @ Xs ) @ Ys ) @ ( listre8180072825634266816at_nat @ R2 ) )
% 2.86/3.14 => ( ! [Y2: set_Pr1261947904930325089at_nat] :
% 2.86/3.14 ( ( Ys
% 2.86/3.14 = ( cons_s6881495754146722583at_nat @ Y2 @ Xs ) )
% 2.86/3.14 => ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y2 ) @ R2 ) )
% 2.86/3.14 => ~ ! [Zs2: list_s1210847774152347623at_nat] :
% 2.86/3.14 ( ( Ys
% 2.86/3.14 = ( cons_s6881495754146722583at_nat @ X @ Zs2 ) )
% 2.86/3.14 => ~ ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ Xs @ Zs2 ) @ ( listre8180072825634266816at_nat @ R2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % Cons_listrel1E1
% 2.86/3.14 thf(fact_4678_Cons__listrel1E1,axiom,
% 2.86/3.14 ! [X: int,Xs: list_int,Ys: list_int,R2: set_Pr958786334691620121nt_int] :
% 2.86/3.14 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ ( cons_int @ X @ Xs ) @ Ys ) @ ( listrel1_int @ R2 ) )
% 2.86/3.14 => ( ! [Y2: int] :
% 2.86/3.14 ( ( Ys
% 2.86/3.14 = ( cons_int @ Y2 @ Xs ) )
% 2.86/3.14 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y2 ) @ R2 ) )
% 2.86/3.14 => ~ ! [Zs2: list_int] :
% 2.86/3.14 ( ( Ys
% 2.86/3.14 = ( cons_int @ X @ Zs2 ) )
% 2.86/3.14 => ~ ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs @ Zs2 ) @ ( listrel1_int @ R2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % Cons_listrel1E1
% 2.86/3.14 thf(fact_4679_Cons__listrel1E1,axiom,
% 2.86/3.14 ! [X: nat,Xs: list_nat,Ys: list_nat,R2: set_Pr1261947904930325089at_nat] :
% 2.86/3.14 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ ( cons_nat @ X @ Xs ) @ Ys ) @ ( listrel1_nat @ R2 ) )
% 2.86/3.14 => ( ! [Y2: nat] :
% 2.86/3.14 ( ( Ys
% 2.86/3.14 = ( cons_nat @ Y2 @ Xs ) )
% 2.86/3.14 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y2 ) @ R2 ) )
% 2.86/3.14 => ~ ! [Zs2: list_nat] :
% 2.86/3.14 ( ( Ys
% 2.86/3.14 = ( cons_nat @ X @ Zs2 ) )
% 2.86/3.14 => ~ ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs @ Zs2 ) @ ( listrel1_nat @ R2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % Cons_listrel1E1
% 2.86/3.14 thf(fact_4680_Cons__listrel1E1,axiom,
% 2.86/3.14 ! [X: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn,Ys: list_P8527749157015355191n_assn,R2: set_Pr8116311503512020807n_assn] :
% 2.86/3.14 ( ( member3994142547374651152n_assn @ ( produc3014731801419794263n_assn @ ( cons_P2971678138204555879n_assn @ X @ Xs ) @ Ys ) @ ( listre4270255209692100112n_assn @ R2 ) )
% 2.86/3.14 => ( ! [Y2: produc6575502325842934193n_assn] :
% 2.86/3.14 ( ( Ys
% 2.86/3.14 = ( cons_P2971678138204555879n_assn @ Y2 @ Xs ) )
% 2.86/3.14 => ~ ( member4743710847862083984n_assn @ ( produc6128706242671166167n_assn @ X @ Y2 ) @ R2 ) )
% 2.86/3.14 => ~ ! [Zs2: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( Ys
% 2.86/3.14 = ( cons_P2971678138204555879n_assn @ X @ Zs2 ) )
% 2.86/3.14 => ~ ( member3994142547374651152n_assn @ ( produc3014731801419794263n_assn @ Xs @ Zs2 ) @ ( listre4270255209692100112n_assn @ R2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % Cons_listrel1E1
% 2.86/3.14 thf(fact_4681_listrel1I1,axiom,
% 2.86/3.14 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,R2: set_Pr4329608150637261639at_nat,Xs: list_s1210847774152347623at_nat] :
% 2.86/3.14 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ R2 )
% 2.86/3.14 => ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ ( cons_s6881495754146722583at_nat @ X @ Xs ) @ ( cons_s6881495754146722583at_nat @ Y @ Xs ) ) @ ( listre8180072825634266816at_nat @ R2 ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % listrel1I1
% 2.86/3.14 thf(fact_4682_listrel1I1,axiom,
% 2.86/3.14 ! [X: int,Y: int,R2: set_Pr958786334691620121nt_int,Xs: list_int] :
% 2.86/3.14 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R2 )
% 2.86/3.14 => ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ ( cons_int @ X @ Xs ) @ ( cons_int @ Y @ Xs ) ) @ ( listrel1_int @ R2 ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % listrel1I1
% 2.86/3.14 thf(fact_4683_listrel1I1,axiom,
% 2.86/3.14 ! [X: nat,Y: nat,R2: set_Pr1261947904930325089at_nat,Xs: list_nat] :
% 2.86/3.14 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R2 )
% 2.86/3.14 => ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ ( cons_nat @ X @ Xs ) @ ( cons_nat @ Y @ Xs ) ) @ ( listrel1_nat @ R2 ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % listrel1I1
% 2.86/3.14 thf(fact_4684_listrel1I1,axiom,
% 2.86/3.14 ! [X: produc6575502325842934193n_assn,Y: produc6575502325842934193n_assn,R2: set_Pr8116311503512020807n_assn,Xs: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( member4743710847862083984n_assn @ ( produc6128706242671166167n_assn @ X @ Y ) @ R2 )
% 2.86/3.14 => ( member3994142547374651152n_assn @ ( produc3014731801419794263n_assn @ ( cons_P2971678138204555879n_assn @ X @ Xs ) @ ( cons_P2971678138204555879n_assn @ Y @ Xs ) ) @ ( listre4270255209692100112n_assn @ R2 ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % listrel1I1
% 2.86/3.14 thf(fact_4685_listrel__Cons2,axiom,
% 2.86/3.14 ! [Xs: list_int,Y: int,Ys: list_int,R2: set_Pr958786334691620121nt_int] :
% 2.86/3.14 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs @ ( cons_int @ Y @ Ys ) ) @ ( listrel_int_int @ R2 ) )
% 2.86/3.14 => ~ ! [X3: int,Xs2: list_int] :
% 2.86/3.14 ( ( Xs
% 2.86/3.14 = ( cons_int @ X3 @ Xs2 ) )
% 2.86/3.14 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y ) @ R2 )
% 2.86/3.14 => ~ ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs2 @ Ys ) @ ( listrel_int_int @ R2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % listrel_Cons2
% 2.86/3.14 thf(fact_4686_listrel__Cons2,axiom,
% 2.86/3.14 ! [Xs: list_nat,Y: int,Ys: list_int,R2: set_Pr7995236796853374141at_int] :
% 2.86/3.14 ( ( member4850886304473975718st_int @ ( produc7739558402351520821st_int @ Xs @ ( cons_int @ Y @ Ys ) ) @ ( listrel_nat_int @ R2 ) )
% 2.86/3.14 => ~ ! [X3: nat,Xs2: list_nat] :
% 2.86/3.14 ( ( Xs
% 2.86/3.14 = ( cons_nat @ X3 @ Xs2 ) )
% 2.86/3.14 => ( ( member4262671552274231302at_int @ ( product_Pair_nat_int @ X3 @ Y ) @ R2 )
% 2.86/3.14 => ~ ( member4850886304473975718st_int @ ( produc7739558402351520821st_int @ Xs2 @ Ys ) @ ( listrel_nat_int @ R2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % listrel_Cons2
% 2.86/3.14 thf(fact_4687_listrel__Cons2,axiom,
% 2.86/3.14 ! [Xs: list_int,Y: nat,Ys: list_nat,R2: set_Pr3448869479623346877nt_nat] :
% 2.86/3.14 ( ( member9189046780804443046st_nat @ ( produc4542114716404682293st_nat @ Xs @ ( cons_nat @ Y @ Ys ) ) @ ( listrel_int_nat @ R2 ) )
% 2.86/3.14 => ~ ! [X3: int,Xs2: list_int] :
% 2.86/3.14 ( ( Xs
% 2.86/3.14 = ( cons_int @ X3 @ Xs2 ) )
% 2.86/3.14 => ( ( member216504246829706758nt_nat @ ( product_Pair_int_nat @ X3 @ Y ) @ R2 )
% 2.86/3.14 => ~ ( member9189046780804443046st_nat @ ( produc4542114716404682293st_nat @ Xs2 @ Ys ) @ ( listrel_int_nat @ R2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % listrel_Cons2
% 2.86/3.14 thf(fact_4688_listrel__Cons2,axiom,
% 2.86/3.14 ! [Xs: list_nat,Y: nat,Ys: list_nat,R2: set_Pr1261947904930325089at_nat] :
% 2.86/3.14 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs @ ( cons_nat @ Y @ Ys ) ) @ ( listrel_nat_nat @ R2 ) )
% 2.86/3.14 => ~ ! [X3: nat,Xs2: list_nat] :
% 2.86/3.14 ( ( Xs
% 2.86/3.14 = ( cons_nat @ X3 @ Xs2 ) )
% 2.86/3.14 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y ) @ R2 )
% 2.86/3.14 => ~ ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs2 @ Ys ) @ ( listrel_nat_nat @ R2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % listrel_Cons2
% 2.86/3.14 thf(fact_4689_listrel__Cons2,axiom,
% 2.86/3.14 ! [Xs: list_P8527749157015355191n_assn,Y: int,Ys: list_int,R2: set_Pr2181989527757714242sn_int] :
% 2.86/3.14 ( ( member5295696281703116473st_int @ ( produc1996262876970182428st_int @ Xs @ ( cons_int @ Y @ Ys ) ) @ ( listre8029020076619294380sn_int @ R2 ) )
% 2.86/3.14 => ~ ! [X3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( Xs
% 2.86/3.14 = ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) )
% 2.86/3.14 => ( ( member5792320502188913699sn_int @ ( produc6453891449406693510sn_int @ X3 @ Y ) @ R2 )
% 2.86/3.14 => ~ ( member5295696281703116473st_int @ ( produc1996262876970182428st_int @ Xs2 @ Ys ) @ ( listre8029020076619294380sn_int @ R2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % listrel_Cons2
% 2.86/3.14 thf(fact_4690_listrel__Cons2,axiom,
% 2.86/3.14 ! [Xs: list_P8527749157015355191n_assn,Y: nat,Ys: list_nat,R2: set_Pr4672072672689440998sn_nat] :
% 2.86/3.14 ( ( member7785779426634843229st_nat @ ( produc6174113896479379136st_nat @ Xs @ ( cons_nat @ Y @ Ys ) ) @ ( listre8031510547128344656sn_nat @ R2 ) )
% 2.86/3.14 => ~ ! [X3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( Xs
% 2.86/3.14 = ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) )
% 2.86/3.14 => ( ( member746799484843334599sn_nat @ ( produc6456381919915743786sn_nat @ X3 @ Y ) @ R2 )
% 2.86/3.14 => ~ ( member7785779426634843229st_nat @ ( produc6174113896479379136st_nat @ Xs2 @ Ys ) @ ( listre8031510547128344656sn_nat @ R2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % listrel_Cons2
% 2.86/3.14 thf(fact_4691_listrel__Cons2,axiom,
% 2.86/3.14 ! [Xs: list_int,Y: produc6575502325842934193n_assn,Ys: list_P8527749157015355191n_assn,R2: set_Pr3255386646789011632n_assn] :
% 2.86/3.14 ( ( member490958779117458567n_assn @ ( produc4510294837168919970n_assn @ Xs @ ( cons_P2971678138204555879n_assn @ Y @ Ys ) ) @ ( listre4888949683985722578n_assn @ R2 ) )
% 2.86/3.14 => ~ ! [X3: int,Xs2: list_int] :
% 2.86/3.14 ( ( Xs
% 2.86/3.14 = ( cons_int @ X3 @ Xs2 ) )
% 2.86/3.14 => ( ( member241480614033477777n_assn @ ( produc3313821056773121708n_assn @ X3 @ Y ) @ R2 )
% 2.86/3.14 => ~ ( member490958779117458567n_assn @ ( produc4510294837168919970n_assn @ Xs2 @ Ys ) @ ( listre4888949683985722578n_assn @ R2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % listrel_Cons2
% 2.86/3.14 thf(fact_4692_listrel__Cons2,axiom,
% 2.86/3.14 ! [Xs: list_nat,Y: produc6575502325842934193n_assn,Ys: list_P8527749157015355191n_assn,R2: set_Pr247834672394327052n_assn] :
% 2.86/3.14 ( ( member3687432546746012131n_assn @ ( produc7706768604797473534n_assn @ Xs @ ( cons_P2971678138204555879n_assn @ Y @ Ys ) ) @ ( listre3128913020232611374n_assn @ R2 ) )
% 2.86/3.14 => ~ ! [X3: nat,Xs2: list_nat] :
% 2.86/3.14 ( ( Xs
% 2.86/3.14 = ( cons_nat @ X3 @ Xs2 ) )
% 2.86/3.14 => ( ( member7704815987135142381n_assn @ ( produc1553784393020010504n_assn @ X3 @ Y ) @ R2 )
% 2.86/3.14 => ~ ( member3687432546746012131n_assn @ ( produc7706768604797473534n_assn @ Xs2 @ Ys ) @ ( listre3128913020232611374n_assn @ R2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % listrel_Cons2
% 2.86/3.14 thf(fact_4693_listrel__Cons2,axiom,
% 2.86/3.14 ! [Xs: list_P8527749157015355191n_assn,Y: produc6575502325842934193n_assn,Ys: list_P8527749157015355191n_assn,R2: set_Pr8116311503512020807n_assn] :
% 2.86/3.14 ( ( member3994142547374651152n_assn @ ( produc3014731801419794263n_assn @ Xs @ ( cons_P2971678138204555879n_assn @ Y @ Ys ) ) @ ( listre5253995379918703921n_assn @ R2 ) )
% 2.86/3.14 => ~ ! [X3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( Xs
% 2.86/3.14 = ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) )
% 2.86/3.14 => ( ( member4743710847862083984n_assn @ ( produc6128706242671166167n_assn @ X3 @ Y ) @ R2 )
% 2.86/3.14 => ~ ( member3994142547374651152n_assn @ ( produc3014731801419794263n_assn @ Xs2 @ Ys ) @ ( listre5253995379918703921n_assn @ R2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % listrel_Cons2
% 2.86/3.14 thf(fact_4694_listrel__Cons2,axiom,
% 2.86/3.14 ! [Xs: list_s1210847774152347623at_nat,Y: set_Pr1261947904930325089at_nat,Ys: list_s1210847774152347623at_nat,R2: set_Pr4329608150637261639at_nat] :
% 2.86/3.14 ( ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ Xs @ ( cons_s6881495754146722583at_nat @ Y @ Ys ) ) @ ( listre2047417242196832561at_nat @ R2 ) )
% 2.86/3.14 => ~ ! [X3: set_Pr1261947904930325089at_nat,Xs2: list_s1210847774152347623at_nat] :
% 2.86/3.14 ( ( Xs
% 2.86/3.14 = ( cons_s6881495754146722583at_nat @ X3 @ Xs2 ) )
% 2.86/3.14 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y ) @ R2 )
% 2.86/3.14 => ~ ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ Xs2 @ Ys ) @ ( listre2047417242196832561at_nat @ R2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % listrel_Cons2
% 2.86/3.14 thf(fact_4695_listrel__Cons1,axiom,
% 2.86/3.14 ! [Y: int,Ys: list_int,Xs: list_int,R2: set_Pr958786334691620121nt_int] :
% 2.86/3.14 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ ( cons_int @ Y @ Ys ) @ Xs ) @ ( listrel_int_int @ R2 ) )
% 2.86/3.14 => ~ ! [Y2: int,Ys5: list_int] :
% 2.86/3.14 ( ( Xs
% 2.86/3.14 = ( cons_int @ Y2 @ Ys5 ) )
% 2.86/3.14 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y @ Y2 ) @ R2 )
% 2.86/3.14 => ~ ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Ys @ Ys5 ) @ ( listrel_int_int @ R2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % listrel_Cons1
% 2.86/3.14 thf(fact_4696_listrel__Cons1,axiom,
% 2.86/3.14 ! [Y: int,Ys: list_int,Xs: list_nat,R2: set_Pr3448869479623346877nt_nat] :
% 2.86/3.14 ( ( member9189046780804443046st_nat @ ( produc4542114716404682293st_nat @ ( cons_int @ Y @ Ys ) @ Xs ) @ ( listrel_int_nat @ R2 ) )
% 2.86/3.14 => ~ ! [Y2: nat,Ys5: list_nat] :
% 2.86/3.14 ( ( Xs
% 2.86/3.14 = ( cons_nat @ Y2 @ Ys5 ) )
% 2.86/3.14 => ( ( member216504246829706758nt_nat @ ( product_Pair_int_nat @ Y @ Y2 ) @ R2 )
% 2.86/3.14 => ~ ( member9189046780804443046st_nat @ ( produc4542114716404682293st_nat @ Ys @ Ys5 ) @ ( listrel_int_nat @ R2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % listrel_Cons1
% 2.86/3.14 thf(fact_4697_listrel__Cons1,axiom,
% 2.86/3.14 ! [Y: nat,Ys: list_nat,Xs: list_int,R2: set_Pr7995236796853374141at_int] :
% 2.86/3.14 ( ( member4850886304473975718st_int @ ( produc7739558402351520821st_int @ ( cons_nat @ Y @ Ys ) @ Xs ) @ ( listrel_nat_int @ R2 ) )
% 2.86/3.14 => ~ ! [Y2: int,Ys5: list_int] :
% 2.86/3.14 ( ( Xs
% 2.86/3.14 = ( cons_int @ Y2 @ Ys5 ) )
% 2.86/3.14 => ( ( member4262671552274231302at_int @ ( product_Pair_nat_int @ Y @ Y2 ) @ R2 )
% 2.86/3.14 => ~ ( member4850886304473975718st_int @ ( produc7739558402351520821st_int @ Ys @ Ys5 ) @ ( listrel_nat_int @ R2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % listrel_Cons1
% 2.86/3.14 thf(fact_4698_listrel__Cons1,axiom,
% 2.86/3.14 ! [Y: nat,Ys: list_nat,Xs: list_nat,R2: set_Pr1261947904930325089at_nat] :
% 2.86/3.14 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ ( cons_nat @ Y @ Ys ) @ Xs ) @ ( listrel_nat_nat @ R2 ) )
% 2.86/3.14 => ~ ! [Y2: nat,Ys5: list_nat] :
% 2.86/3.14 ( ( Xs
% 2.86/3.14 = ( cons_nat @ Y2 @ Ys5 ) )
% 2.86/3.14 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y @ Y2 ) @ R2 )
% 2.86/3.14 => ~ ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Ys @ Ys5 ) @ ( listrel_nat_nat @ R2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % listrel_Cons1
% 2.86/3.14 thf(fact_4699_listrel__Cons1,axiom,
% 2.86/3.14 ! [Y: int,Ys: list_int,Xs: list_P8527749157015355191n_assn,R2: set_Pr3255386646789011632n_assn] :
% 2.86/3.14 ( ( member490958779117458567n_assn @ ( produc4510294837168919970n_assn @ ( cons_int @ Y @ Ys ) @ Xs ) @ ( listre4888949683985722578n_assn @ R2 ) )
% 2.86/3.14 => ~ ! [Y2: produc6575502325842934193n_assn,Ys5: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( Xs
% 2.86/3.14 = ( cons_P2971678138204555879n_assn @ Y2 @ Ys5 ) )
% 2.86/3.14 => ( ( member241480614033477777n_assn @ ( produc3313821056773121708n_assn @ Y @ Y2 ) @ R2 )
% 2.86/3.14 => ~ ( member490958779117458567n_assn @ ( produc4510294837168919970n_assn @ Ys @ Ys5 ) @ ( listre4888949683985722578n_assn @ R2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % listrel_Cons1
% 2.86/3.14 thf(fact_4700_listrel__Cons1,axiom,
% 2.86/3.14 ! [Y: nat,Ys: list_nat,Xs: list_P8527749157015355191n_assn,R2: set_Pr247834672394327052n_assn] :
% 2.86/3.14 ( ( member3687432546746012131n_assn @ ( produc7706768604797473534n_assn @ ( cons_nat @ Y @ Ys ) @ Xs ) @ ( listre3128913020232611374n_assn @ R2 ) )
% 2.86/3.14 => ~ ! [Y2: produc6575502325842934193n_assn,Ys5: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( Xs
% 2.86/3.14 = ( cons_P2971678138204555879n_assn @ Y2 @ Ys5 ) )
% 2.86/3.14 => ( ( member7704815987135142381n_assn @ ( produc1553784393020010504n_assn @ Y @ Y2 ) @ R2 )
% 2.86/3.14 => ~ ( member3687432546746012131n_assn @ ( produc7706768604797473534n_assn @ Ys @ Ys5 ) @ ( listre3128913020232611374n_assn @ R2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % listrel_Cons1
% 2.86/3.14 thf(fact_4701_listrel__Cons1,axiom,
% 2.86/3.14 ! [Y: produc6575502325842934193n_assn,Ys: list_P8527749157015355191n_assn,Xs: list_int,R2: set_Pr2181989527757714242sn_int] :
% 2.86/3.14 ( ( member5295696281703116473st_int @ ( produc1996262876970182428st_int @ ( cons_P2971678138204555879n_assn @ Y @ Ys ) @ Xs ) @ ( listre8029020076619294380sn_int @ R2 ) )
% 2.86/3.14 => ~ ! [Y2: int,Ys5: list_int] :
% 2.86/3.14 ( ( Xs
% 2.86/3.14 = ( cons_int @ Y2 @ Ys5 ) )
% 2.86/3.14 => ( ( member5792320502188913699sn_int @ ( produc6453891449406693510sn_int @ Y @ Y2 ) @ R2 )
% 2.86/3.14 => ~ ( member5295696281703116473st_int @ ( produc1996262876970182428st_int @ Ys @ Ys5 ) @ ( listre8029020076619294380sn_int @ R2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % listrel_Cons1
% 2.86/3.14 thf(fact_4702_listrel__Cons1,axiom,
% 2.86/3.14 ! [Y: produc6575502325842934193n_assn,Ys: list_P8527749157015355191n_assn,Xs: list_nat,R2: set_Pr4672072672689440998sn_nat] :
% 2.86/3.14 ( ( member7785779426634843229st_nat @ ( produc6174113896479379136st_nat @ ( cons_P2971678138204555879n_assn @ Y @ Ys ) @ Xs ) @ ( listre8031510547128344656sn_nat @ R2 ) )
% 2.86/3.14 => ~ ! [Y2: nat,Ys5: list_nat] :
% 2.86/3.14 ( ( Xs
% 2.86/3.14 = ( cons_nat @ Y2 @ Ys5 ) )
% 2.86/3.14 => ( ( member746799484843334599sn_nat @ ( produc6456381919915743786sn_nat @ Y @ Y2 ) @ R2 )
% 2.86/3.14 => ~ ( member7785779426634843229st_nat @ ( produc6174113896479379136st_nat @ Ys @ Ys5 ) @ ( listre8031510547128344656sn_nat @ R2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % listrel_Cons1
% 2.86/3.14 thf(fact_4703_listrel__Cons1,axiom,
% 2.86/3.14 ! [Y: produc6575502325842934193n_assn,Ys: list_P8527749157015355191n_assn,Xs: list_P8527749157015355191n_assn,R2: set_Pr8116311503512020807n_assn] :
% 2.86/3.14 ( ( member3994142547374651152n_assn @ ( produc3014731801419794263n_assn @ ( cons_P2971678138204555879n_assn @ Y @ Ys ) @ Xs ) @ ( listre5253995379918703921n_assn @ R2 ) )
% 2.86/3.14 => ~ ! [Y2: produc6575502325842934193n_assn,Ys5: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( Xs
% 2.86/3.14 = ( cons_P2971678138204555879n_assn @ Y2 @ Ys5 ) )
% 2.86/3.14 => ( ( member4743710847862083984n_assn @ ( produc6128706242671166167n_assn @ Y @ Y2 ) @ R2 )
% 2.86/3.14 => ~ ( member3994142547374651152n_assn @ ( produc3014731801419794263n_assn @ Ys @ Ys5 ) @ ( listre5253995379918703921n_assn @ R2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % listrel_Cons1
% 2.86/3.14 thf(fact_4704_listrel__Cons1,axiom,
% 2.86/3.14 ! [Y: set_Pr1261947904930325089at_nat,Ys: list_s1210847774152347623at_nat,Xs: list_s1210847774152347623at_nat,R2: set_Pr4329608150637261639at_nat] :
% 2.86/3.14 ( ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ ( cons_s6881495754146722583at_nat @ Y @ Ys ) @ Xs ) @ ( listre2047417242196832561at_nat @ R2 ) )
% 2.86/3.14 => ~ ! [Y2: set_Pr1261947904930325089at_nat,Ys5: list_s1210847774152347623at_nat] :
% 2.86/3.14 ( ( Xs
% 2.86/3.14 = ( cons_s6881495754146722583at_nat @ Y2 @ Ys5 ) )
% 2.86/3.14 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y @ Y2 ) @ R2 )
% 2.86/3.14 => ~ ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ Ys @ Ys5 ) @ ( listre2047417242196832561at_nat @ R2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % listrel_Cons1
% 2.86/3.14 thf(fact_4705_listrel_OCons,axiom,
% 2.86/3.14 ! [X: int,Y: int,R2: set_Pr958786334691620121nt_int,Xs: list_int,Ys: list_int] :
% 2.86/3.14 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R2 )
% 2.86/3.14 => ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs @ Ys ) @ ( listrel_int_int @ R2 ) )
% 2.86/3.14 => ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ ( cons_int @ X @ Xs ) @ ( cons_int @ Y @ Ys ) ) @ ( listrel_int_int @ R2 ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % listrel.Cons
% 2.86/3.14 thf(fact_4706_listrel_OCons,axiom,
% 2.86/3.14 ! [X: int,Y: nat,R2: set_Pr3448869479623346877nt_nat,Xs: list_int,Ys: list_nat] :
% 2.86/3.14 ( ( member216504246829706758nt_nat @ ( product_Pair_int_nat @ X @ Y ) @ R2 )
% 2.86/3.14 => ( ( member9189046780804443046st_nat @ ( produc4542114716404682293st_nat @ Xs @ Ys ) @ ( listrel_int_nat @ R2 ) )
% 2.86/3.14 => ( member9189046780804443046st_nat @ ( produc4542114716404682293st_nat @ ( cons_int @ X @ Xs ) @ ( cons_nat @ Y @ Ys ) ) @ ( listrel_int_nat @ R2 ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % listrel.Cons
% 2.86/3.14 thf(fact_4707_listrel_OCons,axiom,
% 2.86/3.14 ! [X: nat,Y: int,R2: set_Pr7995236796853374141at_int,Xs: list_nat,Ys: list_int] :
% 2.86/3.14 ( ( member4262671552274231302at_int @ ( product_Pair_nat_int @ X @ Y ) @ R2 )
% 2.86/3.14 => ( ( member4850886304473975718st_int @ ( produc7739558402351520821st_int @ Xs @ Ys ) @ ( listrel_nat_int @ R2 ) )
% 2.86/3.14 => ( member4850886304473975718st_int @ ( produc7739558402351520821st_int @ ( cons_nat @ X @ Xs ) @ ( cons_int @ Y @ Ys ) ) @ ( listrel_nat_int @ R2 ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % listrel.Cons
% 2.86/3.14 thf(fact_4708_listrel_OCons,axiom,
% 2.86/3.14 ! [X: nat,Y: nat,R2: set_Pr1261947904930325089at_nat,Xs: list_nat,Ys: list_nat] :
% 2.86/3.14 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R2 )
% 2.86/3.14 => ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs @ Ys ) @ ( listrel_nat_nat @ R2 ) )
% 2.86/3.14 => ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ ( cons_nat @ X @ Xs ) @ ( cons_nat @ Y @ Ys ) ) @ ( listrel_nat_nat @ R2 ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % listrel.Cons
% 2.86/3.14 thf(fact_4709_listrel_OCons,axiom,
% 2.86/3.14 ! [X: int,Y: produc6575502325842934193n_assn,R2: set_Pr3255386646789011632n_assn,Xs: list_int,Ys: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( member241480614033477777n_assn @ ( produc3313821056773121708n_assn @ X @ Y ) @ R2 )
% 2.86/3.14 => ( ( member490958779117458567n_assn @ ( produc4510294837168919970n_assn @ Xs @ Ys ) @ ( listre4888949683985722578n_assn @ R2 ) )
% 2.86/3.14 => ( member490958779117458567n_assn @ ( produc4510294837168919970n_assn @ ( cons_int @ X @ Xs ) @ ( cons_P2971678138204555879n_assn @ Y @ Ys ) ) @ ( listre4888949683985722578n_assn @ R2 ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % listrel.Cons
% 2.86/3.14 thf(fact_4710_listrel_OCons,axiom,
% 2.86/3.14 ! [X: nat,Y: produc6575502325842934193n_assn,R2: set_Pr247834672394327052n_assn,Xs: list_nat,Ys: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( member7704815987135142381n_assn @ ( produc1553784393020010504n_assn @ X @ Y ) @ R2 )
% 2.86/3.14 => ( ( member3687432546746012131n_assn @ ( produc7706768604797473534n_assn @ Xs @ Ys ) @ ( listre3128913020232611374n_assn @ R2 ) )
% 2.86/3.14 => ( member3687432546746012131n_assn @ ( produc7706768604797473534n_assn @ ( cons_nat @ X @ Xs ) @ ( cons_P2971678138204555879n_assn @ Y @ Ys ) ) @ ( listre3128913020232611374n_assn @ R2 ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % listrel.Cons
% 2.86/3.14 thf(fact_4711_listrel_OCons,axiom,
% 2.86/3.14 ! [X: produc6575502325842934193n_assn,Y: int,R2: set_Pr2181989527757714242sn_int,Xs: list_P8527749157015355191n_assn,Ys: list_int] :
% 2.86/3.14 ( ( member5792320502188913699sn_int @ ( produc6453891449406693510sn_int @ X @ Y ) @ R2 )
% 2.86/3.14 => ( ( member5295696281703116473st_int @ ( produc1996262876970182428st_int @ Xs @ Ys ) @ ( listre8029020076619294380sn_int @ R2 ) )
% 2.86/3.14 => ( member5295696281703116473st_int @ ( produc1996262876970182428st_int @ ( cons_P2971678138204555879n_assn @ X @ Xs ) @ ( cons_int @ Y @ Ys ) ) @ ( listre8029020076619294380sn_int @ R2 ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % listrel.Cons
% 2.86/3.14 thf(fact_4712_listrel_OCons,axiom,
% 2.86/3.14 ! [X: produc6575502325842934193n_assn,Y: nat,R2: set_Pr4672072672689440998sn_nat,Xs: list_P8527749157015355191n_assn,Ys: list_nat] :
% 2.86/3.14 ( ( member746799484843334599sn_nat @ ( produc6456381919915743786sn_nat @ X @ Y ) @ R2 )
% 2.86/3.14 => ( ( member7785779426634843229st_nat @ ( produc6174113896479379136st_nat @ Xs @ Ys ) @ ( listre8031510547128344656sn_nat @ R2 ) )
% 2.86/3.14 => ( member7785779426634843229st_nat @ ( produc6174113896479379136st_nat @ ( cons_P2971678138204555879n_assn @ X @ Xs ) @ ( cons_nat @ Y @ Ys ) ) @ ( listre8031510547128344656sn_nat @ R2 ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % listrel.Cons
% 2.86/3.14 thf(fact_4713_listrel_OCons,axiom,
% 2.86/3.14 ! [X: produc6575502325842934193n_assn,Y: produc6575502325842934193n_assn,R2: set_Pr8116311503512020807n_assn,Xs: list_P8527749157015355191n_assn,Ys: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( member4743710847862083984n_assn @ ( produc6128706242671166167n_assn @ X @ Y ) @ R2 )
% 2.86/3.14 => ( ( member3994142547374651152n_assn @ ( produc3014731801419794263n_assn @ Xs @ Ys ) @ ( listre5253995379918703921n_assn @ R2 ) )
% 2.86/3.14 => ( member3994142547374651152n_assn @ ( produc3014731801419794263n_assn @ ( cons_P2971678138204555879n_assn @ X @ Xs ) @ ( cons_P2971678138204555879n_assn @ Y @ Ys ) ) @ ( listre5253995379918703921n_assn @ R2 ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % listrel.Cons
% 2.86/3.14 thf(fact_4714_listrel_OCons,axiom,
% 2.86/3.14 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,R2: set_Pr4329608150637261639at_nat,Xs: list_s1210847774152347623at_nat,Ys: list_s1210847774152347623at_nat] :
% 2.86/3.14 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ R2 )
% 2.86/3.14 => ( ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ Xs @ Ys ) @ ( listre2047417242196832561at_nat @ R2 ) )
% 2.86/3.14 => ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ ( cons_s6881495754146722583at_nat @ X @ Xs ) @ ( cons_s6881495754146722583at_nat @ Y @ Ys ) ) @ ( listre2047417242196832561at_nat @ R2 ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % listrel.Cons
% 2.86/3.14 thf(fact_4715_list_Osize_I4_J,axiom,
% 2.86/3.14 ! [X21: produc6575502325842934193n_assn,X222: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( size_s6829681357464350627n_assn @ ( cons_P2971678138204555879n_assn @ X21 @ X222 ) )
% 2.86/3.14 = ( plus_plus_nat @ ( size_s6829681357464350627n_assn @ X222 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list.size(4)
% 2.86/3.14 thf(fact_4716_list_Osize_I4_J,axiom,
% 2.86/3.14 ! [X21: c,X222: list_c] :
% 2.86/3.14 ( ( size_size_list_c @ ( cons_c @ X21 @ X222 ) )
% 2.86/3.14 = ( plus_plus_nat @ ( size_size_list_c @ X222 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list.size(4)
% 2.86/3.14 thf(fact_4717_list_Osize_I4_J,axiom,
% 2.86/3.14 ! [X21: d,X222: list_d] :
% 2.86/3.14 ( ( size_size_list_d @ ( cons_d @ X21 @ X222 ) )
% 2.86/3.14 = ( plus_plus_nat @ ( size_size_list_d @ X222 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list.size(4)
% 2.86/3.14 thf(fact_4718_list_Osize_I4_J,axiom,
% 2.86/3.14 ! [X21: nat,X222: list_nat] :
% 2.86/3.14 ( ( size_size_list_nat @ ( cons_nat @ X21 @ X222 ) )
% 2.86/3.14 = ( plus_plus_nat @ ( size_size_list_nat @ X222 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list.size(4)
% 2.86/3.14 thf(fact_4719_list_Osize_I4_J,axiom,
% 2.86/3.14 ! [X21: int,X222: list_int] :
% 2.86/3.14 ( ( size_size_list_int @ ( cons_int @ X21 @ X222 ) )
% 2.86/3.14 = ( plus_plus_nat @ ( size_size_list_int @ X222 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list.size(4)
% 2.86/3.14 thf(fact_4720_nth__Cons_H,axiom,
% 2.86/3.14 ! [N: nat,X: int,Xs: list_int] :
% 2.86/3.14 ( ( ( N = zero_zero_nat )
% 2.86/3.14 => ( ( nth_int @ ( cons_int @ X @ Xs ) @ N )
% 2.86/3.14 = X ) )
% 2.86/3.14 & ( ( N != zero_zero_nat )
% 2.86/3.14 => ( ( nth_int @ ( cons_int @ X @ Xs ) @ N )
% 2.86/3.14 = ( nth_int @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % nth_Cons'
% 2.86/3.14 thf(fact_4721_nth__Cons_H,axiom,
% 2.86/3.14 ! [N: nat,X: nat,Xs: list_nat] :
% 2.86/3.14 ( ( ( N = zero_zero_nat )
% 2.86/3.14 => ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ N )
% 2.86/3.14 = X ) )
% 2.86/3.14 & ( ( N != zero_zero_nat )
% 2.86/3.14 => ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ N )
% 2.86/3.14 = ( nth_nat @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % nth_Cons'
% 2.86/3.14 thf(fact_4722_nth__Cons_H,axiom,
% 2.86/3.14 ! [N: nat,X: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( ( N = zero_zero_nat )
% 2.86/3.14 => ( ( nth_Pr1769885009046257848n_assn @ ( cons_P2971678138204555879n_assn @ X @ Xs ) @ N )
% 2.86/3.14 = X ) )
% 2.86/3.14 & ( ( N != zero_zero_nat )
% 2.86/3.14 => ( ( nth_Pr1769885009046257848n_assn @ ( cons_P2971678138204555879n_assn @ X @ Xs ) @ N )
% 2.86/3.14 = ( nth_Pr1769885009046257848n_assn @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % nth_Cons'
% 2.86/3.14 thf(fact_4723_nth__equal__first__eq,axiom,
% 2.86/3.14 ! [X: produc3843707927480180839at_nat,Xs: list_P5464809261938338413at_nat,N: nat] :
% 2.86/3.14 ( ~ ( member8757157785044589968at_nat @ X @ ( set_Pr3765526544606949372at_nat @ Xs ) )
% 2.86/3.14 => ( ( ord_less_eq_nat @ N @ ( size_s1588839187904960729at_nat @ Xs ) )
% 2.86/3.14 => ( ( ( nth_Pr1239524528086697198at_nat @ ( cons_P3940603068885512221at_nat @ X @ Xs ) @ N )
% 2.86/3.14 = X )
% 2.86/3.14 = ( N = zero_zero_nat ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % nth_equal_first_eq
% 2.86/3.14 thf(fact_4724_nth__equal__first__eq,axiom,
% 2.86/3.14 ! [X: product_prod_nat_nat,Xs: list_P6011104703257516679at_nat,N: nat] :
% 2.86/3.14 ( ~ ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 2.86/3.14 => ( ( ord_less_eq_nat @ N @ ( size_s5460976970255530739at_nat @ Xs ) )
% 2.86/3.14 => ( ( ( nth_Pr7617993195940197384at_nat @ ( cons_P6512896166579812791at_nat @ X @ Xs ) @ N )
% 2.86/3.14 = X )
% 2.86/3.14 = ( N = zero_zero_nat ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % nth_equal_first_eq
% 2.86/3.14 thf(fact_4725_nth__equal__first__eq,axiom,
% 2.86/3.14 ! [X: produc3658429121746597890et_nat > $o,Xs: list_P7985473006766602707_nat_o,N: nat] :
% 2.86/3.14 ( ~ ( member6576561426505652726_nat_o @ X @ ( set_Pr400311997697478754_nat_o @ Xs ) )
% 2.86/3.14 => ( ( ord_less_eq_nat @ N @ ( size_s8908918004648414271_nat_o @ Xs ) )
% 2.86/3.14 => ( ( ( nth_Pr6840583978799713108_nat_o @ ( cons_P6219271836124797827_nat_o @ X @ Xs ) @ N )
% 2.86/3.14 = X )
% 2.86/3.14 = ( N = zero_zero_nat ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % nth_equal_first_eq
% 2.86/3.14 thf(fact_4726_nth__equal__first__eq,axiom,
% 2.86/3.14 ! [X: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn,N: nat] :
% 2.86/3.14 ( ~ ( member7957490590177025114n_assn @ X @ ( set_Pr1139785259514867910n_assn @ Xs ) )
% 2.86/3.14 => ( ( ord_less_eq_nat @ N @ ( size_s6829681357464350627n_assn @ Xs ) )
% 2.86/3.14 => ( ( ( nth_Pr1769885009046257848n_assn @ ( cons_P2971678138204555879n_assn @ X @ Xs ) @ N )
% 2.86/3.14 = X )
% 2.86/3.14 = ( N = zero_zero_nat ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % nth_equal_first_eq
% 2.86/3.14 thf(fact_4727_nth__equal__first__eq,axiom,
% 2.86/3.14 ! [X: c,Xs: list_c,N: nat] :
% 2.86/3.14 ( ~ ( member_c @ X @ ( set_c2 @ Xs ) )
% 2.86/3.14 => ( ( ord_less_eq_nat @ N @ ( size_size_list_c @ Xs ) )
% 2.86/3.14 => ( ( ( nth_c @ ( cons_c @ X @ Xs ) @ N )
% 2.86/3.14 = X )
% 2.86/3.14 = ( N = zero_zero_nat ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % nth_equal_first_eq
% 2.86/3.14 thf(fact_4728_nth__equal__first__eq,axiom,
% 2.86/3.14 ! [X: d,Xs: list_d,N: nat] :
% 2.86/3.14 ( ~ ( member_d @ X @ ( set_d2 @ Xs ) )
% 2.86/3.14 => ( ( ord_less_eq_nat @ N @ ( size_size_list_d @ Xs ) )
% 2.86/3.14 => ( ( ( nth_d @ ( cons_d @ X @ Xs ) @ N )
% 2.86/3.14 = X )
% 2.86/3.14 = ( N = zero_zero_nat ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % nth_equal_first_eq
% 2.86/3.14 thf(fact_4729_nth__equal__first__eq,axiom,
% 2.86/3.14 ! [X: nat,Xs: list_nat,N: nat] :
% 2.86/3.14 ( ~ ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 2.86/3.14 => ( ( ord_less_eq_nat @ N @ ( size_size_list_nat @ Xs ) )
% 2.86/3.14 => ( ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ N )
% 2.86/3.14 = X )
% 2.86/3.14 = ( N = zero_zero_nat ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % nth_equal_first_eq
% 2.86/3.14 thf(fact_4730_nth__equal__first__eq,axiom,
% 2.86/3.14 ! [X: int,Xs: list_int,N: nat] :
% 2.86/3.14 ( ~ ( member_int @ X @ ( set_int2 @ Xs ) )
% 2.86/3.14 => ( ( ord_less_eq_nat @ N @ ( size_size_list_int @ Xs ) )
% 2.86/3.14 => ( ( ( nth_int @ ( cons_int @ X @ Xs ) @ N )
% 2.86/3.14 = X )
% 2.86/3.14 = ( N = zero_zero_nat ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % nth_equal_first_eq
% 2.86/3.14 thf(fact_4731_nth__non__equal__first__eq,axiom,
% 2.86/3.14 ! [X: int,Y: int,Xs: list_int,N: nat] :
% 2.86/3.14 ( ( X != Y )
% 2.86/3.14 => ( ( ( nth_int @ ( cons_int @ X @ Xs ) @ N )
% 2.86/3.14 = Y )
% 2.86/3.14 = ( ( ( nth_int @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) )
% 2.86/3.14 = Y )
% 2.86/3.14 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % nth_non_equal_first_eq
% 2.86/3.14 thf(fact_4732_nth__non__equal__first__eq,axiom,
% 2.86/3.14 ! [X: nat,Y: nat,Xs: list_nat,N: nat] :
% 2.86/3.14 ( ( X != Y )
% 2.86/3.14 => ( ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ N )
% 2.86/3.14 = Y )
% 2.86/3.14 = ( ( ( nth_nat @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) )
% 2.86/3.14 = Y )
% 2.86/3.14 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % nth_non_equal_first_eq
% 2.86/3.14 thf(fact_4733_nth__non__equal__first__eq,axiom,
% 2.86/3.14 ! [X: produc6575502325842934193n_assn,Y: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn,N: nat] :
% 2.86/3.14 ( ( X != Y )
% 2.86/3.14 => ( ( ( nth_Pr1769885009046257848n_assn @ ( cons_P2971678138204555879n_assn @ X @ Xs ) @ N )
% 2.86/3.14 = Y )
% 2.86/3.14 = ( ( ( nth_Pr1769885009046257848n_assn @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) )
% 2.86/3.14 = Y )
% 2.86/3.14 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % nth_non_equal_first_eq
% 2.86/3.14 thf(fact_4734_slice__Cons,axiom,
% 2.86/3.14 ! [Begin: nat,End: nat,X: int,Xs: list_int] :
% 2.86/3.14 ( ( ( ( Begin = zero_zero_nat )
% 2.86/3.14 & ( ord_less_nat @ zero_zero_nat @ End ) )
% 2.86/3.14 => ( ( slice_int @ Begin @ End @ ( cons_int @ X @ Xs ) )
% 2.86/3.14 = ( cons_int @ X @ ( slice_int @ Begin @ ( minus_minus_nat @ End @ one_one_nat ) @ Xs ) ) ) )
% 2.86/3.14 & ( ~ ( ( Begin = zero_zero_nat )
% 2.86/3.14 & ( ord_less_nat @ zero_zero_nat @ End ) )
% 2.86/3.14 => ( ( slice_int @ Begin @ End @ ( cons_int @ X @ Xs ) )
% 2.86/3.14 = ( slice_int @ ( minus_minus_nat @ Begin @ one_one_nat ) @ ( minus_minus_nat @ End @ one_one_nat ) @ Xs ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % slice_Cons
% 2.86/3.14 thf(fact_4735_slice__Cons,axiom,
% 2.86/3.14 ! [Begin: nat,End: nat,X: nat,Xs: list_nat] :
% 2.86/3.14 ( ( ( ( Begin = zero_zero_nat )
% 2.86/3.14 & ( ord_less_nat @ zero_zero_nat @ End ) )
% 2.86/3.14 => ( ( slice_nat @ Begin @ End @ ( cons_nat @ X @ Xs ) )
% 2.86/3.14 = ( cons_nat @ X @ ( slice_nat @ Begin @ ( minus_minus_nat @ End @ one_one_nat ) @ Xs ) ) ) )
% 2.86/3.14 & ( ~ ( ( Begin = zero_zero_nat )
% 2.86/3.14 & ( ord_less_nat @ zero_zero_nat @ End ) )
% 2.86/3.14 => ( ( slice_nat @ Begin @ End @ ( cons_nat @ X @ Xs ) )
% 2.86/3.14 = ( slice_nat @ ( minus_minus_nat @ Begin @ one_one_nat ) @ ( minus_minus_nat @ End @ one_one_nat ) @ Xs ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % slice_Cons
% 2.86/3.14 thf(fact_4736_slice__Cons,axiom,
% 2.86/3.14 ! [Begin: nat,End: nat,X: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( ( ( Begin = zero_zero_nat )
% 2.86/3.14 & ( ord_less_nat @ zero_zero_nat @ End ) )
% 2.86/3.14 => ( ( slice_7964966981652229398n_assn @ Begin @ End @ ( cons_P2971678138204555879n_assn @ X @ Xs ) )
% 2.86/3.14 = ( cons_P2971678138204555879n_assn @ X @ ( slice_7964966981652229398n_assn @ Begin @ ( minus_minus_nat @ End @ one_one_nat ) @ Xs ) ) ) )
% 2.86/3.14 & ( ~ ( ( Begin = zero_zero_nat )
% 2.86/3.14 & ( ord_less_nat @ zero_zero_nat @ End ) )
% 2.86/3.14 => ( ( slice_7964966981652229398n_assn @ Begin @ End @ ( cons_P2971678138204555879n_assn @ X @ Xs ) )
% 2.86/3.14 = ( slice_7964966981652229398n_assn @ ( minus_minus_nat @ Begin @ one_one_nat ) @ ( minus_minus_nat @ End @ one_one_nat ) @ Xs ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % slice_Cons
% 2.86/3.14 thf(fact_4737_times__assn__raw_Opelims_I1_J,axiom,
% 2.86/3.14 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Y: $o] :
% 2.86/3.14 ( ( ( times_assn_raw @ X @ Xa @ Xb )
% 2.86/3.14 = Y )
% 2.86/3.14 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 2.86/3.14 => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.86/3.14 ( ( Xb
% 2.86/3.14 = ( produc7507926704131184380et_nat @ H @ As ) )
% 2.86/3.14 => ( ( Y
% 2.86/3.14 = ( ? [As1: set_nat,As22: set_nat] :
% 2.86/3.14 ( ( As
% 2.86/3.14 = ( sup_sup_set_nat @ As1 @ As22 ) )
% 2.86/3.14 & ( ( inf_inf_set_nat @ As1 @ As22 )
% 2.86/3.14 = bot_bot_set_nat )
% 2.86/3.14 & ( X @ ( produc7507926704131184380et_nat @ H @ As1 ) )
% 2.86/3.14 & ( Xa @ ( produc7507926704131184380et_nat @ H @ As22 ) ) ) ) )
% 2.86/3.14 => ~ ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H @ As ) ) ) ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % times_assn_raw.pelims(1)
% 2.86/3.14 thf(fact_4738_length__Cons,axiom,
% 2.86/3.14 ! [X: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( size_s6829681357464350627n_assn @ ( cons_P2971678138204555879n_assn @ X @ Xs ) )
% 2.86/3.14 = ( suc @ ( size_s6829681357464350627n_assn @ Xs ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % length_Cons
% 2.86/3.14 thf(fact_4739_length__Cons,axiom,
% 2.86/3.14 ! [X: c,Xs: list_c] :
% 2.86/3.14 ( ( size_size_list_c @ ( cons_c @ X @ Xs ) )
% 2.86/3.14 = ( suc @ ( size_size_list_c @ Xs ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % length_Cons
% 2.86/3.14 thf(fact_4740_length__Cons,axiom,
% 2.86/3.14 ! [X: d,Xs: list_d] :
% 2.86/3.14 ( ( size_size_list_d @ ( cons_d @ X @ Xs ) )
% 2.86/3.14 = ( suc @ ( size_size_list_d @ Xs ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % length_Cons
% 2.86/3.14 thf(fact_4741_length__Cons,axiom,
% 2.86/3.14 ! [X: nat,Xs: list_nat] :
% 2.86/3.14 ( ( size_size_list_nat @ ( cons_nat @ X @ Xs ) )
% 2.86/3.14 = ( suc @ ( size_size_list_nat @ Xs ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % length_Cons
% 2.86/3.14 thf(fact_4742_length__Cons,axiom,
% 2.86/3.14 ! [X: int,Xs: list_int] :
% 2.86/3.14 ( ( size_size_list_int @ ( cons_int @ X @ Xs ) )
% 2.86/3.14 = ( suc @ ( size_size_list_int @ Xs ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % length_Cons
% 2.86/3.14 thf(fact_4743_Cons__lenlex__iff,axiom,
% 2.86/3.14 ! [M2: set_Pr1261947904930325089at_nat,Ms: list_s1210847774152347623at_nat,N: set_Pr1261947904930325089at_nat,Ns: list_s1210847774152347623at_nat,R2: set_Pr4329608150637261639at_nat] :
% 2.86/3.14 ( ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ ( cons_s6881495754146722583at_nat @ M2 @ Ms ) @ ( cons_s6881495754146722583at_nat @ N @ Ns ) ) @ ( lenlex1357538814655152620at_nat @ R2 ) )
% 2.86/3.14 = ( ( ord_less_nat @ ( size_s8736152011456118867at_nat @ Ms ) @ ( size_s8736152011456118867at_nat @ Ns ) )
% 2.86/3.14 | ( ( ( size_s8736152011456118867at_nat @ Ms )
% 2.86/3.14 = ( size_s8736152011456118867at_nat @ Ns ) )
% 2.86/3.14 & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ M2 @ N ) @ R2 ) )
% 2.86/3.14 | ( ( M2 = N )
% 2.86/3.14 & ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ Ms @ Ns ) @ ( lenlex1357538814655152620at_nat @ R2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % Cons_lenlex_iff
% 2.86/3.14 thf(fact_4744_Cons__lenlex__iff,axiom,
% 2.86/3.14 ! [M2: produc6575502325842934193n_assn,Ms: list_P8527749157015355191n_assn,N: produc6575502325842934193n_assn,Ns: list_P8527749157015355191n_assn,R2: set_Pr8116311503512020807n_assn] :
% 2.86/3.14 ( ( member3994142547374651152n_assn @ ( produc3014731801419794263n_assn @ ( cons_P2971678138204555879n_assn @ M2 @ Ms ) @ ( cons_P2971678138204555879n_assn @ N @ Ns ) ) @ ( lenlex6671093235567761724n_assn @ R2 ) )
% 2.86/3.14 = ( ( ord_less_nat @ ( size_s6829681357464350627n_assn @ Ms ) @ ( size_s6829681357464350627n_assn @ Ns ) )
% 2.86/3.14 | ( ( ( size_s6829681357464350627n_assn @ Ms )
% 2.86/3.14 = ( size_s6829681357464350627n_assn @ Ns ) )
% 2.86/3.14 & ( member4743710847862083984n_assn @ ( produc6128706242671166167n_assn @ M2 @ N ) @ R2 ) )
% 2.86/3.14 | ( ( M2 = N )
% 2.86/3.14 & ( member3994142547374651152n_assn @ ( produc3014731801419794263n_assn @ Ms @ Ns ) @ ( lenlex6671093235567761724n_assn @ R2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % Cons_lenlex_iff
% 2.86/3.14 thf(fact_4745_Cons__lenlex__iff,axiom,
% 2.86/3.14 ! [M2: c,Ms: list_c,N: c,Ns: list_c,R2: set_Product_prod_c_c] :
% 2.86/3.14 ( ( member7012247553653173456list_c @ ( produc5515445818230282391list_c @ ( cons_c @ M2 @ Ms ) @ ( cons_c @ N @ Ns ) ) @ ( lenlex_c @ R2 ) )
% 2.86/3.14 = ( ( ord_less_nat @ ( size_size_list_c @ Ms ) @ ( size_size_list_c @ Ns ) )
% 2.86/3.14 | ( ( ( size_size_list_c @ Ms )
% 2.86/3.14 = ( size_size_list_c @ Ns ) )
% 2.86/3.14 & ( member5074992359041316560od_c_c @ ( product_Pair_c_c @ M2 @ N ) @ R2 ) )
% 2.86/3.14 | ( ( M2 = N )
% 2.86/3.14 & ( member7012247553653173456list_c @ ( produc5515445818230282391list_c @ Ms @ Ns ) @ ( lenlex_c @ R2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % Cons_lenlex_iff
% 2.86/3.14 thf(fact_4746_Cons__lenlex__iff,axiom,
% 2.86/3.14 ! [M2: d,Ms: list_d,N: d,Ns: list_d,R2: set_Product_prod_d_d] :
% 2.86/3.14 ( ( member1810801192463332112list_d @ ( produc242965421297323863list_d @ ( cons_d @ M2 @ Ms ) @ ( cons_d @ N @ Ns ) ) @ ( lenlex_d @ R2 ) )
% 2.86/3.14 = ( ( ord_less_nat @ ( size_size_list_d @ Ms ) @ ( size_size_list_d @ Ns ) )
% 2.86/3.14 | ( ( ( size_size_list_d @ Ms )
% 2.86/3.14 = ( size_size_list_d @ Ns ) )
% 2.86/3.14 & ( member2287536781371869328od_d_d @ ( product_Pair_d_d @ M2 @ N ) @ R2 ) )
% 2.86/3.14 | ( ( M2 = N )
% 2.86/3.14 & ( member1810801192463332112list_d @ ( produc242965421297323863list_d @ Ms @ Ns ) @ ( lenlex_d @ R2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % Cons_lenlex_iff
% 2.86/3.14 thf(fact_4747_Cons__lenlex__iff,axiom,
% 2.86/3.14 ! [M2: nat,Ms: list_nat,N: nat,Ns: list_nat,R2: set_Pr1261947904930325089at_nat] :
% 2.86/3.14 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ ( cons_nat @ M2 @ Ms ) @ ( cons_nat @ N @ Ns ) ) @ ( lenlex_nat @ R2 ) )
% 2.86/3.14 = ( ( ord_less_nat @ ( size_size_list_nat @ Ms ) @ ( size_size_list_nat @ Ns ) )
% 2.86/3.14 | ( ( ( size_size_list_nat @ Ms )
% 2.86/3.14 = ( size_size_list_nat @ Ns ) )
% 2.86/3.14 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M2 @ N ) @ R2 ) )
% 2.86/3.14 | ( ( M2 = N )
% 2.86/3.14 & ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Ms @ Ns ) @ ( lenlex_nat @ R2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % Cons_lenlex_iff
% 2.86/3.14 thf(fact_4748_Cons__lenlex__iff,axiom,
% 2.86/3.14 ! [M2: int,Ms: list_int,N: int,Ns: list_int,R2: set_Pr958786334691620121nt_int] :
% 2.86/3.14 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ ( cons_int @ M2 @ Ms ) @ ( cons_int @ N @ Ns ) ) @ ( lenlex_int @ R2 ) )
% 2.86/3.14 = ( ( ord_less_nat @ ( size_size_list_int @ Ms ) @ ( size_size_list_int @ Ns ) )
% 2.86/3.14 | ( ( ( size_size_list_int @ Ms )
% 2.86/3.14 = ( size_size_list_int @ Ns ) )
% 2.86/3.14 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ M2 @ N ) @ R2 ) )
% 2.86/3.14 | ( ( M2 = N )
% 2.86/3.14 & ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Ms @ Ns ) @ ( lenlex_int @ R2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % Cons_lenlex_iff
% 2.86/3.14 thf(fact_4749_Cons__in__lex,axiom,
% 2.86/3.14 ! [X: set_Pr1261947904930325089at_nat,Xs: list_s1210847774152347623at_nat,Y: set_Pr1261947904930325089at_nat,Ys: list_s1210847774152347623at_nat,R2: set_Pr4329608150637261639at_nat] :
% 2.86/3.14 ( ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ ( cons_s6881495754146722583at_nat @ X @ Xs ) @ ( cons_s6881495754146722583at_nat @ Y @ Ys ) ) @ ( lex_se2245640040323279819at_nat @ R2 ) )
% 2.86/3.14 = ( ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ R2 )
% 2.86/3.14 & ( ( size_s8736152011456118867at_nat @ Xs )
% 2.86/3.14 = ( size_s8736152011456118867at_nat @ Ys ) ) )
% 2.86/3.14 | ( ( X = Y )
% 2.86/3.14 & ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ Xs @ Ys ) @ ( lex_se2245640040323279819at_nat @ R2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % Cons_in_lex
% 2.86/3.14 thf(fact_4750_Cons__in__lex,axiom,
% 2.86/3.14 ! [X: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn,Y: produc6575502325842934193n_assn,Ys: list_P8527749157015355191n_assn,R2: set_Pr8116311503512020807n_assn] :
% 2.86/3.14 ( ( member3994142547374651152n_assn @ ( produc3014731801419794263n_assn @ ( cons_P2971678138204555879n_assn @ X @ Xs ) @ ( cons_P2971678138204555879n_assn @ Y @ Ys ) ) @ ( lex_Pr7559194461235888923n_assn @ R2 ) )
% 2.86/3.14 = ( ( ( member4743710847862083984n_assn @ ( produc6128706242671166167n_assn @ X @ Y ) @ R2 )
% 2.86/3.14 & ( ( size_s6829681357464350627n_assn @ Xs )
% 2.86/3.14 = ( size_s6829681357464350627n_assn @ Ys ) ) )
% 2.86/3.14 | ( ( X = Y )
% 2.86/3.14 & ( member3994142547374651152n_assn @ ( produc3014731801419794263n_assn @ Xs @ Ys ) @ ( lex_Pr7559194461235888923n_assn @ R2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % Cons_in_lex
% 2.86/3.14 thf(fact_4751_Cons__in__lex,axiom,
% 2.86/3.14 ! [X: c,Xs: list_c,Y: c,Ys: list_c,R2: set_Product_prod_c_c] :
% 2.86/3.14 ( ( member7012247553653173456list_c @ ( produc5515445818230282391list_c @ ( cons_c @ X @ Xs ) @ ( cons_c @ Y @ Ys ) ) @ ( lex_c @ R2 ) )
% 2.86/3.14 = ( ( ( member5074992359041316560od_c_c @ ( product_Pair_c_c @ X @ Y ) @ R2 )
% 2.86/3.14 & ( ( size_size_list_c @ Xs )
% 2.86/3.14 = ( size_size_list_c @ Ys ) ) )
% 2.86/3.14 | ( ( X = Y )
% 2.86/3.14 & ( member7012247553653173456list_c @ ( produc5515445818230282391list_c @ Xs @ Ys ) @ ( lex_c @ R2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % Cons_in_lex
% 2.86/3.14 thf(fact_4752_Cons__in__lex,axiom,
% 2.86/3.14 ! [X: d,Xs: list_d,Y: d,Ys: list_d,R2: set_Product_prod_d_d] :
% 2.86/3.14 ( ( member1810801192463332112list_d @ ( produc242965421297323863list_d @ ( cons_d @ X @ Xs ) @ ( cons_d @ Y @ Ys ) ) @ ( lex_d @ R2 ) )
% 2.86/3.14 = ( ( ( member2287536781371869328od_d_d @ ( product_Pair_d_d @ X @ Y ) @ R2 )
% 2.86/3.14 & ( ( size_size_list_d @ Xs )
% 2.86/3.14 = ( size_size_list_d @ Ys ) ) )
% 2.86/3.14 | ( ( X = Y )
% 2.86/3.14 & ( member1810801192463332112list_d @ ( produc242965421297323863list_d @ Xs @ Ys ) @ ( lex_d @ R2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % Cons_in_lex
% 2.86/3.14 thf(fact_4753_Cons__in__lex,axiom,
% 2.86/3.14 ! [X: nat,Xs: list_nat,Y: nat,Ys: list_nat,R2: set_Pr1261947904930325089at_nat] :
% 2.86/3.14 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ ( cons_nat @ X @ Xs ) @ ( cons_nat @ Y @ Ys ) ) @ ( lex_nat @ R2 ) )
% 2.86/3.14 = ( ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R2 )
% 2.86/3.14 & ( ( size_size_list_nat @ Xs )
% 2.86/3.14 = ( size_size_list_nat @ Ys ) ) )
% 2.86/3.14 | ( ( X = Y )
% 2.86/3.14 & ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs @ Ys ) @ ( lex_nat @ R2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % Cons_in_lex
% 2.86/3.14 thf(fact_4754_Cons__in__lex,axiom,
% 2.86/3.14 ! [X: int,Xs: list_int,Y: int,Ys: list_int,R2: set_Pr958786334691620121nt_int] :
% 2.86/3.14 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ ( cons_int @ X @ Xs ) @ ( cons_int @ Y @ Ys ) ) @ ( lex_int @ R2 ) )
% 2.86/3.14 = ( ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R2 )
% 2.86/3.14 & ( ( size_size_list_int @ Xs )
% 2.86/3.14 = ( size_size_list_int @ Ys ) ) )
% 2.86/3.14 | ( ( X = Y )
% 2.86/3.14 & ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs @ Ys ) @ ( lex_int @ R2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % Cons_in_lex
% 2.86/3.14 thf(fact_4755_list__assn_Oelims,axiom,
% 2.86/3.14 ! [X: int > int > assn,Xa: list_int,Xb: list_int,Y: assn] :
% 2.86/3.14 ( ( ( vEBT_L74593716426352029nt_int @ X @ Xa @ Xb )
% 2.86/3.14 = Y )
% 2.86/3.14 => ( ( ( Xa = nil_int )
% 2.86/3.14 => ( ( Xb = nil_int )
% 2.86/3.14 => ( Y != one_one_assn ) ) )
% 2.86/3.14 => ( ! [A4: int,As: list_int] :
% 2.86/3.14 ( ( Xa
% 2.86/3.14 = ( cons_int @ A4 @ As ) )
% 2.86/3.14 => ! [C4: int,Cs2: list_int] :
% 2.86/3.14 ( ( Xb
% 2.86/3.14 = ( cons_int @ C4 @ Cs2 ) )
% 2.86/3.14 => ( Y
% 2.86/3.14 != ( times_times_assn @ ( X @ A4 @ C4 ) @ ( vEBT_L74593716426352029nt_int @ X @ As @ Cs2 ) ) ) ) )
% 2.86/3.14 => ( ( ? [V3: int,Va: list_int] :
% 2.86/3.14 ( Xa
% 2.86/3.14 = ( cons_int @ V3 @ Va ) )
% 2.86/3.14 => ( ( Xb = nil_int )
% 2.86/3.14 => ( Y != bot_bot_assn ) ) )
% 2.86/3.14 => ~ ( ( Xa = nil_int )
% 2.86/3.14 => ( ? [V3: int,Va: list_int] :
% 2.86/3.14 ( Xb
% 2.86/3.14 = ( cons_int @ V3 @ Va ) )
% 2.86/3.14 => ( Y != bot_bot_assn ) ) ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn.elims
% 2.86/3.14 thf(fact_4756_list__assn_Oelims,axiom,
% 2.86/3.14 ! [X: int > nat > assn,Xa: list_int,Xb: list_nat,Y: assn] :
% 2.86/3.14 ( ( ( vEBT_L77084186935402305nt_nat @ X @ Xa @ Xb )
% 2.86/3.14 = Y )
% 2.86/3.14 => ( ( ( Xa = nil_int )
% 2.86/3.14 => ( ( Xb = nil_nat )
% 2.86/3.14 => ( Y != one_one_assn ) ) )
% 2.86/3.14 => ( ! [A4: int,As: list_int] :
% 2.86/3.14 ( ( Xa
% 2.86/3.14 = ( cons_int @ A4 @ As ) )
% 2.86/3.14 => ! [C4: nat,Cs2: list_nat] :
% 2.86/3.14 ( ( Xb
% 2.86/3.14 = ( cons_nat @ C4 @ Cs2 ) )
% 2.86/3.14 => ( Y
% 2.86/3.14 != ( times_times_assn @ ( X @ A4 @ C4 ) @ ( vEBT_L77084186935402305nt_nat @ X @ As @ Cs2 ) ) ) ) )
% 2.86/3.14 => ( ( ? [V3: int,Va: list_int] :
% 2.86/3.14 ( Xa
% 2.86/3.14 = ( cons_int @ V3 @ Va ) )
% 2.86/3.14 => ( ( Xb = nil_nat )
% 2.86/3.14 => ( Y != bot_bot_assn ) ) )
% 2.86/3.14 => ~ ( ( Xa = nil_int )
% 2.86/3.14 => ( ? [V3: nat,Va: list_nat] :
% 2.86/3.14 ( Xb
% 2.86/3.14 = ( cons_nat @ V3 @ Va ) )
% 2.86/3.14 => ( Y != bot_bot_assn ) ) ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn.elims
% 2.86/3.14 thf(fact_4757_list__assn_Oelims,axiom,
% 2.86/3.14 ! [X: int > produc6575502325842934193n_assn > assn,Xa: list_int,Xb: list_P8527749157015355191n_assn,Y: assn] :
% 2.86/3.14 ( ( ( vEBT_L1620274777744359680n_assn @ X @ Xa @ Xb )
% 2.86/3.14 = Y )
% 2.86/3.14 => ( ( ( Xa = nil_int )
% 2.86/3.14 => ( ( Xb = nil_Pr5671120429643327159n_assn )
% 2.86/3.14 => ( Y != one_one_assn ) ) )
% 2.86/3.14 => ( ! [A4: int,As: list_int] :
% 2.86/3.14 ( ( Xa
% 2.86/3.14 = ( cons_int @ A4 @ As ) )
% 2.86/3.14 => ! [C4: produc6575502325842934193n_assn,Cs2: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( Xb
% 2.86/3.14 = ( cons_P2971678138204555879n_assn @ C4 @ Cs2 ) )
% 2.86/3.14 => ( Y
% 2.86/3.14 != ( times_times_assn @ ( X @ A4 @ C4 ) @ ( vEBT_L1620274777744359680n_assn @ X @ As @ Cs2 ) ) ) ) )
% 2.86/3.14 => ( ( ? [V3: int,Va: list_int] :
% 2.86/3.14 ( Xa
% 2.86/3.14 = ( cons_int @ V3 @ Va ) )
% 2.86/3.14 => ( ( Xb = nil_Pr5671120429643327159n_assn )
% 2.86/3.14 => ( Y != bot_bot_assn ) ) )
% 2.86/3.14 => ~ ( ( Xa = nil_int )
% 2.86/3.14 => ( ? [V3: produc6575502325842934193n_assn,Va: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( Xb
% 2.86/3.14 = ( cons_P2971678138204555879n_assn @ V3 @ Va ) )
% 2.86/3.14 => ( Y != bot_bot_assn ) ) ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn.elims
% 2.86/3.14 thf(fact_4758_list__assn_Oelims,axiom,
% 2.86/3.14 ! [X: nat > int > assn,Xa: list_nat,Xb: list_int,Y: assn] :
% 2.86/3.14 ( ( ( vEBT_L8298612041380073281at_int @ X @ Xa @ Xb )
% 2.86/3.14 = Y )
% 2.86/3.14 => ( ( ( Xa = nil_nat )
% 2.86/3.14 => ( ( Xb = nil_int )
% 2.86/3.14 => ( Y != one_one_assn ) ) )
% 2.86/3.14 => ( ! [A4: nat,As: list_nat] :
% 2.86/3.14 ( ( Xa
% 2.86/3.14 = ( cons_nat @ A4 @ As ) )
% 2.86/3.14 => ! [C4: int,Cs2: list_int] :
% 2.86/3.14 ( ( Xb
% 2.86/3.14 = ( cons_int @ C4 @ Cs2 ) )
% 2.86/3.14 => ( Y
% 2.86/3.14 != ( times_times_assn @ ( X @ A4 @ C4 ) @ ( vEBT_L8298612041380073281at_int @ X @ As @ Cs2 ) ) ) ) )
% 2.86/3.14 => ( ( ? [V3: nat,Va: list_nat] :
% 2.86/3.14 ( Xa
% 2.86/3.14 = ( cons_nat @ V3 @ Va ) )
% 2.86/3.14 => ( ( Xb = nil_int )
% 2.86/3.14 => ( Y != bot_bot_assn ) ) )
% 2.86/3.14 => ~ ( ( Xa = nil_nat )
% 2.86/3.14 => ( ? [V3: int,Va: list_int] :
% 2.86/3.14 ( Xb
% 2.86/3.14 = ( cons_int @ V3 @ Va ) )
% 2.86/3.14 => ( Y != bot_bot_assn ) ) ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn.elims
% 2.86/3.14 thf(fact_4759_list__assn_Oelims,axiom,
% 2.86/3.14 ! [X: nat > nat > assn,Xa: list_nat,Xb: list_nat,Y: assn] :
% 2.86/3.14 ( ( ( vEBT_L8301102511889123557at_nat @ X @ Xa @ Xb )
% 2.86/3.14 = Y )
% 2.86/3.14 => ( ( ( Xa = nil_nat )
% 2.86/3.14 => ( ( Xb = nil_nat )
% 2.86/3.14 => ( Y != one_one_assn ) ) )
% 2.86/3.14 => ( ! [A4: nat,As: list_nat] :
% 2.86/3.14 ( ( Xa
% 2.86/3.14 = ( cons_nat @ A4 @ As ) )
% 2.86/3.14 => ! [C4: nat,Cs2: list_nat] :
% 2.86/3.14 ( ( Xb
% 2.86/3.14 = ( cons_nat @ C4 @ Cs2 ) )
% 2.86/3.14 => ( Y
% 2.86/3.14 != ( times_times_assn @ ( X @ A4 @ C4 ) @ ( vEBT_L8301102511889123557at_nat @ X @ As @ Cs2 ) ) ) ) )
% 2.86/3.14 => ( ( ? [V3: nat,Va: list_nat] :
% 2.86/3.14 ( Xa
% 2.86/3.14 = ( cons_nat @ V3 @ Va ) )
% 2.86/3.14 => ( ( Xb = nil_nat )
% 2.86/3.14 => ( Y != bot_bot_assn ) ) )
% 2.86/3.14 => ~ ( ( Xa = nil_nat )
% 2.86/3.14 => ( ? [V3: nat,Va: list_nat] :
% 2.86/3.14 ( Xb
% 2.86/3.14 = ( cons_nat @ V3 @ Va ) )
% 2.86/3.14 => ( Y != bot_bot_assn ) ) ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn.elims
% 2.86/3.14 thf(fact_4760_list__assn_Oelims,axiom,
% 2.86/3.14 ! [X: nat > produc6575502325842934193n_assn > assn,Xa: list_nat,Xb: list_P8527749157015355191n_assn,Y: assn] :
% 2.86/3.14 ( ( ( vEBT_L9083610150846024284n_assn @ X @ Xa @ Xb )
% 2.86/3.14 = Y )
% 2.86/3.14 => ( ( ( Xa = nil_nat )
% 2.86/3.14 => ( ( Xb = nil_Pr5671120429643327159n_assn )
% 2.86/3.14 => ( Y != one_one_assn ) ) )
% 2.86/3.14 => ( ! [A4: nat,As: list_nat] :
% 2.86/3.14 ( ( Xa
% 2.86/3.14 = ( cons_nat @ A4 @ As ) )
% 2.86/3.14 => ! [C4: produc6575502325842934193n_assn,Cs2: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( Xb
% 2.86/3.14 = ( cons_P2971678138204555879n_assn @ C4 @ Cs2 ) )
% 2.86/3.14 => ( Y
% 2.86/3.14 != ( times_times_assn @ ( X @ A4 @ C4 ) @ ( vEBT_L9083610150846024284n_assn @ X @ As @ Cs2 ) ) ) ) )
% 2.86/3.14 => ( ( ? [V3: nat,Va: list_nat] :
% 2.86/3.14 ( Xa
% 2.86/3.14 = ( cons_nat @ V3 @ Va ) )
% 2.86/3.14 => ( ( Xb = nil_Pr5671120429643327159n_assn )
% 2.86/3.14 => ( Y != bot_bot_assn ) ) )
% 2.86/3.14 => ~ ( ( Xa = nil_nat )
% 2.86/3.14 => ( ? [V3: produc6575502325842934193n_assn,Va: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( Xb
% 2.86/3.14 = ( cons_P2971678138204555879n_assn @ V3 @ Va ) )
% 2.86/3.14 => ( Y != bot_bot_assn ) ) ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn.elims
% 2.86/3.14 thf(fact_4761_list__assn_Oelims,axiom,
% 2.86/3.14 ! [X: produc6575502325842934193n_assn > int > assn,Xa: list_P8527749157015355191n_assn,Xb: list_int,Y: assn] :
% 2.86/3.14 ( ( ( vEBT_L4760345170377931482sn_int @ X @ Xa @ Xb )
% 2.86/3.14 = Y )
% 2.86/3.14 => ( ( ( Xa = nil_Pr5671120429643327159n_assn )
% 2.86/3.14 => ( ( Xb = nil_int )
% 2.86/3.14 => ( Y != one_one_assn ) ) )
% 2.86/3.14 => ( ! [A4: produc6575502325842934193n_assn,As: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( Xa
% 2.86/3.14 = ( cons_P2971678138204555879n_assn @ A4 @ As ) )
% 2.86/3.14 => ! [C4: int,Cs2: list_int] :
% 2.86/3.14 ( ( Xb
% 2.86/3.14 = ( cons_int @ C4 @ Cs2 ) )
% 2.86/3.14 => ( Y
% 2.86/3.14 != ( times_times_assn @ ( X @ A4 @ C4 ) @ ( vEBT_L4760345170377931482sn_int @ X @ As @ Cs2 ) ) ) ) )
% 2.86/3.14 => ( ( ? [V3: produc6575502325842934193n_assn,Va: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( Xa
% 2.86/3.14 = ( cons_P2971678138204555879n_assn @ V3 @ Va ) )
% 2.86/3.14 => ( ( Xb = nil_int )
% 2.86/3.14 => ( Y != bot_bot_assn ) ) )
% 2.86/3.14 => ~ ( ( Xa = nil_Pr5671120429643327159n_assn )
% 2.86/3.14 => ( ? [V3: int,Va: list_int] :
% 2.86/3.14 ( Xb
% 2.86/3.14 = ( cons_int @ V3 @ Va ) )
% 2.86/3.14 => ( Y != bot_bot_assn ) ) ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn.elims
% 2.86/3.14 thf(fact_4762_list__assn_Oelims,axiom,
% 2.86/3.14 ! [X: produc6575502325842934193n_assn > nat > assn,Xa: list_P8527749157015355191n_assn,Xb: list_nat,Y: assn] :
% 2.86/3.14 ( ( ( vEBT_L4762835640886981758sn_nat @ X @ Xa @ Xb )
% 2.86/3.14 = Y )
% 2.86/3.14 => ( ( ( Xa = nil_Pr5671120429643327159n_assn )
% 2.86/3.14 => ( ( Xb = nil_nat )
% 2.86/3.14 => ( Y != one_one_assn ) ) )
% 2.86/3.14 => ( ! [A4: produc6575502325842934193n_assn,As: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( Xa
% 2.86/3.14 = ( cons_P2971678138204555879n_assn @ A4 @ As ) )
% 2.86/3.14 => ! [C4: nat,Cs2: list_nat] :
% 2.86/3.14 ( ( Xb
% 2.86/3.14 = ( cons_nat @ C4 @ Cs2 ) )
% 2.86/3.14 => ( Y
% 2.86/3.14 != ( times_times_assn @ ( X @ A4 @ C4 ) @ ( vEBT_L4762835640886981758sn_nat @ X @ As @ Cs2 ) ) ) ) )
% 2.86/3.14 => ( ( ? [V3: produc6575502325842934193n_assn,Va: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( Xa
% 2.86/3.14 = ( cons_P2971678138204555879n_assn @ V3 @ Va ) )
% 2.86/3.14 => ( ( Xb = nil_nat )
% 2.86/3.14 => ( Y != bot_bot_assn ) ) )
% 2.86/3.14 => ~ ( ( Xa = nil_Pr5671120429643327159n_assn )
% 2.86/3.14 => ( ? [V3: nat,Va: list_nat] :
% 2.86/3.14 ( Xb
% 2.86/3.14 = ( cons_nat @ V3 @ Va ) )
% 2.86/3.14 => ( Y != bot_bot_assn ) ) ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn.elims
% 2.86/3.14 thf(fact_4763_list__assn_Oelims,axiom,
% 2.86/3.14 ! [X: produc6575502325842934193n_assn > produc6575502325842934193n_assn > assn,Xa: list_P8527749157015355191n_assn,Xb: list_P8527749157015355191n_assn,Y: assn] :
% 2.86/3.14 ( ( ( vEBT_L3108143461992071043n_assn @ X @ Xa @ Xb )
% 2.86/3.14 = Y )
% 2.86/3.14 => ( ( ( Xa = nil_Pr5671120429643327159n_assn )
% 2.86/3.14 => ( ( Xb = nil_Pr5671120429643327159n_assn )
% 2.86/3.14 => ( Y != one_one_assn ) ) )
% 2.86/3.14 => ( ! [A4: produc6575502325842934193n_assn,As: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( Xa
% 2.86/3.14 = ( cons_P2971678138204555879n_assn @ A4 @ As ) )
% 2.86/3.14 => ! [C4: produc6575502325842934193n_assn,Cs2: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( Xb
% 2.86/3.14 = ( cons_P2971678138204555879n_assn @ C4 @ Cs2 ) )
% 2.86/3.14 => ( Y
% 2.86/3.14 != ( times_times_assn @ ( X @ A4 @ C4 ) @ ( vEBT_L3108143461992071043n_assn @ X @ As @ Cs2 ) ) ) ) )
% 2.86/3.14 => ( ( ? [V3: produc6575502325842934193n_assn,Va: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( Xa
% 2.86/3.14 = ( cons_P2971678138204555879n_assn @ V3 @ Va ) )
% 2.86/3.14 => ( ( Xb = nil_Pr5671120429643327159n_assn )
% 2.86/3.14 => ( Y != bot_bot_assn ) ) )
% 2.86/3.14 => ~ ( ( Xa = nil_Pr5671120429643327159n_assn )
% 2.86/3.14 => ( ? [V3: produc6575502325842934193n_assn,Va: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( Xb
% 2.86/3.14 = ( cons_P2971678138204555879n_assn @ V3 @ Va ) )
% 2.86/3.14 => ( Y != bot_bot_assn ) ) ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn.elims
% 2.86/3.14 thf(fact_4764_count__list_Osimps_I2_J,axiom,
% 2.86/3.14 ! [X: int,Y: int,Xs: list_int] :
% 2.86/3.14 ( ( ( X = Y )
% 2.86/3.14 => ( ( count_list_int @ ( cons_int @ X @ Xs ) @ Y )
% 2.86/3.14 = ( plus_plus_nat @ ( count_list_int @ Xs @ Y ) @ one_one_nat ) ) )
% 2.86/3.14 & ( ( X != Y )
% 2.86/3.14 => ( ( count_list_int @ ( cons_int @ X @ Xs ) @ Y )
% 2.86/3.14 = ( count_list_int @ Xs @ Y ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % count_list.simps(2)
% 2.86/3.14 thf(fact_4765_count__list_Osimps_I2_J,axiom,
% 2.86/3.14 ! [X: nat,Y: nat,Xs: list_nat] :
% 2.86/3.14 ( ( ( X = Y )
% 2.86/3.14 => ( ( count_list_nat @ ( cons_nat @ X @ Xs ) @ Y )
% 2.86/3.14 = ( plus_plus_nat @ ( count_list_nat @ Xs @ Y ) @ one_one_nat ) ) )
% 2.86/3.14 & ( ( X != Y )
% 2.86/3.14 => ( ( count_list_nat @ ( cons_nat @ X @ Xs ) @ Y )
% 2.86/3.14 = ( count_list_nat @ Xs @ Y ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % count_list.simps(2)
% 2.86/3.14 thf(fact_4766_count__list_Osimps_I2_J,axiom,
% 2.86/3.14 ! [X: produc6575502325842934193n_assn,Y: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( ( X = Y )
% 2.86/3.14 => ( ( count_2530312006313534765n_assn @ ( cons_P2971678138204555879n_assn @ X @ Xs ) @ Y )
% 2.86/3.14 = ( plus_plus_nat @ ( count_2530312006313534765n_assn @ Xs @ Y ) @ one_one_nat ) ) )
% 2.86/3.14 & ( ( X != Y )
% 2.86/3.14 => ( ( count_2530312006313534765n_assn @ ( cons_P2971678138204555879n_assn @ X @ Xs ) @ Y )
% 2.86/3.14 = ( count_2530312006313534765n_assn @ Xs @ Y ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % count_list.simps(2)
% 2.86/3.14 thf(fact_4767_count__notin,axiom,
% 2.86/3.14 ! [X: produc3843707927480180839at_nat,Xs: list_P5464809261938338413at_nat] :
% 2.86/3.14 ( ~ ( member8757157785044589968at_nat @ X @ ( set_Pr3765526544606949372at_nat @ Xs ) )
% 2.86/3.14 => ( ( count_1483299019173949923at_nat @ Xs @ X )
% 2.86/3.14 = zero_zero_nat ) ) ).
% 2.86/3.14
% 2.86/3.14 % count_notin
% 2.86/3.14 thf(fact_4768_count__notin,axiom,
% 2.86/3.14 ! [X: product_prod_nat_nat,Xs: list_P6011104703257516679at_nat] :
% 2.86/3.14 ( ~ ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 2.86/3.14 => ( ( count_4203492906077236349at_nat @ Xs @ X )
% 2.86/3.14 = zero_zero_nat ) ) ).
% 2.86/3.14
% 2.86/3.14 % count_notin
% 2.86/3.14 thf(fact_4769_count__notin,axiom,
% 2.86/3.14 ! [X: produc3658429121746597890et_nat > $o,Xs: list_P7985473006766602707_nat_o] :
% 2.86/3.14 ( ~ ( member6576561426505652726_nat_o @ X @ ( set_Pr400311997697478754_nat_o @ Xs ) )
% 2.86/3.14 => ( ( count_5695430372156137289_nat_o @ Xs @ X )
% 2.86/3.14 = zero_zero_nat ) ) ).
% 2.86/3.14
% 2.86/3.14 % count_notin
% 2.86/3.14 thf(fact_4770_count__notin,axiom,
% 2.86/3.14 ! [X: int,Xs: list_int] :
% 2.86/3.14 ( ~ ( member_int @ X @ ( set_int2 @ Xs ) )
% 2.86/3.14 => ( ( count_list_int @ Xs @ X )
% 2.86/3.14 = zero_zero_nat ) ) ).
% 2.86/3.14
% 2.86/3.14 % count_notin
% 2.86/3.14 thf(fact_4771_count__notin,axiom,
% 2.86/3.14 ! [X: nat,Xs: list_nat] :
% 2.86/3.14 ( ~ ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 2.86/3.14 => ( ( count_list_nat @ Xs @ X )
% 2.86/3.14 = zero_zero_nat ) ) ).
% 2.86/3.14
% 2.86/3.14 % count_notin
% 2.86/3.14 thf(fact_4772_count__notin,axiom,
% 2.86/3.14 ! [X: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ~ ( member7957490590177025114n_assn @ X @ ( set_Pr1139785259514867910n_assn @ Xs ) )
% 2.86/3.14 => ( ( count_2530312006313534765n_assn @ Xs @ X )
% 2.86/3.14 = zero_zero_nat ) ) ).
% 2.86/3.14
% 2.86/3.14 % count_notin
% 2.86/3.14 thf(fact_4773_power__decreasing__iff,axiom,
% 2.86/3.14 ! [B2: rat,M2: nat,N: nat] :
% 2.86/3.14 ( ( ord_less_rat @ zero_zero_rat @ B2 )
% 2.86/3.14 => ( ( ord_less_rat @ B2 @ one_one_rat )
% 2.86/3.14 => ( ( ord_less_eq_rat @ ( power_power_rat @ B2 @ M2 ) @ ( power_power_rat @ B2 @ N ) )
% 2.86/3.14 = ( ord_less_eq_nat @ N @ M2 ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_decreasing_iff
% 2.86/3.14 thf(fact_4774_power__decreasing__iff,axiom,
% 2.86/3.14 ! [B2: code_integer,M2: nat,N: nat] :
% 2.86/3.14 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B2 )
% 2.86/3.14 => ( ( ord_le6747313008572928689nteger @ B2 @ one_one_Code_integer )
% 2.86/3.14 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ B2 @ M2 ) @ ( power_8256067586552552935nteger @ B2 @ N ) )
% 2.86/3.14 = ( ord_less_eq_nat @ N @ M2 ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_decreasing_iff
% 2.86/3.14 thf(fact_4775_power__decreasing__iff,axiom,
% 2.86/3.14 ! [B2: nat,M2: nat,N: nat] :
% 2.86/3.14 ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 2.86/3.14 => ( ( ord_less_nat @ B2 @ one_one_nat )
% 2.86/3.14 => ( ( ord_less_eq_nat @ ( power_power_nat @ B2 @ M2 ) @ ( power_power_nat @ B2 @ N ) )
% 2.86/3.14 = ( ord_less_eq_nat @ N @ M2 ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_decreasing_iff
% 2.86/3.14 thf(fact_4776_power__decreasing__iff,axiom,
% 2.86/3.14 ! [B2: int,M2: nat,N: nat] :
% 2.86/3.14 ( ( ord_less_int @ zero_zero_int @ B2 )
% 2.86/3.14 => ( ( ord_less_int @ B2 @ one_one_int )
% 2.86/3.14 => ( ( ord_less_eq_int @ ( power_power_int @ B2 @ M2 ) @ ( power_power_int @ B2 @ N ) )
% 2.86/3.14 = ( ord_less_eq_nat @ N @ M2 ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_decreasing_iff
% 2.86/3.14 thf(fact_4777_in__measures_I2_J,axiom,
% 2.86/3.14 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,F4: set_Pr1261947904930325089at_nat > nat,Fs: list_s9130966667114977576at_nat] :
% 2.86/3.14 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( measur2694323259624372065at_nat @ ( cons_s2538900923071588440at_nat @ F4 @ Fs ) ) )
% 2.86/3.14 = ( ( ord_less_nat @ ( F4 @ X ) @ ( F4 @ Y ) )
% 2.86/3.14 | ( ( ( F4 @ X )
% 2.86/3.14 = ( F4 @ Y ) )
% 2.86/3.14 & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( measur2694323259624372065at_nat @ Fs ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % in_measures(2)
% 2.86/3.14 thf(fact_4778_in__measures_I2_J,axiom,
% 2.86/3.14 ! [X: nat,Y: nat,F4: nat > nat,Fs: list_nat_nat] :
% 2.86/3.14 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( measures_nat @ ( cons_nat_nat @ F4 @ Fs ) ) )
% 2.86/3.14 = ( ( ord_less_nat @ ( F4 @ X ) @ ( F4 @ Y ) )
% 2.86/3.14 | ( ( ( F4 @ X )
% 2.86/3.14 = ( F4 @ Y ) )
% 2.86/3.14 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( measures_nat @ Fs ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % in_measures(2)
% 2.86/3.14 thf(fact_4779_nat__zero__less__power__iff,axiom,
% 2.86/3.14 ! [X: nat,N: nat] :
% 2.86/3.14 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) )
% 2.86/3.14 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 2.86/3.14 | ( N = zero_zero_nat ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % nat_zero_less_power_iff
% 2.86/3.14 thf(fact_4780_zip__eq__Nil__iff,axiom,
% 2.86/3.14 ! [Xs: list_int,Ys: list_int] :
% 2.86/3.14 ( ( ( zip_int_int @ Xs @ Ys )
% 2.86/3.14 = nil_Pr2300489316682597567nt_int )
% 2.86/3.14 = ( ( Xs = nil_int )
% 2.86/3.14 | ( Ys = nil_int ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % zip_eq_Nil_iff
% 2.86/3.14 thf(fact_4781_zip__eq__Nil__iff,axiom,
% 2.86/3.14 ! [Xs: list_int,Ys: list_nat] :
% 2.86/3.14 ( ( ( zip_int_nat @ Xs @ Ys )
% 2.86/3.14 = nil_Pr6478340336191794275nt_nat )
% 2.86/3.14 = ( ( Xs = nil_int )
% 2.86/3.14 | ( Ys = nil_nat ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % zip_eq_Nil_iff
% 2.86/3.14 thf(fact_4782_zip__eq__Nil__iff,axiom,
% 2.86/3.14 ! [Xs: list_int,Ys: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( ( zip_in7098856637274830732n_assn @ Xs @ Ys )
% 2.86/3.14 = nil_Pr2440414457004260852n_assn )
% 2.86/3.14 = ( ( Xs = nil_int )
% 2.86/3.14 | ( Ys = nil_Pr5671120429643327159n_assn ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % zip_eq_Nil_iff
% 2.86/3.14 thf(fact_4783_zip__eq__Nil__iff,axiom,
% 2.86/3.14 ! [Xs: list_nat,Ys: list_int] :
% 2.86/3.14 ( ( ( zip_nat_int @ Xs @ Ys )
% 2.86/3.14 = nil_Pr1301135604781543011at_int )
% 2.86/3.14 = ( ( Xs = nil_nat )
% 2.86/3.14 | ( Ys = nil_int ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % zip_eq_Nil_iff
% 2.86/3.14 thf(fact_4784_zip__eq__Nil__iff,axiom,
% 2.86/3.14 ! [Xs: list_nat,Ys: list_nat] :
% 2.86/3.14 ( ( ( zip_nat_nat @ Xs @ Ys )
% 2.86/3.14 = nil_Pr5478986624290739719at_nat )
% 2.86/3.14 = ( ( Xs = nil_nat )
% 2.86/3.14 | ( Ys = nil_nat ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % zip_eq_Nil_iff
% 2.86/3.14 thf(fact_4785_zip__eq__Nil__iff,axiom,
% 2.86/3.14 ! [Xs: list_nat,Ys: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( ( zip_na5338819973521719528n_assn @ Xs @ Ys )
% 2.86/3.14 = nil_Pr680377793251149648n_assn )
% 2.86/3.14 = ( ( Xs = nil_nat )
% 2.86/3.14 | ( Ys = nil_Pr5671120429643327159n_assn ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % zip_eq_Nil_iff
% 2.86/3.14 thf(fact_4786_zip__eq__Nil__iff,axiom,
% 2.86/3.14 ! [Xs: list_P8527749157015355191n_assn,Ys: list_int] :
% 2.86/3.14 ( ( ( zip_Pr1015554993053626726sn_int @ Xs @ Ys )
% 2.86/3.14 = nil_Pr7991254345159696774sn_int )
% 2.86/3.14 = ( ( Xs = nil_Pr5671120429643327159n_assn )
% 2.86/3.14 | ( Ys = nil_int ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % zip_eq_Nil_iff
% 2.86/3.14 thf(fact_4787_zip__eq__Nil__iff,axiom,
% 2.86/3.14 ! [Xs: list_P8527749157015355191n_assn,Ys: list_nat] :
% 2.86/3.14 ( ( ( zip_Pr1018045463562677002sn_nat @ Xs @ Ys )
% 2.86/3.14 = nil_Pr2945733327814117674sn_nat )
% 2.86/3.14 = ( ( Xs = nil_Pr5671120429643327159n_assn )
% 2.86/3.14 | ( Ys = nil_nat ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % zip_eq_Nil_iff
% 2.86/3.14 thf(fact_4788_zip__eq__Nil__iff,axiom,
% 2.86/3.14 ! [Xs: list_P8527749157015355191n_assn,Ys: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( ( zip_Pr8806919808394484215n_assn @ Xs @ Ys )
% 2.86/3.14 = nil_Pr4327835960982145133n_assn )
% 2.86/3.14 = ( ( Xs = nil_Pr5671120429643327159n_assn )
% 2.86/3.14 | ( Ys = nil_Pr5671120429643327159n_assn ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % zip_eq_Nil_iff
% 2.86/3.14 thf(fact_4789_zip__eq__Nil__iff,axiom,
% 2.86/3.14 ! [Xs: list_assn,Ys: list_assn] :
% 2.86/3.14 ( ( ( zip_assn_assn @ Xs @ Ys )
% 2.86/3.14 = nil_Pr5671120429643327159n_assn )
% 2.86/3.14 = ( ( Xs = nil_assn )
% 2.86/3.14 | ( Ys = nil_assn ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % zip_eq_Nil_iff
% 2.86/3.14 thf(fact_4790_Nil__eq__zip__iff,axiom,
% 2.86/3.14 ! [Xs: list_int,Ys: list_int] :
% 2.86/3.14 ( ( nil_Pr2300489316682597567nt_int
% 2.86/3.14 = ( zip_int_int @ Xs @ Ys ) )
% 2.86/3.14 = ( ( Xs = nil_int )
% 2.86/3.14 | ( Ys = nil_int ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % Nil_eq_zip_iff
% 2.86/3.14 thf(fact_4791_Nil__eq__zip__iff,axiom,
% 2.86/3.14 ! [Xs: list_int,Ys: list_nat] :
% 2.86/3.14 ( ( nil_Pr6478340336191794275nt_nat
% 2.86/3.14 = ( zip_int_nat @ Xs @ Ys ) )
% 2.86/3.14 = ( ( Xs = nil_int )
% 2.86/3.14 | ( Ys = nil_nat ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % Nil_eq_zip_iff
% 2.86/3.14 thf(fact_4792_Nil__eq__zip__iff,axiom,
% 2.86/3.14 ! [Xs: list_int,Ys: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( nil_Pr2440414457004260852n_assn
% 2.86/3.14 = ( zip_in7098856637274830732n_assn @ Xs @ Ys ) )
% 2.86/3.14 = ( ( Xs = nil_int )
% 2.86/3.14 | ( Ys = nil_Pr5671120429643327159n_assn ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % Nil_eq_zip_iff
% 2.86/3.14 thf(fact_4793_Nil__eq__zip__iff,axiom,
% 2.86/3.14 ! [Xs: list_nat,Ys: list_int] :
% 2.86/3.14 ( ( nil_Pr1301135604781543011at_int
% 2.86/3.14 = ( zip_nat_int @ Xs @ Ys ) )
% 2.86/3.14 = ( ( Xs = nil_nat )
% 2.86/3.14 | ( Ys = nil_int ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % Nil_eq_zip_iff
% 2.86/3.14 thf(fact_4794_Nil__eq__zip__iff,axiom,
% 2.86/3.14 ! [Xs: list_nat,Ys: list_nat] :
% 2.86/3.14 ( ( nil_Pr5478986624290739719at_nat
% 2.86/3.14 = ( zip_nat_nat @ Xs @ Ys ) )
% 2.86/3.14 = ( ( Xs = nil_nat )
% 2.86/3.14 | ( Ys = nil_nat ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % Nil_eq_zip_iff
% 2.86/3.14 thf(fact_4795_Nil__eq__zip__iff,axiom,
% 2.86/3.14 ! [Xs: list_nat,Ys: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( nil_Pr680377793251149648n_assn
% 2.86/3.14 = ( zip_na5338819973521719528n_assn @ Xs @ Ys ) )
% 2.86/3.14 = ( ( Xs = nil_nat )
% 2.86/3.14 | ( Ys = nil_Pr5671120429643327159n_assn ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % Nil_eq_zip_iff
% 2.86/3.14 thf(fact_4796_Nil__eq__zip__iff,axiom,
% 2.86/3.14 ! [Xs: list_P8527749157015355191n_assn,Ys: list_int] :
% 2.86/3.14 ( ( nil_Pr7991254345159696774sn_int
% 2.86/3.14 = ( zip_Pr1015554993053626726sn_int @ Xs @ Ys ) )
% 2.86/3.14 = ( ( Xs = nil_Pr5671120429643327159n_assn )
% 2.86/3.14 | ( Ys = nil_int ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % Nil_eq_zip_iff
% 2.86/3.14 thf(fact_4797_Nil__eq__zip__iff,axiom,
% 2.86/3.14 ! [Xs: list_P8527749157015355191n_assn,Ys: list_nat] :
% 2.86/3.14 ( ( nil_Pr2945733327814117674sn_nat
% 2.86/3.14 = ( zip_Pr1018045463562677002sn_nat @ Xs @ Ys ) )
% 2.86/3.14 = ( ( Xs = nil_Pr5671120429643327159n_assn )
% 2.86/3.14 | ( Ys = nil_nat ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % Nil_eq_zip_iff
% 2.86/3.14 thf(fact_4798_Nil__eq__zip__iff,axiom,
% 2.86/3.14 ! [Xs: list_P8527749157015355191n_assn,Ys: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( nil_Pr4327835960982145133n_assn
% 2.86/3.14 = ( zip_Pr8806919808394484215n_assn @ Xs @ Ys ) )
% 2.86/3.14 = ( ( Xs = nil_Pr5671120429643327159n_assn )
% 2.86/3.14 | ( Ys = nil_Pr5671120429643327159n_assn ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % Nil_eq_zip_iff
% 2.86/3.14 thf(fact_4799_Nil__eq__zip__iff,axiom,
% 2.86/3.14 ! [Xs: list_assn,Ys: list_assn] :
% 2.86/3.14 ( ( nil_Pr5671120429643327159n_assn
% 2.86/3.14 = ( zip_assn_assn @ Xs @ Ys ) )
% 2.86/3.14 = ( ( Xs = nil_assn )
% 2.86/3.14 | ( Ys = nil_assn ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % Nil_eq_zip_iff
% 2.86/3.14 thf(fact_4800_zip__Nil,axiom,
% 2.86/3.14 ! [Ys: list_assn] :
% 2.86/3.14 ( ( zip_assn_assn @ nil_assn @ Ys )
% 2.86/3.14 = nil_Pr5671120429643327159n_assn ) ).
% 2.86/3.14
% 2.86/3.14 % zip_Nil
% 2.86/3.14 thf(fact_4801_Nil__is__rev__conv,axiom,
% 2.86/3.14 ! [Xs: list_int] :
% 2.86/3.14 ( ( nil_int
% 2.86/3.14 = ( rev_int @ Xs ) )
% 2.86/3.14 = ( Xs = nil_int ) ) ).
% 2.86/3.14
% 2.86/3.14 % Nil_is_rev_conv
% 2.86/3.14 thf(fact_4802_Nil__is__rev__conv,axiom,
% 2.86/3.14 ! [Xs: list_nat] :
% 2.86/3.14 ( ( nil_nat
% 2.86/3.14 = ( rev_nat @ Xs ) )
% 2.86/3.14 = ( Xs = nil_nat ) ) ).
% 2.86/3.14
% 2.86/3.14 % Nil_is_rev_conv
% 2.86/3.14 thf(fact_4803_Nil__is__rev__conv,axiom,
% 2.86/3.14 ! [Xs: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( nil_Pr5671120429643327159n_assn
% 2.86/3.14 = ( rev_Pr4855572775806611735n_assn @ Xs ) )
% 2.86/3.14 = ( Xs = nil_Pr5671120429643327159n_assn ) ) ).
% 2.86/3.14
% 2.86/3.14 % Nil_is_rev_conv
% 2.86/3.14 thf(fact_4804_rev__is__Nil__conv,axiom,
% 2.86/3.14 ! [Xs: list_int] :
% 2.86/3.14 ( ( ( rev_int @ Xs )
% 2.86/3.14 = nil_int )
% 2.86/3.14 = ( Xs = nil_int ) ) ).
% 2.86/3.14
% 2.86/3.14 % rev_is_Nil_conv
% 2.86/3.14 thf(fact_4805_rev__is__Nil__conv,axiom,
% 2.86/3.14 ! [Xs: list_nat] :
% 2.86/3.14 ( ( ( rev_nat @ Xs )
% 2.86/3.14 = nil_nat )
% 2.86/3.14 = ( Xs = nil_nat ) ) ).
% 2.86/3.14
% 2.86/3.14 % rev_is_Nil_conv
% 2.86/3.14 thf(fact_4806_rev__is__Nil__conv,axiom,
% 2.86/3.14 ! [Xs: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( ( rev_Pr4855572775806611735n_assn @ Xs )
% 2.86/3.14 = nil_Pr5671120429643327159n_assn )
% 2.86/3.14 = ( Xs = nil_Pr5671120429643327159n_assn ) ) ).
% 2.86/3.14
% 2.86/3.14 % rev_is_Nil_conv
% 2.86/3.14 thf(fact_4807_list__update__nonempty,axiom,
% 2.86/3.14 ! [Xs: list_int,K3: nat,X: int] :
% 2.86/3.14 ( ( ( list_update_int @ Xs @ K3 @ X )
% 2.86/3.14 = nil_int )
% 2.86/3.14 = ( Xs = nil_int ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_update_nonempty
% 2.86/3.14 thf(fact_4808_list__update__nonempty,axiom,
% 2.86/3.14 ! [Xs: list_nat,K3: nat,X: nat] :
% 2.86/3.14 ( ( ( list_update_nat @ Xs @ K3 @ X )
% 2.86/3.14 = nil_nat )
% 2.86/3.14 = ( Xs = nil_nat ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_update_nonempty
% 2.86/3.14 thf(fact_4809_list__update__nonempty,axiom,
% 2.86/3.14 ! [Xs: list_P8527749157015355191n_assn,K3: nat,X: produc6575502325842934193n_assn] :
% 2.86/3.14 ( ( ( list_u4534839942911652127n_assn @ Xs @ K3 @ X )
% 2.86/3.14 = nil_Pr5671120429643327159n_assn )
% 2.86/3.14 = ( Xs = nil_Pr5671120429643327159n_assn ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_update_nonempty
% 2.86/3.14 thf(fact_4810_list__update__nonempty,axiom,
% 2.86/3.14 ! [Xs: list_c,K3: nat,X: c] :
% 2.86/3.14 ( ( ( list_update_c @ Xs @ K3 @ X )
% 2.86/3.14 = nil_c )
% 2.86/3.14 = ( Xs = nil_c ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_update_nonempty
% 2.86/3.14 thf(fact_4811_list__update__nonempty,axiom,
% 2.86/3.14 ! [Xs: list_d,K3: nat,X: d] :
% 2.86/3.14 ( ( ( list_update_d @ Xs @ K3 @ X )
% 2.86/3.14 = nil_d )
% 2.86/3.14 = ( Xs = nil_d ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_update_nonempty
% 2.86/3.14 thf(fact_4812_enumerate__simps_I1_J,axiom,
% 2.86/3.14 ! [N: nat] :
% 2.86/3.14 ( ( enumerate_int @ N @ nil_int )
% 2.86/3.14 = nil_Pr1301135604781543011at_int ) ).
% 2.86/3.14
% 2.86/3.14 % enumerate_simps(1)
% 2.86/3.14 thf(fact_4813_enumerate__simps_I1_J,axiom,
% 2.86/3.14 ! [N: nat] :
% 2.86/3.14 ( ( enumerate_nat @ N @ nil_nat )
% 2.86/3.14 = nil_Pr5478986624290739719at_nat ) ).
% 2.86/3.14
% 2.86/3.14 % enumerate_simps(1)
% 2.86/3.14 thf(fact_4814_enumerate__simps_I1_J,axiom,
% 2.86/3.14 ! [N: nat] :
% 2.86/3.14 ( ( enumer9200277086812776726n_assn @ N @ nil_Pr5671120429643327159n_assn )
% 2.86/3.14 = nil_Pr680377793251149648n_assn ) ).
% 2.86/3.14
% 2.86/3.14 % enumerate_simps(1)
% 2.86/3.14 thf(fact_4815_rotate1__is__Nil__conv,axiom,
% 2.86/3.14 ! [Xs: list_int] :
% 2.86/3.14 ( ( ( rotate1_int @ Xs )
% 2.86/3.14 = nil_int )
% 2.86/3.14 = ( Xs = nil_int ) ) ).
% 2.86/3.14
% 2.86/3.14 % rotate1_is_Nil_conv
% 2.86/3.14 thf(fact_4816_rotate1__is__Nil__conv,axiom,
% 2.86/3.14 ! [Xs: list_nat] :
% 2.86/3.14 ( ( ( rotate1_nat @ Xs )
% 2.86/3.14 = nil_nat )
% 2.86/3.14 = ( Xs = nil_nat ) ) ).
% 2.86/3.14
% 2.86/3.14 % rotate1_is_Nil_conv
% 2.86/3.14 thf(fact_4817_rotate1__is__Nil__conv,axiom,
% 2.86/3.14 ! [Xs: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( ( rotate328796349445179396n_assn @ Xs )
% 2.86/3.14 = nil_Pr5671120429643327159n_assn )
% 2.86/3.14 = ( Xs = nil_Pr5671120429643327159n_assn ) ) ).
% 2.86/3.14
% 2.86/3.14 % rotate1_is_Nil_conv
% 2.86/3.14 thf(fact_4818_list__ex__simps_I2_J,axiom,
% 2.86/3.14 ! [P: int > $o] :
% 2.86/3.14 ~ ( list_ex_int @ P @ nil_int ) ).
% 2.86/3.14
% 2.86/3.14 % list_ex_simps(2)
% 2.86/3.14 thf(fact_4819_list__ex__simps_I2_J,axiom,
% 2.86/3.14 ! [P: nat > $o] :
% 2.86/3.14 ~ ( list_ex_nat @ P @ nil_nat ) ).
% 2.86/3.14
% 2.86/3.14 % list_ex_simps(2)
% 2.86/3.14 thf(fact_4820_list__ex__simps_I2_J,axiom,
% 2.86/3.14 ! [P: produc6575502325842934193n_assn > $o] :
% 2.86/3.14 ~ ( list_e1087220904399170805n_assn @ P @ nil_Pr5671120429643327159n_assn ) ).
% 2.86/3.14
% 2.86/3.14 % list_ex_simps(2)
% 2.86/3.14 thf(fact_4821_slice__Nil,axiom,
% 2.86/3.14 ! [Begin: nat,End: nat] :
% 2.86/3.14 ( ( slice_int @ Begin @ End @ nil_int )
% 2.86/3.14 = nil_int ) ).
% 2.86/3.14
% 2.86/3.14 % slice_Nil
% 2.86/3.14 thf(fact_4822_slice__Nil,axiom,
% 2.86/3.14 ! [Begin: nat,End: nat] :
% 2.86/3.14 ( ( slice_nat @ Begin @ End @ nil_nat )
% 2.86/3.14 = nil_nat ) ).
% 2.86/3.14
% 2.86/3.14 % slice_Nil
% 2.86/3.14 thf(fact_4823_slice__Nil,axiom,
% 2.86/3.14 ! [Begin: nat,End: nat] :
% 2.86/3.14 ( ( slice_7964966981652229398n_assn @ Begin @ End @ nil_Pr5671120429643327159n_assn )
% 2.86/3.14 = nil_Pr5671120429643327159n_assn ) ).
% 2.86/3.14
% 2.86/3.14 % slice_Nil
% 2.86/3.14 thf(fact_4824_slice__eq__bounds__empty,axiom,
% 2.86/3.14 ! [I: nat,Xs: list_int] :
% 2.86/3.14 ( ( slice_int @ I @ I @ Xs )
% 2.86/3.14 = nil_int ) ).
% 2.86/3.14
% 2.86/3.14 % slice_eq_bounds_empty
% 2.86/3.14 thf(fact_4825_slice__eq__bounds__empty,axiom,
% 2.86/3.14 ! [I: nat,Xs: list_nat] :
% 2.86/3.14 ( ( slice_nat @ I @ I @ Xs )
% 2.86/3.14 = nil_nat ) ).
% 2.86/3.14
% 2.86/3.14 % slice_eq_bounds_empty
% 2.86/3.14 thf(fact_4826_slice__eq__bounds__empty,axiom,
% 2.86/3.14 ! [I: nat,Xs: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( slice_7964966981652229398n_assn @ I @ I @ Xs )
% 2.86/3.14 = nil_Pr5671120429643327159n_assn ) ).
% 2.86/3.14
% 2.86/3.14 % slice_eq_bounds_empty
% 2.86/3.14 thf(fact_4827_in__measures_I1_J,axiom,
% 2.86/3.14 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 2.86/3.14 ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( measur2694323259624372065at_nat @ nil_se7398569966080822440at_nat ) ) ).
% 2.86/3.14
% 2.86/3.14 % in_measures(1)
% 2.86/3.14 thf(fact_4828_in__measures_I1_J,axiom,
% 2.86/3.14 ! [X: nat,Y: nat] :
% 2.86/3.14 ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( measures_nat @ nil_nat_nat ) ) ).
% 2.86/3.14
% 2.86/3.14 % in_measures(1)
% 2.86/3.14 thf(fact_4829_power__inject__exp,axiom,
% 2.86/3.14 ! [A2: rat,M2: nat,N: nat] :
% 2.86/3.14 ( ( ord_less_rat @ one_one_rat @ A2 )
% 2.86/3.14 => ( ( ( power_power_rat @ A2 @ M2 )
% 2.86/3.14 = ( power_power_rat @ A2 @ N ) )
% 2.86/3.14 = ( M2 = N ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_inject_exp
% 2.86/3.14 thf(fact_4830_power__inject__exp,axiom,
% 2.86/3.14 ! [A2: code_integer,M2: nat,N: nat] :
% 2.86/3.14 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A2 )
% 2.86/3.14 => ( ( ( power_8256067586552552935nteger @ A2 @ M2 )
% 2.86/3.14 = ( power_8256067586552552935nteger @ A2 @ N ) )
% 2.86/3.14 = ( M2 = N ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_inject_exp
% 2.86/3.14 thf(fact_4831_power__inject__exp,axiom,
% 2.86/3.14 ! [A2: nat,M2: nat,N: nat] :
% 2.86/3.14 ( ( ord_less_nat @ one_one_nat @ A2 )
% 2.86/3.14 => ( ( ( power_power_nat @ A2 @ M2 )
% 2.86/3.14 = ( power_power_nat @ A2 @ N ) )
% 2.86/3.14 = ( M2 = N ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_inject_exp
% 2.86/3.14 thf(fact_4832_power__inject__exp,axiom,
% 2.86/3.14 ! [A2: int,M2: nat,N: nat] :
% 2.86/3.14 ( ( ord_less_int @ one_one_int @ A2 )
% 2.86/3.14 => ( ( ( power_power_int @ A2 @ M2 )
% 2.86/3.14 = ( power_power_int @ A2 @ N ) )
% 2.86/3.14 = ( M2 = N ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_inject_exp
% 2.86/3.14 thf(fact_4833_set__empty,axiom,
% 2.86/3.14 ! [Xs: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( ( set_Pr1139785259514867910n_assn @ Xs )
% 2.86/3.14 = bot_bo1176836662018730877n_assn )
% 2.86/3.14 = ( Xs = nil_Pr5671120429643327159n_assn ) ) ).
% 2.86/3.14
% 2.86/3.14 % set_empty
% 2.86/3.14 thf(fact_4834_set__empty,axiom,
% 2.86/3.14 ! [Xs: list_P5464809261938338413at_nat] :
% 2.86/3.14 ( ( ( set_Pr3765526544606949372at_nat @ Xs )
% 2.86/3.14 = bot_bo228742789529271731at_nat )
% 2.86/3.14 = ( Xs = nil_Pr8341282898164651117at_nat ) ) ).
% 2.86/3.14
% 2.86/3.14 % set_empty
% 2.86/3.14 thf(fact_4835_set__empty,axiom,
% 2.86/3.14 ! [Xs: list_P6011104703257516679at_nat] :
% 2.86/3.14 ( ( ( set_Pr5648618587558075414at_nat @ Xs )
% 2.86/3.14 = bot_bo2099793752762293965at_nat )
% 2.86/3.14 = ( Xs = nil_Pr5478986624290739719at_nat ) ) ).
% 2.86/3.14
% 2.86/3.14 % set_empty
% 2.86/3.14 thf(fact_4836_set__empty,axiom,
% 2.86/3.14 ! [Xs: list_o] :
% 2.86/3.14 ( ( ( set_o2 @ Xs )
% 2.86/3.14 = bot_bot_set_o )
% 2.86/3.14 = ( Xs = nil_o ) ) ).
% 2.86/3.14
% 2.86/3.14 % set_empty
% 2.86/3.14 thf(fact_4837_set__empty,axiom,
% 2.86/3.14 ! [Xs: list_nat] :
% 2.86/3.14 ( ( ( set_nat2 @ Xs )
% 2.86/3.14 = bot_bot_set_nat )
% 2.86/3.14 = ( Xs = nil_nat ) ) ).
% 2.86/3.14
% 2.86/3.14 % set_empty
% 2.86/3.14 thf(fact_4838_set__empty,axiom,
% 2.86/3.14 ! [Xs: list_int] :
% 2.86/3.14 ( ( ( set_int2 @ Xs )
% 2.86/3.14 = bot_bot_set_int )
% 2.86/3.14 = ( Xs = nil_int ) ) ).
% 2.86/3.14
% 2.86/3.14 % set_empty
% 2.86/3.14 thf(fact_4839_set__empty2,axiom,
% 2.86/3.14 ! [Xs: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( bot_bo1176836662018730877n_assn
% 2.86/3.14 = ( set_Pr1139785259514867910n_assn @ Xs ) )
% 2.86/3.14 = ( Xs = nil_Pr5671120429643327159n_assn ) ) ).
% 2.86/3.14
% 2.86/3.14 % set_empty2
% 2.86/3.14 thf(fact_4840_set__empty2,axiom,
% 2.86/3.14 ! [Xs: list_P5464809261938338413at_nat] :
% 2.86/3.14 ( ( bot_bo228742789529271731at_nat
% 2.86/3.14 = ( set_Pr3765526544606949372at_nat @ Xs ) )
% 2.86/3.14 = ( Xs = nil_Pr8341282898164651117at_nat ) ) ).
% 2.86/3.14
% 2.86/3.14 % set_empty2
% 2.86/3.14 thf(fact_4841_set__empty2,axiom,
% 2.86/3.14 ! [Xs: list_P6011104703257516679at_nat] :
% 2.86/3.14 ( ( bot_bo2099793752762293965at_nat
% 2.86/3.14 = ( set_Pr5648618587558075414at_nat @ Xs ) )
% 2.86/3.14 = ( Xs = nil_Pr5478986624290739719at_nat ) ) ).
% 2.86/3.14
% 2.86/3.14 % set_empty2
% 2.86/3.14 thf(fact_4842_set__empty2,axiom,
% 2.86/3.14 ! [Xs: list_o] :
% 2.86/3.14 ( ( bot_bot_set_o
% 2.86/3.14 = ( set_o2 @ Xs ) )
% 2.86/3.14 = ( Xs = nil_o ) ) ).
% 2.86/3.14
% 2.86/3.14 % set_empty2
% 2.86/3.14 thf(fact_4843_set__empty2,axiom,
% 2.86/3.14 ! [Xs: list_nat] :
% 2.86/3.14 ( ( bot_bot_set_nat
% 2.86/3.14 = ( set_nat2 @ Xs ) )
% 2.86/3.14 = ( Xs = nil_nat ) ) ).
% 2.86/3.14
% 2.86/3.14 % set_empty2
% 2.86/3.14 thf(fact_4844_set__empty2,axiom,
% 2.86/3.14 ! [Xs: list_int] :
% 2.86/3.14 ( ( bot_bot_set_int
% 2.86/3.14 = ( set_int2 @ Xs ) )
% 2.86/3.14 = ( Xs = nil_int ) ) ).
% 2.86/3.14
% 2.86/3.14 % set_empty2
% 2.86/3.14 thf(fact_4845_length__0__conv,axiom,
% 2.86/3.14 ! [Xs: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( ( size_s6829681357464350627n_assn @ Xs )
% 2.86/3.14 = zero_zero_nat )
% 2.86/3.14 = ( Xs = nil_Pr5671120429643327159n_assn ) ) ).
% 2.86/3.14
% 2.86/3.14 % length_0_conv
% 2.86/3.14 thf(fact_4846_length__0__conv,axiom,
% 2.86/3.14 ! [Xs: list_c] :
% 2.86/3.14 ( ( ( size_size_list_c @ Xs )
% 2.86/3.14 = zero_zero_nat )
% 2.86/3.14 = ( Xs = nil_c ) ) ).
% 2.86/3.14
% 2.86/3.14 % length_0_conv
% 2.86/3.14 thf(fact_4847_length__0__conv,axiom,
% 2.86/3.14 ! [Xs: list_d] :
% 2.86/3.14 ( ( ( size_size_list_d @ Xs )
% 2.86/3.14 = zero_zero_nat )
% 2.86/3.14 = ( Xs = nil_d ) ) ).
% 2.86/3.14
% 2.86/3.14 % length_0_conv
% 2.86/3.14 thf(fact_4848_length__0__conv,axiom,
% 2.86/3.14 ! [Xs: list_nat] :
% 2.86/3.14 ( ( ( size_size_list_nat @ Xs )
% 2.86/3.14 = zero_zero_nat )
% 2.86/3.14 = ( Xs = nil_nat ) ) ).
% 2.86/3.14
% 2.86/3.14 % length_0_conv
% 2.86/3.14 thf(fact_4849_length__0__conv,axiom,
% 2.86/3.14 ! [Xs: list_int] :
% 2.86/3.14 ( ( ( size_size_list_int @ Xs )
% 2.86/3.14 = zero_zero_nat )
% 2.86/3.14 = ( Xs = nil_int ) ) ).
% 2.86/3.14
% 2.86/3.14 % length_0_conv
% 2.86/3.14 thf(fact_4850_singleton__rev__conv,axiom,
% 2.86/3.14 ! [X: int,Xs: list_int] :
% 2.86/3.14 ( ( ( cons_int @ X @ nil_int )
% 2.86/3.14 = ( rev_int @ Xs ) )
% 2.86/3.14 = ( ( cons_int @ X @ nil_int )
% 2.86/3.14 = Xs ) ) ).
% 2.86/3.14
% 2.86/3.14 % singleton_rev_conv
% 2.86/3.14 thf(fact_4851_singleton__rev__conv,axiom,
% 2.86/3.14 ! [X: nat,Xs: list_nat] :
% 2.86/3.14 ( ( ( cons_nat @ X @ nil_nat )
% 2.86/3.14 = ( rev_nat @ Xs ) )
% 2.86/3.14 = ( ( cons_nat @ X @ nil_nat )
% 2.86/3.14 = Xs ) ) ).
% 2.86/3.14
% 2.86/3.14 % singleton_rev_conv
% 2.86/3.14 thf(fact_4852_singleton__rev__conv,axiom,
% 2.86/3.14 ! [X: produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( ( cons_P2971678138204555879n_assn @ X @ nil_Pr5671120429643327159n_assn )
% 2.86/3.14 = ( rev_Pr4855572775806611735n_assn @ Xs ) )
% 2.86/3.14 = ( ( cons_P2971678138204555879n_assn @ X @ nil_Pr5671120429643327159n_assn )
% 2.86/3.14 = Xs ) ) ).
% 2.86/3.14
% 2.86/3.14 % singleton_rev_conv
% 2.86/3.14 thf(fact_4853_rev__singleton__conv,axiom,
% 2.86/3.14 ! [Xs: list_int,X: int] :
% 2.86/3.14 ( ( ( rev_int @ Xs )
% 2.86/3.14 = ( cons_int @ X @ nil_int ) )
% 2.86/3.14 = ( Xs
% 2.86/3.14 = ( cons_int @ X @ nil_int ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % rev_singleton_conv
% 2.86/3.14 thf(fact_4854_rev__singleton__conv,axiom,
% 2.86/3.14 ! [Xs: list_nat,X: nat] :
% 2.86/3.14 ( ( ( rev_nat @ Xs )
% 2.86/3.14 = ( cons_nat @ X @ nil_nat ) )
% 2.86/3.14 = ( Xs
% 2.86/3.14 = ( cons_nat @ X @ nil_nat ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % rev_singleton_conv
% 2.86/3.14 thf(fact_4855_rev__singleton__conv,axiom,
% 2.86/3.14 ! [Xs: list_P8527749157015355191n_assn,X: produc6575502325842934193n_assn] :
% 2.86/3.14 ( ( ( rev_Pr4855572775806611735n_assn @ Xs )
% 2.86/3.14 = ( cons_P2971678138204555879n_assn @ X @ nil_Pr5671120429643327159n_assn ) )
% 2.86/3.14 = ( Xs
% 2.86/3.14 = ( cons_P2971678138204555879n_assn @ X @ nil_Pr5671120429643327159n_assn ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % rev_singleton_conv
% 2.86/3.14 thf(fact_4856_Nil__lenlex__iff1,axiom,
% 2.86/3.14 ! [Ns: list_int,R2: set_Pr958786334691620121nt_int] :
% 2.86/3.14 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ nil_int @ Ns ) @ ( lenlex_int @ R2 ) )
% 2.86/3.14 = ( Ns != nil_int ) ) ).
% 2.86/3.14
% 2.86/3.14 % Nil_lenlex_iff1
% 2.86/3.14 thf(fact_4857_Nil__lenlex__iff1,axiom,
% 2.86/3.14 ! [Ns: list_nat,R2: set_Pr1261947904930325089at_nat] :
% 2.86/3.14 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ nil_nat @ Ns ) @ ( lenlex_nat @ R2 ) )
% 2.86/3.14 = ( Ns != nil_nat ) ) ).
% 2.86/3.14
% 2.86/3.14 % Nil_lenlex_iff1
% 2.86/3.14 thf(fact_4858_Nil__lenlex__iff1,axiom,
% 2.86/3.14 ! [Ns: list_P8527749157015355191n_assn,R2: set_Pr8116311503512020807n_assn] :
% 2.86/3.14 ( ( member3994142547374651152n_assn @ ( produc3014731801419794263n_assn @ nil_Pr5671120429643327159n_assn @ Ns ) @ ( lenlex6671093235567761724n_assn @ R2 ) )
% 2.86/3.14 = ( Ns != nil_Pr5671120429643327159n_assn ) ) ).
% 2.86/3.14
% 2.86/3.14 % Nil_lenlex_iff1
% 2.86/3.14 thf(fact_4859_insert__Nil,axiom,
% 2.86/3.14 ! [X: int] :
% 2.86/3.14 ( ( insert_int @ X @ nil_int )
% 2.86/3.14 = ( cons_int @ X @ nil_int ) ) ).
% 2.86/3.14
% 2.86/3.14 % insert_Nil
% 2.86/3.14 thf(fact_4860_insert__Nil,axiom,
% 2.86/3.14 ! [X: nat] :
% 2.86/3.14 ( ( insert_nat @ X @ nil_nat )
% 2.86/3.14 = ( cons_nat @ X @ nil_nat ) ) ).
% 2.86/3.14
% 2.86/3.14 % insert_Nil
% 2.86/3.14 thf(fact_4861_insert__Nil,axiom,
% 2.86/3.14 ! [X: produc6575502325842934193n_assn] :
% 2.86/3.14 ( ( insert3246601298802261197n_assn @ X @ nil_Pr5671120429643327159n_assn )
% 2.86/3.14 = ( cons_P2971678138204555879n_assn @ X @ nil_Pr5671120429643327159n_assn ) ) ).
% 2.86/3.14
% 2.86/3.14 % insert_Nil
% 2.86/3.14 thf(fact_4862_list__assn__aux__simps_I1_J,axiom,
% 2.86/3.14 ! [P: int > int > assn,L3: list_int] :
% 2.86/3.14 ( ( vEBT_L74593716426352029nt_int @ P @ nil_int @ L3 )
% 2.86/3.14 = ( pure_assn @ ( L3 = nil_int ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn_aux_simps(1)
% 2.86/3.14 thf(fact_4863_list__assn__aux__simps_I1_J,axiom,
% 2.86/3.14 ! [P: int > nat > assn,L3: list_nat] :
% 2.86/3.14 ( ( vEBT_L77084186935402305nt_nat @ P @ nil_int @ L3 )
% 2.86/3.14 = ( pure_assn @ ( L3 = nil_nat ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn_aux_simps(1)
% 2.86/3.14 thf(fact_4864_list__assn__aux__simps_I1_J,axiom,
% 2.86/3.14 ! [P: int > produc6575502325842934193n_assn > assn,L3: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( vEBT_L1620274777744359680n_assn @ P @ nil_int @ L3 )
% 2.86/3.14 = ( pure_assn @ ( L3 = nil_Pr5671120429643327159n_assn ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn_aux_simps(1)
% 2.86/3.14 thf(fact_4865_list__assn__aux__simps_I1_J,axiom,
% 2.86/3.14 ! [P: nat > int > assn,L3: list_int] :
% 2.86/3.14 ( ( vEBT_L8298612041380073281at_int @ P @ nil_nat @ L3 )
% 2.86/3.14 = ( pure_assn @ ( L3 = nil_int ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn_aux_simps(1)
% 2.86/3.14 thf(fact_4866_list__assn__aux__simps_I1_J,axiom,
% 2.86/3.14 ! [P: nat > nat > assn,L3: list_nat] :
% 2.86/3.14 ( ( vEBT_L8301102511889123557at_nat @ P @ nil_nat @ L3 )
% 2.86/3.14 = ( pure_assn @ ( L3 = nil_nat ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn_aux_simps(1)
% 2.86/3.14 thf(fact_4867_list__assn__aux__simps_I1_J,axiom,
% 2.86/3.14 ! [P: nat > produc6575502325842934193n_assn > assn,L3: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( vEBT_L9083610150846024284n_assn @ P @ nil_nat @ L3 )
% 2.86/3.14 = ( pure_assn @ ( L3 = nil_Pr5671120429643327159n_assn ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn_aux_simps(1)
% 2.86/3.14 thf(fact_4868_list__assn__aux__simps_I1_J,axiom,
% 2.86/3.14 ! [P: produc6575502325842934193n_assn > int > assn,L3: list_int] :
% 2.86/3.14 ( ( vEBT_L4760345170377931482sn_int @ P @ nil_Pr5671120429643327159n_assn @ L3 )
% 2.86/3.14 = ( pure_assn @ ( L3 = nil_int ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn_aux_simps(1)
% 2.86/3.14 thf(fact_4869_list__assn__aux__simps_I1_J,axiom,
% 2.86/3.14 ! [P: produc6575502325842934193n_assn > nat > assn,L3: list_nat] :
% 2.86/3.14 ( ( vEBT_L4762835640886981758sn_nat @ P @ nil_Pr5671120429643327159n_assn @ L3 )
% 2.86/3.14 = ( pure_assn @ ( L3 = nil_nat ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn_aux_simps(1)
% 2.86/3.14 thf(fact_4870_list__assn__aux__simps_I1_J,axiom,
% 2.86/3.14 ! [P: produc6575502325842934193n_assn > produc6575502325842934193n_assn > assn,L3: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( vEBT_L3108143461992071043n_assn @ P @ nil_Pr5671120429643327159n_assn @ L3 )
% 2.86/3.14 = ( pure_assn @ ( L3 = nil_Pr5671120429643327159n_assn ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn_aux_simps(1)
% 2.86/3.14 thf(fact_4871_list__assn__aux__simps_I2_J,axiom,
% 2.86/3.14 ! [P: int > int > assn,L: list_int] :
% 2.86/3.14 ( ( vEBT_L74593716426352029nt_int @ P @ L @ nil_int )
% 2.86/3.14 = ( pure_assn @ ( L = nil_int ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn_aux_simps(2)
% 2.86/3.14 thf(fact_4872_list__assn__aux__simps_I2_J,axiom,
% 2.86/3.14 ! [P: nat > int > assn,L: list_nat] :
% 2.86/3.14 ( ( vEBT_L8298612041380073281at_int @ P @ L @ nil_int )
% 2.86/3.14 = ( pure_assn @ ( L = nil_nat ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn_aux_simps(2)
% 2.86/3.14 thf(fact_4873_list__assn__aux__simps_I2_J,axiom,
% 2.86/3.14 ! [P: produc6575502325842934193n_assn > int > assn,L: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( vEBT_L4760345170377931482sn_int @ P @ L @ nil_int )
% 2.86/3.14 = ( pure_assn @ ( L = nil_Pr5671120429643327159n_assn ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn_aux_simps(2)
% 2.86/3.14 thf(fact_4874_list__assn__aux__simps_I2_J,axiom,
% 2.86/3.14 ! [P: int > nat > assn,L: list_int] :
% 2.86/3.14 ( ( vEBT_L77084186935402305nt_nat @ P @ L @ nil_nat )
% 2.86/3.14 = ( pure_assn @ ( L = nil_int ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn_aux_simps(2)
% 2.86/3.14 thf(fact_4875_list__assn__aux__simps_I2_J,axiom,
% 2.86/3.14 ! [P: nat > nat > assn,L: list_nat] :
% 2.86/3.14 ( ( vEBT_L8301102511889123557at_nat @ P @ L @ nil_nat )
% 2.86/3.14 = ( pure_assn @ ( L = nil_nat ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn_aux_simps(2)
% 2.86/3.14 thf(fact_4876_list__assn__aux__simps_I2_J,axiom,
% 2.86/3.14 ! [P: produc6575502325842934193n_assn > nat > assn,L: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( vEBT_L4762835640886981758sn_nat @ P @ L @ nil_nat )
% 2.86/3.14 = ( pure_assn @ ( L = nil_Pr5671120429643327159n_assn ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn_aux_simps(2)
% 2.86/3.14 thf(fact_4877_list__assn__aux__simps_I2_J,axiom,
% 2.86/3.14 ! [P: int > produc6575502325842934193n_assn > assn,L: list_int] :
% 2.86/3.14 ( ( vEBT_L1620274777744359680n_assn @ P @ L @ nil_Pr5671120429643327159n_assn )
% 2.86/3.14 = ( pure_assn @ ( L = nil_int ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn_aux_simps(2)
% 2.86/3.14 thf(fact_4878_list__assn__aux__simps_I2_J,axiom,
% 2.86/3.14 ! [P: nat > produc6575502325842934193n_assn > assn,L: list_nat] :
% 2.86/3.14 ( ( vEBT_L9083610150846024284n_assn @ P @ L @ nil_Pr5671120429643327159n_assn )
% 2.86/3.14 = ( pure_assn @ ( L = nil_nat ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn_aux_simps(2)
% 2.86/3.14 thf(fact_4879_list__assn__aux__simps_I2_J,axiom,
% 2.86/3.14 ! [P: produc6575502325842934193n_assn > produc6575502325842934193n_assn > assn,L: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( vEBT_L3108143461992071043n_assn @ P @ L @ nil_Pr5671120429643327159n_assn )
% 2.86/3.14 = ( pure_assn @ ( L = nil_Pr5671120429643327159n_assn ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_assn_aux_simps(2)
% 2.86/3.14 thf(fact_4880_power__strict__increasing__iff,axiom,
% 2.86/3.14 ! [B2: rat,X: nat,Y: nat] :
% 2.86/3.14 ( ( ord_less_rat @ one_one_rat @ B2 )
% 2.86/3.14 => ( ( ord_less_rat @ ( power_power_rat @ B2 @ X ) @ ( power_power_rat @ B2 @ Y ) )
% 2.86/3.14 = ( ord_less_nat @ X @ Y ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_strict_increasing_iff
% 2.86/3.14 thf(fact_4881_power__strict__increasing__iff,axiom,
% 2.86/3.14 ! [B2: code_integer,X: nat,Y: nat] :
% 2.86/3.14 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B2 )
% 2.86/3.14 => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ B2 @ X ) @ ( power_8256067586552552935nteger @ B2 @ Y ) )
% 2.86/3.14 = ( ord_less_nat @ X @ Y ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_strict_increasing_iff
% 2.86/3.14 thf(fact_4882_power__strict__increasing__iff,axiom,
% 2.86/3.14 ! [B2: nat,X: nat,Y: nat] :
% 2.86/3.14 ( ( ord_less_nat @ one_one_nat @ B2 )
% 2.86/3.14 => ( ( ord_less_nat @ ( power_power_nat @ B2 @ X ) @ ( power_power_nat @ B2 @ Y ) )
% 2.86/3.14 = ( ord_less_nat @ X @ Y ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_strict_increasing_iff
% 2.86/3.14 thf(fact_4883_power__strict__increasing__iff,axiom,
% 2.86/3.14 ! [B2: int,X: nat,Y: nat] :
% 2.86/3.14 ( ( ord_less_int @ one_one_int @ B2 )
% 2.86/3.14 => ( ( ord_less_int @ ( power_power_int @ B2 @ X ) @ ( power_power_int @ B2 @ Y ) )
% 2.86/3.14 = ( ord_less_nat @ X @ Y ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_strict_increasing_iff
% 2.86/3.14 thf(fact_4884_power__eq__0__iff,axiom,
% 2.86/3.14 ! [A2: code_integer,N: nat] :
% 2.86/3.14 ( ( ( power_8256067586552552935nteger @ A2 @ N )
% 2.86/3.14 = zero_z3403309356797280102nteger )
% 2.86/3.14 = ( ( A2 = zero_z3403309356797280102nteger )
% 2.86/3.14 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_eq_0_iff
% 2.86/3.14 thf(fact_4885_power__eq__0__iff,axiom,
% 2.86/3.14 ! [A2: rat,N: nat] :
% 2.86/3.14 ( ( ( power_power_rat @ A2 @ N )
% 2.86/3.14 = zero_zero_rat )
% 2.86/3.14 = ( ( A2 = zero_zero_rat )
% 2.86/3.14 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_eq_0_iff
% 2.86/3.14 thf(fact_4886_power__eq__0__iff,axiom,
% 2.86/3.14 ! [A2: nat,N: nat] :
% 2.86/3.14 ( ( ( power_power_nat @ A2 @ N )
% 2.86/3.14 = zero_zero_nat )
% 2.86/3.14 = ( ( A2 = zero_zero_nat )
% 2.86/3.14 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_eq_0_iff
% 2.86/3.14 thf(fact_4887_power__eq__0__iff,axiom,
% 2.86/3.14 ! [A2: int,N: nat] :
% 2.86/3.14 ( ( ( power_power_int @ A2 @ N )
% 2.86/3.14 = zero_zero_int )
% 2.86/3.14 = ( ( A2 = zero_zero_int )
% 2.86/3.14 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_eq_0_iff
% 2.86/3.14 thf(fact_4888_length__greater__0__conv,axiom,
% 2.86/3.14 ! [Xs: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( ord_less_nat @ zero_zero_nat @ ( size_s6829681357464350627n_assn @ Xs ) )
% 2.86/3.14 = ( Xs != nil_Pr5671120429643327159n_assn ) ) ).
% 2.86/3.14
% 2.86/3.14 % length_greater_0_conv
% 2.86/3.14 thf(fact_4889_length__greater__0__conv,axiom,
% 2.86/3.14 ! [Xs: list_c] :
% 2.86/3.14 ( ( ord_less_nat @ zero_zero_nat @ ( size_size_list_c @ Xs ) )
% 2.86/3.14 = ( Xs != nil_c ) ) ).
% 2.86/3.14
% 2.86/3.14 % length_greater_0_conv
% 2.86/3.14 thf(fact_4890_length__greater__0__conv,axiom,
% 2.86/3.14 ! [Xs: list_d] :
% 2.86/3.14 ( ( ord_less_nat @ zero_zero_nat @ ( size_size_list_d @ Xs ) )
% 2.86/3.14 = ( Xs != nil_d ) ) ).
% 2.86/3.14
% 2.86/3.14 % length_greater_0_conv
% 2.86/3.14 thf(fact_4891_length__greater__0__conv,axiom,
% 2.86/3.14 ! [Xs: list_nat] :
% 2.86/3.14 ( ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs ) )
% 2.86/3.14 = ( Xs != nil_nat ) ) ).
% 2.86/3.14
% 2.86/3.14 % length_greater_0_conv
% 2.86/3.14 thf(fact_4892_length__greater__0__conv,axiom,
% 2.86/3.14 ! [Xs: list_int] :
% 2.86/3.14 ( ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs ) )
% 2.86/3.14 = ( Xs != nil_int ) ) ).
% 2.86/3.14
% 2.86/3.14 % length_greater_0_conv
% 2.86/3.14 thf(fact_4893_power__strict__decreasing__iff,axiom,
% 2.86/3.14 ! [B2: rat,M2: nat,N: nat] :
% 2.86/3.14 ( ( ord_less_rat @ zero_zero_rat @ B2 )
% 2.86/3.14 => ( ( ord_less_rat @ B2 @ one_one_rat )
% 2.86/3.14 => ( ( ord_less_rat @ ( power_power_rat @ B2 @ M2 ) @ ( power_power_rat @ B2 @ N ) )
% 2.86/3.14 = ( ord_less_nat @ N @ M2 ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_strict_decreasing_iff
% 2.86/3.14 thf(fact_4894_power__strict__decreasing__iff,axiom,
% 2.86/3.14 ! [B2: code_integer,M2: nat,N: nat] :
% 2.86/3.14 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B2 )
% 2.86/3.14 => ( ( ord_le6747313008572928689nteger @ B2 @ one_one_Code_integer )
% 2.86/3.14 => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ B2 @ M2 ) @ ( power_8256067586552552935nteger @ B2 @ N ) )
% 2.86/3.14 = ( ord_less_nat @ N @ M2 ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_strict_decreasing_iff
% 2.86/3.14 thf(fact_4895_power__strict__decreasing__iff,axiom,
% 2.86/3.14 ! [B2: nat,M2: nat,N: nat] :
% 2.86/3.14 ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 2.86/3.14 => ( ( ord_less_nat @ B2 @ one_one_nat )
% 2.86/3.14 => ( ( ord_less_nat @ ( power_power_nat @ B2 @ M2 ) @ ( power_power_nat @ B2 @ N ) )
% 2.86/3.14 = ( ord_less_nat @ N @ M2 ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_strict_decreasing_iff
% 2.86/3.14 thf(fact_4896_power__strict__decreasing__iff,axiom,
% 2.86/3.14 ! [B2: int,M2: nat,N: nat] :
% 2.86/3.14 ( ( ord_less_int @ zero_zero_int @ B2 )
% 2.86/3.14 => ( ( ord_less_int @ B2 @ one_one_int )
% 2.86/3.14 => ( ( ord_less_int @ ( power_power_int @ B2 @ M2 ) @ ( power_power_int @ B2 @ N ) )
% 2.86/3.14 = ( ord_less_nat @ N @ M2 ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_strict_decreasing_iff
% 2.86/3.14 thf(fact_4897_power__mono__iff,axiom,
% 2.86/3.14 ! [A2: code_integer,B2: code_integer,N: nat] :
% 2.86/3.14 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 2.86/3.14 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B2 )
% 2.86/3.14 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.14 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A2 @ N ) @ ( power_8256067586552552935nteger @ B2 @ N ) )
% 2.86/3.14 = ( ord_le3102999989581377725nteger @ A2 @ B2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_mono_iff
% 2.86/3.14 thf(fact_4898_power__mono__iff,axiom,
% 2.86/3.14 ! [A2: rat,B2: rat,N: nat] :
% 2.86/3.14 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 2.86/3.14 => ( ( ord_less_eq_rat @ zero_zero_rat @ B2 )
% 2.86/3.14 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.14 => ( ( ord_less_eq_rat @ ( power_power_rat @ A2 @ N ) @ ( power_power_rat @ B2 @ N ) )
% 2.86/3.14 = ( ord_less_eq_rat @ A2 @ B2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_mono_iff
% 2.86/3.14 thf(fact_4899_power__mono__iff,axiom,
% 2.86/3.14 ! [A2: nat,B2: nat,N: nat] :
% 2.86/3.14 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 2.86/3.14 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 2.86/3.14 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.14 => ( ( ord_less_eq_nat @ ( power_power_nat @ A2 @ N ) @ ( power_power_nat @ B2 @ N ) )
% 2.86/3.14 = ( ord_less_eq_nat @ A2 @ B2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_mono_iff
% 2.86/3.14 thf(fact_4900_power__mono__iff,axiom,
% 2.86/3.14 ! [A2: int,B2: int,N: nat] :
% 2.86/3.14 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 2.86/3.14 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 2.86/3.14 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.14 => ( ( ord_less_eq_int @ ( power_power_int @ A2 @ N ) @ ( power_power_int @ B2 @ N ) )
% 2.86/3.14 = ( ord_less_eq_int @ A2 @ B2 ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_mono_iff
% 2.86/3.14 thf(fact_4901_power__increasing__iff,axiom,
% 2.86/3.14 ! [B2: rat,X: nat,Y: nat] :
% 2.86/3.14 ( ( ord_less_rat @ one_one_rat @ B2 )
% 2.86/3.14 => ( ( ord_less_eq_rat @ ( power_power_rat @ B2 @ X ) @ ( power_power_rat @ B2 @ Y ) )
% 2.86/3.14 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_increasing_iff
% 2.86/3.14 thf(fact_4902_power__increasing__iff,axiom,
% 2.86/3.14 ! [B2: code_integer,X: nat,Y: nat] :
% 2.86/3.14 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B2 )
% 2.86/3.14 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ B2 @ X ) @ ( power_8256067586552552935nteger @ B2 @ Y ) )
% 2.86/3.14 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_increasing_iff
% 2.86/3.14 thf(fact_4903_power__increasing__iff,axiom,
% 2.86/3.14 ! [B2: nat,X: nat,Y: nat] :
% 2.86/3.14 ( ( ord_less_nat @ one_one_nat @ B2 )
% 2.86/3.14 => ( ( ord_less_eq_nat @ ( power_power_nat @ B2 @ X ) @ ( power_power_nat @ B2 @ Y ) )
% 2.86/3.14 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_increasing_iff
% 2.86/3.14 thf(fact_4904_power__increasing__iff,axiom,
% 2.86/3.14 ! [B2: int,X: nat,Y: nat] :
% 2.86/3.14 ( ( ord_less_int @ one_one_int @ B2 )
% 2.86/3.14 => ( ( ord_less_eq_int @ ( power_power_int @ B2 @ X ) @ ( power_power_int @ B2 @ Y ) )
% 2.86/3.14 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_increasing_iff
% 2.86/3.14 thf(fact_4905_length__ge__1__conv,axiom,
% 2.86/3.14 ! [L: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( size_s6829681357464350627n_assn @ L ) )
% 2.86/3.14 = ( L != nil_Pr5671120429643327159n_assn ) ) ).
% 2.86/3.14
% 2.86/3.14 % length_ge_1_conv
% 2.86/3.14 thf(fact_4906_length__ge__1__conv,axiom,
% 2.86/3.14 ! [L: list_c] :
% 2.86/3.14 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( size_size_list_c @ L ) )
% 2.86/3.14 = ( L != nil_c ) ) ).
% 2.86/3.14
% 2.86/3.14 % length_ge_1_conv
% 2.86/3.14 thf(fact_4907_length__ge__1__conv,axiom,
% 2.86/3.14 ! [L: list_d] :
% 2.86/3.14 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( size_size_list_d @ L ) )
% 2.86/3.14 = ( L != nil_d ) ) ).
% 2.86/3.14
% 2.86/3.14 % length_ge_1_conv
% 2.86/3.14 thf(fact_4908_length__ge__1__conv,axiom,
% 2.86/3.14 ! [L: list_nat] :
% 2.86/3.14 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( size_size_list_nat @ L ) )
% 2.86/3.14 = ( L != nil_nat ) ) ).
% 2.86/3.14
% 2.86/3.14 % length_ge_1_conv
% 2.86/3.14 thf(fact_4909_length__ge__1__conv,axiom,
% 2.86/3.14 ! [L: list_int] :
% 2.86/3.14 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( size_size_list_int @ L ) )
% 2.86/3.14 = ( L != nil_int ) ) ).
% 2.86/3.14
% 2.86/3.14 % length_ge_1_conv
% 2.86/3.14 thf(fact_4910_transpose_Ocases,axiom,
% 2.86/3.14 ! [X: list_list_int] :
% 2.86/3.14 ( ( X != nil_list_int )
% 2.86/3.14 => ( ! [Xss: list_list_int] :
% 2.86/3.14 ( X
% 2.86/3.14 != ( cons_list_int @ nil_int @ Xss ) )
% 2.86/3.14 => ~ ! [X3: int,Xs2: list_int,Xss: list_list_int] :
% 2.86/3.14 ( X
% 2.86/3.14 != ( cons_list_int @ ( cons_int @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % transpose.cases
% 2.86/3.14 thf(fact_4911_transpose_Ocases,axiom,
% 2.86/3.14 ! [X: list_list_nat] :
% 2.86/3.14 ( ( X != nil_list_nat )
% 2.86/3.14 => ( ! [Xss: list_list_nat] :
% 2.86/3.14 ( X
% 2.86/3.14 != ( cons_list_nat @ nil_nat @ Xss ) )
% 2.86/3.14 => ~ ! [X3: nat,Xs2: list_nat,Xss: list_list_nat] :
% 2.86/3.14 ( X
% 2.86/3.14 != ( cons_list_nat @ ( cons_nat @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % transpose.cases
% 2.86/3.14 thf(fact_4912_transpose_Ocases,axiom,
% 2.86/3.14 ! [X: list_l6351802567095793725n_assn] :
% 2.86/3.14 ( ( X != nil_li5476096274760905021n_assn )
% 2.86/3.14 => ( ! [Xss: list_l6351802567095793725n_assn] :
% 2.86/3.14 ( X
% 2.86/3.14 != ( cons_l2423627976422276333n_assn @ nil_Pr5671120429643327159n_assn @ Xss ) )
% 2.86/3.14 => ~ ! [X3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn,Xss: list_l6351802567095793725n_assn] :
% 2.86/3.14 ( X
% 2.86/3.14 != ( cons_l2423627976422276333n_assn @ ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % transpose.cases
% 2.86/3.14 thf(fact_4913_Nil__lenlex__iff2,axiom,
% 2.86/3.14 ! [Ns: list_int,R2: set_Pr958786334691620121nt_int] :
% 2.86/3.14 ~ ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Ns @ nil_int ) @ ( lenlex_int @ R2 ) ) ).
% 2.86/3.14
% 2.86/3.14 % Nil_lenlex_iff2
% 2.86/3.14 thf(fact_4914_Nil__lenlex__iff2,axiom,
% 2.86/3.14 ! [Ns: list_nat,R2: set_Pr1261947904930325089at_nat] :
% 2.86/3.14 ~ ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Ns @ nil_nat ) @ ( lenlex_nat @ R2 ) ) ).
% 2.86/3.14
% 2.86/3.14 % Nil_lenlex_iff2
% 2.86/3.14 thf(fact_4915_Nil__lenlex__iff2,axiom,
% 2.86/3.14 ! [Ns: list_P8527749157015355191n_assn,R2: set_Pr8116311503512020807n_assn] :
% 2.86/3.14 ~ ( member3994142547374651152n_assn @ ( produc3014731801419794263n_assn @ Ns @ nil_Pr5671120429643327159n_assn ) @ ( lenlex6671093235567761724n_assn @ R2 ) ) ).
% 2.86/3.14
% 2.86/3.14 % Nil_lenlex_iff2
% 2.86/3.14 thf(fact_4916_Nil2__notin__lex,axiom,
% 2.86/3.14 ! [Xs: list_int,R2: set_Pr958786334691620121nt_int] :
% 2.86/3.14 ~ ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs @ nil_int ) @ ( lex_int @ R2 ) ) ).
% 2.86/3.14
% 2.86/3.14 % Nil2_notin_lex
% 2.86/3.14 thf(fact_4917_Nil2__notin__lex,axiom,
% 2.86/3.14 ! [Xs: list_nat,R2: set_Pr1261947904930325089at_nat] :
% 2.86/3.14 ~ ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs @ nil_nat ) @ ( lex_nat @ R2 ) ) ).
% 2.86/3.14
% 2.86/3.14 % Nil2_notin_lex
% 2.86/3.14 thf(fact_4918_Nil2__notin__lex,axiom,
% 2.86/3.14 ! [Xs: list_P8527749157015355191n_assn,R2: set_Pr8116311503512020807n_assn] :
% 2.86/3.14 ~ ( member3994142547374651152n_assn @ ( produc3014731801419794263n_assn @ Xs @ nil_Pr5671120429643327159n_assn ) @ ( lex_Pr7559194461235888923n_assn @ R2 ) ) ).
% 2.86/3.14
% 2.86/3.14 % Nil2_notin_lex
% 2.86/3.14 thf(fact_4919_Nil__notin__lex,axiom,
% 2.86/3.14 ! [Ys: list_int,R2: set_Pr958786334691620121nt_int] :
% 2.86/3.14 ~ ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ nil_int @ Ys ) @ ( lex_int @ R2 ) ) ).
% 2.86/3.14
% 2.86/3.14 % Nil_notin_lex
% 2.86/3.14 thf(fact_4920_Nil__notin__lex,axiom,
% 2.86/3.14 ! [Ys: list_nat,R2: set_Pr1261947904930325089at_nat] :
% 2.86/3.14 ~ ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ nil_nat @ Ys ) @ ( lex_nat @ R2 ) ) ).
% 2.86/3.14
% 2.86/3.14 % Nil_notin_lex
% 2.86/3.14 thf(fact_4921_Nil__notin__lex,axiom,
% 2.86/3.14 ! [Ys: list_P8527749157015355191n_assn,R2: set_Pr8116311503512020807n_assn] :
% 2.86/3.14 ~ ( member3994142547374651152n_assn @ ( produc3014731801419794263n_assn @ nil_Pr5671120429643327159n_assn @ Ys ) @ ( lex_Pr7559194461235888923n_assn @ R2 ) ) ).
% 2.86/3.14
% 2.86/3.14 % Nil_notin_lex
% 2.86/3.14 thf(fact_4922_zip_Osimps_I1_J,axiom,
% 2.86/3.14 ! [Xs: list_assn] :
% 2.86/3.14 ( ( zip_assn_assn @ Xs @ nil_assn )
% 2.86/3.14 = nil_Pr5671120429643327159n_assn ) ).
% 2.86/3.14
% 2.86/3.14 % zip.simps(1)
% 2.86/3.14 thf(fact_4923_mset__distrib,axiom,
% 2.86/3.14 ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat,M5: multis2468970476368604999at_nat,N7: multis2468970476368604999at_nat] :
% 2.86/3.14 ( ( ( plus_p7104986032573967614at_nat @ A @ B )
% 2.86/3.14 = ( plus_p7104986032573967614at_nat @ M5 @ N7 ) )
% 2.86/3.14 => ~ ! [Am: multis2468970476368604999at_nat,An: multis2468970476368604999at_nat] :
% 2.86/3.14 ( ( A
% 2.86/3.14 = ( plus_p7104986032573967614at_nat @ Am @ An ) )
% 2.86/3.14 => ! [Bm: multis2468970476368604999at_nat,Bn: multis2468970476368604999at_nat] :
% 2.86/3.14 ( ( B
% 2.86/3.14 = ( plus_p7104986032573967614at_nat @ Bm @ Bn ) )
% 2.86/3.14 => ( ( M5
% 2.86/3.14 = ( plus_p7104986032573967614at_nat @ Am @ Bm ) )
% 2.86/3.14 => ( N7
% 2.86/3.14 != ( plus_p7104986032573967614at_nat @ An @ Bn ) ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % mset_distrib
% 2.86/3.14 thf(fact_4924_count__list_Osimps_I1_J,axiom,
% 2.86/3.14 ! [Y: int] :
% 2.86/3.14 ( ( count_list_int @ nil_int @ Y )
% 2.86/3.14 = zero_zero_nat ) ).
% 2.86/3.14
% 2.86/3.14 % count_list.simps(1)
% 2.86/3.14 thf(fact_4925_count__list_Osimps_I1_J,axiom,
% 2.86/3.14 ! [Y: nat] :
% 2.86/3.14 ( ( count_list_nat @ nil_nat @ Y )
% 2.86/3.14 = zero_zero_nat ) ).
% 2.86/3.14
% 2.86/3.14 % count_list.simps(1)
% 2.86/3.14 thf(fact_4926_count__list_Osimps_I1_J,axiom,
% 2.86/3.14 ! [Y: produc6575502325842934193n_assn] :
% 2.86/3.14 ( ( count_2530312006313534765n_assn @ nil_Pr5671120429643327159n_assn @ Y )
% 2.86/3.14 = zero_zero_nat ) ).
% 2.86/3.14
% 2.86/3.14 % count_list.simps(1)
% 2.86/3.14 thf(fact_4927_product_Osimps_I1_J,axiom,
% 2.86/3.14 ! [Uu: list_assn] :
% 2.86/3.14 ( ( product_assn_assn @ nil_assn @ Uu )
% 2.86/3.14 = nil_Pr5671120429643327159n_assn ) ).
% 2.86/3.14
% 2.86/3.14 % product.simps(1)
% 2.86/3.14 thf(fact_4928_power__commutes,axiom,
% 2.86/3.14 ! [A2: code_integer,N: nat] :
% 2.86/3.14 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A2 @ N ) @ A2 )
% 2.86/3.14 = ( times_3573771949741848930nteger @ A2 @ ( power_8256067586552552935nteger @ A2 @ N ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_commutes
% 2.86/3.14 thf(fact_4929_power__commutes,axiom,
% 2.86/3.14 ! [A2: assn,N: nat] :
% 2.86/3.14 ( ( times_times_assn @ ( power_power_assn @ A2 @ N ) @ A2 )
% 2.86/3.14 = ( times_times_assn @ A2 @ ( power_power_assn @ A2 @ N ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_commutes
% 2.86/3.14 thf(fact_4930_power__commutes,axiom,
% 2.86/3.14 ! [A2: rat,N: nat] :
% 2.86/3.14 ( ( times_times_rat @ ( power_power_rat @ A2 @ N ) @ A2 )
% 2.86/3.14 = ( times_times_rat @ A2 @ ( power_power_rat @ A2 @ N ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_commutes
% 2.86/3.14 thf(fact_4931_power__commutes,axiom,
% 2.86/3.14 ! [A2: nat,N: nat] :
% 2.86/3.14 ( ( times_times_nat @ ( power_power_nat @ A2 @ N ) @ A2 )
% 2.86/3.14 = ( times_times_nat @ A2 @ ( power_power_nat @ A2 @ N ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_commutes
% 2.86/3.14 thf(fact_4932_power__commutes,axiom,
% 2.86/3.14 ! [A2: int,N: nat] :
% 2.86/3.14 ( ( times_times_int @ ( power_power_int @ A2 @ N ) @ A2 )
% 2.86/3.14 = ( times_times_int @ A2 @ ( power_power_int @ A2 @ N ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_commutes
% 2.86/3.14 thf(fact_4933_power__mult__distrib,axiom,
% 2.86/3.14 ! [A2: code_integer,B2: code_integer,N: nat] :
% 2.86/3.14 ( ( power_8256067586552552935nteger @ ( times_3573771949741848930nteger @ A2 @ B2 ) @ N )
% 2.86/3.14 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A2 @ N ) @ ( power_8256067586552552935nteger @ B2 @ N ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_mult_distrib
% 2.86/3.14 thf(fact_4934_power__mult__distrib,axiom,
% 2.86/3.14 ! [A2: assn,B2: assn,N: nat] :
% 2.86/3.14 ( ( power_power_assn @ ( times_times_assn @ A2 @ B2 ) @ N )
% 2.86/3.14 = ( times_times_assn @ ( power_power_assn @ A2 @ N ) @ ( power_power_assn @ B2 @ N ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_mult_distrib
% 2.86/3.14 thf(fact_4935_power__mult__distrib,axiom,
% 2.86/3.14 ! [A2: rat,B2: rat,N: nat] :
% 2.86/3.14 ( ( power_power_rat @ ( times_times_rat @ A2 @ B2 ) @ N )
% 2.86/3.14 = ( times_times_rat @ ( power_power_rat @ A2 @ N ) @ ( power_power_rat @ B2 @ N ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_mult_distrib
% 2.86/3.14 thf(fact_4936_power__mult__distrib,axiom,
% 2.86/3.14 ! [A2: nat,B2: nat,N: nat] :
% 2.86/3.14 ( ( power_power_nat @ ( times_times_nat @ A2 @ B2 ) @ N )
% 2.86/3.14 = ( times_times_nat @ ( power_power_nat @ A2 @ N ) @ ( power_power_nat @ B2 @ N ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_mult_distrib
% 2.86/3.14 thf(fact_4937_power__mult__distrib,axiom,
% 2.86/3.14 ! [A2: int,B2: int,N: nat] :
% 2.86/3.14 ( ( power_power_int @ ( times_times_int @ A2 @ B2 ) @ N )
% 2.86/3.14 = ( times_times_int @ ( power_power_int @ A2 @ N ) @ ( power_power_int @ B2 @ N ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_mult_distrib
% 2.86/3.14 thf(fact_4938_power__commuting__commutes,axiom,
% 2.86/3.14 ! [X: code_integer,Y: code_integer,N: nat] :
% 2.86/3.14 ( ( ( times_3573771949741848930nteger @ X @ Y )
% 2.86/3.14 = ( times_3573771949741848930nteger @ Y @ X ) )
% 2.86/3.14 => ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ X @ N ) @ Y )
% 2.86/3.14 = ( times_3573771949741848930nteger @ Y @ ( power_8256067586552552935nteger @ X @ N ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_commuting_commutes
% 2.86/3.14 thf(fact_4939_power__commuting__commutes,axiom,
% 2.86/3.14 ! [X: assn,Y: assn,N: nat] :
% 2.86/3.14 ( ( ( times_times_assn @ X @ Y )
% 2.86/3.14 = ( times_times_assn @ Y @ X ) )
% 2.86/3.14 => ( ( times_times_assn @ ( power_power_assn @ X @ N ) @ Y )
% 2.86/3.14 = ( times_times_assn @ Y @ ( power_power_assn @ X @ N ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_commuting_commutes
% 2.86/3.14 thf(fact_4940_power__commuting__commutes,axiom,
% 2.86/3.14 ! [X: rat,Y: rat,N: nat] :
% 2.86/3.14 ( ( ( times_times_rat @ X @ Y )
% 2.86/3.14 = ( times_times_rat @ Y @ X ) )
% 2.86/3.14 => ( ( times_times_rat @ ( power_power_rat @ X @ N ) @ Y )
% 2.86/3.14 = ( times_times_rat @ Y @ ( power_power_rat @ X @ N ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_commuting_commutes
% 2.86/3.14 thf(fact_4941_power__commuting__commutes,axiom,
% 2.86/3.14 ! [X: nat,Y: nat,N: nat] :
% 2.86/3.14 ( ( ( times_times_nat @ X @ Y )
% 2.86/3.14 = ( times_times_nat @ Y @ X ) )
% 2.86/3.14 => ( ( times_times_nat @ ( power_power_nat @ X @ N ) @ Y )
% 2.86/3.14 = ( times_times_nat @ Y @ ( power_power_nat @ X @ N ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_commuting_commutes
% 2.86/3.14 thf(fact_4942_power__commuting__commutes,axiom,
% 2.86/3.14 ! [X: int,Y: int,N: nat] :
% 2.86/3.14 ( ( ( times_times_int @ X @ Y )
% 2.86/3.14 = ( times_times_int @ Y @ X ) )
% 2.86/3.14 => ( ( times_times_int @ ( power_power_int @ X @ N ) @ Y )
% 2.86/3.14 = ( times_times_int @ Y @ ( power_power_int @ X @ N ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % power_commuting_commutes
% 2.86/3.14 thf(fact_4943_successively_Ocases,axiom,
% 2.86/3.14 ! [X: produc5834231552977413017st_int] :
% 2.86/3.14 ( ! [P5: int > int > $o] :
% 2.86/3.14 ( X
% 2.86/3.14 != ( produc8618682346314911123st_int @ P5 @ nil_int ) )
% 2.86/3.14 => ( ! [P5: int > int > $o,X3: int] :
% 2.86/3.14 ( X
% 2.86/3.14 != ( produc8618682346314911123st_int @ P5 @ ( cons_int @ X3 @ nil_int ) ) )
% 2.86/3.14 => ~ ! [P5: int > int > $o,X3: int,Y2: int,Xs2: list_int] :
% 2.86/3.14 ( X
% 2.86/3.14 != ( produc8618682346314911123st_int @ P5 @ ( cons_int @ X3 @ ( cons_int @ Y2 @ Xs2 ) ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % successively.cases
% 2.86/3.14 thf(fact_4944_successively_Ocases,axiom,
% 2.86/3.14 ! [X: produc254973753779126261st_nat] :
% 2.86/3.14 ( ! [P5: nat > nat > $o] :
% 2.86/3.14 ( X
% 2.86/3.14 != ( produc4727192421694094319st_nat @ P5 @ nil_nat ) )
% 2.86/3.14 => ( ! [P5: nat > nat > $o,X3: nat] :
% 2.86/3.14 ( X
% 2.86/3.14 != ( produc4727192421694094319st_nat @ P5 @ ( cons_nat @ X3 @ nil_nat ) ) )
% 2.86/3.14 => ~ ! [P5: nat > nat > $o,X3: nat,Y2: nat,Xs2: list_nat] :
% 2.86/3.14 ( X
% 2.86/3.14 != ( produc4727192421694094319st_nat @ P5 @ ( cons_nat @ X3 @ ( cons_nat @ Y2 @ Xs2 ) ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % successively.cases
% 2.86/3.14 thf(fact_4945_successively_Ocases,axiom,
% 2.86/3.14 ! [X: produc4530688714081574576n_assn] :
% 2.86/3.14 ( ! [P5: produc6575502325842934193n_assn > produc6575502325842934193n_assn > $o] :
% 2.86/3.14 ( X
% 2.86/3.14 != ( produc6115016301897879072n_assn @ P5 @ nil_Pr5671120429643327159n_assn ) )
% 2.86/3.14 => ( ! [P5: produc6575502325842934193n_assn > produc6575502325842934193n_assn > $o,X3: produc6575502325842934193n_assn] :
% 2.86/3.14 ( X
% 2.86/3.14 != ( produc6115016301897879072n_assn @ P5 @ ( cons_P2971678138204555879n_assn @ X3 @ nil_Pr5671120429643327159n_assn ) ) )
% 2.86/3.14 => ~ ! [P5: produc6575502325842934193n_assn > produc6575502325842934193n_assn > $o,X3: produc6575502325842934193n_assn,Y2: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( X
% 2.86/3.14 != ( produc6115016301897879072n_assn @ P5 @ ( cons_P2971678138204555879n_assn @ X3 @ ( cons_P2971678138204555879n_assn @ Y2 @ Xs2 ) ) ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % successively.cases
% 2.86/3.14 thf(fact_4946_sorted__wrt_Ocases,axiom,
% 2.86/3.14 ! [X: produc5834231552977413017st_int] :
% 2.86/3.14 ( ! [P5: int > int > $o] :
% 2.86/3.14 ( X
% 2.86/3.14 != ( produc8618682346314911123st_int @ P5 @ nil_int ) )
% 2.86/3.14 => ~ ! [P5: int > int > $o,X3: int,Ys5: list_int] :
% 2.86/3.14 ( X
% 2.86/3.14 != ( produc8618682346314911123st_int @ P5 @ ( cons_int @ X3 @ Ys5 ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % sorted_wrt.cases
% 2.86/3.14 thf(fact_4947_sorted__wrt_Ocases,axiom,
% 2.86/3.14 ! [X: produc254973753779126261st_nat] :
% 2.86/3.14 ( ! [P5: nat > nat > $o] :
% 2.86/3.14 ( X
% 2.86/3.14 != ( produc4727192421694094319st_nat @ P5 @ nil_nat ) )
% 2.86/3.14 => ~ ! [P5: nat > nat > $o,X3: nat,Ys5: list_nat] :
% 2.86/3.14 ( X
% 2.86/3.14 != ( produc4727192421694094319st_nat @ P5 @ ( cons_nat @ X3 @ Ys5 ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % sorted_wrt.cases
% 2.86/3.14 thf(fact_4948_sorted__wrt_Ocases,axiom,
% 2.86/3.14 ! [X: produc4530688714081574576n_assn] :
% 2.86/3.14 ( ! [P5: produc6575502325842934193n_assn > produc6575502325842934193n_assn > $o] :
% 2.86/3.14 ( X
% 2.86/3.14 != ( produc6115016301897879072n_assn @ P5 @ nil_Pr5671120429643327159n_assn ) )
% 2.86/3.14 => ~ ! [P5: produc6575502325842934193n_assn > produc6575502325842934193n_assn > $o,X3: produc6575502325842934193n_assn,Ys5: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( X
% 2.86/3.14 != ( produc6115016301897879072n_assn @ P5 @ ( cons_P2971678138204555879n_assn @ X3 @ Ys5 ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % sorted_wrt.cases
% 2.86/3.14 thf(fact_4949_neq__NilE,axiom,
% 2.86/3.14 ! [L: list_int] :
% 2.86/3.14 ( ( L != nil_int )
% 2.86/3.14 => ~ ! [X3: int,Xs2: list_int] :
% 2.86/3.14 ( L
% 2.86/3.14 != ( cons_int @ X3 @ Xs2 ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % neq_NilE
% 2.86/3.14 thf(fact_4950_neq__NilE,axiom,
% 2.86/3.14 ! [L: list_nat] :
% 2.86/3.14 ( ( L != nil_nat )
% 2.86/3.14 => ~ ! [X3: nat,Xs2: list_nat] :
% 2.86/3.14 ( L
% 2.86/3.14 != ( cons_nat @ X3 @ Xs2 ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % neq_NilE
% 2.86/3.14 thf(fact_4951_neq__NilE,axiom,
% 2.86/3.14 ! [L: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( ( L != nil_Pr5671120429643327159n_assn )
% 2.86/3.14 => ~ ! [X3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn] :
% 2.86/3.14 ( L
% 2.86/3.14 != ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % neq_NilE
% 2.86/3.14 thf(fact_4952_list__2pre__induct,axiom,
% 2.86/3.14 ! [P: list_int > list_int > $o,W1: list_int,W2: list_int] :
% 2.86/3.14 ( ( P @ nil_int @ nil_int )
% 2.86/3.14 => ( ! [E2: int,W12: list_int,W22: list_int] :
% 2.86/3.14 ( ( P @ W12 @ W22 )
% 2.86/3.14 => ( P @ ( cons_int @ E2 @ W12 ) @ W22 ) )
% 2.86/3.14 => ( ! [E2: int,W13: list_int,W23: list_int] :
% 2.86/3.14 ( ( P @ W13 @ W23 )
% 2.86/3.14 => ( P @ W13 @ ( cons_int @ E2 @ W23 ) ) )
% 2.86/3.14 => ( P @ W1 @ W2 ) ) ) ) ).
% 2.86/3.14
% 2.86/3.14 % list_2pre_induct
% 2.86/3.14 thf(fact_4953_list__2pre__induct,axiom,
% 2.86/3.14 ! [P: list_int > list_nat > $o,W1: list_int,W2: list_nat] :
% 2.86/3.15 ( ( P @ nil_int @ nil_nat )
% 2.86/3.15 => ( ! [E2: int,W12: list_int,W22: list_nat] :
% 2.86/3.15 ( ( P @ W12 @ W22 )
% 2.86/3.15 => ( P @ ( cons_int @ E2 @ W12 ) @ W22 ) )
% 2.86/3.15 => ( ! [E2: nat,W13: list_int,W23: list_nat] :
% 2.86/3.15 ( ( P @ W13 @ W23 )
% 2.86/3.15 => ( P @ W13 @ ( cons_nat @ E2 @ W23 ) ) )
% 2.86/3.15 => ( P @ W1 @ W2 ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_2pre_induct
% 2.86/3.15 thf(fact_4954_list__2pre__induct,axiom,
% 2.86/3.15 ! [P: list_int > list_P8527749157015355191n_assn > $o,W1: list_int,W2: list_P8527749157015355191n_assn] :
% 2.86/3.15 ( ( P @ nil_int @ nil_Pr5671120429643327159n_assn )
% 2.86/3.15 => ( ! [E2: int,W12: list_int,W22: list_P8527749157015355191n_assn] :
% 2.86/3.15 ( ( P @ W12 @ W22 )
% 2.86/3.15 => ( P @ ( cons_int @ E2 @ W12 ) @ W22 ) )
% 2.86/3.15 => ( ! [E2: produc6575502325842934193n_assn,W13: list_int,W23: list_P8527749157015355191n_assn] :
% 2.86/3.15 ( ( P @ W13 @ W23 )
% 2.86/3.15 => ( P @ W13 @ ( cons_P2971678138204555879n_assn @ E2 @ W23 ) ) )
% 2.86/3.15 => ( P @ W1 @ W2 ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_2pre_induct
% 2.86/3.15 thf(fact_4955_list__2pre__induct,axiom,
% 2.86/3.15 ! [P: list_nat > list_int > $o,W1: list_nat,W2: list_int] :
% 2.86/3.15 ( ( P @ nil_nat @ nil_int )
% 2.86/3.15 => ( ! [E2: nat,W12: list_nat,W22: list_int] :
% 2.86/3.15 ( ( P @ W12 @ W22 )
% 2.86/3.15 => ( P @ ( cons_nat @ E2 @ W12 ) @ W22 ) )
% 2.86/3.15 => ( ! [E2: int,W13: list_nat,W23: list_int] :
% 2.86/3.15 ( ( P @ W13 @ W23 )
% 2.86/3.15 => ( P @ W13 @ ( cons_int @ E2 @ W23 ) ) )
% 2.86/3.15 => ( P @ W1 @ W2 ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_2pre_induct
% 2.86/3.15 thf(fact_4956_list__2pre__induct,axiom,
% 2.86/3.15 ! [P: list_nat > list_nat > $o,W1: list_nat,W2: list_nat] :
% 2.86/3.15 ( ( P @ nil_nat @ nil_nat )
% 2.86/3.15 => ( ! [E2: nat,W12: list_nat,W22: list_nat] :
% 2.86/3.15 ( ( P @ W12 @ W22 )
% 2.86/3.15 => ( P @ ( cons_nat @ E2 @ W12 ) @ W22 ) )
% 2.86/3.15 => ( ! [E2: nat,W13: list_nat,W23: list_nat] :
% 2.86/3.15 ( ( P @ W13 @ W23 )
% 2.86/3.15 => ( P @ W13 @ ( cons_nat @ E2 @ W23 ) ) )
% 2.86/3.15 => ( P @ W1 @ W2 ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_2pre_induct
% 2.86/3.15 thf(fact_4957_list__2pre__induct,axiom,
% 2.86/3.15 ! [P: list_nat > list_P8527749157015355191n_assn > $o,W1: list_nat,W2: list_P8527749157015355191n_assn] :
% 2.86/3.15 ( ( P @ nil_nat @ nil_Pr5671120429643327159n_assn )
% 2.86/3.15 => ( ! [E2: nat,W12: list_nat,W22: list_P8527749157015355191n_assn] :
% 2.86/3.15 ( ( P @ W12 @ W22 )
% 2.86/3.15 => ( P @ ( cons_nat @ E2 @ W12 ) @ W22 ) )
% 2.86/3.15 => ( ! [E2: produc6575502325842934193n_assn,W13: list_nat,W23: list_P8527749157015355191n_assn] :
% 2.86/3.15 ( ( P @ W13 @ W23 )
% 2.86/3.15 => ( P @ W13 @ ( cons_P2971678138204555879n_assn @ E2 @ W23 ) ) )
% 2.86/3.15 => ( P @ W1 @ W2 ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_2pre_induct
% 2.86/3.15 thf(fact_4958_list__2pre__induct,axiom,
% 2.86/3.15 ! [P: list_P8527749157015355191n_assn > list_int > $o,W1: list_P8527749157015355191n_assn,W2: list_int] :
% 2.86/3.15 ( ( P @ nil_Pr5671120429643327159n_assn @ nil_int )
% 2.86/3.15 => ( ! [E2: produc6575502325842934193n_assn,W12: list_P8527749157015355191n_assn,W22: list_int] :
% 2.86/3.15 ( ( P @ W12 @ W22 )
% 2.86/3.15 => ( P @ ( cons_P2971678138204555879n_assn @ E2 @ W12 ) @ W22 ) )
% 2.86/3.15 => ( ! [E2: int,W13: list_P8527749157015355191n_assn,W23: list_int] :
% 2.86/3.15 ( ( P @ W13 @ W23 )
% 2.86/3.15 => ( P @ W13 @ ( cons_int @ E2 @ W23 ) ) )
% 2.86/3.15 => ( P @ W1 @ W2 ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_2pre_induct
% 2.86/3.15 thf(fact_4959_list__2pre__induct,axiom,
% 2.86/3.15 ! [P: list_P8527749157015355191n_assn > list_nat > $o,W1: list_P8527749157015355191n_assn,W2: list_nat] :
% 2.86/3.15 ( ( P @ nil_Pr5671120429643327159n_assn @ nil_nat )
% 2.86/3.15 => ( ! [E2: produc6575502325842934193n_assn,W12: list_P8527749157015355191n_assn,W22: list_nat] :
% 2.86/3.15 ( ( P @ W12 @ W22 )
% 2.86/3.15 => ( P @ ( cons_P2971678138204555879n_assn @ E2 @ W12 ) @ W22 ) )
% 2.86/3.15 => ( ! [E2: nat,W13: list_P8527749157015355191n_assn,W23: list_nat] :
% 2.86/3.15 ( ( P @ W13 @ W23 )
% 2.86/3.15 => ( P @ W13 @ ( cons_nat @ E2 @ W23 ) ) )
% 2.86/3.15 => ( P @ W1 @ W2 ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_2pre_induct
% 2.86/3.15 thf(fact_4960_list__2pre__induct,axiom,
% 2.86/3.15 ! [P: list_P8527749157015355191n_assn > list_P8527749157015355191n_assn > $o,W1: list_P8527749157015355191n_assn,W2: list_P8527749157015355191n_assn] :
% 2.86/3.15 ( ( P @ nil_Pr5671120429643327159n_assn @ nil_Pr5671120429643327159n_assn )
% 2.86/3.15 => ( ! [E2: produc6575502325842934193n_assn,W12: list_P8527749157015355191n_assn,W22: list_P8527749157015355191n_assn] :
% 2.86/3.15 ( ( P @ W12 @ W22 )
% 2.86/3.15 => ( P @ ( cons_P2971678138204555879n_assn @ E2 @ W12 ) @ W22 ) )
% 2.86/3.15 => ( ! [E2: produc6575502325842934193n_assn,W13: list_P8527749157015355191n_assn,W23: list_P8527749157015355191n_assn] :
% 2.86/3.15 ( ( P @ W13 @ W23 )
% 2.86/3.15 => ( P @ W13 @ ( cons_P2971678138204555879n_assn @ E2 @ W23 ) ) )
% 2.86/3.15 => ( P @ W1 @ W2 ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_2pre_induct
% 2.86/3.15 thf(fact_4961_list__induct__first2,axiom,
% 2.86/3.15 ! [P: list_int > $o,Xs: list_int] :
% 2.86/3.15 ( ( P @ nil_int )
% 2.86/3.15 => ( ! [X3: int] : ( P @ ( cons_int @ X3 @ nil_int ) )
% 2.86/3.15 => ( ! [X12: int,X23: int,Xs2: list_int] :
% 2.86/3.15 ( ( P @ Xs2 )
% 2.86/3.15 => ( P @ ( cons_int @ X12 @ ( cons_int @ X23 @ Xs2 ) ) ) )
% 2.86/3.15 => ( P @ Xs ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct_first2
% 2.86/3.15 thf(fact_4962_list__induct__first2,axiom,
% 2.86/3.15 ! [P: list_nat > $o,Xs: list_nat] :
% 2.86/3.15 ( ( P @ nil_nat )
% 2.86/3.15 => ( ! [X3: nat] : ( P @ ( cons_nat @ X3 @ nil_nat ) )
% 2.86/3.15 => ( ! [X12: nat,X23: nat,Xs2: list_nat] :
% 2.86/3.15 ( ( P @ Xs2 )
% 2.86/3.15 => ( P @ ( cons_nat @ X12 @ ( cons_nat @ X23 @ Xs2 ) ) ) )
% 2.86/3.15 => ( P @ Xs ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct_first2
% 2.86/3.15 thf(fact_4963_list__induct__first2,axiom,
% 2.86/3.15 ! [P: list_P8527749157015355191n_assn > $o,Xs: list_P8527749157015355191n_assn] :
% 2.86/3.15 ( ( P @ nil_Pr5671120429643327159n_assn )
% 2.86/3.15 => ( ! [X3: produc6575502325842934193n_assn] : ( P @ ( cons_P2971678138204555879n_assn @ X3 @ nil_Pr5671120429643327159n_assn ) )
% 2.86/3.15 => ( ! [X12: produc6575502325842934193n_assn,X23: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn] :
% 2.86/3.15 ( ( P @ Xs2 )
% 2.86/3.15 => ( P @ ( cons_P2971678138204555879n_assn @ X12 @ ( cons_P2971678138204555879n_assn @ X23 @ Xs2 ) ) ) )
% 2.86/3.15 => ( P @ Xs ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct_first2
% 2.86/3.15 thf(fact_4964_mergesort__by__rel__merge__induct,axiom,
% 2.86/3.15 ! [P: list_int > list_int > $o,R: int > int > $o,Xs: list_int,Ys: list_int] :
% 2.86/3.15 ( ! [Xs2: list_int] : ( P @ Xs2 @ nil_int )
% 2.86/3.15 => ( ! [X_1: list_int] : ( P @ nil_int @ X_1 )
% 2.86/3.15 => ( ! [X3: int,Xs2: list_int,Y2: int,Ys5: list_int] :
% 2.86/3.15 ( ( R @ X3 @ Y2 )
% 2.86/3.15 => ( ( P @ Xs2 @ ( cons_int @ Y2 @ Ys5 ) )
% 2.86/3.15 => ( P @ ( cons_int @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys5 ) ) ) )
% 2.86/3.15 => ( ! [X3: int,Xs2: list_int,Y2: int,Ys5: list_int] :
% 2.86/3.15 ( ~ ( R @ X3 @ Y2 )
% 2.86/3.15 => ( ( P @ ( cons_int @ X3 @ Xs2 ) @ Ys5 )
% 2.86/3.15 => ( P @ ( cons_int @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys5 ) ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % mergesort_by_rel_merge_induct
% 2.86/3.15 thf(fact_4965_mergesort__by__rel__merge__induct,axiom,
% 2.86/3.15 ! [P: list_nat > list_int > $o,R: nat > int > $o,Xs: list_nat,Ys: list_int] :
% 2.86/3.15 ( ! [Xs2: list_nat] : ( P @ Xs2 @ nil_int )
% 2.86/3.15 => ( ! [X_1: list_int] : ( P @ nil_nat @ X_1 )
% 2.86/3.15 => ( ! [X3: nat,Xs2: list_nat,Y2: int,Ys5: list_int] :
% 2.86/3.15 ( ( R @ X3 @ Y2 )
% 2.86/3.15 => ( ( P @ Xs2 @ ( cons_int @ Y2 @ Ys5 ) )
% 2.86/3.15 => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys5 ) ) ) )
% 2.86/3.15 => ( ! [X3: nat,Xs2: list_nat,Y2: int,Ys5: list_int] :
% 2.86/3.15 ( ~ ( R @ X3 @ Y2 )
% 2.86/3.15 => ( ( P @ ( cons_nat @ X3 @ Xs2 ) @ Ys5 )
% 2.86/3.15 => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys5 ) ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % mergesort_by_rel_merge_induct
% 2.86/3.15 thf(fact_4966_mergesort__by__rel__merge__induct,axiom,
% 2.86/3.15 ! [P: list_P8527749157015355191n_assn > list_int > $o,R: produc6575502325842934193n_assn > int > $o,Xs: list_P8527749157015355191n_assn,Ys: list_int] :
% 2.86/3.15 ( ! [Xs2: list_P8527749157015355191n_assn] : ( P @ Xs2 @ nil_int )
% 2.86/3.15 => ( ! [X_1: list_int] : ( P @ nil_Pr5671120429643327159n_assn @ X_1 )
% 2.86/3.15 => ( ! [X3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn,Y2: int,Ys5: list_int] :
% 2.86/3.15 ( ( R @ X3 @ Y2 )
% 2.86/3.15 => ( ( P @ Xs2 @ ( cons_int @ Y2 @ Ys5 ) )
% 2.86/3.15 => ( P @ ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys5 ) ) ) )
% 2.86/3.15 => ( ! [X3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn,Y2: int,Ys5: list_int] :
% 2.86/3.15 ( ~ ( R @ X3 @ Y2 )
% 2.86/3.15 => ( ( P @ ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) @ Ys5 )
% 2.86/3.15 => ( P @ ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys5 ) ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % mergesort_by_rel_merge_induct
% 2.86/3.15 thf(fact_4967_mergesort__by__rel__merge__induct,axiom,
% 2.86/3.15 ! [P: list_int > list_nat > $o,R: int > nat > $o,Xs: list_int,Ys: list_nat] :
% 2.86/3.15 ( ! [Xs2: list_int] : ( P @ Xs2 @ nil_nat )
% 2.86/3.15 => ( ! [X_1: list_nat] : ( P @ nil_int @ X_1 )
% 2.86/3.15 => ( ! [X3: int,Xs2: list_int,Y2: nat,Ys5: list_nat] :
% 2.86/3.15 ( ( R @ X3 @ Y2 )
% 2.86/3.15 => ( ( P @ Xs2 @ ( cons_nat @ Y2 @ Ys5 ) )
% 2.86/3.15 => ( P @ ( cons_int @ X3 @ Xs2 ) @ ( cons_nat @ Y2 @ Ys5 ) ) ) )
% 2.86/3.15 => ( ! [X3: int,Xs2: list_int,Y2: nat,Ys5: list_nat] :
% 2.86/3.15 ( ~ ( R @ X3 @ Y2 )
% 2.86/3.15 => ( ( P @ ( cons_int @ X3 @ Xs2 ) @ Ys5 )
% 2.86/3.15 => ( P @ ( cons_int @ X3 @ Xs2 ) @ ( cons_nat @ Y2 @ Ys5 ) ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % mergesort_by_rel_merge_induct
% 2.86/3.15 thf(fact_4968_mergesort__by__rel__merge__induct,axiom,
% 2.86/3.15 ! [P: list_nat > list_nat > $o,R: nat > nat > $o,Xs: list_nat,Ys: list_nat] :
% 2.86/3.15 ( ! [Xs2: list_nat] : ( P @ Xs2 @ nil_nat )
% 2.86/3.15 => ( ! [X_1: list_nat] : ( P @ nil_nat @ X_1 )
% 2.86/3.15 => ( ! [X3: nat,Xs2: list_nat,Y2: nat,Ys5: list_nat] :
% 2.86/3.15 ( ( R @ X3 @ Y2 )
% 2.86/3.15 => ( ( P @ Xs2 @ ( cons_nat @ Y2 @ Ys5 ) )
% 2.86/3.15 => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_nat @ Y2 @ Ys5 ) ) ) )
% 2.86/3.15 => ( ! [X3: nat,Xs2: list_nat,Y2: nat,Ys5: list_nat] :
% 2.86/3.15 ( ~ ( R @ X3 @ Y2 )
% 2.86/3.15 => ( ( P @ ( cons_nat @ X3 @ Xs2 ) @ Ys5 )
% 2.86/3.15 => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_nat @ Y2 @ Ys5 ) ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % mergesort_by_rel_merge_induct
% 2.86/3.15 thf(fact_4969_mergesort__by__rel__merge__induct,axiom,
% 2.86/3.15 ! [P: list_P8527749157015355191n_assn > list_nat > $o,R: produc6575502325842934193n_assn > nat > $o,Xs: list_P8527749157015355191n_assn,Ys: list_nat] :
% 2.86/3.15 ( ! [Xs2: list_P8527749157015355191n_assn] : ( P @ Xs2 @ nil_nat )
% 2.86/3.15 => ( ! [X_1: list_nat] : ( P @ nil_Pr5671120429643327159n_assn @ X_1 )
% 2.86/3.15 => ( ! [X3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn,Y2: nat,Ys5: list_nat] :
% 2.86/3.15 ( ( R @ X3 @ Y2 )
% 2.86/3.15 => ( ( P @ Xs2 @ ( cons_nat @ Y2 @ Ys5 ) )
% 2.86/3.15 => ( P @ ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) @ ( cons_nat @ Y2 @ Ys5 ) ) ) )
% 2.86/3.15 => ( ! [X3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn,Y2: nat,Ys5: list_nat] :
% 2.86/3.15 ( ~ ( R @ X3 @ Y2 )
% 2.86/3.15 => ( ( P @ ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) @ Ys5 )
% 2.86/3.15 => ( P @ ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) @ ( cons_nat @ Y2 @ Ys5 ) ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % mergesort_by_rel_merge_induct
% 2.86/3.15 thf(fact_4970_mergesort__by__rel__merge__induct,axiom,
% 2.86/3.15 ! [P: list_int > list_P8527749157015355191n_assn > $o,R: int > produc6575502325842934193n_assn > $o,Xs: list_int,Ys: list_P8527749157015355191n_assn] :
% 2.86/3.15 ( ! [Xs2: list_int] : ( P @ Xs2 @ nil_Pr5671120429643327159n_assn )
% 2.86/3.15 => ( ! [X_1: list_P8527749157015355191n_assn] : ( P @ nil_int @ X_1 )
% 2.86/3.15 => ( ! [X3: int,Xs2: list_int,Y2: produc6575502325842934193n_assn,Ys5: list_P8527749157015355191n_assn] :
% 2.86/3.15 ( ( R @ X3 @ Y2 )
% 2.86/3.15 => ( ( P @ Xs2 @ ( cons_P2971678138204555879n_assn @ Y2 @ Ys5 ) )
% 2.86/3.15 => ( P @ ( cons_int @ X3 @ Xs2 ) @ ( cons_P2971678138204555879n_assn @ Y2 @ Ys5 ) ) ) )
% 2.86/3.15 => ( ! [X3: int,Xs2: list_int,Y2: produc6575502325842934193n_assn,Ys5: list_P8527749157015355191n_assn] :
% 2.86/3.15 ( ~ ( R @ X3 @ Y2 )
% 2.86/3.15 => ( ( P @ ( cons_int @ X3 @ Xs2 ) @ Ys5 )
% 2.86/3.15 => ( P @ ( cons_int @ X3 @ Xs2 ) @ ( cons_P2971678138204555879n_assn @ Y2 @ Ys5 ) ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % mergesort_by_rel_merge_induct
% 2.86/3.15 thf(fact_4971_mergesort__by__rel__merge__induct,axiom,
% 2.86/3.15 ! [P: list_nat > list_P8527749157015355191n_assn > $o,R: nat > produc6575502325842934193n_assn > $o,Xs: list_nat,Ys: list_P8527749157015355191n_assn] :
% 2.86/3.15 ( ! [Xs2: list_nat] : ( P @ Xs2 @ nil_Pr5671120429643327159n_assn )
% 2.86/3.15 => ( ! [X_1: list_P8527749157015355191n_assn] : ( P @ nil_nat @ X_1 )
% 2.86/3.15 => ( ! [X3: nat,Xs2: list_nat,Y2: produc6575502325842934193n_assn,Ys5: list_P8527749157015355191n_assn] :
% 2.86/3.15 ( ( R @ X3 @ Y2 )
% 2.86/3.15 => ( ( P @ Xs2 @ ( cons_P2971678138204555879n_assn @ Y2 @ Ys5 ) )
% 2.86/3.15 => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_P2971678138204555879n_assn @ Y2 @ Ys5 ) ) ) )
% 2.86/3.15 => ( ! [X3: nat,Xs2: list_nat,Y2: produc6575502325842934193n_assn,Ys5: list_P8527749157015355191n_assn] :
% 2.86/3.15 ( ~ ( R @ X3 @ Y2 )
% 2.86/3.15 => ( ( P @ ( cons_nat @ X3 @ Xs2 ) @ Ys5 )
% 2.86/3.15 => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_P2971678138204555879n_assn @ Y2 @ Ys5 ) ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % mergesort_by_rel_merge_induct
% 2.86/3.15 thf(fact_4972_mergesort__by__rel__merge__induct,axiom,
% 2.86/3.15 ! [P: list_P8527749157015355191n_assn > list_P8527749157015355191n_assn > $o,R: produc6575502325842934193n_assn > produc6575502325842934193n_assn > $o,Xs: list_P8527749157015355191n_assn,Ys: list_P8527749157015355191n_assn] :
% 2.86/3.15 ( ! [Xs2: list_P8527749157015355191n_assn] : ( P @ Xs2 @ nil_Pr5671120429643327159n_assn )
% 2.86/3.15 => ( ! [X_1: list_P8527749157015355191n_assn] : ( P @ nil_Pr5671120429643327159n_assn @ X_1 )
% 2.86/3.15 => ( ! [X3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn,Y2: produc6575502325842934193n_assn,Ys5: list_P8527749157015355191n_assn] :
% 2.86/3.15 ( ( R @ X3 @ Y2 )
% 2.86/3.15 => ( ( P @ Xs2 @ ( cons_P2971678138204555879n_assn @ Y2 @ Ys5 ) )
% 2.86/3.15 => ( P @ ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) @ ( cons_P2971678138204555879n_assn @ Y2 @ Ys5 ) ) ) )
% 2.86/3.15 => ( ! [X3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn,Y2: produc6575502325842934193n_assn,Ys5: list_P8527749157015355191n_assn] :
% 2.86/3.15 ( ~ ( R @ X3 @ Y2 )
% 2.86/3.15 => ( ( P @ ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) @ Ys5 )
% 2.86/3.15 => ( P @ ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) @ ( cons_P2971678138204555879n_assn @ Y2 @ Ys5 ) ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % mergesort_by_rel_merge_induct
% 2.86/3.15 thf(fact_4973_list_Odistinct_I1_J,axiom,
% 2.86/3.15 ! [X21: int,X222: list_int] :
% 2.86/3.15 ( nil_int
% 2.86/3.15 != ( cons_int @ X21 @ X222 ) ) ).
% 2.86/3.15
% 2.86/3.15 % list.distinct(1)
% 2.86/3.15 thf(fact_4974_list_Odistinct_I1_J,axiom,
% 2.86/3.15 ! [X21: nat,X222: list_nat] :
% 2.86/3.15 ( nil_nat
% 2.86/3.15 != ( cons_nat @ X21 @ X222 ) ) ).
% 2.86/3.15
% 2.86/3.15 % list.distinct(1)
% 2.86/3.15 thf(fact_4975_list_Odistinct_I1_J,axiom,
% 2.86/3.15 ! [X21: produc6575502325842934193n_assn,X222: list_P8527749157015355191n_assn] :
% 2.86/3.15 ( nil_Pr5671120429643327159n_assn
% 2.86/3.15 != ( cons_P2971678138204555879n_assn @ X21 @ X222 ) ) ).
% 2.86/3.15
% 2.86/3.15 % list.distinct(1)
% 2.86/3.15 thf(fact_4976_list_OdiscI,axiom,
% 2.86/3.15 ! [List: list_int,X21: int,X222: list_int] :
% 2.86/3.15 ( ( List
% 2.86/3.15 = ( cons_int @ X21 @ X222 ) )
% 2.86/3.15 => ( List != nil_int ) ) ).
% 2.86/3.15
% 2.86/3.15 % list.discI
% 2.86/3.15 thf(fact_4977_list_OdiscI,axiom,
% 2.86/3.15 ! [List: list_nat,X21: nat,X222: list_nat] :
% 2.86/3.15 ( ( List
% 2.86/3.15 = ( cons_nat @ X21 @ X222 ) )
% 2.86/3.15 => ( List != nil_nat ) ) ).
% 2.86/3.15
% 2.86/3.15 % list.discI
% 2.86/3.15 thf(fact_4978_list_OdiscI,axiom,
% 2.86/3.15 ! [List: list_P8527749157015355191n_assn,X21: produc6575502325842934193n_assn,X222: list_P8527749157015355191n_assn] :
% 2.86/3.15 ( ( List
% 2.86/3.15 = ( cons_P2971678138204555879n_assn @ X21 @ X222 ) )
% 2.86/3.15 => ( List != nil_Pr5671120429643327159n_assn ) ) ).
% 2.86/3.15
% 2.86/3.15 % list.discI
% 2.86/3.15 thf(fact_4979_list_Oexhaust,axiom,
% 2.86/3.15 ! [Y: list_int] :
% 2.86/3.15 ( ( Y != nil_int )
% 2.86/3.15 => ~ ! [X212: int,X223: list_int] :
% 2.86/3.15 ( Y
% 2.86/3.15 != ( cons_int @ X212 @ X223 ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list.exhaust
% 2.86/3.15 thf(fact_4980_list_Oexhaust,axiom,
% 2.86/3.15 ! [Y: list_nat] :
% 2.86/3.15 ( ( Y != nil_nat )
% 2.86/3.15 => ~ ! [X212: nat,X223: list_nat] :
% 2.86/3.15 ( Y
% 2.86/3.15 != ( cons_nat @ X212 @ X223 ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list.exhaust
% 2.86/3.15 thf(fact_4981_list_Oexhaust,axiom,
% 2.86/3.15 ! [Y: list_P8527749157015355191n_assn] :
% 2.86/3.15 ( ( Y != nil_Pr5671120429643327159n_assn )
% 2.86/3.15 => ~ ! [X212: produc6575502325842934193n_assn,X223: list_P8527749157015355191n_assn] :
% 2.86/3.15 ( Y
% 2.86/3.15 != ( cons_P2971678138204555879n_assn @ X212 @ X223 ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list.exhaust
% 2.86/3.15 thf(fact_4982_min__list_Ocases,axiom,
% 2.86/3.15 ! [X: list_int] :
% 2.86/3.15 ( ! [X3: int,Xs2: list_int] :
% 2.86/3.15 ( X
% 2.86/3.15 != ( cons_int @ X3 @ Xs2 ) )
% 2.86/3.15 => ( X = nil_int ) ) ).
% 2.86/3.15
% 2.86/3.15 % min_list.cases
% 2.86/3.15 thf(fact_4983_min__list_Ocases,axiom,
% 2.86/3.15 ! [X: list_nat] :
% 2.86/3.15 ( ! [X3: nat,Xs2: list_nat] :
% 2.86/3.15 ( X
% 2.86/3.15 != ( cons_nat @ X3 @ Xs2 ) )
% 2.86/3.15 => ( X = nil_nat ) ) ).
% 2.86/3.15
% 2.86/3.15 % min_list.cases
% 2.86/3.15 thf(fact_4984_remdups__adj_Ocases,axiom,
% 2.86/3.15 ! [X: list_int] :
% 2.86/3.15 ( ( X != nil_int )
% 2.86/3.15 => ( ! [X3: int] :
% 2.86/3.15 ( X
% 2.86/3.15 != ( cons_int @ X3 @ nil_int ) )
% 2.86/3.15 => ~ ! [X3: int,Y2: int,Xs2: list_int] :
% 2.86/3.15 ( X
% 2.86/3.15 != ( cons_int @ X3 @ ( cons_int @ Y2 @ Xs2 ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % remdups_adj.cases
% 2.86/3.15 thf(fact_4985_remdups__adj_Ocases,axiom,
% 2.86/3.15 ! [X: list_nat] :
% 2.86/3.15 ( ( X != nil_nat )
% 2.86/3.15 => ( ! [X3: nat] :
% 2.86/3.15 ( X
% 2.86/3.15 != ( cons_nat @ X3 @ nil_nat ) )
% 2.86/3.15 => ~ ! [X3: nat,Y2: nat,Xs2: list_nat] :
% 2.86/3.15 ( X
% 2.86/3.15 != ( cons_nat @ X3 @ ( cons_nat @ Y2 @ Xs2 ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % remdups_adj.cases
% 2.86/3.15 thf(fact_4986_remdups__adj_Ocases,axiom,
% 2.86/3.15 ! [X: list_P8527749157015355191n_assn] :
% 2.86/3.15 ( ( X != nil_Pr5671120429643327159n_assn )
% 2.86/3.15 => ( ! [X3: produc6575502325842934193n_assn] :
% 2.86/3.15 ( X
% 2.86/3.15 != ( cons_P2971678138204555879n_assn @ X3 @ nil_Pr5671120429643327159n_assn ) )
% 2.86/3.15 => ~ ! [X3: produc6575502325842934193n_assn,Y2: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn] :
% 2.86/3.15 ( X
% 2.86/3.15 != ( cons_P2971678138204555879n_assn @ X3 @ ( cons_P2971678138204555879n_assn @ Y2 @ Xs2 ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % remdups_adj.cases
% 2.86/3.15 thf(fact_4987_neq__Nil__conv,axiom,
% 2.86/3.15 ! [Xs: list_int] :
% 2.86/3.15 ( ( Xs != nil_int )
% 2.86/3.15 = ( ? [Y5: int,Ys3: list_int] :
% 2.86/3.15 ( Xs
% 2.86/3.15 = ( cons_int @ Y5 @ Ys3 ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % neq_Nil_conv
% 2.86/3.15 thf(fact_4988_neq__Nil__conv,axiom,
% 2.86/3.15 ! [Xs: list_nat] :
% 2.86/3.15 ( ( Xs != nil_nat )
% 2.86/3.15 = ( ? [Y5: nat,Ys3: list_nat] :
% 2.86/3.15 ( Xs
% 2.86/3.15 = ( cons_nat @ Y5 @ Ys3 ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % neq_Nil_conv
% 2.86/3.15 thf(fact_4989_neq__Nil__conv,axiom,
% 2.86/3.15 ! [Xs: list_P8527749157015355191n_assn] :
% 2.86/3.15 ( ( Xs != nil_Pr5671120429643327159n_assn )
% 2.86/3.15 = ( ? [Y5: produc6575502325842934193n_assn,Ys3: list_P8527749157015355191n_assn] :
% 2.86/3.15 ( Xs
% 2.86/3.15 = ( cons_P2971678138204555879n_assn @ Y5 @ Ys3 ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % neq_Nil_conv
% 2.86/3.15 thf(fact_4990_list__induct2_H,axiom,
% 2.86/3.15 ! [P: list_int > list_int > $o,Xs: list_int,Ys: list_int] :
% 2.86/3.15 ( ( P @ nil_int @ nil_int )
% 2.86/3.15 => ( ! [X3: int,Xs2: list_int] : ( P @ ( cons_int @ X3 @ Xs2 ) @ nil_int )
% 2.86/3.15 => ( ! [Y2: int,Ys5: list_int] : ( P @ nil_int @ ( cons_int @ Y2 @ Ys5 ) )
% 2.86/3.15 => ( ! [X3: int,Xs2: list_int,Y2: int,Ys5: list_int] :
% 2.86/3.15 ( ( P @ Xs2 @ Ys5 )
% 2.86/3.15 => ( P @ ( cons_int @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys5 ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct2'
% 2.86/3.15 thf(fact_4991_list__induct2_H,axiom,
% 2.86/3.15 ! [P: list_int > list_nat > $o,Xs: list_int,Ys: list_nat] :
% 2.86/3.15 ( ( P @ nil_int @ nil_nat )
% 2.86/3.15 => ( ! [X3: int,Xs2: list_int] : ( P @ ( cons_int @ X3 @ Xs2 ) @ nil_nat )
% 2.86/3.15 => ( ! [Y2: nat,Ys5: list_nat] : ( P @ nil_int @ ( cons_nat @ Y2 @ Ys5 ) )
% 2.86/3.15 => ( ! [X3: int,Xs2: list_int,Y2: nat,Ys5: list_nat] :
% 2.86/3.15 ( ( P @ Xs2 @ Ys5 )
% 2.86/3.15 => ( P @ ( cons_int @ X3 @ Xs2 ) @ ( cons_nat @ Y2 @ Ys5 ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct2'
% 2.86/3.15 thf(fact_4992_list__induct2_H,axiom,
% 2.86/3.15 ! [P: list_int > list_P8527749157015355191n_assn > $o,Xs: list_int,Ys: list_P8527749157015355191n_assn] :
% 2.86/3.15 ( ( P @ nil_int @ nil_Pr5671120429643327159n_assn )
% 2.86/3.15 => ( ! [X3: int,Xs2: list_int] : ( P @ ( cons_int @ X3 @ Xs2 ) @ nil_Pr5671120429643327159n_assn )
% 2.86/3.15 => ( ! [Y2: produc6575502325842934193n_assn,Ys5: list_P8527749157015355191n_assn] : ( P @ nil_int @ ( cons_P2971678138204555879n_assn @ Y2 @ Ys5 ) )
% 2.86/3.15 => ( ! [X3: int,Xs2: list_int,Y2: produc6575502325842934193n_assn,Ys5: list_P8527749157015355191n_assn] :
% 2.86/3.15 ( ( P @ Xs2 @ Ys5 )
% 2.86/3.15 => ( P @ ( cons_int @ X3 @ Xs2 ) @ ( cons_P2971678138204555879n_assn @ Y2 @ Ys5 ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct2'
% 2.86/3.15 thf(fact_4993_list__induct2_H,axiom,
% 2.86/3.15 ! [P: list_nat > list_int > $o,Xs: list_nat,Ys: list_int] :
% 2.86/3.15 ( ( P @ nil_nat @ nil_int )
% 2.86/3.15 => ( ! [X3: nat,Xs2: list_nat] : ( P @ ( cons_nat @ X3 @ Xs2 ) @ nil_int )
% 2.86/3.15 => ( ! [Y2: int,Ys5: list_int] : ( P @ nil_nat @ ( cons_int @ Y2 @ Ys5 ) )
% 2.86/3.15 => ( ! [X3: nat,Xs2: list_nat,Y2: int,Ys5: list_int] :
% 2.86/3.15 ( ( P @ Xs2 @ Ys5 )
% 2.86/3.15 => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys5 ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct2'
% 2.86/3.15 thf(fact_4994_list__induct2_H,axiom,
% 2.86/3.15 ! [P: list_nat > list_nat > $o,Xs: list_nat,Ys: list_nat] :
% 2.86/3.15 ( ( P @ nil_nat @ nil_nat )
% 2.86/3.15 => ( ! [X3: nat,Xs2: list_nat] : ( P @ ( cons_nat @ X3 @ Xs2 ) @ nil_nat )
% 2.86/3.15 => ( ! [Y2: nat,Ys5: list_nat] : ( P @ nil_nat @ ( cons_nat @ Y2 @ Ys5 ) )
% 2.86/3.15 => ( ! [X3: nat,Xs2: list_nat,Y2: nat,Ys5: list_nat] :
% 2.86/3.15 ( ( P @ Xs2 @ Ys5 )
% 2.86/3.15 => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_nat @ Y2 @ Ys5 ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct2'
% 2.86/3.15 thf(fact_4995_list__induct2_H,axiom,
% 2.86/3.15 ! [P: list_nat > list_P8527749157015355191n_assn > $o,Xs: list_nat,Ys: list_P8527749157015355191n_assn] :
% 2.86/3.15 ( ( P @ nil_nat @ nil_Pr5671120429643327159n_assn )
% 2.86/3.15 => ( ! [X3: nat,Xs2: list_nat] : ( P @ ( cons_nat @ X3 @ Xs2 ) @ nil_Pr5671120429643327159n_assn )
% 2.86/3.15 => ( ! [Y2: produc6575502325842934193n_assn,Ys5: list_P8527749157015355191n_assn] : ( P @ nil_nat @ ( cons_P2971678138204555879n_assn @ Y2 @ Ys5 ) )
% 2.86/3.15 => ( ! [X3: nat,Xs2: list_nat,Y2: produc6575502325842934193n_assn,Ys5: list_P8527749157015355191n_assn] :
% 2.86/3.15 ( ( P @ Xs2 @ Ys5 )
% 2.86/3.15 => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_P2971678138204555879n_assn @ Y2 @ Ys5 ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct2'
% 2.86/3.15 thf(fact_4996_list__induct2_H,axiom,
% 2.86/3.15 ! [P: list_P8527749157015355191n_assn > list_int > $o,Xs: list_P8527749157015355191n_assn,Ys: list_int] :
% 2.86/3.15 ( ( P @ nil_Pr5671120429643327159n_assn @ nil_int )
% 2.86/3.15 => ( ! [X3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn] : ( P @ ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) @ nil_int )
% 2.86/3.15 => ( ! [Y2: int,Ys5: list_int] : ( P @ nil_Pr5671120429643327159n_assn @ ( cons_int @ Y2 @ Ys5 ) )
% 2.86/3.15 => ( ! [X3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn,Y2: int,Ys5: list_int] :
% 2.86/3.15 ( ( P @ Xs2 @ Ys5 )
% 2.86/3.15 => ( P @ ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys5 ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct2'
% 2.86/3.15 thf(fact_4997_list__induct2_H,axiom,
% 2.86/3.15 ! [P: list_P8527749157015355191n_assn > list_nat > $o,Xs: list_P8527749157015355191n_assn,Ys: list_nat] :
% 2.86/3.15 ( ( P @ nil_Pr5671120429643327159n_assn @ nil_nat )
% 2.86/3.15 => ( ! [X3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn] : ( P @ ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) @ nil_nat )
% 2.86/3.15 => ( ! [Y2: nat,Ys5: list_nat] : ( P @ nil_Pr5671120429643327159n_assn @ ( cons_nat @ Y2 @ Ys5 ) )
% 2.86/3.15 => ( ! [X3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn,Y2: nat,Ys5: list_nat] :
% 2.86/3.15 ( ( P @ Xs2 @ Ys5 )
% 2.86/3.15 => ( P @ ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) @ ( cons_nat @ Y2 @ Ys5 ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct2'
% 2.86/3.15 thf(fact_4998_list__induct2_H,axiom,
% 2.86/3.15 ! [P: list_P8527749157015355191n_assn > list_P8527749157015355191n_assn > $o,Xs: list_P8527749157015355191n_assn,Ys: list_P8527749157015355191n_assn] :
% 2.86/3.15 ( ( P @ nil_Pr5671120429643327159n_assn @ nil_Pr5671120429643327159n_assn )
% 2.86/3.15 => ( ! [X3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn] : ( P @ ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) @ nil_Pr5671120429643327159n_assn )
% 2.86/3.15 => ( ! [Y2: produc6575502325842934193n_assn,Ys5: list_P8527749157015355191n_assn] : ( P @ nil_Pr5671120429643327159n_assn @ ( cons_P2971678138204555879n_assn @ Y2 @ Ys5 ) )
% 2.86/3.15 => ( ! [X3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn,Y2: produc6575502325842934193n_assn,Ys5: list_P8527749157015355191n_assn] :
% 2.86/3.15 ( ( P @ Xs2 @ Ys5 )
% 2.86/3.15 => ( P @ ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) @ ( cons_P2971678138204555879n_assn @ Y2 @ Ys5 ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct2'
% 2.86/3.15 thf(fact_4999_list__nonempty__induct,axiom,
% 2.86/3.15 ! [Xs: list_int,P: list_int > $o] :
% 2.86/3.15 ( ( Xs != nil_int )
% 2.86/3.15 => ( ! [X3: int] : ( P @ ( cons_int @ X3 @ nil_int ) )
% 2.86/3.15 => ( ! [X3: int,Xs2: list_int] :
% 2.86/3.15 ( ( Xs2 != nil_int )
% 2.86/3.15 => ( ( P @ Xs2 )
% 2.86/3.15 => ( P @ ( cons_int @ X3 @ Xs2 ) ) ) )
% 2.86/3.15 => ( P @ Xs ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_nonempty_induct
% 2.86/3.15 thf(fact_5000_list__nonempty__induct,axiom,
% 2.86/3.15 ! [Xs: list_nat,P: list_nat > $o] :
% 2.86/3.15 ( ( Xs != nil_nat )
% 2.86/3.15 => ( ! [X3: nat] : ( P @ ( cons_nat @ X3 @ nil_nat ) )
% 2.86/3.15 => ( ! [X3: nat,Xs2: list_nat] :
% 2.86/3.15 ( ( Xs2 != nil_nat )
% 2.86/3.15 => ( ( P @ Xs2 )
% 2.86/3.15 => ( P @ ( cons_nat @ X3 @ Xs2 ) ) ) )
% 2.86/3.15 => ( P @ Xs ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_nonempty_induct
% 2.86/3.15 thf(fact_5001_list__nonempty__induct,axiom,
% 2.86/3.15 ! [Xs: list_P8527749157015355191n_assn,P: list_P8527749157015355191n_assn > $o] :
% 2.86/3.15 ( ( Xs != nil_Pr5671120429643327159n_assn )
% 2.86/3.15 => ( ! [X3: produc6575502325842934193n_assn] : ( P @ ( cons_P2971678138204555879n_assn @ X3 @ nil_Pr5671120429643327159n_assn ) )
% 2.86/3.15 => ( ! [X3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn] :
% 2.86/3.15 ( ( Xs2 != nil_Pr5671120429643327159n_assn )
% 2.86/3.15 => ( ( P @ Xs2 )
% 2.86/3.15 => ( P @ ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) ) ) )
% 2.86/3.15 => ( P @ Xs ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_nonempty_induct
% 2.86/3.15 thf(fact_5002_distinct_Osimps_I1_J,axiom,
% 2.86/3.15 distinct_int @ nil_int ).
% 2.86/3.15
% 2.86/3.15 % distinct.simps(1)
% 2.86/3.15 thf(fact_5003_distinct_Osimps_I1_J,axiom,
% 2.86/3.15 distinct_nat @ nil_nat ).
% 2.86/3.15
% 2.86/3.15 % distinct.simps(1)
% 2.86/3.15 thf(fact_5004_distinct_Osimps_I1_J,axiom,
% 2.86/3.15 distin4809818325527169450n_assn @ nil_Pr5671120429643327159n_assn ).
% 2.86/3.15
% 2.86/3.15 % distinct.simps(1)
% 2.86/3.15 thf(fact_5005_sorted__wrt_Osimps_I1_J,axiom,
% 2.86/3.15 ! [P: produc6575502325842934193n_assn > produc6575502325842934193n_assn > $o] : ( sorted3986126766855596574n_assn @ P @ nil_Pr5671120429643327159n_assn ) ).
% 2.86/3.15
% 2.86/3.15 % sorted_wrt.simps(1)
% 2.86/3.15 thf(fact_5006_sorted__wrt_Osimps_I1_J,axiom,
% 2.86/3.15 ! [P: nat > nat > $o] : ( sorted_wrt_nat @ P @ nil_nat ) ).
% 2.86/3.15
% 2.86/3.15 % sorted_wrt.simps(1)
% 2.86/3.15 thf(fact_5007_sorted__wrt_Osimps_I1_J,axiom,
% 2.86/3.15 ! [P: int > int > $o] : ( sorted_wrt_int @ P @ nil_int ) ).
% 2.86/3.15
% 2.86/3.15 % sorted_wrt.simps(1)
% 2.86/3.15 thf(fact_5008_rev_Osimps_I1_J,axiom,
% 2.86/3.15 ( ( rev_int @ nil_int )
% 2.86/3.15 = nil_int ) ).
% 2.86/3.15
% 2.86/3.15 % rev.simps(1)
% 2.86/3.15 thf(fact_5009_rev_Osimps_I1_J,axiom,
% 2.86/3.15 ( ( rev_nat @ nil_nat )
% 2.86/3.15 = nil_nat ) ).
% 2.86/3.15
% 2.86/3.15 % rev.simps(1)
% 2.86/3.15 thf(fact_5010_rev_Osimps_I1_J,axiom,
% 2.86/3.15 ( ( rev_Pr4855572775806611735n_assn @ nil_Pr5671120429643327159n_assn )
% 2.86/3.15 = nil_Pr5671120429643327159n_assn ) ).
% 2.86/3.15
% 2.86/3.15 % rev.simps(1)
% 2.86/3.15 thf(fact_5011_list__update_Osimps_I1_J,axiom,
% 2.86/3.15 ! [I: nat,V2: int] :
% 2.86/3.15 ( ( list_update_int @ nil_int @ I @ V2 )
% 2.86/3.15 = nil_int ) ).
% 2.86/3.15
% 2.86/3.15 % list_update.simps(1)
% 2.86/3.15 thf(fact_5012_list__update_Osimps_I1_J,axiom,
% 2.86/3.15 ! [I: nat,V2: nat] :
% 2.86/3.15 ( ( list_update_nat @ nil_nat @ I @ V2 )
% 2.86/3.15 = nil_nat ) ).
% 2.86/3.15
% 2.86/3.15 % list_update.simps(1)
% 2.86/3.15 thf(fact_5013_list__update_Osimps_I1_J,axiom,
% 2.86/3.15 ! [I: nat,V2: produc6575502325842934193n_assn] :
% 2.86/3.15 ( ( list_u4534839942911652127n_assn @ nil_Pr5671120429643327159n_assn @ I @ V2 )
% 2.86/3.15 = nil_Pr5671120429643327159n_assn ) ).
% 2.86/3.15
% 2.86/3.15 % list_update.simps(1)
% 2.86/3.15 thf(fact_5014_list__update_Osimps_I1_J,axiom,
% 2.86/3.15 ! [I: nat,V2: c] :
% 2.86/3.15 ( ( list_update_c @ nil_c @ I @ V2 )
% 2.86/3.15 = nil_c ) ).
% 2.86/3.15
% 2.86/3.15 % list_update.simps(1)
% 2.86/3.15 thf(fact_5015_list__update_Osimps_I1_J,axiom,
% 2.86/3.15 ! [I: nat,V2: d] :
% 2.86/3.15 ( ( list_update_d @ nil_d @ I @ V2 )
% 2.86/3.15 = nil_d ) ).
% 2.86/3.15
% 2.86/3.15 % list_update.simps(1)
% 2.86/3.15 thf(fact_5016_list__update__code_I1_J,axiom,
% 2.86/3.15 ! [I: nat,Y: int] :
% 2.86/3.15 ( ( list_update_int @ nil_int @ I @ Y )
% 2.86/3.15 = nil_int ) ).
% 2.86/3.15
% 2.86/3.15 % list_update_code(1)
% 2.86/3.15 thf(fact_5017_list__update__code_I1_J,axiom,
% 2.86/3.15 ! [I: nat,Y: nat] :
% 2.86/3.15 ( ( list_update_nat @ nil_nat @ I @ Y )
% 2.86/3.15 = nil_nat ) ).
% 2.86/3.15
% 2.86/3.15 % list_update_code(1)
% 2.86/3.15 thf(fact_5018_list__update__code_I1_J,axiom,
% 2.86/3.15 ! [I: nat,Y: produc6575502325842934193n_assn] :
% 2.86/3.15 ( ( list_u4534839942911652127n_assn @ nil_Pr5671120429643327159n_assn @ I @ Y )
% 2.86/3.15 = nil_Pr5671120429643327159n_assn ) ).
% 2.86/3.15
% 2.86/3.15 % list_update_code(1)
% 2.86/3.15 thf(fact_5019_list__update__code_I1_J,axiom,
% 2.86/3.15 ! [I: nat,Y: c] :
% 2.86/3.15 ( ( list_update_c @ nil_c @ I @ Y )
% 2.86/3.15 = nil_c ) ).
% 2.86/3.15
% 2.86/3.15 % list_update_code(1)
% 2.86/3.15 thf(fact_5020_list__update__code_I1_J,axiom,
% 2.86/3.15 ! [I: nat,Y: d] :
% 2.86/3.15 ( ( list_update_d @ nil_d @ I @ Y )
% 2.86/3.15 = nil_d ) ).
% 2.86/3.15
% 2.86/3.15 % list_update_code(1)
% 2.86/3.15 thf(fact_5021_butlast_Osimps_I1_J,axiom,
% 2.86/3.15 ( ( butlast_int @ nil_int )
% 2.86/3.15 = nil_int ) ).
% 2.86/3.15
% 2.86/3.15 % butlast.simps(1)
% 2.86/3.15 thf(fact_5022_butlast_Osimps_I1_J,axiom,
% 2.86/3.15 ( ( butlast_nat @ nil_nat )
% 2.86/3.15 = nil_nat ) ).
% 2.86/3.15
% 2.86/3.15 % butlast.simps(1)
% 2.86/3.15 thf(fact_5023_butlast_Osimps_I1_J,axiom,
% 2.86/3.15 ( ( butlas3012047794866324995n_assn @ nil_Pr5671120429643327159n_assn )
% 2.86/3.15 = nil_Pr5671120429643327159n_assn ) ).
% 2.86/3.15
% 2.86/3.15 % butlast.simps(1)
% 2.86/3.15 thf(fact_5024_remove1_Osimps_I1_J,axiom,
% 2.86/3.15 ! [X: int] :
% 2.86/3.15 ( ( remove1_int @ X @ nil_int )
% 2.86/3.15 = nil_int ) ).
% 2.86/3.15
% 2.86/3.15 % remove1.simps(1)
% 2.86/3.15 thf(fact_5025_remove1_Osimps_I1_J,axiom,
% 2.86/3.15 ! [X: nat] :
% 2.86/3.15 ( ( remove1_nat @ X @ nil_nat )
% 2.86/3.15 = nil_nat ) ).
% 2.86/3.15
% 2.86/3.15 % remove1.simps(1)
% 2.86/3.15 thf(fact_5026_remove1_Osimps_I1_J,axiom,
% 2.86/3.15 ! [X: produc6575502325842934193n_assn] :
% 2.86/3.15 ( ( remove1670527618125605709n_assn @ X @ nil_Pr5671120429643327159n_assn )
% 2.86/3.15 = nil_Pr5671120429643327159n_assn ) ).
% 2.86/3.15
% 2.86/3.15 % remove1.simps(1)
% 2.86/3.15 thf(fact_5027_removeAll_Osimps_I1_J,axiom,
% 2.86/3.15 ! [X: int] :
% 2.86/3.15 ( ( removeAll_int @ X @ nil_int )
% 2.86/3.15 = nil_int ) ).
% 2.86/3.15
% 2.86/3.15 % removeAll.simps(1)
% 2.86/3.15 thf(fact_5028_removeAll_Osimps_I1_J,axiom,
% 2.86/3.15 ! [X: nat] :
% 2.86/3.15 ( ( removeAll_nat @ X @ nil_nat )
% 2.86/3.15 = nil_nat ) ).
% 2.86/3.15
% 2.86/3.15 % removeAll.simps(1)
% 2.86/3.15 thf(fact_5029_removeAll_Osimps_I1_J,axiom,
% 2.86/3.15 ! [X: produc6575502325842934193n_assn] :
% 2.86/3.15 ( ( remove1763081955827946941n_assn @ X @ nil_Pr5671120429643327159n_assn )
% 2.86/3.15 = nil_Pr5671120429643327159n_assn ) ).
% 2.86/3.15
% 2.86/3.15 % removeAll.simps(1)
% 2.86/3.15 thf(fact_5030_merge_Osimps_I1_J,axiom,
% 2.86/3.15 ! [L23: list_int] :
% 2.86/3.15 ( ( merge_int @ nil_int @ L23 )
% 2.86/3.15 = L23 ) ).
% 2.86/3.15
% 2.86/3.15 % merge.simps(1)
% 2.86/3.15 thf(fact_5031_merge_Osimps_I1_J,axiom,
% 2.86/3.15 ! [L23: list_nat] :
% 2.86/3.15 ( ( merge_nat @ nil_nat @ L23 )
% 2.86/3.15 = L23 ) ).
% 2.86/3.15
% 2.86/3.15 % merge.simps(1)
% 2.86/3.15 thf(fact_5032_rotate1_Osimps_I1_J,axiom,
% 2.86/3.15 ( ( rotate1_int @ nil_int )
% 2.86/3.15 = nil_int ) ).
% 2.86/3.15
% 2.86/3.15 % rotate1.simps(1)
% 2.86/3.15 thf(fact_5033_rotate1_Osimps_I1_J,axiom,
% 2.86/3.15 ( ( rotate1_nat @ nil_nat )
% 2.86/3.15 = nil_nat ) ).
% 2.86/3.15
% 2.86/3.15 % rotate1.simps(1)
% 2.86/3.15 thf(fact_5034_rotate1_Osimps_I1_J,axiom,
% 2.86/3.15 ( ( rotate328796349445179396n_assn @ nil_Pr5671120429643327159n_assn )
% 2.86/3.15 = nil_Pr5671120429643327159n_assn ) ).
% 2.86/3.15
% 2.86/3.15 % rotate1.simps(1)
% 2.86/3.15 thf(fact_5035_zipf_Osimps_I1_J,axiom,
% 2.86/3.15 ! [F4: int > int > int] :
% 2.86/3.15 ( ( zipf_int_int_int @ F4 @ nil_int @ nil_int )
% 2.86/3.15 = nil_int ) ).
% 2.86/3.15
% 2.86/3.15 % zipf.simps(1)
% 2.86/3.15 thf(fact_5036_zipf_Osimps_I1_J,axiom,
% 2.86/3.15 ! [F4: int > int > nat] :
% 2.86/3.15 ( ( zipf_int_int_nat @ F4 @ nil_int @ nil_int )
% 2.86/3.15 = nil_nat ) ).
% 2.86/3.15
% 2.86/3.15 % zipf.simps(1)
% 2.86/3.15 thf(fact_5037_zipf_Osimps_I1_J,axiom,
% 2.86/3.15 ! [F4: int > nat > int] :
% 2.86/3.15 ( ( zipf_int_nat_int @ F4 @ nil_int @ nil_nat )
% 2.86/3.15 = nil_int ) ).
% 2.86/3.15
% 2.86/3.15 % zipf.simps(1)
% 2.86/3.15 thf(fact_5038_zipf_Osimps_I1_J,axiom,
% 2.86/3.15 ! [F4: int > nat > nat] :
% 2.86/3.15 ( ( zipf_int_nat_nat @ F4 @ nil_int @ nil_nat )
% 2.86/3.15 = nil_nat ) ).
% 2.86/3.15
% 2.86/3.15 % zipf.simps(1)
% 2.86/3.15 thf(fact_5039_zipf_Osimps_I1_J,axiom,
% 2.86/3.15 ! [F4: nat > int > int] :
% 2.86/3.15 ( ( zipf_nat_int_int @ F4 @ nil_nat @ nil_int )
% 2.86/3.15 = nil_int ) ).
% 2.86/3.15
% 2.86/3.15 % zipf.simps(1)
% 2.86/3.15 thf(fact_5040_zipf_Osimps_I1_J,axiom,
% 2.86/3.15 ! [F4: nat > int > nat] :
% 2.86/3.15 ( ( zipf_nat_int_nat @ F4 @ nil_nat @ nil_int )
% 2.86/3.15 = nil_nat ) ).
% 2.86/3.15
% 2.86/3.15 % zipf.simps(1)
% 2.86/3.15 thf(fact_5041_zipf_Osimps_I1_J,axiom,
% 2.86/3.15 ! [F4: nat > nat > int] :
% 2.86/3.15 ( ( zipf_nat_nat_int @ F4 @ nil_nat @ nil_nat )
% 2.86/3.15 = nil_int ) ).
% 2.86/3.15
% 2.86/3.15 % zipf.simps(1)
% 2.86/3.15 thf(fact_5042_zipf_Osimps_I1_J,axiom,
% 2.86/3.15 ! [F4: nat > nat > nat] :
% 2.86/3.15 ( ( zipf_nat_nat_nat @ F4 @ nil_nat @ nil_nat )
% 2.86/3.15 = nil_nat ) ).
% 2.86/3.15
% 2.86/3.15 % zipf.simps(1)
% 2.86/3.15 thf(fact_5043_zipf_Osimps_I1_J,axiom,
% 2.86/3.15 ! [F4: int > int > produc6575502325842934193n_assn] :
% 2.86/3.15 ( ( zipf_i7756021159461276697n_assn @ F4 @ nil_int @ nil_int )
% 2.86/3.15 = nil_Pr5671120429643327159n_assn ) ).
% 2.86/3.15
% 2.86/3.15 % zipf.simps(1)
% 2.86/3.15 thf(fact_5044_zipf_Osimps_I1_J,axiom,
% 2.86/3.15 ! [F4: int > nat > produc6575502325842934193n_assn] :
% 2.86/3.15 ( ( zipf_i5995984495708165493n_assn @ F4 @ nil_int @ nil_nat )
% 2.86/3.15 = nil_Pr5671120429643327159n_assn ) ).
% 2.86/3.15
% 2.86/3.15 % zipf.simps(1)
% 2.86/3.15 thf(fact_5045_null__rec_I2_J,axiom,
% 2.86/3.15 null_int @ nil_int ).
% 2.86/3.15
% 2.86/3.15 % null_rec(2)
% 2.86/3.15 thf(fact_5046_null__rec_I2_J,axiom,
% 2.86/3.15 null_nat @ nil_nat ).
% 2.86/3.15
% 2.86/3.15 % null_rec(2)
% 2.86/3.15 thf(fact_5047_null__rec_I2_J,axiom,
% 2.86/3.15 null_P7596217980778516671n_assn @ nil_Pr5671120429643327159n_assn ).
% 2.86/3.15
% 2.86/3.15 % null_rec(2)
% 2.86/3.15 thf(fact_5048_eq__Nil__null,axiom,
% 2.86/3.15 ! [Xs: list_int] :
% 2.86/3.15 ( ( Xs = nil_int )
% 2.86/3.15 = ( null_int @ Xs ) ) ).
% 2.86/3.15
% 2.86/3.15 % eq_Nil_null
% 2.86/3.15 thf(fact_5049_eq__Nil__null,axiom,
% 2.86/3.15 ! [Xs: list_nat] :
% 2.86/3.15 ( ( Xs = nil_nat )
% 2.86/3.15 = ( null_nat @ Xs ) ) ).
% 2.86/3.15
% 2.86/3.15 % eq_Nil_null
% 2.86/3.15 thf(fact_5050_eq__Nil__null,axiom,
% 2.86/3.15 ! [Xs: list_P8527749157015355191n_assn] :
% 2.86/3.15 ( ( Xs = nil_Pr5671120429643327159n_assn )
% 2.86/3.15 = ( null_P7596217980778516671n_assn @ Xs ) ) ).
% 2.86/3.15
% 2.86/3.15 % eq_Nil_null
% 2.86/3.15 thf(fact_5051_zero__less__power,axiom,
% 2.86/3.15 ! [A2: rat,N: nat] :
% 2.86/3.15 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 2.86/3.15 => ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A2 @ N ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % zero_less_power
% 2.86/3.15 thf(fact_5052_zero__less__power,axiom,
% 2.86/3.15 ! [A2: code_integer,N: nat] :
% 2.86/3.15 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 )
% 2.86/3.15 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A2 @ N ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % zero_less_power
% 2.86/3.15 thf(fact_5053_zero__less__power,axiom,
% 2.86/3.15 ! [A2: nat,N: nat] :
% 2.86/3.15 ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 2.86/3.15 => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A2 @ N ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % zero_less_power
% 2.86/3.15 thf(fact_5054_zero__less__power,axiom,
% 2.86/3.15 ! [A2: int,N: nat] :
% 2.86/3.15 ( ( ord_less_int @ zero_zero_int @ A2 )
% 2.86/3.15 => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A2 @ N ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % zero_less_power
% 2.86/3.15 thf(fact_5055_left__right__inverse__power,axiom,
% 2.86/3.15 ! [X: code_integer,Y: code_integer,N: nat] :
% 2.86/3.15 ( ( ( times_3573771949741848930nteger @ X @ Y )
% 2.86/3.15 = one_one_Code_integer )
% 2.86/3.15 => ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ X @ N ) @ ( power_8256067586552552935nteger @ Y @ N ) )
% 2.86/3.15 = one_one_Code_integer ) ) ).
% 2.86/3.15
% 2.86/3.15 % left_right_inverse_power
% 2.86/3.15 thf(fact_5056_left__right__inverse__power,axiom,
% 2.86/3.15 ! [X: assn,Y: assn,N: nat] :
% 2.86/3.15 ( ( ( times_times_assn @ X @ Y )
% 2.86/3.15 = one_one_assn )
% 2.86/3.15 => ( ( times_times_assn @ ( power_power_assn @ X @ N ) @ ( power_power_assn @ Y @ N ) )
% 2.86/3.15 = one_one_assn ) ) ).
% 2.86/3.15
% 2.86/3.15 % left_right_inverse_power
% 2.86/3.15 thf(fact_5057_left__right__inverse__power,axiom,
% 2.86/3.15 ! [X: rat,Y: rat,N: nat] :
% 2.86/3.15 ( ( ( times_times_rat @ X @ Y )
% 2.86/3.15 = one_one_rat )
% 2.86/3.15 => ( ( times_times_rat @ ( power_power_rat @ X @ N ) @ ( power_power_rat @ Y @ N ) )
% 2.86/3.15 = one_one_rat ) ) ).
% 2.86/3.15
% 2.86/3.15 % left_right_inverse_power
% 2.86/3.15 thf(fact_5058_left__right__inverse__power,axiom,
% 2.86/3.15 ! [X: nat,Y: nat,N: nat] :
% 2.86/3.15 ( ( ( times_times_nat @ X @ Y )
% 2.86/3.15 = one_one_nat )
% 2.86/3.15 => ( ( times_times_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y @ N ) )
% 2.86/3.15 = one_one_nat ) ) ).
% 2.86/3.15
% 2.86/3.15 % left_right_inverse_power
% 2.86/3.15 thf(fact_5059_left__right__inverse__power,axiom,
% 2.86/3.15 ! [X: int,Y: int,N: nat] :
% 2.86/3.15 ( ( ( times_times_int @ X @ Y )
% 2.86/3.15 = one_one_int )
% 2.86/3.15 => ( ( times_times_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y @ N ) )
% 2.86/3.15 = one_one_int ) ) ).
% 2.86/3.15
% 2.86/3.15 % left_right_inverse_power
% 2.86/3.15 thf(fact_5060_power__Suc,axiom,
% 2.86/3.15 ! [A2: code_integer,N: nat] :
% 2.86/3.15 ( ( power_8256067586552552935nteger @ A2 @ ( suc @ N ) )
% 2.86/3.15 = ( times_3573771949741848930nteger @ A2 @ ( power_8256067586552552935nteger @ A2 @ N ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % power_Suc
% 2.86/3.15 thf(fact_5061_power__Suc,axiom,
% 2.86/3.15 ! [A2: assn,N: nat] :
% 2.86/3.15 ( ( power_power_assn @ A2 @ ( suc @ N ) )
% 2.86/3.15 = ( times_times_assn @ A2 @ ( power_power_assn @ A2 @ N ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % power_Suc
% 2.86/3.15 thf(fact_5062_power__Suc,axiom,
% 2.86/3.15 ! [A2: rat,N: nat] :
% 2.86/3.15 ( ( power_power_rat @ A2 @ ( suc @ N ) )
% 2.86/3.15 = ( times_times_rat @ A2 @ ( power_power_rat @ A2 @ N ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % power_Suc
% 2.86/3.15 thf(fact_5063_power__Suc,axiom,
% 2.86/3.15 ! [A2: nat,N: nat] :
% 2.86/3.15 ( ( power_power_nat @ A2 @ ( suc @ N ) )
% 2.86/3.15 = ( times_times_nat @ A2 @ ( power_power_nat @ A2 @ N ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % power_Suc
% 2.86/3.15 thf(fact_5064_power__Suc,axiom,
% 2.86/3.15 ! [A2: int,N: nat] :
% 2.86/3.15 ( ( power_power_int @ A2 @ ( suc @ N ) )
% 2.86/3.15 = ( times_times_int @ A2 @ ( power_power_int @ A2 @ N ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % power_Suc
% 2.86/3.15 thf(fact_5065_power__Suc2,axiom,
% 2.86/3.15 ! [A2: code_integer,N: nat] :
% 2.86/3.15 ( ( power_8256067586552552935nteger @ A2 @ ( suc @ N ) )
% 2.86/3.15 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A2 @ N ) @ A2 ) ) ).
% 2.86/3.15
% 2.86/3.15 % power_Suc2
% 2.86/3.15 thf(fact_5066_power__Suc2,axiom,
% 2.86/3.15 ! [A2: assn,N: nat] :
% 2.86/3.15 ( ( power_power_assn @ A2 @ ( suc @ N ) )
% 2.86/3.15 = ( times_times_assn @ ( power_power_assn @ A2 @ N ) @ A2 ) ) ).
% 2.86/3.15
% 2.86/3.15 % power_Suc2
% 2.86/3.15 thf(fact_5067_power__Suc2,axiom,
% 2.86/3.15 ! [A2: rat,N: nat] :
% 2.86/3.15 ( ( power_power_rat @ A2 @ ( suc @ N ) )
% 2.86/3.15 = ( times_times_rat @ ( power_power_rat @ A2 @ N ) @ A2 ) ) ).
% 2.86/3.15
% 2.86/3.15 % power_Suc2
% 2.86/3.15 thf(fact_5068_power__Suc2,axiom,
% 2.86/3.15 ! [A2: nat,N: nat] :
% 2.86/3.15 ( ( power_power_nat @ A2 @ ( suc @ N ) )
% 2.86/3.15 = ( times_times_nat @ ( power_power_nat @ A2 @ N ) @ A2 ) ) ).
% 2.86/3.15
% 2.86/3.15 % power_Suc2
% 2.86/3.15 thf(fact_5069_power__Suc2,axiom,
% 2.86/3.15 ! [A2: int,N: nat] :
% 2.86/3.15 ( ( power_power_int @ A2 @ ( suc @ N ) )
% 2.86/3.15 = ( times_times_int @ ( power_power_int @ A2 @ N ) @ A2 ) ) ).
% 2.86/3.15
% 2.86/3.15 % power_Suc2
% 2.86/3.15 thf(fact_5070_power__add,axiom,
% 2.86/3.15 ! [A2: code_integer,M2: nat,N: nat] :
% 2.86/3.15 ( ( power_8256067586552552935nteger @ A2 @ ( plus_plus_nat @ M2 @ N ) )
% 2.86/3.15 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A2 @ M2 ) @ ( power_8256067586552552935nteger @ A2 @ N ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % power_add
% 2.86/3.15 thf(fact_5071_power__add,axiom,
% 2.86/3.15 ! [A2: assn,M2: nat,N: nat] :
% 2.86/3.15 ( ( power_power_assn @ A2 @ ( plus_plus_nat @ M2 @ N ) )
% 2.86/3.15 = ( times_times_assn @ ( power_power_assn @ A2 @ M2 ) @ ( power_power_assn @ A2 @ N ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % power_add
% 2.86/3.15 thf(fact_5072_power__add,axiom,
% 2.86/3.15 ! [A2: rat,M2: nat,N: nat] :
% 2.86/3.15 ( ( power_power_rat @ A2 @ ( plus_plus_nat @ M2 @ N ) )
% 2.86/3.15 = ( times_times_rat @ ( power_power_rat @ A2 @ M2 ) @ ( power_power_rat @ A2 @ N ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % power_add
% 2.86/3.15 thf(fact_5073_power__add,axiom,
% 2.86/3.15 ! [A2: nat,M2: nat,N: nat] :
% 2.86/3.15 ( ( power_power_nat @ A2 @ ( plus_plus_nat @ M2 @ N ) )
% 2.86/3.15 = ( times_times_nat @ ( power_power_nat @ A2 @ M2 ) @ ( power_power_nat @ A2 @ N ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % power_add
% 2.86/3.15 thf(fact_5074_power__add,axiom,
% 2.86/3.15 ! [A2: int,M2: nat,N: nat] :
% 2.86/3.15 ( ( power_power_int @ A2 @ ( plus_plus_nat @ M2 @ N ) )
% 2.86/3.15 = ( times_times_int @ ( power_power_int @ A2 @ M2 ) @ ( power_power_int @ A2 @ N ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % power_add
% 2.86/3.15 thf(fact_5075_nat__power__less__imp__less,axiom,
% 2.86/3.15 ! [I: nat,M2: nat,N: nat] :
% 2.86/3.15 ( ( ord_less_nat @ zero_zero_nat @ I )
% 2.86/3.15 => ( ( ord_less_nat @ ( power_power_nat @ I @ M2 ) @ ( power_power_nat @ I @ N ) )
% 2.86/3.15 => ( ord_less_nat @ M2 @ N ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % nat_power_less_imp_less
% 2.86/3.15 thf(fact_5076_list__induct2,axiom,
% 2.86/3.15 ! [Xs: list_c,Ys: list_c,P: list_c > list_c > $o] :
% 2.86/3.15 ( ( ( size_size_list_c @ Xs )
% 2.86/3.15 = ( size_size_list_c @ Ys ) )
% 2.86/3.15 => ( ( P @ nil_c @ nil_c )
% 2.86/3.15 => ( ! [X3: c,Xs2: list_c,Y2: c,Ys5: list_c] :
% 2.86/3.15 ( ( ( size_size_list_c @ Xs2 )
% 2.86/3.15 = ( size_size_list_c @ Ys5 ) )
% 2.86/3.15 => ( ( P @ Xs2 @ Ys5 )
% 2.86/3.15 => ( P @ ( cons_c @ X3 @ Xs2 ) @ ( cons_c @ Y2 @ Ys5 ) ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct2
% 2.86/3.15 thf(fact_5077_list__induct2,axiom,
% 2.86/3.15 ! [Xs: list_c,Ys: list_d,P: list_c > list_d > $o] :
% 2.86/3.15 ( ( ( size_size_list_c @ Xs )
% 2.86/3.15 = ( size_size_list_d @ Ys ) )
% 2.86/3.15 => ( ( P @ nil_c @ nil_d )
% 2.86/3.15 => ( ! [X3: c,Xs2: list_c,Y2: d,Ys5: list_d] :
% 2.86/3.15 ( ( ( size_size_list_c @ Xs2 )
% 2.86/3.15 = ( size_size_list_d @ Ys5 ) )
% 2.86/3.15 => ( ( P @ Xs2 @ Ys5 )
% 2.86/3.15 => ( P @ ( cons_c @ X3 @ Xs2 ) @ ( cons_d @ Y2 @ Ys5 ) ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct2
% 2.86/3.15 thf(fact_5078_list__induct2,axiom,
% 2.86/3.15 ! [Xs: list_c,Ys: list_nat,P: list_c > list_nat > $o] :
% 2.86/3.15 ( ( ( size_size_list_c @ Xs )
% 2.86/3.15 = ( size_size_list_nat @ Ys ) )
% 2.86/3.15 => ( ( P @ nil_c @ nil_nat )
% 2.86/3.15 => ( ! [X3: c,Xs2: list_c,Y2: nat,Ys5: list_nat] :
% 2.86/3.15 ( ( ( size_size_list_c @ Xs2 )
% 2.86/3.15 = ( size_size_list_nat @ Ys5 ) )
% 2.86/3.15 => ( ( P @ Xs2 @ Ys5 )
% 2.86/3.15 => ( P @ ( cons_c @ X3 @ Xs2 ) @ ( cons_nat @ Y2 @ Ys5 ) ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct2
% 2.86/3.15 thf(fact_5079_list__induct2,axiom,
% 2.86/3.15 ! [Xs: list_c,Ys: list_int,P: list_c > list_int > $o] :
% 2.86/3.15 ( ( ( size_size_list_c @ Xs )
% 2.86/3.15 = ( size_size_list_int @ Ys ) )
% 2.86/3.15 => ( ( P @ nil_c @ nil_int )
% 2.86/3.15 => ( ! [X3: c,Xs2: list_c,Y2: int,Ys5: list_int] :
% 2.86/3.15 ( ( ( size_size_list_c @ Xs2 )
% 2.86/3.15 = ( size_size_list_int @ Ys5 ) )
% 2.86/3.15 => ( ( P @ Xs2 @ Ys5 )
% 2.86/3.15 => ( P @ ( cons_c @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys5 ) ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct2
% 2.86/3.15 thf(fact_5080_list__induct2,axiom,
% 2.86/3.15 ! [Xs: list_d,Ys: list_c,P: list_d > list_c > $o] :
% 2.86/3.15 ( ( ( size_size_list_d @ Xs )
% 2.86/3.15 = ( size_size_list_c @ Ys ) )
% 2.86/3.15 => ( ( P @ nil_d @ nil_c )
% 2.86/3.15 => ( ! [X3: d,Xs2: list_d,Y2: c,Ys5: list_c] :
% 2.86/3.15 ( ( ( size_size_list_d @ Xs2 )
% 2.86/3.15 = ( size_size_list_c @ Ys5 ) )
% 2.86/3.15 => ( ( P @ Xs2 @ Ys5 )
% 2.86/3.15 => ( P @ ( cons_d @ X3 @ Xs2 ) @ ( cons_c @ Y2 @ Ys5 ) ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct2
% 2.86/3.15 thf(fact_5081_list__induct2,axiom,
% 2.86/3.15 ! [Xs: list_d,Ys: list_d,P: list_d > list_d > $o] :
% 2.86/3.15 ( ( ( size_size_list_d @ Xs )
% 2.86/3.15 = ( size_size_list_d @ Ys ) )
% 2.86/3.15 => ( ( P @ nil_d @ nil_d )
% 2.86/3.15 => ( ! [X3: d,Xs2: list_d,Y2: d,Ys5: list_d] :
% 2.86/3.15 ( ( ( size_size_list_d @ Xs2 )
% 2.86/3.15 = ( size_size_list_d @ Ys5 ) )
% 2.86/3.15 => ( ( P @ Xs2 @ Ys5 )
% 2.86/3.15 => ( P @ ( cons_d @ X3 @ Xs2 ) @ ( cons_d @ Y2 @ Ys5 ) ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct2
% 2.86/3.15 thf(fact_5082_list__induct2,axiom,
% 2.86/3.15 ! [Xs: list_d,Ys: list_nat,P: list_d > list_nat > $o] :
% 2.86/3.15 ( ( ( size_size_list_d @ Xs )
% 2.86/3.15 = ( size_size_list_nat @ Ys ) )
% 2.86/3.15 => ( ( P @ nil_d @ nil_nat )
% 2.86/3.15 => ( ! [X3: d,Xs2: list_d,Y2: nat,Ys5: list_nat] :
% 2.86/3.15 ( ( ( size_size_list_d @ Xs2 )
% 2.86/3.15 = ( size_size_list_nat @ Ys5 ) )
% 2.86/3.15 => ( ( P @ Xs2 @ Ys5 )
% 2.86/3.15 => ( P @ ( cons_d @ X3 @ Xs2 ) @ ( cons_nat @ Y2 @ Ys5 ) ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct2
% 2.86/3.15 thf(fact_5083_list__induct2,axiom,
% 2.86/3.15 ! [Xs: list_d,Ys: list_int,P: list_d > list_int > $o] :
% 2.86/3.15 ( ( ( size_size_list_d @ Xs )
% 2.86/3.15 = ( size_size_list_int @ Ys ) )
% 2.86/3.15 => ( ( P @ nil_d @ nil_int )
% 2.86/3.15 => ( ! [X3: d,Xs2: list_d,Y2: int,Ys5: list_int] :
% 2.86/3.15 ( ( ( size_size_list_d @ Xs2 )
% 2.86/3.15 = ( size_size_list_int @ Ys5 ) )
% 2.86/3.15 => ( ( P @ Xs2 @ Ys5 )
% 2.86/3.15 => ( P @ ( cons_d @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys5 ) ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct2
% 2.86/3.15 thf(fact_5084_list__induct2,axiom,
% 2.86/3.15 ! [Xs: list_nat,Ys: list_c,P: list_nat > list_c > $o] :
% 2.86/3.15 ( ( ( size_size_list_nat @ Xs )
% 2.86/3.15 = ( size_size_list_c @ Ys ) )
% 2.86/3.15 => ( ( P @ nil_nat @ nil_c )
% 2.86/3.15 => ( ! [X3: nat,Xs2: list_nat,Y2: c,Ys5: list_c] :
% 2.86/3.15 ( ( ( size_size_list_nat @ Xs2 )
% 2.86/3.15 = ( size_size_list_c @ Ys5 ) )
% 2.86/3.15 => ( ( P @ Xs2 @ Ys5 )
% 2.86/3.15 => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_c @ Y2 @ Ys5 ) ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct2
% 2.86/3.15 thf(fact_5085_list__induct2,axiom,
% 2.86/3.15 ! [Xs: list_nat,Ys: list_d,P: list_nat > list_d > $o] :
% 2.86/3.15 ( ( ( size_size_list_nat @ Xs )
% 2.86/3.15 = ( size_size_list_d @ Ys ) )
% 2.86/3.15 => ( ( P @ nil_nat @ nil_d )
% 2.86/3.15 => ( ! [X3: nat,Xs2: list_nat,Y2: d,Ys5: list_d] :
% 2.86/3.15 ( ( ( size_size_list_nat @ Xs2 )
% 2.86/3.15 = ( size_size_list_d @ Ys5 ) )
% 2.86/3.15 => ( ( P @ Xs2 @ Ys5 )
% 2.86/3.15 => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_d @ Y2 @ Ys5 ) ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct2
% 2.86/3.15 thf(fact_5086_list__induct3,axiom,
% 2.86/3.15 ! [Xs: list_c,Ys: list_c,Zs: list_c,P: list_c > list_c > list_c > $o] :
% 2.86/3.15 ( ( ( size_size_list_c @ Xs )
% 2.86/3.15 = ( size_size_list_c @ Ys ) )
% 2.86/3.15 => ( ( ( size_size_list_c @ Ys )
% 2.86/3.15 = ( size_size_list_c @ Zs ) )
% 2.86/3.15 => ( ( P @ nil_c @ nil_c @ nil_c )
% 2.86/3.15 => ( ! [X3: c,Xs2: list_c,Y2: c,Ys5: list_c,Z4: c,Zs2: list_c] :
% 2.86/3.15 ( ( ( size_size_list_c @ Xs2 )
% 2.86/3.15 = ( size_size_list_c @ Ys5 ) )
% 2.86/3.15 => ( ( ( size_size_list_c @ Ys5 )
% 2.86/3.15 = ( size_size_list_c @ Zs2 ) )
% 2.86/3.15 => ( ( P @ Xs2 @ Ys5 @ Zs2 )
% 2.86/3.15 => ( P @ ( cons_c @ X3 @ Xs2 ) @ ( cons_c @ Y2 @ Ys5 ) @ ( cons_c @ Z4 @ Zs2 ) ) ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct3
% 2.86/3.15 thf(fact_5087_list__induct3,axiom,
% 2.86/3.15 ! [Xs: list_c,Ys: list_c,Zs: list_d,P: list_c > list_c > list_d > $o] :
% 2.86/3.15 ( ( ( size_size_list_c @ Xs )
% 2.86/3.15 = ( size_size_list_c @ Ys ) )
% 2.86/3.15 => ( ( ( size_size_list_c @ Ys )
% 2.86/3.15 = ( size_size_list_d @ Zs ) )
% 2.86/3.15 => ( ( P @ nil_c @ nil_c @ nil_d )
% 2.86/3.15 => ( ! [X3: c,Xs2: list_c,Y2: c,Ys5: list_c,Z4: d,Zs2: list_d] :
% 2.86/3.15 ( ( ( size_size_list_c @ Xs2 )
% 2.86/3.15 = ( size_size_list_c @ Ys5 ) )
% 2.86/3.15 => ( ( ( size_size_list_c @ Ys5 )
% 2.86/3.15 = ( size_size_list_d @ Zs2 ) )
% 2.86/3.15 => ( ( P @ Xs2 @ Ys5 @ Zs2 )
% 2.86/3.15 => ( P @ ( cons_c @ X3 @ Xs2 ) @ ( cons_c @ Y2 @ Ys5 ) @ ( cons_d @ Z4 @ Zs2 ) ) ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct3
% 2.86/3.15 thf(fact_5088_list__induct3,axiom,
% 2.86/3.15 ! [Xs: list_c,Ys: list_c,Zs: list_nat,P: list_c > list_c > list_nat > $o] :
% 2.86/3.15 ( ( ( size_size_list_c @ Xs )
% 2.86/3.15 = ( size_size_list_c @ Ys ) )
% 2.86/3.15 => ( ( ( size_size_list_c @ Ys )
% 2.86/3.15 = ( size_size_list_nat @ Zs ) )
% 2.86/3.15 => ( ( P @ nil_c @ nil_c @ nil_nat )
% 2.86/3.15 => ( ! [X3: c,Xs2: list_c,Y2: c,Ys5: list_c,Z4: nat,Zs2: list_nat] :
% 2.86/3.15 ( ( ( size_size_list_c @ Xs2 )
% 2.86/3.15 = ( size_size_list_c @ Ys5 ) )
% 2.86/3.15 => ( ( ( size_size_list_c @ Ys5 )
% 2.86/3.15 = ( size_size_list_nat @ Zs2 ) )
% 2.86/3.15 => ( ( P @ Xs2 @ Ys5 @ Zs2 )
% 2.86/3.15 => ( P @ ( cons_c @ X3 @ Xs2 ) @ ( cons_c @ Y2 @ Ys5 ) @ ( cons_nat @ Z4 @ Zs2 ) ) ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct3
% 2.86/3.15 thf(fact_5089_list__induct3,axiom,
% 2.86/3.15 ! [Xs: list_c,Ys: list_c,Zs: list_int,P: list_c > list_c > list_int > $o] :
% 2.86/3.15 ( ( ( size_size_list_c @ Xs )
% 2.86/3.15 = ( size_size_list_c @ Ys ) )
% 2.86/3.15 => ( ( ( size_size_list_c @ Ys )
% 2.86/3.15 = ( size_size_list_int @ Zs ) )
% 2.86/3.15 => ( ( P @ nil_c @ nil_c @ nil_int )
% 2.86/3.15 => ( ! [X3: c,Xs2: list_c,Y2: c,Ys5: list_c,Z4: int,Zs2: list_int] :
% 2.86/3.15 ( ( ( size_size_list_c @ Xs2 )
% 2.86/3.15 = ( size_size_list_c @ Ys5 ) )
% 2.86/3.15 => ( ( ( size_size_list_c @ Ys5 )
% 2.86/3.15 = ( size_size_list_int @ Zs2 ) )
% 2.86/3.15 => ( ( P @ Xs2 @ Ys5 @ Zs2 )
% 2.86/3.15 => ( P @ ( cons_c @ X3 @ Xs2 ) @ ( cons_c @ Y2 @ Ys5 ) @ ( cons_int @ Z4 @ Zs2 ) ) ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct3
% 2.86/3.15 thf(fact_5090_list__induct3,axiom,
% 2.86/3.15 ! [Xs: list_c,Ys: list_d,Zs: list_c,P: list_c > list_d > list_c > $o] :
% 2.86/3.15 ( ( ( size_size_list_c @ Xs )
% 2.86/3.15 = ( size_size_list_d @ Ys ) )
% 2.86/3.15 => ( ( ( size_size_list_d @ Ys )
% 2.86/3.15 = ( size_size_list_c @ Zs ) )
% 2.86/3.15 => ( ( P @ nil_c @ nil_d @ nil_c )
% 2.86/3.15 => ( ! [X3: c,Xs2: list_c,Y2: d,Ys5: list_d,Z4: c,Zs2: list_c] :
% 2.86/3.15 ( ( ( size_size_list_c @ Xs2 )
% 2.86/3.15 = ( size_size_list_d @ Ys5 ) )
% 2.86/3.15 => ( ( ( size_size_list_d @ Ys5 )
% 2.86/3.15 = ( size_size_list_c @ Zs2 ) )
% 2.86/3.15 => ( ( P @ Xs2 @ Ys5 @ Zs2 )
% 2.86/3.15 => ( P @ ( cons_c @ X3 @ Xs2 ) @ ( cons_d @ Y2 @ Ys5 ) @ ( cons_c @ Z4 @ Zs2 ) ) ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct3
% 2.86/3.15 thf(fact_5091_list__induct3,axiom,
% 2.86/3.15 ! [Xs: list_c,Ys: list_d,Zs: list_d,P: list_c > list_d > list_d > $o] :
% 2.86/3.15 ( ( ( size_size_list_c @ Xs )
% 2.86/3.15 = ( size_size_list_d @ Ys ) )
% 2.86/3.15 => ( ( ( size_size_list_d @ Ys )
% 2.86/3.15 = ( size_size_list_d @ Zs ) )
% 2.86/3.15 => ( ( P @ nil_c @ nil_d @ nil_d )
% 2.86/3.15 => ( ! [X3: c,Xs2: list_c,Y2: d,Ys5: list_d,Z4: d,Zs2: list_d] :
% 2.86/3.15 ( ( ( size_size_list_c @ Xs2 )
% 2.86/3.15 = ( size_size_list_d @ Ys5 ) )
% 2.86/3.15 => ( ( ( size_size_list_d @ Ys5 )
% 2.86/3.15 = ( size_size_list_d @ Zs2 ) )
% 2.86/3.15 => ( ( P @ Xs2 @ Ys5 @ Zs2 )
% 2.86/3.15 => ( P @ ( cons_c @ X3 @ Xs2 ) @ ( cons_d @ Y2 @ Ys5 ) @ ( cons_d @ Z4 @ Zs2 ) ) ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct3
% 2.86/3.15 thf(fact_5092_list__induct3,axiom,
% 2.86/3.15 ! [Xs: list_c,Ys: list_d,Zs: list_nat,P: list_c > list_d > list_nat > $o] :
% 2.86/3.15 ( ( ( size_size_list_c @ Xs )
% 2.86/3.15 = ( size_size_list_d @ Ys ) )
% 2.86/3.15 => ( ( ( size_size_list_d @ Ys )
% 2.86/3.15 = ( size_size_list_nat @ Zs ) )
% 2.86/3.15 => ( ( P @ nil_c @ nil_d @ nil_nat )
% 2.86/3.15 => ( ! [X3: c,Xs2: list_c,Y2: d,Ys5: list_d,Z4: nat,Zs2: list_nat] :
% 2.86/3.15 ( ( ( size_size_list_c @ Xs2 )
% 2.86/3.15 = ( size_size_list_d @ Ys5 ) )
% 2.86/3.15 => ( ( ( size_size_list_d @ Ys5 )
% 2.86/3.15 = ( size_size_list_nat @ Zs2 ) )
% 2.86/3.15 => ( ( P @ Xs2 @ Ys5 @ Zs2 )
% 2.86/3.15 => ( P @ ( cons_c @ X3 @ Xs2 ) @ ( cons_d @ Y2 @ Ys5 ) @ ( cons_nat @ Z4 @ Zs2 ) ) ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct3
% 2.86/3.15 thf(fact_5093_list__induct3,axiom,
% 2.86/3.15 ! [Xs: list_c,Ys: list_d,Zs: list_int,P: list_c > list_d > list_int > $o] :
% 2.86/3.15 ( ( ( size_size_list_c @ Xs )
% 2.86/3.15 = ( size_size_list_d @ Ys ) )
% 2.86/3.15 => ( ( ( size_size_list_d @ Ys )
% 2.86/3.15 = ( size_size_list_int @ Zs ) )
% 2.86/3.15 => ( ( P @ nil_c @ nil_d @ nil_int )
% 2.86/3.15 => ( ! [X3: c,Xs2: list_c,Y2: d,Ys5: list_d,Z4: int,Zs2: list_int] :
% 2.86/3.15 ( ( ( size_size_list_c @ Xs2 )
% 2.86/3.15 = ( size_size_list_d @ Ys5 ) )
% 2.86/3.15 => ( ( ( size_size_list_d @ Ys5 )
% 2.86/3.15 = ( size_size_list_int @ Zs2 ) )
% 2.86/3.15 => ( ( P @ Xs2 @ Ys5 @ Zs2 )
% 2.86/3.15 => ( P @ ( cons_c @ X3 @ Xs2 ) @ ( cons_d @ Y2 @ Ys5 ) @ ( cons_int @ Z4 @ Zs2 ) ) ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct3
% 2.86/3.15 thf(fact_5094_list__induct3,axiom,
% 2.86/3.15 ! [Xs: list_c,Ys: list_nat,Zs: list_c,P: list_c > list_nat > list_c > $o] :
% 2.86/3.15 ( ( ( size_size_list_c @ Xs )
% 2.86/3.15 = ( size_size_list_nat @ Ys ) )
% 2.86/3.15 => ( ( ( size_size_list_nat @ Ys )
% 2.86/3.15 = ( size_size_list_c @ Zs ) )
% 2.86/3.15 => ( ( P @ nil_c @ nil_nat @ nil_c )
% 2.86/3.15 => ( ! [X3: c,Xs2: list_c,Y2: nat,Ys5: list_nat,Z4: c,Zs2: list_c] :
% 2.86/3.15 ( ( ( size_size_list_c @ Xs2 )
% 2.86/3.15 = ( size_size_list_nat @ Ys5 ) )
% 2.86/3.15 => ( ( ( size_size_list_nat @ Ys5 )
% 2.86/3.15 = ( size_size_list_c @ Zs2 ) )
% 2.86/3.15 => ( ( P @ Xs2 @ Ys5 @ Zs2 )
% 2.86/3.15 => ( P @ ( cons_c @ X3 @ Xs2 ) @ ( cons_nat @ Y2 @ Ys5 ) @ ( cons_c @ Z4 @ Zs2 ) ) ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct3
% 2.86/3.15 thf(fact_5095_list__induct3,axiom,
% 2.86/3.15 ! [Xs: list_c,Ys: list_nat,Zs: list_d,P: list_c > list_nat > list_d > $o] :
% 2.86/3.15 ( ( ( size_size_list_c @ Xs )
% 2.86/3.15 = ( size_size_list_nat @ Ys ) )
% 2.86/3.15 => ( ( ( size_size_list_nat @ Ys )
% 2.86/3.15 = ( size_size_list_d @ Zs ) )
% 2.86/3.15 => ( ( P @ nil_c @ nil_nat @ nil_d )
% 2.86/3.15 => ( ! [X3: c,Xs2: list_c,Y2: nat,Ys5: list_nat,Z4: d,Zs2: list_d] :
% 2.86/3.15 ( ( ( size_size_list_c @ Xs2 )
% 2.86/3.15 = ( size_size_list_nat @ Ys5 ) )
% 2.86/3.15 => ( ( ( size_size_list_nat @ Ys5 )
% 2.86/3.15 = ( size_size_list_d @ Zs2 ) )
% 2.86/3.15 => ( ( P @ Xs2 @ Ys5 @ Zs2 )
% 2.86/3.15 => ( P @ ( cons_c @ X3 @ Xs2 ) @ ( cons_nat @ Y2 @ Ys5 ) @ ( cons_d @ Z4 @ Zs2 ) ) ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct3
% 2.86/3.15 thf(fact_5096_list__induct4,axiom,
% 2.86/3.15 ! [Xs: list_nat,Ys: list_nat,Zs: list_int,Ws: list_c,P: list_nat > list_nat > list_int > list_c > $o] :
% 2.86/3.15 ( ( ( size_size_list_nat @ Xs )
% 2.86/3.15 = ( size_size_list_nat @ Ys ) )
% 2.86/3.15 => ( ( ( size_size_list_nat @ Ys )
% 2.86/3.15 = ( size_size_list_int @ Zs ) )
% 2.86/3.15 => ( ( ( size_size_list_int @ Zs )
% 2.86/3.15 = ( size_size_list_c @ Ws ) )
% 2.86/3.15 => ( ( P @ nil_nat @ nil_nat @ nil_int @ nil_c )
% 2.86/3.15 => ( ! [X3: nat,Xs2: list_nat,Y2: nat,Ys5: list_nat,Z4: int,Zs2: list_int,W3: c,Ws2: list_c] :
% 2.86/3.15 ( ( ( size_size_list_nat @ Xs2 )
% 2.86/3.15 = ( size_size_list_nat @ Ys5 ) )
% 2.86/3.15 => ( ( ( size_size_list_nat @ Ys5 )
% 2.86/3.15 = ( size_size_list_int @ Zs2 ) )
% 2.86/3.15 => ( ( ( size_size_list_int @ Zs2 )
% 2.86/3.15 = ( size_size_list_c @ Ws2 ) )
% 2.86/3.15 => ( ( P @ Xs2 @ Ys5 @ Zs2 @ Ws2 )
% 2.86/3.15 => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_nat @ Y2 @ Ys5 ) @ ( cons_int @ Z4 @ Zs2 ) @ ( cons_c @ W3 @ Ws2 ) ) ) ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct4
% 2.86/3.15 thf(fact_5097_list__induct4,axiom,
% 2.86/3.15 ! [Xs: list_nat,Ys: list_nat,Zs: list_int,Ws: list_d,P: list_nat > list_nat > list_int > list_d > $o] :
% 2.86/3.15 ( ( ( size_size_list_nat @ Xs )
% 2.86/3.15 = ( size_size_list_nat @ Ys ) )
% 2.86/3.15 => ( ( ( size_size_list_nat @ Ys )
% 2.86/3.15 = ( size_size_list_int @ Zs ) )
% 2.86/3.15 => ( ( ( size_size_list_int @ Zs )
% 2.86/3.15 = ( size_size_list_d @ Ws ) )
% 2.86/3.15 => ( ( P @ nil_nat @ nil_nat @ nil_int @ nil_d )
% 2.86/3.15 => ( ! [X3: nat,Xs2: list_nat,Y2: nat,Ys5: list_nat,Z4: int,Zs2: list_int,W3: d,Ws2: list_d] :
% 2.86/3.15 ( ( ( size_size_list_nat @ Xs2 )
% 2.86/3.15 = ( size_size_list_nat @ Ys5 ) )
% 2.86/3.15 => ( ( ( size_size_list_nat @ Ys5 )
% 2.86/3.15 = ( size_size_list_int @ Zs2 ) )
% 2.86/3.15 => ( ( ( size_size_list_int @ Zs2 )
% 2.86/3.15 = ( size_size_list_d @ Ws2 ) )
% 2.86/3.15 => ( ( P @ Xs2 @ Ys5 @ Zs2 @ Ws2 )
% 2.86/3.15 => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_nat @ Y2 @ Ys5 ) @ ( cons_int @ Z4 @ Zs2 ) @ ( cons_d @ W3 @ Ws2 ) ) ) ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct4
% 2.86/3.15 thf(fact_5098_list__induct4,axiom,
% 2.86/3.15 ! [Xs: list_nat,Ys: list_nat,Zs: list_int,Ws: list_nat,P: list_nat > list_nat > list_int > list_nat > $o] :
% 2.86/3.15 ( ( ( size_size_list_nat @ Xs )
% 2.86/3.15 = ( size_size_list_nat @ Ys ) )
% 2.86/3.15 => ( ( ( size_size_list_nat @ Ys )
% 2.86/3.15 = ( size_size_list_int @ Zs ) )
% 2.86/3.15 => ( ( ( size_size_list_int @ Zs )
% 2.86/3.15 = ( size_size_list_nat @ Ws ) )
% 2.86/3.15 => ( ( P @ nil_nat @ nil_nat @ nil_int @ nil_nat )
% 2.86/3.15 => ( ! [X3: nat,Xs2: list_nat,Y2: nat,Ys5: list_nat,Z4: int,Zs2: list_int,W3: nat,Ws2: list_nat] :
% 2.86/3.15 ( ( ( size_size_list_nat @ Xs2 )
% 2.86/3.15 = ( size_size_list_nat @ Ys5 ) )
% 2.86/3.15 => ( ( ( size_size_list_nat @ Ys5 )
% 2.86/3.15 = ( size_size_list_int @ Zs2 ) )
% 2.86/3.15 => ( ( ( size_size_list_int @ Zs2 )
% 2.86/3.15 = ( size_size_list_nat @ Ws2 ) )
% 2.86/3.15 => ( ( P @ Xs2 @ Ys5 @ Zs2 @ Ws2 )
% 2.86/3.15 => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_nat @ Y2 @ Ys5 ) @ ( cons_int @ Z4 @ Zs2 ) @ ( cons_nat @ W3 @ Ws2 ) ) ) ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct4
% 2.86/3.15 thf(fact_5099_list__induct4,axiom,
% 2.86/3.15 ! [Xs: list_nat,Ys: list_nat,Zs: list_int,Ws: list_int,P: list_nat > list_nat > list_int > list_int > $o] :
% 2.86/3.15 ( ( ( size_size_list_nat @ Xs )
% 2.86/3.15 = ( size_size_list_nat @ Ys ) )
% 2.86/3.15 => ( ( ( size_size_list_nat @ Ys )
% 2.86/3.15 = ( size_size_list_int @ Zs ) )
% 2.86/3.15 => ( ( ( size_size_list_int @ Zs )
% 2.86/3.15 = ( size_size_list_int @ Ws ) )
% 2.86/3.15 => ( ( P @ nil_nat @ nil_nat @ nil_int @ nil_int )
% 2.86/3.15 => ( ! [X3: nat,Xs2: list_nat,Y2: nat,Ys5: list_nat,Z4: int,Zs2: list_int,W3: int,Ws2: list_int] :
% 2.86/3.15 ( ( ( size_size_list_nat @ Xs2 )
% 2.86/3.15 = ( size_size_list_nat @ Ys5 ) )
% 2.86/3.15 => ( ( ( size_size_list_nat @ Ys5 )
% 2.86/3.15 = ( size_size_list_int @ Zs2 ) )
% 2.86/3.15 => ( ( ( size_size_list_int @ Zs2 )
% 2.86/3.15 = ( size_size_list_int @ Ws2 ) )
% 2.86/3.15 => ( ( P @ Xs2 @ Ys5 @ Zs2 @ Ws2 )
% 2.86/3.15 => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_nat @ Y2 @ Ys5 ) @ ( cons_int @ Z4 @ Zs2 ) @ ( cons_int @ W3 @ Ws2 ) ) ) ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct4
% 2.86/3.15 thf(fact_5100_list__induct4,axiom,
% 2.86/3.15 ! [Xs: list_nat,Ys: list_int,Zs: list_c,Ws: list_c,P: list_nat > list_int > list_c > list_c > $o] :
% 2.86/3.15 ( ( ( size_size_list_nat @ Xs )
% 2.86/3.15 = ( size_size_list_int @ Ys ) )
% 2.86/3.15 => ( ( ( size_size_list_int @ Ys )
% 2.86/3.15 = ( size_size_list_c @ Zs ) )
% 2.86/3.15 => ( ( ( size_size_list_c @ Zs )
% 2.86/3.15 = ( size_size_list_c @ Ws ) )
% 2.86/3.15 => ( ( P @ nil_nat @ nil_int @ nil_c @ nil_c )
% 2.86/3.15 => ( ! [X3: nat,Xs2: list_nat,Y2: int,Ys5: list_int,Z4: c,Zs2: list_c,W3: c,Ws2: list_c] :
% 2.86/3.15 ( ( ( size_size_list_nat @ Xs2 )
% 2.86/3.15 = ( size_size_list_int @ Ys5 ) )
% 2.86/3.15 => ( ( ( size_size_list_int @ Ys5 )
% 2.86/3.15 = ( size_size_list_c @ Zs2 ) )
% 2.86/3.15 => ( ( ( size_size_list_c @ Zs2 )
% 2.86/3.15 = ( size_size_list_c @ Ws2 ) )
% 2.86/3.15 => ( ( P @ Xs2 @ Ys5 @ Zs2 @ Ws2 )
% 2.86/3.15 => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys5 ) @ ( cons_c @ Z4 @ Zs2 ) @ ( cons_c @ W3 @ Ws2 ) ) ) ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct4
% 2.86/3.15 thf(fact_5101_list__induct4,axiom,
% 2.86/3.15 ! [Xs: list_nat,Ys: list_int,Zs: list_c,Ws: list_d,P: list_nat > list_int > list_c > list_d > $o] :
% 2.86/3.15 ( ( ( size_size_list_nat @ Xs )
% 2.86/3.15 = ( size_size_list_int @ Ys ) )
% 2.86/3.15 => ( ( ( size_size_list_int @ Ys )
% 2.86/3.15 = ( size_size_list_c @ Zs ) )
% 2.86/3.15 => ( ( ( size_size_list_c @ Zs )
% 2.86/3.15 = ( size_size_list_d @ Ws ) )
% 2.86/3.15 => ( ( P @ nil_nat @ nil_int @ nil_c @ nil_d )
% 2.86/3.15 => ( ! [X3: nat,Xs2: list_nat,Y2: int,Ys5: list_int,Z4: c,Zs2: list_c,W3: d,Ws2: list_d] :
% 2.86/3.15 ( ( ( size_size_list_nat @ Xs2 )
% 2.86/3.15 = ( size_size_list_int @ Ys5 ) )
% 2.86/3.15 => ( ( ( size_size_list_int @ Ys5 )
% 2.86/3.15 = ( size_size_list_c @ Zs2 ) )
% 2.86/3.15 => ( ( ( size_size_list_c @ Zs2 )
% 2.86/3.15 = ( size_size_list_d @ Ws2 ) )
% 2.86/3.15 => ( ( P @ Xs2 @ Ys5 @ Zs2 @ Ws2 )
% 2.86/3.15 => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys5 ) @ ( cons_c @ Z4 @ Zs2 ) @ ( cons_d @ W3 @ Ws2 ) ) ) ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct4
% 2.86/3.15 thf(fact_5102_list__induct4,axiom,
% 2.86/3.15 ! [Xs: list_nat,Ys: list_int,Zs: list_c,Ws: list_nat,P: list_nat > list_int > list_c > list_nat > $o] :
% 2.86/3.15 ( ( ( size_size_list_nat @ Xs )
% 2.86/3.15 = ( size_size_list_int @ Ys ) )
% 2.86/3.15 => ( ( ( size_size_list_int @ Ys )
% 2.86/3.15 = ( size_size_list_c @ Zs ) )
% 2.86/3.15 => ( ( ( size_size_list_c @ Zs )
% 2.86/3.15 = ( size_size_list_nat @ Ws ) )
% 2.86/3.15 => ( ( P @ nil_nat @ nil_int @ nil_c @ nil_nat )
% 2.86/3.15 => ( ! [X3: nat,Xs2: list_nat,Y2: int,Ys5: list_int,Z4: c,Zs2: list_c,W3: nat,Ws2: list_nat] :
% 2.86/3.15 ( ( ( size_size_list_nat @ Xs2 )
% 2.86/3.15 = ( size_size_list_int @ Ys5 ) )
% 2.86/3.15 => ( ( ( size_size_list_int @ Ys5 )
% 2.86/3.15 = ( size_size_list_c @ Zs2 ) )
% 2.86/3.15 => ( ( ( size_size_list_c @ Zs2 )
% 2.86/3.15 = ( size_size_list_nat @ Ws2 ) )
% 2.86/3.15 => ( ( P @ Xs2 @ Ys5 @ Zs2 @ Ws2 )
% 2.86/3.15 => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys5 ) @ ( cons_c @ Z4 @ Zs2 ) @ ( cons_nat @ W3 @ Ws2 ) ) ) ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct4
% 2.86/3.15 thf(fact_5103_list__induct4,axiom,
% 2.86/3.15 ! [Xs: list_nat,Ys: list_int,Zs: list_c,Ws: list_int,P: list_nat > list_int > list_c > list_int > $o] :
% 2.86/3.15 ( ( ( size_size_list_nat @ Xs )
% 2.86/3.15 = ( size_size_list_int @ Ys ) )
% 2.86/3.15 => ( ( ( size_size_list_int @ Ys )
% 2.86/3.15 = ( size_size_list_c @ Zs ) )
% 2.86/3.15 => ( ( ( size_size_list_c @ Zs )
% 2.86/3.15 = ( size_size_list_int @ Ws ) )
% 2.86/3.15 => ( ( P @ nil_nat @ nil_int @ nil_c @ nil_int )
% 2.86/3.15 => ( ! [X3: nat,Xs2: list_nat,Y2: int,Ys5: list_int,Z4: c,Zs2: list_c,W3: int,Ws2: list_int] :
% 2.86/3.15 ( ( ( size_size_list_nat @ Xs2 )
% 2.86/3.15 = ( size_size_list_int @ Ys5 ) )
% 2.86/3.15 => ( ( ( size_size_list_int @ Ys5 )
% 2.86/3.15 = ( size_size_list_c @ Zs2 ) )
% 2.86/3.15 => ( ( ( size_size_list_c @ Zs2 )
% 2.86/3.15 = ( size_size_list_int @ Ws2 ) )
% 2.86/3.15 => ( ( P @ Xs2 @ Ys5 @ Zs2 @ Ws2 )
% 2.86/3.15 => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys5 ) @ ( cons_c @ Z4 @ Zs2 ) @ ( cons_int @ W3 @ Ws2 ) ) ) ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct4
% 2.86/3.15 thf(fact_5104_list__induct4,axiom,
% 2.86/3.15 ! [Xs: list_nat,Ys: list_int,Zs: list_d,Ws: list_c,P: list_nat > list_int > list_d > list_c > $o] :
% 2.86/3.15 ( ( ( size_size_list_nat @ Xs )
% 2.86/3.15 = ( size_size_list_int @ Ys ) )
% 2.86/3.15 => ( ( ( size_size_list_int @ Ys )
% 2.86/3.15 = ( size_size_list_d @ Zs ) )
% 2.86/3.15 => ( ( ( size_size_list_d @ Zs )
% 2.86/3.15 = ( size_size_list_c @ Ws ) )
% 2.86/3.15 => ( ( P @ nil_nat @ nil_int @ nil_d @ nil_c )
% 2.86/3.15 => ( ! [X3: nat,Xs2: list_nat,Y2: int,Ys5: list_int,Z4: d,Zs2: list_d,W3: c,Ws2: list_c] :
% 2.86/3.15 ( ( ( size_size_list_nat @ Xs2 )
% 2.86/3.15 = ( size_size_list_int @ Ys5 ) )
% 2.86/3.15 => ( ( ( size_size_list_int @ Ys5 )
% 2.86/3.15 = ( size_size_list_d @ Zs2 ) )
% 2.86/3.15 => ( ( ( size_size_list_d @ Zs2 )
% 2.86/3.15 = ( size_size_list_c @ Ws2 ) )
% 2.86/3.15 => ( ( P @ Xs2 @ Ys5 @ Zs2 @ Ws2 )
% 2.86/3.15 => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys5 ) @ ( cons_d @ Z4 @ Zs2 ) @ ( cons_c @ W3 @ Ws2 ) ) ) ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct4
% 2.86/3.15 thf(fact_5105_list__induct4,axiom,
% 2.86/3.15 ! [Xs: list_nat,Ys: list_int,Zs: list_d,Ws: list_d,P: list_nat > list_int > list_d > list_d > $o] :
% 2.86/3.15 ( ( ( size_size_list_nat @ Xs )
% 2.86/3.15 = ( size_size_list_int @ Ys ) )
% 2.86/3.15 => ( ( ( size_size_list_int @ Ys )
% 2.86/3.15 = ( size_size_list_d @ Zs ) )
% 2.86/3.15 => ( ( ( size_size_list_d @ Zs )
% 2.86/3.15 = ( size_size_list_d @ Ws ) )
% 2.86/3.15 => ( ( P @ nil_nat @ nil_int @ nil_d @ nil_d )
% 2.86/3.15 => ( ! [X3: nat,Xs2: list_nat,Y2: int,Ys5: list_int,Z4: d,Zs2: list_d,W3: d,Ws2: list_d] :
% 2.86/3.15 ( ( ( size_size_list_nat @ Xs2 )
% 2.86/3.15 = ( size_size_list_int @ Ys5 ) )
% 2.86/3.15 => ( ( ( size_size_list_int @ Ys5 )
% 2.86/3.15 = ( size_size_list_d @ Zs2 ) )
% 2.86/3.15 => ( ( ( size_size_list_d @ Zs2 )
% 2.86/3.15 = ( size_size_list_d @ Ws2 ) )
% 2.86/3.15 => ( ( P @ Xs2 @ Ys5 @ Zs2 @ Ws2 )
% 2.86/3.15 => ( P @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys5 ) @ ( cons_d @ Z4 @ Zs2 ) @ ( cons_d @ W3 @ Ws2 ) ) ) ) ) )
% 2.86/3.15 => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % list_induct4
% 2.86/3.15 thf(fact_5106_power__gt__expt,axiom,
% 2.86/3.15 ! [N: nat,K3: nat] :
% 2.86/3.15 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 2.86/3.15 => ( ord_less_nat @ K3 @ ( power_power_nat @ N @ K3 ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % power_gt_expt
% 2.86/3.15 thf(fact_5107_greaterThan__Suc,axiom,
% 2.86/3.15 ! [K3: nat] :
% 2.86/3.15 ( ( set_or1210151606488870762an_nat @ ( suc @ K3 ) )
% 2.86/3.15 = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K3 ) @ ( insert_nat2 @ ( suc @ K3 ) @ bot_bot_set_nat ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % greaterThan_Suc
% 2.86/3.15 thf(fact_5108_nat__int__comparison_I2_J,axiom,
% 2.86/3.15 ( ord_less_nat
% 2.86/3.15 = ( ^ [A3: nat,B3: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % nat_int_comparison(2)
% 2.86/3.15 thf(fact_5109_zdiff__int__split,axiom,
% 2.86/3.15 ! [P: int > $o,X: nat,Y: nat] :
% 2.86/3.15 ( ( P @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X @ Y ) ) )
% 2.86/3.15 = ( ( ( ord_less_eq_nat @ Y @ X )
% 2.86/3.15 => ( P @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y ) ) ) )
% 2.86/3.15 & ( ( ord_less_nat @ X @ Y )
% 2.86/3.15 => ( P @ zero_zero_int ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % zdiff_int_split
% 2.86/3.15 thf(fact_5110_imp__le__cong,axiom,
% 2.86/3.15 ! [X: int,X6: int,P: $o,P3: $o] :
% 2.86/3.15 ( ( X = X6 )
% 2.86/3.15 => ( ( ( ord_less_eq_int @ zero_zero_int @ X6 )
% 2.86/3.15 => ( P = P3 ) )
% 2.86/3.15 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 2.86/3.15 => P )
% 2.86/3.15 = ( ( ord_less_eq_int @ zero_zero_int @ X6 )
% 2.86/3.15 => P3 ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % imp_le_cong
% 2.86/3.15 thf(fact_5111_conj__le__cong,axiom,
% 2.86/3.15 ! [X: int,X6: int,P: $o,P3: $o] :
% 2.86/3.15 ( ( X = X6 )
% 2.86/3.15 => ( ( ( ord_less_eq_int @ zero_zero_int @ X6 )
% 2.86/3.15 => ( P = P3 ) )
% 2.86/3.15 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 2.86/3.15 & P )
% 2.86/3.15 = ( ( ord_less_eq_int @ zero_zero_int @ X6 )
% 2.86/3.15 & P3 ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % conj_le_cong
% 2.86/3.15 thf(fact_5112_incr__mult__lemma,axiom,
% 2.86/3.15 ! [D2: int,P: int > $o,K3: int] :
% 2.86/3.15 ( ( ord_less_int @ zero_zero_int @ D2 )
% 2.86/3.15 => ( ! [X3: int] :
% 2.86/3.15 ( ( P @ X3 )
% 2.86/3.15 => ( P @ ( plus_plus_int @ X3 @ D2 ) ) )
% 2.86/3.15 => ( ( ord_less_eq_int @ zero_zero_int @ K3 )
% 2.86/3.15 => ! [X7: int] :
% 2.86/3.15 ( ( P @ X7 )
% 2.86/3.15 => ( P @ ( plus_plus_int @ X7 @ ( times_times_int @ K3 @ D2 ) ) ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % incr_mult_lemma
% 2.86/3.15 thf(fact_5113_decr__mult__lemma,axiom,
% 2.86/3.15 ! [D2: int,P: int > $o,K3: int] :
% 2.86/3.15 ( ( ord_less_int @ zero_zero_int @ D2 )
% 2.86/3.15 => ( ! [X3: int] :
% 2.86/3.15 ( ( P @ X3 )
% 2.86/3.15 => ( P @ ( minus_minus_int @ X3 @ D2 ) ) )
% 2.86/3.15 => ( ( ord_less_eq_int @ zero_zero_int @ K3 )
% 2.86/3.15 => ! [X7: int] :
% 2.86/3.15 ( ( P @ X7 )
% 2.86/3.15 => ( P @ ( minus_minus_int @ X7 @ ( times_times_int @ K3 @ D2 ) ) ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % decr_mult_lemma
% 2.86/3.15 thf(fact_5114_minusinfinity,axiom,
% 2.86/3.15 ! [D2: int,P1: int > $o,P: int > $o] :
% 2.86/3.15 ( ( ord_less_int @ zero_zero_int @ D2 )
% 2.86/3.15 => ( ! [X3: int,K: int] :
% 2.86/3.15 ( ( P1 @ X3 )
% 2.86/3.15 = ( P1 @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D2 ) ) ) )
% 2.86/3.15 => ( ? [Z3: int] :
% 2.86/3.15 ! [X3: int] :
% 2.86/3.15 ( ( ord_less_int @ X3 @ Z3 )
% 2.86/3.15 => ( ( P @ X3 )
% 2.86/3.15 = ( P1 @ X3 ) ) )
% 2.86/3.15 => ( ? [X_12: int] : ( P1 @ X_12 )
% 2.86/3.15 => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % minusinfinity
% 2.86/3.15 thf(fact_5115_plusinfinity,axiom,
% 2.86/3.15 ! [D2: int,P3: int > $o,P: int > $o] :
% 2.86/3.15 ( ( ord_less_int @ zero_zero_int @ D2 )
% 2.86/3.15 => ( ! [X3: int,K: int] :
% 2.86/3.15 ( ( P3 @ X3 )
% 2.86/3.15 = ( P3 @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D2 ) ) ) )
% 2.86/3.15 => ( ? [Z3: int] :
% 2.86/3.15 ! [X3: int] :
% 2.86/3.15 ( ( ord_less_int @ Z3 @ X3 )
% 2.86/3.15 => ( ( P @ X3 )
% 2.86/3.15 = ( P3 @ X3 ) ) )
% 2.86/3.15 => ( ? [X_12: int] : ( P3 @ X_12 )
% 2.86/3.15 => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % plusinfinity
% 2.86/3.15 thf(fact_5116_pos__int__cases,axiom,
% 2.86/3.15 ! [K3: int] :
% 2.86/3.15 ( ( ord_less_int @ zero_zero_int @ K3 )
% 2.86/3.15 => ~ ! [N5: nat] :
% 2.86/3.15 ( ( K3
% 2.86/3.15 = ( semiri1314217659103216013at_int @ N5 ) )
% 2.86/3.15 => ~ ( ord_less_nat @ zero_zero_nat @ N5 ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % pos_int_cases
% 2.86/3.15 thf(fact_5117_zero__less__imp__eq__int,axiom,
% 2.86/3.15 ! [K3: int] :
% 2.86/3.15 ( ( ord_less_int @ zero_zero_int @ K3 )
% 2.86/3.15 => ? [N5: nat] :
% 2.86/3.15 ( ( ord_less_nat @ zero_zero_nat @ N5 )
% 2.86/3.15 & ( K3
% 2.86/3.15 = ( semiri1314217659103216013at_int @ N5 ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % zero_less_imp_eq_int
% 2.86/3.15 thf(fact_5118_zmult__zless__mono2__lemma,axiom,
% 2.86/3.15 ! [I: int,J: int,K3: nat] :
% 2.86/3.15 ( ( ord_less_int @ I @ J )
% 2.86/3.15 => ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 2.86/3.15 => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K3 ) @ I ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K3 ) @ J ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % zmult_zless_mono2_lemma
% 2.86/3.15 thf(fact_5119_eucl__rel__int__iff,axiom,
% 2.86/3.15 ! [K3: int,L: int,Q6: int,R2: int] :
% 2.86/3.15 ( ( eucl_rel_int @ K3 @ L @ ( product_Pair_int_int @ Q6 @ R2 ) )
% 2.86/3.15 = ( ( K3
% 2.86/3.15 = ( plus_plus_int @ ( times_times_int @ L @ Q6 ) @ R2 ) )
% 2.86/3.15 & ( ( ord_less_int @ zero_zero_int @ L )
% 2.86/3.15 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 2.86/3.15 & ( ord_less_int @ R2 @ L ) ) )
% 2.86/3.15 & ( ~ ( ord_less_int @ zero_zero_int @ L )
% 2.86/3.15 => ( ( ( ord_less_int @ L @ zero_zero_int )
% 2.86/3.15 => ( ( ord_less_int @ L @ R2 )
% 2.86/3.15 & ( ord_less_eq_int @ R2 @ zero_zero_int ) ) )
% 2.86/3.15 & ( ~ ( ord_less_int @ L @ zero_zero_int )
% 2.86/3.15 => ( Q6 = zero_zero_int ) ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % eucl_rel_int_iff
% 2.86/3.15 thf(fact_5120_nat0__intermed__int__val,axiom,
% 2.86/3.15 ! [N: nat,F4: nat > int,K3: int] :
% 2.86/3.15 ( ! [I5: nat] :
% 2.86/3.15 ( ( ord_less_nat @ I5 @ N )
% 2.86/3.15 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F4 @ ( plus_plus_nat @ I5 @ one_one_nat ) ) @ ( F4 @ I5 ) ) ) @ one_one_int ) )
% 2.86/3.15 => ( ( ord_less_eq_int @ ( F4 @ zero_zero_nat ) @ K3 )
% 2.86/3.15 => ( ( ord_less_eq_int @ K3 @ ( F4 @ N ) )
% 2.86/3.15 => ? [I5: nat] :
% 2.86/3.15 ( ( ord_less_eq_nat @ I5 @ N )
% 2.86/3.15 & ( ( F4 @ I5 )
% 2.86/3.15 = K3 ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % nat0_intermed_int_val
% 2.86/3.15 thf(fact_5121_unique__remainder,axiom,
% 2.86/3.15 ! [A2: int,B2: int,Q6: int,R2: int,Q7: int,R5: int] :
% 2.86/3.15 ( ( eucl_rel_int @ A2 @ B2 @ ( product_Pair_int_int @ Q6 @ R2 ) )
% 2.86/3.15 => ( ( eucl_rel_int @ A2 @ B2 @ ( product_Pair_int_int @ Q7 @ R5 ) )
% 2.86/3.15 => ( R2 = R5 ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % unique_remainder
% 2.86/3.15 thf(fact_5122_unique__quotient,axiom,
% 2.86/3.15 ! [A2: int,B2: int,Q6: int,R2: int,Q7: int,R5: int] :
% 2.86/3.15 ( ( eucl_rel_int @ A2 @ B2 @ ( product_Pair_int_int @ Q6 @ R2 ) )
% 2.86/3.15 => ( ( eucl_rel_int @ A2 @ B2 @ ( product_Pair_int_int @ Q7 @ R5 ) )
% 2.86/3.15 => ( Q6 = Q7 ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % unique_quotient
% 2.86/3.15 thf(fact_5123_eucl__rel__int__by0,axiom,
% 2.86/3.15 ! [K3: int] : ( eucl_rel_int @ K3 @ zero_zero_int @ ( product_Pair_int_int @ zero_zero_int @ K3 ) ) ).
% 2.86/3.15
% 2.86/3.15 % eucl_rel_int_by0
% 2.86/3.15 thf(fact_5124_eucl__rel__int__dividesI,axiom,
% 2.86/3.15 ! [L: int,K3: int,Q6: int] :
% 2.86/3.15 ( ( L != zero_zero_int )
% 2.86/3.15 => ( ( K3
% 2.86/3.15 = ( times_times_int @ Q6 @ L ) )
% 2.86/3.15 => ( eucl_rel_int @ K3 @ L @ ( product_Pair_int_int @ Q6 @ zero_zero_int ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % eucl_rel_int_dividesI
% 2.86/3.15 thf(fact_5125_nat__intermed__int__val,axiom,
% 2.86/3.15 ! [M2: nat,N: nat,F4: nat > int,K3: int] :
% 2.86/3.15 ( ! [I5: nat] :
% 2.86/3.15 ( ( ( ord_less_eq_nat @ M2 @ I5 )
% 2.86/3.15 & ( ord_less_nat @ I5 @ N ) )
% 2.86/3.15 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F4 @ ( suc @ I5 ) ) @ ( F4 @ I5 ) ) ) @ one_one_int ) )
% 2.86/3.15 => ( ( ord_less_eq_nat @ M2 @ N )
% 2.86/3.15 => ( ( ord_less_eq_int @ ( F4 @ M2 ) @ K3 )
% 2.86/3.15 => ( ( ord_less_eq_int @ K3 @ ( F4 @ N ) )
% 2.86/3.15 => ? [I5: nat] :
% 2.86/3.15 ( ( ord_less_eq_nat @ M2 @ I5 )
% 2.86/3.15 & ( ord_less_eq_nat @ I5 @ N )
% 2.86/3.15 & ( ( F4 @ I5 )
% 2.86/3.15 = K3 ) ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % nat_intermed_int_val
% 2.86/3.15 thf(fact_5126_incr__lemma,axiom,
% 2.86/3.15 ! [D2: int,Z: int,X: int] :
% 2.86/3.15 ( ( ord_less_int @ zero_zero_int @ D2 )
% 2.86/3.15 => ( ord_less_int @ Z @ ( plus_plus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z ) ) @ one_one_int ) @ D2 ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % incr_lemma
% 2.86/3.15 thf(fact_5127_decr__lemma,axiom,
% 2.86/3.15 ! [D2: int,X: int,Z: int] :
% 2.86/3.15 ( ( ord_less_int @ zero_zero_int @ D2 )
% 2.86/3.15 => ( ord_less_int @ ( minus_minus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z ) ) @ one_one_int ) @ D2 ) ) @ Z ) ) ).
% 2.86/3.15
% 2.86/3.15 % decr_lemma
% 2.86/3.15 thf(fact_5128_nat__ivt__aux,axiom,
% 2.86/3.15 ! [N: nat,F4: nat > int,K3: int] :
% 2.86/3.15 ( ! [I5: nat] :
% 2.86/3.15 ( ( ord_less_nat @ I5 @ N )
% 2.86/3.15 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F4 @ ( suc @ I5 ) ) @ ( F4 @ I5 ) ) ) @ one_one_int ) )
% 2.86/3.15 => ( ( ord_less_eq_int @ ( F4 @ zero_zero_nat ) @ K3 )
% 2.86/3.15 => ( ( ord_less_eq_int @ K3 @ ( F4 @ N ) )
% 2.86/3.15 => ? [I5: nat] :
% 2.86/3.15 ( ( ord_less_eq_nat @ I5 @ N )
% 2.86/3.15 & ( ( F4 @ I5 )
% 2.86/3.15 = K3 ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % nat_ivt_aux
% 2.86/3.15 thf(fact_5129_upto__aux__rec,axiom,
% 2.86/3.15 ( upto_aux
% 2.86/3.15 = ( ^ [I4: int,J2: int,Js: list_int] : ( if_list_int @ ( ord_less_int @ J2 @ I4 ) @ Js @ ( upto_aux @ I4 @ ( minus_minus_int @ J2 @ one_one_int ) @ ( cons_int @ J2 @ Js ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % upto_aux_rec
% 2.86/3.15 thf(fact_5130_eucl__rel__int_Osimps,axiom,
% 2.86/3.15 ( eucl_rel_int
% 2.86/3.15 = ( ^ [A12: int,A23: int,A32: product_prod_int_int] :
% 2.86/3.15 ( ? [K4: int] :
% 2.86/3.15 ( ( A12 = K4 )
% 2.86/3.15 & ( A23 = zero_zero_int )
% 2.86/3.15 & ( A32
% 2.86/3.15 = ( product_Pair_int_int @ zero_zero_int @ K4 ) ) )
% 2.86/3.15 | ? [L4: int,K4: int,Q8: int] :
% 2.86/3.15 ( ( A12 = K4 )
% 2.86/3.15 & ( A23 = L4 )
% 2.86/3.15 & ( A32
% 2.86/3.15 = ( product_Pair_int_int @ Q8 @ zero_zero_int ) )
% 2.86/3.15 & ( L4 != zero_zero_int )
% 2.86/3.15 & ( K4
% 2.86/3.15 = ( times_times_int @ Q8 @ L4 ) ) )
% 2.86/3.15 | ? [R4: int,L4: int,K4: int,Q8: int] :
% 2.86/3.15 ( ( A12 = K4 )
% 2.86/3.15 & ( A23 = L4 )
% 2.86/3.15 & ( A32
% 2.86/3.15 = ( product_Pair_int_int @ Q8 @ R4 ) )
% 2.86/3.15 & ( ( sgn_sgn_int @ R4 )
% 2.86/3.15 = ( sgn_sgn_int @ L4 ) )
% 2.86/3.15 & ( ord_less_int @ ( abs_abs_int @ R4 ) @ ( abs_abs_int @ L4 ) )
% 2.86/3.15 & ( K4
% 2.86/3.15 = ( plus_plus_int @ ( times_times_int @ Q8 @ L4 ) @ R4 ) ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % eucl_rel_int.simps
% 2.86/3.15 thf(fact_5131_eucl__rel__int_Ocases,axiom,
% 2.86/3.15 ! [A1: int,A22: int,A33: product_prod_int_int] :
% 2.86/3.15 ( ( eucl_rel_int @ A1 @ A22 @ A33 )
% 2.86/3.15 => ( ( ( A22 = zero_zero_int )
% 2.86/3.15 => ( A33
% 2.86/3.15 != ( product_Pair_int_int @ zero_zero_int @ A1 ) ) )
% 2.86/3.15 => ( ! [Q5: int] :
% 2.86/3.15 ( ( A33
% 2.86/3.15 = ( product_Pair_int_int @ Q5 @ zero_zero_int ) )
% 2.86/3.15 => ( ( A22 != zero_zero_int )
% 2.86/3.15 => ( A1
% 2.86/3.15 != ( times_times_int @ Q5 @ A22 ) ) ) )
% 2.86/3.15 => ~ ! [R6: int,Q5: int] :
% 2.86/3.15 ( ( A33
% 2.86/3.15 = ( product_Pair_int_int @ Q5 @ R6 ) )
% 2.86/3.15 => ( ( ( sgn_sgn_int @ R6 )
% 2.86/3.15 = ( sgn_sgn_int @ A22 ) )
% 2.86/3.15 => ( ( ord_less_int @ ( abs_abs_int @ R6 ) @ ( abs_abs_int @ A22 ) )
% 2.86/3.15 => ( A1
% 2.86/3.15 != ( plus_plus_int @ ( times_times_int @ Q5 @ A22 ) @ R6 ) ) ) ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % eucl_rel_int.cases
% 2.86/3.15 thf(fact_5132_eucl__rel__int__remainderI,axiom,
% 2.86/3.15 ! [R2: int,L: int,K3: int,Q6: int] :
% 2.86/3.15 ( ( ( sgn_sgn_int @ R2 )
% 2.86/3.15 = ( sgn_sgn_int @ L ) )
% 2.86/3.15 => ( ( ord_less_int @ ( abs_abs_int @ R2 ) @ ( abs_abs_int @ L ) )
% 2.86/3.15 => ( ( K3
% 2.86/3.15 = ( plus_plus_int @ ( times_times_int @ Q6 @ L ) @ R2 ) )
% 2.86/3.15 => ( eucl_rel_int @ K3 @ L @ ( product_Pair_int_int @ Q6 @ R2 ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % eucl_rel_int_remainderI
% 2.86/3.15 thf(fact_5133_int__power__div__base,axiom,
% 2.86/3.15 ! [M2: nat,K3: int] :
% 2.86/3.15 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 2.86/3.15 => ( ( ord_less_int @ zero_zero_int @ K3 )
% 2.86/3.15 => ( ( divide_divide_int @ ( power_power_int @ K3 @ M2 ) @ K3 )
% 2.86/3.15 = ( power_power_int @ K3 @ ( minus_minus_nat @ M2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % int_power_div_base
% 2.86/3.15 thf(fact_5134_merge__true__star,axiom,
% 2.86/3.15 ( ( times_times_assn @ top_top_assn @ top_top_assn )
% 2.86/3.15 = top_top_assn ) ).
% 2.86/3.15
% 2.86/3.15 % merge_true_star
% 2.86/3.15 thf(fact_5135_assn__basic__inequalities_I1_J,axiom,
% 2.86/3.15 top_top_assn != one_one_assn ).
% 2.86/3.15
% 2.86/3.15 % assn_basic_inequalities(1)
% 2.86/3.15 thf(fact_5136_entt__true,axiom,
% 2.86/3.15 ! [A: assn] : ( entailst @ A @ top_top_assn ) ).
% 2.86/3.15
% 2.86/3.15 % entt_true
% 2.86/3.15 thf(fact_5137_assn__basic__inequalities_I5_J,axiom,
% 2.86/3.15 top_top_assn != bot_bot_assn ).
% 2.86/3.15
% 2.86/3.15 % assn_basic_inequalities(5)
% 2.86/3.15 thf(fact_5138_entt__star__true__simp_I1_J,axiom,
% 2.86/3.15 ! [A: assn,B: assn] :
% 2.86/3.15 ( ( entailst @ A @ ( times_times_assn @ B @ top_top_assn ) )
% 2.86/3.15 = ( entailst @ A @ B ) ) ).
% 2.86/3.15
% 2.86/3.15 % entt_star_true_simp(1)
% 2.86/3.15 thf(fact_5139_entt__star__true__simp_I2_J,axiom,
% 2.86/3.15 ! [A: assn,B: assn] :
% 2.86/3.15 ( ( entailst @ ( times_times_assn @ A @ top_top_assn ) @ B )
% 2.86/3.15 = ( entailst @ A @ B ) ) ).
% 2.86/3.15
% 2.86/3.15 % entt_star_true_simp(2)
% 2.86/3.15 thf(fact_5140_merge__true__star__ctx,axiom,
% 2.86/3.15 ! [P: assn] :
% 2.86/3.15 ( ( times_times_assn @ top_top_assn @ ( times_times_assn @ top_top_assn @ P ) )
% 2.86/3.15 = ( times_times_assn @ top_top_assn @ P ) ) ).
% 2.86/3.15
% 2.86/3.15 % merge_true_star_ctx
% 2.86/3.15 thf(fact_5141_ent__true,axiom,
% 2.86/3.15 ! [P: assn] : ( entails @ P @ top_top_assn ) ).
% 2.86/3.15
% 2.86/3.15 % ent_true
% 2.86/3.15 thf(fact_5142_norm__assertion__simps_I12_J,axiom,
% 2.86/3.15 ! [X: assn] :
% 2.86/3.15 ( ( sup_sup_assn @ X @ top_top_assn )
% 2.86/3.15 = top_top_assn ) ).
% 2.86/3.15
% 2.86/3.15 % norm_assertion_simps(12)
% 2.86/3.15 thf(fact_5143_norm__assertion__simps_I11_J,axiom,
% 2.86/3.15 ! [X: assn] :
% 2.86/3.15 ( ( sup_sup_assn @ top_top_assn @ X )
% 2.86/3.15 = top_top_assn ) ).
% 2.86/3.15
% 2.86/3.15 % norm_assertion_simps(11)
% 2.86/3.15 thf(fact_5144_norm__assertion__simps_I4_J,axiom,
% 2.86/3.15 ! [X: assn] :
% 2.86/3.15 ( ( inf_inf_assn @ X @ top_top_assn )
% 2.86/3.15 = X ) ).
% 2.86/3.15
% 2.86/3.15 % norm_assertion_simps(4)
% 2.86/3.15 thf(fact_5145_norm__assertion__simps_I3_J,axiom,
% 2.86/3.15 ! [X: assn] :
% 2.86/3.15 ( ( inf_inf_assn @ top_top_assn @ X )
% 2.86/3.15 = X ) ).
% 2.86/3.15
% 2.86/3.15 % norm_assertion_simps(3)
% 2.86/3.15 thf(fact_5146_fact__less__mono__nat,axiom,
% 2.86/3.15 ! [M2: nat,N: nat] :
% 2.86/3.15 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 2.86/3.15 => ( ( ord_less_nat @ M2 @ N )
% 2.86/3.15 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M2 ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % fact_less_mono_nat
% 2.86/3.15 thf(fact_5147_mod__star__trueI,axiom,
% 2.86/3.15 ! [P: assn,H2: produc3658429121746597890et_nat] :
% 2.86/3.15 ( ( rep_assn @ P @ H2 )
% 2.86/3.15 => ( rep_assn @ ( times_times_assn @ P @ top_top_assn ) @ H2 ) ) ).
% 2.86/3.15
% 2.86/3.15 % mod_star_trueI
% 2.86/3.15 thf(fact_5148_mod__star__trueE,axiom,
% 2.86/3.15 ! [P: assn,H2: produc3658429121746597890et_nat] :
% 2.86/3.15 ( ( rep_assn @ ( times_times_assn @ P @ top_top_assn ) @ H2 )
% 2.86/3.15 => ~ ! [H5: produc3658429121746597890et_nat] :
% 2.86/3.15 ~ ( rep_assn @ P @ H5 ) ) ).
% 2.86/3.15
% 2.86/3.15 % mod_star_trueE
% 2.86/3.15 thf(fact_5149_ent__star__mono__true,axiom,
% 2.86/3.15 ! [A: assn,A6: assn,B: assn,B9: assn] :
% 2.86/3.15 ( ( entails @ A @ ( times_times_assn @ A6 @ top_top_assn ) )
% 2.86/3.15 => ( ( entails @ B @ ( times_times_assn @ B9 @ top_top_assn ) )
% 2.86/3.15 => ( entails @ ( times_times_assn @ ( times_times_assn @ A @ B ) @ top_top_assn ) @ ( times_times_assn @ ( times_times_assn @ A6 @ B9 ) @ top_top_assn ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % ent_star_mono_true
% 2.86/3.15 thf(fact_5150_ent__refl__true,axiom,
% 2.86/3.15 ! [A: assn] : ( entails @ A @ ( times_times_assn @ A @ top_top_assn ) ) ).
% 2.86/3.15
% 2.86/3.15 % ent_refl_true
% 2.86/3.15 thf(fact_5151_ent__true__drop_I1_J,axiom,
% 2.86/3.15 ! [P: assn,Q: assn,R: assn] :
% 2.86/3.15 ( ( entails @ P @ ( times_times_assn @ Q @ top_top_assn ) )
% 2.86/3.15 => ( entails @ ( times_times_assn @ P @ R ) @ ( times_times_assn @ Q @ top_top_assn ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % ent_true_drop(1)
% 2.86/3.15 thf(fact_5152_ent__true__drop_I2_J,axiom,
% 2.86/3.15 ! [P: assn,Q: assn] :
% 2.86/3.15 ( ( entails @ P @ Q )
% 2.86/3.15 => ( entails @ P @ ( times_times_assn @ Q @ top_top_assn ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % ent_true_drop(2)
% 2.86/3.15 thf(fact_5153_div__int__unique,axiom,
% 2.86/3.15 ! [K3: int,L: int,Q6: int,R2: int] :
% 2.86/3.15 ( ( eucl_rel_int @ K3 @ L @ ( product_Pair_int_int @ Q6 @ R2 ) )
% 2.86/3.15 => ( ( divide_divide_int @ K3 @ L )
% 2.86/3.15 = Q6 ) ) ).
% 2.86/3.15
% 2.86/3.15 % div_int_unique
% 2.86/3.15 thf(fact_5154_mod__h__bot__iff_I2_J,axiom,
% 2.86/3.15 ! [H2: heap_e7401611519738050253t_unit] : ( rep_assn @ top_top_assn @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) ) ).
% 2.86/3.15
% 2.86/3.15 % mod_h_bot_iff(2)
% 2.86/3.15 thf(fact_5155_entt__def__true,axiom,
% 2.86/3.15 ( entailst
% 2.86/3.15 = ( ^ [P2: assn,Q2: assn] : ( entails @ ( times_times_assn @ P2 @ top_top_assn ) @ ( times_times_assn @ Q2 @ top_top_assn ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % entt_def_true
% 2.86/3.15 thf(fact_5156_entailst__def,axiom,
% 2.86/3.15 ( entailst
% 2.86/3.15 = ( ^ [A5: assn,B7: assn] : ( entails @ A5 @ ( times_times_assn @ B7 @ top_top_assn ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % entailst_def
% 2.86/3.15 thf(fact_5157_enttI__true,axiom,
% 2.86/3.15 ! [P: assn,Q: assn] :
% 2.86/3.15 ( ( entails @ ( times_times_assn @ P @ top_top_assn ) @ ( times_times_assn @ Q @ top_top_assn ) )
% 2.86/3.15 => ( entailst @ P @ Q ) ) ).
% 2.86/3.15
% 2.86/3.15 % enttI_true
% 2.86/3.15 thf(fact_5158_enttI,axiom,
% 2.86/3.15 ! [A: assn,B: assn] :
% 2.86/3.15 ( ( entails @ A @ ( times_times_assn @ B @ top_top_assn ) )
% 2.86/3.15 => ( entailst @ A @ B ) ) ).
% 2.86/3.15
% 2.86/3.15 % enttI
% 2.86/3.15 thf(fact_5159_enttD,axiom,
% 2.86/3.15 ! [A: assn,B: assn] :
% 2.86/3.15 ( ( entailst @ A @ B )
% 2.86/3.15 => ( entails @ A @ ( times_times_assn @ B @ top_top_assn ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % enttD
% 2.86/3.15 thf(fact_5160_entails__solve__init_I1_J,axiom,
% 2.86/3.15 ! [P: assn,Q: assn] :
% 2.86/3.15 ( ( fI_QUERY @ P @ Q @ top_top_assn )
% 2.86/3.15 => ( entails @ P @ ( times_times_assn @ Q @ top_top_assn ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % entails_solve_init(1)
% 2.86/3.15 thf(fact_5161_div__less,axiom,
% 2.86/3.15 ! [M2: nat,N: nat] :
% 2.86/3.15 ( ( ord_less_nat @ M2 @ N )
% 2.86/3.15 => ( ( divide_divide_nat @ M2 @ N )
% 2.86/3.15 = zero_zero_nat ) ) ).
% 2.86/3.15
% 2.86/3.15 % div_less
% 2.86/3.15 thf(fact_5162_div__mult__self__is__m,axiom,
% 2.86/3.15 ! [N: nat,M2: nat] :
% 2.86/3.15 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.15 => ( ( divide_divide_nat @ ( times_times_nat @ M2 @ N ) @ N )
% 2.86/3.15 = M2 ) ) ).
% 2.86/3.15
% 2.86/3.15 % div_mult_self_is_m
% 2.86/3.15 thf(fact_5163_div__mult__self1__is__m,axiom,
% 2.86/3.15 ! [N: nat,M2: nat] :
% 2.86/3.15 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.15 => ( ( divide_divide_nat @ ( times_times_nat @ N @ M2 ) @ N )
% 2.86/3.15 = M2 ) ) ).
% 2.86/3.15
% 2.86/3.15 % div_mult_self1_is_m
% 2.86/3.15 thf(fact_5164_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 2.86/3.15 ! [M2: nat,N: nat] :
% 2.86/3.15 ( ( ( divide_divide_nat @ M2 @ N )
% 2.86/3.15 = zero_zero_nat )
% 2.86/3.15 = ( ( ord_less_nat @ M2 @ N )
% 2.86/3.15 | ( N = zero_zero_nat ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % Euclidean_Division.div_eq_0_iff
% 2.86/3.15 thf(fact_5165_less__mult__imp__div__less,axiom,
% 2.86/3.15 ! [M2: nat,I: nat,N: nat] :
% 2.86/3.15 ( ( ord_less_nat @ M2 @ ( times_times_nat @ I @ N ) )
% 2.86/3.15 => ( ord_less_nat @ ( divide_divide_nat @ M2 @ N ) @ I ) ) ).
% 2.86/3.15
% 2.86/3.15 % less_mult_imp_div_less
% 2.86/3.15 thf(fact_5166_div__greater__zero__iff,axiom,
% 2.86/3.15 ! [M2: nat,N: nat] :
% 2.86/3.15 ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M2 @ N ) )
% 2.86/3.15 = ( ( ord_less_eq_nat @ N @ M2 )
% 2.86/3.15 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % div_greater_zero_iff
% 2.86/3.15 thf(fact_5167_div__le__mono2,axiom,
% 2.86/3.15 ! [M2: nat,N: nat,K3: nat] :
% 2.86/3.15 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 2.86/3.15 => ( ( ord_less_eq_nat @ M2 @ N )
% 2.86/3.15 => ( ord_less_eq_nat @ ( divide_divide_nat @ K3 @ N ) @ ( divide_divide_nat @ K3 @ M2 ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % div_le_mono2
% 2.86/3.15 thf(fact_5168_div__less__iff__less__mult,axiom,
% 2.86/3.15 ! [Q6: nat,M2: nat,N: nat] :
% 2.86/3.15 ( ( ord_less_nat @ zero_zero_nat @ Q6 )
% 2.86/3.15 => ( ( ord_less_nat @ ( divide_divide_nat @ M2 @ Q6 ) @ N )
% 2.86/3.15 = ( ord_less_nat @ M2 @ ( times_times_nat @ N @ Q6 ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % div_less_iff_less_mult
% 2.86/3.15 thf(fact_5169_div__eq__dividend__iff,axiom,
% 2.86/3.15 ! [M2: nat,N: nat] :
% 2.86/3.15 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 2.86/3.15 => ( ( ( divide_divide_nat @ M2 @ N )
% 2.86/3.15 = M2 )
% 2.86/3.15 = ( N = one_one_nat ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % div_eq_dividend_iff
% 2.86/3.15 thf(fact_5170_div__less__dividend,axiom,
% 2.86/3.15 ! [N: nat,M2: nat] :
% 2.86/3.15 ( ( ord_less_nat @ one_one_nat @ N )
% 2.86/3.15 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 2.86/3.15 => ( ord_less_nat @ ( divide_divide_nat @ M2 @ N ) @ M2 ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % div_less_dividend
% 2.86/3.15 thf(fact_5171_div__if,axiom,
% 2.86/3.15 ( divide_divide_nat
% 2.86/3.15 = ( ^ [M: nat,N2: nat] :
% 2.86/3.15 ( if_nat
% 2.86/3.15 @ ( ( ord_less_nat @ M @ N2 )
% 2.86/3.15 | ( N2 = zero_zero_nat ) )
% 2.86/3.15 @ zero_zero_nat
% 2.86/3.15 @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % div_if
% 2.86/3.15 thf(fact_5172_less__eq__div__iff__mult__less__eq,axiom,
% 2.86/3.15 ! [Q6: nat,M2: nat,N: nat] :
% 2.86/3.15 ( ( ord_less_nat @ zero_zero_nat @ Q6 )
% 2.86/3.15 => ( ( ord_less_eq_nat @ M2 @ ( divide_divide_nat @ N @ Q6 ) )
% 2.86/3.15 = ( ord_less_eq_nat @ ( times_times_nat @ M2 @ Q6 ) @ N ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % less_eq_div_iff_mult_less_eq
% 2.86/3.15 thf(fact_5173_div__nat__eqI,axiom,
% 2.86/3.15 ! [N: nat,Q6: nat,M2: nat] :
% 2.86/3.15 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q6 ) @ M2 )
% 2.86/3.15 => ( ( ord_less_nat @ M2 @ ( times_times_nat @ N @ ( suc @ Q6 ) ) )
% 2.86/3.15 => ( ( divide_divide_nat @ M2 @ N )
% 2.86/3.15 = Q6 ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % div_nat_eqI
% 2.86/3.15 thf(fact_5174_split__div,axiom,
% 2.86/3.15 ! [P: nat > $o,M2: nat,N: nat] :
% 2.86/3.15 ( ( P @ ( divide_divide_nat @ M2 @ N ) )
% 2.86/3.15 = ( ( ( N = zero_zero_nat )
% 2.86/3.15 => ( P @ zero_zero_nat ) )
% 2.86/3.15 & ( ( N != zero_zero_nat )
% 2.86/3.15 => ! [I4: nat,J2: nat] :
% 2.86/3.15 ( ( ord_less_nat @ J2 @ N )
% 2.86/3.15 => ( ( M2
% 2.86/3.15 = ( plus_plus_nat @ ( times_times_nat @ N @ I4 ) @ J2 ) )
% 2.86/3.15 => ( P @ I4 ) ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % split_div
% 2.86/3.15 thf(fact_5175_dividend__less__div__times,axiom,
% 2.86/3.15 ! [N: nat,M2: nat] :
% 2.86/3.15 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.15 => ( ord_less_nat @ M2 @ ( plus_plus_nat @ N @ ( times_times_nat @ ( divide_divide_nat @ M2 @ N ) @ N ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % dividend_less_div_times
% 2.86/3.15 thf(fact_5176_dividend__less__times__div,axiom,
% 2.86/3.15 ! [N: nat,M2: nat] :
% 2.86/3.15 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.15 => ( ord_less_nat @ M2 @ ( plus_plus_nat @ N @ ( times_times_nat @ N @ ( divide_divide_nat @ M2 @ N ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % dividend_less_times_div
% 2.86/3.15 thf(fact_5177_nat__mult__div__cancel1,axiom,
% 2.86/3.15 ! [K3: nat,M2: nat,N: nat] :
% 2.86/3.15 ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 2.86/3.15 => ( ( divide_divide_nat @ ( times_times_nat @ K3 @ M2 ) @ ( times_times_nat @ K3 @ N ) )
% 2.86/3.15 = ( divide_divide_nat @ M2 @ N ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % nat_mult_div_cancel1
% 2.86/3.15 thf(fact_5178_le__div__geq,axiom,
% 2.86/3.15 ! [N: nat,M2: nat] :
% 2.86/3.15 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.15 => ( ( ord_less_eq_nat @ N @ M2 )
% 2.86/3.15 => ( ( divide_divide_nat @ M2 @ N )
% 2.86/3.15 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M2 @ N ) @ N ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % le_div_geq
% 2.86/3.15 thf(fact_5179_split__div_H,axiom,
% 2.86/3.15 ! [P: nat > $o,M2: nat,N: nat] :
% 2.86/3.15 ( ( P @ ( divide_divide_nat @ M2 @ N ) )
% 2.86/3.15 = ( ( ( N = zero_zero_nat )
% 2.86/3.15 & ( P @ zero_zero_nat ) )
% 2.86/3.15 | ? [Q8: nat] :
% 2.86/3.15 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q8 ) @ M2 )
% 2.86/3.15 & ( ord_less_nat @ M2 @ ( times_times_nat @ N @ ( suc @ Q8 ) ) )
% 2.86/3.15 & ( P @ Q8 ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % split_div'
% 2.86/3.15 thf(fact_5180_div__geq,axiom,
% 2.86/3.15 ! [N: nat,M2: nat] :
% 2.86/3.15 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.15 => ( ~ ( ord_less_nat @ M2 @ N )
% 2.86/3.15 => ( ( divide_divide_nat @ M2 @ N )
% 2.86/3.15 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M2 @ N ) @ N ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % div_geq
% 2.86/3.15 thf(fact_5181_mod__less,axiom,
% 2.86/3.15 ! [M2: nat,N: nat] :
% 2.86/3.15 ( ( ord_less_nat @ M2 @ N )
% 2.86/3.15 => ( ( modulo_modulo_nat @ M2 @ N )
% 2.86/3.15 = M2 ) ) ).
% 2.86/3.15
% 2.86/3.15 % mod_less
% 2.86/3.15 thf(fact_5182_mod__less__divisor,axiom,
% 2.86/3.15 ! [N: nat,M2: nat] :
% 2.86/3.15 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.15 => ( ord_less_nat @ ( modulo_modulo_nat @ M2 @ N ) @ N ) ) ).
% 2.86/3.15
% 2.86/3.15 % mod_less_divisor
% 2.86/3.15 thf(fact_5183_div__less__mono,axiom,
% 2.86/3.15 ! [A: nat,B: nat,N: nat] :
% 2.86/3.15 ( ( ord_less_nat @ A @ B )
% 2.86/3.15 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.15 => ( ( ( modulo_modulo_nat @ A @ N )
% 2.86/3.15 = zero_zero_nat )
% 2.86/3.15 => ( ( ( modulo_modulo_nat @ B @ N )
% 2.86/3.15 = zero_zero_nat )
% 2.86/3.15 => ( ord_less_nat @ ( divide_divide_nat @ A @ N ) @ ( divide_divide_nat @ B @ N ) ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % div_less_mono
% 2.86/3.15 thf(fact_5184_mod__induct,axiom,
% 2.86/3.15 ! [P: nat > $o,N: nat,P6: nat,M2: nat] :
% 2.86/3.15 ( ( P @ N )
% 2.86/3.15 => ( ( ord_less_nat @ N @ P6 )
% 2.86/3.15 => ( ( ord_less_nat @ M2 @ P6 )
% 2.86/3.15 => ( ! [N5: nat] :
% 2.86/3.15 ( ( ord_less_nat @ N5 @ P6 )
% 2.86/3.15 => ( ( P @ N5 )
% 2.86/3.15 => ( P @ ( modulo_modulo_nat @ ( suc @ N5 ) @ P6 ) ) ) )
% 2.86/3.15 => ( P @ M2 ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % mod_induct
% 2.86/3.15 thf(fact_5185_mod__geq,axiom,
% 2.86/3.15 ! [M2: nat,N: nat] :
% 2.86/3.15 ( ~ ( ord_less_nat @ M2 @ N )
% 2.86/3.15 => ( ( modulo_modulo_nat @ M2 @ N )
% 2.86/3.15 = ( modulo_modulo_nat @ ( minus_minus_nat @ M2 @ N ) @ N ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % mod_geq
% 2.86/3.15 thf(fact_5186_mod__if,axiom,
% 2.86/3.15 ( modulo_modulo_nat
% 2.86/3.15 = ( ^ [M: nat,N2: nat] : ( if_nat @ ( ord_less_nat @ M @ N2 ) @ M @ ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % mod_if
% 2.86/3.15 thf(fact_5187_mod__le__divisor,axiom,
% 2.86/3.15 ! [N: nat,M2: nat] :
% 2.86/3.15 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.15 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M2 @ N ) @ N ) ) ).
% 2.86/3.15
% 2.86/3.15 % mod_le_divisor
% 2.86/3.15 thf(fact_5188_split__mod,axiom,
% 2.86/3.15 ! [P: nat > $o,M2: nat,N: nat] :
% 2.86/3.15 ( ( P @ ( modulo_modulo_nat @ M2 @ N ) )
% 2.86/3.15 = ( ( ( N = zero_zero_nat )
% 2.86/3.15 => ( P @ M2 ) )
% 2.86/3.15 & ( ( N != zero_zero_nat )
% 2.86/3.15 => ! [I4: nat,J2: nat] :
% 2.86/3.15 ( ( ord_less_nat @ J2 @ N )
% 2.86/3.15 => ( ( M2
% 2.86/3.15 = ( plus_plus_nat @ ( times_times_nat @ N @ I4 ) @ J2 ) )
% 2.86/3.15 => ( P @ J2 ) ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % split_mod
% 2.86/3.15 thf(fact_5189_verit__le__mono__div,axiom,
% 2.86/3.15 ! [A: nat,B: nat,N: nat] :
% 2.86/3.15 ( ( ord_less_nat @ A @ B )
% 2.86/3.15 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.15 => ( ord_less_eq_nat
% 2.86/3.15 @ ( plus_plus_nat @ ( divide_divide_nat @ A @ N )
% 2.86/3.15 @ ( if_nat
% 2.86/3.15 @ ( ( modulo_modulo_nat @ B @ N )
% 2.86/3.15 = zero_zero_nat )
% 2.86/3.15 @ one_one_nat
% 2.86/3.15 @ zero_zero_nat ) )
% 2.86/3.15 @ ( divide_divide_nat @ B @ N ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % verit_le_mono_div
% 2.86/3.15 thf(fact_5190_Suc__times__mod__eq,axiom,
% 2.86/3.15 ! [M2: nat,N: nat] :
% 2.86/3.15 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M2 )
% 2.86/3.15 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M2 @ N ) ) @ M2 )
% 2.86/3.15 = one_one_nat ) ) ).
% 2.86/3.15
% 2.86/3.15 % Suc_times_mod_eq
% 2.86/3.15 thf(fact_5191_gcd__nat__induct,axiom,
% 2.86/3.15 ! [P: nat > nat > $o,M2: nat,N: nat] :
% 2.86/3.15 ( ! [M6: nat] : ( P @ M6 @ zero_zero_nat )
% 2.86/3.15 => ( ! [M6: nat,N5: nat] :
% 2.86/3.15 ( ( ord_less_nat @ zero_zero_nat @ N5 )
% 2.86/3.15 => ( ( P @ N5 @ ( modulo_modulo_nat @ M6 @ N5 ) )
% 2.86/3.15 => ( P @ M6 @ N5 ) ) )
% 2.86/3.15 => ( P @ M2 @ N ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % gcd_nat_induct
% 2.86/3.15 thf(fact_5192_mod__int__unique,axiom,
% 2.86/3.15 ! [K3: int,L: int,Q6: int,R2: int] :
% 2.86/3.15 ( ( eucl_rel_int @ K3 @ L @ ( product_Pair_int_int @ Q6 @ R2 ) )
% 2.86/3.15 => ( ( modulo_modulo_int @ K3 @ L )
% 2.86/3.15 = R2 ) ) ).
% 2.86/3.15
% 2.86/3.15 % mod_int_unique
% 2.86/3.15 thf(fact_5193_eucl__rel__int,axiom,
% 2.86/3.15 ! [K3: int,L: int] : ( eucl_rel_int @ K3 @ L @ ( product_Pair_int_int @ ( divide_divide_int @ K3 @ L ) @ ( modulo_modulo_int @ K3 @ L ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % eucl_rel_int
% 2.86/3.15 thf(fact_5194_bezw__0,axiom,
% 2.86/3.15 ! [X: nat] :
% 2.86/3.15 ( ( bezw @ X @ zero_zero_nat )
% 2.86/3.15 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) ).
% 2.86/3.15
% 2.86/3.15 % bezw_0
% 2.86/3.15 thf(fact_5195_minus__assn__def,axiom,
% 2.86/3.15 ( minus_minus_assn
% 2.86/3.15 = ( ^ [A3: assn,B3: assn] : ( inf_inf_assn @ A3 @ ( uminus_uminus_assn @ B3 ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % minus_assn_def
% 2.86/3.15 thf(fact_5196_int__cases4,axiom,
% 2.86/3.15 ! [M2: int] :
% 2.86/3.15 ( ! [N5: nat] :
% 2.86/3.15 ( M2
% 2.86/3.15 != ( semiri1314217659103216013at_int @ N5 ) )
% 2.86/3.15 => ~ ! [N5: nat] :
% 2.86/3.15 ( ( ord_less_nat @ zero_zero_nat @ N5 )
% 2.86/3.15 => ( M2
% 2.86/3.15 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N5 ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % int_cases4
% 2.86/3.15 thf(fact_5197_int__cases3,axiom,
% 2.86/3.15 ! [K3: int] :
% 2.86/3.15 ( ( K3 != zero_zero_int )
% 2.86/3.15 => ( ! [N5: nat] :
% 2.86/3.15 ( ( K3
% 2.86/3.15 = ( semiri1314217659103216013at_int @ N5 ) )
% 2.86/3.15 => ~ ( ord_less_nat @ zero_zero_nat @ N5 ) )
% 2.86/3.15 => ~ ! [N5: nat] :
% 2.86/3.15 ( ( K3
% 2.86/3.15 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N5 ) ) )
% 2.86/3.15 => ~ ( ord_less_nat @ zero_zero_nat @ N5 ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % int_cases3
% 2.86/3.15 thf(fact_5198_neg__int__cases,axiom,
% 2.86/3.15 ! [K3: int] :
% 2.86/3.15 ( ( ord_less_int @ K3 @ zero_zero_int )
% 2.86/3.15 => ~ ! [N5: nat] :
% 2.86/3.15 ( ( K3
% 2.86/3.15 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N5 ) ) )
% 2.86/3.15 => ~ ( ord_less_nat @ zero_zero_nat @ N5 ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % neg_int_cases
% 2.86/3.15 thf(fact_5199_zminus1__lemma,axiom,
% 2.86/3.15 ! [A2: int,B2: int,Q6: int,R2: int] :
% 2.86/3.15 ( ( eucl_rel_int @ A2 @ B2 @ ( product_Pair_int_int @ Q6 @ R2 ) )
% 2.86/3.15 => ( ( B2 != zero_zero_int )
% 2.86/3.15 => ( eucl_rel_int @ ( uminus_uminus_int @ A2 ) @ B2 @ ( product_Pair_int_int @ ( if_int @ ( R2 = zero_zero_int ) @ ( uminus_uminus_int @ Q6 ) @ ( minus_minus_int @ ( uminus_uminus_int @ Q6 ) @ one_one_int ) ) @ ( if_int @ ( R2 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ B2 @ R2 ) ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % zminus1_lemma
% 2.86/3.15 thf(fact_5200_entails__solve__finalize_I1_J,axiom,
% 2.86/3.15 ! [M5: list_P8527749157015355191n_assn,P: assn] : ( fI_RESULT @ M5 @ P @ one_one_assn @ top_top_assn ) ).
% 2.86/3.15
% 2.86/3.15 % entails_solve_finalize(1)
% 2.86/3.15 thf(fact_5201_frame__inference__finalize,axiom,
% 2.86/3.15 ! [M5: list_P8527749157015355191n_assn,F: assn] : ( fI_RESULT @ M5 @ F @ one_one_assn @ F ) ).
% 2.86/3.15
% 2.86/3.15 % frame_inference_finalize
% 2.86/3.15 thf(fact_5202_entails__solve__finalize_I2_J,axiom,
% 2.86/3.15 ! [M5: list_P8527749157015355191n_assn] : ( fI_RESULT @ M5 @ one_one_assn @ one_one_assn @ one_one_assn ) ).
% 2.86/3.15
% 2.86/3.15 % entails_solve_finalize(2)
% 2.86/3.15 thf(fact_5203_Sup__nat__empty,axiom,
% 2.86/3.15 ( ( complete_Sup_Sup_nat @ bot_bot_set_nat )
% 2.86/3.15 = zero_zero_nat ) ).
% 2.86/3.15
% 2.86/3.15 % Sup_nat_empty
% 2.86/3.15 thf(fact_5204_upto__rec__numeral_I2_J,axiom,
% 2.86/3.15 ! [M2: num,N: num] :
% 2.86/3.15 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 2.86/3.15 => ( ( upto @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 2.86/3.15 = ( cons_int @ ( numeral_numeral_int @ M2 ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M2 ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 2.86/3.15 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 2.86/3.15 => ( ( upto @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 2.86/3.15 = nil_int ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % upto_rec_numeral(2)
% 2.86/3.15 thf(fact_5205_upto__empty,axiom,
% 2.86/3.15 ! [J: int,I: int] :
% 2.86/3.15 ( ( ord_less_int @ J @ I )
% 2.86/3.15 => ( ( upto @ I @ J )
% 2.86/3.15 = nil_int ) ) ).
% 2.86/3.15
% 2.86/3.15 % upto_empty
% 2.86/3.15 thf(fact_5206_upto__Nil2,axiom,
% 2.86/3.15 ! [I: int,J: int] :
% 2.86/3.15 ( ( nil_int
% 2.86/3.15 = ( upto @ I @ J ) )
% 2.86/3.15 = ( ord_less_int @ J @ I ) ) ).
% 2.86/3.15
% 2.86/3.15 % upto_Nil2
% 2.86/3.15 thf(fact_5207_upto__Nil,axiom,
% 2.86/3.15 ! [I: int,J: int] :
% 2.86/3.15 ( ( ( upto @ I @ J )
% 2.86/3.15 = nil_int )
% 2.86/3.15 = ( ord_less_int @ J @ I ) ) ).
% 2.86/3.15
% 2.86/3.15 % upto_Nil
% 2.86/3.15 thf(fact_5208_upto__single,axiom,
% 2.86/3.15 ! [I: int] :
% 2.86/3.15 ( ( upto @ I @ I )
% 2.86/3.15 = ( cons_int @ I @ nil_int ) ) ).
% 2.86/3.15
% 2.86/3.15 % upto_single
% 2.86/3.15 thf(fact_5209_nth__upto,axiom,
% 2.86/3.15 ! [I: int,K3: nat,J: int] :
% 2.86/3.15 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K3 ) ) @ J )
% 2.86/3.15 => ( ( nth_int @ ( upto @ I @ J ) @ K3 )
% 2.86/3.15 = ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K3 ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % nth_upto
% 2.86/3.15 thf(fact_5210_upto__rec__numeral_I1_J,axiom,
% 2.86/3.15 ! [M2: num,N: num] :
% 2.86/3.15 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) )
% 2.86/3.15 => ( ( upto @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) )
% 2.86/3.15 = ( cons_int @ ( numeral_numeral_int @ M2 ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M2 ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 2.86/3.15 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) )
% 2.86/3.15 => ( ( upto @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) )
% 2.86/3.15 = nil_int ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % upto_rec_numeral(1)
% 2.86/3.15 thf(fact_5211_upto__rec__numeral_I4_J,axiom,
% 2.86/3.15 ! [M2: num,N: num] :
% 2.86/3.15 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 2.86/3.15 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 2.86/3.15 = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 2.86/3.15 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 2.86/3.15 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 2.86/3.15 = nil_int ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % upto_rec_numeral(4)
% 2.86/3.15 thf(fact_5212_upto__rec__numeral_I3_J,axiom,
% 2.86/3.15 ! [M2: num,N: num] :
% 2.86/3.15 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) )
% 2.86/3.15 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) )
% 2.86/3.15 = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 2.86/3.15 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) )
% 2.86/3.15 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) )
% 2.86/3.15 = nil_int ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % upto_rec_numeral(3)
% 2.86/3.15 thf(fact_5213_distinct__upto,axiom,
% 2.86/3.15 ! [I: int,J: int] : ( distinct_int @ ( upto @ I @ J ) ) ).
% 2.86/3.15
% 2.86/3.15 % distinct_upto
% 2.86/3.15 thf(fact_5214_sorted__upto,axiom,
% 2.86/3.15 ! [M2: int,N: int] : ( sorted_wrt_int @ ord_less_eq_int @ ( upto @ M2 @ N ) ) ).
% 2.86/3.15
% 2.86/3.15 % sorted_upto
% 2.86/3.15 thf(fact_5215_sorted__wrt__upto,axiom,
% 2.86/3.15 ! [I: int,J: int] : ( sorted_wrt_int @ ord_less_int @ ( upto @ I @ J ) ) ).
% 2.86/3.15
% 2.86/3.15 % sorted_wrt_upto
% 2.86/3.15 thf(fact_5216_upto__aux__def,axiom,
% 2.86/3.15 ( upto_aux
% 2.86/3.15 = ( ^ [I4: int,J2: int] : ( append_int @ ( upto @ I4 @ J2 ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % upto_aux_def
% 2.86/3.15 thf(fact_5217_upto__code,axiom,
% 2.86/3.15 ( upto
% 2.86/3.15 = ( ^ [I4: int,J2: int] : ( upto_aux @ I4 @ J2 @ nil_int ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % upto_code
% 2.86/3.15 thf(fact_5218_upto__split2,axiom,
% 2.86/3.15 ! [I: int,J: int,K3: int] :
% 2.86/3.15 ( ( ord_less_eq_int @ I @ J )
% 2.86/3.15 => ( ( ord_less_eq_int @ J @ K3 )
% 2.86/3.15 => ( ( upto @ I @ K3 )
% 2.86/3.15 = ( append_int @ ( upto @ I @ J ) @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K3 ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % upto_split2
% 2.86/3.15 thf(fact_5219_upto__split1,axiom,
% 2.86/3.15 ! [I: int,J: int,K3: int] :
% 2.86/3.15 ( ( ord_less_eq_int @ I @ J )
% 2.86/3.15 => ( ( ord_less_eq_int @ J @ K3 )
% 2.86/3.15 => ( ( upto @ I @ K3 )
% 2.86/3.15 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( upto @ J @ K3 ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % upto_split1
% 2.86/3.15 thf(fact_5220_upto__rec1,axiom,
% 2.86/3.15 ! [I: int,J: int] :
% 2.86/3.15 ( ( ord_less_eq_int @ I @ J )
% 2.86/3.15 => ( ( upto @ I @ J )
% 2.86/3.15 = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % upto_rec1
% 2.86/3.15 thf(fact_5221_upto_Osimps,axiom,
% 2.86/3.15 ( upto
% 2.86/3.15 = ( ^ [I4: int,J2: int] : ( if_list_int @ ( ord_less_eq_int @ I4 @ J2 ) @ ( cons_int @ I4 @ ( upto @ ( plus_plus_int @ I4 @ one_one_int ) @ J2 ) ) @ nil_int ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % upto.simps
% 2.86/3.15 thf(fact_5222_upto_Oelims,axiom,
% 2.86/3.15 ! [X: int,Xa: int,Y: list_int] :
% 2.86/3.15 ( ( ( upto @ X @ Xa )
% 2.86/3.15 = Y )
% 2.86/3.15 => ( ( ( ord_less_eq_int @ X @ Xa )
% 2.86/3.15 => ( Y
% 2.86/3.15 = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa ) ) ) )
% 2.86/3.15 & ( ~ ( ord_less_eq_int @ X @ Xa )
% 2.86/3.15 => ( Y = nil_int ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % upto.elims
% 2.86/3.15 thf(fact_5223_upto__rec2,axiom,
% 2.86/3.15 ! [I: int,J: int] :
% 2.86/3.15 ( ( ord_less_eq_int @ I @ J )
% 2.86/3.15 => ( ( upto @ I @ J )
% 2.86/3.15 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ nil_int ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % upto_rec2
% 2.86/3.15 thf(fact_5224_upto__split3,axiom,
% 2.86/3.15 ! [I: int,J: int,K3: int] :
% 2.86/3.15 ( ( ord_less_eq_int @ I @ J )
% 2.86/3.15 => ( ( ord_less_eq_int @ J @ K3 )
% 2.86/3.15 => ( ( upto @ I @ K3 )
% 2.86/3.15 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K3 ) ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % upto_split3
% 2.86/3.15 thf(fact_5225_numeral__power__less__nat__cancel__iff,axiom,
% 2.86/3.15 ! [X: num,N: nat,A2: int] :
% 2.86/3.15 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) @ ( nat2 @ A2 ) )
% 2.86/3.15 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A2 ) ) ).
% 2.86/3.15
% 2.86/3.15 % numeral_power_less_nat_cancel_iff
% 2.86/3.15 thf(fact_5226_nat__less__numeral__power__cancel__iff,axiom,
% 2.86/3.15 ! [A2: int,X: num,N: nat] :
% 2.86/3.15 ( ( ord_less_nat @ ( nat2 @ A2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 2.86/3.15 = ( ord_less_int @ A2 @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % nat_less_numeral_power_cancel_iff
% 2.86/3.15 thf(fact_5227_zless__nat__conj,axiom,
% 2.86/3.15 ! [W: int,Z: int] :
% 2.86/3.15 ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 2.86/3.15 = ( ( ord_less_int @ zero_zero_int @ Z )
% 2.86/3.15 & ( ord_less_int @ W @ Z ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % zless_nat_conj
% 2.86/3.15 thf(fact_5228_zero__less__nat__eq,axiom,
% 2.86/3.15 ! [Z: int] :
% 2.86/3.15 ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z ) )
% 2.86/3.15 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 2.86/3.15
% 2.86/3.15 % zero_less_nat_eq
% 2.86/3.15 thf(fact_5229_length__upto,axiom,
% 2.86/3.15 ! [I: int,J: int] :
% 2.86/3.15 ( ( size_size_list_int @ ( upto @ I @ J ) )
% 2.86/3.15 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J @ I ) @ one_one_int ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % length_upto
% 2.86/3.15 thf(fact_5230_one__less__nat__eq,axiom,
% 2.86/3.15 ! [Z: int] :
% 2.86/3.15 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z ) )
% 2.86/3.15 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 2.86/3.15
% 2.86/3.15 % one_less_nat_eq
% 2.86/3.15 thf(fact_5231_nat__mono__iff,axiom,
% 2.86/3.15 ! [Z: int,W: int] :
% 2.86/3.15 ( ( ord_less_int @ zero_zero_int @ Z )
% 2.86/3.15 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 2.86/3.15 = ( ord_less_int @ W @ Z ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % nat_mono_iff
% 2.86/3.15 thf(fact_5232_zless__nat__eq__int__zless,axiom,
% 2.86/3.15 ! [M2: nat,Z: int] :
% 2.86/3.15 ( ( ord_less_nat @ M2 @ ( nat2 @ Z ) )
% 2.86/3.15 = ( ord_less_int @ ( semiri1314217659103216013at_int @ M2 ) @ Z ) ) ).
% 2.86/3.15
% 2.86/3.15 % zless_nat_eq_int_zless
% 2.86/3.15 thf(fact_5233_nat__less__eq__zless,axiom,
% 2.86/3.15 ! [W: int,Z: int] :
% 2.86/3.15 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 2.86/3.15 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 2.86/3.15 = ( ord_less_int @ W @ Z ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % nat_less_eq_zless
% 2.86/3.15 thf(fact_5234_nat__less__iff,axiom,
% 2.86/3.15 ! [W: int,M2: nat] :
% 2.86/3.15 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 2.86/3.15 => ( ( ord_less_nat @ ( nat2 @ W ) @ M2 )
% 2.86/3.15 = ( ord_less_int @ W @ ( semiri1314217659103216013at_int @ M2 ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % nat_less_iff
% 2.86/3.15 thf(fact_5235_neg__eucl__rel__int__mult__2,axiom,
% 2.86/3.15 ! [B2: int,A2: int,Q6: int,R2: int] :
% 2.86/3.15 ( ( ord_less_eq_int @ B2 @ zero_zero_int )
% 2.86/3.15 => ( ( eucl_rel_int @ ( plus_plus_int @ A2 @ one_one_int ) @ B2 @ ( product_Pair_int_int @ Q6 @ R2 ) )
% 2.86/3.15 => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) @ ( product_Pair_int_int @ Q6 @ ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R2 ) @ one_one_int ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % neg_eucl_rel_int_mult_2
% 2.86/3.15 thf(fact_5236_pos__eucl__rel__int__mult__2,axiom,
% 2.86/3.15 ! [B2: int,A2: int,Q6: int,R2: int] :
% 2.86/3.15 ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 2.86/3.15 => ( ( eucl_rel_int @ A2 @ B2 @ ( product_Pair_int_int @ Q6 @ R2 ) )
% 2.86/3.15 => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) @ ( product_Pair_int_int @ Q6 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R2 ) ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % pos_eucl_rel_int_mult_2
% 2.86/3.15 thf(fact_5237_mod2__gr__0,axiom,
% 2.86/3.15 ! [M2: nat] :
% 2.86/3.15 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 2.86/3.15 = ( ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.86/3.15 = one_one_nat ) ) ).
% 2.86/3.15
% 2.86/3.15 % mod2_gr_0
% 2.86/3.15 thf(fact_5238_less__exp,axiom,
% 2.86/3.15 ! [N: nat] : ( ord_less_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 2.86/3.15
% 2.86/3.15 % less_exp
% 2.86/3.15 thf(fact_5239_less__2__cases,axiom,
% 2.86/3.15 ! [N: nat] :
% 2.86/3.15 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.86/3.15 => ( ( N = zero_zero_nat )
% 2.86/3.15 | ( N
% 2.86/3.15 = ( suc @ zero_zero_nat ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % less_2_cases
% 2.86/3.15 thf(fact_5240_less__2__cases__iff,axiom,
% 2.86/3.15 ! [N: nat] :
% 2.86/3.15 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.86/3.15 = ( ( N = zero_zero_nat )
% 2.86/3.15 | ( N
% 2.86/3.15 = ( suc @ zero_zero_nat ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % less_2_cases_iff
% 2.86/3.15 thf(fact_5241_div__2__gt__zero,axiom,
% 2.86/3.15 ! [N: nat] :
% 2.86/3.15 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 2.86/3.15 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % div_2_gt_zero
% 2.86/3.15 thf(fact_5242_Suc__n__div__2__gt__zero,axiom,
% 2.86/3.15 ! [N: nat] :
% 2.86/3.15 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.15 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % Suc_n_div_2_gt_zero
% 2.86/3.15 thf(fact_5243_ex__power__ivl1,axiom,
% 2.86/3.15 ! [B2: nat,K3: nat] :
% 2.86/3.15 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 )
% 2.86/3.15 => ( ( ord_less_eq_nat @ one_one_nat @ K3 )
% 2.86/3.15 => ? [N5: nat] :
% 2.86/3.15 ( ( ord_less_eq_nat @ ( power_power_nat @ B2 @ N5 ) @ K3 )
% 2.86/3.15 & ( ord_less_nat @ K3 @ ( power_power_nat @ B2 @ ( plus_plus_nat @ N5 @ one_one_nat ) ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % ex_power_ivl1
% 2.86/3.15 thf(fact_5244_ex__power__ivl2,axiom,
% 2.86/3.15 ! [B2: nat,K3: nat] :
% 2.86/3.15 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 )
% 2.86/3.15 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K3 )
% 2.86/3.15 => ? [N5: nat] :
% 2.86/3.15 ( ( ord_less_nat @ ( power_power_nat @ B2 @ N5 ) @ K3 )
% 2.86/3.15 & ( ord_less_eq_nat @ K3 @ ( power_power_nat @ B2 @ ( plus_plus_nat @ N5 @ one_one_nat ) ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % ex_power_ivl2
% 2.86/3.15 thf(fact_5245_nat__bit__induct,axiom,
% 2.86/3.15 ! [P: nat > $o,N: nat] :
% 2.86/3.15 ( ( P @ zero_zero_nat )
% 2.86/3.15 => ( ! [N5: nat] :
% 2.86/3.15 ( ( P @ N5 )
% 2.86/3.15 => ( ( ord_less_nat @ zero_zero_nat @ N5 )
% 2.86/3.15 => ( P @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N5 ) ) ) )
% 2.86/3.15 => ( ! [N5: nat] :
% 2.86/3.15 ( ( P @ N5 )
% 2.86/3.15 => ( P @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N5 ) ) ) )
% 2.86/3.15 => ( P @ N ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % nat_bit_induct
% 2.86/3.15 thf(fact_5246_take__bit__of__Suc__0,axiom,
% 2.86/3.15 ! [N: nat] :
% 2.86/3.15 ( ( bit_se2925701944663578781it_nat @ N @ ( suc @ zero_zero_nat ) )
% 2.86/3.15 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % take_bit_of_Suc_0
% 2.86/3.15 thf(fact_5247_uminus__dvd__conv_I1_J,axiom,
% 2.86/3.15 ( dvd_dvd_int
% 2.86/3.15 = ( ^ [D5: int] : ( dvd_dvd_int @ ( uminus_uminus_int @ D5 ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % uminus_dvd_conv(1)
% 2.86/3.15 thf(fact_5248_uminus__dvd__conv_I2_J,axiom,
% 2.86/3.15 ( dvd_dvd_int
% 2.86/3.15 = ( ^ [D5: int,T2: int] : ( dvd_dvd_int @ D5 @ ( uminus_uminus_int @ T2 ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % uminus_dvd_conv(2)
% 2.86/3.15 thf(fact_5249_nat__dvd__not__less,axiom,
% 2.86/3.15 ! [M2: nat,N: nat] :
% 2.86/3.15 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 2.86/3.15 => ( ( ord_less_nat @ M2 @ N )
% 2.86/3.15 => ~ ( dvd_dvd_nat @ N @ M2 ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % nat_dvd_not_less
% 2.86/3.15 thf(fact_5250_dvd__pos__nat,axiom,
% 2.86/3.15 ! [N: nat,M2: nat] :
% 2.86/3.15 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.15 => ( ( dvd_dvd_nat @ M2 @ N )
% 2.86/3.15 => ( ord_less_nat @ zero_zero_nat @ M2 ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % dvd_pos_nat
% 2.86/3.15 thf(fact_5251_dvd__minus__self,axiom,
% 2.86/3.15 ! [M2: nat,N: nat] :
% 2.86/3.15 ( ( dvd_dvd_nat @ M2 @ ( minus_minus_nat @ N @ M2 ) )
% 2.86/3.15 = ( ( ord_less_nat @ N @ M2 )
% 2.86/3.15 | ( dvd_dvd_nat @ M2 @ N ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % dvd_minus_self
% 2.86/3.15 thf(fact_5252_zdvd__mono,axiom,
% 2.86/3.15 ! [K3: int,M2: int,T: int] :
% 2.86/3.15 ( ( K3 != zero_zero_int )
% 2.86/3.15 => ( ( dvd_dvd_int @ M2 @ T )
% 2.86/3.15 = ( dvd_dvd_int @ ( times_times_int @ K3 @ M2 ) @ ( times_times_int @ K3 @ T ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % zdvd_mono
% 2.86/3.15 thf(fact_5253_dvd__imp__le,axiom,
% 2.86/3.15 ! [K3: nat,N: nat] :
% 2.86/3.15 ( ( dvd_dvd_nat @ K3 @ N )
% 2.86/3.15 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.15 => ( ord_less_eq_nat @ K3 @ N ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % dvd_imp_le
% 2.86/3.15 thf(fact_5254_nat__mult__dvd__cancel1,axiom,
% 2.86/3.15 ! [K3: nat,M2: nat,N: nat] :
% 2.86/3.15 ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 2.86/3.15 => ( ( dvd_dvd_nat @ ( times_times_nat @ K3 @ M2 ) @ ( times_times_nat @ K3 @ N ) )
% 2.86/3.15 = ( dvd_dvd_nat @ M2 @ N ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % nat_mult_dvd_cancel1
% 2.86/3.15 thf(fact_5255_dvd__mult__cancel,axiom,
% 2.86/3.15 ! [K3: nat,M2: nat,N: nat] :
% 2.86/3.15 ( ( dvd_dvd_nat @ ( times_times_nat @ K3 @ M2 ) @ ( times_times_nat @ K3 @ N ) )
% 2.86/3.15 => ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 2.86/3.15 => ( dvd_dvd_nat @ M2 @ N ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % dvd_mult_cancel
% 2.86/3.15 thf(fact_5256_mod__greater__zero__iff__not__dvd,axiom,
% 2.86/3.15 ! [M2: nat,N: nat] :
% 2.86/3.15 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M2 @ N ) )
% 2.86/3.15 = ( ~ ( dvd_dvd_nat @ N @ M2 ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % mod_greater_zero_iff_not_dvd
% 2.86/3.15 thf(fact_5257_dvd__mult__cancel2,axiom,
% 2.86/3.15 ! [M2: nat,N: nat] :
% 2.86/3.15 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 2.86/3.15 => ( ( dvd_dvd_nat @ ( times_times_nat @ N @ M2 ) @ M2 )
% 2.86/3.15 = ( N = one_one_nat ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % dvd_mult_cancel2
% 2.86/3.15 thf(fact_5258_dvd__mult__cancel1,axiom,
% 2.86/3.15 ! [M2: nat,N: nat] :
% 2.86/3.15 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 2.86/3.15 => ( ( dvd_dvd_nat @ ( times_times_nat @ M2 @ N ) @ M2 )
% 2.86/3.15 = ( N = one_one_nat ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % dvd_mult_cancel1
% 2.86/3.15 thf(fact_5259_even__even__mod__4__iff,axiom,
% 2.86/3.15 ! [N: nat] :
% 2.86/3.15 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 2.86/3.15 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % even_even_mod_4_iff
% 2.86/3.15 thf(fact_5260_mod__nat__eqI,axiom,
% 2.86/3.15 ! [R2: nat,N: nat,M2: nat] :
% 2.86/3.15 ( ( ord_less_nat @ R2 @ N )
% 2.86/3.15 => ( ( ord_less_eq_nat @ R2 @ M2 )
% 2.86/3.15 => ( ( dvd_dvd_nat @ N @ ( minus_minus_nat @ M2 @ R2 ) )
% 2.86/3.15 => ( ( modulo_modulo_nat @ M2 @ N )
% 2.86/3.15 = R2 ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % mod_nat_eqI
% 2.86/3.15 thf(fact_5261_power__dvd__imp__le,axiom,
% 2.86/3.15 ! [I: nat,M2: nat,N: nat] :
% 2.86/3.15 ( ( dvd_dvd_nat @ ( power_power_nat @ I @ M2 ) @ ( power_power_nat @ I @ N ) )
% 2.86/3.15 => ( ( ord_less_nat @ one_one_nat @ I )
% 2.86/3.15 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % power_dvd_imp_le
% 2.86/3.15 thf(fact_5262_take__bit__nat__eq__self,axiom,
% 2.86/3.15 ! [M2: nat,N: nat] :
% 2.86/3.15 ( ( ord_less_nat @ M2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 2.86/3.15 => ( ( bit_se2925701944663578781it_nat @ N @ M2 )
% 2.86/3.15 = M2 ) ) ).
% 2.86/3.15
% 2.86/3.15 % take_bit_nat_eq_self
% 2.86/3.15 thf(fact_5263_take__bit__nat__less__exp,axiom,
% 2.86/3.15 ! [N: nat,M2: nat] : ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 2.86/3.15
% 2.86/3.15 % take_bit_nat_less_exp
% 2.86/3.15 thf(fact_5264_take__bit__nat__eq__self__iff,axiom,
% 2.86/3.15 ! [N: nat,M2: nat] :
% 2.86/3.15 ( ( ( bit_se2925701944663578781it_nat @ N @ M2 )
% 2.86/3.15 = M2 )
% 2.86/3.15 = ( ord_less_nat @ M2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % take_bit_nat_eq_self_iff
% 2.86/3.15 thf(fact_5265_take__bit__nat__less__self__iff,axiom,
% 2.86/3.15 ! [N: nat,M2: nat] :
% 2.86/3.15 ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M2 ) @ M2 )
% 2.86/3.15 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M2 ) ) ).
% 2.86/3.15
% 2.86/3.15 % take_bit_nat_less_self_iff
% 2.86/3.15 thf(fact_5266_take__bit__int__less__eq,axiom,
% 2.86/3.15 ! [N: nat,K3: int] :
% 2.86/3.15 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K3 )
% 2.86/3.15 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.15 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K3 ) @ ( minus_minus_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % take_bit_int_less_eq
% 2.86/3.15 thf(fact_5267_even__mod__4__div__2,axiom,
% 2.86/3.15 ! [N: nat] :
% 2.86/3.15 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 2.86/3.15 = ( suc @ zero_zero_nat ) )
% 2.86/3.15 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % even_mod_4_div_2
% 2.86/3.15 thf(fact_5268_even__diff__nat,axiom,
% 2.86/3.15 ! [M2: nat,N: nat] :
% 2.86/3.15 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M2 @ N ) )
% 2.86/3.15 = ( ( ord_less_nat @ M2 @ N )
% 2.86/3.15 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % even_diff_nat
% 2.86/3.15 thf(fact_5269_odd__pos,axiom,
% 2.86/3.15 ! [N: nat] :
% 2.86/3.15 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 2.86/3.15 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 2.86/3.15
% 2.86/3.15 % odd_pos
% 2.86/3.15 thf(fact_5270_Divides_Oadjust__div__eq,axiom,
% 2.86/3.15 ! [Q6: int,R2: int] :
% 2.86/3.15 ( ( adjust_div @ ( product_Pair_int_int @ Q6 @ R2 ) )
% 2.86/3.15 = ( plus_plus_int @ Q6 @ ( zero_n2684676970156552555ol_int @ ( R2 != zero_zero_int ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % Divides.adjust_div_eq
% 2.86/3.15 thf(fact_5271_odd__mod__4__div__2,axiom,
% 2.86/3.15 ! [N: nat] :
% 2.86/3.15 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 2.86/3.15 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 2.86/3.15 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % odd_mod_4_div_2
% 2.86/3.15 thf(fact_5272_xor__num_Ocases,axiom,
% 2.86/3.15 ! [X: product_prod_num_num] :
% 2.86/3.15 ( ( X
% 2.86/3.15 != ( product_Pair_num_num @ one @ one ) )
% 2.86/3.15 => ( ! [N5: num] :
% 2.86/3.15 ( X
% 2.86/3.15 != ( product_Pair_num_num @ one @ ( bit0 @ N5 ) ) )
% 2.86/3.15 => ( ! [N5: num] :
% 2.86/3.15 ( X
% 2.86/3.15 != ( product_Pair_num_num @ one @ ( bit1 @ N5 ) ) )
% 2.86/3.15 => ( ! [M6: num] :
% 2.86/3.15 ( X
% 2.86/3.15 != ( product_Pair_num_num @ ( bit0 @ M6 ) @ one ) )
% 2.86/3.15 => ( ! [M6: num,N5: num] :
% 2.86/3.15 ( X
% 2.86/3.15 != ( product_Pair_num_num @ ( bit0 @ M6 ) @ ( bit0 @ N5 ) ) )
% 2.86/3.15 => ( ! [M6: num,N5: num] :
% 2.86/3.15 ( X
% 2.86/3.15 != ( product_Pair_num_num @ ( bit0 @ M6 ) @ ( bit1 @ N5 ) ) )
% 2.86/3.15 => ( ! [M6: num] :
% 2.86/3.15 ( X
% 2.86/3.15 != ( product_Pair_num_num @ ( bit1 @ M6 ) @ one ) )
% 2.86/3.15 => ( ! [M6: num,N5: num] :
% 2.86/3.15 ( X
% 2.86/3.15 != ( product_Pair_num_num @ ( bit1 @ M6 ) @ ( bit0 @ N5 ) ) )
% 2.86/3.15 => ~ ! [M6: num,N5: num] :
% 2.86/3.15 ( X
% 2.86/3.15 != ( product_Pair_num_num @ ( bit1 @ M6 ) @ ( bit1 @ N5 ) ) ) ) ) ) ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % xor_num.cases
% 2.86/3.15 thf(fact_5273_divmod_H__nat__def,axiom,
% 2.86/3.15 ( unique5055182867167087721od_nat
% 2.86/3.15 = ( ^ [M: num,N2: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % divmod'_nat_def
% 2.86/3.15 thf(fact_5274_divmod__int__def,axiom,
% 2.86/3.15 ( unique5052692396658037445od_int
% 2.86/3.15 = ( ^ [M: num,N2: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % divmod_int_def
% 2.86/3.15 thf(fact_5275_divmod__BitM__2__eq,axiom,
% 2.86/3.15 ! [M2: num] :
% 2.86/3.15 ( ( unique5052692396658037445od_int @ ( bitM @ M2 ) @ ( bit0 @ one ) )
% 2.86/3.15 = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ one_one_int ) @ one_one_int ) ) ).
% 2.86/3.15
% 2.86/3.15 % divmod_BitM_2_eq
% 2.86/3.15 thf(fact_5276_less__numeral__Suc,axiom,
% 2.86/3.15 ! [K3: num,N: nat] :
% 2.86/3.15 ( ( ord_less_nat @ ( numeral_numeral_nat @ K3 ) @ ( suc @ N ) )
% 2.86/3.15 = ( ord_less_nat @ ( pred_numeral @ K3 ) @ N ) ) ).
% 2.86/3.15
% 2.86/3.15 % less_numeral_Suc
% 2.86/3.15 thf(fact_5277_less__Suc__numeral,axiom,
% 2.86/3.15 ! [N: nat,K3: num] :
% 2.86/3.15 ( ( ord_less_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K3 ) )
% 2.86/3.15 = ( ord_less_nat @ N @ ( pred_numeral @ K3 ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % less_Suc_numeral
% 2.86/3.15 thf(fact_5278_divmod__nat__def,axiom,
% 2.86/3.15 ( divmod_nat
% 2.86/3.15 = ( ^ [M: nat,N2: nat] : ( product_Pair_nat_nat @ ( divide_divide_nat @ M @ N2 ) @ ( modulo_modulo_nat @ M @ N2 ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % divmod_nat_def
% 2.86/3.15 thf(fact_5279_mask__nat__positive__iff,axiom,
% 2.86/3.15 ! [N: nat] :
% 2.86/3.15 ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 2.86/3.15 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 2.86/3.15
% 2.86/3.15 % mask_nat_positive_iff
% 2.86/3.15 thf(fact_5280_less__mask,axiom,
% 2.86/3.15 ! [N: nat] :
% 2.86/3.15 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 2.86/3.15 => ( ord_less_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % less_mask
% 2.86/3.15 thf(fact_5281_mask__nat__less__exp,axiom,
% 2.86/3.15 ! [N: nat] : ( ord_less_nat @ ( bit_se2002935070580805687sk_nat @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 2.86/3.15
% 2.86/3.15 % mask_nat_less_exp
% 2.86/3.15 thf(fact_5282_and__int_Opelims,axiom,
% 2.86/3.15 ! [X: int,Xa: int,Y: int] :
% 2.86/3.15 ( ( ( bit_se725231765392027082nd_int @ X @ Xa )
% 2.86/3.15 = Y )
% 2.86/3.15 => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa ) )
% 2.86/3.15 => ~ ( ( ( ( ( member_int @ X @ ( insert_int2 @ zero_zero_int @ ( insert_int2 @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 2.86/3.15 & ( member_int @ Xa @ ( insert_int2 @ zero_zero_int @ ( insert_int2 @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 2.86/3.15 => ( Y
% 2.86/3.15 = ( uminus_uminus_int
% 2.86/3.15 @ ( zero_n2684676970156552555ol_int
% 2.86/3.15 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 2.86/3.15 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 2.86/3.15 & ( ~ ( ( member_int @ X @ ( insert_int2 @ zero_zero_int @ ( insert_int2 @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 2.86/3.15 & ( member_int @ Xa @ ( insert_int2 @ zero_zero_int @ ( insert_int2 @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 2.86/3.15 => ( Y
% 2.86/3.15 = ( plus_plus_int
% 2.86/3.15 @ ( zero_n2684676970156552555ol_int
% 2.86/3.15 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 2.86/3.15 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 2.86/3.15 @ ( 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 ) ) ) ) ) ) ) ) )
% 2.86/3.15 => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % and_int.pelims
% 2.86/3.15 thf(fact_5283_and__int_Opsimps,axiom,
% 2.86/3.15 ! [K3: int,L: int] :
% 2.86/3.15 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K3 @ L ) )
% 2.86/3.15 => ( ( ( ( member_int @ K3 @ ( insert_int2 @ zero_zero_int @ ( insert_int2 @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 2.86/3.15 & ( member_int @ L @ ( insert_int2 @ zero_zero_int @ ( insert_int2 @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 2.86/3.15 => ( ( bit_se725231765392027082nd_int @ K3 @ L )
% 2.86/3.15 = ( uminus_uminus_int
% 2.86/3.15 @ ( zero_n2684676970156552555ol_int
% 2.86/3.15 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 2.86/3.15 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ) ) )
% 2.86/3.15 & ( ~ ( ( member_int @ K3 @ ( insert_int2 @ zero_zero_int @ ( insert_int2 @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 2.86/3.15 & ( member_int @ L @ ( insert_int2 @ zero_zero_int @ ( insert_int2 @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 2.86/3.15 => ( ( bit_se725231765392027082nd_int @ K3 @ L )
% 2.86/3.15 = ( plus_plus_int
% 2.86/3.15 @ ( zero_n2684676970156552555ol_int
% 2.86/3.15 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 2.86/3.15 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 2.86/3.15 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % and_int.psimps
% 2.86/3.15 thf(fact_5284_bit__imp__take__bit__positive,axiom,
% 2.86/3.15 ! [N: nat,M2: nat,K3: int] :
% 2.86/3.15 ( ( ord_less_nat @ N @ M2 )
% 2.86/3.15 => ( ( bit_se1146084159140164899it_int @ K3 @ N )
% 2.86/3.15 => ( ord_less_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ M2 @ K3 ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % bit_imp_take_bit_positive
% 2.86/3.15 thf(fact_5285_int__bit__bound,axiom,
% 2.86/3.15 ! [K3: int] :
% 2.86/3.15 ~ ! [N5: nat] :
% 2.86/3.15 ( ! [M3: nat] :
% 2.86/3.15 ( ( ord_less_eq_nat @ N5 @ M3 )
% 2.86/3.15 => ( ( bit_se1146084159140164899it_int @ K3 @ M3 )
% 2.86/3.15 = ( bit_se1146084159140164899it_int @ K3 @ N5 ) ) )
% 2.86/3.15 => ~ ( ( ord_less_nat @ zero_zero_nat @ N5 )
% 2.86/3.15 => ( ( bit_se1146084159140164899it_int @ K3 @ ( minus_minus_nat @ N5 @ one_one_nat ) )
% 2.86/3.15 = ( ~ ( bit_se1146084159140164899it_int @ K3 @ N5 ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % int_bit_bound
% 2.86/3.15 thf(fact_5286_and__int_Opinduct,axiom,
% 2.86/3.15 ! [A0: int,A1: int,P: int > int > $o] :
% 2.86/3.15 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 2.86/3.15 => ( ! [K: int,L2: int] :
% 2.86/3.15 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L2 ) )
% 2.86/3.15 => ( ( ~ ( ( member_int @ K @ ( insert_int2 @ zero_zero_int @ ( insert_int2 @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 2.86/3.15 & ( member_int @ L2 @ ( insert_int2 @ zero_zero_int @ ( insert_int2 @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 2.86/3.15 => ( P @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 2.86/3.15 => ( P @ K @ L2 ) ) )
% 2.86/3.15 => ( P @ A0 @ A1 ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % and_int.pinduct
% 2.86/3.15 thf(fact_5287_upto_Opsimps,axiom,
% 2.86/3.15 ! [I: int,J: int] :
% 2.86/3.15 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I @ J ) )
% 2.86/3.15 => ( ( ( ord_less_eq_int @ I @ J )
% 2.86/3.15 => ( ( upto @ I @ J )
% 2.86/3.15 = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) )
% 2.86/3.15 & ( ~ ( ord_less_eq_int @ I @ J )
% 2.86/3.15 => ( ( upto @ I @ J )
% 2.86/3.15 = nil_int ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % upto.psimps
% 2.86/3.15 thf(fact_5288_upto_Opelims,axiom,
% 2.86/3.15 ! [X: int,Xa: int,Y: list_int] :
% 2.86/3.15 ( ( ( upto @ X @ Xa )
% 2.86/3.15 = Y )
% 2.86/3.15 => ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa ) )
% 2.86/3.15 => ~ ( ( ( ( ord_less_eq_int @ X @ Xa )
% 2.86/3.15 => ( Y
% 2.86/3.15 = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa ) ) ) )
% 2.86/3.15 & ( ~ ( ord_less_eq_int @ X @ Xa )
% 2.86/3.15 => ( Y = nil_int ) ) )
% 2.86/3.15 => ~ ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % upto.pelims
% 2.86/3.15 thf(fact_5289_upto_Opinduct,axiom,
% 2.86/3.15 ! [A0: int,A1: int,P: int > int > $o] :
% 2.86/3.15 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 2.86/3.15 => ( ! [I5: int,J3: int] :
% 2.86/3.15 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I5 @ J3 ) )
% 2.86/3.15 => ( ( ( ord_less_eq_int @ I5 @ J3 )
% 2.86/3.15 => ( P @ ( plus_plus_int @ I5 @ one_one_int ) @ J3 ) )
% 2.86/3.15 => ( P @ I5 @ J3 ) ) )
% 2.86/3.15 => ( P @ A0 @ A1 ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % upto.pinduct
% 2.86/3.15 thf(fact_5290_num__of__nat_Osimps_I2_J,axiom,
% 2.86/3.15 ! [N: nat] :
% 2.86/3.15 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.15 => ( ( num_of_nat @ ( suc @ N ) )
% 2.86/3.15 = ( inc @ ( num_of_nat @ N ) ) ) )
% 2.86/3.15 & ( ~ ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.15 => ( ( num_of_nat @ ( suc @ N ) )
% 2.86/3.15 = one ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % num_of_nat.simps(2)
% 2.86/3.15 thf(fact_5291_binomial__code,axiom,
% 2.86/3.15 ( binomial
% 2.86/3.15 = ( ^ [N2: nat,K4: nat] : ( if_nat @ ( ord_less_nat @ N2 @ K4 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K4 ) ) @ ( binomial @ N2 @ ( minus_minus_nat @ N2 @ K4 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N2 @ K4 ) @ one_one_nat ) @ N2 @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K4 ) ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % binomial_code
% 2.86/3.15 thf(fact_5292_set__decode__plus__power__2,axiom,
% 2.86/3.15 ! [N: nat,Z: nat] :
% 2.86/3.15 ( ~ ( member_nat @ N @ ( nat_set_decode @ Z ) )
% 2.86/3.15 => ( ( nat_set_decode @ ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ Z ) )
% 2.86/3.15 = ( insert_nat2 @ N @ ( nat_set_decode @ Z ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % set_decode_plus_power_2
% 2.86/3.15 thf(fact_5293_binomial__eq__0__iff,axiom,
% 2.86/3.15 ! [N: nat,K3: nat] :
% 2.86/3.15 ( ( ( binomial @ N @ K3 )
% 2.86/3.15 = zero_zero_nat )
% 2.86/3.15 = ( ord_less_nat @ N @ K3 ) ) ).
% 2.86/3.15
% 2.86/3.15 % binomial_eq_0_iff
% 2.86/3.15 thf(fact_5294_set__decode__zero,axiom,
% 2.86/3.15 ( ( nat_set_decode @ zero_zero_nat )
% 2.86/3.15 = bot_bot_set_nat ) ).
% 2.86/3.15
% 2.86/3.15 % set_decode_zero
% 2.86/3.15 thf(fact_5295_zero__less__binomial__iff,axiom,
% 2.86/3.15 ! [N: nat,K3: nat] :
% 2.86/3.15 ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K3 ) )
% 2.86/3.15 = ( ord_less_eq_nat @ K3 @ N ) ) ).
% 2.86/3.15
% 2.86/3.15 % zero_less_binomial_iff
% 2.86/3.15 thf(fact_5296_binomial__eq__0,axiom,
% 2.86/3.15 ! [N: nat,K3: nat] :
% 2.86/3.15 ( ( ord_less_nat @ N @ K3 )
% 2.86/3.15 => ( ( binomial @ N @ K3 )
% 2.86/3.15 = zero_zero_nat ) ) ).
% 2.86/3.15
% 2.86/3.15 % binomial_eq_0
% 2.86/3.15 thf(fact_5297_zero__less__binomial,axiom,
% 2.86/3.15 ! [K3: nat,N: nat] :
% 2.86/3.15 ( ( ord_less_eq_nat @ K3 @ N )
% 2.86/3.15 => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K3 ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % zero_less_binomial
% 2.86/3.15 thf(fact_5298_prod__decode__aux_Ocases,axiom,
% 2.86/3.15 ! [X: product_prod_nat_nat] :
% 2.86/3.15 ~ ! [K: nat,M6: nat] :
% 2.86/3.15 ( X
% 2.86/3.15 != ( product_Pair_nat_nat @ K @ M6 ) ) ).
% 2.86/3.15
% 2.86/3.15 % prod_decode_aux.cases
% 2.86/3.15 thf(fact_5299_numeral__num__of__nat,axiom,
% 2.86/3.15 ! [N: nat] :
% 2.86/3.15 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.15 => ( ( numeral_numeral_nat @ ( num_of_nat @ N ) )
% 2.86/3.15 = N ) ) ).
% 2.86/3.15
% 2.86/3.15 % numeral_num_of_nat
% 2.86/3.15 thf(fact_5300_choose__reduce__nat,axiom,
% 2.86/3.15 ! [N: nat,K3: nat] :
% 2.86/3.15 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.15 => ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 2.86/3.15 => ( ( binomial @ N @ K3 )
% 2.86/3.15 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K3 @ one_one_nat ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K3 ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % choose_reduce_nat
% 2.86/3.15 thf(fact_5301_times__binomial__minus1__eq,axiom,
% 2.86/3.15 ! [K3: nat,N: nat] :
% 2.86/3.15 ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 2.86/3.15 => ( ( times_times_nat @ K3 @ ( binomial @ N @ K3 ) )
% 2.86/3.15 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K3 @ one_one_nat ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % times_binomial_minus1_eq
% 2.86/3.15 thf(fact_5302_num__of__nat__double,axiom,
% 2.86/3.15 ! [N: nat] :
% 2.86/3.15 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.15 => ( ( num_of_nat @ ( plus_plus_nat @ N @ N ) )
% 2.86/3.15 = ( bit0 @ ( num_of_nat @ N ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % num_of_nat_double
% 2.86/3.15 thf(fact_5303_num__of__nat__plus__distrib,axiom,
% 2.86/3.15 ! [M2: nat,N: nat] :
% 2.86/3.15 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 2.86/3.15 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.15 => ( ( num_of_nat @ ( plus_plus_nat @ M2 @ N ) )
% 2.86/3.15 = ( plus_plus_num @ ( num_of_nat @ M2 ) @ ( num_of_nat @ N ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % num_of_nat_plus_distrib
% 2.86/3.15 thf(fact_5304_binomial__addition__formula,axiom,
% 2.86/3.15 ! [N: nat,K3: nat] :
% 2.86/3.15 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.15 => ( ( binomial @ N @ ( suc @ K3 ) )
% 2.86/3.15 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( suc @ K3 ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K3 ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % binomial_addition_formula
% 2.86/3.15 thf(fact_5305_prod__decode__aux_Oelims,axiom,
% 2.86/3.15 ! [X: nat,Xa: nat,Y: product_prod_nat_nat] :
% 2.86/3.15 ( ( ( nat_prod_decode_aux @ X @ Xa )
% 2.86/3.15 = Y )
% 2.86/3.15 => ( ( ( ord_less_eq_nat @ Xa @ X )
% 2.86/3.15 => ( Y
% 2.86/3.15 = ( product_Pair_nat_nat @ Xa @ ( minus_minus_nat @ X @ Xa ) ) ) )
% 2.86/3.15 & ( ~ ( ord_less_eq_nat @ Xa @ X )
% 2.86/3.15 => ( Y
% 2.86/3.15 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa @ ( suc @ X ) ) ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % prod_decode_aux.elims
% 2.86/3.15 thf(fact_5306_prod__decode__aux_Osimps,axiom,
% 2.86/3.15 ( nat_prod_decode_aux
% 2.86/3.15 = ( ^ [K4: nat,M: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ M @ K4 ) @ ( product_Pair_nat_nat @ M @ ( minus_minus_nat @ K4 @ M ) ) @ ( nat_prod_decode_aux @ ( suc @ K4 ) @ ( minus_minus_nat @ M @ ( suc @ K4 ) ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % prod_decode_aux.simps
% 2.86/3.15 thf(fact_5307_cppi,axiom,
% 2.86/3.15 ! [D: int,P: int > $o,P3: int > $o,A: set_int] :
% 2.86/3.15 ( ( ord_less_int @ zero_zero_int @ D )
% 2.86/3.15 => ( ? [Z3: int] :
% 2.86/3.15 ! [X3: int] :
% 2.86/3.15 ( ( ord_less_int @ Z3 @ X3 )
% 2.86/3.15 => ( ( P @ X3 )
% 2.86/3.15 = ( P3 @ X3 ) ) )
% 2.86/3.15 => ( ! [X3: int] :
% 2.86/3.15 ( ! [Xa2: int] :
% 2.86/3.15 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.86/3.15 => ! [Xb2: int] :
% 2.86/3.15 ( ( member_int @ Xb2 @ A )
% 2.86/3.15 => ( X3
% 2.86/3.15 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 2.86/3.15 => ( ( P @ X3 )
% 2.86/3.15 => ( P @ ( plus_plus_int @ X3 @ D ) ) ) )
% 2.86/3.15 => ( ! [X3: int,K: int] :
% 2.86/3.15 ( ( P3 @ X3 )
% 2.86/3.15 = ( P3 @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D ) ) ) )
% 2.86/3.15 => ( ( ? [X8: int] : ( P @ X8 ) )
% 2.86/3.15 = ( ? [X2: int] :
% 2.86/3.15 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.86/3.15 & ( P3 @ X2 ) )
% 2.86/3.15 | ? [X2: int] :
% 2.86/3.15 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.86/3.15 & ? [Y5: int] :
% 2.86/3.15 ( ( member_int @ Y5 @ A )
% 2.86/3.15 & ( P @ ( minus_minus_int @ Y5 @ X2 ) ) ) ) ) ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % cppi
% 2.86/3.15 thf(fact_5308_atLeastAtMost__upto,axiom,
% 2.86/3.15 ( set_or1266510415728281911st_int
% 2.86/3.15 = ( ^ [I4: int,J2: int] : ( set_int2 @ ( upto @ I4 @ J2 ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % atLeastAtMost_upto
% 2.86/3.15 thf(fact_5309_bset_I1_J,axiom,
% 2.86/3.15 ! [D: int,B: set_int,P: int > $o,Q: int > $o] :
% 2.86/3.15 ( ! [X3: int] :
% 2.86/3.15 ( ! [Xa2: int] :
% 2.86/3.15 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.86/3.15 => ! [Xb2: int] :
% 2.86/3.15 ( ( member_int @ Xb2 @ B )
% 2.86/3.15 => ( X3
% 2.86/3.15 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 2.86/3.15 => ( ( P @ X3 )
% 2.86/3.15 => ( P @ ( minus_minus_int @ X3 @ D ) ) ) )
% 2.86/3.15 => ( ! [X3: int] :
% 2.86/3.15 ( ! [Xa2: int] :
% 2.86/3.15 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.86/3.15 => ! [Xb2: int] :
% 2.86/3.15 ( ( member_int @ Xb2 @ B )
% 2.86/3.15 => ( X3
% 2.86/3.15 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 2.86/3.15 => ( ( Q @ X3 )
% 2.86/3.15 => ( Q @ ( minus_minus_int @ X3 @ D ) ) ) )
% 2.86/3.15 => ! [X7: int] :
% 2.86/3.15 ( ! [Xa3: int] :
% 2.86/3.15 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.86/3.15 => ! [Xb3: int] :
% 2.86/3.15 ( ( member_int @ Xb3 @ B )
% 2.86/3.15 => ( X7
% 2.86/3.15 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 2.86/3.15 => ( ( ( P @ X7 )
% 2.86/3.15 & ( Q @ X7 ) )
% 2.86/3.15 => ( ( P @ ( minus_minus_int @ X7 @ D ) )
% 2.86/3.15 & ( Q @ ( minus_minus_int @ X7 @ D ) ) ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % bset(1)
% 2.86/3.15 thf(fact_5310_bset_I2_J,axiom,
% 2.86/3.15 ! [D: int,B: set_int,P: int > $o,Q: int > $o] :
% 2.86/3.15 ( ! [X3: int] :
% 2.86/3.15 ( ! [Xa2: int] :
% 2.86/3.15 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.86/3.15 => ! [Xb2: int] :
% 2.86/3.15 ( ( member_int @ Xb2 @ B )
% 2.86/3.15 => ( X3
% 2.86/3.15 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 2.86/3.15 => ( ( P @ X3 )
% 2.86/3.15 => ( P @ ( minus_minus_int @ X3 @ D ) ) ) )
% 2.86/3.15 => ( ! [X3: int] :
% 2.86/3.15 ( ! [Xa2: int] :
% 2.86/3.15 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.86/3.15 => ! [Xb2: int] :
% 2.86/3.15 ( ( member_int @ Xb2 @ B )
% 2.86/3.15 => ( X3
% 2.86/3.15 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 2.86/3.15 => ( ( Q @ X3 )
% 2.86/3.15 => ( Q @ ( minus_minus_int @ X3 @ D ) ) ) )
% 2.86/3.15 => ! [X7: int] :
% 2.86/3.15 ( ! [Xa3: int] :
% 2.86/3.15 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.86/3.15 => ! [Xb3: int] :
% 2.86/3.15 ( ( member_int @ Xb3 @ B )
% 2.86/3.15 => ( X7
% 2.86/3.15 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 2.86/3.15 => ( ( ( P @ X7 )
% 2.86/3.15 | ( Q @ X7 ) )
% 2.86/3.15 => ( ( P @ ( minus_minus_int @ X7 @ D ) )
% 2.86/3.15 | ( Q @ ( minus_minus_int @ X7 @ D ) ) ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % bset(2)
% 2.86/3.15 thf(fact_5311_aset_I1_J,axiom,
% 2.86/3.15 ! [D: int,A: set_int,P: int > $o,Q: int > $o] :
% 2.86/3.15 ( ! [X3: int] :
% 2.86/3.15 ( ! [Xa2: int] :
% 2.86/3.15 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.86/3.15 => ! [Xb2: int] :
% 2.86/3.15 ( ( member_int @ Xb2 @ A )
% 2.86/3.15 => ( X3
% 2.86/3.15 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 2.86/3.15 => ( ( P @ X3 )
% 2.86/3.15 => ( P @ ( plus_plus_int @ X3 @ D ) ) ) )
% 2.86/3.15 => ( ! [X3: int] :
% 2.86/3.15 ( ! [Xa2: int] :
% 2.86/3.15 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.86/3.15 => ! [Xb2: int] :
% 2.86/3.15 ( ( member_int @ Xb2 @ A )
% 2.86/3.15 => ( X3
% 2.86/3.15 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 2.86/3.15 => ( ( Q @ X3 )
% 2.86/3.15 => ( Q @ ( plus_plus_int @ X3 @ D ) ) ) )
% 2.86/3.15 => ! [X7: int] :
% 2.86/3.15 ( ! [Xa3: int] :
% 2.86/3.15 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.86/3.15 => ! [Xb3: int] :
% 2.86/3.15 ( ( member_int @ Xb3 @ A )
% 2.86/3.15 => ( X7
% 2.86/3.15 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 2.86/3.15 => ( ( ( P @ X7 )
% 2.86/3.15 & ( Q @ X7 ) )
% 2.86/3.15 => ( ( P @ ( plus_plus_int @ X7 @ D ) )
% 2.86/3.15 & ( Q @ ( plus_plus_int @ X7 @ D ) ) ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % aset(1)
% 2.86/3.15 thf(fact_5312_aset_I2_J,axiom,
% 2.86/3.15 ! [D: int,A: set_int,P: int > $o,Q: int > $o] :
% 2.86/3.15 ( ! [X3: int] :
% 2.86/3.15 ( ! [Xa2: int] :
% 2.86/3.15 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.86/3.15 => ! [Xb2: int] :
% 2.86/3.15 ( ( member_int @ Xb2 @ A )
% 2.86/3.15 => ( X3
% 2.86/3.15 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 2.86/3.15 => ( ( P @ X3 )
% 2.86/3.15 => ( P @ ( plus_plus_int @ X3 @ D ) ) ) )
% 2.86/3.15 => ( ! [X3: int] :
% 2.86/3.15 ( ! [Xa2: int] :
% 2.86/3.15 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.86/3.15 => ! [Xb2: int] :
% 2.86/3.15 ( ( member_int @ Xb2 @ A )
% 2.86/3.15 => ( X3
% 2.86/3.15 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 2.86/3.15 => ( ( Q @ X3 )
% 2.86/3.15 => ( Q @ ( plus_plus_int @ X3 @ D ) ) ) )
% 2.86/3.15 => ! [X7: int] :
% 2.86/3.15 ( ! [Xa3: int] :
% 2.86/3.15 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.86/3.15 => ! [Xb3: int] :
% 2.86/3.15 ( ( member_int @ Xb3 @ A )
% 2.86/3.15 => ( X7
% 2.86/3.15 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 2.86/3.15 => ( ( ( P @ X7 )
% 2.86/3.15 | ( Q @ X7 ) )
% 2.86/3.15 => ( ( P @ ( plus_plus_int @ X7 @ D ) )
% 2.86/3.15 | ( Q @ ( plus_plus_int @ X7 @ D ) ) ) ) ) ) ) ).
% 2.86/3.15
% 2.86/3.15 % aset(2)
% 2.86/3.15 thf(fact_5313_aset_I10_J,axiom,
% 2.86/3.15 ! [D2: int,D: int,A: set_int,T: int] :
% 2.86/3.15 ( ( dvd_dvd_int @ D2 @ D )
% 2.86/3.15 => ! [X7: int] :
% 2.86/3.15 ( ! [Xa3: int] :
% 2.86/3.15 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.86/3.15 => ! [Xb3: int] :
% 2.86/3.15 ( ( member_int @ Xb3 @ A )
% 2.86/3.15 => ( X7
% 2.86/3.15 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 2.86/3.15 => ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X7 @ T ) )
% 2.86/3.16 => ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( plus_plus_int @ X7 @ D ) @ T ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % aset(10)
% 2.86/3.16 thf(fact_5314_aset_I9_J,axiom,
% 2.86/3.16 ! [D2: int,D: int,A: set_int,T: int] :
% 2.86/3.16 ( ( dvd_dvd_int @ D2 @ D )
% 2.86/3.16 => ! [X7: int] :
% 2.86/3.16 ( ! [Xa3: int] :
% 2.86/3.16 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.86/3.16 => ! [Xb3: int] :
% 2.86/3.16 ( ( member_int @ Xb3 @ A )
% 2.86/3.16 => ( X7
% 2.86/3.16 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 2.86/3.16 => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X7 @ T ) )
% 2.86/3.16 => ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( plus_plus_int @ X7 @ D ) @ T ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % aset(9)
% 2.86/3.16 thf(fact_5315_bset_I10_J,axiom,
% 2.86/3.16 ! [D2: int,D: int,B: set_int,T: int] :
% 2.86/3.16 ( ( dvd_dvd_int @ D2 @ D )
% 2.86/3.16 => ! [X7: int] :
% 2.86/3.16 ( ! [Xa3: int] :
% 2.86/3.16 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.86/3.16 => ! [Xb3: int] :
% 2.86/3.16 ( ( member_int @ Xb3 @ B )
% 2.86/3.16 => ( X7
% 2.86/3.16 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 2.86/3.16 => ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X7 @ T ) )
% 2.86/3.16 => ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X7 @ D ) @ T ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % bset(10)
% 2.86/3.16 thf(fact_5316_bset_I9_J,axiom,
% 2.86/3.16 ! [D2: int,D: int,B: set_int,T: int] :
% 2.86/3.16 ( ( dvd_dvd_int @ D2 @ D )
% 2.86/3.16 => ! [X7: int] :
% 2.86/3.16 ( ! [Xa3: int] :
% 2.86/3.16 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.86/3.16 => ! [Xb3: int] :
% 2.86/3.16 ( ( member_int @ Xb3 @ B )
% 2.86/3.16 => ( X7
% 2.86/3.16 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 2.86/3.16 => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X7 @ T ) )
% 2.86/3.16 => ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X7 @ D ) @ T ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % bset(9)
% 2.86/3.16 thf(fact_5317_periodic__finite__ex,axiom,
% 2.86/3.16 ! [D2: int,P: int > $o] :
% 2.86/3.16 ( ( ord_less_int @ zero_zero_int @ D2 )
% 2.86/3.16 => ( ! [X3: int,K: int] :
% 2.86/3.16 ( ( P @ X3 )
% 2.86/3.16 = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D2 ) ) ) )
% 2.86/3.16 => ( ( ? [X8: int] : ( P @ X8 ) )
% 2.86/3.16 = ( ? [X2: int] :
% 2.86/3.16 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D2 ) )
% 2.86/3.16 & ( P @ X2 ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % periodic_finite_ex
% 2.86/3.16 thf(fact_5318_aset_I7_J,axiom,
% 2.86/3.16 ! [D: int,A: set_int,T: int] :
% 2.86/3.16 ( ( ord_less_int @ zero_zero_int @ D )
% 2.86/3.16 => ! [X7: int] :
% 2.86/3.16 ( ! [Xa3: int] :
% 2.86/3.16 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.86/3.16 => ! [Xb3: int] :
% 2.86/3.16 ( ( member_int @ Xb3 @ A )
% 2.86/3.16 => ( X7
% 2.86/3.16 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 2.86/3.16 => ( ( ord_less_int @ T @ X7 )
% 2.86/3.16 => ( ord_less_int @ T @ ( plus_plus_int @ X7 @ D ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % aset(7)
% 2.86/3.16 thf(fact_5319_aset_I5_J,axiom,
% 2.86/3.16 ! [D: int,T: int,A: set_int] :
% 2.86/3.16 ( ( ord_less_int @ zero_zero_int @ D )
% 2.86/3.16 => ( ( member_int @ T @ A )
% 2.86/3.16 => ! [X7: int] :
% 2.86/3.16 ( ! [Xa3: int] :
% 2.86/3.16 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.86/3.16 => ! [Xb3: int] :
% 2.86/3.16 ( ( member_int @ Xb3 @ A )
% 2.86/3.16 => ( X7
% 2.86/3.16 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 2.86/3.16 => ( ( ord_less_int @ X7 @ T )
% 2.86/3.16 => ( ord_less_int @ ( plus_plus_int @ X7 @ D ) @ T ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % aset(5)
% 2.86/3.16 thf(fact_5320_aset_I4_J,axiom,
% 2.86/3.16 ! [D: int,T: int,A: set_int] :
% 2.86/3.16 ( ( ord_less_int @ zero_zero_int @ D )
% 2.86/3.16 => ( ( member_int @ T @ A )
% 2.86/3.16 => ! [X7: int] :
% 2.86/3.16 ( ! [Xa3: int] :
% 2.86/3.16 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.86/3.16 => ! [Xb3: int] :
% 2.86/3.16 ( ( member_int @ Xb3 @ A )
% 2.86/3.16 => ( X7
% 2.86/3.16 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 2.86/3.16 => ( ( X7 != T )
% 2.86/3.16 => ( ( plus_plus_int @ X7 @ D )
% 2.86/3.16 != T ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % aset(4)
% 2.86/3.16 thf(fact_5321_aset_I3_J,axiom,
% 2.86/3.16 ! [D: int,T: int,A: set_int] :
% 2.86/3.16 ( ( ord_less_int @ zero_zero_int @ D )
% 2.86/3.16 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A )
% 2.86/3.16 => ! [X7: int] :
% 2.86/3.16 ( ! [Xa3: int] :
% 2.86/3.16 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.86/3.16 => ! [Xb3: int] :
% 2.86/3.16 ( ( member_int @ Xb3 @ A )
% 2.86/3.16 => ( X7
% 2.86/3.16 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 2.86/3.16 => ( ( X7 = T )
% 2.86/3.16 => ( ( plus_plus_int @ X7 @ D )
% 2.86/3.16 = T ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % aset(3)
% 2.86/3.16 thf(fact_5322_bset_I7_J,axiom,
% 2.86/3.16 ! [D: int,T: int,B: set_int] :
% 2.86/3.16 ( ( ord_less_int @ zero_zero_int @ D )
% 2.86/3.16 => ( ( member_int @ T @ B )
% 2.86/3.16 => ! [X7: int] :
% 2.86/3.16 ( ! [Xa3: int] :
% 2.86/3.16 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.86/3.16 => ! [Xb3: int] :
% 2.86/3.16 ( ( member_int @ Xb3 @ B )
% 2.86/3.16 => ( X7
% 2.86/3.16 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 2.86/3.16 => ( ( ord_less_int @ T @ X7 )
% 2.86/3.16 => ( ord_less_int @ T @ ( minus_minus_int @ X7 @ D ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % bset(7)
% 2.86/3.16 thf(fact_5323_bset_I5_J,axiom,
% 2.86/3.16 ! [D: int,B: set_int,T: int] :
% 2.86/3.16 ( ( ord_less_int @ zero_zero_int @ D )
% 2.86/3.16 => ! [X7: int] :
% 2.86/3.16 ( ! [Xa3: int] :
% 2.86/3.16 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.86/3.16 => ! [Xb3: int] :
% 2.86/3.16 ( ( member_int @ Xb3 @ B )
% 2.86/3.16 => ( X7
% 2.86/3.16 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 2.86/3.16 => ( ( ord_less_int @ X7 @ T )
% 2.86/3.16 => ( ord_less_int @ ( minus_minus_int @ X7 @ D ) @ T ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % bset(5)
% 2.86/3.16 thf(fact_5324_bset_I4_J,axiom,
% 2.86/3.16 ! [D: int,T: int,B: set_int] :
% 2.86/3.16 ( ( ord_less_int @ zero_zero_int @ D )
% 2.86/3.16 => ( ( member_int @ T @ B )
% 2.86/3.16 => ! [X7: int] :
% 2.86/3.16 ( ! [Xa3: int] :
% 2.86/3.16 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.86/3.16 => ! [Xb3: int] :
% 2.86/3.16 ( ( member_int @ Xb3 @ B )
% 2.86/3.16 => ( X7
% 2.86/3.16 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 2.86/3.16 => ( ( X7 != T )
% 2.86/3.16 => ( ( minus_minus_int @ X7 @ D )
% 2.86/3.16 != T ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % bset(4)
% 2.86/3.16 thf(fact_5325_bset_I3_J,axiom,
% 2.86/3.16 ! [D: int,T: int,B: set_int] :
% 2.86/3.16 ( ( ord_less_int @ zero_zero_int @ D )
% 2.86/3.16 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B )
% 2.86/3.16 => ! [X7: int] :
% 2.86/3.16 ( ! [Xa3: int] :
% 2.86/3.16 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.86/3.16 => ! [Xb3: int] :
% 2.86/3.16 ( ( member_int @ Xb3 @ B )
% 2.86/3.16 => ( X7
% 2.86/3.16 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 2.86/3.16 => ( ( X7 = T )
% 2.86/3.16 => ( ( minus_minus_int @ X7 @ D )
% 2.86/3.16 = T ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % bset(3)
% 2.86/3.16 thf(fact_5326_simp__from__to,axiom,
% 2.86/3.16 ( set_or1266510415728281911st_int
% 2.86/3.16 = ( ^ [I4: int,J2: int] : ( if_set_int @ ( ord_less_int @ J2 @ I4 ) @ bot_bot_set_int @ ( insert_int2 @ I4 @ ( set_or1266510415728281911st_int @ ( plus_plus_int @ I4 @ one_one_int ) @ J2 ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % simp_from_to
% 2.86/3.16 thf(fact_5327_bset_I6_J,axiom,
% 2.86/3.16 ! [D: int,B: set_int,T: int] :
% 2.86/3.16 ( ( ord_less_int @ zero_zero_int @ D )
% 2.86/3.16 => ! [X7: int] :
% 2.86/3.16 ( ! [Xa3: int] :
% 2.86/3.16 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.86/3.16 => ! [Xb3: int] :
% 2.86/3.16 ( ( member_int @ Xb3 @ B )
% 2.86/3.16 => ( X7
% 2.86/3.16 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 2.86/3.16 => ( ( ord_less_eq_int @ X7 @ T )
% 2.86/3.16 => ( ord_less_eq_int @ ( minus_minus_int @ X7 @ D ) @ T ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % bset(6)
% 2.86/3.16 thf(fact_5328_bset_I8_J,axiom,
% 2.86/3.16 ! [D: int,T: int,B: set_int] :
% 2.86/3.16 ( ( ord_less_int @ zero_zero_int @ D )
% 2.86/3.16 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B )
% 2.86/3.16 => ! [X7: int] :
% 2.86/3.16 ( ! [Xa3: int] :
% 2.86/3.16 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.86/3.16 => ! [Xb3: int] :
% 2.86/3.16 ( ( member_int @ Xb3 @ B )
% 2.86/3.16 => ( X7
% 2.86/3.16 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 2.86/3.16 => ( ( ord_less_eq_int @ T @ X7 )
% 2.86/3.16 => ( ord_less_eq_int @ T @ ( minus_minus_int @ X7 @ D ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % bset(8)
% 2.86/3.16 thf(fact_5329_aset_I6_J,axiom,
% 2.86/3.16 ! [D: int,T: int,A: set_int] :
% 2.86/3.16 ( ( ord_less_int @ zero_zero_int @ D )
% 2.86/3.16 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A )
% 2.86/3.16 => ! [X7: int] :
% 2.86/3.16 ( ! [Xa3: int] :
% 2.86/3.16 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.86/3.16 => ! [Xb3: int] :
% 2.86/3.16 ( ( member_int @ Xb3 @ A )
% 2.86/3.16 => ( X7
% 2.86/3.16 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 2.86/3.16 => ( ( ord_less_eq_int @ X7 @ T )
% 2.86/3.16 => ( ord_less_eq_int @ ( plus_plus_int @ X7 @ D ) @ T ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % aset(6)
% 2.86/3.16 thf(fact_5330_aset_I8_J,axiom,
% 2.86/3.16 ! [D: int,A: set_int,T: int] :
% 2.86/3.16 ( ( ord_less_int @ zero_zero_int @ D )
% 2.86/3.16 => ! [X7: int] :
% 2.86/3.16 ( ! [Xa3: int] :
% 2.86/3.16 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.86/3.16 => ! [Xb3: int] :
% 2.86/3.16 ( ( member_int @ Xb3 @ A )
% 2.86/3.16 => ( X7
% 2.86/3.16 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 2.86/3.16 => ( ( ord_less_eq_int @ T @ X7 )
% 2.86/3.16 => ( ord_less_eq_int @ T @ ( plus_plus_int @ X7 @ D ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % aset(8)
% 2.86/3.16 thf(fact_5331_cpmi,axiom,
% 2.86/3.16 ! [D: int,P: int > $o,P3: int > $o,B: set_int] :
% 2.86/3.16 ( ( ord_less_int @ zero_zero_int @ D )
% 2.86/3.16 => ( ? [Z3: int] :
% 2.86/3.16 ! [X3: int] :
% 2.86/3.16 ( ( ord_less_int @ X3 @ Z3 )
% 2.86/3.16 => ( ( P @ X3 )
% 2.86/3.16 = ( P3 @ X3 ) ) )
% 2.86/3.16 => ( ! [X3: int] :
% 2.86/3.16 ( ! [Xa2: int] :
% 2.86/3.16 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.86/3.16 => ! [Xb2: int] :
% 2.86/3.16 ( ( member_int @ Xb2 @ B )
% 2.86/3.16 => ( X3
% 2.86/3.16 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 2.86/3.16 => ( ( P @ X3 )
% 2.86/3.16 => ( P @ ( minus_minus_int @ X3 @ D ) ) ) )
% 2.86/3.16 => ( ! [X3: int,K: int] :
% 2.86/3.16 ( ( P3 @ X3 )
% 2.86/3.16 = ( P3 @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D ) ) ) )
% 2.86/3.16 => ( ( ? [X8: int] : ( P @ X8 ) )
% 2.86/3.16 = ( ? [X2: int] :
% 2.86/3.16 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.86/3.16 & ( P3 @ X2 ) )
% 2.86/3.16 | ? [X2: int] :
% 2.86/3.16 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.86/3.16 & ? [Y5: int] :
% 2.86/3.16 ( ( member_int @ Y5 @ B )
% 2.86/3.16 & ( P @ ( plus_plus_int @ Y5 @ X2 ) ) ) ) ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % cpmi
% 2.86/3.16 thf(fact_5332_less__eq,axiom,
% 2.86/3.16 ! [M2: nat,N: nat] :
% 2.86/3.16 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M2 @ N ) @ ( transi6264000038957366511cl_nat @ pred_nat ) )
% 2.86/3.16 = ( ord_less_nat @ M2 @ N ) ) ).
% 2.86/3.16
% 2.86/3.16 % less_eq
% 2.86/3.16 thf(fact_5333_all__nat__less,axiom,
% 2.86/3.16 ! [N: nat,P: nat > $o] :
% 2.86/3.16 ( ( ! [M: nat] :
% 2.86/3.16 ( ( ord_less_eq_nat @ M @ N )
% 2.86/3.16 => ( P @ M ) ) )
% 2.86/3.16 = ( ! [X2: nat] :
% 2.86/3.16 ( ( member_nat @ X2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 2.86/3.16 => ( P @ X2 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % all_nat_less
% 2.86/3.16 thf(fact_5334_ex__nat__less,axiom,
% 2.86/3.16 ! [N: nat,P: nat > $o] :
% 2.86/3.16 ( ( ? [M: nat] :
% 2.86/3.16 ( ( ord_less_eq_nat @ M @ N )
% 2.86/3.16 & ( P @ M ) ) )
% 2.86/3.16 = ( ? [X2: nat] :
% 2.86/3.16 ( ( member_nat @ X2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 2.86/3.16 & ( P @ X2 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % ex_nat_less
% 2.86/3.16 thf(fact_5335_atLeast0__atMost__Suc,axiom,
% 2.86/3.16 ! [N: nat] :
% 2.86/3.16 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 2.86/3.16 = ( insert_nat2 @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % atLeast0_atMost_Suc
% 2.86/3.16 thf(fact_5336_atLeastAtMost__insertL,axiom,
% 2.86/3.16 ! [M2: nat,N: nat] :
% 2.86/3.16 ( ( ord_less_eq_nat @ M2 @ N )
% 2.86/3.16 => ( ( insert_nat2 @ M2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) )
% 2.86/3.16 = ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % atLeastAtMost_insertL
% 2.86/3.16 thf(fact_5337_atLeastAtMostSuc__conv,axiom,
% 2.86/3.16 ! [M2: nat,N: nat] :
% 2.86/3.16 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 2.86/3.16 => ( ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) )
% 2.86/3.16 = ( insert_nat2 @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % atLeastAtMostSuc_conv
% 2.86/3.16 thf(fact_5338_Icc__eq__insert__lb__nat,axiom,
% 2.86/3.16 ! [M2: nat,N: nat] :
% 2.86/3.16 ( ( ord_less_eq_nat @ M2 @ N )
% 2.86/3.16 => ( ( set_or1269000886237332187st_nat @ M2 @ N )
% 2.86/3.16 = ( insert_nat2 @ M2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % Icc_eq_insert_lb_nat
% 2.86/3.16 thf(fact_5339_greaterThanLessThan__upto,axiom,
% 2.86/3.16 ( set_or5832277885323065728an_int
% 2.86/3.16 = ( ^ [I4: int,J2: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I4 @ one_one_int ) @ ( minus_minus_int @ J2 @ one_one_int ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % greaterThanLessThan_upto
% 2.86/3.16 thf(fact_5340_atLeast1__atMost__eq__remove0,axiom,
% 2.86/3.16 ! [N: nat] :
% 2.86/3.16 ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N )
% 2.86/3.16 = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N ) @ ( insert_nat2 @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % atLeast1_atMost_eq_remove0
% 2.86/3.16 thf(fact_5341_atMost__0,axiom,
% 2.86/3.16 ( ( set_ord_atMost_nat @ zero_zero_nat )
% 2.86/3.16 = ( insert_nat2 @ zero_zero_nat @ bot_bot_set_nat ) ) ).
% 2.86/3.16
% 2.86/3.16 % atMost_0
% 2.86/3.16 thf(fact_5342_atMost__Suc,axiom,
% 2.86/3.16 ! [K3: nat] :
% 2.86/3.16 ( ( set_ord_atMost_nat @ ( suc @ K3 ) )
% 2.86/3.16 = ( insert_nat2 @ ( suc @ K3 ) @ ( set_ord_atMost_nat @ K3 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % atMost_Suc
% 2.86/3.16 thf(fact_5343_atMost__nat__numeral,axiom,
% 2.86/3.16 ! [K3: num] :
% 2.86/3.16 ( ( set_ord_atMost_nat @ ( numeral_numeral_nat @ K3 ) )
% 2.86/3.16 = ( insert_nat2 @ ( numeral_numeral_nat @ K3 ) @ ( set_ord_atMost_nat @ ( pred_numeral @ K3 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % atMost_nat_numeral
% 2.86/3.16 thf(fact_5344_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 2.86/3.16 ! [N: nat,J: nat,I: nat] :
% 2.86/3.16 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ ( suc @ I ) ) )
% 2.86/3.16 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) ) @ N )
% 2.86/3.16 = ( suc @ ( plus_plus_nat @ I @ N ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % nth_sorted_list_of_set_greaterThanLessThan
% 2.86/3.16 thf(fact_5345_sorted__list__of__set__atMost__Suc,axiom,
% 2.86/3.16 ! [K3: nat] :
% 2.86/3.16 ( ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ ( suc @ K3 ) ) )
% 2.86/3.16 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ K3 ) ) @ ( cons_nat @ ( suc @ K3 ) @ nil_nat ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % sorted_list_of_set_atMost_Suc
% 2.86/3.16 thf(fact_5346_sorted__list__of__set__greaterThanLessThan,axiom,
% 2.86/3.16 ! [I: nat,J: nat] :
% 2.86/3.16 ( ( ord_less_nat @ ( suc @ I ) @ J )
% 2.86/3.16 => ( ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) )
% 2.86/3.16 = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % sorted_list_of_set_greaterThanLessThan
% 2.86/3.16 thf(fact_5347_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 2.86/3.16 ! [N: nat] :
% 2.86/3.16 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 2.86/3.16 = ( insert_nat2 @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % atLeast0_atMost_Suc_eq_insert_0
% 2.86/3.16 thf(fact_5348_atMost__Suc__eq__insert__0,axiom,
% 2.86/3.16 ! [N: nat] :
% 2.86/3.16 ( ( set_ord_atMost_nat @ ( suc @ N ) )
% 2.86/3.16 = ( insert_nat2 @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % atMost_Suc_eq_insert_0
% 2.86/3.16 thf(fact_5349_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 2.86/3.16 ! [N: nat,J: nat,I: nat] :
% 2.86/3.16 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ I ) )
% 2.86/3.16 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) ) @ N )
% 2.86/3.16 = ( suc @ ( plus_plus_nat @ I @ N ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % nth_sorted_list_of_set_greaterThanAtMost
% 2.86/3.16 thf(fact_5350_finite__nat__set__iff__bounded,axiom,
% 2.86/3.16 ( finite_finite_nat
% 2.86/3.16 = ( ^ [N8: set_nat] :
% 2.86/3.16 ? [M: nat] :
% 2.86/3.16 ! [X2: nat] :
% 2.86/3.16 ( ( member_nat @ X2 @ N8 )
% 2.86/3.16 => ( ord_less_nat @ X2 @ M ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % finite_nat_set_iff_bounded
% 2.86/3.16 thf(fact_5351_bounded__nat__set__is__finite,axiom,
% 2.86/3.16 ! [N7: set_nat,N: nat] :
% 2.86/3.16 ( ! [X3: nat] :
% 2.86/3.16 ( ( member_nat @ X3 @ N7 )
% 2.86/3.16 => ( ord_less_nat @ X3 @ N ) )
% 2.86/3.16 => ( finite_finite_nat @ N7 ) ) ).
% 2.86/3.16
% 2.86/3.16 % bounded_nat_set_is_finite
% 2.86/3.16 thf(fact_5352_sorted__list__of__set__greaterThanAtMost,axiom,
% 2.86/3.16 ! [I: nat,J: nat] :
% 2.86/3.16 ( ( ord_less_eq_nat @ ( suc @ I ) @ J )
% 2.86/3.16 => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) )
% 2.86/3.16 = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % sorted_list_of_set_greaterThanAtMost
% 2.86/3.16 thf(fact_5353_Gcd__remove0__nat,axiom,
% 2.86/3.16 ! [M5: set_nat] :
% 2.86/3.16 ( ( finite_finite_nat @ M5 )
% 2.86/3.16 => ( ( gcd_Gcd_nat @ M5 )
% 2.86/3.16 = ( gcd_Gcd_nat @ ( minus_minus_set_nat @ M5 @ ( insert_nat2 @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % Gcd_remove0_nat
% 2.86/3.16 thf(fact_5354_set__encode__insert,axiom,
% 2.86/3.16 ! [A: set_nat,N: nat] :
% 2.86/3.16 ( ( finite_finite_nat @ A )
% 2.86/3.16 => ( ~ ( member_nat @ N @ A )
% 2.86/3.16 => ( ( nat_set_encode @ ( insert_nat2 @ N @ A ) )
% 2.86/3.16 = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( nat_set_encode @ A ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % set_encode_insert
% 2.86/3.16 thf(fact_5355_set__encode__empty,axiom,
% 2.86/3.16 ( ( nat_set_encode @ bot_bot_set_nat )
% 2.86/3.16 = zero_zero_nat ) ).
% 2.86/3.16
% 2.86/3.16 % set_encode_empty
% 2.86/3.16 thf(fact_5356_greaterThanAtMost__upto,axiom,
% 2.86/3.16 ( set_or6656581121297822940st_int
% 2.86/3.16 = ( ^ [I4: int,J2: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I4 @ one_one_int ) @ J2 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % greaterThanAtMost_upto
% 2.86/3.16 thf(fact_5357_unbounded__k__infinite,axiom,
% 2.86/3.16 ! [K3: nat,S: set_nat] :
% 2.86/3.16 ( ! [M6: nat] :
% 2.86/3.16 ( ( ord_less_nat @ K3 @ M6 )
% 2.86/3.16 => ? [N9: nat] :
% 2.86/3.16 ( ( ord_less_nat @ M6 @ N9 )
% 2.86/3.16 & ( member_nat @ N9 @ S ) ) )
% 2.86/3.16 => ~ ( finite_finite_nat @ S ) ) ).
% 2.86/3.16
% 2.86/3.16 % unbounded_k_infinite
% 2.86/3.16 thf(fact_5358_infinite__nat__iff__unbounded,axiom,
% 2.86/3.16 ! [S: set_nat] :
% 2.86/3.16 ( ( ~ ( finite_finite_nat @ S ) )
% 2.86/3.16 = ( ! [M: nat] :
% 2.86/3.16 ? [N2: nat] :
% 2.86/3.16 ( ( ord_less_nat @ M @ N2 )
% 2.86/3.16 & ( member_nat @ N2 @ S ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % infinite_nat_iff_unbounded
% 2.86/3.16 thf(fact_5359_sorted__list__of__set__lessThan__Suc,axiom,
% 2.86/3.16 ! [K3: nat] :
% 2.86/3.16 ( ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ ( suc @ K3 ) ) )
% 2.86/3.16 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ K3 ) ) @ ( cons_nat @ K3 @ nil_nat ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % sorted_list_of_set_lessThan_Suc
% 2.86/3.16 thf(fact_5360_lessThan__0,axiom,
% 2.86/3.16 ( ( set_ord_lessThan_nat @ zero_zero_nat )
% 2.86/3.16 = bot_bot_set_nat ) ).
% 2.86/3.16
% 2.86/3.16 % lessThan_0
% 2.86/3.16 thf(fact_5361_atLeastLessThan__singleton,axiom,
% 2.86/3.16 ! [M2: nat] :
% 2.86/3.16 ( ( set_or4665077453230672383an_nat @ M2 @ ( suc @ M2 ) )
% 2.86/3.16 = ( insert_nat2 @ M2 @ bot_bot_set_nat ) ) ).
% 2.86/3.16
% 2.86/3.16 % atLeastLessThan_singleton
% 2.86/3.16 thf(fact_5362_ex__nat__less__eq,axiom,
% 2.86/3.16 ! [N: nat,P: nat > $o] :
% 2.86/3.16 ( ( ? [M: nat] :
% 2.86/3.16 ( ( ord_less_nat @ M @ N )
% 2.86/3.16 & ( P @ M ) ) )
% 2.86/3.16 = ( ? [X2: nat] :
% 2.86/3.16 ( ( member_nat @ X2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 2.86/3.16 & ( P @ X2 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % ex_nat_less_eq
% 2.86/3.16 thf(fact_5363_all__nat__less__eq,axiom,
% 2.86/3.16 ! [N: nat,P: nat > $o] :
% 2.86/3.16 ( ( ! [M: nat] :
% 2.86/3.16 ( ( ord_less_nat @ M @ N )
% 2.86/3.16 => ( P @ M ) ) )
% 2.86/3.16 = ( ! [X2: nat] :
% 2.86/3.16 ( ( member_nat @ X2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 2.86/3.16 => ( P @ X2 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % all_nat_less_eq
% 2.86/3.16 thf(fact_5364_lessThan__empty__iff,axiom,
% 2.86/3.16 ! [N: nat] :
% 2.86/3.16 ( ( ( set_ord_lessThan_nat @ N )
% 2.86/3.16 = bot_bot_set_nat )
% 2.86/3.16 = ( N = zero_zero_nat ) ) ).
% 2.86/3.16
% 2.86/3.16 % lessThan_empty_iff
% 2.86/3.16 thf(fact_5365_lessThan__Suc,axiom,
% 2.86/3.16 ! [K3: nat] :
% 2.86/3.16 ( ( set_ord_lessThan_nat @ ( suc @ K3 ) )
% 2.86/3.16 = ( insert_nat2 @ K3 @ ( set_ord_lessThan_nat @ K3 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % lessThan_Suc
% 2.86/3.16 thf(fact_5366_atLeastLessThan0,axiom,
% 2.86/3.16 ! [M2: nat] :
% 2.86/3.16 ( ( set_or4665077453230672383an_nat @ M2 @ zero_zero_nat )
% 2.86/3.16 = bot_bot_set_nat ) ).
% 2.86/3.16
% 2.86/3.16 % atLeastLessThan0
% 2.86/3.16 thf(fact_5367_atLeast1__lessThan__eq__remove0,axiom,
% 2.86/3.16 ! [N: nat] :
% 2.86/3.16 ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N )
% 2.86/3.16 = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N ) @ ( insert_nat2 @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % atLeast1_lessThan_eq_remove0
% 2.86/3.16 thf(fact_5368_atLeast0__lessThan__Suc,axiom,
% 2.86/3.16 ! [N: nat] :
% 2.86/3.16 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 2.86/3.16 = ( insert_nat2 @ N @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % atLeast0_lessThan_Suc
% 2.86/3.16 thf(fact_5369_lessThan__nat__numeral,axiom,
% 2.86/3.16 ! [K3: num] :
% 2.86/3.16 ( ( set_ord_lessThan_nat @ ( numeral_numeral_nat @ K3 ) )
% 2.86/3.16 = ( insert_nat2 @ ( pred_numeral @ K3 ) @ ( set_ord_lessThan_nat @ ( pred_numeral @ K3 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % lessThan_nat_numeral
% 2.86/3.16 thf(fact_5370_lessThan__Suc__eq__insert__0,axiom,
% 2.86/3.16 ! [N: nat] :
% 2.86/3.16 ( ( set_ord_lessThan_nat @ ( suc @ N ) )
% 2.86/3.16 = ( insert_nat2 @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % lessThan_Suc_eq_insert_0
% 2.86/3.16 thf(fact_5371_atLeastLessThanSuc,axiom,
% 2.86/3.16 ! [M2: nat,N: nat] :
% 2.86/3.16 ( ( ( ord_less_eq_nat @ M2 @ N )
% 2.86/3.16 => ( ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N ) )
% 2.86/3.16 = ( insert_nat2 @ N @ ( set_or4665077453230672383an_nat @ M2 @ N ) ) ) )
% 2.86/3.16 & ( ~ ( ord_less_eq_nat @ M2 @ N )
% 2.86/3.16 => ( ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N ) )
% 2.86/3.16 = bot_bot_set_nat ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % atLeastLessThanSuc
% 2.86/3.16 thf(fact_5372_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 2.86/3.16 ! [N: nat] :
% 2.86/3.16 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 2.86/3.16 = ( insert_nat2 @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % atLeast0_lessThan_Suc_eq_insert_0
% 2.86/3.16 thf(fact_5373_atLeastLessThan__nat__numeral,axiom,
% 2.86/3.16 ! [M2: nat,K3: num] :
% 2.86/3.16 ( ( ( ord_less_eq_nat @ M2 @ ( pred_numeral @ K3 ) )
% 2.86/3.16 => ( ( set_or4665077453230672383an_nat @ M2 @ ( numeral_numeral_nat @ K3 ) )
% 2.86/3.16 = ( insert_nat2 @ ( pred_numeral @ K3 ) @ ( set_or4665077453230672383an_nat @ M2 @ ( pred_numeral @ K3 ) ) ) ) )
% 2.86/3.16 & ( ~ ( ord_less_eq_nat @ M2 @ ( pred_numeral @ K3 ) )
% 2.86/3.16 => ( ( set_or4665077453230672383an_nat @ M2 @ ( numeral_numeral_nat @ K3 ) )
% 2.86/3.16 = bot_bot_set_nat ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % atLeastLessThan_nat_numeral
% 2.86/3.16 thf(fact_5374_atLeastLessThan__upto,axiom,
% 2.86/3.16 ( set_or4662586982721622107an_int
% 2.86/3.16 = ( ^ [I4: int,J2: int] : ( set_int2 @ ( upto @ I4 @ ( minus_minus_int @ J2 @ one_one_int ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % atLeastLessThan_upto
% 2.86/3.16 thf(fact_5375_atLeast__Suc,axiom,
% 2.86/3.16 ! [K3: nat] :
% 2.86/3.16 ( ( set_ord_atLeast_nat @ ( suc @ K3 ) )
% 2.86/3.16 = ( minus_minus_set_nat @ ( set_ord_atLeast_nat @ K3 ) @ ( insert_nat2 @ K3 @ bot_bot_set_nat ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % atLeast_Suc
% 2.86/3.16 thf(fact_5376_card__Collect__less__nat,axiom,
% 2.86/3.16 ! [N: nat] :
% 2.86/3.16 ( ( finite_card_nat
% 2.86/3.16 @ ( collect_nat
% 2.86/3.16 @ ^ [I4: nat] : ( ord_less_nat @ I4 @ N ) ) )
% 2.86/3.16 = N ) ).
% 2.86/3.16
% 2.86/3.16 % card_Collect_less_nat
% 2.86/3.16 thf(fact_5377_finite__Collect__less__nat,axiom,
% 2.86/3.16 ! [K3: nat] :
% 2.86/3.16 ( finite_finite_nat
% 2.86/3.16 @ ( collect_nat
% 2.86/3.16 @ ^ [N2: nat] : ( ord_less_nat @ N2 @ K3 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % finite_Collect_less_nat
% 2.86/3.16 thf(fact_5378_card__less__Suc2,axiom,
% 2.86/3.16 ! [M5: set_nat,I: nat] :
% 2.86/3.16 ( ~ ( member_nat @ zero_zero_nat @ M5 )
% 2.86/3.16 => ( ( finite_card_nat
% 2.86/3.16 @ ( collect_nat
% 2.86/3.16 @ ^ [K4: nat] :
% 2.86/3.16 ( ( member_nat @ ( suc @ K4 ) @ M5 )
% 2.86/3.16 & ( ord_less_nat @ K4 @ I ) ) ) )
% 2.86/3.16 = ( finite_card_nat
% 2.86/3.16 @ ( collect_nat
% 2.86/3.16 @ ^ [K4: nat] :
% 2.86/3.16 ( ( member_nat @ K4 @ M5 )
% 2.86/3.16 & ( ord_less_nat @ K4 @ ( suc @ I ) ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % card_less_Suc2
% 2.86/3.16 thf(fact_5379_card__less__Suc,axiom,
% 2.86/3.16 ! [M5: set_nat,I: nat] :
% 2.86/3.16 ( ( member_nat @ zero_zero_nat @ M5 )
% 2.86/3.16 => ( ( suc
% 2.86/3.16 @ ( finite_card_nat
% 2.86/3.16 @ ( collect_nat
% 2.86/3.16 @ ^ [K4: nat] :
% 2.86/3.16 ( ( member_nat @ ( suc @ K4 ) @ M5 )
% 2.86/3.16 & ( ord_less_nat @ K4 @ I ) ) ) ) )
% 2.86/3.16 = ( finite_card_nat
% 2.86/3.16 @ ( collect_nat
% 2.86/3.16 @ ^ [K4: nat] :
% 2.86/3.16 ( ( member_nat @ K4 @ M5 )
% 2.86/3.16 & ( ord_less_nat @ K4 @ ( suc @ I ) ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % card_less_Suc
% 2.86/3.16 thf(fact_5380_card__less,axiom,
% 2.86/3.16 ! [M5: set_nat,I: nat] :
% 2.86/3.16 ( ( member_nat @ zero_zero_nat @ M5 )
% 2.86/3.16 => ( ( finite_card_nat
% 2.86/3.16 @ ( collect_nat
% 2.86/3.16 @ ^ [K4: nat] :
% 2.86/3.16 ( ( member_nat @ K4 @ M5 )
% 2.86/3.16 & ( ord_less_nat @ K4 @ ( suc @ I ) ) ) ) )
% 2.86/3.16 != zero_zero_nat ) ) ).
% 2.86/3.16
% 2.86/3.16 % card_less
% 2.86/3.16 thf(fact_5381_finite__M__bounded__by__nat,axiom,
% 2.86/3.16 ! [P: nat > $o,I: nat] :
% 2.86/3.16 ( finite_finite_nat
% 2.86/3.16 @ ( collect_nat
% 2.86/3.16 @ ^ [K4: nat] :
% 2.86/3.16 ( ( P @ K4 )
% 2.86/3.16 & ( ord_less_nat @ K4 @ I ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % finite_M_bounded_by_nat
% 2.86/3.16 thf(fact_5382_nat__less__as__int,axiom,
% 2.86/3.16 ( ord_less_nat
% 2.86/3.16 = ( ^ [A3: nat,B3: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % nat_less_as_int
% 2.86/3.16 thf(fact_5383_finite__divisors__nat,axiom,
% 2.86/3.16 ! [M2: nat] :
% 2.86/3.16 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 2.86/3.16 => ( finite_finite_nat
% 2.86/3.16 @ ( collect_nat
% 2.86/3.16 @ ^ [D5: nat] : ( dvd_dvd_nat @ D5 @ M2 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % finite_divisors_nat
% 2.86/3.16 thf(fact_5384_range__mod,axiom,
% 2.86/3.16 ! [N: nat] :
% 2.86/3.16 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.16 => ( ( image_nat_nat
% 2.86/3.16 @ ^ [M: nat] : ( modulo_modulo_nat @ M @ N )
% 2.86/3.16 @ top_top_set_nat )
% 2.86/3.16 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % range_mod
% 2.86/3.16 thf(fact_5385_image__minus__const__atLeastLessThan__nat,axiom,
% 2.86/3.16 ! [C: nat,Y: nat,X: nat] :
% 2.86/3.16 ( ( ( ord_less_nat @ C @ Y )
% 2.86/3.16 => ( ( image_nat_nat
% 2.86/3.16 @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C )
% 2.86/3.16 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 2.86/3.16 = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X @ C ) @ ( minus_minus_nat @ Y @ C ) ) ) )
% 2.86/3.16 & ( ~ ( ord_less_nat @ C @ Y )
% 2.86/3.16 => ( ( ( ord_less_nat @ X @ Y )
% 2.86/3.16 => ( ( image_nat_nat
% 2.86/3.16 @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C )
% 2.86/3.16 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 2.86/3.16 = ( insert_nat2 @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 2.86/3.16 & ( ~ ( ord_less_nat @ X @ Y )
% 2.86/3.16 => ( ( image_nat_nat
% 2.86/3.16 @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C )
% 2.86/3.16 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 2.86/3.16 = bot_bot_set_nat ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % image_minus_const_atLeastLessThan_nat
% 2.86/3.16 thf(fact_5386_Sup__nat__def,axiom,
% 2.86/3.16 ( complete_Sup_Sup_nat
% 2.86/3.16 = ( ^ [X8: set_nat] : ( if_nat @ ( X8 = bot_bot_set_nat ) @ zero_zero_nat @ ( lattic8265883725875713057ax_nat @ X8 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % Sup_nat_def
% 2.86/3.16 thf(fact_5387_mask__eq__sum__exp__nat,axiom,
% 2.86/3.16 ! [N: nat] :
% 2.86/3.16 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( suc @ zero_zero_nat ) )
% 2.86/3.16 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.86/3.16 @ ( collect_nat
% 2.86/3.16 @ ^ [Q8: nat] : ( ord_less_nat @ Q8 @ N ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % mask_eq_sum_exp_nat
% 2.86/3.16 thf(fact_5388_divmod__nat__if,axiom,
% 2.86/3.16 ( divmod_nat
% 2.86/3.16 = ( ^ [M: nat,N2: nat] :
% 2.86/3.16 ( if_Pro6206227464963214023at_nat
% 2.86/3.16 @ ( ( N2 = zero_zero_nat )
% 2.86/3.16 | ( ord_less_nat @ M @ N2 ) )
% 2.86/3.16 @ ( product_Pair_nat_nat @ zero_zero_nat @ M )
% 2.86/3.16 @ ( produc2626176000494625587at_nat
% 2.86/3.16 @ ^ [Q8: nat] : ( product_Pair_nat_nat @ ( suc @ Q8 ) )
% 2.86/3.16 @ ( divmod_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % divmod_nat_if
% 2.86/3.16 thf(fact_5389_divmod__step__nat__def,axiom,
% 2.86/3.16 ( unique5026877609467782581ep_nat
% 2.86/3.16 = ( ^ [L4: num] :
% 2.86/3.16 ( produc2626176000494625587at_nat
% 2.86/3.16 @ ^ [Q8: nat,R4: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L4 ) @ R4 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q8 ) @ one_one_nat ) @ ( minus_minus_nat @ R4 @ ( numeral_numeral_nat @ L4 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q8 ) @ R4 ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % divmod_step_nat_def
% 2.86/3.16 thf(fact_5390_divmod__step__int__def,axiom,
% 2.86/3.16 ( unique5024387138958732305ep_int
% 2.86/3.16 = ( ^ [L4: num] :
% 2.86/3.16 ( produc4245557441103728435nt_int
% 2.86/3.16 @ ^ [Q8: int,R4: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L4 ) @ R4 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q8 ) @ one_one_int ) @ ( minus_minus_int @ R4 @ ( numeral_numeral_int @ L4 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q8 ) @ R4 ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % divmod_step_int_def
% 2.86/3.16 thf(fact_5391_wf__less,axiom,
% 2.86/3.16 wf_nat @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ).
% 2.86/3.16
% 2.86/3.16 % wf_less
% 2.86/3.16 thf(fact_5392_natLeq__on__wo__rel,axiom,
% 2.86/3.16 ! [N: nat] :
% 2.86/3.16 ( bNF_We3818239936649020644el_nat
% 2.86/3.16 @ ( collec3392354462482085612at_nat
% 2.86/3.16 @ ( produc6081775807080527818_nat_o
% 2.86/3.16 @ ^ [X2: nat,Y5: nat] :
% 2.86/3.16 ( ( ord_less_nat @ X2 @ N )
% 2.86/3.16 & ( ord_less_nat @ Y5 @ N )
% 2.86/3.16 & ( ord_less_eq_nat @ X2 @ Y5 ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % natLeq_on_wo_rel
% 2.86/3.16 thf(fact_5393_Field__natLeq__on,axiom,
% 2.86/3.16 ! [N: nat] :
% 2.86/3.16 ( ( field_nat
% 2.86/3.16 @ ( collec3392354462482085612at_nat
% 2.86/3.16 @ ( produc6081775807080527818_nat_o
% 2.86/3.16 @ ^ [X2: nat,Y5: nat] :
% 2.86/3.16 ( ( ord_less_nat @ X2 @ N )
% 2.86/3.16 & ( ord_less_nat @ Y5 @ N )
% 2.86/3.16 & ( ord_less_eq_nat @ X2 @ Y5 ) ) ) ) )
% 2.86/3.16 = ( collect_nat
% 2.86/3.16 @ ^ [X2: nat] : ( ord_less_nat @ X2 @ N ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % Field_natLeq_on
% 2.86/3.16 thf(fact_5394_natLess__def,axiom,
% 2.86/3.16 ( bNF_Ca8459412986667044542atLess
% 2.86/3.16 = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % natLess_def
% 2.86/3.16 thf(fact_5395_sort__upto,axiom,
% 2.86/3.16 ! [I: int,J: int] :
% 2.86/3.16 ( ( linord1735203802627413978nt_int
% 2.86/3.16 @ ^ [X2: int] : X2
% 2.86/3.16 @ ( upto @ I @ J ) )
% 2.86/3.16 = ( upto @ I @ J ) ) ).
% 2.86/3.16
% 2.86/3.16 % sort_upto
% 2.86/3.16 thf(fact_5396_remdups__upt,axiom,
% 2.86/3.16 ! [M2: nat,N: nat] :
% 2.86/3.16 ( ( remdups_nat @ ( upt @ M2 @ N ) )
% 2.86/3.16 = ( upt @ M2 @ N ) ) ).
% 2.86/3.16
% 2.86/3.16 % remdups_upt
% 2.86/3.16 thf(fact_5397_sort__upt,axiom,
% 2.86/3.16 ! [M2: nat,N: nat] :
% 2.86/3.16 ( ( linord738340561235409698at_nat
% 2.86/3.16 @ ^ [X2: nat] : X2
% 2.86/3.16 @ ( upt @ M2 @ N ) )
% 2.86/3.16 = ( upt @ M2 @ N ) ) ).
% 2.86/3.16
% 2.86/3.16 % sort_upt
% 2.86/3.16 thf(fact_5398_tl__upt,axiom,
% 2.86/3.16 ! [M2: nat,N: nat] :
% 2.86/3.16 ( ( tl_nat @ ( upt @ M2 @ N ) )
% 2.86/3.16 = ( upt @ ( suc @ M2 ) @ N ) ) ).
% 2.86/3.16
% 2.86/3.16 % tl_upt
% 2.86/3.16 thf(fact_5399_hd__upt,axiom,
% 2.86/3.16 ! [I: nat,J: nat] :
% 2.86/3.16 ( ( ord_less_nat @ I @ J )
% 2.86/3.16 => ( ( hd_nat @ ( upt @ I @ J ) )
% 2.86/3.16 = I ) ) ).
% 2.86/3.16
% 2.86/3.16 % hd_upt
% 2.86/3.16 thf(fact_5400_drop__upt,axiom,
% 2.86/3.16 ! [M2: nat,I: nat,J: nat] :
% 2.86/3.16 ( ( drop_nat @ M2 @ ( upt @ I @ J ) )
% 2.86/3.16 = ( upt @ ( plus_plus_nat @ I @ M2 ) @ J ) ) ).
% 2.86/3.16
% 2.86/3.16 % drop_upt
% 2.86/3.16 thf(fact_5401_take__upt,axiom,
% 2.86/3.16 ! [I: nat,M2: nat,N: nat] :
% 2.86/3.16 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ M2 ) @ N )
% 2.86/3.16 => ( ( take_nat @ M2 @ ( upt @ I @ N ) )
% 2.86/3.16 = ( upt @ I @ ( plus_plus_nat @ I @ M2 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % take_upt
% 2.86/3.16 thf(fact_5402_upt__0__eq__Nil__conv,axiom,
% 2.86/3.16 ! [J: nat] :
% 2.86/3.16 ( ( ( upt @ zero_zero_nat @ J )
% 2.86/3.16 = nil_nat )
% 2.86/3.16 = ( J = zero_zero_nat ) ) ).
% 2.86/3.16
% 2.86/3.16 % upt_0_eq_Nil_conv
% 2.86/3.16 thf(fact_5403_upt__conv__Nil,axiom,
% 2.86/3.16 ! [J: nat,I: nat] :
% 2.86/3.16 ( ( ord_less_eq_nat @ J @ I )
% 2.86/3.16 => ( ( upt @ I @ J )
% 2.86/3.16 = nil_nat ) ) ).
% 2.86/3.16
% 2.86/3.16 % upt_conv_Nil
% 2.86/3.16 thf(fact_5404_upt__merge,axiom,
% 2.86/3.16 ! [I: nat,J: nat,K3: nat] :
% 2.86/3.16 ( ( ( ord_less_eq_nat @ I @ J )
% 2.86/3.16 & ( ord_less_eq_nat @ J @ K3 ) )
% 2.86/3.16 => ( ( append_nat @ ( upt @ I @ J ) @ ( upt @ J @ K3 ) )
% 2.86/3.16 = ( upt @ I @ K3 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % upt_merge
% 2.86/3.16 thf(fact_5405_sorted__list__of__set__range,axiom,
% 2.86/3.16 ! [M2: nat,N: nat] :
% 2.86/3.16 ( ( linord2614967742042102400et_nat @ ( set_or4665077453230672383an_nat @ M2 @ N ) )
% 2.86/3.16 = ( upt @ M2 @ N ) ) ).
% 2.86/3.16
% 2.86/3.16 % sorted_list_of_set_range
% 2.86/3.16 thf(fact_5406_length__upt,axiom,
% 2.86/3.16 ! [I: nat,J: nat] :
% 2.86/3.16 ( ( size_size_list_nat @ ( upt @ I @ J ) )
% 2.86/3.16 = ( minus_minus_nat @ J @ I ) ) ).
% 2.86/3.16
% 2.86/3.16 % length_upt
% 2.86/3.16 thf(fact_5407_last__upt,axiom,
% 2.86/3.16 ! [I: nat,J: nat] :
% 2.86/3.16 ( ( ord_less_nat @ I @ J )
% 2.86/3.16 => ( ( last_nat @ ( upt @ I @ J ) )
% 2.86/3.16 = ( minus_minus_nat @ J @ one_one_nat ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % last_upt
% 2.86/3.16 thf(fact_5408_upt__eq__Nil__conv,axiom,
% 2.86/3.16 ! [I: nat,J: nat] :
% 2.86/3.16 ( ( ( upt @ I @ J )
% 2.86/3.16 = nil_nat )
% 2.86/3.16 = ( ( J = zero_zero_nat )
% 2.86/3.16 | ( ord_less_eq_nat @ J @ I ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % upt_eq_Nil_conv
% 2.86/3.16 thf(fact_5409_nth__upt,axiom,
% 2.86/3.16 ! [I: nat,K3: nat,J: nat] :
% 2.86/3.16 ( ( ord_less_nat @ ( plus_plus_nat @ I @ K3 ) @ J )
% 2.86/3.16 => ( ( nth_nat @ ( upt @ I @ J ) @ K3 )
% 2.86/3.16 = ( plus_plus_nat @ I @ K3 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % nth_upt
% 2.86/3.16 thf(fact_5410_upt__rec__numeral,axiom,
% 2.86/3.16 ! [M2: num,N: num] :
% 2.86/3.16 ( ( ( ord_less_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 2.86/3.16 => ( ( upt @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 2.86/3.16 = ( cons_nat @ ( numeral_numeral_nat @ M2 ) @ ( upt @ ( suc @ ( numeral_numeral_nat @ M2 ) ) @ ( numeral_numeral_nat @ N ) ) ) ) )
% 2.86/3.16 & ( ~ ( ord_less_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 2.86/3.16 => ( ( upt @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 2.86/3.16 = nil_nat ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % upt_rec_numeral
% 2.86/3.16 thf(fact_5411_atLeastLessThan__upt,axiom,
% 2.86/3.16 ( set_or4665077453230672383an_nat
% 2.86/3.16 = ( ^ [I4: nat,J2: nat] : ( set_nat2 @ ( upt @ I4 @ J2 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % atLeastLessThan_upt
% 2.86/3.16 thf(fact_5412_distinct__upt,axiom,
% 2.86/3.16 ! [I: nat,J: nat] : ( distinct_nat @ ( upt @ I @ J ) ) ).
% 2.86/3.16
% 2.86/3.16 % distinct_upt
% 2.86/3.16 thf(fact_5413_map__add__upt_H,axiom,
% 2.86/3.16 ! [Ofs: nat,A2: nat,B2: nat] :
% 2.86/3.16 ( ( map_nat_nat
% 2.86/3.16 @ ^ [I4: nat] : ( plus_plus_nat @ I4 @ Ofs )
% 2.86/3.16 @ ( upt @ A2 @ B2 ) )
% 2.86/3.16 = ( upt @ ( plus_plus_nat @ A2 @ Ofs ) @ ( plus_plus_nat @ B2 @ Ofs ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % map_add_upt'
% 2.86/3.16 thf(fact_5414_map__Suc__upt,axiom,
% 2.86/3.16 ! [M2: nat,N: nat] :
% 2.86/3.16 ( ( map_nat_nat @ suc @ ( upt @ M2 @ N ) )
% 2.86/3.16 = ( upt @ ( suc @ M2 ) @ ( suc @ N ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % map_Suc_upt
% 2.86/3.16 thf(fact_5415_atLeastAtMost__upt,axiom,
% 2.86/3.16 ( set_or1269000886237332187st_nat
% 2.86/3.16 = ( ^ [N2: nat,M: nat] : ( set_nat2 @ ( upt @ N2 @ ( suc @ M ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % atLeastAtMost_upt
% 2.86/3.16 thf(fact_5416_butlast__upt,axiom,
% 2.86/3.16 ! [M2: nat,N: nat] :
% 2.86/3.16 ( ( butlast_nat @ ( upt @ M2 @ N ) )
% 2.86/3.16 = ( upt @ M2 @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % butlast_upt
% 2.86/3.16 thf(fact_5417_atLeast__upt,axiom,
% 2.86/3.16 ( set_ord_lessThan_nat
% 2.86/3.16 = ( ^ [N2: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ N2 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % atLeast_upt
% 2.86/3.16 thf(fact_5418_upt__conv__Cons__Cons,axiom,
% 2.86/3.16 ! [M2: nat,N: nat,Ns: list_nat,Q6: nat] :
% 2.86/3.16 ( ( ( cons_nat @ M2 @ ( cons_nat @ N @ Ns ) )
% 2.86/3.16 = ( upt @ M2 @ Q6 ) )
% 2.86/3.16 = ( ( cons_nat @ N @ Ns )
% 2.86/3.16 = ( upt @ ( suc @ M2 ) @ Q6 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % upt_conv_Cons_Cons
% 2.86/3.16 thf(fact_5419_upt__0,axiom,
% 2.86/3.16 ! [I: nat] :
% 2.86/3.16 ( ( upt @ I @ zero_zero_nat )
% 2.86/3.16 = nil_nat ) ).
% 2.86/3.16
% 2.86/3.16 % upt_0
% 2.86/3.16 thf(fact_5420_sorted__wrt__upt,axiom,
% 2.86/3.16 ! [M2: nat,N: nat] : ( sorted_wrt_nat @ ord_less_nat @ ( upt @ M2 @ N ) ) ).
% 2.86/3.16
% 2.86/3.16 % sorted_wrt_upt
% 2.86/3.16 thf(fact_5421_map__add__upt,axiom,
% 2.86/3.16 ! [N: nat,M2: nat] :
% 2.86/3.16 ( ( map_nat_nat
% 2.86/3.16 @ ^ [I4: nat] : ( plus_plus_nat @ I4 @ N )
% 2.86/3.16 @ ( upt @ zero_zero_nat @ M2 ) )
% 2.86/3.16 = ( upt @ N @ ( plus_plus_nat @ M2 @ N ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % map_add_upt
% 2.86/3.16 thf(fact_5422_sorted__upt,axiom,
% 2.86/3.16 ! [M2: nat,N: nat] : ( sorted_wrt_nat @ ord_less_eq_nat @ ( upt @ M2 @ N ) ) ).
% 2.86/3.16
% 2.86/3.16 % sorted_upt
% 2.86/3.16 thf(fact_5423_greaterThanAtMost__upt,axiom,
% 2.86/3.16 ( set_or6659071591806873216st_nat
% 2.86/3.16 = ( ^ [N2: nat,M: nat] : ( set_nat2 @ ( upt @ ( suc @ N2 ) @ ( suc @ M ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % greaterThanAtMost_upt
% 2.86/3.16 thf(fact_5424_upt__eq__append__conv,axiom,
% 2.86/3.16 ! [I: nat,J: nat,Xs: list_nat,Ys: list_nat] :
% 2.86/3.16 ( ( ord_less_eq_nat @ I @ J )
% 2.86/3.16 => ( ( ( upt @ I @ J )
% 2.86/3.16 = ( append_nat @ Xs @ Ys ) )
% 2.86/3.16 = ( ? [K4: nat] :
% 2.86/3.16 ( ( ord_less_eq_nat @ I @ K4 )
% 2.86/3.16 & ( ord_less_eq_nat @ K4 @ J )
% 2.86/3.16 & ( ( upt @ I @ K4 )
% 2.86/3.16 = Xs )
% 2.86/3.16 & ( ( upt @ K4 @ J )
% 2.86/3.16 = Ys ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % upt_eq_append_conv
% 2.86/3.16 thf(fact_5425_greaterThanLessThan__upt,axiom,
% 2.86/3.16 ( set_or5834768355832116004an_nat
% 2.86/3.16 = ( ^ [N2: nat,M: nat] : ( set_nat2 @ ( upt @ ( suc @ N2 ) @ M ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % greaterThanLessThan_upt
% 2.86/3.16 thf(fact_5426_atMost__upto,axiom,
% 2.86/3.16 ( set_ord_atMost_nat
% 2.86/3.16 = ( ^ [N2: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ ( suc @ N2 ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % atMost_upto
% 2.86/3.16 thf(fact_5427_upt__conv__Cons,axiom,
% 2.86/3.16 ! [I: nat,J: nat] :
% 2.86/3.16 ( ( ord_less_nat @ I @ J )
% 2.86/3.16 => ( ( upt @ I @ J )
% 2.86/3.16 = ( cons_nat @ I @ ( upt @ ( suc @ I ) @ J ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % upt_conv_Cons
% 2.86/3.16 thf(fact_5428_upt__filter__extend,axiom,
% 2.86/3.16 ! [U: nat,U3: nat,P: nat > $o] :
% 2.86/3.16 ( ( ord_less_eq_nat @ U @ U3 )
% 2.86/3.16 => ( ! [I5: nat] :
% 2.86/3.16 ( ( ( ord_less_eq_nat @ U @ I5 )
% 2.86/3.16 & ( ord_less_nat @ I5 @ U3 ) )
% 2.86/3.16 => ~ ( P @ I5 ) )
% 2.86/3.16 => ( ( filter_nat2 @ P @ ( upt @ zero_zero_nat @ U ) )
% 2.86/3.16 = ( filter_nat2 @ P @ ( upt @ zero_zero_nat @ U3 ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % upt_filter_extend
% 2.86/3.16 thf(fact_5429_map__decr__upt,axiom,
% 2.86/3.16 ! [M2: nat,N: nat] :
% 2.86/3.16 ( ( map_nat_nat
% 2.86/3.16 @ ^ [N2: nat] : ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 2.86/3.16 @ ( upt @ ( suc @ M2 ) @ ( suc @ N ) ) )
% 2.86/3.16 = ( upt @ M2 @ N ) ) ).
% 2.86/3.16
% 2.86/3.16 % map_decr_upt
% 2.86/3.16 thf(fact_5430_upt__append,axiom,
% 2.86/3.16 ! [I: nat,J: nat] :
% 2.86/3.16 ( ( ord_less_nat @ I @ J )
% 2.86/3.16 => ( ( append_nat @ ( upt @ zero_zero_nat @ I ) @ ( upt @ I @ J ) )
% 2.86/3.16 = ( upt @ zero_zero_nat @ J ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % upt_append
% 2.86/3.16 thf(fact_5431_upt__add__eq__append,axiom,
% 2.86/3.16 ! [I: nat,J: nat,K3: nat] :
% 2.86/3.16 ( ( ord_less_eq_nat @ I @ J )
% 2.86/3.16 => ( ( upt @ I @ ( plus_plus_nat @ J @ K3 ) )
% 2.86/3.16 = ( append_nat @ ( upt @ I @ J ) @ ( upt @ J @ ( plus_plus_nat @ J @ K3 ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % upt_add_eq_append
% 2.86/3.16 thf(fact_5432_upt__eq__Cons__conv,axiom,
% 2.86/3.16 ! [I: nat,J: nat,X: nat,Xs: list_nat] :
% 2.86/3.16 ( ( ( upt @ I @ J )
% 2.86/3.16 = ( cons_nat @ X @ Xs ) )
% 2.86/3.16 = ( ( ord_less_nat @ I @ J )
% 2.86/3.16 & ( I = X )
% 2.86/3.16 & ( ( upt @ ( plus_plus_nat @ I @ one_one_nat ) @ J )
% 2.86/3.16 = Xs ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % upt_eq_Cons_conv
% 2.86/3.16 thf(fact_5433_upt__rec,axiom,
% 2.86/3.16 ( upt
% 2.86/3.16 = ( ^ [I4: nat,J2: nat] : ( if_list_nat @ ( ord_less_nat @ I4 @ J2 ) @ ( cons_nat @ I4 @ ( upt @ ( suc @ I4 ) @ J2 ) ) @ nil_nat ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % upt_rec
% 2.86/3.16 thf(fact_5434_upt__eq__lel__conv,axiom,
% 2.86/3.16 ! [L: nat,H2: nat,Is1: list_nat,I: nat,Is2: list_nat] :
% 2.86/3.16 ( ( ( upt @ L @ H2 )
% 2.86/3.16 = ( append_nat @ Is1 @ ( cons_nat @ I @ Is2 ) ) )
% 2.86/3.16 = ( ( Is1
% 2.86/3.16 = ( upt @ L @ I ) )
% 2.86/3.16 & ( Is2
% 2.86/3.16 = ( upt @ ( suc @ I ) @ H2 ) )
% 2.86/3.16 & ( ord_less_eq_nat @ L @ I )
% 2.86/3.16 & ( ord_less_nat @ I @ H2 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % upt_eq_lel_conv
% 2.86/3.16 thf(fact_5435_upt__Suc,axiom,
% 2.86/3.16 ! [I: nat,J: nat] :
% 2.86/3.16 ( ( ( ord_less_eq_nat @ I @ J )
% 2.86/3.16 => ( ( upt @ I @ ( suc @ J ) )
% 2.86/3.16 = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) )
% 2.86/3.16 & ( ~ ( ord_less_eq_nat @ I @ J )
% 2.86/3.16 => ( ( upt @ I @ ( suc @ J ) )
% 2.86/3.16 = nil_nat ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % upt_Suc
% 2.86/3.16 thf(fact_5436_upt__Suc__append,axiom,
% 2.86/3.16 ! [I: nat,J: nat] :
% 2.86/3.16 ( ( ord_less_eq_nat @ I @ J )
% 2.86/3.16 => ( ( upt @ I @ ( suc @ J ) )
% 2.86/3.16 = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % upt_Suc_append
% 2.86/3.16 thf(fact_5437_divmod__step__integer__def,axiom,
% 2.86/3.16 ( unique4921790084139445826nteger
% 2.86/3.16 = ( ^ [L4: num] :
% 2.86/3.16 ( produc6916734918728496179nteger
% 2.86/3.16 @ ^ [Q8: code_integer,R4: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L4 ) @ R4 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q8 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R4 @ ( numera6620942414471956472nteger @ L4 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q8 ) @ R4 ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % divmod_step_integer_def
% 2.86/3.16 thf(fact_5438_atLeastPlusOneLessThan__greaterThanLessThan__integer,axiom,
% 2.86/3.16 ! [L: code_integer,U: code_integer] :
% 2.86/3.16 ( ( set_or8404916559141939852nteger @ ( plus_p5714425477246183910nteger @ L @ one_one_Code_integer ) @ U )
% 2.86/3.16 = ( set_or4266950643985792945nteger @ L @ U ) ) ).
% 2.86/3.16
% 2.86/3.16 % atLeastPlusOneLessThan_greaterThanLessThan_integer
% 2.86/3.16 thf(fact_5439_atLeastLessThanPlusOne__atLeastAtMost__integer,axiom,
% 2.86/3.16 ! [L: code_integer,U: code_integer] :
% 2.86/3.16 ( ( set_or8404916559141939852nteger @ L @ ( plus_p5714425477246183910nteger @ U @ one_one_Code_integer ) )
% 2.86/3.16 = ( set_or189985376899183464nteger @ L @ U ) ) ).
% 2.86/3.16
% 2.86/3.16 % atLeastLessThanPlusOne_atLeastAtMost_integer
% 2.86/3.16 thf(fact_5440_atLeastPlusOneAtMost__greaterThanAtMost__integer,axiom,
% 2.86/3.16 ! [L: code_integer,U: code_integer] :
% 2.86/3.16 ( ( set_or189985376899183464nteger @ ( plus_p5714425477246183910nteger @ L @ one_one_Code_integer ) @ U )
% 2.86/3.16 = ( set_or2715278749043346189nteger @ L @ U ) ) ).
% 2.86/3.16
% 2.86/3.16 % atLeastPlusOneAtMost_greaterThanAtMost_integer
% 2.86/3.16 thf(fact_5441_image__add__integer__atLeastLessThan,axiom,
% 2.86/3.16 ! [L: code_integer,U: code_integer] :
% 2.86/3.16 ( ( image_4470545334726330049nteger
% 2.86/3.16 @ ^ [X2: code_integer] : ( plus_p5714425477246183910nteger @ X2 @ L )
% 2.86/3.16 @ ( set_or8404916559141939852nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ U @ L ) ) )
% 2.86/3.16 = ( set_or8404916559141939852nteger @ L @ U ) ) ).
% 2.86/3.16
% 2.86/3.16 % image_add_integer_atLeastLessThan
% 2.86/3.16 thf(fact_5442_divmod__integer_H__def,axiom,
% 2.86/3.16 ( unique3479559517661332726nteger
% 2.86/3.16 = ( ^ [M: num,N2: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N2 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % divmod_integer'_def
% 2.86/3.16 thf(fact_5443_finite__enumerate,axiom,
% 2.86/3.16 ! [S: set_nat] :
% 2.86/3.16 ( ( finite_finite_nat @ S )
% 2.86/3.16 => ? [R6: nat > nat] :
% 2.86/3.16 ( ( strict1292158309912662752at_nat @ R6 @ ( set_ord_lessThan_nat @ ( finite_card_nat @ S ) ) )
% 2.86/3.16 & ! [N9: nat] :
% 2.86/3.16 ( ( ord_less_nat @ N9 @ ( finite_card_nat @ S ) )
% 2.86/3.16 => ( member_nat @ ( R6 @ N9 ) @ S ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % finite_enumerate
% 2.86/3.16 thf(fact_5444_finite__atLeastLessThan__integer,axiom,
% 2.86/3.16 ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or8404916559141939852nteger @ L @ U ) ) ).
% 2.86/3.16
% 2.86/3.16 % finite_atLeastLessThan_integer
% 2.86/3.16 thf(fact_5445_finite__atLeastAtMost__integer,axiom,
% 2.86/3.16 ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or189985376899183464nteger @ L @ U ) ) ).
% 2.86/3.16
% 2.86/3.16 % finite_atLeastAtMost_integer
% 2.86/3.16 thf(fact_5446_finite__greaterThanLessThan__integer,axiom,
% 2.86/3.16 ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or4266950643985792945nteger @ L @ U ) ) ).
% 2.86/3.16
% 2.86/3.16 % finite_greaterThanLessThan_integer
% 2.86/3.16 thf(fact_5447_finite__greaterThanAtMost__integer,axiom,
% 2.86/3.16 ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or2715278749043346189nteger @ L @ U ) ) ).
% 2.86/3.16
% 2.86/3.16 % finite_greaterThanAtMost_integer
% 2.86/3.16 thf(fact_5448_finite__atLeastZeroLessThan__integer,axiom,
% 2.86/3.16 ! [U: code_integer] : ( finite6017078050557962740nteger @ ( set_or8404916559141939852nteger @ zero_z3403309356797280102nteger @ U ) ) ).
% 2.86/3.16
% 2.86/3.16 % finite_atLeastZeroLessThan_integer
% 2.86/3.16 thf(fact_5449_bit__cut__integer__def,axiom,
% 2.86/3.16 ( code_bit_cut_integer
% 2.86/3.16 = ( ^ [K4: code_integer] :
% 2.86/3.16 ( produc6677183202524767010eger_o @ ( divide6298287555418463151nteger @ K4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 2.86/3.16 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ K4 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % bit_cut_integer_def
% 2.86/3.16 thf(fact_5450_divmod__integer__def,axiom,
% 2.86/3.16 ( code_divmod_integer
% 2.86/3.16 = ( ^ [K4: code_integer,L4: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ K4 @ L4 ) @ ( modulo364778990260209775nteger @ K4 @ L4 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % divmod_integer_def
% 2.86/3.16 thf(fact_5451_bit__cut__integer__code,axiom,
% 2.86/3.16 ( code_bit_cut_integer
% 2.86/3.16 = ( ^ [K4: code_integer] :
% 2.86/3.16 ( if_Pro5737122678794959658eger_o @ ( K4 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 2.86/3.16 @ ( produc9125791028180074456eger_o
% 2.86/3.16 @ ^ [R4: code_integer,S6: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K4 ) @ R4 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R4 ) @ S6 ) ) @ ( S6 = one_one_Code_integer ) )
% 2.86/3.16 @ ( code_divmod_abs @ K4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % bit_cut_integer_code
% 2.86/3.16 thf(fact_5452_image__atLeastZeroLessThan__integer,axiom,
% 2.86/3.16 ! [U: code_integer] :
% 2.86/3.16 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ U )
% 2.86/3.16 => ( ( set_or8404916559141939852nteger @ zero_z3403309356797280102nteger @ U )
% 2.86/3.16 = ( image_1215581382706833972nteger @ semiri4939895301339042750nteger @ ( set_ord_lessThan_nat @ ( code_nat_of_integer @ U ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % image_atLeastZeroLessThan_integer
% 2.86/3.16 thf(fact_5453_divmod__abs__code_I6_J,axiom,
% 2.86/3.16 ! [J: code_integer] :
% 2.86/3.16 ( ( code_divmod_abs @ zero_z3403309356797280102nteger @ J )
% 2.86/3.16 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ) ).
% 2.86/3.16
% 2.86/3.16 % divmod_abs_code(6)
% 2.86/3.16 thf(fact_5454_divmod__abs__code_I5_J,axiom,
% 2.86/3.16 ! [J: code_integer] :
% 2.86/3.16 ( ( code_divmod_abs @ J @ zero_z3403309356797280102nteger )
% 2.86/3.16 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ J ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % divmod_abs_code(5)
% 2.86/3.16 thf(fact_5455_nat__of__integer__less__iff,axiom,
% 2.86/3.16 ! [X: code_integer,Y: code_integer] :
% 2.86/3.16 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 2.86/3.16 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 2.86/3.16 => ( ( ord_less_nat @ ( code_nat_of_integer @ X ) @ ( code_nat_of_integer @ Y ) )
% 2.86/3.16 = ( ord_le6747313008572928689nteger @ X @ Y ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % nat_of_integer_less_iff
% 2.86/3.16 thf(fact_5456_divmod__abs__def,axiom,
% 2.86/3.16 ( code_divmod_abs
% 2.86/3.16 = ( ^ [K4: code_integer,L4: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( abs_abs_Code_integer @ K4 ) @ ( abs_abs_Code_integer @ L4 ) ) @ ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K4 ) @ ( abs_abs_Code_integer @ L4 ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % divmod_abs_def
% 2.86/3.16 thf(fact_5457_divmod__integer__code,axiom,
% 2.86/3.16 ( code_divmod_integer
% 2.86/3.16 = ( ^ [K4: code_integer,L4: code_integer] :
% 2.86/3.16 ( if_Pro6119634080678213985nteger @ ( K4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 2.86/3.16 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L4 )
% 2.86/3.16 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K4 ) @ ( code_divmod_abs @ K4 @ L4 )
% 2.86/3.16 @ ( produc6916734918728496179nteger
% 2.86/3.16 @ ^ [R4: code_integer,S6: code_integer] : ( if_Pro6119634080678213985nteger @ ( S6 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R4 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R4 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ L4 @ S6 ) ) )
% 2.86/3.16 @ ( code_divmod_abs @ K4 @ L4 ) ) )
% 2.86/3.16 @ ( if_Pro6119634080678213985nteger @ ( L4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K4 )
% 2.86/3.16 @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 2.86/3.16 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K4 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K4 @ L4 )
% 2.86/3.16 @ ( produc6916734918728496179nteger
% 2.86/3.16 @ ^ [R4: code_integer,S6: code_integer] : ( if_Pro6119634080678213985nteger @ ( S6 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R4 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R4 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ L4 ) @ S6 ) ) )
% 2.86/3.16 @ ( code_divmod_abs @ K4 @ L4 ) ) ) ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % divmod_integer_code
% 2.86/3.16 thf(fact_5458_Gcd__eq__Max,axiom,
% 2.86/3.16 ! [M5: set_nat] :
% 2.86/3.16 ( ( finite_finite_nat @ M5 )
% 2.86/3.16 => ( ( M5 != bot_bot_set_nat )
% 2.86/3.16 => ( ~ ( member_nat @ zero_zero_nat @ M5 )
% 2.86/3.16 => ( ( gcd_Gcd_nat @ M5 )
% 2.86/3.16 = ( lattic8265883725875713057ax_nat
% 2.86/3.16 @ ( comple7806235888213564991et_nat
% 2.86/3.16 @ ( image_nat_set_nat
% 2.86/3.16 @ ^ [M: nat] :
% 2.86/3.16 ( collect_nat
% 2.86/3.16 @ ^ [D5: nat] : ( dvd_dvd_nat @ D5 @ M ) )
% 2.86/3.16 @ M5 ) ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % Gcd_eq_Max
% 2.86/3.16 thf(fact_5459_INT__greaterThan__UNIV,axiom,
% 2.86/3.16 ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ set_or1210151606488870762an_nat @ top_top_set_nat ) )
% 2.86/3.16 = bot_bot_set_nat ) ).
% 2.86/3.16
% 2.86/3.16 % INT_greaterThan_UNIV
% 2.86/3.16 thf(fact_5460_times__int_Oabs__eq,axiom,
% 2.86/3.16 ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 2.86/3.16 ( ( times_times_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 2.86/3.16 = ( abs_Integ
% 2.86/3.16 @ ( produc27273713700761075at_nat
% 2.86/3.16 @ ^ [X2: nat,Y5: nat] :
% 2.86/3.16 ( produc2626176000494625587at_nat
% 2.86/3.16 @ ^ [U4: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ U4 ) @ ( times_times_nat @ Y5 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X2 @ V4 ) @ ( times_times_nat @ Y5 @ U4 ) ) ) )
% 2.86/3.16 @ Xa
% 2.86/3.16 @ X ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % times_int.abs_eq
% 2.86/3.16 thf(fact_5461_Inf__nat__def1,axiom,
% 2.86/3.16 ! [K5: set_nat] :
% 2.86/3.16 ( ( K5 != bot_bot_set_nat )
% 2.86/3.16 => ( member_nat @ ( complete_Inf_Inf_nat @ K5 ) @ K5 ) ) ).
% 2.86/3.16
% 2.86/3.16 % Inf_nat_def1
% 2.86/3.16 thf(fact_5462_eq__Abs__Integ,axiom,
% 2.86/3.16 ! [Z: int] :
% 2.86/3.16 ~ ! [X3: nat,Y2: nat] :
% 2.86/3.16 ( Z
% 2.86/3.16 != ( abs_Integ @ ( product_Pair_nat_nat @ X3 @ Y2 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % eq_Abs_Integ
% 2.86/3.16 thf(fact_5463_zero__int__def,axiom,
% 2.86/3.16 ( zero_zero_int
% 2.86/3.16 = ( abs_Integ @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % zero_int_def
% 2.86/3.16 thf(fact_5464_int__def,axiom,
% 2.86/3.16 ( semiri1314217659103216013at_int
% 2.86/3.16 = ( ^ [N2: nat] : ( abs_Integ @ ( product_Pair_nat_nat @ N2 @ zero_zero_nat ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % int_def
% 2.86/3.16 thf(fact_5465_uminus__int_Oabs__eq,axiom,
% 2.86/3.16 ! [X: product_prod_nat_nat] :
% 2.86/3.16 ( ( uminus_uminus_int @ ( abs_Integ @ X ) )
% 2.86/3.16 = ( abs_Integ
% 2.86/3.16 @ ( produc2626176000494625587at_nat
% 2.86/3.16 @ ^ [X2: nat,Y5: nat] : ( product_Pair_nat_nat @ Y5 @ X2 )
% 2.86/3.16 @ X ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % uminus_int.abs_eq
% 2.86/3.16 thf(fact_5466_one__int__def,axiom,
% 2.86/3.16 ( one_one_int
% 2.86/3.16 = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % one_int_def
% 2.86/3.16 thf(fact_5467_less__int_Oabs__eq,axiom,
% 2.86/3.16 ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 2.86/3.16 ( ( ord_less_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 2.86/3.16 = ( produc8739625826339149834_nat_o
% 2.86/3.16 @ ^ [X2: nat,Y5: nat] :
% 2.86/3.16 ( produc6081775807080527818_nat_o
% 2.86/3.16 @ ^ [U4: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U4 @ Y5 ) ) )
% 2.86/3.16 @ Xa
% 2.86/3.16 @ X ) ) ).
% 2.86/3.16
% 2.86/3.16 % less_int.abs_eq
% 2.86/3.16 thf(fact_5468_plus__int_Oabs__eq,axiom,
% 2.86/3.16 ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 2.86/3.16 ( ( plus_plus_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 2.86/3.16 = ( abs_Integ
% 2.86/3.16 @ ( produc27273713700761075at_nat
% 2.86/3.16 @ ^ [X2: nat,Y5: nat] :
% 2.86/3.16 ( produc2626176000494625587at_nat
% 2.86/3.16 @ ^ [U4: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ U4 ) @ ( plus_plus_nat @ Y5 @ V4 ) ) )
% 2.86/3.16 @ Xa
% 2.86/3.16 @ X ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % plus_int.abs_eq
% 2.86/3.16 thf(fact_5469_minus__int_Oabs__eq,axiom,
% 2.86/3.16 ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 2.86/3.16 ( ( minus_minus_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 2.86/3.16 = ( abs_Integ
% 2.86/3.16 @ ( produc27273713700761075at_nat
% 2.86/3.16 @ ^ [X2: nat,Y5: nat] :
% 2.86/3.16 ( produc2626176000494625587at_nat
% 2.86/3.16 @ ^ [U4: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ Y5 @ U4 ) ) )
% 2.86/3.16 @ Xa
% 2.86/3.16 @ X ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % minus_int.abs_eq
% 2.86/3.16 thf(fact_5470_divmod__integer__eq__cases,axiom,
% 2.86/3.16 ( code_divmod_integer
% 2.86/3.16 = ( ^ [K4: code_integer,L4: code_integer] :
% 2.86/3.16 ( if_Pro6119634080678213985nteger @ ( K4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 2.86/3.16 @ ( if_Pro6119634080678213985nteger @ ( L4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K4 )
% 2.86/3.16 @ ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ produc6499014454317279255nteger @ times_3573771949741848930nteger ) @ sgn_sgn_Code_integer @ L4
% 2.86/3.16 @ ( if_Pro6119634080678213985nteger
% 2.86/3.16 @ ( ( sgn_sgn_Code_integer @ K4 )
% 2.86/3.16 = ( sgn_sgn_Code_integer @ L4 ) )
% 2.86/3.16 @ ( code_divmod_abs @ K4 @ L4 )
% 2.86/3.16 @ ( produc6916734918728496179nteger
% 2.86/3.16 @ ^ [R4: code_integer,S6: code_integer] : ( if_Pro6119634080678213985nteger @ ( S6 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R4 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R4 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ L4 ) @ S6 ) ) )
% 2.86/3.16 @ ( code_divmod_abs @ K4 @ L4 ) ) ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % divmod_integer_eq_cases
% 2.86/3.16 thf(fact_5471_less__int_Orep__eq,axiom,
% 2.86/3.16 ( ord_less_int
% 2.86/3.16 = ( ^ [X2: int,Xa4: int] :
% 2.86/3.16 ( produc8739625826339149834_nat_o
% 2.86/3.16 @ ^ [Y5: nat,Z5: nat] :
% 2.86/3.16 ( produc6081775807080527818_nat_o
% 2.86/3.16 @ ^ [U4: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y5 @ V4 ) @ ( plus_plus_nat @ U4 @ Z5 ) ) )
% 2.86/3.16 @ ( rep_Integ @ X2 )
% 2.86/3.16 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % less_int.rep_eq
% 2.86/3.16 thf(fact_5472_assn__aci_I11_J,axiom,
% 2.86/3.16 ! [X: assn,Y: assn,A2: assn,B2: assn] :
% 2.86/3.16 ( ( syntax7398250324933576852n_assn @ ( times_times_assn @ X @ Y ) @ A2 )
% 2.86/3.16 => ( ( times_times_assn @ A2 @ B2 )
% 2.86/3.16 = ( times_times_assn @ B2 @ A2 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % assn_aci(11)
% 2.86/3.16 thf(fact_5473_uminus__int__def,axiom,
% 2.86/3.16 ( uminus_uminus_int
% 2.86/3.16 = ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ
% 2.86/3.16 @ ( produc2626176000494625587at_nat
% 2.86/3.16 @ ^ [X2: nat,Y5: nat] : ( product_Pair_nat_nat @ Y5 @ X2 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % uminus_int_def
% 2.86/3.16 thf(fact_5474_times__int__def,axiom,
% 2.86/3.16 ( times_times_int
% 2.86/3.16 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 2.86/3.16 @ ( produc27273713700761075at_nat
% 2.86/3.16 @ ^ [X2: nat,Y5: nat] :
% 2.86/3.16 ( produc2626176000494625587at_nat
% 2.86/3.16 @ ^ [U4: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ U4 ) @ ( times_times_nat @ Y5 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X2 @ V4 ) @ ( times_times_nat @ Y5 @ U4 ) ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % times_int_def
% 2.86/3.16 thf(fact_5475_minus__int__def,axiom,
% 2.86/3.16 ( minus_minus_int
% 2.86/3.16 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 2.86/3.16 @ ( produc27273713700761075at_nat
% 2.86/3.16 @ ^ [X2: nat,Y5: nat] :
% 2.86/3.16 ( produc2626176000494625587at_nat
% 2.86/3.16 @ ^ [U4: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ Y5 @ U4 ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % minus_int_def
% 2.86/3.16 thf(fact_5476_plus__int__def,axiom,
% 2.86/3.16 ( plus_plus_int
% 2.86/3.16 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 2.86/3.16 @ ( produc27273713700761075at_nat
% 2.86/3.16 @ ^ [X2: nat,Y5: nat] :
% 2.86/3.16 ( produc2626176000494625587at_nat
% 2.86/3.16 @ ^ [U4: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ U4 ) @ ( plus_plus_nat @ Y5 @ V4 ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % plus_int_def
% 2.86/3.16 thf(fact_5477_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 2.86/3.16 ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 2.86/3.16 @ ^ [X2: nat,Y5: nat] : ( ord_less_eq_nat @ Y5 @ X2 )
% 2.86/3.16 @ ^ [X2: nat,Y5: nat] : ( ord_less_nat @ Y5 @ X2 ) ) ).
% 2.86/3.16
% 2.86/3.16 % max_nat.semilattice_neutr_order_axioms
% 2.86/3.16 thf(fact_5478_mono__times__nat,axiom,
% 2.86/3.16 ! [N: nat] :
% 2.86/3.16 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.16 => ( order_mono_nat_nat @ ( times_times_nat @ N ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % mono_times_nat
% 2.86/3.16 thf(fact_5479_less__int__def,axiom,
% 2.86/3.16 ( ord_less_int
% 2.86/3.16 = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 2.86/3.16 @ ( produc8739625826339149834_nat_o
% 2.86/3.16 @ ^ [X2: nat,Y5: nat] :
% 2.86/3.16 ( produc6081775807080527818_nat_o
% 2.86/3.16 @ ^ [U4: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U4 @ Y5 ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % less_int_def
% 2.86/3.16 thf(fact_5480_bezw_Oelims,axiom,
% 2.86/3.16 ! [X: nat,Xa: nat,Y: product_prod_int_int] :
% 2.86/3.16 ( ( ( bezw @ X @ Xa )
% 2.86/3.16 = Y )
% 2.86/3.16 => ( ( ( Xa = zero_zero_nat )
% 2.86/3.16 => ( Y
% 2.86/3.16 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 2.86/3.16 & ( ( Xa != zero_zero_nat )
% 2.86/3.16 => ( Y
% 2.86/3.16 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa ) ) ) ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % bezw.elims
% 2.86/3.16 thf(fact_5481_bezw_Osimps,axiom,
% 2.86/3.16 ( bezw
% 2.86/3.16 = ( ^ [X2: nat,Y5: nat] : ( if_Pro3027730157355071871nt_int @ ( Y5 = zero_zero_nat ) @ ( product_Pair_int_int @ one_one_int @ zero_zero_int ) @ ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y5 @ ( modulo_modulo_nat @ X2 @ Y5 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y5 @ ( modulo_modulo_nat @ X2 @ Y5 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y5 @ ( modulo_modulo_nat @ X2 @ Y5 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X2 @ Y5 ) ) ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % bezw.simps
% 2.86/3.16 thf(fact_5482_bezw__non__0,axiom,
% 2.86/3.16 ! [Y: nat,X: nat] :
% 2.86/3.16 ( ( ord_less_nat @ zero_zero_nat @ Y )
% 2.86/3.16 => ( ( bezw @ X @ Y )
% 2.86/3.16 = ( 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 ) ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % bezw_non_0
% 2.86/3.16 thf(fact_5483_bezw_Opelims,axiom,
% 2.86/3.16 ! [X: nat,Xa: nat,Y: product_prod_int_int] :
% 2.86/3.16 ( ( ( bezw @ X @ Xa )
% 2.86/3.16 = Y )
% 2.86/3.16 => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa ) )
% 2.86/3.16 => ~ ( ( ( ( Xa = zero_zero_nat )
% 2.86/3.16 => ( Y
% 2.86/3.16 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 2.86/3.16 & ( ( Xa != zero_zero_nat )
% 2.86/3.16 => ( Y
% 2.86/3.16 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa ) ) ) ) ) ) ) )
% 2.86/3.16 => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % bezw.pelims
% 2.86/3.16 thf(fact_5484_mod__pure,axiom,
% 2.86/3.16 ! [B2: $o,H2: produc3658429121746597890et_nat] :
% 2.86/3.16 ( ( rep_assn @ ( pure_assn @ B2 ) @ H2 )
% 2.86/3.16 = ( ( ( produc8586169260539613262et_nat @ H2 )
% 2.86/3.16 = bot_bot_set_nat )
% 2.86/3.16 & B2 ) ) ).
% 2.86/3.16
% 2.86/3.16 % mod_pure
% 2.86/3.16 thf(fact_5485_mod__emp,axiom,
% 2.86/3.16 ! [H2: produc3658429121746597890et_nat] :
% 2.86/3.16 ( ( rep_assn @ one_one_assn @ H2 )
% 2.86/3.16 = ( ( produc8586169260539613262et_nat @ H2 )
% 2.86/3.16 = bot_bot_set_nat ) ) ).
% 2.86/3.16
% 2.86/3.16 % mod_emp
% 2.86/3.16 thf(fact_5486_fi__match__entails,axiom,
% 2.86/3.16 ! [M2: list_P8527749157015355191n_assn] :
% 2.86/3.16 ( ! [X3: produc6575502325842934193n_assn] :
% 2.86/3.16 ( ( member7957490590177025114n_assn @ X3 @ ( set_Pr1139785259514867910n_assn @ M2 ) )
% 2.86/3.16 => ( produc7274209992780475162assn_o @ entails @ X3 ) )
% 2.86/3.16 => ( entails @ ( foldr_assn_assn @ times_times_assn @ ( map_Pr8991440229025900053n_assn @ produc9167289414957590229n_assn @ M2 ) @ one_one_assn ) @ ( foldr_assn_assn @ times_times_assn @ ( map_Pr8991440229025900053n_assn @ produc2051961928117032727n_assn @ M2 ) @ one_one_assn ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % fi_match_entails
% 2.86/3.16 thf(fact_5487_mod__star__trueE_H,axiom,
% 2.86/3.16 ! [P: assn,H2: produc3658429121746597890et_nat] :
% 2.86/3.16 ( ( rep_assn @ ( times_times_assn @ P @ top_top_assn ) @ H2 )
% 2.86/3.16 => ~ ! [H5: produc3658429121746597890et_nat] :
% 2.86/3.16 ( ( ( produc1824681642469235216et_nat @ H5 )
% 2.86/3.16 = ( produc1824681642469235216et_nat @ H2 ) )
% 2.86/3.16 => ( ( ord_less_eq_set_nat @ ( produc8586169260539613262et_nat @ H5 ) @ ( produc8586169260539613262et_nat @ H2 ) )
% 2.86/3.16 => ~ ( rep_assn @ P @ H5 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % mod_star_trueE'
% 2.86/3.16 thf(fact_5488_FI__RESULT__def,axiom,
% 2.86/3.16 ( fI_RESULT
% 2.86/3.16 = ( ^ [M7: list_P8527749157015355191n_assn,UP: assn,UQ: assn,F3: assn] :
% 2.86/3.16 ( ! [X2: produc6575502325842934193n_assn] :
% 2.86/3.16 ( ( member7957490590177025114n_assn @ X2 @ ( set_Pr1139785259514867910n_assn @ M7 ) )
% 2.86/3.16 => ( produc7274209992780475162assn_o @ entails @ X2 ) )
% 2.86/3.16 => ( entails @ ( times_times_assn @ ( foldr_assn_assn @ times_times_assn @ ( map_Pr8991440229025900053n_assn @ produc9167289414957590229n_assn @ M7 ) @ one_one_assn ) @ UP ) @ ( times_times_assn @ ( times_times_assn @ ( foldr_assn_assn @ times_times_assn @ ( map_Pr8991440229025900053n_assn @ produc2051961928117032727n_assn @ M7 ) @ one_one_assn ) @ UQ ) @ F3 ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % FI_RESULT_def
% 2.86/3.16 thf(fact_5489_prod__decode__aux_Opelims,axiom,
% 2.86/3.16 ! [X: nat,Xa: nat,Y: product_prod_nat_nat] :
% 2.86/3.16 ( ( ( nat_prod_decode_aux @ X @ Xa )
% 2.86/3.16 = Y )
% 2.86/3.16 => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa ) )
% 2.86/3.16 => ~ ( ( ( ( ord_less_eq_nat @ Xa @ X )
% 2.86/3.16 => ( Y
% 2.86/3.16 = ( product_Pair_nat_nat @ Xa @ ( minus_minus_nat @ X @ Xa ) ) ) )
% 2.86/3.16 & ( ~ ( ord_less_eq_nat @ Xa @ X )
% 2.86/3.16 => ( Y
% 2.86/3.16 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa @ ( suc @ X ) ) ) ) ) )
% 2.86/3.16 => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % prod_decode_aux.pelims
% 2.86/3.16 thf(fact_5490_FI__def,axiom,
% 2.86/3.16 ( fi
% 2.86/3.16 = ( ^ [M: list_P8527749157015355191n_assn,P7: assn,Q8: assn,Up: assn,Uq: assn,F6: assn] :
% 2.86/3.16 ( ! [X2: produc6575502325842934193n_assn] :
% 2.86/3.16 ( ( member7957490590177025114n_assn @ X2 @ ( set_Pr1139785259514867910n_assn @ M ) )
% 2.86/3.16 => ( produc7274209992780475162assn_o @ entails @ X2 ) )
% 2.86/3.16 => ( entails @ ( times_times_assn @ ( times_times_assn @ ( foldr_assn_assn @ times_times_assn @ ( map_Pr8991440229025900053n_assn @ produc9167289414957590229n_assn @ M ) @ one_one_assn ) @ P7 ) @ Up ) @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ ( foldr_assn_assn @ times_times_assn @ ( map_Pr8991440229025900053n_assn @ produc2051961928117032727n_assn @ M ) @ one_one_assn ) @ Q8 ) @ Uq ) @ F6 ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % FI_def
% 2.86/3.16 thf(fact_5491_FI__p__nomatch,axiom,
% 2.86/3.16 ! [M2: list_P8527749157015355191n_assn,Ps2: assn,Qs: assn,Q6: assn,P6: assn,Up2: assn,Uq2: assn,F4: assn] :
% 2.86/3.16 ( ( fi @ M2 @ Ps2 @ ( times_times_assn @ Qs @ Q6 ) @ ( times_times_assn @ P6 @ Up2 ) @ Uq2 @ F4 )
% 2.86/3.16 => ( fi @ M2 @ ( times_times_assn @ Ps2 @ P6 ) @ ( times_times_assn @ Qs @ Q6 ) @ Up2 @ Uq2 @ F4 ) ) ).
% 2.86/3.16
% 2.86/3.16 % FI_p_nomatch
% 2.86/3.16 thf(fact_5492_FI__finalize,axiom,
% 2.86/3.16 ! [M2: list_P8527749157015355191n_assn,P6: assn,Up2: assn,Q6: assn,Uq2: assn,F4: assn] :
% 2.86/3.16 ( ( fI_RESULT @ M2 @ ( times_times_assn @ P6 @ Up2 ) @ ( times_times_assn @ Q6 @ Uq2 ) @ F4 )
% 2.86/3.16 => ( fi @ M2 @ P6 @ Q6 @ Up2 @ Uq2 @ F4 ) ) ).
% 2.86/3.16
% 2.86/3.16 % FI_finalize
% 2.86/3.16 thf(fact_5493_FI__init,axiom,
% 2.86/3.16 ! [P: assn,Q: assn,F: assn] :
% 2.86/3.16 ( ( fi @ nil_Pr5671120429643327159n_assn @ ( times_times_assn @ sln @ P ) @ ( times_times_assn @ sln @ Q ) @ sln @ sln @ F )
% 2.86/3.16 => ( fI_QUERY @ P @ Q @ F ) ) ).
% 2.86/3.16
% 2.86/3.16 % FI_init
% 2.86/3.16 thf(fact_5494_SLN__right,axiom,
% 2.86/3.16 ! [P: assn] :
% 2.86/3.16 ( ( times_times_assn @ P @ sln )
% 2.86/3.16 = P ) ).
% 2.86/3.16
% 2.86/3.16 % SLN_right
% 2.86/3.16 thf(fact_5495_SLN__left,axiom,
% 2.86/3.16 ! [P: assn] :
% 2.86/3.16 ( ( times_times_assn @ sln @ P )
% 2.86/3.16 = P ) ).
% 2.86/3.16
% 2.86/3.16 % SLN_left
% 2.86/3.16 thf(fact_5496_SLN__def,axiom,
% 2.86/3.16 sln = one_one_assn ).
% 2.86/3.16
% 2.86/3.16 % SLN_def
% 2.86/3.16 thf(fact_5497_FI__q__nomatch,axiom,
% 2.86/3.16 ! [M2: list_P8527749157015355191n_assn,Up2: assn,Qs: assn,Q6: assn,Uq2: assn,F4: assn] :
% 2.86/3.16 ( ( fi @ M2 @ ( times_times_assn @ sln @ Up2 ) @ Qs @ sln @ ( times_times_assn @ Q6 @ Uq2 ) @ F4 )
% 2.86/3.16 => ( fi @ M2 @ sln @ ( times_times_assn @ Qs @ Q6 ) @ Up2 @ Uq2 @ F4 ) ) ).
% 2.86/3.16
% 2.86/3.16 % FI_q_nomatch
% 2.86/3.16 thf(fact_5498_FI__match,axiom,
% 2.86/3.16 ! [P6: assn,Q6: assn,M2: list_P8527749157015355191n_assn,Ps2: assn,Up2: assn,Qs: assn,Uq2: assn,F4: assn] :
% 2.86/3.16 ( ( entails @ P6 @ Q6 )
% 2.86/3.16 => ( ( fi @ ( cons_P2971678138204555879n_assn @ ( produc118845697133431529n_assn @ P6 @ Q6 ) @ M2 ) @ ( times_times_assn @ Ps2 @ Up2 ) @ ( times_times_assn @ Qs @ Uq2 ) @ sln @ sln @ F4 )
% 2.86/3.16 => ( fi @ M2 @ ( times_times_assn @ Ps2 @ P6 ) @ ( times_times_assn @ Qs @ Q6 ) @ Up2 @ Uq2 @ F4 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % FI_match
% 2.86/3.16 thf(fact_5499_pred__nat__trancl__eq__le,axiom,
% 2.86/3.16 ! [M2: nat,N: nat] :
% 2.86/3.16 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M2 @ N ) @ ( transi2905341329935302413cl_nat @ pred_nat ) )
% 2.86/3.16 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 2.86/3.16
% 2.86/3.16 % pred_nat_trancl_eq_le
% 2.86/3.16 thf(fact_5500_vimage__Suc__insert__Suc,axiom,
% 2.86/3.16 ! [N: nat,A: set_nat] :
% 2.86/3.16 ( ( vimage_nat_nat @ suc @ ( insert_nat2 @ ( suc @ N ) @ A ) )
% 2.86/3.16 = ( insert_nat2 @ N @ ( vimage_nat_nat @ suc @ A ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % vimage_Suc_insert_Suc
% 2.86/3.16 thf(fact_5501_vimage__Suc__insert__0,axiom,
% 2.86/3.16 ! [A: set_nat] :
% 2.86/3.16 ( ( vimage_nat_nat @ suc @ ( insert_nat2 @ zero_zero_nat @ A ) )
% 2.86/3.16 = ( vimage_nat_nat @ suc @ A ) ) ).
% 2.86/3.16
% 2.86/3.16 % vimage_Suc_insert_0
% 2.86/3.16 thf(fact_5502_finite__le__enumerate,axiom,
% 2.86/3.16 ! [S: set_nat,N: nat] :
% 2.86/3.16 ( ( finite_finite_nat @ S )
% 2.86/3.16 => ( ( ord_less_nat @ N @ ( finite_card_nat @ S ) )
% 2.86/3.16 => ( ord_less_eq_nat @ N @ ( infini8530281810654367211te_nat @ S @ N ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % finite_le_enumerate
% 2.86/3.16 thf(fact_5503_less__natural_Orsp,axiom,
% 2.86/3.16 ( bNF_re578469030762574527_nat_o
% 2.86/3.16 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 2.86/3.16 @ ( bNF_re4705727531993890431at_o_o
% 2.86/3.16 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 2.86/3.16 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 ) )
% 2.86/3.16 @ ord_less_nat
% 2.86/3.16 @ ord_less_nat ) ).
% 2.86/3.16
% 2.86/3.16 % less_natural.rsp
% 2.86/3.16 thf(fact_5504_times__int_Otransfer,axiom,
% 2.86/3.16 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 2.86/3.16 @ ( produc27273713700761075at_nat
% 2.86/3.16 @ ^ [X2: nat,Y5: nat] :
% 2.86/3.16 ( produc2626176000494625587at_nat
% 2.86/3.16 @ ^ [U4: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ U4 ) @ ( times_times_nat @ Y5 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X2 @ V4 ) @ ( times_times_nat @ Y5 @ U4 ) ) ) ) )
% 2.86/3.16 @ times_times_int ) ).
% 2.86/3.16
% 2.86/3.16 % times_int.transfer
% 2.86/3.16 thf(fact_5505_zero__int_Otransfer,axiom,
% 2.86/3.16 pcr_int @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ zero_zero_int ).
% 2.86/3.16
% 2.86/3.16 % zero_int.transfer
% 2.86/3.16 thf(fact_5506_int__transfer,axiom,
% 2.86/3.16 ( bNF_re6830278522597306478at_int
% 2.86/3.16 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 2.86/3.16 @ pcr_int
% 2.86/3.16 @ ^ [N2: nat] : ( product_Pair_nat_nat @ N2 @ zero_zero_nat )
% 2.86/3.16 @ semiri1314217659103216013at_int ) ).
% 2.86/3.16
% 2.86/3.16 % int_transfer
% 2.86/3.16 thf(fact_5507_uminus__int_Otransfer,axiom,
% 2.86/3.16 ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int
% 2.86/3.16 @ ( produc2626176000494625587at_nat
% 2.86/3.16 @ ^ [X2: nat,Y5: nat] : ( product_Pair_nat_nat @ Y5 @ X2 ) )
% 2.86/3.16 @ uminus_uminus_int ) ).
% 2.86/3.16
% 2.86/3.16 % uminus_int.transfer
% 2.86/3.16 thf(fact_5508_one__int_Otransfer,axiom,
% 2.86/3.16 pcr_int @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ one_one_int ).
% 2.86/3.16
% 2.86/3.16 % one_int.transfer
% 2.86/3.16 thf(fact_5509_less__int_Otransfer,axiom,
% 2.86/3.16 ( bNF_re717283939379294677_int_o @ pcr_int
% 2.86/3.16 @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 2.86/3.16 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 ) )
% 2.86/3.16 @ ( produc8739625826339149834_nat_o
% 2.86/3.16 @ ^ [X2: nat,Y5: nat] :
% 2.86/3.16 ( produc6081775807080527818_nat_o
% 2.86/3.16 @ ^ [U4: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U4 @ Y5 ) ) ) )
% 2.86/3.16 @ ord_less_int ) ).
% 2.86/3.16
% 2.86/3.16 % less_int.transfer
% 2.86/3.16 thf(fact_5510_plus__int_Otransfer,axiom,
% 2.86/3.16 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 2.86/3.16 @ ( produc27273713700761075at_nat
% 2.86/3.16 @ ^ [X2: nat,Y5: nat] :
% 2.86/3.16 ( produc2626176000494625587at_nat
% 2.86/3.16 @ ^ [U4: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ U4 ) @ ( plus_plus_nat @ Y5 @ V4 ) ) ) )
% 2.86/3.16 @ plus_plus_int ) ).
% 2.86/3.16
% 2.86/3.16 % plus_int.transfer
% 2.86/3.16 thf(fact_5511_minus__int_Otransfer,axiom,
% 2.86/3.16 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 2.86/3.16 @ ( produc27273713700761075at_nat
% 2.86/3.16 @ ^ [X2: nat,Y5: nat] :
% 2.86/3.16 ( produc2626176000494625587at_nat
% 2.86/3.16 @ ^ [U4: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ Y5 @ U4 ) ) ) )
% 2.86/3.16 @ minus_minus_int ) ).
% 2.86/3.16
% 2.86/3.16 % minus_int.transfer
% 2.86/3.16 thf(fact_5512_times__int_Orsp,axiom,
% 2.86/3.16 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 2.86/3.16 @ ( produc27273713700761075at_nat
% 2.86/3.16 @ ^ [X2: nat,Y5: nat] :
% 2.86/3.16 ( produc2626176000494625587at_nat
% 2.86/3.16 @ ^ [U4: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ U4 ) @ ( times_times_nat @ Y5 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X2 @ V4 ) @ ( times_times_nat @ Y5 @ U4 ) ) ) ) )
% 2.86/3.16 @ ( produc27273713700761075at_nat
% 2.86/3.16 @ ^ [X2: nat,Y5: nat] :
% 2.86/3.16 ( produc2626176000494625587at_nat
% 2.86/3.16 @ ^ [U4: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ U4 ) @ ( times_times_nat @ Y5 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X2 @ V4 ) @ ( times_times_nat @ Y5 @ U4 ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % times_int.rsp
% 2.86/3.16 thf(fact_5513_intrel__iff,axiom,
% 2.86/3.16 ! [X: nat,Y: nat,U: nat,V2: nat] :
% 2.86/3.16 ( ( intrel @ ( product_Pair_nat_nat @ X @ Y ) @ ( product_Pair_nat_nat @ U @ V2 ) )
% 2.86/3.16 = ( ( plus_plus_nat @ X @ V2 )
% 2.86/3.16 = ( plus_plus_nat @ U @ Y ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % intrel_iff
% 2.86/3.16 thf(fact_5514_filterlim__Suc,axiom,
% 2.86/3.16 filterlim_nat_nat @ suc @ at_top_nat @ at_top_nat ).
% 2.86/3.16
% 2.86/3.16 % filterlim_Suc
% 2.86/3.16 thf(fact_5515_zero__int_Orsp,axiom,
% 2.86/3.16 intrel @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 2.86/3.16
% 2.86/3.16 % zero_int.rsp
% 2.86/3.16 thf(fact_5516_filterlim__atMost__at__top,axiom,
% 2.86/3.16 filter3212408913953519116et_nat @ set_ord_atMost_nat @ ( finite3254316476582989077op_nat @ top_top_set_nat ) @ at_top_nat ).
% 2.86/3.16
% 2.86/3.16 % filterlim_atMost_at_top
% 2.86/3.16 thf(fact_5517_filterlim__lessThan__at__top,axiom,
% 2.86/3.16 filter3212408913953519116et_nat @ set_ord_lessThan_nat @ ( finite3254316476582989077op_nat @ top_top_set_nat ) @ at_top_nat ).
% 2.86/3.16
% 2.86/3.16 % filterlim_lessThan_at_top
% 2.86/3.16 thf(fact_5518_uminus__int_Orsp,axiom,
% 2.86/3.16 ( bNF_re2241393799969408733at_nat @ intrel @ intrel
% 2.86/3.16 @ ( produc2626176000494625587at_nat
% 2.86/3.16 @ ^ [X2: nat,Y5: nat] : ( product_Pair_nat_nat @ Y5 @ X2 ) )
% 2.86/3.16 @ ( produc2626176000494625587at_nat
% 2.86/3.16 @ ^ [X2: nat,Y5: nat] : ( product_Pair_nat_nat @ Y5 @ X2 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % uminus_int.rsp
% 2.86/3.16 thf(fact_5519_one__int_Orsp,axiom,
% 2.86/3.16 intrel @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ).
% 2.86/3.16
% 2.86/3.16 % one_int.rsp
% 2.86/3.16 thf(fact_5520_less__int_Orsp,axiom,
% 2.86/3.16 ( bNF_re4202695980764964119_nat_o @ intrel
% 2.86/3.16 @ ( bNF_re3666534408544137501at_o_o @ intrel
% 2.86/3.16 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 ) )
% 2.86/3.16 @ ( produc8739625826339149834_nat_o
% 2.86/3.16 @ ^ [X2: nat,Y5: nat] :
% 2.86/3.16 ( produc6081775807080527818_nat_o
% 2.86/3.16 @ ^ [U4: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U4 @ Y5 ) ) ) )
% 2.86/3.16 @ ( produc8739625826339149834_nat_o
% 2.86/3.16 @ ^ [X2: nat,Y5: nat] :
% 2.86/3.16 ( produc6081775807080527818_nat_o
% 2.86/3.16 @ ^ [U4: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U4 @ Y5 ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % less_int.rsp
% 2.86/3.16 thf(fact_5521_minus__int_Orsp,axiom,
% 2.86/3.16 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 2.86/3.16 @ ( produc27273713700761075at_nat
% 2.86/3.16 @ ^ [X2: nat,Y5: nat] :
% 2.86/3.16 ( produc2626176000494625587at_nat
% 2.86/3.16 @ ^ [U4: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ Y5 @ U4 ) ) ) )
% 2.86/3.16 @ ( produc27273713700761075at_nat
% 2.86/3.16 @ ^ [X2: nat,Y5: nat] :
% 2.86/3.16 ( produc2626176000494625587at_nat
% 2.86/3.16 @ ^ [U4: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ Y5 @ U4 ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % minus_int.rsp
% 2.86/3.16 thf(fact_5522_plus__int_Orsp,axiom,
% 2.86/3.16 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 2.86/3.16 @ ( produc27273713700761075at_nat
% 2.86/3.16 @ ^ [X2: nat,Y5: nat] :
% 2.86/3.16 ( produc2626176000494625587at_nat
% 2.86/3.16 @ ^ [U4: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ U4 ) @ ( plus_plus_nat @ Y5 @ V4 ) ) ) )
% 2.86/3.16 @ ( produc27273713700761075at_nat
% 2.86/3.16 @ ^ [X2: nat,Y5: nat] :
% 2.86/3.16 ( produc2626176000494625587at_nat
% 2.86/3.16 @ ^ [U4: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ U4 ) @ ( plus_plus_nat @ Y5 @ V4 ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % plus_int.rsp
% 2.86/3.16 thf(fact_5523_trivial__limit__sequentially,axiom,
% 2.86/3.16 at_top_nat != bot_bot_filter_nat ).
% 2.86/3.16
% 2.86/3.16 % trivial_limit_sequentially
% 2.86/3.16 thf(fact_5524_eventually__sequentially__Suc,axiom,
% 2.86/3.16 ! [P: nat > $o] :
% 2.86/3.16 ( ( eventually_nat
% 2.86/3.16 @ ^ [I4: nat] : ( P @ ( suc @ I4 ) )
% 2.86/3.16 @ at_top_nat )
% 2.86/3.16 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 2.86/3.16
% 2.86/3.16 % eventually_sequentially_Suc
% 2.86/3.16 thf(fact_5525_eventually__sequentially__seg,axiom,
% 2.86/3.16 ! [P: nat > $o,K3: nat] :
% 2.86/3.16 ( ( eventually_nat
% 2.86/3.16 @ ^ [N2: nat] : ( P @ ( plus_plus_nat @ N2 @ K3 ) )
% 2.86/3.16 @ at_top_nat )
% 2.86/3.16 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 2.86/3.16
% 2.86/3.16 % eventually_sequentially_seg
% 2.86/3.16 thf(fact_5526_eventually__False__sequentially,axiom,
% 2.86/3.16 ~ ( eventually_nat
% 2.86/3.16 @ ^ [N2: nat] : $false
% 2.86/3.16 @ at_top_nat ) ).
% 2.86/3.16
% 2.86/3.16 % eventually_False_sequentially
% 2.86/3.16 thf(fact_5527_eventually__sequentiallyI,axiom,
% 2.86/3.16 ! [C: nat,P: nat > $o] :
% 2.86/3.16 ( ! [X3: nat] :
% 2.86/3.16 ( ( ord_less_eq_nat @ C @ X3 )
% 2.86/3.16 => ( P @ X3 ) )
% 2.86/3.16 => ( eventually_nat @ P @ at_top_nat ) ) ).
% 2.86/3.16
% 2.86/3.16 % eventually_sequentiallyI
% 2.86/3.16 thf(fact_5528_eventually__sequentially,axiom,
% 2.86/3.16 ! [P: nat > $o] :
% 2.86/3.16 ( ( eventually_nat @ P @ at_top_nat )
% 2.86/3.16 = ( ? [N8: nat] :
% 2.86/3.16 ! [N2: nat] :
% 2.86/3.16 ( ( ord_less_eq_nat @ N8 @ N2 )
% 2.86/3.16 => ( P @ N2 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % eventually_sequentially
% 2.86/3.16 thf(fact_5529_le__sequentially,axiom,
% 2.86/3.16 ! [F: filter_nat] :
% 2.86/3.16 ( ( ord_le2510731241096832064er_nat @ F @ at_top_nat )
% 2.86/3.16 = ( ! [N8: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N8 ) @ F ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % le_sequentially
% 2.86/3.16 thf(fact_5530_bit__concat__bit__iff,axiom,
% 2.86/3.16 ! [M2: nat,K3: int,L: int,N: nat] :
% 2.86/3.16 ( ( bit_se1146084159140164899it_int @ ( bit_concat_bit @ M2 @ K3 @ L ) @ N )
% 2.86/3.16 = ( ( ( ord_less_nat @ N @ M2 )
% 2.86/3.16 & ( bit_se1146084159140164899it_int @ K3 @ N ) )
% 2.86/3.16 | ( ( ord_less_eq_nat @ M2 @ N )
% 2.86/3.16 & ( bit_se1146084159140164899it_int @ L @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % bit_concat_bit_iff
% 2.86/3.16 thf(fact_5531_bot__nat__0_Oordering__top__axioms,axiom,
% 2.86/3.16 ( ordering_top_nat
% 2.86/3.16 @ ^ [X2: nat,Y5: nat] : ( ord_less_eq_nat @ Y5 @ X2 )
% 2.86/3.16 @ ^ [X2: nat,Y5: nat] : ( ord_less_nat @ Y5 @ X2 )
% 2.86/3.16 @ zero_zero_nat ) ).
% 2.86/3.16
% 2.86/3.16 % bot_nat_0.ordering_top_axioms
% 2.86/3.16 thf(fact_5532_pair__lessI2,axiom,
% 2.86/3.16 ! [A2: nat,B2: nat,S3: nat,T: nat] :
% 2.86/3.16 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.16 => ( ( ord_less_nat @ S3 @ T )
% 2.86/3.16 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A2 @ S3 ) @ ( product_Pair_nat_nat @ B2 @ T ) ) @ fun_pair_less ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % pair_lessI2
% 2.86/3.16 thf(fact_5533_pair__less__iff1,axiom,
% 2.86/3.16 ! [X: nat,Y: nat,Z: nat] :
% 2.86/3.16 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( product_Pair_nat_nat @ X @ Z ) ) @ fun_pair_less )
% 2.86/3.16 = ( ord_less_nat @ Y @ Z ) ) ).
% 2.86/3.16
% 2.86/3.16 % pair_less_iff1
% 2.86/3.16 thf(fact_5534_pair__lessI1,axiom,
% 2.86/3.16 ! [A2: nat,B2: nat,S3: nat,T: nat] :
% 2.86/3.16 ( ( ord_less_nat @ A2 @ B2 )
% 2.86/3.16 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A2 @ S3 ) @ ( product_Pair_nat_nat @ B2 @ T ) ) @ fun_pair_less ) ) ).
% 2.86/3.16
% 2.86/3.16 % pair_lessI1
% 2.86/3.16 thf(fact_5535_smin__insertI,axiom,
% 2.86/3.16 ! [X: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat,Y: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat] :
% 2.86/3.16 ( ( member8440522571783428010at_nat @ X @ XS )
% 2.86/3.16 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_less )
% 2.86/3.16 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ YS ) @ fun_min_strict )
% 2.86/3.16 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ ( insert8211810215607154385at_nat @ Y @ YS ) ) @ fun_min_strict ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % smin_insertI
% 2.86/3.16 thf(fact_5536_pair__leqI2,axiom,
% 2.86/3.16 ! [A2: nat,B2: nat,S3: nat,T: nat] :
% 2.86/3.16 ( ( ord_less_eq_nat @ A2 @ B2 )
% 2.86/3.16 => ( ( ord_less_eq_nat @ S3 @ T )
% 2.86/3.16 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A2 @ S3 ) @ ( product_Pair_nat_nat @ B2 @ T ) ) @ fun_pair_leq ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % pair_leqI2
% 2.86/3.16 thf(fact_5537_smin__emptyI,axiom,
% 2.86/3.16 ! [X4: set_Pr1261947904930325089at_nat] :
% 2.86/3.16 ( ( X4 != bot_bo2099793752762293965at_nat )
% 2.86/3.16 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ bot_bo2099793752762293965at_nat ) @ fun_min_strict ) ) ).
% 2.86/3.16
% 2.86/3.16 % smin_emptyI
% 2.86/3.16 thf(fact_5538_pair__leqI1,axiom,
% 2.86/3.16 ! [A2: nat,B2: nat,S3: nat,T: nat] :
% 2.86/3.16 ( ( ord_less_nat @ A2 @ B2 )
% 2.86/3.16 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A2 @ S3 ) @ ( product_Pair_nat_nat @ B2 @ T ) ) @ fun_pair_leq ) ) ).
% 2.86/3.16
% 2.86/3.16 % pair_leqI1
% 2.86/3.16 thf(fact_5539_wmax__insertI,axiom,
% 2.86/3.16 ! [Y: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat] :
% 2.86/3.16 ( ( member8440522571783428010at_nat @ Y @ YS )
% 2.86/3.16 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_leq )
% 2.86/3.16 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ YS ) @ fun_max_weak )
% 2.86/3.16 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( insert8211810215607154385at_nat @ X @ XS ) @ YS ) @ fun_max_weak ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % wmax_insertI
% 2.86/3.16 thf(fact_5540_wmin__insertI,axiom,
% 2.86/3.16 ! [X: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat,Y: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat] :
% 2.86/3.16 ( ( member8440522571783428010at_nat @ X @ XS )
% 2.86/3.16 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_leq )
% 2.86/3.16 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ YS ) @ fun_min_weak )
% 2.86/3.16 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ ( insert8211810215607154385at_nat @ Y @ YS ) ) @ fun_min_weak ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % wmin_insertI
% 2.86/3.16 thf(fact_5541_wmax__emptyI,axiom,
% 2.86/3.16 ! [X4: set_Pr1261947904930325089at_nat] :
% 2.86/3.16 ( ( finite6177210948735845034at_nat @ X4 )
% 2.86/3.16 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ X4 ) @ fun_max_weak ) ) ).
% 2.86/3.16
% 2.86/3.16 % wmax_emptyI
% 2.86/3.16 thf(fact_5542_wmin__emptyI,axiom,
% 2.86/3.16 ! [X4: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ bot_bo2099793752762293965at_nat ) @ fun_min_weak ) ).
% 2.86/3.16
% 2.86/3.16 % wmin_emptyI
% 2.86/3.16 thf(fact_5543_min__rpair__set,axiom,
% 2.86/3.16 fun_re2478310338295953701at_nat @ ( produc9060074326276436823at_nat @ fun_min_strict @ fun_min_weak ) ).
% 2.86/3.16
% 2.86/3.16 % min_rpair_set
% 2.86/3.16 thf(fact_5544_max__weak__def,axiom,
% 2.86/3.16 ( fun_max_weak
% 2.86/3.16 = ( sup_su5525570899277871387at_nat @ ( max_ex8135407076693332796at_nat @ fun_pair_leq ) @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ bot_bo2099793752762293965at_nat ) @ bot_bo228742789529271731at_nat ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % max_weak_def
% 2.86/3.16 thf(fact_5545_min__weak__def,axiom,
% 2.86/3.16 ( fun_min_weak
% 2.86/3.16 = ( sup_su5525570899277871387at_nat @ ( min_ex6901939911449802026at_nat @ fun_pair_leq ) @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ bot_bo2099793752762293965at_nat ) @ bot_bo228742789529271731at_nat ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % min_weak_def
% 2.86/3.16 thf(fact_5546_smax__insertI,axiom,
% 2.86/3.16 ! [Y: product_prod_nat_nat,Y6: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,X4: set_Pr1261947904930325089at_nat] :
% 2.86/3.16 ( ( member8440522571783428010at_nat @ Y @ Y6 )
% 2.86/3.16 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_less )
% 2.86/3.16 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y6 ) @ fun_max_strict )
% 2.86/3.16 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( insert8211810215607154385at_nat @ X @ X4 ) @ Y6 ) @ fun_max_strict ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % smax_insertI
% 2.86/3.16 thf(fact_5547_max__rpair__set,axiom,
% 2.86/3.16 fun_re2478310338295953701at_nat @ ( produc9060074326276436823at_nat @ fun_max_strict @ fun_max_weak ) ).
% 2.86/3.16
% 2.86/3.16 % max_rpair_set
% 2.86/3.16 thf(fact_5548_smax__emptyI,axiom,
% 2.86/3.16 ! [Y6: set_Pr1261947904930325089at_nat] :
% 2.86/3.16 ( ( finite6177210948735845034at_nat @ Y6 )
% 2.86/3.16 => ( ( Y6 != bot_bo2099793752762293965at_nat )
% 2.86/3.16 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ Y6 ) @ fun_max_strict ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % smax_emptyI
% 2.86/3.16 thf(fact_5549_wmsI,axiom,
% 2.86/3.16 ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat,Z6: multis2468970476368604999at_nat] :
% 2.86/3.16 ( ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( set_ms8126754132646256062at_nat @ A ) @ ( set_ms8126754132646256062at_nat @ B ) ) @ fun_max_strict )
% 2.86/3.16 | ( ( A = zero_z1048942125864253310at_nat )
% 2.86/3.16 & ( B = zero_z1048942125864253310at_nat ) ) )
% 2.86/3.16 => ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ ( plus_p7104986032573967614at_nat @ Z6 @ A ) @ ( plus_p7104986032573967614at_nat @ Z6 @ B ) ) @ ms_weak ) ) ).
% 2.86/3.16
% 2.86/3.16 % wmsI
% 2.86/3.16 thf(fact_5550_smsI,axiom,
% 2.86/3.16 ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat,Z6: multis2468970476368604999at_nat] :
% 2.86/3.16 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( set_ms8126754132646256062at_nat @ A ) @ ( set_ms8126754132646256062at_nat @ B ) ) @ fun_max_strict )
% 2.86/3.16 => ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ ( plus_p7104986032573967614at_nat @ Z6 @ A ) @ ( plus_p7104986032573967614at_nat @ Z6 @ B ) ) @ ms_strict ) ) ).
% 2.86/3.16
% 2.86/3.16 % smsI
% 2.86/3.16 thf(fact_5551_ms__reduction__pair,axiom,
% 2.86/3.16 fun_re7357418987779152907at_nat @ ( produc5245064249948416855at_nat @ ms_strict @ ms_weak ) ).
% 2.86/3.16
% 2.86/3.16 % ms_reduction_pair
% 2.86/3.16 thf(fact_5552_ms__weakI1,axiom,
% 2.86/3.16 ! [Z6: multis2468970476368604999at_nat,Z7: multis2468970476368604999at_nat,A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 2.86/3.16 ( ( pw_leq @ Z6 @ Z7 )
% 2.86/3.16 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( set_ms8126754132646256062at_nat @ A ) @ ( set_ms8126754132646256062at_nat @ B ) ) @ fun_max_strict )
% 2.86/3.16 => ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ ( plus_p7104986032573967614at_nat @ Z6 @ A ) @ ( plus_p7104986032573967614at_nat @ Z7 @ B ) ) @ ms_weak ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % ms_weakI1
% 2.86/3.16 thf(fact_5553_ms__strictI,axiom,
% 2.86/3.16 ! [Z6: multis2468970476368604999at_nat,Z7: multis2468970476368604999at_nat,A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 2.86/3.16 ( ( pw_leq @ Z6 @ Z7 )
% 2.86/3.16 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( set_ms8126754132646256062at_nat @ A ) @ ( set_ms8126754132646256062at_nat @ B ) ) @ fun_max_strict )
% 2.86/3.16 => ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ ( plus_p7104986032573967614at_nat @ Z6 @ A ) @ ( plus_p7104986032573967614at_nat @ Z7 @ B ) ) @ ms_strict ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % ms_strictI
% 2.86/3.16 thf(fact_5554_pw__leq__lstep,axiom,
% 2.86/3.16 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 2.86/3.16 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_leq )
% 2.86/3.16 => ( pw_leq @ ( add_ms2612439473150266591at_nat @ X @ zero_z1048942125864253310at_nat ) @ ( add_ms2612439473150266591at_nat @ Y @ zero_z1048942125864253310at_nat ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % pw_leq_lstep
% 2.86/3.16 thf(fact_5555_pw__leq__step,axiom,
% 2.86/3.16 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat,X4: multis2468970476368604999at_nat,Y6: multis2468970476368604999at_nat] :
% 2.86/3.16 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_leq )
% 2.86/3.16 => ( ( pw_leq @ X4 @ Y6 )
% 2.86/3.16 => ( pw_leq @ ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ X @ zero_z1048942125864253310at_nat ) @ X4 ) @ ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ Y @ zero_z1048942125864253310at_nat ) @ Y6 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % pw_leq_step
% 2.86/3.16 thf(fact_5556_pw__leq_Osimps,axiom,
% 2.86/3.16 ( pw_leq
% 2.86/3.16 = ( ^ [A12: multis2468970476368604999at_nat,A23: multis2468970476368604999at_nat] :
% 2.86/3.16 ( ( ( A12 = zero_z1048942125864253310at_nat )
% 2.86/3.16 & ( A23 = zero_z1048942125864253310at_nat ) )
% 2.86/3.16 | ? [X2: product_prod_nat_nat,Y5: product_prod_nat_nat,X8: multis2468970476368604999at_nat,Y7: multis2468970476368604999at_nat] :
% 2.86/3.16 ( ( A12
% 2.86/3.16 = ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ X2 @ zero_z1048942125864253310at_nat ) @ X8 ) )
% 2.86/3.16 & ( A23
% 2.86/3.16 = ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ Y5 @ zero_z1048942125864253310at_nat ) @ Y7 ) )
% 2.86/3.16 & ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X2 @ Y5 ) @ fun_pair_leq )
% 2.86/3.16 & ( pw_leq @ X8 @ Y7 ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % pw_leq.simps
% 2.86/3.16 thf(fact_5557_pw__leq_Ocases,axiom,
% 2.86/3.16 ! [A1: multis2468970476368604999at_nat,A22: multis2468970476368604999at_nat] :
% 2.86/3.16 ( ( pw_leq @ A1 @ A22 )
% 2.86/3.16 => ( ( ( A1 = zero_z1048942125864253310at_nat )
% 2.86/3.16 => ( A22 != zero_z1048942125864253310at_nat ) )
% 2.86/3.16 => ~ ! [X3: product_prod_nat_nat,Y2: product_prod_nat_nat,X9: multis2468970476368604999at_nat] :
% 2.86/3.16 ( ( A1
% 2.86/3.16 = ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ X3 @ zero_z1048942125864253310at_nat ) @ X9 ) )
% 2.86/3.16 => ! [Y8: multis2468970476368604999at_nat] :
% 2.86/3.16 ( ( A22
% 2.86/3.16 = ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ Y2 @ zero_z1048942125864253310at_nat ) @ Y8 ) )
% 2.86/3.16 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X3 @ Y2 ) @ fun_pair_leq )
% 2.86/3.16 => ~ ( pw_leq @ X9 @ Y8 ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % pw_leq.cases
% 2.86/3.16 thf(fact_5558_ms__weakI2,axiom,
% 2.86/3.16 ! [Z6: multis2468970476368604999at_nat,Z7: multis2468970476368604999at_nat] :
% 2.86/3.16 ( ( pw_leq @ Z6 @ Z7 )
% 2.86/3.16 => ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ ( plus_p7104986032573967614at_nat @ Z6 @ zero_z1048942125864253310at_nat ) @ ( plus_p7104986032573967614at_nat @ Z7 @ zero_z1048942125864253310at_nat ) ) @ ms_weak ) ) ).
% 2.86/3.16
% 2.86/3.16 % ms_weakI2
% 2.86/3.16 thf(fact_5559_pw__leq__split,axiom,
% 2.86/3.16 ! [X4: multis2468970476368604999at_nat,Y6: multis2468970476368604999at_nat] :
% 2.86/3.16 ( ( pw_leq @ X4 @ Y6 )
% 2.86/3.16 => ? [A9: multis2468970476368604999at_nat,B5: multis2468970476368604999at_nat,Z8: multis2468970476368604999at_nat] :
% 2.86/3.16 ( ( X4
% 2.86/3.16 = ( plus_p7104986032573967614at_nat @ A9 @ Z8 ) )
% 2.86/3.16 & ( Y6
% 2.86/3.16 = ( plus_p7104986032573967614at_nat @ B5 @ Z8 ) )
% 2.86/3.16 & ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( set_ms8126754132646256062at_nat @ A9 ) @ ( set_ms8126754132646256062at_nat @ B5 ) ) @ fun_max_strict )
% 2.86/3.16 | ( ( B5 = zero_z1048942125864253310at_nat )
% 2.86/3.16 & ( A9 = zero_z1048942125864253310at_nat ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % pw_leq_split
% 2.86/3.16 thf(fact_5560_less__than__iff,axiom,
% 2.86/3.16 ! [X: nat,Y: nat] :
% 2.86/3.16 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ less_than )
% 2.86/3.16 = ( ord_less_nat @ X @ Y ) ) ).
% 2.86/3.16
% 2.86/3.16 % less_than_iff
% 2.86/3.16 thf(fact_5561_natLeq__on__well__order__on,axiom,
% 2.86/3.16 ! [N: nat] :
% 2.86/3.16 ( order_2888998067076097458on_nat
% 2.86/3.16 @ ( collect_nat
% 2.86/3.16 @ ^ [X2: nat] : ( ord_less_nat @ X2 @ N ) )
% 2.86/3.16 @ ( collec3392354462482085612at_nat
% 2.86/3.16 @ ( produc6081775807080527818_nat_o
% 2.86/3.16 @ ^ [X2: nat,Y5: nat] :
% 2.86/3.16 ( ( ord_less_nat @ X2 @ N )
% 2.86/3.16 & ( ord_less_nat @ Y5 @ N )
% 2.86/3.16 & ( ord_less_eq_nat @ X2 @ Y5 ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % natLeq_on_well_order_on
% 2.86/3.16 thf(fact_5562_natLeq__on__Well__order,axiom,
% 2.86/3.16 ! [N: nat] :
% 2.86/3.16 ( order_2888998067076097458on_nat
% 2.86/3.16 @ ( field_nat
% 2.86/3.16 @ ( collec3392354462482085612at_nat
% 2.86/3.16 @ ( produc6081775807080527818_nat_o
% 2.86/3.16 @ ^ [X2: nat,Y5: nat] :
% 2.86/3.16 ( ( ord_less_nat @ X2 @ N )
% 2.86/3.16 & ( ord_less_nat @ Y5 @ N )
% 2.86/3.16 & ( ord_less_eq_nat @ X2 @ Y5 ) ) ) ) )
% 2.86/3.16 @ ( collec3392354462482085612at_nat
% 2.86/3.16 @ ( produc6081775807080527818_nat_o
% 2.86/3.16 @ ^ [X2: nat,Y5: nat] :
% 2.86/3.16 ( ( ord_less_nat @ X2 @ N )
% 2.86/3.16 & ( ord_less_nat @ Y5 @ N )
% 2.86/3.16 & ( ord_less_eq_nat @ X2 @ Y5 ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % natLeq_on_Well_order
% 2.86/3.16 thf(fact_5563_eventually__prod__sequentially,axiom,
% 2.86/3.16 ! [P: product_prod_nat_nat > $o] :
% 2.86/3.16 ( ( eventu1038000079068216329at_nat @ P @ ( prod_filter_nat_nat @ at_top_nat @ at_top_nat ) )
% 2.86/3.16 = ( ? [N8: nat] :
% 2.86/3.16 ! [M: nat] :
% 2.86/3.16 ( ( ord_less_eq_nat @ N8 @ M )
% 2.86/3.16 => ! [N2: nat] :
% 2.86/3.16 ( ( ord_less_eq_nat @ N8 @ N2 )
% 2.86/3.16 => ( P @ ( product_Pair_nat_nat @ N2 @ M ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % eventually_prod_sequentially
% 2.86/3.16 thf(fact_5564_UNIV__bool,axiom,
% 2.86/3.16 ( top_top_set_o
% 2.86/3.16 = ( insert_o2 @ $false @ ( insert_o2 @ $true @ bot_bot_set_o ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % UNIV_bool
% 2.86/3.16 thf(fact_5565_ctwo__Cnotzero,axiom,
% 2.86/3.16 ( ~ ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ bNF_Cardinal_ctwo @ bNF_Cardinal_czero_o ) @ bNF_We2654380646378065620so_o_o )
% 2.86/3.16 & ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ bNF_Cardinal_ctwo ) @ bNF_Cardinal_ctwo ) ) ).
% 2.86/3.16
% 2.86/3.16 % ctwo_Cnotzero
% 2.86/3.16 thf(fact_5566_ctwo__ordLess__natLeq,axiom,
% 2.86/3.16 member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ bNF_Cardinal_ctwo @ bNF_Ca8665028551170535155natLeq ) @ bNF_We8182288985678559134_o_nat ).
% 2.86/3.16
% 2.86/3.16 % ctwo_ordLess_natLeq
% 2.86/3.16 thf(fact_5567_natLeq__underS__less,axiom,
% 2.86/3.16 ! [N: nat] :
% 2.86/3.16 ( ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N )
% 2.86/3.16 = ( collect_nat
% 2.86/3.16 @ ^ [X2: nat] : ( ord_less_nat @ X2 @ N ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % natLeq_underS_less
% 2.86/3.16 thf(fact_5568_Restr__natLeq2,axiom,
% 2.86/3.16 ! [N: nat] :
% 2.86/3.16 ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 2.86/3.16 @ ( produc457027306803732586at_nat @ ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N )
% 2.86/3.16 @ ^ [Uu2: nat] : ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N ) ) )
% 2.86/3.16 = ( collec3392354462482085612at_nat
% 2.86/3.16 @ ( produc6081775807080527818_nat_o
% 2.86/3.16 @ ^ [X2: nat,Y5: nat] :
% 2.86/3.16 ( ( ord_less_nat @ X2 @ N )
% 2.86/3.16 & ( ord_less_nat @ Y5 @ N )
% 2.86/3.16 & ( ord_less_eq_nat @ X2 @ Y5 ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % Restr_natLeq2
% 2.86/3.16 thf(fact_5569_Restr__natLeq,axiom,
% 2.86/3.16 ! [N: nat] :
% 2.86/3.16 ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 2.86/3.16 @ ( produc457027306803732586at_nat
% 2.86/3.16 @ ( collect_nat
% 2.86/3.16 @ ^ [X2: nat] : ( ord_less_nat @ X2 @ N ) )
% 2.86/3.16 @ ^ [Uu2: nat] :
% 2.86/3.16 ( collect_nat
% 2.86/3.16 @ ^ [X2: nat] : ( ord_less_nat @ X2 @ N ) ) ) )
% 2.86/3.16 = ( collec3392354462482085612at_nat
% 2.86/3.16 @ ( produc6081775807080527818_nat_o
% 2.86/3.16 @ ^ [X2: nat,Y5: nat] :
% 2.86/3.16 ( ( ord_less_nat @ X2 @ N )
% 2.86/3.16 & ( ord_less_nat @ Y5 @ N )
% 2.86/3.16 & ( ord_less_eq_nat @ X2 @ Y5 ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % Restr_natLeq
% 2.86/3.16 thf(fact_5570_card__of__nat,axiom,
% 2.86/3.16 member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ top_top_set_nat ) @ bNF_Ca8665028551170535155natLeq ) @ bNF_We5258908940166488438at_nat ).
% 2.86/3.16
% 2.86/3.16 % card_of_nat
% 2.86/3.16 thf(fact_5571_card__of__Field__natLeq,axiom,
% 2.86/3.16 member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ ( field_nat @ bNF_Ca8665028551170535155natLeq ) ) @ bNF_Ca8665028551170535155natLeq ) @ bNF_We5258908940166488438at_nat ).
% 2.86/3.16
% 2.86/3.16 % card_of_Field_natLeq
% 2.86/3.16 thf(fact_5572_plus__rat_Otransfer,axiom,
% 2.86/3.16 ( bNF_re7627151682743391978at_rat @ pcr_rat @ ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat )
% 2.86/3.16 @ ^ [X2: product_prod_int_int,Y5: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ Y5 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y5 ) @ ( product_snd_int_int @ X2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X2 ) @ ( product_snd_int_int @ Y5 ) ) )
% 2.86/3.16 @ plus_plus_rat ) ).
% 2.86/3.16
% 2.86/3.16 % plus_rat.transfer
% 2.86/3.16 thf(fact_5573_one__rat_Otransfer,axiom,
% 2.86/3.16 pcr_rat @ ( product_Pair_int_int @ one_one_int @ one_one_int ) @ one_one_rat ).
% 2.86/3.16
% 2.86/3.16 % one_rat.transfer
% 2.86/3.16 thf(fact_5574_zero__rat_Otransfer,axiom,
% 2.86/3.16 pcr_rat @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ zero_zero_rat ).
% 2.86/3.16
% 2.86/3.16 % zero_rat.transfer
% 2.86/3.16 thf(fact_5575_times__rat_Otransfer,axiom,
% 2.86/3.16 ( bNF_re7627151682743391978at_rat @ pcr_rat @ ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat )
% 2.86/3.16 @ ^ [X2: product_prod_int_int,Y5: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_fst_int_int @ Y5 ) ) @ ( times_times_int @ ( product_snd_int_int @ X2 ) @ ( product_snd_int_int @ Y5 ) ) )
% 2.86/3.16 @ times_times_rat ) ).
% 2.86/3.16
% 2.86/3.16 % times_rat.transfer
% 2.86/3.16 thf(fact_5576_uminus__rat_Otransfer,axiom,
% 2.86/3.16 ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat
% 2.86/3.16 @ ^ [X2: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X2 ) ) @ ( product_snd_int_int @ X2 ) )
% 2.86/3.16 @ uminus_uminus_rat ) ).
% 2.86/3.16
% 2.86/3.16 % uminus_rat.transfer
% 2.86/3.16 thf(fact_5577_normalize__negative,axiom,
% 2.86/3.16 ! [Q6: int,P6: int] :
% 2.86/3.16 ( ( ord_less_int @ Q6 @ zero_zero_int )
% 2.86/3.16 => ( ( normalize @ ( product_Pair_int_int @ P6 @ Q6 ) )
% 2.86/3.16 = ( normalize @ ( product_Pair_int_int @ ( uminus_uminus_int @ P6 ) @ ( uminus_uminus_int @ Q6 ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % normalize_negative
% 2.86/3.16 thf(fact_5578_inverse__rat_Otransfer,axiom,
% 2.86/3.16 ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat
% 2.86/3.16 @ ^ [X2: product_prod_int_int] :
% 2.86/3.16 ( if_Pro3027730157355071871nt_int
% 2.86/3.16 @ ( ( product_fst_int_int @ X2 )
% 2.86/3.16 = zero_zero_int )
% 2.86/3.16 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 2.86/3.16 @ ( product_Pair_int_int @ ( product_snd_int_int @ X2 ) @ ( product_fst_int_int @ X2 ) ) )
% 2.86/3.16 @ inverse_inverse_rat ) ).
% 2.86/3.16
% 2.86/3.16 % inverse_rat.transfer
% 2.86/3.16 thf(fact_5579_normalize__denom__zero,axiom,
% 2.86/3.16 ! [P6: int] :
% 2.86/3.16 ( ( normalize @ ( product_Pair_int_int @ P6 @ zero_zero_int ) )
% 2.86/3.16 = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 2.86/3.16
% 2.86/3.16 % normalize_denom_zero
% 2.86/3.16 thf(fact_5580_normalize__denom__pos,axiom,
% 2.86/3.16 ! [R2: product_prod_int_int,P6: int,Q6: int] :
% 2.86/3.16 ( ( ( normalize @ R2 )
% 2.86/3.16 = ( product_Pair_int_int @ P6 @ Q6 ) )
% 2.86/3.16 => ( ord_less_int @ zero_zero_int @ Q6 ) ) ).
% 2.86/3.16
% 2.86/3.16 % normalize_denom_pos
% 2.86/3.16 thf(fact_5581_normalize__crossproduct,axiom,
% 2.86/3.16 ! [Q6: int,S3: int,P6: int,R2: int] :
% 2.86/3.16 ( ( Q6 != zero_zero_int )
% 2.86/3.16 => ( ( S3 != zero_zero_int )
% 2.86/3.16 => ( ( ( normalize @ ( product_Pair_int_int @ P6 @ Q6 ) )
% 2.86/3.16 = ( normalize @ ( product_Pair_int_int @ R2 @ S3 ) ) )
% 2.86/3.16 => ( ( times_times_int @ P6 @ S3 )
% 2.86/3.16 = ( times_times_int @ R2 @ Q6 ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % normalize_crossproduct
% 2.86/3.16 thf(fact_5582_rat__inverse__code,axiom,
% 2.86/3.16 ! [P6: rat] :
% 2.86/3.16 ( ( quotient_of @ ( inverse_inverse_rat @ P6 ) )
% 2.86/3.16 = ( produc4245557441103728435nt_int
% 2.86/3.16 @ ^ [A3: int,B3: int] : ( if_Pro3027730157355071871nt_int @ ( A3 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ ( times_times_int @ ( sgn_sgn_int @ A3 ) @ B3 ) @ ( abs_abs_int @ A3 ) ) )
% 2.86/3.16 @ ( quotient_of @ P6 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % rat_inverse_code
% 2.86/3.16 thf(fact_5583_normalize__def,axiom,
% 2.86/3.16 ( normalize
% 2.86/3.16 = ( ^ [P7: product_prod_int_int] :
% 2.86/3.16 ( 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 ) ) ) )
% 2.86/3.16 @ ( if_Pro3027730157355071871nt_int
% 2.86/3.16 @ ( ( product_snd_int_int @ P7 )
% 2.86/3.16 = zero_zero_int )
% 2.86/3.16 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 2.86/3.16 @ ( 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 ) ) ) ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % normalize_def
% 2.86/3.16 thf(fact_5584_quotient__of__number_I3_J,axiom,
% 2.86/3.16 ! [K3: num] :
% 2.86/3.16 ( ( quotient_of @ ( numeral_numeral_rat @ K3 ) )
% 2.86/3.16 = ( product_Pair_int_int @ ( numeral_numeral_int @ K3 ) @ one_one_int ) ) ).
% 2.86/3.16
% 2.86/3.16 % quotient_of_number(3)
% 2.86/3.16 thf(fact_5585_rat__one__code,axiom,
% 2.86/3.16 ( ( quotient_of @ one_one_rat )
% 2.86/3.16 = ( product_Pair_int_int @ one_one_int @ one_one_int ) ) ).
% 2.86/3.16
% 2.86/3.16 % rat_one_code
% 2.86/3.16 thf(fact_5586_rat__zero__code,axiom,
% 2.86/3.16 ( ( quotient_of @ zero_zero_rat )
% 2.86/3.16 = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 2.86/3.16
% 2.86/3.16 % rat_zero_code
% 2.86/3.16 thf(fact_5587_quotient__of__number_I5_J,axiom,
% 2.86/3.16 ! [K3: num] :
% 2.86/3.16 ( ( quotient_of @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K3 ) ) )
% 2.86/3.16 = ( product_Pair_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K3 ) ) @ one_one_int ) ) ).
% 2.86/3.16
% 2.86/3.16 % quotient_of_number(5)
% 2.86/3.16 thf(fact_5588_quotient__of__number_I4_J,axiom,
% 2.86/3.16 ( ( quotient_of @ ( uminus_uminus_rat @ one_one_rat ) )
% 2.86/3.16 = ( product_Pair_int_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ) ) ).
% 2.86/3.16
% 2.86/3.16 % quotient_of_number(4)
% 2.86/3.16 thf(fact_5589_Gcd__int__set__eq__fold,axiom,
% 2.86/3.16 ! [Xs: list_int] :
% 2.86/3.16 ( ( gcd_Gcd_int @ ( set_int2 @ Xs ) )
% 2.86/3.16 = ( fold_int_int @ gcd_gcd_int @ Xs @ zero_zero_int ) ) ).
% 2.86/3.16
% 2.86/3.16 % Gcd_int_set_eq_fold
% 2.86/3.16 thf(fact_5590_quotient__of__div,axiom,
% 2.86/3.16 ! [R2: rat,N: int,D2: int] :
% 2.86/3.16 ( ( ( quotient_of @ R2 )
% 2.86/3.16 = ( product_Pair_int_int @ N @ D2 ) )
% 2.86/3.16 => ( R2
% 2.86/3.16 = ( divide_divide_rat @ ( ring_1_of_int_rat @ N ) @ ( ring_1_of_int_rat @ D2 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % quotient_of_div
% 2.86/3.16 thf(fact_5591_quotient__of__denom__pos,axiom,
% 2.86/3.16 ! [R2: rat,P6: int,Q6: int] :
% 2.86/3.16 ( ( ( quotient_of @ R2 )
% 2.86/3.16 = ( product_Pair_int_int @ P6 @ Q6 ) )
% 2.86/3.16 => ( ord_less_int @ zero_zero_int @ Q6 ) ) ).
% 2.86/3.16
% 2.86/3.16 % quotient_of_denom_pos
% 2.86/3.16 thf(fact_5592_rat__abs__code,axiom,
% 2.86/3.16 ! [P6: rat] :
% 2.86/3.16 ( ( quotient_of @ ( abs_abs_rat @ P6 ) )
% 2.86/3.16 = ( produc4245557441103728435nt_int
% 2.86/3.16 @ ^ [A3: int] : ( product_Pair_int_int @ ( abs_abs_int @ A3 ) )
% 2.86/3.16 @ ( quotient_of @ P6 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % rat_abs_code
% 2.86/3.16 thf(fact_5593_rat__sgn__code,axiom,
% 2.86/3.16 ! [P6: rat] :
% 2.86/3.16 ( ( quotient_of @ ( sgn_sgn_rat @ P6 ) )
% 2.86/3.16 = ( product_Pair_int_int @ ( sgn_sgn_int @ ( product_fst_int_int @ ( quotient_of @ P6 ) ) ) @ one_one_int ) ) ).
% 2.86/3.16
% 2.86/3.16 % rat_sgn_code
% 2.86/3.16 thf(fact_5594_rat__uminus__code,axiom,
% 2.86/3.16 ! [P6: rat] :
% 2.86/3.16 ( ( quotient_of @ ( uminus_uminus_rat @ P6 ) )
% 2.86/3.16 = ( produc4245557441103728435nt_int
% 2.86/3.16 @ ^ [A3: int] : ( product_Pair_int_int @ ( uminus_uminus_int @ A3 ) )
% 2.86/3.16 @ ( quotient_of @ P6 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % rat_uminus_code
% 2.86/3.16 thf(fact_5595_rat__divide__code,axiom,
% 2.86/3.16 ! [P6: rat,Q6: rat] :
% 2.86/3.16 ( ( quotient_of @ ( divide_divide_rat @ P6 @ Q6 ) )
% 2.86/3.16 = ( produc4245557441103728435nt_int
% 2.86/3.16 @ ^ [A3: int,C5: int] :
% 2.86/3.16 ( produc4245557441103728435nt_int
% 2.86/3.16 @ ^ [B3: int,D5: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A3 @ D5 ) @ ( times_times_int @ C5 @ B3 ) ) )
% 2.86/3.16 @ ( quotient_of @ Q6 ) )
% 2.86/3.16 @ ( quotient_of @ P6 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % rat_divide_code
% 2.86/3.16 thf(fact_5596_rat__minus__code,axiom,
% 2.86/3.16 ! [P6: rat,Q6: rat] :
% 2.86/3.16 ( ( quotient_of @ ( minus_minus_rat @ P6 @ Q6 ) )
% 2.86/3.16 = ( produc4245557441103728435nt_int
% 2.86/3.16 @ ^ [A3: int,C5: int] :
% 2.86/3.16 ( produc4245557441103728435nt_int
% 2.86/3.16 @ ^ [B3: int,D5: int] : ( normalize @ ( product_Pair_int_int @ ( minus_minus_int @ ( times_times_int @ A3 @ D5 ) @ ( times_times_int @ B3 @ C5 ) ) @ ( times_times_int @ C5 @ D5 ) ) )
% 2.86/3.16 @ ( quotient_of @ Q6 ) )
% 2.86/3.16 @ ( quotient_of @ P6 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % rat_minus_code
% 2.86/3.16 thf(fact_5597_rat__times__code,axiom,
% 2.86/3.16 ! [P6: rat,Q6: rat] :
% 2.86/3.16 ( ( quotient_of @ ( times_times_rat @ P6 @ Q6 ) )
% 2.86/3.16 = ( produc4245557441103728435nt_int
% 2.86/3.16 @ ^ [A3: int,C5: int] :
% 2.86/3.16 ( produc4245557441103728435nt_int
% 2.86/3.16 @ ^ [B3: int,D5: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A3 @ B3 ) @ ( times_times_int @ C5 @ D5 ) ) )
% 2.86/3.16 @ ( quotient_of @ Q6 ) )
% 2.86/3.16 @ ( quotient_of @ P6 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % rat_times_code
% 2.86/3.16 thf(fact_5598_rat__plus__code,axiom,
% 2.86/3.16 ! [P6: rat,Q6: rat] :
% 2.86/3.16 ( ( quotient_of @ ( plus_plus_rat @ P6 @ Q6 ) )
% 2.86/3.16 = ( produc4245557441103728435nt_int
% 2.86/3.16 @ ^ [A3: int,C5: int] :
% 2.86/3.16 ( produc4245557441103728435nt_int
% 2.86/3.16 @ ^ [B3: int,D5: int] : ( normalize @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ A3 @ D5 ) @ ( times_times_int @ B3 @ C5 ) ) @ ( times_times_int @ C5 @ D5 ) ) )
% 2.86/3.16 @ ( quotient_of @ Q6 ) )
% 2.86/3.16 @ ( quotient_of @ P6 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % rat_plus_code
% 2.86/3.16 thf(fact_5599_quotient__of__int,axiom,
% 2.86/3.16 ! [A2: int] :
% 2.86/3.16 ( ( quotient_of @ ( of_int @ A2 ) )
% 2.86/3.16 = ( product_Pair_int_int @ A2 @ one_one_int ) ) ).
% 2.86/3.16
% 2.86/3.16 % quotient_of_int
% 2.86/3.16 thf(fact_5600_Frct__code__post_I5_J,axiom,
% 2.86/3.16 ! [K3: num] :
% 2.86/3.16 ( ( frct @ ( product_Pair_int_int @ one_one_int @ ( numeral_numeral_int @ K3 ) ) )
% 2.86/3.16 = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ K3 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % Frct_code_post(5)
% 2.86/3.16 thf(fact_5601_gcd__pos__nat,axiom,
% 2.86/3.16 ! [M2: nat,N: nat] :
% 2.86/3.16 ( ( ord_less_nat @ zero_zero_nat @ ( gcd_gcd_nat @ M2 @ N ) )
% 2.86/3.16 = ( ( M2 != zero_zero_nat )
% 2.86/3.16 | ( N != zero_zero_nat ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % gcd_pos_nat
% 2.86/3.16 thf(fact_5602_Gcd__in,axiom,
% 2.86/3.16 ! [A: set_nat] :
% 2.86/3.16 ( ! [A4: nat,B4: nat] :
% 2.86/3.16 ( ( member_nat @ A4 @ A )
% 2.86/3.16 => ( ( member_nat @ B4 @ A )
% 2.86/3.16 => ( member_nat @ ( gcd_gcd_nat @ A4 @ B4 ) @ A ) ) )
% 2.86/3.16 => ( ( A != bot_bot_set_nat )
% 2.86/3.16 => ( member_nat @ ( gcd_Gcd_nat @ A ) @ A ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % Gcd_in
% 2.86/3.16 thf(fact_5603_Gcd__nat__set__eq__fold,axiom,
% 2.86/3.16 ! [Xs: list_nat] :
% 2.86/3.16 ( ( gcd_Gcd_nat @ ( set_nat2 @ Xs ) )
% 2.86/3.16 = ( fold_nat_nat @ gcd_gcd_nat @ Xs @ zero_zero_nat ) ) ).
% 2.86/3.16
% 2.86/3.16 % Gcd_nat_set_eq_fold
% 2.86/3.16 thf(fact_5604_Frct__code__post_I6_J,axiom,
% 2.86/3.16 ! [K3: num,L: num] :
% 2.86/3.16 ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K3 ) @ ( numeral_numeral_int @ L ) ) )
% 2.86/3.16 = ( divide_divide_rat @ ( numeral_numeral_rat @ K3 ) @ ( numeral_numeral_rat @ L ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % Frct_code_post(6)
% 2.86/3.16 thf(fact_5605_gcd__is__Max__divisors__nat,axiom,
% 2.86/3.16 ! [N: nat,M2: nat] :
% 2.86/3.16 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.16 => ( ( gcd_gcd_nat @ M2 @ N )
% 2.86/3.16 = ( lattic8265883725875713057ax_nat
% 2.86/3.16 @ ( collect_nat
% 2.86/3.16 @ ^ [D5: nat] :
% 2.86/3.16 ( ( dvd_dvd_nat @ D5 @ M2 )
% 2.86/3.16 & ( dvd_dvd_nat @ D5 @ N ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % gcd_is_Max_divisors_nat
% 2.86/3.16 thf(fact_5606_Frct__code__post_I4_J,axiom,
% 2.86/3.16 ! [K3: num] :
% 2.86/3.16 ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K3 ) @ one_one_int ) )
% 2.86/3.16 = ( numeral_numeral_rat @ K3 ) ) ).
% 2.86/3.16
% 2.86/3.16 % Frct_code_post(4)
% 2.86/3.16 thf(fact_5607_Frct__code__post_I2_J,axiom,
% 2.86/3.16 ! [A2: int] :
% 2.86/3.16 ( ( frct @ ( product_Pair_int_int @ A2 @ zero_zero_int ) )
% 2.86/3.16 = zero_zero_rat ) ).
% 2.86/3.16
% 2.86/3.16 % Frct_code_post(2)
% 2.86/3.16 thf(fact_5608_Frct__code__post_I1_J,axiom,
% 2.86/3.16 ! [A2: int] :
% 2.86/3.16 ( ( frct @ ( product_Pair_int_int @ zero_zero_int @ A2 ) )
% 2.86/3.16 = zero_zero_rat ) ).
% 2.86/3.16
% 2.86/3.16 % Frct_code_post(1)
% 2.86/3.16 thf(fact_5609_Frct__code__post_I3_J,axiom,
% 2.86/3.16 ( ( frct @ ( product_Pair_int_int @ one_one_int @ one_one_int ) )
% 2.86/3.16 = one_one_rat ) ).
% 2.86/3.16
% 2.86/3.16 % Frct_code_post(3)
% 2.86/3.16 thf(fact_5610_Frct__code__post_I8_J,axiom,
% 2.86/3.16 ! [A2: int,B2: int] :
% 2.86/3.16 ( ( frct @ ( product_Pair_int_int @ A2 @ ( uminus_uminus_int @ B2 ) ) )
% 2.86/3.16 = ( uminus_uminus_rat @ ( frct @ ( product_Pair_int_int @ A2 @ B2 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % Frct_code_post(8)
% 2.86/3.16 thf(fact_5611_Frct__code__post_I7_J,axiom,
% 2.86/3.16 ! [A2: int,B2: int] :
% 2.86/3.16 ( ( frct @ ( product_Pair_int_int @ ( uminus_uminus_int @ A2 ) @ B2 ) )
% 2.86/3.16 = ( uminus_uminus_rat @ ( frct @ ( product_Pair_int_int @ A2 @ B2 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % Frct_code_post(7)
% 2.86/3.16 thf(fact_5612_gcd__nat_Opelims,axiom,
% 2.86/3.16 ! [X: nat,Xa: nat,Y: nat] :
% 2.86/3.16 ( ( ( gcd_gcd_nat @ X @ Xa )
% 2.86/3.16 = Y )
% 2.86/3.16 => ( ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa ) )
% 2.86/3.16 => ~ ( ( ( ( Xa = zero_zero_nat )
% 2.86/3.16 => ( Y = X ) )
% 2.86/3.16 & ( ( Xa != zero_zero_nat )
% 2.86/3.16 => ( Y
% 2.86/3.16 = ( gcd_gcd_nat @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) ) )
% 2.86/3.16 => ~ ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % gcd_nat.pelims
% 2.86/3.16 thf(fact_5613_plus__rat_Orsp,axiom,
% 2.86/3.16 ( bNF_re5228765855967844073nt_int @ ratrel @ ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel )
% 2.86/3.16 @ ^ [X2: product_prod_int_int,Y5: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ Y5 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y5 ) @ ( product_snd_int_int @ X2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X2 ) @ ( product_snd_int_int @ Y5 ) ) )
% 2.86/3.16 @ ^ [X2: product_prod_int_int,Y5: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ Y5 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y5 ) @ ( product_snd_int_int @ X2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X2 ) @ ( product_snd_int_int @ Y5 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % plus_rat.rsp
% 2.86/3.16 thf(fact_5614_one__rat_Orsp,axiom,
% 2.86/3.16 ratrel @ ( product_Pair_int_int @ one_one_int @ one_one_int ) @ ( product_Pair_int_int @ one_one_int @ one_one_int ) ).
% 2.86/3.16
% 2.86/3.16 % one_rat.rsp
% 2.86/3.16 thf(fact_5615_zero__rat_Orsp,axiom,
% 2.86/3.16 ratrel @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ).
% 2.86/3.16
% 2.86/3.16 % zero_rat.rsp
% 2.86/3.16 thf(fact_5616_Fract_Orsp,axiom,
% 2.86/3.16 ( bNF_re157797125943740599nt_int
% 2.86/3.16 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 2.86/3.16 @ ( bNF_re6250860962936578807nt_int
% 2.86/3.16 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 2.86/3.16 @ ratrel )
% 2.86/3.16 @ ^ [A3: int,B3: int] : ( if_Pro3027730157355071871nt_int @ ( B3 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A3 @ B3 ) )
% 2.86/3.16 @ ^ [A3: int,B3: int] : ( if_Pro3027730157355071871nt_int @ ( B3 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A3 @ B3 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % Fract.rsp
% 2.86/3.16 thf(fact_5617_times__rat_Orsp,axiom,
% 2.86/3.16 ( bNF_re5228765855967844073nt_int @ ratrel @ ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel )
% 2.86/3.16 @ ^ [X2: product_prod_int_int,Y5: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_fst_int_int @ Y5 ) ) @ ( times_times_int @ ( product_snd_int_int @ X2 ) @ ( product_snd_int_int @ Y5 ) ) )
% 2.86/3.16 @ ^ [X2: product_prod_int_int,Y5: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_fst_int_int @ Y5 ) ) @ ( times_times_int @ ( product_snd_int_int @ X2 ) @ ( product_snd_int_int @ Y5 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % times_rat.rsp
% 2.86/3.16 thf(fact_5618_uminus__rat_Orsp,axiom,
% 2.86/3.16 ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel
% 2.86/3.16 @ ^ [X2: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X2 ) ) @ ( product_snd_int_int @ X2 ) )
% 2.86/3.16 @ ^ [X2: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X2 ) ) @ ( product_snd_int_int @ X2 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % uminus_rat.rsp
% 2.86/3.16 thf(fact_5619_inverse__rat_Orsp,axiom,
% 2.86/3.16 ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel
% 2.86/3.16 @ ^ [X2: product_prod_int_int] :
% 2.86/3.16 ( if_Pro3027730157355071871nt_int
% 2.86/3.16 @ ( ( product_fst_int_int @ X2 )
% 2.86/3.16 = zero_zero_int )
% 2.86/3.16 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 2.86/3.16 @ ( product_Pair_int_int @ ( product_snd_int_int @ X2 ) @ ( product_fst_int_int @ X2 ) ) )
% 2.86/3.16 @ ^ [X2: product_prod_int_int] :
% 2.86/3.16 ( if_Pro3027730157355071871nt_int
% 2.86/3.16 @ ( ( product_fst_int_int @ X2 )
% 2.86/3.16 = zero_zero_int )
% 2.86/3.16 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 2.86/3.16 @ ( product_Pair_int_int @ ( product_snd_int_int @ X2 ) @ ( product_fst_int_int @ X2 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % inverse_rat.rsp
% 2.86/3.16 thf(fact_5620_plus__rat_Oabs__eq,axiom,
% 2.86/3.16 ! [Xa: product_prod_int_int,X: product_prod_int_int] :
% 2.86/3.16 ( ( ratrel @ Xa @ Xa )
% 2.86/3.16 => ( ( ratrel @ X @ X )
% 2.86/3.16 => ( ( plus_plus_rat @ ( abs_Rat @ Xa ) @ ( abs_Rat @ X ) )
% 2.86/3.16 = ( 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 ) ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % plus_rat.abs_eq
% 2.86/3.16 thf(fact_5621_inverse__rat_Oabs__eq,axiom,
% 2.86/3.16 ! [X: product_prod_int_int] :
% 2.86/3.16 ( ( ratrel @ X @ X )
% 2.86/3.16 => ( ( inverse_inverse_rat @ ( abs_Rat @ X ) )
% 2.86/3.16 = ( abs_Rat
% 2.86/3.16 @ ( if_Pro3027730157355071871nt_int
% 2.86/3.16 @ ( ( product_fst_int_int @ X )
% 2.86/3.16 = zero_zero_int )
% 2.86/3.16 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 2.86/3.16 @ ( product_Pair_int_int @ ( product_snd_int_int @ X ) @ ( product_fst_int_int @ X ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % inverse_rat.abs_eq
% 2.86/3.16 thf(fact_5622_one__rat__def,axiom,
% 2.86/3.16 ( one_one_rat
% 2.86/3.16 = ( abs_Rat @ ( product_Pair_int_int @ one_one_int @ one_one_int ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % one_rat_def
% 2.86/3.16 thf(fact_5623_zero__rat__def,axiom,
% 2.86/3.16 ( zero_zero_rat
% 2.86/3.16 = ( abs_Rat @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % zero_rat_def
% 2.86/3.16 thf(fact_5624_uminus__rat_Oabs__eq,axiom,
% 2.86/3.16 ! [X: product_prod_int_int] :
% 2.86/3.16 ( ( ratrel @ X @ X )
% 2.86/3.16 => ( ( uminus_uminus_rat @ ( abs_Rat @ X ) )
% 2.86/3.16 = ( abs_Rat @ ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X ) ) @ ( product_snd_int_int @ X ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % uminus_rat.abs_eq
% 2.86/3.16 thf(fact_5625_times__rat_Oabs__eq,axiom,
% 2.86/3.16 ! [Xa: product_prod_int_int,X: product_prod_int_int] :
% 2.86/3.16 ( ( ratrel @ Xa @ Xa )
% 2.86/3.16 => ( ( ratrel @ X @ X )
% 2.86/3.16 => ( ( times_times_rat @ ( abs_Rat @ Xa ) @ ( abs_Rat @ X ) )
% 2.86/3.16 = ( abs_Rat @ ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ Xa ) @ ( product_fst_int_int @ X ) ) @ ( times_times_int @ ( product_snd_int_int @ Xa ) @ ( product_snd_int_int @ X ) ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % times_rat.abs_eq
% 2.86/3.16 thf(fact_5626_inverse__rat__def,axiom,
% 2.86/3.16 ( inverse_inverse_rat
% 2.86/3.16 = ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat
% 2.86/3.16 @ ^ [X2: product_prod_int_int] :
% 2.86/3.16 ( if_Pro3027730157355071871nt_int
% 2.86/3.16 @ ( ( product_fst_int_int @ X2 )
% 2.86/3.16 = zero_zero_int )
% 2.86/3.16 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 2.86/3.16 @ ( product_Pair_int_int @ ( product_snd_int_int @ X2 ) @ ( product_fst_int_int @ X2 ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % inverse_rat_def
% 2.86/3.16 thf(fact_5627_uminus__rat__def,axiom,
% 2.86/3.16 ( uminus_uminus_rat
% 2.86/3.16 = ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat
% 2.86/3.16 @ ^ [X2: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X2 ) ) @ ( product_snd_int_int @ X2 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % uminus_rat_def
% 2.86/3.16 thf(fact_5628_plus__rat__def,axiom,
% 2.86/3.16 ( plus_plus_rat
% 2.86/3.16 = ( map_fu4333342158222067775at_rat @ rep_Rat @ ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat )
% 2.86/3.16 @ ^ [X2: product_prod_int_int,Y5: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ Y5 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y5 ) @ ( product_snd_int_int @ X2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X2 ) @ ( product_snd_int_int @ Y5 ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % plus_rat_def
% 2.86/3.16 thf(fact_5629_times__rat__def,axiom,
% 2.86/3.16 ( times_times_rat
% 2.86/3.16 = ( map_fu4333342158222067775at_rat @ rep_Rat @ ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat )
% 2.86/3.16 @ ^ [X2: product_prod_int_int,Y5: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_fst_int_int @ Y5 ) ) @ ( times_times_int @ ( product_snd_int_int @ X2 ) @ ( product_snd_int_int @ Y5 ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % times_rat_def
% 2.86/3.16 thf(fact_5630_Rep__assn__inverse,axiom,
% 2.86/3.16 ! [X: assn] :
% 2.86/3.16 ( ( abs_assn @ ( rep_assn @ X ) )
% 2.86/3.16 = X ) ).
% 2.86/3.16
% 2.86/3.16 % Rep_assn_inverse
% 2.86/3.16 thf(fact_5631_Abs__assn__eqI_I2_J,axiom,
% 2.86/3.16 ! [P: produc3658429121746597890et_nat > $o,Pr: assn] :
% 2.86/3.16 ( ! [H: produc3658429121746597890et_nat] :
% 2.86/3.16 ( ( P @ H )
% 2.86/3.16 = ( rep_assn @ Pr @ H ) )
% 2.86/3.16 => ( Pr
% 2.86/3.16 = ( abs_assn @ P ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % Abs_assn_eqI(2)
% 2.86/3.16 thf(fact_5632_Abs__assn__eqI_I1_J,axiom,
% 2.86/3.16 ! [P: produc3658429121746597890et_nat > $o,Pr: assn] :
% 2.86/3.16 ( ! [H: produc3658429121746597890et_nat] :
% 2.86/3.16 ( ( P @ H )
% 2.86/3.16 = ( rep_assn @ Pr @ H ) )
% 2.86/3.16 => ( ( abs_assn @ P )
% 2.86/3.16 = Pr ) ) ).
% 2.86/3.16
% 2.86/3.16 % Abs_assn_eqI(1)
% 2.86/3.16 thf(fact_5633_pure__assn__def,axiom,
% 2.86/3.16 ( pure_assn
% 2.86/3.16 = ( ^ [B3: $o] : ( abs_assn @ ( pure_a825153325127701367it_nat @ B3 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % pure_assn_def
% 2.86/3.16 thf(fact_5634_bot__assn__def,axiom,
% 2.86/3.16 ( bot_bot_assn
% 2.86/3.16 = ( abs_assn
% 2.86/3.16 @ ^ [Uu2: produc3658429121746597890et_nat] : $false ) ) ).
% 2.86/3.16
% 2.86/3.16 % bot_assn_def
% 2.86/3.16 thf(fact_5635_one__assn__def,axiom,
% 2.86/3.16 ( one_one_assn
% 2.86/3.16 = ( abs_assn @ one_assn_raw ) ) ).
% 2.86/3.16
% 2.86/3.16 % one_assn_def
% 2.86/3.16 thf(fact_5636_sup__assn__def,axiom,
% 2.86/3.16 ( sup_sup_assn
% 2.86/3.16 = ( ^ [P2: assn,Q2: assn] :
% 2.86/3.16 ( abs_assn
% 2.86/3.16 @ ^ [H3: produc3658429121746597890et_nat] :
% 2.86/3.16 ( ( rep_assn @ P2 @ H3 )
% 2.86/3.16 | ( rep_assn @ Q2 @ H3 ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % sup_assn_def
% 2.86/3.16 thf(fact_5637_inf__assn__def,axiom,
% 2.86/3.16 ( inf_inf_assn
% 2.86/3.16 = ( ^ [P2: assn,Q2: assn] :
% 2.86/3.16 ( abs_assn
% 2.86/3.16 @ ^ [H3: produc3658429121746597890et_nat] :
% 2.86/3.16 ( ( rep_assn @ P2 @ H3 )
% 2.86/3.16 & ( rep_assn @ Q2 @ H3 ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % inf_assn_def
% 2.86/3.16 thf(fact_5638_times__assn__def,axiom,
% 2.86/3.16 ( times_times_assn
% 2.86/3.16 = ( ^ [P2: assn,Q2: assn] : ( abs_assn @ ( times_assn_raw @ ( rep_assn @ P2 ) @ ( rep_assn @ Q2 ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % times_assn_def
% 2.86/3.16 thf(fact_5639_wand__assn__def,axiom,
% 2.86/3.16 ( wand_assn
% 2.86/3.16 = ( ^ [P2: assn,Q2: assn] : ( abs_assn @ ( wand_raw @ ( rep_assn @ P2 ) @ ( rep_assn @ Q2 ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % wand_assn_def
% 2.86/3.16 thf(fact_5640_uminus__assn__def,axiom,
% 2.86/3.16 ( uminus_uminus_assn
% 2.86/3.16 = ( ^ [P2: assn] :
% 2.86/3.16 ( abs_assn
% 2.86/3.16 @ ^ [H3: produc3658429121746597890et_nat] :
% 2.86/3.16 ( ( in_range @ H3 )
% 2.86/3.16 & ~ ( rep_assn @ P2 @ H3 ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % uminus_assn_def
% 2.86/3.16 thf(fact_5641_in__range__empty,axiom,
% 2.86/3.16 ! [H2: heap_e7401611519738050253t_unit] : ( in_range @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) ) ).
% 2.86/3.16
% 2.86/3.16 % in_range_empty
% 2.86/3.16 thf(fact_5642_mod__true,axiom,
% 2.86/3.16 ! [H2: produc3658429121746597890et_nat] :
% 2.86/3.16 ( ( rep_assn @ top_top_assn @ H2 )
% 2.86/3.16 = ( in_range @ H2 ) ) ).
% 2.86/3.16
% 2.86/3.16 % mod_true
% 2.86/3.16 thf(fact_5643_in__range__dist__union,axiom,
% 2.86/3.16 ! [H2: heap_e7401611519738050253t_unit,As2: set_nat,As3: set_nat] :
% 2.86/3.16 ( ( in_range @ ( produc7507926704131184380et_nat @ H2 @ ( sup_sup_set_nat @ As2 @ As3 ) ) )
% 2.86/3.16 = ( ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 2.86/3.16 & ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As3 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % in_range_dist_union
% 2.86/3.16 thf(fact_5644_mod__not__dist,axiom,
% 2.86/3.16 ! [P: assn,H2: produc3658429121746597890et_nat] :
% 2.86/3.16 ( ( rep_assn @ ( uminus_uminus_assn @ P ) @ H2 )
% 2.86/3.16 = ( ( in_range @ H2 )
% 2.86/3.16 & ~ ( rep_assn @ P @ H2 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % mod_not_dist
% 2.86/3.16 thf(fact_5645_in__range__subset,axiom,
% 2.86/3.16 ! [As2: set_nat,As3: set_nat,H2: heap_e7401611519738050253t_unit] :
% 2.86/3.16 ( ( ord_less_eq_set_nat @ As2 @ As3 )
% 2.86/3.16 => ( ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As3 ) )
% 2.86/3.16 => ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As2 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % in_range_subset
% 2.86/3.16 thf(fact_5646_models__in__range,axiom,
% 2.86/3.16 ! [P: assn,H2: produc3658429121746597890et_nat] :
% 2.86/3.16 ( ( rep_assn @ P @ H2 )
% 2.86/3.16 => ( in_range @ H2 ) ) ).
% 2.86/3.16
% 2.86/3.16 % models_in_range
% 2.86/3.16 thf(fact_5647_top__assn__def,axiom,
% 2.86/3.16 ( top_top_assn
% 2.86/3.16 = ( abs_assn @ in_range ) ) ).
% 2.86/3.16
% 2.86/3.16 % top_assn_def
% 2.86/3.16 thf(fact_5648_wand__assnI,axiom,
% 2.86/3.16 ! [H2: heap_e7401611519738050253t_unit,As2: set_nat,Q: assn,R: assn] :
% 2.86/3.16 ( ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 2.86/3.16 => ( ! [H5: heap_e7401611519738050253t_unit,As4: set_nat] :
% 2.86/3.16 ( ( ( inf_inf_set_nat @ As2 @ As4 )
% 2.86/3.16 = bot_bot_set_nat )
% 2.86/3.16 => ( ( relH @ As2 @ H2 @ H5 )
% 2.86/3.16 => ( ( in_range @ ( produc7507926704131184380et_nat @ H5 @ As2 ) )
% 2.86/3.16 => ( ( rep_assn @ Q @ ( produc7507926704131184380et_nat @ H5 @ As4 ) )
% 2.86/3.16 => ( rep_assn @ R @ ( produc7507926704131184380et_nat @ H5 @ ( sup_sup_set_nat @ As2 @ As4 ) ) ) ) ) ) )
% 2.86/3.16 => ( rep_assn @ ( wand_assn @ Q @ R ) @ ( produc7507926704131184380et_nat @ H2 @ As2 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % wand_assnI
% 2.86/3.16 thf(fact_5649_wand__raw_Oelims_I3_J,axiom,
% 2.86/3.16 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 2.86/3.16 ( ~ ( wand_raw @ X @ Xa @ Xb )
% 2.86/3.16 => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.86/3.16 ( ( Xb
% 2.86/3.16 = ( produc7507926704131184380et_nat @ H @ As ) )
% 2.86/3.16 => ( ( in_range @ ( produc7507926704131184380et_nat @ H @ As ) )
% 2.86/3.16 & ! [H5: heap_e7401611519738050253t_unit,As4: set_nat] :
% 2.86/3.16 ( ( ( ( inf_inf_set_nat @ As @ As4 )
% 2.86/3.16 = bot_bot_set_nat )
% 2.86/3.16 & ( relH @ As @ H @ H5 )
% 2.86/3.16 & ( in_range @ ( produc7507926704131184380et_nat @ H5 @ As ) )
% 2.86/3.16 & ( X @ ( produc7507926704131184380et_nat @ H5 @ As4 ) ) )
% 2.86/3.16 => ( Xa @ ( produc7507926704131184380et_nat @ H5 @ ( sup_sup_set_nat @ As @ As4 ) ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % wand_raw.elims(3)
% 2.86/3.16 thf(fact_5650_relH__dist__union,axiom,
% 2.86/3.16 ! [As2: set_nat,As3: set_nat,H2: heap_e7401611519738050253t_unit,H4: heap_e7401611519738050253t_unit] :
% 2.86/3.16 ( ( relH @ ( sup_sup_set_nat @ As2 @ As3 ) @ H2 @ H4 )
% 2.86/3.16 = ( ( relH @ As2 @ H2 @ H4 )
% 2.86/3.16 & ( relH @ As3 @ H2 @ H4 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % relH_dist_union
% 2.86/3.16 thf(fact_5651_relH__refl,axiom,
% 2.86/3.16 ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 2.86/3.16 ( ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 2.86/3.16 => ( relH @ As2 @ H2 @ H2 ) ) ).
% 2.86/3.16
% 2.86/3.16 % relH_refl
% 2.86/3.16 thf(fact_5652_relH__in__rangeI_I1_J,axiom,
% 2.86/3.16 ! [As2: set_nat,H2: heap_e7401611519738050253t_unit,H4: heap_e7401611519738050253t_unit] :
% 2.86/3.16 ( ( relH @ As2 @ H2 @ H4 )
% 2.86/3.16 => ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As2 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % relH_in_rangeI(1)
% 2.86/3.16 thf(fact_5653_relH__in__rangeI_I2_J,axiom,
% 2.86/3.16 ! [As2: set_nat,H2: heap_e7401611519738050253t_unit,H4: heap_e7401611519738050253t_unit] :
% 2.86/3.16 ( ( relH @ As2 @ H2 @ H4 )
% 2.86/3.16 => ( in_range @ ( produc7507926704131184380et_nat @ H4 @ As2 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % relH_in_rangeI(2)
% 2.86/3.16 thf(fact_5654_mod__relH,axiom,
% 2.86/3.16 ! [As2: set_nat,H2: heap_e7401611519738050253t_unit,H4: heap_e7401611519738050253t_unit,P: assn] :
% 2.86/3.16 ( ( relH @ As2 @ H2 @ H4 )
% 2.86/3.16 => ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 2.86/3.16 = ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H4 @ As2 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % mod_relH
% 2.86/3.16 thf(fact_5655_relH__trans,axiom,
% 2.86/3.16 ! [As2: set_nat,H12: heap_e7401611519738050253t_unit,H23: heap_e7401611519738050253t_unit,H32: heap_e7401611519738050253t_unit] :
% 2.86/3.16 ( ( relH @ As2 @ H12 @ H23 )
% 2.86/3.16 => ( ( relH @ As2 @ H23 @ H32 )
% 2.86/3.16 => ( relH @ As2 @ H12 @ H32 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % relH_trans
% 2.86/3.16 thf(fact_5656_relH__sym,axiom,
% 2.86/3.16 ! [As2: set_nat,H2: heap_e7401611519738050253t_unit,H4: heap_e7401611519738050253t_unit] :
% 2.86/3.16 ( ( relH @ As2 @ H2 @ H4 )
% 2.86/3.16 => ( relH @ As2 @ H4 @ H2 ) ) ).
% 2.86/3.16
% 2.86/3.16 % relH_sym
% 2.86/3.16 thf(fact_5657_relH__subset,axiom,
% 2.86/3.16 ! [Bs: set_nat,H2: heap_e7401611519738050253t_unit,H4: heap_e7401611519738050253t_unit,As2: set_nat] :
% 2.86/3.16 ( ( relH @ Bs @ H2 @ H4 )
% 2.86/3.16 => ( ( ord_less_eq_set_nat @ As2 @ Bs )
% 2.86/3.16 => ( relH @ As2 @ H2 @ H4 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % relH_subset
% 2.86/3.16 thf(fact_5658_wand__raw_Osimps,axiom,
% 2.86/3.16 ! [P: produc3658429121746597890et_nat > $o,Q: produc3658429121746597890et_nat > $o,H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 2.86/3.16 ( ( wand_raw @ P @ Q @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 2.86/3.16 = ( ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 2.86/3.16 & ! [H6: heap_e7401611519738050253t_unit,As5: set_nat] :
% 2.86/3.16 ( ( ( ( inf_inf_set_nat @ As2 @ As5 )
% 2.86/3.16 = bot_bot_set_nat )
% 2.86/3.16 & ( relH @ As2 @ H2 @ H6 )
% 2.86/3.16 & ( in_range @ ( produc7507926704131184380et_nat @ H6 @ As2 ) )
% 2.86/3.16 & ( P @ ( produc7507926704131184380et_nat @ H6 @ As5 ) ) )
% 2.86/3.16 => ( Q @ ( produc7507926704131184380et_nat @ H6 @ ( sup_sup_set_nat @ As2 @ As5 ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % wand_raw.simps
% 2.86/3.16 thf(fact_5659_wand__raw_Oelims_I1_J,axiom,
% 2.86/3.16 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Y: $o] :
% 2.86/3.16 ( ( ( wand_raw @ X @ Xa @ Xb )
% 2.86/3.16 = Y )
% 2.86/3.16 => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.86/3.16 ( ( Xb
% 2.86/3.16 = ( produc7507926704131184380et_nat @ H @ As ) )
% 2.86/3.16 => ( Y
% 2.86/3.16 = ( ~ ( ( in_range @ ( produc7507926704131184380et_nat @ H @ As ) )
% 2.86/3.16 & ! [H6: heap_e7401611519738050253t_unit,As5: set_nat] :
% 2.86/3.16 ( ( ( ( inf_inf_set_nat @ As @ As5 )
% 2.86/3.16 = bot_bot_set_nat )
% 2.86/3.16 & ( relH @ As @ H @ H6 )
% 2.86/3.16 & ( in_range @ ( produc7507926704131184380et_nat @ H6 @ As ) )
% 2.86/3.16 & ( X @ ( produc7507926704131184380et_nat @ H6 @ As5 ) ) )
% 2.86/3.16 => ( Xa @ ( produc7507926704131184380et_nat @ H6 @ ( sup_sup_set_nat @ As @ As5 ) ) ) ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % wand_raw.elims(1)
% 2.86/3.16 thf(fact_5660_wand__raw_Oelims_I2_J,axiom,
% 2.86/3.16 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 2.86/3.16 ( ( wand_raw @ X @ Xa @ Xb )
% 2.86/3.16 => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.86/3.16 ( ( Xb
% 2.86/3.16 = ( produc7507926704131184380et_nat @ H @ As ) )
% 2.86/3.16 => ~ ( ( in_range @ ( produc7507926704131184380et_nat @ H @ As ) )
% 2.86/3.16 & ! [H7: heap_e7401611519738050253t_unit,As6: set_nat] :
% 2.86/3.16 ( ( ( ( inf_inf_set_nat @ As @ As6 )
% 2.86/3.16 = bot_bot_set_nat )
% 2.86/3.16 & ( relH @ As @ H @ H7 )
% 2.86/3.16 & ( in_range @ ( produc7507926704131184380et_nat @ H7 @ As ) )
% 2.86/3.16 & ( X @ ( produc7507926704131184380et_nat @ H7 @ As6 ) ) )
% 2.86/3.16 => ( Xa @ ( produc7507926704131184380et_nat @ H7 @ ( sup_sup_set_nat @ As @ As6 ) ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % wand_raw.elims(2)
% 2.86/3.16 thf(fact_5661_wand__raw_Opelims_I3_J,axiom,
% 2.86/3.16 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 2.86/3.16 ( ~ ( wand_raw @ X @ Xa @ Xb )
% 2.86/3.16 => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 2.86/3.16 => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.86/3.16 ( ( Xb
% 2.86/3.16 = ( produc7507926704131184380et_nat @ H @ As ) )
% 2.86/3.16 => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H @ As ) ) ) )
% 2.86/3.16 => ( ( in_range @ ( produc7507926704131184380et_nat @ H @ As ) )
% 2.86/3.16 & ! [H5: heap_e7401611519738050253t_unit,As4: set_nat] :
% 2.86/3.16 ( ( ( ( inf_inf_set_nat @ As @ As4 )
% 2.86/3.16 = bot_bot_set_nat )
% 2.86/3.16 & ( relH @ As @ H @ H5 )
% 2.86/3.16 & ( in_range @ ( produc7507926704131184380et_nat @ H5 @ As ) )
% 2.86/3.16 & ( X @ ( produc7507926704131184380et_nat @ H5 @ As4 ) ) )
% 2.86/3.16 => ( Xa @ ( produc7507926704131184380et_nat @ H5 @ ( sup_sup_set_nat @ As @ As4 ) ) ) ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % wand_raw.pelims(3)
% 2.86/3.16 thf(fact_5662_wand__raw_Opelims_I2_J,axiom,
% 2.86/3.16 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 2.86/3.16 ( ( wand_raw @ X @ Xa @ Xb )
% 2.86/3.16 => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 2.86/3.16 => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.86/3.16 ( ( Xb
% 2.86/3.16 = ( produc7507926704131184380et_nat @ H @ As ) )
% 2.86/3.16 => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H @ As ) ) ) )
% 2.86/3.16 => ~ ( ( in_range @ ( produc7507926704131184380et_nat @ H @ As ) )
% 2.86/3.16 & ! [H7: heap_e7401611519738050253t_unit,As6: set_nat] :
% 2.86/3.16 ( ( ( ( inf_inf_set_nat @ As @ As6 )
% 2.86/3.16 = bot_bot_set_nat )
% 2.86/3.16 & ( relH @ As @ H @ H7 )
% 2.86/3.16 & ( in_range @ ( produc7507926704131184380et_nat @ H7 @ As ) )
% 2.86/3.16 & ( X @ ( produc7507926704131184380et_nat @ H7 @ As6 ) ) )
% 2.86/3.16 => ( Xa @ ( produc7507926704131184380et_nat @ H7 @ ( sup_sup_set_nat @ As @ As6 ) ) ) ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % wand_raw.pelims(2)
% 2.86/3.16 thf(fact_5663_wand__raw_Opelims_I1_J,axiom,
% 2.86/3.16 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Y: $o] :
% 2.86/3.16 ( ( ( wand_raw @ X @ Xa @ Xb )
% 2.86/3.16 = Y )
% 2.86/3.16 => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 2.86/3.16 => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.86/3.16 ( ( Xb
% 2.86/3.16 = ( produc7507926704131184380et_nat @ H @ As ) )
% 2.86/3.16 => ( ( Y
% 2.86/3.16 = ( ( in_range @ ( produc7507926704131184380et_nat @ H @ As ) )
% 2.86/3.16 & ! [H6: heap_e7401611519738050253t_unit,As5: set_nat] :
% 2.86/3.16 ( ( ( ( inf_inf_set_nat @ As @ As5 )
% 2.86/3.16 = bot_bot_set_nat )
% 2.86/3.16 & ( relH @ As @ H @ H6 )
% 2.86/3.16 & ( in_range @ ( produc7507926704131184380et_nat @ H6 @ As ) )
% 2.86/3.16 & ( X @ ( produc7507926704131184380et_nat @ H6 @ As5 ) ) )
% 2.86/3.16 => ( Xa @ ( produc7507926704131184380et_nat @ H6 @ ( sup_sup_set_nat @ As @ As5 ) ) ) ) ) )
% 2.86/3.16 => ~ ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H @ As ) ) ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % wand_raw.pelims(1)
% 2.86/3.16 thf(fact_5664_normalize__stable,axiom,
% 2.86/3.16 ! [Q6: int,P6: int] :
% 2.86/3.16 ( ( ord_less_int @ zero_zero_int @ Q6 )
% 2.86/3.16 => ( ( algebr932160517623751201me_int @ P6 @ Q6 )
% 2.86/3.16 => ( ( normalize @ ( product_Pair_int_int @ P6 @ Q6 ) )
% 2.86/3.16 = ( product_Pair_int_int @ P6 @ Q6 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % normalize_stable
% 2.86/3.16 thf(fact_5665_normalize__coprime,axiom,
% 2.86/3.16 ! [R2: product_prod_int_int,P6: int,Q6: int] :
% 2.86/3.16 ( ( ( normalize @ R2 )
% 2.86/3.16 = ( product_Pair_int_int @ P6 @ Q6 ) )
% 2.86/3.16 => ( algebr932160517623751201me_int @ P6 @ Q6 ) ) ).
% 2.86/3.16
% 2.86/3.16 % normalize_coprime
% 2.86/3.16 thf(fact_5666_quotient__of__coprime,axiom,
% 2.86/3.16 ! [R2: rat,P6: int,Q6: int] :
% 2.86/3.16 ( ( ( quotient_of @ R2 )
% 2.86/3.16 = ( product_Pair_int_int @ P6 @ Q6 ) )
% 2.86/3.16 => ( algebr932160517623751201me_int @ P6 @ Q6 ) ) ).
% 2.86/3.16
% 2.86/3.16 % quotient_of_coprime
% 2.86/3.16 thf(fact_5667_coprime__diff__one__right__nat,axiom,
% 2.86/3.16 ! [N: nat] :
% 2.86/3.16 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.16 => ( algebr934650988132801477me_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % coprime_diff_one_right_nat
% 2.86/3.16 thf(fact_5668_coprime__diff__one__left__nat,axiom,
% 2.86/3.16 ! [N: nat] :
% 2.86/3.16 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.16 => ( algebr934650988132801477me_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ N ) ) ).
% 2.86/3.16
% 2.86/3.16 % coprime_diff_one_left_nat
% 2.86/3.16 thf(fact_5669_Fract_Otransfer,axiom,
% 2.86/3.16 ( bNF_re3461391660133120880nt_rat
% 2.86/3.16 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 2.86/3.16 @ ( bNF_re2214769303045360666nt_rat
% 2.86/3.16 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 2.86/3.16 @ pcr_rat )
% 2.86/3.16 @ ^ [A3: int,B3: int] : ( if_Pro3027730157355071871nt_int @ ( B3 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A3 @ B3 ) )
% 2.86/3.16 @ fract ) ).
% 2.86/3.16
% 2.86/3.16 % Fract.transfer
% 2.86/3.16 thf(fact_5670_quotient__of__eq,axiom,
% 2.86/3.16 ! [A2: int,B2: int,P6: int,Q6: int] :
% 2.86/3.16 ( ( ( quotient_of @ ( fract @ A2 @ B2 ) )
% 2.86/3.16 = ( product_Pair_int_int @ P6 @ Q6 ) )
% 2.86/3.16 => ( ( fract @ P6 @ Q6 )
% 2.86/3.16 = ( fract @ A2 @ B2 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % quotient_of_eq
% 2.86/3.16 thf(fact_5671_normalize__eq,axiom,
% 2.86/3.16 ! [A2: int,B2: int,P6: int,Q6: int] :
% 2.86/3.16 ( ( ( normalize @ ( product_Pair_int_int @ A2 @ B2 ) )
% 2.86/3.16 = ( product_Pair_int_int @ P6 @ Q6 ) )
% 2.86/3.16 => ( ( fract @ P6 @ Q6 )
% 2.86/3.16 = ( fract @ A2 @ B2 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % normalize_eq
% 2.86/3.16 thf(fact_5672_quotient__of__Fract,axiom,
% 2.86/3.16 ! [A2: int,B2: int] :
% 2.86/3.16 ( ( quotient_of @ ( fract @ A2 @ B2 ) )
% 2.86/3.16 = ( normalize @ ( product_Pair_int_int @ A2 @ B2 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % quotient_of_Fract
% 2.86/3.16 thf(fact_5673_Fract_Oabs__eq,axiom,
% 2.86/3.16 ( fract
% 2.86/3.16 = ( ^ [Xa4: int,X2: int] : ( abs_Rat @ ( if_Pro3027730157355071871nt_int @ ( X2 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ Xa4 @ X2 ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % Fract.abs_eq
% 2.86/3.16 thf(fact_5674_exhaustive__integer_H_Ocases,axiom,
% 2.86/3.16 ! [X: produc8763457246119570046nteger] :
% 2.86/3.16 ~ ! [F5: code_integer > option6357759511663192854e_term,D3: code_integer,I5: code_integer] :
% 2.86/3.16 ( X
% 2.86/3.16 != ( produc6137756002093451184nteger @ F5 @ ( produc1086072967326762835nteger @ D3 @ I5 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % exhaustive_integer'.cases
% 2.86/3.16 thf(fact_5675_exhaustive__int_H_Ocases,axiom,
% 2.86/3.16 ! [X: produc7773217078559923341nt_int] :
% 2.86/3.16 ~ ! [F5: int > option6357759511663192854e_term,D3: int,I5: int] :
% 2.86/3.16 ( X
% 2.86/3.16 != ( produc4305682042979456191nt_int @ F5 @ ( product_Pair_int_int @ D3 @ I5 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % exhaustive_int'.cases
% 2.86/3.16 thf(fact_5676_full__exhaustive__int_H_Ocases,axiom,
% 2.86/3.16 ! [X: produc2285326912895808259nt_int] :
% 2.86/3.16 ~ ! [F5: produc8551481072490612790e_term > option6357759511663192854e_term,D3: int,I5: int] :
% 2.86/3.16 ( X
% 2.86/3.16 != ( produc5700946648718959541nt_int @ F5 @ ( product_Pair_int_int @ D3 @ I5 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % full_exhaustive_int'.cases
% 2.86/3.16 thf(fact_5677_full__exhaustive__integer_H_Ocases,axiom,
% 2.86/3.16 ! [X: produc1908205239877642774nteger] :
% 2.86/3.16 ~ ! [F5: produc6241069584506657477e_term > option6357759511663192854e_term,D3: code_integer,I5: code_integer] :
% 2.86/3.16 ( X
% 2.86/3.16 != ( produc8603105652947943368nteger @ F5 @ ( produc1086072967326762835nteger @ D3 @ I5 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % full_exhaustive_integer'.cases
% 2.86/3.16 thf(fact_5678_list__encode_Oelims,axiom,
% 2.86/3.16 ! [X: list_nat,Y: nat] :
% 2.86/3.16 ( ( ( nat_list_encode @ X )
% 2.86/3.16 = Y )
% 2.86/3.16 => ( ( ( X = nil_nat )
% 2.86/3.16 => ( Y != zero_zero_nat ) )
% 2.86/3.16 => ~ ! [X3: nat,Xs2: list_nat] :
% 2.86/3.16 ( ( X
% 2.86/3.16 = ( cons_nat @ X3 @ Xs2 ) )
% 2.86/3.16 => ( Y
% 2.86/3.16 != ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X3 @ ( nat_list_encode @ Xs2 ) ) ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % list_encode.elims
% 2.86/3.16 thf(fact_5679_list__encode_Osimps_I2_J,axiom,
% 2.86/3.16 ! [X: nat,Xs: list_nat] :
% 2.86/3.16 ( ( nat_list_encode @ ( cons_nat @ X @ Xs ) )
% 2.86/3.16 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X @ ( nat_list_encode @ Xs ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % list_encode.simps(2)
% 2.86/3.16 thf(fact_5680_le__prod__encode__1,axiom,
% 2.86/3.16 ! [A2: nat,B2: nat] : ( ord_less_eq_nat @ A2 @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % le_prod_encode_1
% 2.86/3.16 thf(fact_5681_le__prod__encode__2,axiom,
% 2.86/3.16 ! [B2: nat,A2: nat] : ( ord_less_eq_nat @ B2 @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A2 @ B2 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % le_prod_encode_2
% 2.86/3.16 thf(fact_5682_list__encode_Opelims,axiom,
% 2.86/3.16 ! [X: list_nat,Y: nat] :
% 2.86/3.16 ( ( ( nat_list_encode @ X )
% 2.86/3.16 = Y )
% 2.86/3.16 => ( ( accp_list_nat @ nat_list_encode_rel @ X )
% 2.86/3.16 => ( ( ( X = nil_nat )
% 2.86/3.16 => ( ( Y = zero_zero_nat )
% 2.86/3.16 => ~ ( accp_list_nat @ nat_list_encode_rel @ nil_nat ) ) )
% 2.86/3.16 => ~ ! [X3: nat,Xs2: list_nat] :
% 2.86/3.16 ( ( X
% 2.86/3.16 = ( cons_nat @ X3 @ Xs2 ) )
% 2.86/3.16 => ( ( Y
% 2.86/3.16 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X3 @ ( nat_list_encode @ Xs2 ) ) ) ) )
% 2.86/3.16 => ~ ( accp_list_nat @ nat_list_encode_rel @ ( cons_nat @ X3 @ Xs2 ) ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % list_encode.pelims
% 2.86/3.16 thf(fact_5683_INFM__nat,axiom,
% 2.86/3.16 ! [P: nat > $o] :
% 2.86/3.16 ( ( frequently_nat @ P @ cofinite_nat )
% 2.86/3.16 = ( ! [M: nat] :
% 2.86/3.16 ? [N2: nat] :
% 2.86/3.16 ( ( ord_less_nat @ M @ N2 )
% 2.86/3.16 & ( P @ N2 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % INFM_nat
% 2.86/3.16 thf(fact_5684_INFM__nat__inductI,axiom,
% 2.86/3.16 ! [P: nat > $o,Q: nat > $o] :
% 2.86/3.16 ( ( P @ zero_zero_nat )
% 2.86/3.16 => ( ! [I5: nat] :
% 2.86/3.16 ( ( P @ I5 )
% 2.86/3.16 => ? [J4: nat] :
% 2.86/3.16 ( ( ord_less_nat @ I5 @ J4 )
% 2.86/3.16 & ( P @ J4 )
% 2.86/3.16 & ( Q @ J4 ) ) )
% 2.86/3.16 => ( frequently_nat @ Q @ cofinite_nat ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % INFM_nat_inductI
% 2.86/3.16 thf(fact_5685_MOST__nat,axiom,
% 2.86/3.16 ! [P: nat > $o] :
% 2.86/3.16 ( ( eventually_nat @ P @ cofinite_nat )
% 2.86/3.16 = ( ? [M: nat] :
% 2.86/3.16 ! [N2: nat] :
% 2.86/3.16 ( ( ord_less_nat @ M @ N2 )
% 2.86/3.16 => ( P @ N2 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % MOST_nat
% 2.86/3.16 thf(fact_5686_cofinite__eq__sequentially,axiom,
% 2.86/3.16 cofinite_nat = at_top_nat ).
% 2.86/3.16
% 2.86/3.16 % cofinite_eq_sequentially
% 2.86/3.16 thf(fact_5687_list__ex__iff__not__all__inverval__int,axiom,
% 2.86/3.16 ! [P: int > $o,I: int,J: int] :
% 2.86/3.16 ( ( list_ex_int @ P @ ( upto @ I @ J ) )
% 2.86/3.16 = ( ~ ( all_interval_int @ ( comp_o_o_int @ (~) @ P ) @ I @ J ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % list_ex_iff_not_all_inverval_int
% 2.86/3.16 thf(fact_5688_all__interval__int__def,axiom,
% 2.86/3.16 ( all_interval_int
% 2.86/3.16 = ( ^ [P2: int > $o,I4: int,J2: int] :
% 2.86/3.16 ! [X2: int] :
% 2.86/3.16 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ I4 @ J2 ) )
% 2.86/3.16 => ( P2 @ X2 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % all_interval_int_def
% 2.86/3.16 thf(fact_5689_list__all__iff__all__interval__int,axiom,
% 2.86/3.16 ! [P: int > $o,I: int,J: int] :
% 2.86/3.16 ( ( list_all_int @ P @ ( upto @ I @ J ) )
% 2.86/3.16 = ( all_interval_int @ P @ I @ J ) ) ).
% 2.86/3.16
% 2.86/3.16 % list_all_iff_all_interval_int
% 2.86/3.16 thf(fact_5690_is__pure__assn__pure,axiom,
% 2.86/3.16 ! [P: $o] : ( is_pure_assn @ ( pure_assn @ P ) ) ).
% 2.86/3.16
% 2.86/3.16 % is_pure_assn_pure
% 2.86/3.16 thf(fact_5691_is__pure__assn__starI,axiom,
% 2.86/3.16 ! [A2: assn,B2: assn] :
% 2.86/3.16 ( ( is_pure_assn @ A2 )
% 2.86/3.16 => ( ( is_pure_assn @ B2 )
% 2.86/3.16 => ( is_pure_assn @ ( times_times_assn @ A2 @ B2 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % is_pure_assn_starI
% 2.86/3.16 thf(fact_5692_Lcm__nat__empty,axiom,
% 2.86/3.16 ( ( gcd_Lcm_nat @ bot_bot_set_nat )
% 2.86/3.16 = one_one_nat ) ).
% 2.86/3.16
% 2.86/3.16 % Lcm_nat_empty
% 2.86/3.16 thf(fact_5693_is__pure__assn__basic__simps_I2_J,axiom,
% 2.86/3.16 is_pure_assn @ one_one_assn ).
% 2.86/3.16
% 2.86/3.16 % is_pure_assn_basic_simps(2)
% 2.86/3.16 thf(fact_5694_is__pure__assn__def,axiom,
% 2.86/3.16 ( is_pure_assn
% 2.86/3.16 = ( ^ [A3: assn] :
% 2.86/3.16 ? [P2: $o] :
% 2.86/3.16 ( A3
% 2.86/3.16 = ( pure_assn @ P2 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % is_pure_assn_def
% 2.86/3.16 thf(fact_5695_is__pure__assnE,axiom,
% 2.86/3.16 ! [A2: assn] :
% 2.86/3.16 ( ( is_pure_assn @ A2 )
% 2.86/3.16 => ~ ! [P5: $o] :
% 2.86/3.16 ( A2
% 2.86/3.16 != ( pure_assn @ P5 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % is_pure_assnE
% 2.86/3.16 thf(fact_5696_is__pure__assn__basic__simps_I1_J,axiom,
% 2.86/3.16 is_pure_assn @ bot_bot_assn ).
% 2.86/3.16
% 2.86/3.16 % is_pure_assn_basic_simps(1)
% 2.86/3.16 thf(fact_5697_Lcm__eq__Max__nat,axiom,
% 2.86/3.16 ! [M5: set_nat] :
% 2.86/3.16 ( ( finite_finite_nat @ M5 )
% 2.86/3.16 => ( ( M5 != bot_bot_set_nat )
% 2.86/3.16 => ( ~ ( member_nat @ zero_zero_nat @ M5 )
% 2.86/3.16 => ( ! [M6: nat,N5: nat] :
% 2.86/3.16 ( ( member_nat @ M6 @ M5 )
% 2.86/3.16 => ( ( member_nat @ N5 @ M5 )
% 2.86/3.16 => ( member_nat @ ( gcd_lcm_nat @ M6 @ N5 ) @ M5 ) ) )
% 2.86/3.16 => ( ( gcd_Lcm_nat @ M5 )
% 2.86/3.16 = ( lattic8265883725875713057ax_nat @ M5 ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % Lcm_eq_Max_nat
% 2.86/3.16 thf(fact_5698_Lcm__nat__insert,axiom,
% 2.86/3.16 ! [N: nat,M5: set_nat] :
% 2.86/3.16 ( ( gcd_Lcm_nat @ ( insert_nat2 @ N @ M5 ) )
% 2.86/3.16 = ( gcd_lcm_nat @ N @ ( gcd_Lcm_nat @ M5 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % Lcm_nat_insert
% 2.86/3.16 thf(fact_5699_Lcm__in__lcm__closed__set__nat,axiom,
% 2.86/3.16 ! [M5: set_nat] :
% 2.86/3.16 ( ( finite_finite_nat @ M5 )
% 2.86/3.16 => ( ( M5 != bot_bot_set_nat )
% 2.86/3.16 => ( ! [M6: nat,N5: nat] :
% 2.86/3.16 ( ( member_nat @ M6 @ M5 )
% 2.86/3.16 => ( ( member_nat @ N5 @ M5 )
% 2.86/3.16 => ( member_nat @ ( gcd_lcm_nat @ M6 @ N5 ) @ M5 ) ) )
% 2.86/3.16 => ( member_nat @ ( gcd_Lcm_nat @ M5 ) @ M5 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % Lcm_in_lcm_closed_set_nat
% 2.86/3.16 thf(fact_5700_lcm__pos__nat,axiom,
% 2.86/3.16 ! [M2: nat,N: nat] :
% 2.86/3.16 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 2.86/3.16 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.16 => ( ord_less_nat @ zero_zero_nat @ ( gcd_lcm_nat @ M2 @ N ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % lcm_pos_nat
% 2.86/3.16 thf(fact_5701_Lcm__nat__set__eq__fold,axiom,
% 2.86/3.16 ! [Xs: list_nat] :
% 2.86/3.16 ( ( gcd_Lcm_nat @ ( set_nat2 @ Xs ) )
% 2.86/3.16 = ( fold_nat_nat @ gcd_lcm_nat @ Xs @ one_one_nat ) ) ).
% 2.86/3.16
% 2.86/3.16 % Lcm_nat_set_eq_fold
% 2.86/3.16 thf(fact_5702_Lcm__int__set__eq__fold,axiom,
% 2.86/3.16 ! [Xs: list_int] :
% 2.86/3.16 ( ( gcd_Lcm_int @ ( set_int2 @ Xs ) )
% 2.86/3.16 = ( fold_int_int @ gcd_lcm_int @ Xs @ one_one_int ) ) ).
% 2.86/3.16
% 2.86/3.16 % Lcm_int_set_eq_fold
% 2.86/3.16 thf(fact_5703_properI,axiom,
% 2.86/3.16 ! [P: produc3658429121746597890et_nat > $o] :
% 2.86/3.16 ( ! [As: set_nat,H: heap_e7401611519738050253t_unit] :
% 2.86/3.16 ( ( P @ ( produc7507926704131184380et_nat @ H @ As ) )
% 2.86/3.16 => ( in_range @ ( produc7507926704131184380et_nat @ H @ As ) ) )
% 2.86/3.16 => ( ! [As: set_nat,H: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit] :
% 2.86/3.16 ( ( P @ ( produc7507926704131184380et_nat @ H @ As ) )
% 2.86/3.16 => ( ( relH @ As @ H @ H5 )
% 2.86/3.16 => ( ( in_range @ ( produc7507926704131184380et_nat @ H5 @ As ) )
% 2.86/3.16 => ( P @ ( produc7507926704131184380et_nat @ H5 @ As ) ) ) ) )
% 2.86/3.16 => ( proper @ P ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % properI
% 2.86/3.16 thf(fact_5704_properD2,axiom,
% 2.86/3.16 ! [P: produc3658429121746597890et_nat > $o,H2: heap_e7401611519738050253t_unit,As2: set_nat,H4: heap_e7401611519738050253t_unit] :
% 2.86/3.16 ( ( proper @ P )
% 2.86/3.16 => ( ( P @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 2.86/3.16 => ( ( relH @ As2 @ H2 @ H4 )
% 2.86/3.16 => ( ( in_range @ ( produc7507926704131184380et_nat @ H4 @ As2 ) )
% 2.86/3.16 => ( P @ ( produc7507926704131184380et_nat @ H4 @ As2 ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % properD2
% 2.86/3.16 thf(fact_5705_bool__assn__proper_I4_J,axiom,
% 2.86/3.16 ! [P: produc3658429121746597890et_nat > $o,Q: produc3658429121746597890et_nat > $o] :
% 2.86/3.16 ( ( proper @ P )
% 2.86/3.16 => ( ( proper @ Q )
% 2.86/3.16 => ( proper
% 2.86/3.16 @ ^ [H3: produc3658429121746597890et_nat] :
% 2.86/3.16 ( ( P @ H3 )
% 2.86/3.16 & ( Q @ H3 ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % bool_assn_proper(4)
% 2.86/3.16 thf(fact_5706_bool__assn__proper_I3_J,axiom,
% 2.86/3.16 ! [P: produc3658429121746597890et_nat > $o,Q: produc3658429121746597890et_nat > $o] :
% 2.86/3.16 ( ( proper @ P )
% 2.86/3.16 => ( ( proper @ Q )
% 2.86/3.16 => ( proper
% 2.86/3.16 @ ^ [H3: produc3658429121746597890et_nat] :
% 2.86/3.16 ( ( P @ H3 )
% 2.86/3.16 | ( Q @ H3 ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % bool_assn_proper(3)
% 2.86/3.16 thf(fact_5707_bool__assn__proper_I2_J,axiom,
% 2.86/3.16 ( proper
% 2.86/3.16 @ ^ [Uu2: produc3658429121746597890et_nat] : $false ) ).
% 2.86/3.16
% 2.86/3.16 % bool_assn_proper(2)
% 2.86/3.16 thf(fact_5708_bool__assn__proper_I1_J,axiom,
% 2.86/3.16 proper @ in_range ).
% 2.86/3.16
% 2.86/3.16 % bool_assn_proper(1)
% 2.86/3.16 thf(fact_5709_one__assn__proper,axiom,
% 2.86/3.16 proper @ one_assn_raw ).
% 2.86/3.16
% 2.86/3.16 % one_assn_proper
% 2.86/3.16 thf(fact_5710_times__assn__proper,axiom,
% 2.86/3.16 ! [P: produc3658429121746597890et_nat > $o,Q: produc3658429121746597890et_nat > $o] :
% 2.86/3.16 ( ( proper @ P )
% 2.86/3.16 => ( ( proper @ Q )
% 2.86/3.16 => ( proper @ ( times_assn_raw @ P @ Q ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % times_assn_proper
% 2.86/3.16 thf(fact_5711_wand__proper,axiom,
% 2.86/3.16 ! [P: produc3658429121746597890et_nat > $o,Q: produc3658429121746597890et_nat > $o] : ( proper @ ( wand_raw @ P @ Q ) ) ).
% 2.86/3.16
% 2.86/3.16 % wand_proper
% 2.86/3.16 thf(fact_5712_bool__assn__proper_I5_J,axiom,
% 2.86/3.16 ! [P: produc3658429121746597890et_nat > $o] :
% 2.86/3.16 ( ( proper @ P )
% 2.86/3.16 => ( proper
% 2.86/3.16 @ ^ [H3: produc3658429121746597890et_nat] :
% 2.86/3.16 ( ( in_range @ H3 )
% 2.86/3.16 & ~ ( P @ H3 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % bool_assn_proper(5)
% 2.86/3.16 thf(fact_5713_pure__assn__proper,axiom,
% 2.86/3.16 ! [B2: $o] : ( proper @ ( pure_a825153325127701367it_nat @ B2 ) ) ).
% 2.86/3.16
% 2.86/3.16 % pure_assn_proper
% 2.86/3.16 thf(fact_5714_Abs__assn__inverse,axiom,
% 2.86/3.16 ! [Y: produc3658429121746597890et_nat > $o] :
% 2.86/3.16 ( ( member6576561426505652726_nat_o @ Y @ ( collec939566748876313656_nat_o @ proper ) )
% 2.86/3.16 => ( ( rep_assn @ ( abs_assn @ Y ) )
% 2.86/3.16 = Y ) ) ).
% 2.86/3.16
% 2.86/3.16 % Abs_assn_inverse
% 2.86/3.16 thf(fact_5715_Abs__assn__cases,axiom,
% 2.86/3.16 ! [X: assn] :
% 2.86/3.16 ~ ! [Y2: produc3658429121746597890et_nat > $o] :
% 2.86/3.16 ( ( X
% 2.86/3.16 = ( abs_assn @ Y2 ) )
% 2.86/3.16 => ~ ( member6576561426505652726_nat_o @ Y2 @ ( collec939566748876313656_nat_o @ proper ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % Abs_assn_cases
% 2.86/3.16 thf(fact_5716_Abs__assn__induct,axiom,
% 2.86/3.16 ! [P: assn > $o,X: assn] :
% 2.86/3.16 ( ! [Y2: produc3658429121746597890et_nat > $o] :
% 2.86/3.16 ( ( member6576561426505652726_nat_o @ Y2 @ ( collec939566748876313656_nat_o @ proper ) )
% 2.86/3.16 => ( P @ ( abs_assn @ Y2 ) ) )
% 2.86/3.16 => ( P @ X ) ) ).
% 2.86/3.16
% 2.86/3.16 % Abs_assn_induct
% 2.86/3.16 thf(fact_5717_Abs__assn__inject,axiom,
% 2.86/3.16 ! [X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat > $o] :
% 2.86/3.16 ( ( member6576561426505652726_nat_o @ X @ ( collec939566748876313656_nat_o @ proper ) )
% 2.86/3.16 => ( ( member6576561426505652726_nat_o @ Y @ ( collec939566748876313656_nat_o @ proper ) )
% 2.86/3.16 => ( ( ( abs_assn @ X )
% 2.86/3.16 = ( abs_assn @ Y ) )
% 2.86/3.16 = ( X = Y ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % Abs_assn_inject
% 2.86/3.16 thf(fact_5718_Rep__assn__induct,axiom,
% 2.86/3.16 ! [Y: produc3658429121746597890et_nat > $o,P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 2.86/3.16 ( ( member6576561426505652726_nat_o @ Y @ ( collec939566748876313656_nat_o @ proper ) )
% 2.86/3.16 => ( ! [X3: assn] : ( P @ ( rep_assn @ X3 ) )
% 2.86/3.16 => ( P @ Y ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % Rep_assn_induct
% 2.86/3.16 thf(fact_5719_Rep__assn__cases,axiom,
% 2.86/3.16 ! [Y: produc3658429121746597890et_nat > $o] :
% 2.86/3.16 ( ( member6576561426505652726_nat_o @ Y @ ( collec939566748876313656_nat_o @ proper ) )
% 2.86/3.16 => ~ ! [X3: assn] :
% 2.86/3.16 ( Y
% 2.86/3.16 != ( rep_assn @ X3 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % Rep_assn_cases
% 2.86/3.16 thf(fact_5720_Rep__assn,axiom,
% 2.86/3.16 ! [X: assn] : ( member6576561426505652726_nat_o @ ( rep_assn @ X ) @ ( collec939566748876313656_nat_o @ proper ) ) ).
% 2.86/3.16
% 2.86/3.16 % Rep_assn
% 2.86/3.16 thf(fact_5721_properD1,axiom,
% 2.86/3.16 ! [P: produc3658429121746597890et_nat > $o,H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 2.86/3.16 ( ( proper @ P )
% 2.86/3.16 => ( ( P @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 2.86/3.16 => ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As2 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % properD1
% 2.86/3.16 thf(fact_5722_proper__iff,axiom,
% 2.86/3.16 ! [P: produc3658429121746597890et_nat > $o,As2: set_nat,H2: heap_e7401611519738050253t_unit,H4: heap_e7401611519738050253t_unit] :
% 2.86/3.16 ( ( proper @ P )
% 2.86/3.16 => ( ( relH @ As2 @ H2 @ H4 )
% 2.86/3.16 => ( ( in_range @ ( produc7507926704131184380et_nat @ H4 @ As2 ) )
% 2.86/3.16 => ( ( P @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 2.86/3.16 = ( P @ ( produc7507926704131184380et_nat @ H4 @ As2 ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % proper_iff
% 2.86/3.16 thf(fact_5723_proper__def,axiom,
% 2.86/3.16 ( proper
% 2.86/3.16 = ( ^ [P2: produc3658429121746597890et_nat > $o] :
% 2.86/3.16 ! [H3: heap_e7401611519738050253t_unit,H6: heap_e7401611519738050253t_unit,As7: set_nat] :
% 2.86/3.16 ( ( ( P2 @ ( produc7507926704131184380et_nat @ H3 @ As7 ) )
% 2.86/3.16 => ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As7 ) ) )
% 2.86/3.16 & ( ( ( P2 @ ( produc7507926704131184380et_nat @ H3 @ As7 ) )
% 2.86/3.16 & ( relH @ As7 @ H3 @ H6 )
% 2.86/3.16 & ( in_range @ ( produc7507926704131184380et_nat @ H6 @ As7 ) ) )
% 2.86/3.16 => ( P2 @ ( produc7507926704131184380et_nat @ H6 @ As7 ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % proper_def
% 2.86/3.16 thf(fact_5724_list__ex__iff__not__all__inverval__nat,axiom,
% 2.86/3.16 ! [P: nat > $o,I: nat,J: nat] :
% 2.86/3.16 ( ( list_ex_nat @ P @ ( upt @ I @ J ) )
% 2.86/3.16 = ( ~ ( all_interval_nat @ ( comp_o_o_nat @ (~) @ P ) @ I @ J ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % list_ex_iff_not_all_inverval_nat
% 2.86/3.16 thf(fact_5725_list__all__iff__all__interval__nat,axiom,
% 2.86/3.16 ! [P: nat > $o,I: nat,J: nat] :
% 2.86/3.16 ( ( list_all_nat @ P @ ( upt @ I @ J ) )
% 2.86/3.16 = ( all_interval_nat @ P @ I @ J ) ) ).
% 2.86/3.16
% 2.86/3.16 % list_all_iff_all_interval_nat
% 2.86/3.16 thf(fact_5726_all__interval__nat__def,axiom,
% 2.86/3.16 ( all_interval_nat
% 2.86/3.16 = ( ^ [P2: nat > $o,I4: nat,J2: nat] :
% 2.86/3.16 ! [X2: nat] :
% 2.86/3.16 ( ( member_nat @ X2 @ ( set_or4665077453230672383an_nat @ I4 @ J2 ) )
% 2.86/3.16 => ( P2 @ X2 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % all_interval_nat_def
% 2.86/3.16 thf(fact_5727_num__of__nat__inverse,axiom,
% 2.86/3.16 ! [N: nat] :
% 2.86/3.16 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.86/3.16 => ( ( nat_of_num @ ( num_of_nat @ N ) )
% 2.86/3.16 = N ) ) ).
% 2.86/3.16
% 2.86/3.16 % num_of_nat_inverse
% 2.86/3.16 thf(fact_5728_nat__of__num__pos,axiom,
% 2.86/3.16 ! [X: num] : ( ord_less_nat @ zero_zero_nat @ ( nat_of_num @ X ) ) ).
% 2.86/3.16
% 2.86/3.16 % nat_of_num_pos
% 2.86/3.16 thf(fact_5729_less__num__def,axiom,
% 2.86/3.16 ( ord_less_num
% 2.86/3.16 = ( ^ [M: num,N2: num] : ( ord_less_nat @ ( nat_of_num @ M ) @ ( nat_of_num @ N2 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % less_num_def
% 2.86/3.16 thf(fact_5730_natural__decr,axiom,
% 2.86/3.16 ! [N: code_natural] :
% 2.86/3.16 ( ( N != zero_z2226904508553997617atural )
% 2.86/3.16 => ( ord_less_nat @ ( minus_minus_nat @ ( code_nat_of_natural @ N ) @ ( suc @ zero_zero_nat ) ) @ ( code_nat_of_natural @ N ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % natural_decr
% 2.86/3.16 thf(fact_5731_less__natural_Orep__eq,axiom,
% 2.86/3.16 ( ord_le5570908160329646204atural
% 2.86/3.16 = ( ^ [X2: code_natural,Xa4: code_natural] : ( ord_less_nat @ ( code_nat_of_natural @ X2 ) @ ( code_nat_of_natural @ Xa4 ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % less_natural.rep_eq
% 2.86/3.16 thf(fact_5732_next_Osimps,axiom,
% 2.86/3.16 ! [V2: code_natural,W: code_natural] :
% 2.86/3.16 ( ( next @ ( produc3574140220909816553atural @ V2 @ W ) )
% 2.86/3.16 = ( produc6639722614265839536atural @ ( plus_p4538020629002901425atural @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ V2 @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ V2 @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( plus_p4538020629002901425atural @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ W @ ( 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 @ W @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ one_one_Code_natural ) ) @ one_one_Code_natural ) @ ( produc3574140220909816553atural @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ V2 @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ V2 @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ W @ ( 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 @ W @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % next.simps
% 2.86/3.16 thf(fact_5733_full__exhaustive__natural_H_Ocases,axiom,
% 2.86/3.16 ! [X: produc989692990947075319atural] :
% 2.86/3.16 ~ ! [F5: produc4972180933644002618e_term > option6357759511663192854e_term,D3: code_natural,I5: code_natural] :
% 2.86/3.16 ( X
% 2.86/3.16 != ( produc3831813291587773865atural @ F5 @ ( produc3574140220909816553atural @ D3 @ I5 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % full_exhaustive_natural'.cases
% 2.86/3.16 thf(fact_5734_exhaustive__natural_H_Ocases,axiom,
% 2.86/3.16 ! [X: produc8731074985263844745atural] :
% 2.86/3.16 ~ ! [F5: code_natural > option6357759511663192854e_term,D3: code_natural,I5: code_natural] :
% 2.86/3.16 ( X
% 2.86/3.16 != ( produc2252593628808123835atural @ F5 @ ( produc3574140220909816553atural @ D3 @ I5 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % exhaustive_natural'.cases
% 2.86/3.16 thf(fact_5735_log_Ocases,axiom,
% 2.86/3.16 ! [X: produc7822875418678951345atural] :
% 2.86/3.16 ~ ! [B4: code_natural,I5: code_natural] :
% 2.86/3.16 ( X
% 2.86/3.16 != ( produc3574140220909816553atural @ B4 @ I5 ) ) ).
% 2.86/3.16
% 2.86/3.16 % log.cases
% 2.86/3.16 thf(fact_5736_split__seed__def,axiom,
% 2.86/3.16 ( split_seed
% 2.86/3.16 = ( ^ [S6: produc7822875418678951345atural] :
% 2.86/3.16 ( produc8282080750456430313atural
% 2.86/3.16 @ ^ [V4: code_natural,W4: code_natural] :
% 2.86/3.16 ( produc8282080750456430313atural
% 2.86/3.16 @ ^ [V5: code_natural,W5: 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ V4 ) @ W5 ) @ ( produc3574140220909816553atural @ V5 @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ W4 ) ) )
% 2.86/3.16 @ ( produc6591912806276919810atural @ ( next @ S6 ) ) )
% 2.86/3.16 @ S6 ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % split_seed_def
% 2.86/3.16 thf(fact_5737_small__lazy_H_Ocases,axiom,
% 2.86/3.16 ! [X: product_prod_int_int] :
% 2.86/3.16 ~ ! [D3: int,I5: int] :
% 2.86/3.16 ( X
% 2.86/3.16 != ( product_Pair_int_int @ D3 @ I5 ) ) ).
% 2.86/3.16
% 2.86/3.16 % small_lazy'.cases
% 2.86/3.16 thf(fact_5738_Random_Orange__def,axiom,
% 2.86/3.16 ( range
% 2.86/3.16 = ( ^ [K4: code_natural] :
% 2.86/3.16 ( produc5538323210962509403atural
% 2.86/3.16 @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ K4 )
% 2.86/3.16 @ ^ [L4: code_natural] :
% 2.86/3.16 ( produc5538323210962509403atural @ next
% 2.86/3.16 @ ^ [V4: code_natural] : ( produc6639722614265839536atural @ ( plus_p4538020629002901425atural @ V4 @ ( times_2397367101498566445atural @ L4 @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 2.86/3.16 @ one_one_Code_natural )
% 2.86/3.16 @ ^ [V4: code_natural] : ( produc6639722614265839536atural @ ( modulo8411746178871703098atural @ V4 @ K4 ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % Random.range_def
% 2.86/3.16 thf(fact_5739_less__natural_Oabs__eq,axiom,
% 2.86/3.16 ! [Xa: nat,X: nat] :
% 2.86/3.16 ( ( ord_le5570908160329646204atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X ) )
% 2.86/3.16 = ( ord_less_nat @ Xa @ X ) ) ).
% 2.86/3.16
% 2.86/3.16 % less_natural.abs_eq
% 2.86/3.16 thf(fact_5740_log_Opelims,axiom,
% 2.86/3.16 ! [X: code_natural,Xa: code_natural,Y: code_natural] :
% 2.86/3.16 ( ( ( log @ X @ Xa )
% 2.86/3.16 = Y )
% 2.86/3.16 => ( ( accp_P8126237942716283194atural @ log_rel @ ( produc3574140220909816553atural @ X @ Xa ) )
% 2.86/3.16 => ~ ( ( ( ( ( ord_le1926595141338095240atural @ X @ one_one_Code_natural )
% 2.86/3.16 | ( ord_le5570908160329646204atural @ Xa @ X ) )
% 2.86/3.16 => ( Y = one_one_Code_natural ) )
% 2.86/3.16 & ( ~ ( ( ord_le1926595141338095240atural @ X @ one_one_Code_natural )
% 2.86/3.16 | ( ord_le5570908160329646204atural @ Xa @ X ) )
% 2.86/3.16 => ( Y
% 2.86/3.16 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( log @ X @ ( divide5121882707175180666atural @ Xa @ X ) ) ) ) ) )
% 2.86/3.16 => ~ ( accp_P8126237942716283194atural @ log_rel @ ( produc3574140220909816553atural @ X @ Xa ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % log.pelims
% 2.86/3.16 thf(fact_5741_in__range_Osimps,axiom,
% 2.86/3.16 ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 2.86/3.16 ( ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 2.86/3.16 = ( ! [X2: nat] :
% 2.86/3.16 ( ( member_nat @ X2 @ As2 )
% 2.86/3.16 => ( ord_less_nat @ X2 @ ( lim_Product_unit @ H2 ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % in_range.simps
% 2.86/3.16 thf(fact_5742_in__range_Oelims_I3_J,axiom,
% 2.86/3.16 ! [X: produc3658429121746597890et_nat] :
% 2.86/3.16 ( ~ ( in_range @ X )
% 2.86/3.16 => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.86/3.16 ( ( X
% 2.86/3.16 = ( produc7507926704131184380et_nat @ H @ As ) )
% 2.86/3.16 => ! [X3: nat] :
% 2.86/3.16 ( ( member_nat @ X3 @ As )
% 2.86/3.16 => ( ord_less_nat @ X3 @ ( lim_Product_unit @ H ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % in_range.elims(3)
% 2.86/3.16 thf(fact_5743_in__range_Oelims_I2_J,axiom,
% 2.86/3.16 ! [X: produc3658429121746597890et_nat] :
% 2.86/3.16 ( ( in_range @ X )
% 2.86/3.16 => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.86/3.16 ( ( X
% 2.86/3.16 = ( produc7507926704131184380et_nat @ H @ As ) )
% 2.86/3.16 => ~ ! [X7: nat] :
% 2.86/3.16 ( ( member_nat @ X7 @ As )
% 2.86/3.16 => ( ord_less_nat @ X7 @ ( lim_Product_unit @ H ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % in_range.elims(2)
% 2.86/3.16 thf(fact_5744_in__range_Oelims_I1_J,axiom,
% 2.86/3.16 ! [X: produc3658429121746597890et_nat,Y: $o] :
% 2.86/3.16 ( ( ( in_range @ X )
% 2.86/3.16 = Y )
% 2.86/3.16 => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.86/3.16 ( ( X
% 2.86/3.16 = ( produc7507926704131184380et_nat @ H @ As ) )
% 2.86/3.16 => ( Y
% 2.86/3.16 = ( ~ ! [X2: nat] :
% 2.86/3.16 ( ( member_nat @ X2 @ As )
% 2.86/3.16 => ( ord_less_nat @ X2 @ ( lim_Product_unit @ H ) ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % in_range.elims(1)
% 2.86/3.16 thf(fact_5745_new__addrs__def,axiom,
% 2.86/3.16 ( hoare_new_addrs
% 2.86/3.16 = ( ^ [H3: heap_e7401611519738050253t_unit,As7: set_nat,H6: heap_e7401611519738050253t_unit] :
% 2.86/3.16 ( sup_sup_set_nat @ As7
% 2.86/3.16 @ ( collect_nat
% 2.86/3.16 @ ^ [A3: nat] :
% 2.86/3.16 ( ( ord_less_eq_nat @ ( lim_Product_unit @ H3 ) @ A3 )
% 2.86/3.16 & ( ord_less_nat @ A3 @ ( lim_Product_unit @ H6 ) ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % new_addrs_def
% 2.86/3.16 thf(fact_5746_execute__assert_H,axiom,
% 2.86/3.16 ! [P: $o,H2: heap_e7401611519738050253t_unit] :
% 2.86/3.16 ( ( P
% 2.86/3.16 => ( ( heap_T875086893843062177t_unit @ ( refine_Imp_assert @ P ) @ H2 )
% 2.86/3.16 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ product_Unity @ ( produc584006145561248582it_nat @ H2 @ zero_zero_nat ) ) ) ) )
% 2.86/3.16 & ( ~ P
% 2.86/3.16 => ( ( heap_T875086893843062177t_unit @ ( refine_Imp_assert @ P ) @ H2 )
% 2.86/3.16 = none_P9117596204409417319it_nat ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % execute_assert'
% 2.86/3.16 thf(fact_5747_assert_H__rule,axiom,
% 2.86/3.16 ! [P: assn,Phi: $o] :
% 2.86/3.16 ( ! [H: produc3658429121746597890et_nat] :
% 2.86/3.16 ( ( rep_assn @ P @ H )
% 2.86/3.16 => Phi )
% 2.86/3.16 => ( hoare_8945653483474564448t_unit @ P @ ( refine_Imp_assert @ Phi )
% 2.86/3.16 @ ^ [Uu2: product_unit] : P ) ) ).
% 2.86/3.16
% 2.86/3.16 % assert'_rule
% 2.86/3.16 thf(fact_5748_wait__def,axiom,
% 2.86/3.16 ( heap_Time_wait
% 2.86/3.16 = ( ^ [N2: nat] :
% 2.86/3.16 ( heap_T6183433275982383450t_unit
% 2.86/3.16 @ ^ [H3: heap_e7401611519738050253t_unit] : ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ product_Unity @ ( produc584006145561248582it_nat @ H3 @ N2 ) ) ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % wait_def
% 2.86/3.16 thf(fact_5749_less__nat__rel,axiom,
% 2.86/3.16 ( ord_less_nat
% 2.86/3.16 = ( transi2163837189807498211lp_nat
% 2.86/3.16 @ ^ [M: nat,N2: nat] :
% 2.86/3.16 ( N2
% 2.86/3.16 = ( suc @ M ) ) ) ) ).
% 2.86/3.16
% 2.86/3.16 % less_nat_rel
% 2.86/3.16 thf(fact_5750_type__definition__assn,axiom,
% 2.86/3.16 type_d3909072315231072503_nat_o @ rep_assn @ abs_assn @ ( collec939566748876313656_nat_o @ proper ) ).
% 2.86/3.16
% 2.86/3.16 % type_definition_assn
% 2.86/3.16
% 2.86/3.16 % Helper facts (35)
% 2.86/3.16 thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 2.86/3.16 ! [X: int,Y: int] :
% 2.86/3.16 ( ( if_int @ $false @ X @ Y )
% 2.86/3.16 = Y ) ).
% 2.86/3.16
% 2.86/3.16 thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 2.86/3.16 ! [X: int,Y: int] :
% 2.86/3.16 ( ( if_int @ $true @ X @ Y )
% 2.86/3.16 = X ) ).
% 2.86/3.16
% 2.86/3.16 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 2.86/3.16 ! [X: nat,Y: nat] :
% 2.86/3.16 ( ( if_nat @ $false @ X @ Y )
% 2.86/3.16 = Y ) ).
% 2.86/3.16
% 2.86/3.16 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 2.86/3.16 ! [X: nat,Y: nat] :
% 2.86/3.16 ( ( if_nat @ $true @ X @ Y )
% 2.86/3.16 = X ) ).
% 2.86/3.16
% 2.86/3.16 thf(help_If_2_1_If_001t__Assertions__Oassn_T,axiom,
% 2.86/3.16 ! [X: assn,Y: assn] :
% 2.86/3.16 ( ( if_assn @ $false @ X @ Y )
% 2.86/3.16 = Y ) ).
% 2.86/3.16
% 2.86/3.16 thf(help_If_1_1_If_001t__Assertions__Oassn_T,axiom,
% 2.86/3.16 ! [X: assn,Y: assn] :
% 2.86/3.16 ( ( if_assn @ $true @ X @ Y )
% 2.86/3.16 = X ) ).
% 2.86/3.16
% 2.86/3.16 thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 2.86/3.16 ! [X: code_integer,Y: code_integer] :
% 2.86/3.16 ( ( if_Code_integer @ $false @ X @ Y )
% 2.86/3.16 = Y ) ).
% 2.86/3.16
% 2.86/3.16 thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 2.86/3.16 ! [X: code_integer,Y: code_integer] :
% 2.86/3.16 ( ( if_Code_integer @ $true @ X @ Y )
% 2.86/3.16 = X ) ).
% 2.86/3.16
% 2.86/3.16 thf(help_If_2_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 2.86/3.16 ! [X: set_int,Y: set_int] :
% 2.86/3.16 ( ( if_set_int @ $false @ X @ Y )
% 2.86/3.16 = Y ) ).
% 2.86/3.16
% 2.86/3.16 thf(help_If_1_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 2.86/3.16 ! [X: set_int,Y: set_int] :
% 2.86/3.16 ( ( if_set_int @ $true @ X @ Y )
% 2.86/3.16 = X ) ).
% 2.86/3.16
% 2.86/3.16 thf(help_If_2_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 2.86/3.16 ! [X: set_nat,Y: set_nat] :
% 2.86/3.16 ( ( if_set_nat @ $false @ X @ Y )
% 2.86/3.16 = Y ) ).
% 2.86/3.16
% 2.86/3.16 thf(help_If_1_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 2.86/3.16 ! [X: set_nat,Y: set_nat] :
% 2.86/3.16 ( ( if_set_nat @ $true @ X @ Y )
% 2.86/3.16 = X ) ).
% 2.86/3.16
% 2.86/3.16 thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 2.86/3.16 ! [X: list_int,Y: list_int] :
% 2.86/3.16 ( ( if_list_int @ $false @ X @ Y )
% 2.86/3.16 = Y ) ).
% 2.86/3.16
% 2.86/3.16 thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 2.86/3.16 ! [X: list_int,Y: list_int] :
% 2.86/3.16 ( ( if_list_int @ $true @ X @ Y )
% 2.86/3.16 = X ) ).
% 2.86/3.16
% 2.86/3.16 thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 2.86/3.16 ! [X: list_nat,Y: list_nat] :
% 2.86/3.16 ( ( if_list_nat @ $false @ X @ Y )
% 2.86/3.16 = Y ) ).
% 2.86/3.16
% 2.86/3.16 thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 2.86/3.16 ! [X: list_nat,Y: list_nat] :
% 2.86/3.16 ( ( if_list_nat @ $true @ X @ Y )
% 2.86/3.16 = X ) ).
% 2.86/3.16
% 2.86/3.16 thf(help_If_2_1_If_001t__Filter__Ofilter_It__Nat__Onat_J_T,axiom,
% 2.86/3.16 ! [X: filter_nat,Y: filter_nat] :
% 2.86/3.16 ( ( if_filter_nat @ $false @ X @ Y )
% 2.86/3.16 = Y ) ).
% 2.86/3.16
% 2.86/3.16 thf(help_If_1_1_If_001t__Filter__Ofilter_It__Nat__Onat_J_T,axiom,
% 2.86/3.16 ! [X: filter_nat,Y: filter_nat] :
% 2.86/3.16 ( ( if_filter_nat @ $true @ X @ Y )
% 2.86/3.16 = X ) ).
% 2.86/3.16
% 2.86/3.16 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 2.86/3.16 ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 2.86/3.16 ( ( if_Pro3027730157355071871nt_int @ $false @ X @ Y )
% 2.86/3.16 = Y ) ).
% 2.86/3.16
% 2.86/3.16 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 2.86/3.16 ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 2.86/3.16 ( ( if_Pro3027730157355071871nt_int @ $true @ X @ Y )
% 2.86/3.16 = X ) ).
% 2.86/3.16
% 2.86/3.16 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 2.86/3.16 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 2.86/3.16 ( ( if_Pro6206227464963214023at_nat @ $false @ X @ Y )
% 2.86/3.16 = Y ) ).
% 2.86/3.16
% 2.86/3.16 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 2.86/3.16 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 2.86/3.16 ( ( if_Pro6206227464963214023at_nat @ $true @ X @ Y )
% 2.86/3.16 = X ) ).
% 2.86/3.16
% 2.86/3.16 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 2.86/3.16 ! [X: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 2.86/3.16 ( ( if_Pro5737122678794959658eger_o @ $false @ X @ Y )
% 2.86/3.16 = Y ) ).
% 2.86/3.16
% 2.86/3.16 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 2.86/3.16 ! [X: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 2.86/3.16 ( ( if_Pro5737122678794959658eger_o @ $true @ X @ Y )
% 2.86/3.16 = X ) ).
% 2.86/3.16
% 2.86/3.16 thf(help_If_2_1_If_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_T,axiom,
% 2.86/3.16 ! [X: list_P6011104703257516679at_nat,Y: list_P6011104703257516679at_nat] :
% 2.86/3.16 ( ( if_lis9186351972506106189at_nat @ $false @ X @ Y )
% 2.86/3.16 = Y ) ).
% 2.86/3.16
% 2.86/3.16 thf(help_If_1_1_If_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_T,axiom,
% 2.86/3.16 ! [X: list_P6011104703257516679at_nat,Y: list_P6011104703257516679at_nat] :
% 2.86/3.16 ( ( if_lis9186351972506106189at_nat @ $true @ X @ Y )
% 2.86/3.16 = X ) ).
% 2.86/3.16
% 2.86/3.16 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 2.86/3.16 ! [X: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 2.86/3.16 ( ( if_Pro6119634080678213985nteger @ $false @ X @ Y )
% 2.86/3.16 = Y ) ).
% 2.86/3.16
% 2.86/3.16 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 2.86/3.16 ! [X: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 2.86/3.16 ( ( if_Pro6119634080678213985nteger @ $true @ X @ Y )
% 2.86/3.16 = X ) ).
% 2.86/3.16
% 2.86/3.16 thf(help_If_2_1_If_001t__List__Olist_It__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J_J_T,axiom,
% 2.86/3.16 ! [X: list_P8527749157015355191n_assn,Y: list_P8527749157015355191n_assn] :
% 2.86/3.16 ( ( if_lis7173127979115136509n_assn @ $false @ X @ Y )
% 2.86/3.16 = Y ) ).
% 3.70/4.02
% 3.70/4.02 thf(help_If_1_1_If_001t__List__Olist_It__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J_J_T,axiom,
% 3.70/4.02 ! [X: list_P8527749157015355191n_assn,Y: list_P8527749157015355191n_assn] :
% 3.70/4.02 ( ( if_lis7173127979115136509n_assn @ $true @ X @ Y )
% 3.70/4.02 = X ) ).
% 3.70/4.02
% 3.70/4.02 thf(help_If_2_1_If_001t__List__Olist_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_J_T,axiom,
% 3.70/4.02 ! [X: list_P7985473006766602707_nat_o,Y: list_P7985473006766602707_nat_o] :
% 3.70/4.02 ( ( if_lis2904118647880296857_nat_o @ $false @ X @ Y )
% 3.70/4.02 = Y ) ).
% 3.70/4.02
% 3.70/4.02 thf(help_If_1_1_If_001t__List__Olist_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_J_T,axiom,
% 3.70/4.02 ! [X: list_P7985473006766602707_nat_o,Y: list_P7985473006766602707_nat_o] :
% 3.70/4.02 ( ( if_lis2904118647880296857_nat_o @ $true @ X @ Y )
% 3.70/4.02 = X ) ).
% 3.70/4.02
% 3.70/4.02 thf(help_If_3_1_If_001t__List__Olist_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_T,axiom,
% 3.70/4.02 ! [P: $o] :
% 3.70/4.02 ( ( P = $true )
% 3.70/4.02 | ( P = $false ) ) ).
% 3.70/4.02
% 3.70/4.02 thf(help_If_2_1_If_001t__List__Olist_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_T,axiom,
% 3.70/4.02 ! [X: list_P5464809261938338413at_nat,Y: list_P5464809261938338413at_nat] :
% 3.70/4.02 ( ( if_lis7508161100780771379at_nat @ $false @ X @ Y )
% 3.70/4.02 = Y ) ).
% 3.70/4.02
% 3.70/4.02 thf(help_If_1_1_If_001t__List__Olist_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_T,axiom,
% 3.70/4.02 ! [X: list_P5464809261938338413at_nat,Y: list_P5464809261938338413at_nat] :
% 3.70/4.02 ( ( if_lis7508161100780771379at_nat @ $true @ X @ Y )
% 3.70/4.02 = X ) ).
% 3.70/4.02
% 3.70/4.02 % Conjectures (1)
% 3.70/4.02 thf(conj_0,conjecture,
% 3.70/4.02 entails @ p @ q ).
% 3.70/4.02
% 3.70/4.02 %------------------------------------------------------------------------------
% 3.70/4.02 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.Gjr5vCZWo5/cvc5---1.0.5_8296.p...
% 3.70/4.02 (declare-sort $$unsorted 0)
% 3.70/4.02 (declare-sort tptp.set_Pr3444600963470892981et_nat 0)
% 3.70/4.02 (declare-sort tptp.produc5657529347773406293et_nat 0)
% 3.70/4.02 (declare-sort tptp.set_Pr1722956316086891245nteger 0)
% 3.70/4.02 (declare-sort tptp.produc824974754969098637nteger 0)
% 3.70/4.02 (declare-sort tptp.set_Pr4708930517165415495nt_int 0)
% 3.70/4.02 (declare-sort tptp.produc2432570611225516007nt_int 0)
% 3.70/4.02 (declare-sort tptp.set_Pr7928877670098842301et_nat 0)
% 3.70/4.02 (declare-sort tptp.produc6830853553727218525et_nat 0)
% 3.70/4.02 (declare-sort tptp.set_Pr8634505666381077339nt_int 0)
% 3.70/4.02 (declare-sort tptp.list_P362550909693114634et_nat 0)
% 3.70/4.02 (declare-sort tptp.set_Pr8536935166611901872et_nat 0)
% 3.70/4.02 (declare-sort tptp.produc2501202720802129403nt_int 0)
% 3.70/4.02 (declare-sort tptp.produc4193628355235574503at_nat 0)
% 3.70/4.02 (declare-sort tptp.produc2732055786443039994et_nat 0)
% 3.70/4.02 (declare-sort tptp.produc1319942482725812455at_nat 0)
% 3.70/4.02 (declare-sort tptp.list_P6548900253507351021at_nat 0)
% 3.70/4.02 (declare-sort tptp.set_Pr5564308138774400199at_nat 0)
% 3.70/4.02 (declare-sort tptp.produc1906917888121415911at_nat 0)
% 3.70/4.02 (declare-sort tptp.list_P7828571989066258726nteger 0)
% 3.70/4.02 (declare-sort tptp.set_Pr1281608226676607948nteger 0)
% 3.70/4.02 (declare-sort tptp.produc989692990947075319atural 0)
% 3.70/4.02 (declare-sort tptp.produc1908205239877642774nteger 0)
% 3.70/4.02 (declare-sort tptp.list_P651320350408439699nt_int 0)
% 3.70/4.02 (declare-sort tptp.set_Pr9222295170931077689nt_int 0)
% 3.70/4.02 (declare-sort tptp.list_P6107040726529854061_nat_o 0)
% 3.70/4.02 (declare-sort tptp.set_Pr2161125870931222855_nat_o 0)
% 3.70/4.02 (declare-sort tptp.produc2285326912895808259nt_int 0)
% 3.70/4.02 (declare-sort tptp.list_P2321686559999237006et_nat 0)
% 3.70/4.02 (declare-sort tptp.set_Pr3286484037609594932et_nat 0)
% 3.70/4.02 (declare-sort tptp.produc4928098042776334183_nat_o 0)
% 3.70/4.02 (declare-sort tptp.produc4530688714081574576n_assn 0)
% 3.70/4.02 (declare-sort tptp.produc3925858234332021118et_nat 0)
% 3.70/4.02 (declare-sort tptp.produc8731074985263844745atural 0)
% 3.70/4.02 (declare-sort tptp.produc8763457246119570046nteger 0)
% 3.70/4.02 (declare-sort tptp.list_P1316552470764441098e_term 0)
% 3.70/4.02 (declare-sort tptp.set_Pr7604974323444597168e_term 0)
% 3.70/4.02 (declare-sort tptp.list_P1743416141875011707e_term 0)
% 3.70/4.02 (declare-sort tptp.set_Pr3642885161833720865e_term 0)
% 3.70/4.02 (declare-sort tptp.list_P8915022641806594461nt_int 0)
% 3.70/4.02 (declare-sort tptp.set_Pr1872883991513573699nt_int 0)
% 3.70/4.02 (declare-sort tptp.set_Pr4333006031979791559at_nat 0)
% 3.70/4.02 (declare-sort tptp.set_Pr6863447823992824007n_assn 0)
% 3.70/4.02 (declare-sort tptp.produc7773217078559923341nt_int 0)
% 3.70/4.02 (declare-sort tptp.set_Pr8551490117392284871at_nat 0)
% 3.70/4.02 (declare-sort tptp.produc424102278133772007at_nat 0)
% 3.70/4.02 (declare-sort tptp.produc337509097454979815n_assn 0)
% 3.70/4.02 (declare-sort tptp.list_s4242580248156217677at_nat 0)
% 3.70/4.02 (declare-sort tptp.produc6756470014200349799atural 0)
% 3.70/4.02 (declare-sort tptp.produc4166570645942440679at_nat 0)
% 3.70/4.02 (declare-sort tptp.list_P5464809261938338413at_nat 0)
% 3.70/4.02 (declare-sort tptp.list_P28140577958321773n_assn 0)
% 3.70/4.02 (declare-sort tptp.set_Pr4329608150637261639at_nat 0)
% 3.70/4.02 (declare-sort tptp.set_Pr8116311503512020807n_assn 0)
% 3.70/4.02 (declare-sort tptp.option8956607266484857688it_nat 0)
% 3.70/4.02 (declare-sort tptp.produc3843707927480180839at_nat 0)
% 3.70/4.02 (declare-sort tptp.produc9053633027152450663n_assn 0)
% 3.70/4.02 (declare-sort tptp.set_Pr457366540195662369at_nat 0)
% 3.70/4.02 (declare-sort tptp.set_Pr488414391616402044st_nat 0)
% 3.70/4.02 (declare-sort tptp.set_Pr4898238009683259096st_int 0)
% 3.70/4.02 (declare-sort tptp.set_Pr7093487733527993602n_assn 0)
% 3.70/4.02 (declare-sort tptp.set_Pr4168565316758867366n_assn 0)
% 3.70/4.02 (declare-sort tptp.list_P8469869581646625389at_nat 0)
% 3.70/4.02 (declare-sort tptp.set_Pr8693737435421807431at_nat 0)
% 3.70/4.02 (declare-sort tptp.produc8664842809031399944it_nat 0)
% 3.70/4.02 (declare-sort tptp.produc732395585841259969at_nat 0)
% 3.70/4.02 (declare-sort tptp.set_Pr1932065953672099015od_o_o 0)
% 3.70/4.02 (declare-sort tptp.produc6654255674790325574st_nat 0)
% 3.70/4.02 (declare-sort tptp.produc4164172529858598818st_int 0)
% 3.70/4.02 (declare-sort tptp.produc2555908794901494476n_assn 0)
% 3.70/4.02 (declare-sort tptp.produc8582807064127716720n_assn 0)
% 3.70/4.02 (declare-sort tptp.list_P7985473006766602707_nat_o 0)
% 3.70/4.02 (declare-sort tptp.produc5835291356934675326atural 0)
% 3.70/4.02 (declare-sort tptp.set_Pr4532377907799695533_nat_o 0)
% 3.70/4.02 (declare-sort tptp.list_i8448526496819171953e_term 0)
% 3.70/4.02 (declare-sort tptp.produc859450856879609959at_nat 0)
% 3.70/4.02 (declare-sort tptp.set_in3461395444621081367e_term 0)
% 3.70/4.02 (declare-sort tptp.produc2934264451710624999od_o_o 0)
% 3.70/4.02 (declare-sort tptp.list_P9062070895058802706et_nat 0)
% 3.70/4.02 (declare-sort tptp.set_Pr3948176798113811640et_nat 0)
% 3.70/4.02 (declare-sort tptp.list_P2911967483291296064sn_nat 0)
% 3.70/4.02 (declare-sort tptp.list_P421884338359569308sn_int 0)
% 3.70/4.02 (declare-sort tptp.list_P7711101519850957926n_assn 0)
% 3.70/4.02 (declare-sort tptp.list_P1495281457390866698n_assn 0)
% 3.70/4.02 (declare-sort tptp.set_Pr4672072672689440998sn_nat 0)
% 3.70/4.02 (declare-sort tptp.set_Pr2181989527757714242sn_int 0)
% 3.70/4.02 (declare-sort tptp.set_Pr247834672394327052n_assn 0)
% 3.70/4.02 (declare-sort tptp.set_Pr3255386646789011632n_assn 0)
% 3.70/4.02 (declare-sort tptp.produc4972180933644002618e_term 0)
% 3.70/4.02 (declare-sort tptp.produc6241069584506657477e_term 0)
% 3.70/4.02 (declare-sort tptp.produc3658429121746597890et_nat 0)
% 3.70/4.02 (declare-sort tptp.list_P5953897101696565392at_nat 0)
% 3.70/4.02 (declare-sort tptp.list_P3463813956764838636at_int 0)
% 3.70/4.02 (declare-sort tptp.list_P1909269847677398966at_nat 0)
% 3.70/4.02 (declare-sort tptp.list_P812186867033400410at_nat 0)
% 3.70/4.02 (declare-sort tptp.set_Pr2539167527615954998at_nat 0)
% 3.70/4.02 (declare-sort tptp.set_Pr49084382684228242at_int 0)
% 3.70/4.02 (declare-sort tptp.set_Pr7717912310451564380at_nat 0)
% 3.70/4.02 (declare-sort tptp.set_Pr6620829329807565824at_nat 0)
% 3.70/4.02 (declare-sort tptp.produc3672657496626091440sn_nat 0)
% 3.70/4.02 (declare-sort tptp.produc8718178513971670540sn_int 0)
% 3.70/4.02 (declare-sort tptp.produc1407301962063123414n_assn 0)
% 3.70/4.02 (declare-sort tptp.produc3167338625816234618n_assn 0)
% 3.70/4.02 (declare-sort tptp.list_s9130966667114977576at_nat 0)
% 3.70/4.02 (declare-sort tptp.produc254973753779126261st_nat 0)
% 3.70/4.02 (declare-sort tptp.produc5834231552977413017st_int 0)
% 3.70/4.02 (declare-sort tptp.set_Pr3451248702717554689st_nat 0)
% 3.70/4.02 (declare-sort tptp.set_Pr7861072320784411741st_int 0)
% 3.70/4.02 (declare-sort tptp.set_Pr5578615432719617117st_nat 0)
% 3.70/4.02 (declare-sort tptp.set_Pr765067013931698361st_int 0)
% 3.70/4.02 (declare-sort tptp.list_l6351802567095793725n_assn 0)
% 3.70/4.02 (declare-sort tptp.produc8551481072490612790e_term 0)
% 3.70/4.02 (declare-sort tptp.list_P5578671422887162913nteger 0)
% 3.70/4.02 (declare-sort tptp.set_Pr4811707699266497531nteger 0)
% 3.70/4.02 (declare-sort tptp.option6357759511663192854e_term 0)
% 3.70/4.02 (declare-sort tptp.set_Pr3005433631314115148st_nat 0)
% 3.70/4.02 (declare-sort tptp.set_Pr7415257249380972200st_int 0)
% 3.70/4.02 (declare-sort tptp.set_Pr6760183905301009355st_nat 0)
% 3.70/4.02 (declare-sort tptp.set_Pr1946635486513090599st_int 0)
% 3.70/4.02 (declare-sort tptp.set_Pr9082979648927643218list_d 0)
% 3.70/4.02 (declare-sort tptp.set_Pr2380792130361903057list_c 0)
% 3.70/4.02 (declare-sort tptp.produc6653097349344004940it_nat 0)
% 3.70/4.02 (declare-sort tptp.produc8373899037510109440at_nat 0)
% 3.70/4.02 (declare-sort tptp.produc4196048018000912732at_int 0)
% 3.70/4.02 (declare-sort tptp.produc7248412053542808358at_nat 0)
% 3.70/4.02 (declare-sort tptp.produc1062882101152166346at_nat 0)
% 3.70/4.02 (declare-sort tptp.set_Pr5674772971416283335list_d 0)
% 3.70/4.02 (declare-sort tptp.set_Pr8195957489705318982list_c 0)
% 3.70/4.02 (declare-sort tptp.set_Pr8760529213406277896list_d 0)
% 3.70/4.02 (declare-sort tptp.set_Pr2058341694840537735list_c 0)
% 3.70/4.02 (declare-sort tptp.produc1828647624359046049st_nat 0)
% 3.70/4.02 (declare-sort tptp.produc8561936516282095101st_int 0)
% 3.70/4.02 (declare-sort tptp.produc3676724955757786621st_nat 0)
% 3.70/4.02 (declare-sort tptp.produc1186641810826059865st_int 0)
% 3.70/4.02 (declare-sort tptp.list_s1210847774152347623at_nat 0)
% 3.70/4.02 (declare-sort tptp.list_P8527749157015355191n_assn 0)
% 3.70/4.02 (declare-sort tptp.set_se7855581050983116737at_nat 0)
% 3.70/4.02 (declare-sort tptp.set_Pr5949110396991348497n_assn 0)
% 3.70/4.02 (declare-sort tptp.produc7822875418678951345atural 0)
% 3.70/4.02 (declare-sort tptp.produc8923325533196201883nteger 0)
% 3.70/4.02 (declare-sort tptp.produc2433097559162738582st_nat 0)
% 3.70/4.02 (declare-sort tptp.produc9166386451085787634st_int 0)
% 3.70/4.02 (declare-sort tptp.produc1766198083622830229st_nat 0)
% 3.70/4.02 (declare-sort tptp.produc8499486975545879281st_int 0)
% 3.70/4.02 (declare-sort tptp.produc1726512871120090780list_d 0)
% 3.70/4.02 (declare-sort tptp.produc1655478831073744795list_c 0)
% 3.70/4.02 (declare-sort tptp.multis2468970476368604999at_nat 0)
% 3.70/4.02 (declare-sort tptp.produc2783776724613635559list_d 0)
% 3.70/4.02 (declare-sort tptp.produc2712742684567289574list_c 0)
% 3.70/4.02 (declare-sort tptp.produc8056257125849822888list_d 0)
% 3.70/4.02 (declare-sort tptp.produc7985223085803476903list_c 0)
% 3.70/4.02 (declare-sort tptp.filter1242075044329608583at_nat 0)
% 3.70/4.02 (declare-sort tptp.list_P6011104703257516679at_nat 0)
% 3.70/4.02 (declare-sort tptp.list_P3521021558325789923at_int 0)
% 3.70/4.02 (declare-sort tptp.list_P8198026277950538467nt_nat 0)
% 3.70/4.02 (declare-sort tptp.list_P5707943133018811711nt_int 0)
% 3.70/4.02 (declare-sort tptp.set_Pr1261947904930325089at_nat 0)
% 3.70/4.02 (declare-sort tptp.set_Pr7995236796853374141at_int 0)
% 3.70/4.02 (declare-sort tptp.set_Pr3448869479623346877nt_nat 0)
% 3.70/4.02 (declare-sort tptp.set_Pr958786334691620121nt_int 0)
% 3.70/4.02 (declare-sort tptp.produc6575502325842934193n_assn 0)
% 3.70/4.02 (declare-sort tptp.list_P1934797086108301456_d_nat 0)
% 3.70/4.02 (declare-sort tptp.list_P8668085978031350508_d_int 0)
% 3.70/4.02 (declare-sort tptp.list_P5561950507774946575_c_nat 0)
% 3.70/4.02 (declare-sort tptp.list_P3071867362843219819_c_int 0)
% 3.70/4.02 (declare-sort tptp.list_P3064893870870525238_nat_d 0)
% 3.70/4.02 (declare-sort tptp.list_P2993859830824179253_nat_c 0)
% 3.70/4.02 (declare-sort tptp.set_Pr3276347184212964150_d_nat 0)
% 3.70/4.02 (declare-sort tptp.set_Pr786264039281237394_d_int 0)
% 3.70/4.02 (declare-sort tptp.set_Pr6903500605879609269_c_nat 0)
% 3.70/4.02 (declare-sort tptp.set_Pr4413417460947882513_c_int 0)
% 3.70/4.02 (declare-sort tptp.set_Pr4406443968975187932_nat_d 0)
% 3.70/4.02 (declare-sort tptp.set_Pr4335409928928841947_nat_c 0)
% 3.70/4.02 (declare-sort tptp.produc6271795597528267376eger_o 0)
% 3.70/4.02 (declare-sort tptp.heap_T5738788834812785303t_unit 0)
% 3.70/4.02 (declare-sort tptp.list_P8926467638345140077od_d_d 0)
% 3.70/4.02 (declare-sort tptp.list_P8855433598298794092od_d_c 0)
% 3.70/4.02 (declare-sort tptp.list_P338744602095350958od_c_d 0)
% 3.70/4.02 (declare-sort tptp.list_P267710562049004973od_c_c 0)
% 3.70/4.02 (declare-sort tptp.set_Product_prod_d_d 0)
% 3.70/4.02 (declare-sort tptp.set_Product_prod_d_c 0)
% 3.70/4.02 (declare-sort tptp.set_Product_prod_c_d 0)
% 3.70/4.02 (declare-sort tptp.set_Product_prod_c_c 0)
% 3.70/4.02 (declare-sort tptp.heap_e7401611519738050253t_unit 0)
% 3.70/4.02 (declare-sort tptp.product_prod_num_num 0)
% 3.70/4.02 (declare-sort tptp.product_prod_nat_nat 0)
% 3.70/4.02 (declare-sort tptp.product_prod_nat_int 0)
% 3.70/4.02 (declare-sort tptp.product_prod_int_nat 0)
% 3.70/4.02 (declare-sort tptp.product_prod_int_int 0)
% 3.70/4.02 (declare-sort tptp.set_Product_prod_o_o 0)
% 3.70/4.02 (declare-sort tptp.list_nat_nat 0)
% 3.70/4.02 (declare-sort tptp.filter_set_nat 0)
% 3.70/4.02 (declare-sort tptp.product_prod_d_nat 0)
% 3.70/4.02 (declare-sort tptp.product_prod_d_int 0)
% 3.70/4.02 (declare-sort tptp.product_prod_c_nat 0)
% 3.70/4.02 (declare-sort tptp.product_prod_c_int 0)
% 3.70/4.02 (declare-sort tptp.product_prod_nat_d 0)
% 3.70/4.02 (declare-sort tptp.product_prod_nat_c 0)
% 3.70/4.02 (declare-sort tptp.list_list_nat 0)
% 3.70/4.02 (declare-sort tptp.list_list_int 0)
% 3.70/4.02 (declare-sort tptp.list_set_nat 0)
% 3.70/4.02 (declare-sort tptp.list_set_int 0)
% 3.70/4.02 (declare-sort tptp.list_Code_integer 0)
% 3.70/4.02 (declare-sort tptp.set_set_nat 0)
% 3.70/4.02 (declare-sort tptp.set_Code_integer 0)
% 3.70/4.02 (declare-sort tptp.product_prod_d_d 0)
% 3.70/4.02 (declare-sort tptp.product_prod_d_c 0)
% 3.70/4.02 (declare-sort tptp.product_prod_c_d 0)
% 3.70/4.02 (declare-sort tptp.product_prod_c_c 0)
% 3.70/4.02 (declare-sort tptp.list_assn 0)
% 3.70/4.02 (declare-sort tptp.product_prod_o_o 0)
% 3.70/4.02 (declare-sort tptp.list_set_o 0)
% 3.70/4.02 (declare-sort tptp.set_assn 0)
% 3.70/4.02 (declare-sort tptp.filter_nat 0)
% 3.70/4.02 (declare-sort tptp.list_rat 0)
% 3.70/4.02 (declare-sort tptp.list_num 0)
% 3.70/4.02 (declare-sort tptp.list_nat 0)
% 3.70/4.02 (declare-sort tptp.list_int 0)
% 3.70/4.02 (declare-sort tptp.set_num 0)
% 3.70/4.02 (declare-sort tptp.set_nat 0)
% 3.70/4.02 (declare-sort tptp.set_int 0)
% 3.70/4.02 (declare-sort tptp.code_natural 0)
% 3.70/4.02 (declare-sort tptp.code_integer 0)
% 3.70/4.02 (declare-sort tptp.product_unit 0)
% 3.70/4.02 (declare-sort tptp.list_d 0)
% 3.70/4.02 (declare-sort tptp.list_c 0)
% 3.70/4.02 (declare-sort tptp.set_d 0)
% 3.70/4.02 (declare-sort tptp.set_c 0)
% 3.70/4.02 (declare-sort tptp.list_o 0)
% 3.70/4.02 (declare-sort tptp.assn 0)
% 3.70/4.02 (declare-sort tptp.set_o 0)
% 3.70/4.02 (declare-sort tptp.rat 0)
% 3.70/4.02 (declare-sort tptp.num 0)
% 3.70/4.02 (declare-sort tptp.nat 0)
% 3.70/4.02 (declare-sort tptp.int 0)
% 3.70/4.02 (declare-sort tptp.d 0)
% 3.70/4.02 (declare-sort tptp.c 0)
% 3.70/4.02 (declare-fun tptp.abs_assn ((-> tptp.produc3658429121746597890et_nat Bool)) tptp.assn)
% 3.70/4.02 (declare-fun tptp.rep_assn (tptp.assn tptp.produc3658429121746597890et_nat) Bool)
% 3.70/4.02 (declare-fun tptp.entails (tptp.assn tptp.assn) Bool)
% 3.70/4.02 (declare-fun tptp.entailst (tptp.assn tptp.assn) Bool)
% 3.70/4.02 (declare-fun tptp.in_range (tptp.produc3658429121746597890et_nat) Bool)
% 3.70/4.02 (declare-fun tptp.is_pure_assn (tptp.assn) Bool)
% 3.70/4.02 (declare-fun tptp.one_assn_raw (tptp.produc3658429121746597890et_nat) Bool)
% 3.70/4.02 (declare-fun tptp.proper ((-> tptp.produc3658429121746597890et_nat Bool)) Bool)
% 3.70/4.02 (declare-fun tptp.pure_assn (Bool) tptp.assn)
% 3.70/4.02 (declare-fun tptp.pure_a825153325127701367it_nat (Bool tptp.produc3658429121746597890et_nat) Bool)
% 3.70/4.02 (declare-fun tptp.relH (tptp.set_nat tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit) Bool)
% 3.70/4.02 (declare-fun tptp.times_assn_raw ((-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat) Bool)
% 3.70/4.02 (declare-fun tptp.times_assn_raw_rel (tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat) Bool)
% 3.70/4.02 (declare-fun tptp.wand_assn (tptp.assn tptp.assn) tptp.assn)
% 3.70/4.02 (declare-fun tptp.wand_raw ((-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat) Bool)
% 3.70/4.02 (declare-fun tptp.wand_raw_rel (tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat) Bool)
% 3.70/4.02 (declare-fun tptp.fi (tptp.list_P8527749157015355191n_assn tptp.assn tptp.assn tptp.assn tptp.assn tptp.assn) Bool)
% 3.70/4.02 (declare-fun tptp.fI_QUERY (tptp.assn tptp.assn tptp.assn) Bool)
% 3.70/4.02 (declare-fun tptp.fI_RESULT (tptp.list_P8527749157015355191n_assn tptp.assn tptp.assn tptp.assn) Bool)
% 3.70/4.02 (declare-fun tptp.sln () tptp.assn)
% 3.70/4.02 (declare-fun tptp.bNF_Cardinal_ctwo () tptp.set_Product_prod_o_o)
% 3.70/4.02 (declare-fun tptp.bNF_Cardinal_czero_o () tptp.set_Product_prod_o_o)
% 3.70/4.02 (declare-fun tptp.bNF_Ca3793111618940312692of_nat (tptp.set_nat) tptp.set_Pr1261947904930325089at_nat)
% 3.70/4.02 (declare-fun tptp.bNF_Ca8331644756375544342r_on_o (tptp.set_o tptp.set_Product_prod_o_o) Bool)
% 3.70/4.02 (declare-fun tptp.bNF_Ca8665028551170535155natLeq () tptp.set_Pr1261947904930325089at_nat)
% 3.70/4.02 (declare-fun tptp.bNF_Ca8459412986667044542atLess () tptp.set_Pr1261947904930325089at_nat)
% 3.70/4.02 (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)
% 3.70/4.02 (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)
% 3.70/4.02 (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)
% 3.70/4.02 (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)
% 3.70/4.02 (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)
% 3.70/4.02 (declare-fun tptp.bNF_re4705727531993890431at_o_o ((-> tptp.nat tptp.nat Bool) (-> Bool Bool Bool) (-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 3.70/4.02 (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)
% 3.70/4.02 (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)
% 3.70/4.02 (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)
% 3.70/4.02 (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)
% 3.70/4.02 (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)
% 3.70/4.02 (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)
% 3.70/4.02 (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)
% 3.70/4.02 (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)
% 3.70/4.02 (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)
% 3.70/4.02 (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)
% 3.70/4.02 (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)
% 3.70/4.02 (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)
% 3.70/4.02 (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)
% 3.70/4.02 (declare-fun tptp.bNF_We2654380646378065620so_o_o () tptp.set_Pr1932065953672099015od_o_o)
% 3.70/4.02 (declare-fun tptp.bNF_We5258908940166488438at_nat () tptp.set_Pr4329608150637261639at_nat)
% 3.70/4.02 (declare-fun tptp.bNF_We8182288985678559134_o_nat () tptp.set_Pr457366540195662369at_nat)
% 3.70/4.02 (declare-fun tptp.bNF_We3818239936649020644el_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.binomial (tptp.nat tptp.nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.bit_and_int_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 3.70/4.02 (declare-fun tptp.bit_concat_bit (tptp.nat tptp.int tptp.int) tptp.int)
% 3.70/4.02 (declare-fun tptp.bit_se725231765392027082nd_int (tptp.int tptp.int) tptp.int)
% 3.70/4.02 (declare-fun tptp.bit_se2002935070580805687sk_nat (tptp.nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.bit_se2923211474154528505it_int (tptp.nat tptp.int) tptp.int)
% 3.70/4.02 (declare-fun tptp.bit_se2925701944663578781it_nat (tptp.nat tptp.nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.bit_se1146084159140164899it_int (tptp.int tptp.nat) Bool)
% 3.70/4.02 (declare-fun tptp.code_bit_cut_integer (tptp.code_integer) tptp.produc6271795597528267376eger_o)
% 3.70/4.02 (declare-fun tptp.code_divmod_abs (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 3.70/4.02 (declare-fun tptp.code_divmod_integer (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 3.70/4.02 (declare-fun tptp.code_nat_of_integer (tptp.code_integer) tptp.nat)
% 3.70/4.02 (declare-fun tptp.code_nat_of_natural (tptp.code_natural) tptp.nat)
% 3.70/4.02 (declare-fun tptp.code_natural_of_nat (tptp.nat) tptp.code_natural)
% 3.70/4.02 (declare-fun tptp.complete_Inf_Inf_nat (tptp.set_nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.comple7806235888213564991et_nat (tptp.set_set_nat) tptp.set_nat)
% 3.70/4.02 (declare-fun tptp.complete_Sup_Sup_nat (tptp.set_nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.adjust_div (tptp.product_prod_int_int) tptp.int)
% 3.70/4.02 (declare-fun tptp.divmod_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 3.70/4.02 (declare-fun tptp.eucl_rel_int (tptp.int tptp.int tptp.product_prod_int_int) Bool)
% 3.70/4.02 (declare-fun tptp.unique5706413561485394159nteger (tptp.produc8923325533196201883nteger) Bool)
% 3.70/4.02 (declare-fun tptp.unique6319869463603278526ux_int (tptp.product_prod_int_int) Bool)
% 3.70/4.02 (declare-fun tptp.unique6322359934112328802ux_nat (tptp.product_prod_nat_nat) Bool)
% 3.70/4.02 (declare-fun tptp.unique3479559517661332726nteger (tptp.num tptp.num) tptp.produc8923325533196201883nteger)
% 3.70/4.02 (declare-fun tptp.unique5052692396658037445od_int (tptp.num tptp.num) tptp.product_prod_int_int)
% 3.70/4.02 (declare-fun tptp.unique5055182867167087721od_nat (tptp.num tptp.num) tptp.product_prod_nat_nat)
% 3.70/4.02 (declare-fun tptp.unique4921790084139445826nteger (tptp.num tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 3.70/4.02 (declare-fun tptp.unique5024387138958732305ep_int (tptp.num tptp.product_prod_int_int) tptp.product_prod_int_int)
% 3.70/4.02 (declare-fun tptp.unique5026877609467782581ep_nat (tptp.num tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 3.70/4.02 (declare-fun tptp.semiri1408675320244567234ct_nat (tptp.nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.inverse_inverse_rat (tptp.rat) tptp.rat)
% 3.70/4.02 (declare-fun tptp.at_top_nat () tptp.filter_nat)
% 3.70/4.02 (declare-fun tptp.cofinite_nat () tptp.filter_nat)
% 3.70/4.02 (declare-fun tptp.eventually_nat ((-> tptp.nat Bool) tptp.filter_nat) Bool)
% 3.70/4.02 (declare-fun tptp.eventu1038000079068216329at_nat ((-> tptp.product_prod_nat_nat Bool) tptp.filter1242075044329608583at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.filterlim_nat_nat ((-> tptp.nat tptp.nat) tptp.filter_nat tptp.filter_nat) Bool)
% 3.70/4.02 (declare-fun tptp.filter3212408913953519116et_nat ((-> tptp.nat tptp.set_nat) tptp.filter_set_nat tptp.filter_nat) Bool)
% 3.70/4.02 (declare-fun tptp.finite3254316476582989077op_nat (tptp.set_nat) tptp.filter_set_nat)
% 3.70/4.02 (declare-fun tptp.frequently_nat ((-> tptp.nat Bool) tptp.filter_nat) Bool)
% 3.70/4.02 (declare-fun tptp.prod_filter_nat_nat (tptp.filter_nat tptp.filter_nat) tptp.filter1242075044329608583at_nat)
% 3.70/4.02 (declare-fun tptp.finite_card_nat (tptp.set_nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.finite6017078050557962740nteger (tptp.set_Code_integer) Bool)
% 3.70/4.02 (declare-fun tptp.finite_finite_nat (tptp.set_nat) Bool)
% 3.70/4.02 (declare-fun tptp.finite6177210948735845034at_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 3.70/4.02 (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)
% 3.70/4.02 (declare-fun tptp.comp_o_o_int ((-> Bool Bool) (-> tptp.int Bool) tptp.int) Bool)
% 3.70/4.02 (declare-fun tptp.comp_o_o_nat ((-> Bool Bool) (-> tptp.nat Bool) tptp.nat) Bool)
% 3.70/4.02 (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)
% 3.70/4.02 (declare-fun tptp.id_o (Bool) Bool)
% 3.70/4.02 (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)
% 3.70/4.02 (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)
% 3.70/4.02 (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)
% 3.70/4.02 (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)
% 3.70/4.02 (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)
% 3.70/4.02 (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)
% 3.70/4.02 (declare-fun tptp.strict1292158309912662752at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 3.70/4.02 (declare-fun tptp.fun_max_strict () tptp.set_Pr4329608150637261639at_nat)
% 3.70/4.02 (declare-fun tptp.fun_max_weak () tptp.set_Pr4329608150637261639at_nat)
% 3.70/4.02 (declare-fun tptp.fun_min_strict () tptp.set_Pr4329608150637261639at_nat)
% 3.70/4.02 (declare-fun tptp.fun_min_weak () tptp.set_Pr4329608150637261639at_nat)
% 3.70/4.02 (declare-fun tptp.fun_pair_leq () tptp.set_Pr8693737435421807431at_nat)
% 3.70/4.02 (declare-fun tptp.fun_pair_less () tptp.set_Pr8693737435421807431at_nat)
% 3.70/4.02 (declare-fun tptp.fun_re7357418987779152907at_nat (tptp.produc4193628355235574503at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.fun_re2478310338295953701at_nat (tptp.produc1319942482725812455at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.gcd_Gcd_int (tptp.set_int) tptp.int)
% 3.70/4.02 (declare-fun tptp.gcd_Gcd_nat (tptp.set_nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.gcd_Lcm_int (tptp.set_int) tptp.int)
% 3.70/4.02 (declare-fun tptp.gcd_Lcm_nat (tptp.set_nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.bezw (tptp.nat tptp.nat) tptp.product_prod_int_int)
% 3.70/4.02 (declare-fun tptp.bezw_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 3.70/4.02 (declare-fun tptp.gcd_gcd_int (tptp.int tptp.int) tptp.int)
% 3.70/4.02 (declare-fun tptp.gcd_gcd_nat (tptp.nat tptp.nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.gcd_lcm_int (tptp.int tptp.int) tptp.int)
% 3.70/4.02 (declare-fun tptp.gcd_lcm_nat (tptp.nat tptp.nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.gcd_nat_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 3.70/4.02 (declare-fun tptp.abs_abs_Code_integer (tptp.code_integer) tptp.code_integer)
% 3.70/4.02 (declare-fun tptp.abs_abs_int (tptp.int) tptp.int)
% 3.70/4.02 (declare-fun tptp.abs_abs_rat (tptp.rat) tptp.rat)
% 3.70/4.02 (declare-fun tptp.minus_minus_assn (tptp.assn tptp.assn) tptp.assn)
% 3.70/4.02 (declare-fun tptp.minus_8373710615458151222nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 3.70/4.02 (declare-fun tptp.minus_minus_int (tptp.int tptp.int) tptp.int)
% 3.70/4.02 (declare-fun tptp.minus_4286766774447292334at_nat (tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat) tptp.multis2468970476368604999at_nat)
% 3.70/4.02 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.minus_minus_rat (tptp.rat tptp.rat) tptp.rat)
% 3.70/4.02 (declare-fun tptp.minus_1801376950450012436_nat_o (tptp.set_Pr4532377907799695533_nat_o tptp.set_Pr4532377907799695533_nat_o) tptp.set_Pr4532377907799695533_nat_o)
% 3.70/4.02 (declare-fun tptp.minus_minus_set_o (tptp.set_o tptp.set_o) tptp.set_o)
% 3.70/4.02 (declare-fun tptp.minus_minus_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 3.70/4.02 (declare-fun tptp.minus_minus_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 3.70/4.02 (declare-fun tptp.minus_2301194108115264760n_assn (tptp.set_Pr5949110396991348497n_assn tptp.set_Pr5949110396991348497n_assn) tptp.set_Pr5949110396991348497n_assn)
% 3.70/4.02 (declare-fun tptp.minus_1356011639430497352at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 3.70/4.02 (declare-fun tptp.minus_3314409938677909166at_nat (tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat) tptp.set_Pr4329608150637261639at_nat)
% 3.70/4.02 (declare-fun tptp.minus_minus_set_c (tptp.set_c tptp.set_c) tptp.set_c)
% 3.70/4.02 (declare-fun tptp.minus_minus_set_d (tptp.set_d tptp.set_d) tptp.set_d)
% 3.70/4.02 (declare-fun tptp.one_one_assn () tptp.assn)
% 3.70/4.02 (declare-fun tptp.one_one_Code_integer () tptp.code_integer)
% 3.70/4.02 (declare-fun tptp.one_one_Code_natural () tptp.code_natural)
% 3.70/4.02 (declare-fun tptp.one_one_int () tptp.int)
% 3.70/4.02 (declare-fun tptp.one_one_nat () tptp.nat)
% 3.70/4.02 (declare-fun tptp.one_one_rat () tptp.rat)
% 3.70/4.02 (declare-fun tptp.plus_p5714425477246183910nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 3.70/4.02 (declare-fun tptp.plus_p4538020629002901425atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 3.70/4.02 (declare-fun tptp.plus_plus_int (tptp.int tptp.int) tptp.int)
% 3.70/4.02 (declare-fun tptp.plus_p7104986032573967614at_nat (tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat) tptp.multis2468970476368604999at_nat)
% 3.70/4.02 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.plus_plus_num (tptp.num tptp.num) tptp.num)
% 3.70/4.02 (declare-fun tptp.plus_plus_rat (tptp.rat tptp.rat) tptp.rat)
% 3.70/4.02 (declare-fun tptp.sgn_sgn_Code_integer (tptp.code_integer) tptp.code_integer)
% 3.70/4.02 (declare-fun tptp.sgn_sgn_int (tptp.int) tptp.int)
% 3.70/4.02 (declare-fun tptp.sgn_sgn_rat (tptp.rat) tptp.rat)
% 3.70/4.02 (declare-fun tptp.times_times_assn (tptp.assn tptp.assn) tptp.assn)
% 3.70/4.02 (declare-fun tptp.times_3573771949741848930nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 3.70/4.02 (declare-fun tptp.times_2397367101498566445atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 3.70/4.02 (declare-fun tptp.times_times_int (tptp.int tptp.int) tptp.int)
% 3.70/4.02 (declare-fun tptp.times_times_nat (tptp.nat tptp.nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.times_times_rat (tptp.rat tptp.rat) tptp.rat)
% 3.70/4.02 (declare-fun tptp.uminus_uminus_assn (tptp.assn) tptp.assn)
% 3.70/4.02 (declare-fun tptp.uminus1351360451143612070nteger (tptp.code_integer) tptp.code_integer)
% 3.70/4.02 (declare-fun tptp.uminus_uminus_int (tptp.int) tptp.int)
% 3.70/4.02 (declare-fun tptp.uminus_uminus_rat (tptp.rat) tptp.rat)
% 3.70/4.02 (declare-fun tptp.zero_z3403309356797280102nteger () tptp.code_integer)
% 3.70/4.02 (declare-fun tptp.zero_z2226904508553997617atural () tptp.code_natural)
% 3.70/4.02 (declare-fun tptp.zero_zero_int () tptp.int)
% 3.70/4.02 (declare-fun tptp.zero_z1048942125864253310at_nat () tptp.multis2468970476368604999at_nat)
% 3.70/4.02 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 3.70/4.02 (declare-fun tptp.zero_zero_rat () tptp.rat)
% 3.70/4.02 (declare-fun tptp.groups3542108847815614940at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.lim_Product_unit (tptp.heap_e7401611519738050253t_unit) tptp.nat)
% 3.70/4.02 (declare-fun tptp.heap_T6183433275982383450t_unit ((-> tptp.heap_e7401611519738050253t_unit tptp.option8956607266484857688it_nat)) tptp.heap_T5738788834812785303t_unit)
% 3.70/4.02 (declare-fun tptp.heap_T875086893843062177t_unit (tptp.heap_T5738788834812785303t_unit tptp.heap_e7401611519738050253t_unit) tptp.option8956607266484857688it_nat)
% 3.70/4.02 (declare-fun tptp.heap_Time_wait (tptp.nat) tptp.heap_T5738788834812785303t_unit)
% 3.70/4.02 (declare-fun tptp.hoare_8945653483474564448t_unit (tptp.assn tptp.heap_T5738788834812785303t_unit (-> tptp.product_unit tptp.assn)) Bool)
% 3.70/4.02 (declare-fun tptp.hoare_new_addrs (tptp.heap_e7401611519738050253t_unit tptp.set_nat tptp.heap_e7401611519738050253t_unit) tptp.set_nat)
% 3.70/4.02 (declare-fun tptp.if_assn (Bool tptp.assn tptp.assn) tptp.assn)
% 3.70/4.02 (declare-fun tptp.if_Code_integer (Bool tptp.code_integer tptp.code_integer) tptp.code_integer)
% 3.70/4.02 (declare-fun tptp.if_filter_nat (Bool tptp.filter_nat tptp.filter_nat) tptp.filter_nat)
% 3.70/4.02 (declare-fun tptp.if_int (Bool tptp.int tptp.int) tptp.int)
% 3.70/4.02 (declare-fun tptp.if_lis2904118647880296857_nat_o (Bool tptp.list_P7985473006766602707_nat_o tptp.list_P7985473006766602707_nat_o) tptp.list_P7985473006766602707_nat_o)
% 3.70/4.02 (declare-fun tptp.if_list_int (Bool tptp.list_int tptp.list_int) tptp.list_int)
% 3.70/4.02 (declare-fun tptp.if_list_nat (Bool tptp.list_nat tptp.list_nat) tptp.list_nat)
% 3.70/4.02 (declare-fun tptp.if_lis7173127979115136509n_assn (Bool tptp.list_P8527749157015355191n_assn tptp.list_P8527749157015355191n_assn) tptp.list_P8527749157015355191n_assn)
% 3.70/4.02 (declare-fun tptp.if_lis9186351972506106189at_nat (Bool tptp.list_P6011104703257516679at_nat tptp.list_P6011104703257516679at_nat) tptp.list_P6011104703257516679at_nat)
% 3.70/4.02 (declare-fun tptp.if_lis7508161100780771379at_nat (Bool tptp.list_P5464809261938338413at_nat tptp.list_P5464809261938338413at_nat) tptp.list_P5464809261938338413at_nat)
% 3.70/4.02 (declare-fun tptp.if_nat (Bool tptp.nat tptp.nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.if_Pro5737122678794959658eger_o (Bool tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o) tptp.produc6271795597528267376eger_o)
% 3.70/4.02 (declare-fun tptp.if_Pro6119634080678213985nteger (Bool tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 3.70/4.02 (declare-fun tptp.if_Pro3027730157355071871nt_int (Bool tptp.product_prod_int_int tptp.product_prod_int_int) tptp.product_prod_int_int)
% 3.70/4.02 (declare-fun tptp.if_Pro6206227464963214023at_nat (Bool tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 3.70/4.02 (declare-fun tptp.if_set_int (Bool tptp.set_int tptp.set_int) tptp.set_int)
% 3.70/4.02 (declare-fun tptp.if_set_nat (Bool tptp.set_nat tptp.set_nat) tptp.set_nat)
% 3.70/4.02 (declare-fun tptp.infini8530281810654367211te_nat (tptp.set_nat tptp.nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.abs_Integ (tptp.product_prod_nat_nat) tptp.int)
% 3.70/4.02 (declare-fun tptp.rep_Integ (tptp.int) tptp.product_prod_nat_nat)
% 3.70/4.02 (declare-fun tptp.intrel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 3.70/4.02 (declare-fun tptp.nat2 (tptp.int) tptp.nat)
% 3.70/4.02 (declare-fun tptp.pcr_int (tptp.product_prod_nat_nat tptp.int) Bool)
% 3.70/4.02 (declare-fun tptp.ring_1_of_int_rat (tptp.int) tptp.rat)
% 3.70/4.02 (declare-fun tptp.inf_inf_assn (tptp.assn tptp.assn) tptp.assn)
% 3.70/4.02 (declare-fun tptp.inf_inf_filter_nat (tptp.filter_nat tptp.filter_nat) tptp.filter_nat)
% 3.70/4.02 (declare-fun tptp.inf_inf_int (tptp.int tptp.int) tptp.int)
% 3.70/4.02 (declare-fun tptp.inf_inf_nat (tptp.nat tptp.nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.inf_in1906310914598751387_nat_o (tptp.set_Pr4532377907799695533_nat_o tptp.set_Pr4532377907799695533_nat_o) tptp.set_Pr4532377907799695533_nat_o)
% 3.70/4.02 (declare-fun tptp.inf_inf_set_o (tptp.set_o tptp.set_o) tptp.set_o)
% 3.70/4.02 (declare-fun tptp.inf_inf_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 3.70/4.02 (declare-fun tptp.inf_inf_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 3.70/4.02 (declare-fun tptp.inf_in2572325071724192079at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 3.70/4.02 (declare-fun tptp.inf_in7913087082777306421at_nat (tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat) tptp.set_Pr4329608150637261639at_nat)
% 3.70/4.02 (declare-fun tptp.semila1623282765462674594er_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat (-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool)) Bool)
% 3.70/4.02 (declare-fun tptp.sup_sup_assn (tptp.assn tptp.assn) tptp.assn)
% 3.70/4.02 (declare-fun tptp.sup_sup_filter_nat (tptp.filter_nat tptp.filter_nat) tptp.filter_nat)
% 3.70/4.02 (declare-fun tptp.sup_sup_int (tptp.int tptp.int) tptp.int)
% 3.70/4.02 (declare-fun tptp.sup_sup_nat (tptp.nat tptp.nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.sup_su5209123915105501825_nat_o (tptp.set_Pr4532377907799695533_nat_o tptp.set_Pr4532377907799695533_nat_o) tptp.set_Pr4532377907799695533_nat_o)
% 3.70/4.02 (declare-fun tptp.sup_sup_set_o (tptp.set_o tptp.set_o) tptp.set_o)
% 3.70/4.02 (declare-fun tptp.sup_sup_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 3.70/4.02 (declare-fun tptp.sup_sup_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 3.70/4.02 (declare-fun tptp.sup_su5769328420594410459od_o_o (tptp.set_Product_prod_o_o tptp.set_Product_prod_o_o) tptp.set_Product_prod_o_o)
% 3.70/4.02 (declare-fun tptp.sup_su1735938885662425829n_assn (tptp.set_Pr5949110396991348497n_assn tptp.set_Pr5949110396991348497n_assn) tptp.set_Pr5949110396991348497n_assn)
% 3.70/4.02 (declare-fun tptp.sup_su6327502436637775413at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 3.70/4.02 (declare-fun tptp.sup_su6664651903789602459at_nat (tptp.set_Pr5564308138774400199at_nat tptp.set_Pr5564308138774400199at_nat) tptp.set_Pr5564308138774400199at_nat)
% 3.70/4.02 (declare-fun tptp.sup_su5525570899277871387at_nat (tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat) tptp.set_Pr4329608150637261639at_nat)
% 3.70/4.02 (declare-fun tptp.sup_su3642409539654194069at_nat (tptp.set_se7855581050983116737at_nat tptp.set_se7855581050983116737at_nat) tptp.set_se7855581050983116737at_nat)
% 3.70/4.02 (declare-fun tptp.lattic8265883725875713057ax_nat (tptp.set_nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.all_interval_int ((-> tptp.int Bool) tptp.int tptp.int) Bool)
% 3.70/4.02 (declare-fun tptp.all_interval_nat ((-> tptp.nat Bool) tptp.nat tptp.nat) Bool)
% 3.70/4.02 (declare-fun tptp.append_int (tptp.list_int tptp.list_int) tptp.list_int)
% 3.70/4.02 (declare-fun tptp.append_nat (tptp.list_nat tptp.list_nat) tptp.list_nat)
% 3.70/4.02 (declare-fun tptp.butlas8287983287669047583_nat_o (tptp.list_P7985473006766602707_nat_o) tptp.list_P7985473006766602707_nat_o)
% 3.70/4.02 (declare-fun tptp.butlast_int (tptp.list_int) tptp.list_int)
% 3.70/4.02 (declare-fun tptp.butlast_nat (tptp.list_nat) tptp.list_nat)
% 3.70/4.02 (declare-fun tptp.butlas3012047794866324995n_assn (tptp.list_P8527749157015355191n_assn) tptp.list_P8527749157015355191n_assn)
% 3.70/4.02 (declare-fun tptp.butlas5569151904373679443at_nat (tptp.list_P6011104703257516679at_nat) tptp.list_P6011104703257516679at_nat)
% 3.70/4.02 (declare-fun tptp.butlas2561766218336428473at_nat (tptp.list_P5464809261938338413at_nat) tptp.list_P5464809261938338413at_nat)
% 3.70/4.02 (declare-fun tptp.butlast_c (tptp.list_c) tptp.list_c)
% 3.70/4.02 (declare-fun tptp.butlast_d (tptp.list_d) tptp.list_d)
% 3.70/4.02 (declare-fun tptp.coset_9017067850271954240_nat_o (tptp.list_P7985473006766602707_nat_o) tptp.set_Pr4532377907799695533_nat_o)
% 3.70/4.02 (declare-fun tptp.coset_o (tptp.list_o) tptp.set_o)
% 3.70/4.02 (declare-fun tptp.coset_int (tptp.list_int) tptp.set_int)
% 3.70/4.02 (declare-fun tptp.coset_nat (tptp.list_nat) tptp.set_nat)
% 3.70/4.02 (declare-fun tptp.coset_703488708621576356n_assn (tptp.list_P8527749157015355191n_assn) tptp.set_Pr5949110396991348497n_assn)
% 3.70/4.02 (declare-fun tptp.coset_6809516720700967924at_nat (tptp.list_P6011104703257516679at_nat) tptp.set_Pr1261947904930325089at_nat)
% 3.70/4.02 (declare-fun tptp.coset_5307619257043544794at_nat (tptp.list_P5464809261938338413at_nat) tptp.set_Pr4329608150637261639at_nat)
% 3.70/4.02 (declare-fun tptp.count_5695430372156137289_nat_o (tptp.list_P7985473006766602707_nat_o (-> tptp.produc3658429121746597890et_nat Bool)) tptp.nat)
% 3.70/4.02 (declare-fun tptp.count_list_int (tptp.list_int tptp.int) tptp.nat)
% 3.70/4.02 (declare-fun tptp.count_list_nat (tptp.list_nat tptp.nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.count_2530312006313534765n_assn (tptp.list_P8527749157015355191n_assn tptp.produc6575502325842934193n_assn) tptp.nat)
% 3.70/4.02 (declare-fun tptp.count_4203492906077236349at_nat (tptp.list_P6011104703257516679at_nat tptp.product_prod_nat_nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.count_1483299019173949923at_nat (tptp.list_P5464809261938338413at_nat tptp.produc3843707927480180839at_nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.distin299582740263731014_nat_o (tptp.list_P7985473006766602707_nat_o) Bool)
% 3.70/4.02 (declare-fun tptp.distinct_o (tptp.list_o) Bool)
% 3.70/4.02 (declare-fun tptp.distin1543349897113766820nteger (tptp.list_Code_integer) Bool)
% 3.70/4.02 (declare-fun tptp.distinct_int (tptp.list_int) Bool)
% 3.70/4.02 (declare-fun tptp.distinct_nat (tptp.list_nat) Bool)
% 3.70/4.02 (declare-fun tptp.distinct_num (tptp.list_num) Bool)
% 3.70/4.02 (declare-fun tptp.distin4809818325527169450n_assn (tptp.list_P8527749157015355191n_assn) Bool)
% 3.70/4.02 (declare-fun tptp.distin3744728255968310194nt_int (tptp.list_P5707943133018811711nt_int) Bool)
% 3.70/4.02 (declare-fun tptp.distin7922579275477506902nt_nat (tptp.list_P8198026277950538467nt_nat) Bool)
% 3.70/4.02 (declare-fun tptp.distin2745374544067255638at_int (tptp.list_P3521021558325789923at_int) Bool)
% 3.70/4.02 (declare-fun tptp.distin6923225563576452346at_nat (tptp.list_P6011104703257516679at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.distin5355857245021852384at_nat (tptp.list_P5464809261938338413at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.distinct_c (tptp.list_c) Bool)
% 3.70/4.02 (declare-fun tptp.distinct_d (tptp.list_d) Bool)
% 3.70/4.02 (declare-fun tptp.drop_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 3.70/4.02 (declare-fun tptp.enumerate_int (tptp.nat tptp.list_int) tptp.list_P3521021558325789923at_int)
% 3.70/4.02 (declare-fun tptp.enumerate_nat (tptp.nat tptp.list_nat) tptp.list_P6011104703257516679at_nat)
% 3.70/4.02 (declare-fun tptp.enumer9200277086812776726n_assn (tptp.nat tptp.list_P8527749157015355191n_assn) tptp.list_P7711101519850957926n_assn)
% 3.70/4.02 (declare-fun tptp.enumerate_c (tptp.nat tptp.list_c) tptp.list_P2993859830824179253_nat_c)
% 3.70/4.02 (declare-fun tptp.enumerate_d (tptp.nat tptp.list_d) tptp.list_P3064893870870525238_nat_d)
% 3.70/4.02 (declare-fun tptp.filter_nat2 ((-> tptp.nat Bool) tptp.list_nat) tptp.list_nat)
% 3.70/4.02 (declare-fun tptp.fold_int_int ((-> tptp.int tptp.int tptp.int) tptp.list_int tptp.int) tptp.int)
% 3.70/4.02 (declare-fun tptp.fold_nat_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.list_nat tptp.nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.foldl_assn_assn ((-> tptp.assn tptp.assn tptp.assn) tptp.assn tptp.list_assn) tptp.assn)
% 3.70/4.02 (declare-fun tptp.foldl_1542389171486570077nteger ((-> tptp.code_integer tptp.code_integer tptp.code_integer) tptp.code_integer tptp.list_Code_integer) tptp.code_integer)
% 3.70/4.02 (declare-fun tptp.foldl_int_int ((-> tptp.int tptp.int tptp.int) tptp.int tptp.list_int) tptp.int)
% 3.70/4.02 (declare-fun tptp.foldl_nat_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.list_nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.foldl_rat_rat ((-> tptp.rat tptp.rat tptp.rat) tptp.rat tptp.list_rat) tptp.rat)
% 3.70/4.02 (declare-fun tptp.foldl_set_o_set_o ((-> tptp.set_o tptp.set_o tptp.set_o) tptp.set_o tptp.list_set_o) tptp.set_o)
% 3.70/4.02 (declare-fun tptp.foldl_6819690284573351271et_int ((-> tptp.set_int tptp.set_int tptp.set_int) tptp.set_int tptp.list_set_int) tptp.set_int)
% 3.70/4.02 (declare-fun tptp.foldl_4988731653086973103et_nat ((-> tptp.set_nat tptp.set_nat tptp.set_nat) tptp.set_nat tptp.list_set_nat) tptp.set_nat)
% 3.70/4.02 (declare-fun tptp.foldl_5307762784932486881at_nat ((-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat tptp.list_s1210847774152347623at_nat) tptp.set_Pr1261947904930325089at_nat)
% 3.70/4.02 (declare-fun tptp.foldl_4541198706405875041at_nat ((-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat) tptp.set_Pr4329608150637261639at_nat tptp.list_s4242580248156217677at_nat) tptp.set_Pr4329608150637261639at_nat)
% 3.70/4.02 (declare-fun tptp.foldr_assn_assn ((-> tptp.assn tptp.assn tptp.assn) tptp.list_assn tptp.assn) tptp.assn)
% 3.70/4.02 (declare-fun tptp.insert8021100735160035049_nat_o ((-> tptp.produc3658429121746597890et_nat Bool) tptp.list_P7985473006766602707_nat_o) tptp.list_P7985473006766602707_nat_o)
% 3.70/4.02 (declare-fun tptp.insert_o (Bool tptp.list_o) tptp.list_o)
% 3.70/4.02 (declare-fun tptp.insert_int (tptp.int tptp.list_int) tptp.list_int)
% 3.70/4.02 (declare-fun tptp.insert_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 3.70/4.02 (declare-fun tptp.insert3246601298802261197n_assn (tptp.produc6575502325842934193n_assn tptp.list_P8527749157015355191n_assn) tptp.list_P8527749157015355191n_assn)
% 3.70/4.02 (declare-fun tptp.insert8944034826898310173at_nat (tptp.product_prod_nat_nat tptp.list_P6011104703257516679at_nat) tptp.list_P6011104703257516679at_nat)
% 3.70/4.02 (declare-fun tptp.insert4149901806602606979at_nat (tptp.produc3843707927480180839at_nat tptp.list_P5464809261938338413at_nat) tptp.list_P5464809261938338413at_nat)
% 3.70/4.02 (declare-fun tptp.last_nat (tptp.list_nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.lenlex_int (tptp.set_Pr958786334691620121nt_int) tptp.set_Pr765067013931698361st_int)
% 3.70/4.02 (declare-fun tptp.lenlex_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr3451248702717554689st_nat)
% 3.70/4.02 (declare-fun tptp.lenlex6671093235567761724n_assn (tptp.set_Pr8116311503512020807n_assn) tptp.set_Pr6863447823992824007n_assn)
% 3.70/4.02 (declare-fun tptp.lenlex1357538814655152620at_nat (tptp.set_Pr4329608150637261639at_nat) tptp.set_Pr4333006031979791559at_nat)
% 3.70/4.02 (declare-fun tptp.lenlex_c (tptp.set_Product_prod_c_c) tptp.set_Pr2058341694840537735list_c)
% 3.70/4.02 (declare-fun tptp.lenlex_d (tptp.set_Product_prod_d_d) tptp.set_Pr5674772971416283335list_d)
% 3.70/4.02 (declare-fun tptp.lex_int (tptp.set_Pr958786334691620121nt_int) tptp.set_Pr765067013931698361st_int)
% 3.70/4.02 (declare-fun tptp.lex_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr3451248702717554689st_nat)
% 3.70/4.02 (declare-fun tptp.lex_Pr7559194461235888923n_assn (tptp.set_Pr8116311503512020807n_assn) tptp.set_Pr6863447823992824007n_assn)
% 3.70/4.02 (declare-fun tptp.lex_se2245640040323279819at_nat (tptp.set_Pr4329608150637261639at_nat) tptp.set_Pr4333006031979791559at_nat)
% 3.70/4.02 (declare-fun tptp.lex_c (tptp.set_Product_prod_c_c) tptp.set_Pr2058341694840537735list_c)
% 3.70/4.02 (declare-fun tptp.lex_d (tptp.set_Product_prod_d_d) tptp.set_Pr5674772971416283335list_d)
% 3.70/4.02 (declare-fun tptp.lexn_int (tptp.set_Pr958786334691620121nt_int tptp.nat) tptp.set_Pr765067013931698361st_int)
% 3.70/4.02 (declare-fun tptp.lexn_nat (tptp.set_Pr1261947904930325089at_nat tptp.nat) tptp.set_Pr3451248702717554689st_nat)
% 3.70/4.02 (declare-fun tptp.lexn_c (tptp.set_Product_prod_c_c tptp.nat) tptp.set_Pr2058341694840537735list_c)
% 3.70/4.02 (declare-fun tptp.lexn_d (tptp.set_Product_prod_d_d tptp.nat) tptp.set_Pr5674772971416283335list_d)
% 3.70/4.02 (declare-fun tptp.linord1735203802627413978nt_int ((-> tptp.int tptp.int) tptp.list_int) tptp.list_int)
% 3.70/4.02 (declare-fun tptp.linord738340561235409698at_nat ((-> tptp.nat tptp.nat) tptp.list_nat) tptp.list_nat)
% 3.70/4.02 (declare-fun tptp.linord2614967742042102400et_nat (tptp.set_nat) tptp.list_nat)
% 3.70/4.02 (declare-fun tptp.cons_nat_nat ((-> tptp.nat tptp.nat) tptp.list_nat_nat) tptp.list_nat_nat)
% 3.70/4.02 (declare-fun tptp.cons_P6219271836124797827_nat_o ((-> tptp.produc3658429121746597890et_nat Bool) tptp.list_P7985473006766602707_nat_o) tptp.list_P7985473006766602707_nat_o)
% 3.70/4.02 (declare-fun tptp.cons_s2538900923071588440at_nat ((-> tptp.set_Pr1261947904930325089at_nat tptp.nat) tptp.list_s9130966667114977576at_nat) tptp.list_s9130966667114977576at_nat)
% 3.70/4.02 (declare-fun tptp.cons_o (Bool tptp.list_o) tptp.list_o)
% 3.70/4.02 (declare-fun tptp.cons_assn (tptp.assn tptp.list_assn) tptp.list_assn)
% 3.70/4.02 (declare-fun tptp.cons_Code_integer (tptp.code_integer tptp.list_Code_integer) tptp.list_Code_integer)
% 3.70/4.02 (declare-fun tptp.cons_int (tptp.int tptp.list_int) tptp.list_int)
% 3.70/4.02 (declare-fun tptp.cons_list_int (tptp.list_int tptp.list_list_int) tptp.list_list_int)
% 3.70/4.02 (declare-fun tptp.cons_list_nat (tptp.list_nat tptp.list_list_nat) tptp.list_list_nat)
% 3.70/4.02 (declare-fun tptp.cons_l2423627976422276333n_assn (tptp.list_P8527749157015355191n_assn tptp.list_l6351802567095793725n_assn) tptp.list_l6351802567095793725n_assn)
% 3.70/4.02 (declare-fun tptp.cons_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 3.70/4.02 (declare-fun tptp.cons_num (tptp.num tptp.list_num) tptp.list_num)
% 3.70/4.02 (declare-fun tptp.cons_P2971678138204555879n_assn (tptp.produc6575502325842934193n_assn tptp.list_P8527749157015355191n_assn) tptp.list_P8527749157015355191n_assn)
% 3.70/4.02 (declare-fun tptp.cons_P3334398858971670639nt_int (tptp.product_prod_int_int tptp.list_P5707943133018811711nt_int) tptp.list_P5707943133018811711nt_int)
% 3.70/4.02 (declare-fun tptp.cons_P7512249878480867347nt_nat (tptp.product_prod_int_nat tptp.list_P8198026277950538467nt_nat) tptp.list_P8198026277950538467nt_nat)
% 3.70/4.02 (declare-fun tptp.cons_P8828502514829229636n_assn (tptp.produc3167338625816234618n_assn tptp.list_P1495281457390866698n_assn) tptp.list_P1495281457390866698n_assn)
% 3.70/4.02 (declare-fun tptp.cons_P2335045147070616083at_int (tptp.product_prod_nat_int tptp.list_P3521021558325789923at_int) tptp.list_P3521021558325789923at_int)
% 3.70/4.02 (declare-fun tptp.cons_P6512896166579812791at_nat (tptp.product_prod_nat_nat tptp.list_P6011104703257516679at_nat) tptp.list_P6011104703257516679at_nat)
% 3.70/4.02 (declare-fun tptp.cons_P7068465851076118432n_assn (tptp.produc1407301962063123414n_assn tptp.list_P7711101519850957926n_assn) tptp.list_P7711101519850957926n_assn)
% 3.70/4.02 (declare-fun tptp.cons_P5155970366129889750sn_int (tptp.produc8718178513971670540sn_int tptp.list_P421884338359569308sn_int) tptp.list_P421884338359569308sn_int)
% 3.70/4.02 (declare-fun tptp.cons_P110449348784310650sn_nat (tptp.produc3672657496626091440sn_nat tptp.list_P2911967483291296064sn_nat) tptp.list_P2911967483291296064sn_nat)
% 3.70/4.02 (declare-fun tptp.cons_P9150528168557782045n_assn (tptp.produc9053633027152450663n_assn tptp.list_P28140577958321773n_assn) tptp.list_P28140577958321773n_assn)
% 3.70/4.02 (declare-fun tptp.cons_P3940603068885512221at_nat (tptp.produc3843707927480180839at_nat tptp.list_P5464809261938338413at_nat) tptp.list_P5464809261938338413at_nat)
% 3.70/4.02 (declare-fun tptp.cons_s6881495754146722583at_nat (tptp.set_Pr1261947904930325089at_nat tptp.list_s1210847774152347623at_nat) tptp.list_s1210847774152347623at_nat)
% 3.70/4.02 (declare-fun tptp.cons_c (tptp.c tptp.list_c) tptp.list_c)
% 3.70/4.02 (declare-fun tptp.cons_d (tptp.d tptp.list_d) tptp.list_d)
% 3.70/4.02 (declare-fun tptp.nil_nat_nat () tptp.list_nat_nat)
% 3.70/4.02 (declare-fun tptp.nil_se7398569966080822440at_nat () tptp.list_s9130966667114977576at_nat)
% 3.70/4.02 (declare-fun tptp.nil_o () tptp.list_o)
% 3.70/4.02 (declare-fun tptp.nil_assn () tptp.list_assn)
% 3.70/4.02 (declare-fun tptp.nil_int () tptp.list_int)
% 3.70/4.02 (declare-fun tptp.nil_list_int () tptp.list_list_int)
% 3.70/4.02 (declare-fun tptp.nil_list_nat () tptp.list_list_nat)
% 3.70/4.02 (declare-fun tptp.nil_li5476096274760905021n_assn () tptp.list_l6351802567095793725n_assn)
% 3.70/4.02 (declare-fun tptp.nil_nat () tptp.list_nat)
% 3.70/4.02 (declare-fun tptp.nil_Pr5671120429643327159n_assn () tptp.list_P8527749157015355191n_assn)
% 3.70/4.02 (declare-fun tptp.nil_Pr2300489316682597567nt_int () tptp.list_P5707943133018811711nt_int)
% 3.70/4.02 (declare-fun tptp.nil_Pr6478340336191794275nt_nat () tptp.list_P8198026277950538467nt_nat)
% 3.70/4.02 (declare-fun tptp.nil_Pr2440414457004260852n_assn () tptp.list_P1495281457390866698n_assn)
% 3.70/4.02 (declare-fun tptp.nil_Pr1301135604781543011at_int () tptp.list_P3521021558325789923at_int)
% 3.70/4.02 (declare-fun tptp.nil_Pr5478986624290739719at_nat () tptp.list_P6011104703257516679at_nat)
% 3.70/4.02 (declare-fun tptp.nil_Pr680377793251149648n_assn () tptp.list_P7711101519850957926n_assn)
% 3.70/4.02 (declare-fun tptp.nil_Pr7991254345159696774sn_int () tptp.list_P421884338359569308sn_int)
% 3.70/4.02 (declare-fun tptp.nil_Pr2945733327814117674sn_nat () tptp.list_P2911967483291296064sn_nat)
% 3.70/4.02 (declare-fun tptp.nil_Pr4327835960982145133n_assn () tptp.list_P28140577958321773n_assn)
% 3.70/4.02 (declare-fun tptp.nil_Pr8341282898164651117at_nat () tptp.list_P5464809261938338413at_nat)
% 3.70/4.02 (declare-fun tptp.nil_c () tptp.list_c)
% 3.70/4.02 (declare-fun tptp.nil_d () tptp.list_d)
% 3.70/4.02 (declare-fun tptp.hd_nat (tptp.list_nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.list_all_int ((-> tptp.int Bool) tptp.list_int) Bool)
% 3.70/4.02 (declare-fun tptp.list_all_nat ((-> tptp.nat Bool) tptp.list_nat) Bool)
% 3.70/4.02 (declare-fun tptp.map_nat_nat ((-> tptp.nat tptp.nat) tptp.list_nat) tptp.list_nat)
% 3.70/4.02 (declare-fun tptp.map_Pr8991440229025900053n_assn ((-> tptp.produc6575502325842934193n_assn tptp.assn) tptp.list_P8527749157015355191n_assn) tptp.list_assn)
% 3.70/4.02 (declare-fun tptp.set_in5217446777445088012e_term (tptp.list_i8448526496819171953e_term) tptp.set_in3461395444621081367e_term)
% 3.70/4.02 (declare-fun tptp.set_Pr8342322266483756581e_term (tptp.list_P1316552470764441098e_term) tptp.set_Pr7604974323444597168e_term)
% 3.70/4.02 (declare-fun tptp.set_Pr400311997697478754_nat_o (tptp.list_P7985473006766602707_nat_o) tptp.set_Pr4532377907799695533_nat_o)
% 3.70/4.02 (declare-fun tptp.set_Pr16608062948090134e_term (tptp.list_P1743416141875011707e_term) tptp.set_Pr3642885161833720865e_term)
% 3.70/4.02 (declare-fun tptp.set_o2 (tptp.list_o) tptp.set_o)
% 3.70/4.02 (declare-fun tptp.set_assn2 (tptp.list_assn) tptp.set_assn)
% 3.70/4.02 (declare-fun tptp.set_Code_integer2 (tptp.list_Code_integer) tptp.set_Code_integer)
% 3.70/4.02 (declare-fun tptp.set_int2 (tptp.list_int) tptp.set_int)
% 3.70/4.02 (declare-fun tptp.set_nat2 (tptp.list_nat) tptp.set_nat)
% 3.70/4.02 (declare-fun tptp.set_num2 (tptp.list_num) tptp.set_num)
% 3.70/4.02 (declare-fun tptp.set_Pr1633835384712236856nt_int (tptp.list_P8915022641806594461nt_int) tptp.set_Pr1872883991513573699nt_int)
% 3.70/4.02 (declare-fun tptp.set_Pr2135590979564877377nteger (tptp.list_P7828571989066258726nteger) tptp.set_Pr1281608226676607948nteger)
% 3.70/4.02 (declare-fun tptp.set_Pr8666615595052072444_nat_o (tptp.list_P6107040726529854061_nat_o) tptp.set_Pr2161125870931222855_nat_o)
% 3.70/4.02 (declare-fun tptp.set_Pr7458301993993767461et_nat (tptp.list_P362550909693114634et_nat) tptp.set_Pr8536935166611901872et_nat)
% 3.70/4.02 (declare-fun tptp.set_Pr364071364088684201et_nat (tptp.list_P2321686559999237006et_nat) tptp.set_Pr3286484037609594932et_nat)
% 3.70/4.02 (declare-fun tptp.set_Pr4943052134776177454nt_int (tptp.list_P651320350408439699nt_int) tptp.set_Pr9222295170931077689nt_int)
% 3.70/4.02 (declare-fun tptp.set_Pr1139785259514867910n_assn (tptp.list_P8527749157015355191n_assn) tptp.set_Pr5949110396991348497n_assn)
% 3.70/4.02 (declare-fun tptp.set_Pr920681315882439344nteger (tptp.list_P5578671422887162913nteger) tptp.set_Pr4811707699266497531nteger)
% 3.70/4.02 (declare-fun tptp.set_Pr3864771053587467565et_nat (tptp.list_P9062070895058802706et_nat) tptp.set_Pr3948176798113811640et_nat)
% 3.70/4.02 (declare-fun tptp.set_Pr2470121279949933262nt_int (tptp.list_P5707943133018811711nt_int) tptp.set_Pr958786334691620121nt_int)
% 3.70/4.02 (declare-fun tptp.set_Pr6647972299459129970nt_nat (tptp.list_P8198026277950538467nt_nat) tptp.set_Pr3448869479623346877nt_nat)
% 3.70/4.02 (declare-fun tptp.set_Pr4510407026980144421n_assn (tptp.list_P1495281457390866698n_assn) tptp.set_Pr3255386646789011632n_assn)
% 3.70/4.02 (declare-fun tptp.set_Pr525428910217828469at_nat (tptp.list_P812186867033400410at_nat) tptp.set_Pr6620829329807565824at_nat)
% 3.70/4.02 (declare-fun tptp.set_Pr1470767568048878706at_int (tptp.list_P3521021558325789923at_int) tptp.set_Pr7995236796853374141at_int)
% 3.70/4.02 (declare-fun tptp.set_Pr5648618587558075414at_nat (tptp.list_P6011104703257516679at_nat) tptp.set_Pr1261947904930325089at_nat)
% 3.70/4.02 (declare-fun tptp.set_Pr6710958862608470481at_nat (tptp.list_P1909269847677398966at_nat) tptp.set_Pr7717912310451564380at_nat)
% 3.70/4.02 (declare-fun tptp.set_Pr4163146846833169104_nat_c (tptp.list_P2993859830824179253_nat_c) tptp.set_Pr4335409928928841947_nat_c)
% 3.70/4.02 (declare-fun tptp.set_Pr8975451644279219196n_assn (tptp.list_P28140577958321773n_assn) tptp.set_Pr8116311503512020807n_assn)
% 3.70/4.02 (declare-fun tptp.set_Pr3658594827066574855at_int (tptp.list_P3463813956764838636at_int) tptp.set_Pr49084382684228242at_int)
% 3.70/4.02 (declare-fun tptp.set_Pr7836445846575771563at_nat (tptp.list_P5953897101696565392at_nat) tptp.set_Pr2539167527615954998at_nat)
% 3.70/4.02 (declare-fun tptp.set_Pr5518436109238095868at_nat (tptp.list_P8469869581646625389at_nat) tptp.set_Pr8693737435421807431at_nat)
% 3.70/4.02 (declare-fun tptp.set_Pr4552580085251402108at_nat (tptp.list_P6548900253507351021at_nat) tptp.set_Pr5564308138774400199at_nat)
% 3.70/4.02 (declare-fun tptp.set_Pr3765526544606949372at_nat (tptp.list_P5464809261938338413at_nat) tptp.set_Pr4329608150637261639at_nat)
% 3.70/4.02 (declare-fun tptp.set_Pr8441393049761402630_c_int (tptp.list_P3071867362843219819_c_int) tptp.set_Pr4413417460947882513_c_int)
% 3.70/4.02 (declare-fun tptp.set_Pr3395872032415823530_c_nat (tptp.list_P5561950507774946575_c_nat) tptp.set_Pr6903500605879609269_c_nat)
% 3.70/4.02 (declare-fun tptp.set_Product_prod_c_c2 (tptp.list_P267710562049004973od_c_c) tptp.set_Product_prod_c_c)
% 3.70/4.02 (declare-fun tptp.set_Product_prod_c_d2 (tptp.list_P338744602095350958od_c_d) tptp.set_Product_prod_c_d)
% 3.70/4.02 (declare-fun tptp.set_Pr453465341863021319_d_int (tptp.list_P8668085978031350508_d_int) tptp.set_Pr786264039281237394_d_int)
% 3.70/4.02 (declare-fun tptp.set_Pr4631316361372218027_d_nat (tptp.list_P1934797086108301456_d_nat) tptp.set_Pr3276347184212964150_d_nat)
% 3.70/4.02 (declare-fun tptp.set_Product_prod_d_c2 (tptp.list_P8855433598298794092od_d_c) tptp.set_Product_prod_d_c)
% 3.70/4.02 (declare-fun tptp.set_Product_prod_d_d2 (tptp.list_P8926467638345140077od_d_d) tptp.set_Product_prod_d_d)
% 3.70/4.02 (declare-fun tptp.set_se5049602875457034614at_nat (tptp.list_s1210847774152347623at_nat) tptp.set_se7855581050983116737at_nat)
% 3.70/4.02 (declare-fun tptp.set_c2 (tptp.list_c) tptp.set_c)
% 3.70/4.02 (declare-fun tptp.set_d2 (tptp.list_d) tptp.set_d)
% 3.70/4.02 (declare-fun tptp.tl_nat (tptp.list_nat) tptp.list_nat)
% 3.70/4.02 (declare-fun tptp.list_e4587384546317177617_nat_o ((-> (-> tptp.produc3658429121746597890et_nat Bool) Bool) tptp.list_P7985473006766602707_nat_o) Bool)
% 3.70/4.02 (declare-fun tptp.list_ex_int ((-> tptp.int Bool) tptp.list_int) Bool)
% 3.70/4.02 (declare-fun tptp.list_ex_nat ((-> tptp.nat Bool) tptp.list_nat) Bool)
% 3.70/4.02 (declare-fun tptp.list_e1087220904399170805n_assn ((-> tptp.produc6575502325842934193n_assn Bool) tptp.list_P8527749157015355191n_assn) Bool)
% 3.70/4.02 (declare-fun tptp.list_e7689525607045846085at_nat ((-> tptp.product_prod_nat_nat Bool) tptp.list_P6011104703257516679at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.list_e5181628221095382443at_nat ((-> tptp.produc3843707927480180839at_nat Bool) tptp.list_P5464809261938338413at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.list_ex_c ((-> tptp.c Bool) tptp.list_c) Bool)
% 3.70/4.02 (declare-fun tptp.list_ex_d ((-> tptp.d Bool) tptp.list_d) Bool)
% 3.70/4.02 (declare-fun tptp.list_u8946639151299769843e_term (tptp.list_i8448526496819171953e_term tptp.nat (-> tptp.int tptp.option6357759511663192854e_term)) tptp.list_i8448526496819171953e_term)
% 3.70/4.02 (declare-fun tptp.list_u877304756163299468e_term (tptp.list_P1316552470764441098e_term tptp.nat (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) tptp.list_P1316552470764441098e_term)
% 3.70/4.02 (declare-fun tptp.list_u6943956310655620667_nat_o (tptp.list_P7985473006766602707_nat_o tptp.nat (-> tptp.produc3658429121746597890et_nat Bool)) tptp.list_P7985473006766602707_nat_o)
% 3.70/4.02 (declare-fun tptp.list_u3533491785856317309e_term (tptp.list_P1743416141875011707e_term tptp.nat (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) tptp.list_P1743416141875011707e_term)
% 3.70/4.02 (declare-fun tptp.list_update_o (tptp.list_o tptp.nat Bool) tptp.list_o)
% 3.70/4.02 (declare-fun tptp.list_update_int (tptp.list_int tptp.nat tptp.int) tptp.list_int)
% 3.70/4.02 (declare-fun tptp.list_update_nat (tptp.list_nat tptp.nat tptp.nat) tptp.list_nat)
% 3.70/4.02 (declare-fun tptp.list_u4780935413889332127nt_int (tptp.list_P8915022641806594461nt_int tptp.nat tptp.produc7773217078559923341nt_int) tptp.list_P8915022641806594461nt_int)
% 3.70/4.02 (declare-fun tptp.list_u234853988314817064nteger (tptp.list_P7828571989066258726nteger tptp.nat tptp.produc1908205239877642774nteger) tptp.list_P7828571989066258726nteger)
% 3.70/4.02 (declare-fun tptp.list_u1913845194572276492et_nat (tptp.list_P362550909693114634et_nat tptp.nat tptp.produc2732055786443039994et_nat) tptp.list_P362550909693114634et_nat)
% 3.70/4.02 (declare-fun tptp.list_u1866171116859985808et_nat (tptp.list_P2321686559999237006et_nat tptp.nat tptp.produc3925858234332021118et_nat) tptp.list_P2321686559999237006et_nat)
% 3.70/4.02 (declare-fun tptp.list_u7736365598306452245nt_int (tptp.list_P651320350408439699nt_int tptp.nat tptp.produc2285326912895808259nt_int) tptp.list_P651320350408439699nt_int)
% 3.70/4.02 (declare-fun tptp.list_u4534839942911652127n_assn (tptp.list_P8527749157015355191n_assn tptp.nat tptp.produc6575502325842934193n_assn) tptp.list_P8527749157015355191n_assn)
% 3.70/4.02 (declare-fun tptp.list_u2254550707601501961nteger (tptp.list_P5578671422887162913nteger tptp.nat tptp.produc8923325533196201883nteger) tptp.list_P5578671422887162913nteger)
% 3.70/4.02 (declare-fun tptp.list_u9060326803697358356et_nat (tptp.list_P9062070895058802706et_nat tptp.nat tptp.produc3658429121746597890et_nat) tptp.list_P9062070895058802706et_nat)
% 3.70/4.02 (declare-fun tptp.list_u3002344382305578791nt_int (tptp.list_P5707943133018811711nt_int tptp.nat tptp.product_prod_int_int) tptp.list_P5707943133018811711nt_int)
% 3.70/4.02 (declare-fun tptp.list_u6180841689913720943at_nat (tptp.list_P6011104703257516679at_nat tptp.nat tptp.product_prod_nat_nat) tptp.list_P6011104703257516679at_nat)
% 3.70/4.02 (declare-fun tptp.list_u4696772448584712917at_nat (tptp.list_P5464809261938338413at_nat tptp.nat tptp.produc3843707927480180839at_nat) tptp.list_P5464809261938338413at_nat)
% 3.70/4.02 (declare-fun tptp.list_u8616212504517173525od_c_c (tptp.list_P267710562049004973od_c_c tptp.nat tptp.product_prod_c_c) tptp.list_P267710562049004973od_c_c)
% 3.70/4.02 (declare-fun tptp.list_u8616212508820402326od_c_d (tptp.list_P338744602095350958od_c_d tptp.nat tptp.product_prod_c_d) tptp.list_P338744602095350958od_c_d)
% 3.70/4.02 (declare-fun tptp.list_u5828756922544497492od_d_c (tptp.list_P8855433598298794092od_d_c tptp.nat tptp.product_prod_d_c) tptp.list_P8855433598298794092od_d_c)
% 3.70/4.02 (declare-fun tptp.list_u5828756926847726293od_d_d (tptp.list_P8926467638345140077od_d_d tptp.nat tptp.product_prod_d_d) tptp.list_P8926467638345140077od_d_d)
% 3.70/4.02 (declare-fun tptp.list_u8444657558853818831at_nat (tptp.list_s1210847774152347623at_nat tptp.nat tptp.set_Pr1261947904930325089at_nat) tptp.list_s1210847774152347623at_nat)
% 3.70/4.02 (declare-fun tptp.list_update_c (tptp.list_c tptp.nat tptp.c) tptp.list_c)
% 3.70/4.02 (declare-fun tptp.list_update_d (tptp.list_d tptp.nat tptp.d) tptp.list_d)
% 3.70/4.02 (declare-fun tptp.listrel1_int (tptp.set_Pr958786334691620121nt_int) tptp.set_Pr765067013931698361st_int)
% 3.70/4.02 (declare-fun tptp.listrel1_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr3451248702717554689st_nat)
% 3.70/4.02 (declare-fun tptp.listre4270255209692100112n_assn (tptp.set_Pr8116311503512020807n_assn) tptp.set_Pr6863447823992824007n_assn)
% 3.70/4.02 (declare-fun tptp.listre8180072825634266816at_nat (tptp.set_Pr4329608150637261639at_nat) tptp.set_Pr4333006031979791559at_nat)
% 3.70/4.02 (declare-fun tptp.listrel1_c (tptp.set_Product_prod_c_c) tptp.set_Pr2058341694840537735list_c)
% 3.70/4.02 (declare-fun tptp.listrel1_d (tptp.set_Product_prod_d_d) tptp.set_Pr5674772971416283335list_d)
% 3.70/4.02 (declare-fun tptp.listrel_int_int (tptp.set_Pr958786334691620121nt_int) tptp.set_Pr765067013931698361st_int)
% 3.70/4.02 (declare-fun tptp.listrel_int_nat (tptp.set_Pr3448869479623346877nt_nat) tptp.set_Pr5578615432719617117st_nat)
% 3.70/4.02 (declare-fun tptp.listre4888949683985722578n_assn (tptp.set_Pr3255386646789011632n_assn) tptp.set_Pr4168565316758867366n_assn)
% 3.70/4.02 (declare-fun tptp.listrel_nat_int (tptp.set_Pr7995236796853374141at_int) tptp.set_Pr7861072320784411741st_int)
% 3.70/4.02 (declare-fun tptp.listrel_nat_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr3451248702717554689st_nat)
% 3.70/4.02 (declare-fun tptp.listre3128913020232611374n_assn (tptp.set_Pr247834672394327052n_assn) tptp.set_Pr7093487733527993602n_assn)
% 3.70/4.02 (declare-fun tptp.listrel_nat_c (tptp.set_Pr4335409928928841947_nat_c) tptp.set_Pr2380792130361903057list_c)
% 3.70/4.02 (declare-fun tptp.listrel_nat_d (tptp.set_Pr4406443968975187932_nat_d) tptp.set_Pr9082979648927643218list_d)
% 3.70/4.02 (declare-fun tptp.listre8029020076619294380sn_int (tptp.set_Pr2181989527757714242sn_int) tptp.set_Pr4898238009683259096st_int)
% 3.70/4.02 (declare-fun tptp.listre8031510547128344656sn_nat (tptp.set_Pr4672072672689440998sn_nat) tptp.set_Pr488414391616402044st_nat)
% 3.70/4.02 (declare-fun tptp.listre5253995379918703921n_assn (tptp.set_Pr8116311503512020807n_assn) tptp.set_Pr6863447823992824007n_assn)
% 3.70/4.02 (declare-fun tptp.listre2047417242196832561at_nat (tptp.set_Pr4329608150637261639at_nat) tptp.set_Pr4333006031979791559at_nat)
% 3.70/4.02 (declare-fun tptp.listrel_c_int (tptp.set_Pr4413417460947882513_c_int) tptp.set_Pr1946635486513090599st_int)
% 3.70/4.02 (declare-fun tptp.listrel_c_nat (tptp.set_Pr6903500605879609269_c_nat) tptp.set_Pr6760183905301009355st_nat)
% 3.70/4.02 (declare-fun tptp.listrel_c_c (tptp.set_Product_prod_c_c) tptp.set_Pr2058341694840537735list_c)
% 3.70/4.02 (declare-fun tptp.listrel_c_d (tptp.set_Product_prod_c_d) tptp.set_Pr8760529213406277896list_d)
% 3.70/4.02 (declare-fun tptp.listrel_d_int (tptp.set_Pr786264039281237394_d_int) tptp.set_Pr7415257249380972200st_int)
% 3.70/4.02 (declare-fun tptp.listrel_d_nat (tptp.set_Pr3276347184212964150_d_nat) tptp.set_Pr3005433631314115148st_nat)
% 3.70/4.02 (declare-fun tptp.listrel_d_c (tptp.set_Product_prod_d_c) tptp.set_Pr8195957489705318982list_c)
% 3.70/4.02 (declare-fun tptp.listrel_d_d (tptp.set_Product_prod_d_d) tptp.set_Pr5674772971416283335list_d)
% 3.70/4.02 (declare-fun tptp.measures_nat (tptp.list_nat_nat) tptp.set_Pr1261947904930325089at_nat)
% 3.70/4.02 (declare-fun tptp.measur2694323259624372065at_nat (tptp.list_s9130966667114977576at_nat) tptp.set_Pr4329608150637261639at_nat)
% 3.70/4.02 (declare-fun tptp.nth_Pr6840583978799713108_nat_o (tptp.list_P7985473006766602707_nat_o tptp.nat tptp.produc3658429121746597890et_nat) Bool)
% 3.70/4.02 (declare-fun tptp.nth_o (tptp.list_o tptp.nat) Bool)
% 3.70/4.02 (declare-fun tptp.nth_Code_integer (tptp.list_Code_integer tptp.nat) tptp.code_integer)
% 3.70/4.02 (declare-fun tptp.nth_int (tptp.list_int tptp.nat) tptp.int)
% 3.70/4.02 (declare-fun tptp.nth_nat (tptp.list_nat tptp.nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.nth_num (tptp.list_num tptp.nat) tptp.num)
% 3.70/4.02 (declare-fun tptp.nth_Pr1769885009046257848n_assn (tptp.list_P8527749157015355191n_assn tptp.nat) tptp.produc6575502325842934193n_assn)
% 3.70/4.02 (declare-fun tptp.nth_Pr3440142176431000676at_int (tptp.list_P3521021558325789923at_int tptp.nat) tptp.product_prod_nat_int)
% 3.70/4.02 (declare-fun tptp.nth_Pr7617993195940197384at_nat (tptp.list_P6011104703257516679at_nat tptp.nat) tptp.product_prod_nat_nat)
% 3.70/4.02 (declare-fun tptp.nth_Pr2476257089995772766_nat_c (tptp.list_P2993859830824179253_nat_c tptp.nat) tptp.product_prod_nat_c)
% 3.70/4.02 (declare-fun tptp.nth_Pr2476257094299001567_nat_d (tptp.list_P3064893870870525238_nat_d tptp.nat) tptp.product_prod_nat_d)
% 3.70/4.02 (declare-fun tptp.nth_Pr1239524528086697198at_nat (tptp.list_P5464809261938338413at_nat tptp.nat) tptp.produc3843707927480180839at_nat)
% 3.70/4.02 (declare-fun tptp.nth_Pr6754503292924006292_c_int (tptp.list_P3071867362843219819_c_int tptp.nat) tptp.product_prod_c_int)
% 3.70/4.02 (declare-fun tptp.nth_Pr1708982275578427192_c_nat (tptp.list_P5561950507774946575_c_nat tptp.nat) tptp.product_prod_c_nat)
% 3.70/4.02 (declare-fun tptp.nth_Product_prod_c_c (tptp.list_P267710562049004973od_c_c tptp.nat) tptp.product_prod_c_c)
% 3.70/4.02 (declare-fun tptp.nth_Product_prod_c_d (tptp.list_P338744602095350958od_c_d tptp.nat) tptp.product_prod_c_d)
% 3.70/4.02 (declare-fun tptp.nth_Pr7989947621880400789_d_int (tptp.list_P8668085978031350508_d_int tptp.nat) tptp.product_prod_d_int)
% 3.70/4.02 (declare-fun tptp.nth_Pr2944426604534821689_d_nat (tptp.list_P1934797086108301456_d_nat tptp.nat) tptp.product_prod_d_nat)
% 3.70/4.02 (declare-fun tptp.nth_Product_prod_d_c (tptp.list_P8855433598298794092od_d_c tptp.nat) tptp.product_prod_d_c)
% 3.70/4.02 (declare-fun tptp.nth_Product_prod_d_d (tptp.list_P8926467638345140077od_d_d tptp.nat) tptp.product_prod_d_d)
% 3.70/4.02 (declare-fun tptp.nth_se5679702624988424552at_nat (tptp.list_s1210847774152347623at_nat tptp.nat) tptp.set_Pr1261947904930325089at_nat)
% 3.70/4.02 (declare-fun tptp.nth_c (tptp.list_c tptp.nat) tptp.c)
% 3.70/4.02 (declare-fun tptp.nth_d (tptp.list_d tptp.nat) tptp.d)
% 3.70/4.02 (declare-fun tptp.null_int (tptp.list_int) Bool)
% 3.70/4.02 (declare-fun tptp.null_nat (tptp.list_nat) Bool)
% 3.70/4.02 (declare-fun tptp.null_P7596217980778516671n_assn (tptp.list_P8527749157015355191n_assn) Bool)
% 3.70/4.02 (declare-fun tptp.product_assn_assn (tptp.list_assn tptp.list_assn) tptp.list_P8527749157015355191n_assn)
% 3.70/4.02 (declare-fun tptp.product_int_int (tptp.list_int tptp.list_int) tptp.list_P5707943133018811711nt_int)
% 3.70/4.02 (declare-fun tptp.product_int_nat (tptp.list_int tptp.list_nat) tptp.list_P8198026277950538467nt_nat)
% 3.70/4.02 (declare-fun tptp.product_nat_int (tptp.list_nat tptp.list_int) tptp.list_P3521021558325789923at_int)
% 3.70/4.02 (declare-fun tptp.product_nat_nat (tptp.list_nat tptp.list_nat) tptp.list_P6011104703257516679at_nat)
% 3.70/4.02 (declare-fun tptp.product_nat_c (tptp.list_nat tptp.list_c) tptp.list_P2993859830824179253_nat_c)
% 3.70/4.02 (declare-fun tptp.product_nat_d (tptp.list_nat tptp.list_d) tptp.list_P3064893870870525238_nat_d)
% 3.70/4.02 (declare-fun tptp.product_c_int (tptp.list_c tptp.list_int) tptp.list_P3071867362843219819_c_int)
% 3.70/4.02 (declare-fun tptp.product_c_nat (tptp.list_c tptp.list_nat) tptp.list_P5561950507774946575_c_nat)
% 3.70/4.02 (declare-fun tptp.product_c_c (tptp.list_c tptp.list_c) tptp.list_P267710562049004973od_c_c)
% 3.70/4.02 (declare-fun tptp.product_c_d (tptp.list_c tptp.list_d) tptp.list_P338744602095350958od_c_d)
% 3.70/4.02 (declare-fun tptp.product_d_int (tptp.list_d tptp.list_int) tptp.list_P8668085978031350508_d_int)
% 3.70/4.02 (declare-fun tptp.product_d_nat (tptp.list_d tptp.list_nat) tptp.list_P1934797086108301456_d_nat)
% 3.70/4.02 (declare-fun tptp.product_d_c (tptp.list_d tptp.list_c) tptp.list_P8855433598298794092od_d_c)
% 3.70/4.02 (declare-fun tptp.product_d_d (tptp.list_d tptp.list_d) tptp.list_P8926467638345140077od_d_d)
% 3.70/4.02 (declare-fun tptp.remdups_nat (tptp.list_nat) tptp.list_nat)
% 3.70/4.02 (declare-fun tptp.remove4235003712227595625_nat_o ((-> tptp.produc3658429121746597890et_nat Bool) tptp.list_P7985473006766602707_nat_o) tptp.list_P7985473006766602707_nat_o)
% 3.70/4.02 (declare-fun tptp.remove1_o (Bool tptp.list_o) tptp.list_o)
% 3.70/4.02 (declare-fun tptp.remove1_int (tptp.int tptp.list_int) tptp.list_int)
% 3.70/4.02 (declare-fun tptp.remove1_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 3.70/4.02 (declare-fun tptp.remove1670527618125605709n_assn (tptp.produc6575502325842934193n_assn tptp.list_P8527749157015355191n_assn) tptp.list_P8527749157015355191n_assn)
% 3.70/4.02 (declare-fun tptp.remove5766854097993331357at_nat (tptp.product_prod_nat_nat tptp.list_P6011104703257516679at_nat) tptp.list_P6011104703257516679at_nat)
% 3.70/4.02 (declare-fun tptp.remove8895909992688781315at_nat (tptp.produc3843707927480180839at_nat tptp.list_P5464809261938338413at_nat) tptp.list_P5464809261938338413at_nat)
% 3.70/4.02 (declare-fun tptp.remove1_c (tptp.c tptp.list_c) tptp.list_c)
% 3.70/4.02 (declare-fun tptp.remove1_d (tptp.d tptp.list_d) tptp.list_d)
% 3.70/4.02 (declare-fun tptp.remove7604696131425036249_nat_o ((-> tptp.produc3658429121746597890et_nat Bool) tptp.list_P7985473006766602707_nat_o) tptp.list_P7985473006766602707_nat_o)
% 3.70/4.02 (declare-fun tptp.removeAll_o (Bool tptp.list_o) tptp.list_o)
% 3.70/4.02 (declare-fun tptp.removeAll_int (tptp.int tptp.list_int) tptp.list_int)
% 3.70/4.02 (declare-fun tptp.removeAll_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 3.70/4.02 (declare-fun tptp.remove1763081955827946941n_assn (tptp.produc6575502325842934193n_assn tptp.list_P8527749157015355191n_assn) tptp.list_P8527749157015355191n_assn)
% 3.70/4.02 (declare-fun tptp.remove3673390508374433037at_nat (tptp.product_prod_nat_nat tptp.list_P6011104703257516679at_nat) tptp.list_P6011104703257516679at_nat)
% 3.70/4.02 (declare-fun tptp.remove4908499291543849587at_nat (tptp.produc3843707927480180839at_nat tptp.list_P5464809261938338413at_nat) tptp.list_P5464809261938338413at_nat)
% 3.70/4.02 (declare-fun tptp.removeAll_c (tptp.c tptp.list_c) tptp.list_c)
% 3.70/4.02 (declare-fun tptp.removeAll_d (tptp.d tptp.list_d) tptp.list_d)
% 3.70/4.02 (declare-fun tptp.rev_int (tptp.list_int) tptp.list_int)
% 3.70/4.02 (declare-fun tptp.rev_nat (tptp.list_nat) tptp.list_nat)
% 3.70/4.02 (declare-fun tptp.rev_Pr4855572775806611735n_assn (tptp.list_P8527749157015355191n_assn) tptp.list_P8527749157015355191n_assn)
% 3.70/4.02 (declare-fun tptp.rev_Pr4566615052912869567_nat_c (tptp.list_P2993859830824179253_nat_c) tptp.list_P2993859830824179253_nat_c)
% 3.70/4.02 (declare-fun tptp.rev_Pr4566615057216098368_nat_d (tptp.list_P3064893870870525238_nat_d) tptp.list_P3064893870870525238_nat_d)
% 3.70/4.02 (declare-fun tptp.rev_Pr8844861255841103093_c_int (tptp.list_P3071867362843219819_c_int) tptp.list_P3071867362843219819_c_int)
% 3.70/4.02 (declare-fun tptp.rev_Pr3799340238495523993_c_nat (tptp.list_P5561950507774946575_c_nat) tptp.list_P5561950507774946575_c_nat)
% 3.70/4.02 (declare-fun tptp.rev_Product_prod_c_c (tptp.list_P267710562049004973od_c_c) tptp.list_P267710562049004973od_c_c)
% 3.70/4.02 (declare-fun tptp.rev_Product_prod_c_d (tptp.list_P338744602095350958od_c_d) tptp.list_P338744602095350958od_c_d)
% 3.70/4.02 (declare-fun tptp.rev_Pr856933547942721782_d_int (tptp.list_P8668085978031350508_d_int) tptp.list_P8668085978031350508_d_int)
% 3.70/4.02 (declare-fun tptp.rev_Pr5034784567451918490_d_nat (tptp.list_P1934797086108301456_d_nat) tptp.list_P1934797086108301456_d_nat)
% 3.70/4.02 (declare-fun tptp.rev_Product_prod_d_c (tptp.list_P8855433598298794092od_d_c) tptp.list_P8855433598298794092od_d_c)
% 3.70/4.02 (declare-fun tptp.rev_Product_prod_d_d (tptp.list_P8926467638345140077od_d_d) tptp.list_P8926467638345140077od_d_d)
% 3.70/4.02 (declare-fun tptp.rev_c (tptp.list_c) tptp.list_c)
% 3.70/4.02 (declare-fun tptp.rev_d (tptp.list_d) tptp.list_d)
% 3.70/4.02 (declare-fun tptp.rotate1_int (tptp.list_int) tptp.list_int)
% 3.70/4.02 (declare-fun tptp.rotate1_nat (tptp.list_nat) tptp.list_nat)
% 3.70/4.02 (declare-fun tptp.rotate328796349445179396n_assn (tptp.list_P8527749157015355191n_assn) tptp.list_P8527749157015355191n_assn)
% 3.70/4.02 (declare-fun tptp.rotate1_c (tptp.list_c) tptp.list_c)
% 3.70/4.02 (declare-fun tptp.rotate1_d (tptp.list_d) tptp.list_d)
% 3.70/4.02 (declare-fun tptp.sorted9199660237762088378_nat_o ((-> (-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) Bool) tptp.list_P7985473006766602707_nat_o) Bool)
% 3.70/4.02 (declare-fun tptp.sorted710888440204495920nteger ((-> tptp.code_integer tptp.code_integer Bool) tptp.list_Code_integer) Bool)
% 3.70/4.02 (declare-fun tptp.sorted_wrt_int ((-> tptp.int tptp.int Bool) tptp.list_int) Bool)
% 3.70/4.02 (declare-fun tptp.sorted_wrt_nat ((-> tptp.nat tptp.nat Bool) tptp.list_nat) Bool)
% 3.70/4.02 (declare-fun tptp.sorted_wrt_num ((-> tptp.num tptp.num Bool) tptp.list_num) Bool)
% 3.70/4.02 (declare-fun tptp.sorted3986126766855596574n_assn ((-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn Bool) tptp.list_P8527749157015355191n_assn) Bool)
% 3.70/4.02 (declare-fun tptp.sorted5214655850825725294at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.list_P6011104703257516679at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.sorted8831241538929206612at_nat ((-> tptp.produc3843707927480180839at_nat tptp.produc3843707927480180839at_nat Bool) tptp.list_P5464809261938338413at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.sorted_wrt_c ((-> tptp.c tptp.c Bool) tptp.list_c) Bool)
% 3.70/4.02 (declare-fun tptp.sorted_wrt_d ((-> tptp.d tptp.d Bool) tptp.list_d) Bool)
% 3.70/4.02 (declare-fun tptp.take_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 3.70/4.02 (declare-fun tptp.union_int (tptp.list_int tptp.list_int) tptp.list_int)
% 3.70/4.02 (declare-fun tptp.union_nat (tptp.list_nat tptp.list_nat) tptp.list_nat)
% 3.70/4.02 (declare-fun tptp.union_944050417204428971n_assn (tptp.list_P8527749157015355191n_assn tptp.list_P8527749157015355191n_assn) tptp.list_P8527749157015355191n_assn)
% 3.70/4.02 (declare-fun tptp.union_4462254032241401953at_nat (tptp.list_P5464809261938338413at_nat tptp.list_P5464809261938338413at_nat) tptp.list_P5464809261938338413at_nat)
% 3.70/4.02 (declare-fun tptp.upt (tptp.nat tptp.nat) tptp.list_nat)
% 3.70/4.02 (declare-fun tptp.upto (tptp.int tptp.int) tptp.list_int)
% 3.70/4.02 (declare-fun tptp.upto_aux (tptp.int tptp.int tptp.list_int) tptp.list_int)
% 3.70/4.02 (declare-fun tptp.upto_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 3.70/4.02 (declare-fun tptp.zip_in8766932505889695135nt_int (tptp.list_i8448526496819171953e_term tptp.list_P5707943133018811711nt_int) tptp.list_P8915022641806594461nt_int)
% 3.70/4.02 (declare-fun tptp.zip_Pr8292346330294042792nteger (tptp.list_P1316552470764441098e_term tptp.list_P5578671422887162913nteger) tptp.list_P7828571989066258726nteger)
% 3.70/4.02 (declare-fun tptp.zip_Pr2849639184604596727_nat_o (tptp.list_P7985473006766602707_nat_o tptp.list_P7985473006766602707_nat_o) tptp.list_P6107040726529854061_nat_o)
% 3.70/4.02 (declare-fun tptp.zip_Pr8136144321567152340et_nat (tptp.list_P7985473006766602707_nat_o tptp.list_P2321686559999237006et_nat) tptp.list_P362550909693114634et_nat)
% 3.70/4.02 (declare-fun tptp.zip_Pr7134870689397686104et_nat (tptp.list_P7985473006766602707_nat_o tptp.list_P9062070895058802706et_nat) tptp.list_P2321686559999237006et_nat)
% 3.70/4.02 (declare-fun tptp.zip_Pr4168994715204986005nt_int (tptp.list_P1743416141875011707e_term tptp.list_P5707943133018811711nt_int) tptp.list_P651320350408439699nt_int)
% 3.70/4.02 (declare-fun tptp.zip_assn_assn (tptp.list_assn tptp.list_assn) tptp.list_P8527749157015355191n_assn)
% 3.70/4.02 (declare-fun tptp.zip_int_int (tptp.list_int tptp.list_int) tptp.list_P5707943133018811711nt_int)
% 3.70/4.02 (declare-fun tptp.zip_int_nat (tptp.list_int tptp.list_nat) tptp.list_P8198026277950538467nt_nat)
% 3.70/4.02 (declare-fun tptp.zip_in7098856637274830732n_assn (tptp.list_int tptp.list_P8527749157015355191n_assn) tptp.list_P1495281457390866698n_assn)
% 3.70/4.02 (declare-fun tptp.zip_in4043968058504772316at_nat (tptp.list_int tptp.list_P6011104703257516679at_nat) tptp.list_P812186867033400410at_nat)
% 3.70/4.02 (declare-fun tptp.zip_nat_int (tptp.list_nat tptp.list_int) tptp.list_P3521021558325789923at_int)
% 3.70/4.02 (declare-fun tptp.zip_nat_nat (tptp.list_nat tptp.list_nat) tptp.list_P6011104703257516679at_nat)
% 3.70/4.02 (declare-fun tptp.zip_na5338819973521719528n_assn (tptp.list_nat tptp.list_P8527749157015355191n_assn) tptp.list_P7711101519850957926n_assn)
% 3.70/4.02 (declare-fun tptp.zip_na1006125974040638520at_nat (tptp.list_nat tptp.list_P6011104703257516679at_nat) tptp.list_P1909269847677398966at_nat)
% 3.70/4.02 (declare-fun tptp.zip_nat_c (tptp.list_nat tptp.list_c) tptp.list_P2993859830824179253_nat_c)
% 3.70/4.02 (declare-fun tptp.zip_nat_d (tptp.list_nat tptp.list_d) tptp.list_P3064893870870525238_nat_d)
% 3.70/4.02 (declare-fun tptp.zip_Pr1015554993053626726sn_int (tptp.list_P8527749157015355191n_assn tptp.list_int) tptp.list_P421884338359569308sn_int)
% 3.70/4.02 (declare-fun tptp.zip_Pr1018045463562677002sn_nat (tptp.list_P8527749157015355191n_assn tptp.list_nat) tptp.list_P2911967483291296064sn_nat)
% 3.70/4.02 (declare-fun tptp.zip_Pr8806919808394484215n_assn (tptp.list_P8527749157015355191n_assn tptp.list_P8527749157015355191n_assn) tptp.list_P28140577958321773n_assn)
% 3.70/4.02 (declare-fun tptp.zip_Pr6866960147343648950at_int (tptp.list_P6011104703257516679at_nat tptp.list_int) tptp.list_P3463813956764838636at_int)
% 3.70/4.02 (declare-fun tptp.zip_Pr6869450617852699226at_nat (tptp.list_P6011104703257516679at_nat tptp.list_nat) tptp.list_P5953897101696565392at_nat)
% 3.70/4.02 (declare-fun tptp.zip_Pr4664179122662387191at_nat (tptp.list_P6011104703257516679at_nat tptp.list_P6011104703257516679at_nat) tptp.list_P8469869581646625389at_nat)
% 3.70/4.02 (declare-fun tptp.zip_Pr2522280425463452279at_nat (tptp.list_P5464809261938338413at_nat tptp.list_P5464809261938338413at_nat) tptp.list_P6548900253507351021at_nat)
% 3.70/4.02 (declare-fun tptp.zip_se5600341670672612855at_nat (tptp.list_s1210847774152347623at_nat tptp.list_s1210847774152347623at_nat) tptp.list_P5464809261938338413at_nat)
% 3.70/4.02 (declare-fun tptp.zip_c_int (tptp.list_c tptp.list_int) tptp.list_P3071867362843219819_c_int)
% 3.70/4.02 (declare-fun tptp.zip_c_nat (tptp.list_c tptp.list_nat) tptp.list_P5561950507774946575_c_nat)
% 3.70/4.02 (declare-fun tptp.zip_c_c (tptp.list_c tptp.list_c) tptp.list_P267710562049004973od_c_c)
% 3.70/4.02 (declare-fun tptp.zip_c_d (tptp.list_c tptp.list_d) tptp.list_P338744602095350958od_c_d)
% 3.70/4.02 (declare-fun tptp.zip_d_int (tptp.list_d tptp.list_int) tptp.list_P8668085978031350508_d_int)
% 3.70/4.02 (declare-fun tptp.zip_d_nat (tptp.list_d tptp.list_nat) tptp.list_P1934797086108301456_d_nat)
% 3.70/4.02 (declare-fun tptp.zip_d_c (tptp.list_d tptp.list_c) tptp.list_P8855433598298794092od_d_c)
% 3.70/4.02 (declare-fun tptp.zip_d_d (tptp.list_d tptp.list_d) tptp.list_P8926467638345140077od_d_d)
% 3.70/4.02 (declare-fun tptp.biject576505603616484041nt_int (tptp.set_Pr1872883991513573699nt_int) Bool)
% 3.70/4.02 (declare-fun tptp.biject9051520373387432658nteger (tptp.set_Pr1281608226676607948nteger) Bool)
% 3.70/4.02 (declare-fun tptp.biject1468766312547416318et_nat (tptp.set_Pr8536935166611901872et_nat) Bool)
% 3.70/4.02 (declare-fun tptp.biject2615096655818420098et_nat (tptp.set_Pr3286484037609594932et_nat) Bool)
% 3.70/4.02 (declare-fun tptp.biject383251550997737151nt_int (tptp.set_Pr9222295170931077689nt_int) Bool)
% 3.70/4.02 (declare-fun tptp.bijective_nat_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.biject3388518990857851981at_nat (tptp.set_Pr4329608150637261639at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.merge_Code_integer (tptp.list_Code_integer tptp.list_Code_integer) tptp.list_Code_integer)
% 3.70/4.02 (declare-fun tptp.merge_int (tptp.list_int tptp.list_int) tptp.list_int)
% 3.70/4.02 (declare-fun tptp.merge_nat (tptp.list_nat tptp.list_nat) tptp.list_nat)
% 3.70/4.02 (declare-fun tptp.merge_num (tptp.list_num tptp.list_num) tptp.list_num)
% 3.70/4.02 (declare-fun tptp.merges1654122896337280797ps_int (tptp.list_int) tptp.list_int)
% 3.70/4.02 (declare-fun tptp.merges1656613366846331073ps_nat (tptp.list_nat) tptp.list_nat)
% 3.70/4.02 (declare-fun tptp.slice_int (tptp.nat tptp.nat tptp.list_int) tptp.list_int)
% 3.70/4.02 (declare-fun tptp.slice_nat (tptp.nat tptp.nat tptp.list_nat) tptp.list_nat)
% 3.70/4.02 (declare-fun tptp.slice_7964966981652229398n_assn (tptp.nat tptp.nat tptp.list_P8527749157015355191n_assn) tptp.list_P8527749157015355191n_assn)
% 3.70/4.02 (declare-fun tptp.slice_c (tptp.nat tptp.nat tptp.list_c) tptp.list_c)
% 3.70/4.02 (declare-fun tptp.slice_d (tptp.nat tptp.nat tptp.list_d) tptp.list_d)
% 3.70/4.02 (declare-fun tptp.zipf_int_int_int ((-> tptp.int tptp.int tptp.int) tptp.list_int tptp.list_int) tptp.list_int)
% 3.70/4.02 (declare-fun tptp.zipf_int_int_nat ((-> tptp.int tptp.int tptp.nat) tptp.list_int tptp.list_int) tptp.list_nat)
% 3.70/4.02 (declare-fun tptp.zipf_i7756021159461276697n_assn ((-> tptp.int tptp.int tptp.produc6575502325842934193n_assn) tptp.list_int tptp.list_int) tptp.list_P8527749157015355191n_assn)
% 3.70/4.02 (declare-fun tptp.zipf_int_nat_int ((-> tptp.int tptp.nat tptp.int) tptp.list_int tptp.list_nat) tptp.list_int)
% 3.70/4.02 (declare-fun tptp.zipf_int_nat_nat ((-> tptp.int tptp.nat tptp.nat) tptp.list_int tptp.list_nat) tptp.list_nat)
% 3.70/4.02 (declare-fun tptp.zipf_i5995984495708165493n_assn ((-> tptp.int tptp.nat tptp.produc6575502325842934193n_assn) tptp.list_int tptp.list_nat) tptp.list_P8527749157015355191n_assn)
% 3.70/4.02 (declare-fun tptp.zipf_nat_int_int ((-> tptp.nat tptp.int tptp.int) tptp.list_nat tptp.list_int) tptp.list_int)
% 3.70/4.02 (declare-fun tptp.zipf_nat_int_nat ((-> tptp.nat tptp.int tptp.nat) tptp.list_nat tptp.list_int) tptp.list_nat)
% 3.70/4.02 (declare-fun tptp.zipf_nat_nat_int ((-> tptp.nat tptp.nat tptp.int) tptp.list_nat tptp.list_nat) tptp.list_int)
% 3.70/4.02 (declare-fun tptp.zipf_nat_nat_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.list_nat tptp.list_nat) tptp.list_nat)
% 3.70/4.02 (declare-fun tptp.zipf_n5773672615478942615_nat_c ((-> tptp.nat tptp.c tptp.product_prod_nat_c) tptp.list_nat tptp.list_c) tptp.list_P2993859830824179253_nat_c)
% 3.70/4.02 (declare-fun tptp.zipf_n3657244561791696409_nat_d ((-> tptp.nat tptp.d tptp.product_prod_nat_d) tptp.list_nat tptp.list_d) tptp.list_P3064893870870525238_nat_d)
% 3.70/4.02 (declare-fun tptp.zipf_c230841880303976139_c_int ((-> tptp.c tptp.int tptp.product_prod_c_int) tptp.list_c tptp.list_int) tptp.list_P3071867362843219819_c_int)
% 3.70/4.02 (declare-fun tptp.zipf_c7084520048314076179_c_nat ((-> tptp.c tptp.nat tptp.product_prod_c_nat) tptp.list_c tptp.list_nat) tptp.list_P5561950507774946575_c_nat)
% 3.70/4.02 (declare-fun tptp.zipf_c684006316856269033od_c_c ((-> tptp.c tptp.c tptp.product_prod_c_c) tptp.list_c tptp.list_c) tptp.list_P267710562049004973od_c_c)
% 3.70/4.02 (declare-fun tptp.zipf_c44566020827681705od_c_d ((-> tptp.c tptp.d tptp.product_prod_c_d) tptp.list_c tptp.list_d) tptp.list_P338744602095350958od_c_d)
% 3.70/4.02 (declare-fun tptp.zipf_d997717096299170253_d_int ((-> tptp.d tptp.int tptp.product_prod_d_int) tptp.list_d tptp.list_int) tptp.list_P8668085978031350508_d_int)
% 3.70/4.02 (declare-fun tptp.zipf_d7851395264309270293_d_nat ((-> tptp.d tptp.nat tptp.product_prod_d_nat) tptp.list_d tptp.list_nat) tptp.list_P1934797086108301456_d_nat)
% 3.70/4.02 (declare-fun tptp.zipf_d1836499321508429225od_d_c ((-> tptp.d tptp.c tptp.product_prod_d_c) tptp.list_d tptp.list_c) tptp.list_P8855433598298794092od_d_c)
% 3.70/4.02 (declare-fun tptp.zipf_d1197059025479841897od_d_d ((-> tptp.d tptp.d tptp.product_prod_d_d) tptp.list_d tptp.list_d) tptp.list_P8926467638345140077od_d_d)
% 3.70/4.02 (declare-fun tptp.add_ms2612439473150266591at_nat (tptp.product_prod_nat_nat tptp.multis2468970476368604999at_nat) tptp.multis2468970476368604999at_nat)
% 3.70/4.02 (declare-fun tptp.ms_strict () tptp.set_Pr8551490117392284871at_nat)
% 3.70/4.02 (declare-fun tptp.ms_weak () tptp.set_Pr8551490117392284871at_nat)
% 3.70/4.02 (declare-fun tptp.pw_leq (tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.set_ms8126754132646256062at_nat (tptp.multis2468970476368604999at_nat) tptp.set_Pr1261947904930325089at_nat)
% 3.70/4.02 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.semiri4939895301339042750nteger (tptp.nat) tptp.code_integer)
% 3.70/4.02 (declare-fun tptp.semiri1314217659103216013at_int (tptp.nat) tptp.int)
% 3.70/4.02 (declare-fun tptp.size_s8908918004648414271_nat_o (tptp.list_P7985473006766602707_nat_o) tptp.nat)
% 3.70/4.02 (declare-fun tptp.size_size_list_o (tptp.list_o) tptp.nat)
% 3.70/4.02 (declare-fun tptp.size_size_list_assn (tptp.list_assn) tptp.nat)
% 3.70/4.02 (declare-fun tptp.size_s3445333598471063425nteger (tptp.list_Code_integer) tptp.nat)
% 3.70/4.02 (declare-fun tptp.size_size_list_int (tptp.list_int) tptp.nat)
% 3.70/4.02 (declare-fun tptp.size_size_list_nat (tptp.list_nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.size_size_list_num (tptp.list_num) tptp.nat)
% 3.70/4.02 (declare-fun tptp.size_s6829681357464350627n_assn (tptp.list_P8527749157015355191n_assn) tptp.nat)
% 3.70/4.02 (declare-fun tptp.size_s2970893825323803983at_int (tptp.list_P3521021558325789923at_int) tptp.nat)
% 3.70/4.02 (declare-fun tptp.size_s5460976970255530739at_nat (tptp.list_P6011104703257516679at_nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.size_s385972143775086793_nat_c (tptp.list_P2993859830824179253_nat_c) tptp.nat)
% 3.70/4.02 (declare-fun tptp.size_s457006183821432778_nat_d (tptp.list_P3064893870870525238_nat_d) tptp.nat)
% 3.70/4.02 (declare-fun tptp.size_s1588839187904960729at_nat (tptp.list_P5464809261938338413at_nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.size_s463979675794127359_c_int (tptp.list_P3071867362843219819_c_int) tptp.nat)
% 3.70/4.02 (declare-fun tptp.size_s2954062820725854115_c_nat (tptp.list_P5561950507774946575_c_nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.size_s2756448709718749209od_c_c (tptp.list_P267710562049004973od_c_c) tptp.nat)
% 3.70/4.02 (declare-fun tptp.size_s2827482749765095194od_c_d (tptp.list_P338744602095350958od_c_d) tptp.nat)
% 3.70/4.02 (declare-fun tptp.size_s6060198290982258048_d_int (tptp.list_P8668085978031350508_d_int) tptp.nat)
% 3.70/4.02 (declare-fun tptp.size_s8550281435913984804_d_nat (tptp.list_P1934797086108301456_d_nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.size_s2120799709113762520od_d_c (tptp.list_P8855433598298794092od_d_c) tptp.nat)
% 3.70/4.02 (declare-fun tptp.size_s2191833749160108505od_d_d (tptp.list_P8926467638345140077od_d_d) tptp.nat)
% 3.70/4.02 (declare-fun tptp.size_s8736152011456118867at_nat (tptp.list_s1210847774152347623at_nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.size_size_list_c (tptp.list_c) tptp.nat)
% 3.70/4.02 (declare-fun tptp.size_size_list_d (tptp.list_d) tptp.nat)
% 3.70/4.02 (declare-fun tptp.size_s8510653225128441779at_nat (tptp.multis2468970476368604999at_nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.nat_list_encode (tptp.list_nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.nat_list_encode_rel (tptp.list_nat tptp.list_nat) Bool)
% 3.70/4.02 (declare-fun tptp.nat_prod_decode_aux (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 3.70/4.02 (declare-fun tptp.nat_pr5047031295181774490ux_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 3.70/4.02 (declare-fun tptp.nat_prod_encode (tptp.product_prod_nat_nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.nat_set_decode (tptp.nat) tptp.set_nat)
% 3.70/4.02 (declare-fun tptp.nat_set_encode (tptp.set_nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.bitM (tptp.num) tptp.num)
% 3.70/4.02 (declare-fun tptp.inc (tptp.num) tptp.num)
% 3.70/4.02 (declare-fun tptp.nat_of_num (tptp.num) tptp.nat)
% 3.70/4.02 (declare-fun tptp.neg_nu7757733837767384882nteger (tptp.code_integer) tptp.code_integer)
% 3.70/4.02 (declare-fun tptp.neg_nu3811975205180677377ec_int (tptp.int) tptp.int)
% 3.70/4.02 (declare-fun tptp.neg_nu3179335615603231917ec_rat (tptp.rat) tptp.rat)
% 3.70/4.02 (declare-fun tptp.bit0 (tptp.num) tptp.num)
% 3.70/4.02 (declare-fun tptp.bit1 (tptp.num) tptp.num)
% 3.70/4.02 (declare-fun tptp.one () tptp.num)
% 3.70/4.02 (declare-fun tptp.num_of_nat (tptp.nat) tptp.num)
% 3.70/4.02 (declare-fun tptp.numera6620942414471956472nteger (tptp.num) tptp.code_integer)
% 3.70/4.02 (declare-fun tptp.numera5444537566228673987atural (tptp.num) tptp.code_natural)
% 3.70/4.02 (declare-fun tptp.numeral_numeral_int (tptp.num) tptp.int)
% 3.70/4.02 (declare-fun tptp.numeral_numeral_nat (tptp.num) tptp.nat)
% 3.70/4.02 (declare-fun tptp.numeral_numeral_rat (tptp.num) tptp.rat)
% 3.70/4.02 (declare-fun tptp.pred_numeral (tptp.num) tptp.nat)
% 3.70/4.02 (declare-fun tptp.none_P9117596204409417319it_nat () tptp.option8956607266484857688it_nat)
% 3.70/4.02 (declare-fun tptp.some_P1914260805536162275it_nat (tptp.produc8664842809031399944it_nat) tptp.option8956607266484857688it_nat)
% 3.70/4.02 (declare-fun tptp.order_underS_nat (tptp.set_Pr1261947904930325089at_nat tptp.nat) tptp.set_nat)
% 3.70/4.02 (declare-fun tptp.order_2888998067076097458on_nat (tptp.set_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.bot_bo7963750851167320836at_o_o ((-> tptp.produc3658429121746597890et_nat Bool)) Bool)
% 3.70/4.02 (declare-fun tptp.bot_bot_o_o (Bool) Bool)
% 3.70/4.02 (declare-fun tptp.bot_bot_int_o (tptp.int) Bool)
% 3.70/4.02 (declare-fun tptp.bot_bot_nat_o (tptp.nat) Bool)
% 3.70/4.02 (declare-fun tptp.bot_bo482883023278783056_nat_o (tptp.product_prod_nat_nat) Bool)
% 3.70/4.02 (declare-fun tptp.bot_bo6829958733157050602_nat_o (tptp.produc3843707927480180839at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.bot_bot_assn () tptp.assn)
% 3.70/4.02 (declare-fun tptp.bot_bot_filter_nat () tptp.filter_nat)
% 3.70/4.02 (declare-fun tptp.bot_bot_nat () tptp.nat)
% 3.70/4.02 (declare-fun tptp.bot_bo7824918357723582233_nat_o () tptp.set_Pr4532377907799695533_nat_o)
% 3.70/4.02 (declare-fun tptp.bot_bot_set_o () tptp.set_o)
% 3.70/4.02 (declare-fun tptp.bot_bot_set_int () tptp.set_int)
% 3.70/4.02 (declare-fun tptp.bot_bot_set_nat () tptp.set_nat)
% 3.70/4.02 (declare-fun tptp.bot_bo7073875226086086771od_o_o () tptp.set_Product_prod_o_o)
% 3.70/4.02 (declare-fun tptp.bot_bo1176836662018730877n_assn () tptp.set_Pr5949110396991348497n_assn)
% 3.70/4.02 (declare-fun tptp.bot_bo1796632182523588997nt_int () tptp.set_Pr958786334691620121nt_int)
% 3.70/4.02 (declare-fun tptp.bot_bo2099793752762293965at_nat () tptp.set_Pr1261947904930325089at_nat)
% 3.70/4.02 (declare-fun tptp.bot_bo5327735625951526323at_nat () tptp.set_Pr8693737435421807431at_nat)
% 3.70/4.02 (declare-fun tptp.bot_bo7193250159860175667at_nat () tptp.set_Pr5564308138774400199at_nat)
% 3.70/4.02 (declare-fun tptp.bot_bo228742789529271731at_nat () tptp.set_Pr4329608150637261639at_nat)
% 3.70/4.02 (declare-fun tptp.bot_bo3083307316010499117at_nat () tptp.set_se7855581050983116737at_nat)
% 3.70/4.02 (declare-fun tptp.bot_bot_set_c () tptp.set_c)
% 3.70/4.02 (declare-fun tptp.bot_bot_set_d () tptp.set_d)
% 3.70/4.02 (declare-fun tptp.ord_less_assn (tptp.assn tptp.assn) Bool)
% 3.70/4.02 (declare-fun tptp.ord_le6747313008572928689nteger (tptp.code_integer tptp.code_integer) Bool)
% 3.70/4.02 (declare-fun tptp.ord_le5570908160329646204atural (tptp.code_natural tptp.code_natural) Bool)
% 3.70/4.02 (declare-fun tptp.ord_less_filter_nat (tptp.filter_nat tptp.filter_nat) Bool)
% 3.70/4.02 (declare-fun tptp.ord_less_int (tptp.int tptp.int) Bool)
% 3.70/4.02 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 3.70/4.02 (declare-fun tptp.ord_less_num (tptp.num tptp.num) Bool)
% 3.70/4.02 (declare-fun tptp.ord_less_rat (tptp.rat tptp.rat) Bool)
% 3.70/4.02 (declare-fun tptp.ord_le2453136405763929_nat_o (tptp.set_Pr4532377907799695533_nat_o tptp.set_Pr4532377907799695533_nat_o) Bool)
% 3.70/4.02 (declare-fun tptp.ord_less_set_o (tptp.set_o tptp.set_o) Bool)
% 3.70/4.02 (declare-fun tptp.ord_less_set_int (tptp.set_int tptp.set_int) Bool)
% 3.70/4.02 (declare-fun tptp.ord_less_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 3.70/4.02 (declare-fun tptp.ord_le7866589430770878221at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.ord_le2604355607129572851at_nat (tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.ord_less_eq_assn (tptp.assn tptp.assn) Bool)
% 3.70/4.02 (declare-fun tptp.ord_le3102999989581377725nteger (tptp.code_integer tptp.code_integer) Bool)
% 3.70/4.02 (declare-fun tptp.ord_le1926595141338095240atural (tptp.code_natural tptp.code_natural) Bool)
% 3.70/4.02 (declare-fun tptp.ord_le2510731241096832064er_nat (tptp.filter_nat tptp.filter_nat) Bool)
% 3.70/4.02 (declare-fun tptp.ord_less_eq_int (tptp.int tptp.int) Bool)
% 3.70/4.02 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 3.70/4.02 (declare-fun tptp.ord_less_eq_num (tptp.num tptp.num) Bool)
% 3.70/4.02 (declare-fun tptp.ord_less_eq_rat (tptp.rat tptp.rat) Bool)
% 3.70/4.02 (declare-fun tptp.ord_le2965882846123202637_nat_o (tptp.set_Pr4532377907799695533_nat_o tptp.set_Pr4532377907799695533_nat_o) Bool)
% 3.70/4.02 (declare-fun tptp.ord_less_eq_set_o (tptp.set_o tptp.set_o) Bool)
% 3.70/4.02 (declare-fun tptp.ord_less_eq_set_int (tptp.set_int tptp.set_int) Bool)
% 3.70/4.02 (declare-fun tptp.ord_less_eq_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 3.70/4.02 (declare-fun tptp.ord_le135402666524580259nt_int (tptp.set_Pr1872883991513573699nt_int tptp.set_Pr1872883991513573699nt_int) Bool)
% 3.70/4.02 (declare-fun tptp.ord_le653643898420964396nteger (tptp.set_Pr1281608226676607948nteger tptp.set_Pr1281608226676607948nteger) Bool)
% 3.70/4.02 (declare-fun tptp.ord_le4763372923235995152et_nat (tptp.set_Pr8536935166611901872et_nat tptp.set_Pr8536935166611901872et_nat) Bool)
% 3.70/4.02 (declare-fun tptp.ord_le5966269811547037844et_nat (tptp.set_Pr3286484037609594932et_nat tptp.set_Pr3286484037609594932et_nat) Bool)
% 3.70/4.02 (declare-fun tptp.ord_le8725513860283290265nt_int (tptp.set_Pr9222295170931077689nt_int tptp.set_Pr9222295170931077689nt_int) Bool)
% 3.70/4.02 (declare-fun tptp.ord_le192195778054999463od_o_o (tptp.set_Product_prod_o_o tptp.set_Product_prod_o_o) Bool)
% 3.70/4.02 (declare-fun tptp.ord_le171416862856029873n_assn (tptp.set_Pr5949110396991348497n_assn tptp.set_Pr5949110396991348497n_assn) Bool)
% 3.70/4.02 (declare-fun tptp.ord_le3146513528884898305at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.ord_le1268244103169919719at_nat (tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.ord_less_eq_set_c (tptp.set_c tptp.set_c) Bool)
% 3.70/4.02 (declare-fun tptp.ord_less_eq_set_d (tptp.set_d tptp.set_d) Bool)
% 3.70/4.02 (declare-fun tptp.ord_max_nat (tptp.nat tptp.nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.ord_min_assn (tptp.assn tptp.assn) tptp.assn)
% 3.70/4.02 (declare-fun tptp.ord_min_Code_integer (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 3.70/4.02 (declare-fun tptp.ord_min_filter_nat (tptp.filter_nat tptp.filter_nat) tptp.filter_nat)
% 3.70/4.02 (declare-fun tptp.ord_min_int (tptp.int tptp.int) tptp.int)
% 3.70/4.02 (declare-fun tptp.ord_min_nat (tptp.nat tptp.nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.ord_min_num (tptp.num tptp.num) tptp.num)
% 3.70/4.02 (declare-fun tptp.ord_min_rat (tptp.rat tptp.rat) tptp.rat)
% 3.70/4.02 (declare-fun tptp.ord_min_set_o (tptp.set_o tptp.set_o) tptp.set_o)
% 3.70/4.02 (declare-fun tptp.ord_min_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 3.70/4.02 (declare-fun tptp.ord_min_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 3.70/4.02 (declare-fun tptp.ord_mi4194197829855655752at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 3.70/4.02 (declare-fun tptp.ord_mi6693596345299712430at_nat (tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat) tptp.set_Pr4329608150637261639at_nat)
% 3.70/4.02 (declare-fun tptp.order_mono_nat_nat ((-> tptp.nat tptp.nat)) Bool)
% 3.70/4.02 (declare-fun tptp.ordering_top_nat ((-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool) tptp.nat) Bool)
% 3.70/4.02 (declare-fun tptp.top_top_assn () tptp.assn)
% 3.70/4.02 (declare-fun tptp.top_top_set_o () tptp.set_o)
% 3.70/4.02 (declare-fun tptp.top_top_set_nat () tptp.set_nat)
% 3.70/4.02 (declare-fun tptp.power_power_assn (tptp.assn tptp.nat) tptp.assn)
% 3.70/4.02 (declare-fun tptp.power_8256067586552552935nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 3.70/4.02 (declare-fun tptp.power_power_int (tptp.int tptp.nat) tptp.int)
% 3.70/4.02 (declare-fun tptp.power_power_nat (tptp.nat tptp.nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.power_power_rat (tptp.rat tptp.nat) tptp.rat)
% 3.70/4.02 (declare-fun tptp.produc6137756002093451184nteger ((-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger) tptp.produc8763457246119570046nteger)
% 3.70/4.02 (declare-fun tptp.produc2252593628808123835atural ((-> tptp.code_natural tptp.option6357759511663192854e_term) tptp.produc7822875418678951345atural) tptp.produc8731074985263844745atural)
% 3.70/4.02 (declare-fun tptp.produc8618682346314911123st_int ((-> tptp.int tptp.int Bool) tptp.list_int) tptp.produc5834231552977413017st_int)
% 3.70/4.02 (declare-fun tptp.produc4305682042979456191nt_int ((-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int) tptp.produc7773217078559923341nt_int)
% 3.70/4.02 (declare-fun tptp.produc4727192421694094319st_nat ((-> tptp.nat tptp.nat Bool) tptp.list_nat) tptp.produc254973753779126261st_nat)
% 3.70/4.02 (declare-fun tptp.produc6115016301897879072n_assn ((-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn Bool) tptp.list_P8527749157015355191n_assn) tptp.produc4530688714081574576n_assn)
% 3.70/4.02 (declare-fun tptp.produc8603105652947943368nteger ((-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger) tptp.produc1908205239877642774nteger)
% 3.70/4.02 (declare-fun tptp.produc3831813291587773865atural ((-> tptp.produc4972180933644002618e_term tptp.option6357759511663192854e_term) tptp.produc7822875418678951345atural) tptp.produc989692990947075319atural)
% 3.70/4.02 (declare-fun tptp.produc7368190662567826135_nat_o ((-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool)) tptp.produc4928098042776334183_nat_o)
% 3.70/4.02 (declare-fun tptp.produc2245416461498447860et_nat ((-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat) tptp.produc2732055786443039994et_nat)
% 3.70/4.02 (declare-fun tptp.produc5001842942810119800et_nat ((-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat) tptp.produc3925858234332021118et_nat)
% 3.70/4.02 (declare-fun tptp.produc5700946648718959541nt_int ((-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int) tptp.produc2285326912895808259nt_int)
% 3.70/4.02 (declare-fun tptp.product_Pair_o_o (Bool Bool) tptp.product_prod_o_o)
% 3.70/4.02 (declare-fun tptp.produc118845697133431529n_assn (tptp.assn tptp.assn) tptp.produc6575502325842934193n_assn)
% 3.70/4.02 (declare-fun tptp.produc6677183202524767010eger_o (tptp.code_integer Bool) tptp.produc6271795597528267376eger_o)
% 3.70/4.02 (declare-fun tptp.produc1086072967326762835nteger (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 3.70/4.02 (declare-fun tptp.produc3574140220909816553atural (tptp.code_natural tptp.code_natural) tptp.produc7822875418678951345atural)
% 3.70/4.02 (declare-fun tptp.produc6639722614265839536atural (tptp.code_natural tptp.produc7822875418678951345atural) tptp.produc5835291356934675326atural)
% 3.70/4.02 (declare-fun tptp.produc584006145561248582it_nat (tptp.heap_e7401611519738050253t_unit tptp.nat) tptp.produc6653097349344004940it_nat)
% 3.70/4.02 (declare-fun tptp.produc7507926704131184380et_nat (tptp.heap_e7401611519738050253t_unit tptp.set_nat) tptp.produc3658429121746597890et_nat)
% 3.70/4.02 (declare-fun tptp.product_Pair_int_int (tptp.int tptp.int) tptp.product_prod_int_int)
% 3.70/4.02 (declare-fun tptp.product_Pair_int_nat (tptp.int tptp.nat) tptp.product_prod_int_nat)
% 3.70/4.02 (declare-fun tptp.produc3313821056773121708n_assn (tptp.int tptp.produc6575502325842934193n_assn) tptp.produc3167338625816234618n_assn)
% 3.70/4.02 (declare-fun tptp.produc3525228511222278652at_nat (tptp.int tptp.product_prod_nat_nat) tptp.produc1062882101152166346at_nat)
% 3.70/4.02 (declare-fun tptp.produc364263696895485585st_int (tptp.list_int tptp.list_int) tptp.produc1186641810826059865st_int)
% 3.70/4.02 (declare-fun tptp.produc4542114716404682293st_nat (tptp.list_int tptp.list_nat) tptp.produc3676724955757786621st_nat)
% 3.70/4.02 (declare-fun tptp.produc4510294837168919970n_assn (tptp.list_int tptp.list_P8527749157015355191n_assn) tptp.produc8582807064127716720n_assn)
% 3.70/4.02 (declare-fun tptp.produc7739558402351520821st_int (tptp.list_nat tptp.list_int) tptp.produc8561936516282095101st_int)
% 3.70/4.02 (declare-fun tptp.produc2694037385005941721st_nat (tptp.list_nat tptp.list_nat) tptp.produc1828647624359046049st_nat)
% 3.70/4.02 (declare-fun tptp.produc7706768604797473534n_assn (tptp.list_nat tptp.list_P8527749157015355191n_assn) tptp.produc2555908794901494476n_assn)
% 3.70/4.02 (declare-fun tptp.produc7723716018658481613list_c (tptp.list_nat tptp.list_c) tptp.produc1655478831073744795list_c)
% 3.70/4.02 (declare-fun tptp.produc7723716022961710414list_d (tptp.list_nat tptp.list_d) tptp.produc1726512871120090780list_d)
% 3.70/4.02 (declare-fun tptp.produc1996262876970182428st_int (tptp.list_P8527749157015355191n_assn tptp.list_int) tptp.produc4164172529858598818st_int)
% 3.70/4.02 (declare-fun tptp.produc6174113896479379136st_nat (tptp.list_P8527749157015355191n_assn tptp.list_nat) tptp.produc6654255674790325574st_nat)
% 3.70/4.02 (declare-fun tptp.produc3014731801419794263n_assn (tptp.list_P8527749157015355191n_assn tptp.list_P8527749157015355191n_assn) tptp.produc337509097454979815n_assn)
% 3.70/4.02 (declare-fun tptp.produc7536900900485677911at_nat (tptp.list_s1210847774152347623at_nat tptp.list_s1210847774152347623at_nat) tptp.produc424102278133772007at_nat)
% 3.70/4.02 (declare-fun tptp.produc1948897715771513579st_int (tptp.list_c tptp.list_int) tptp.produc8499486975545879281st_int)
% 3.70/4.02 (declare-fun tptp.produc6126748735280710287st_nat (tptp.list_c tptp.list_nat) tptp.produc1766198083622830229st_nat)
% 3.70/4.02 (declare-fun tptp.produc5515445818230282391list_c (tptp.list_c tptp.list_c) tptp.produc7985223085803476903list_c)
% 3.70/4.02 (declare-fun tptp.produc5515445822533511192list_d (tptp.list_c tptp.list_d) tptp.produc8056257125849822888list_d)
% 3.70/4.02 (declare-fun tptp.produc2615797191311421932st_int (tptp.list_d tptp.list_int) tptp.produc9166386451085787634st_int)
% 3.70/4.02 (declare-fun tptp.produc6793648210820618640st_nat (tptp.list_d tptp.list_nat) tptp.produc2433097559162738582st_nat)
% 3.70/4.02 (declare-fun tptp.produc242965416994095062list_c (tptp.list_d tptp.list_c) tptp.produc2712742684567289574list_c)
% 3.70/4.02 (declare-fun tptp.produc242965421297323863list_d (tptp.list_d tptp.list_d) tptp.produc2783776724613635559list_d)
% 3.70/4.02 (declare-fun tptp.produc4348348721325984599at_nat (tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat) tptp.produc4166570645942440679at_nat)
% 3.70/4.02 (declare-fun tptp.product_Pair_nat_int (tptp.nat tptp.int) tptp.product_prod_nat_int)
% 3.70/4.02 (declare-fun tptp.product_Pair_nat_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 3.70/4.02 (declare-fun tptp.produc1553784393020010504n_assn (tptp.nat tptp.produc6575502325842934193n_assn) tptp.produc1407301962063123414n_assn)
% 3.70/4.02 (declare-fun tptp.produc487386426758144856at_nat (tptp.nat tptp.product_prod_nat_nat) tptp.produc7248412053542808358at_nat)
% 3.70/4.02 (declare-fun tptp.product_Pair_nat_c (tptp.nat tptp.c) tptp.product_prod_nat_c)
% 3.70/4.02 (declare-fun tptp.product_Pair_nat_d (tptp.nat tptp.d) tptp.product_prod_nat_d)
% 3.70/4.02 (declare-fun tptp.product_Pair_num_num (tptp.num tptp.num) tptp.product_prod_num_num)
% 3.70/4.02 (declare-fun tptp.produc8406175334058502835nt_int (tptp.produc7773217078559923341nt_int tptp.produc7773217078559923341nt_int) tptp.produc2501202720802129403nt_int)
% 3.70/4.02 (declare-fun tptp.produc7954516348491987909nteger (tptp.produc1908205239877642774nteger tptp.produc1908205239877642774nteger) tptp.produc824974754969098637nteger)
% 3.70/4.02 (declare-fun tptp.produc1940133919992309389et_nat (tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat) tptp.produc5657529347773406293et_nat)
% 3.70/4.02 (declare-fun tptp.produc8599840265553166229et_nat (tptp.produc3925858234332021118et_nat tptp.produc3925858234332021118et_nat) tptp.produc6830853553727218525et_nat)
% 3.70/4.02 (declare-fun tptp.produc7601053194514725023nt_int (tptp.produc2285326912895808259nt_int tptp.produc2285326912895808259nt_int) tptp.produc2432570611225516007nt_int)
% 3.70/4.02 (declare-fun tptp.produc6453891449406693510sn_int (tptp.produc6575502325842934193n_assn tptp.int) tptp.produc8718178513971670540sn_int)
% 3.70/4.02 (declare-fun tptp.produc6456381919915743786sn_nat (tptp.produc6575502325842934193n_assn tptp.nat) tptp.produc3672657496626091440sn_nat)
% 3.70/4.02 (declare-fun tptp.produc6128706242671166167n_assn (tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn) tptp.produc9053633027152450663n_assn)
% 3.70/4.02 (declare-fun tptp.produc4480994950612372183atural (tptp.produc7822875418678951345atural tptp.produc7822875418678951345atural) tptp.produc6756470014200349799atural)
% 3.70/4.02 (declare-fun tptp.produc6348220600061155286at_int (tptp.product_prod_nat_nat tptp.int) tptp.produc4196048018000912732at_int)
% 3.70/4.02 (declare-fun tptp.produc6350711070570205562at_nat (tptp.product_prod_nat_nat tptp.nat) tptp.produc8373899037510109440at_nat)
% 3.70/4.02 (declare-fun tptp.produc6161850002892822231at_nat (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.produc859450856879609959at_nat)
% 3.70/4.02 (declare-fun tptp.produc2335810615602371415at_nat (tptp.produc3843707927480180839at_nat tptp.produc3843707927480180839at_nat) tptp.produc1906917888121415911at_nat)
% 3.70/4.02 (declare-fun tptp.produc7133225469290080770it_nat (tptp.product_unit tptp.produc6653097349344004940it_nat) tptp.produc8664842809031399944it_nat)
% 3.70/4.02 (declare-fun tptp.produc763777882069021527od_o_o (tptp.set_Product_prod_o_o tptp.set_Product_prod_o_o) tptp.produc2934264451710624999od_o_o)
% 3.70/4.02 (declare-fun tptp.produc8517790099723286449at_nat (tptp.set_Product_prod_o_o tptp.set_Pr1261947904930325089at_nat) tptp.produc732395585841259969at_nat)
% 3.70/4.02 (declare-fun tptp.produc5245064249948416855at_nat (tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat) tptp.produc4193628355235574503at_nat)
% 3.70/4.02 (declare-fun tptp.produc2922128104949294807at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.produc3843707927480180839at_nat)
% 3.70/4.02 (declare-fun tptp.produc9060074326276436823at_nat (tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat) tptp.produc1319942482725812455at_nat)
% 3.70/4.02 (declare-fun tptp.product_Pair_c_int (tptp.c tptp.int) tptp.product_prod_c_int)
% 3.70/4.02 (declare-fun tptp.product_Pair_c_nat (tptp.c tptp.nat) tptp.product_prod_c_nat)
% 3.70/4.02 (declare-fun tptp.product_Pair_c_c (tptp.c tptp.c) tptp.product_prod_c_c)
% 3.70/4.02 (declare-fun tptp.product_Pair_c_d (tptp.c tptp.d) tptp.product_prod_c_d)
% 3.70/4.02 (declare-fun tptp.product_Pair_d_int (tptp.d tptp.int) tptp.product_prod_d_int)
% 3.70/4.02 (declare-fun tptp.product_Pair_d_nat (tptp.d tptp.nat) tptp.product_prod_d_nat)
% 3.70/4.02 (declare-fun tptp.product_Pair_d_c (tptp.d tptp.c) tptp.product_prod_d_c)
% 3.70/4.02 (declare-fun tptp.product_Pair_d_d (tptp.d tptp.d) tptp.product_prod_d_d)
% 3.70/4.02 (declare-fun tptp.produc457027306803732586at_nat (tptp.set_nat (-> tptp.nat tptp.set_nat)) tptp.set_Pr1261947904930325089at_nat)
% 3.70/4.02 (declare-fun tptp.product_Unity () tptp.product_unit)
% 3.70/4.02 (declare-fun tptp.produc6499014454317279255nteger ((-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 3.70/4.02 (declare-fun tptp.produc9098658269643458507_int_o ((-> tptp.produc7773217078559923341nt_int Bool) (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int) Bool)
% 3.70/4.02 (declare-fun tptp.produc1217013493180205570eger_o ((-> tptp.produc1908205239877642774nteger Bool) (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger) Bool)
% 3.70/4.02 (declare-fun tptp.produc5101573711933517782_nat_o ((-> tptp.produc2732055786443039994et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat) Bool)
% 3.70/4.02 (declare-fun tptp.produc6216949301066131538_nat_o ((-> tptp.produc3925858234332021118et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat) Bool)
% 3.70/4.02 (declare-fun tptp.produc730925184835016917_int_o ((-> tptp.produc2285326912895808259nt_int Bool) (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int) Bool)
% 3.70/4.02 (declare-fun tptp.produc7274209992780475162assn_o ((-> tptp.assn tptp.assn Bool) tptp.produc6575502325842934193n_assn) Bool)
% 3.70/4.02 (declare-fun tptp.produc9125791028180074456eger_o ((-> tptp.code_integer tptp.code_integer tptp.produc6271795597528267376eger_o) tptp.produc8923325533196201883nteger) tptp.produc6271795597528267376eger_o)
% 3.70/4.02 (declare-fun tptp.produc6916734918728496179nteger ((-> tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 3.70/4.02 (declare-fun tptp.produc8282080750456430313atural ((-> tptp.code_natural tptp.code_natural tptp.produc6756470014200349799atural) tptp.produc7822875418678951345atural) tptp.produc6756470014200349799atural)
% 3.70/4.02 (declare-fun tptp.produc4245557441103728435nt_int ((-> tptp.int tptp.int tptp.product_prod_int_int) tptp.product_prod_int_int) tptp.product_prod_int_int)
% 3.70/4.02 (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)
% 3.70/4.02 (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)
% 3.70/4.02 (declare-fun tptp.produc6081775807080527818_nat_o ((-> tptp.nat tptp.nat Bool) tptp.product_prod_nat_nat) Bool)
% 3.70/4.02 (declare-fun tptp.produc2626176000494625587at_nat ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 3.70/4.02 (declare-fun tptp.produc9167289414957590229n_assn (tptp.produc6575502325842934193n_assn) tptp.assn)
% 3.70/4.02 (declare-fun tptp.produc1824681642469235216et_nat (tptp.produc3658429121746597890et_nat) tptp.heap_e7401611519738050253t_unit)
% 3.70/4.02 (declare-fun tptp.product_fst_int_int (tptp.product_prod_int_int) tptp.int)
% 3.70/4.02 (declare-fun tptp.produc2051961928117032727n_assn (tptp.produc6575502325842934193n_assn) tptp.assn)
% 3.70/4.02 (declare-fun tptp.produc6591912806276919810atural (tptp.produc5835291356934675326atural) tptp.produc7822875418678951345atural)
% 3.70/4.02 (declare-fun tptp.produc8586169260539613262et_nat (tptp.produc3658429121746597890et_nat) tptp.set_nat)
% 3.70/4.02 (declare-fun tptp.product_snd_int_int (tptp.product_prod_int_int) tptp.int)
% 3.70/4.02 (declare-fun tptp.produc5538323210962509403atural ((-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural) (-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural) tptp.produc7822875418678951345atural) tptp.produc5835291356934675326atural)
% 3.70/4.02 (declare-fun tptp.inc_shift (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 3.70/4.02 (declare-fun tptp.iterat8892046348760725948atural (tptp.code_natural (-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural) tptp.code_natural tptp.produc7822875418678951345atural) tptp.produc5835291356934675326atural)
% 3.70/4.02 (declare-fun tptp.log (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 3.70/4.02 (declare-fun tptp.log_rel (tptp.produc7822875418678951345atural tptp.produc7822875418678951345atural) Bool)
% 3.70/4.02 (declare-fun tptp.minus_shift (tptp.code_natural tptp.code_natural tptp.code_natural) tptp.code_natural)
% 3.70/4.02 (declare-fun tptp.next (tptp.produc7822875418678951345atural) tptp.produc5835291356934675326atural)
% 3.70/4.02 (declare-fun tptp.range (tptp.code_natural tptp.produc7822875418678951345atural) tptp.produc5835291356934675326atural)
% 3.70/4.02 (declare-fun tptp.split_seed (tptp.produc7822875418678951345atural) tptp.produc6756470014200349799atural)
% 3.70/4.02 (declare-fun tptp.abs_Rat (tptp.product_prod_int_int) tptp.rat)
% 3.70/4.02 (declare-fun tptp.fract (tptp.int tptp.int) tptp.rat)
% 3.70/4.02 (declare-fun tptp.frct (tptp.product_prod_int_int) tptp.rat)
% 3.70/4.02 (declare-fun tptp.rep_Rat (tptp.rat) tptp.product_prod_int_int)
% 3.70/4.02 (declare-fun tptp.normalize (tptp.product_prod_int_int) tptp.product_prod_int_int)
% 3.70/4.02 (declare-fun tptp.of_int (tptp.int) tptp.rat)
% 3.70/4.02 (declare-fun tptp.pcr_rat (tptp.product_prod_int_int tptp.rat) Bool)
% 3.70/4.02 (declare-fun tptp.quotient_of (tptp.rat) tptp.product_prod_int_int)
% 3.70/4.02 (declare-fun tptp.ratrel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 3.70/4.02 (declare-fun tptp.refine_Imp_assert (Bool) tptp.heap_T5738788834812785303t_unit)
% 3.70/4.02 (declare-fun tptp.field_81821745747897882_nat_o (tptp.set_Pr2161125870931222855_nat_o) tptp.set_Pr4532377907799695533_nat_o)
% 3.70/4.02 (declare-fun tptp.field_o (tptp.set_Product_prod_o_o) tptp.set_o)
% 3.70/4.02 (declare-fun tptp.field_int (tptp.set_Pr958786334691620121nt_int) tptp.set_int)
% 3.70/4.02 (declare-fun tptp.field_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_nat)
% 3.70/4.02 (declare-fun tptp.field_4706345496283612622at_nat (tptp.set_Pr8693737435421807431at_nat) tptp.set_Pr1261947904930325089at_nat)
% 3.70/4.02 (declare-fun tptp.field_2862844103579723188at_nat (tptp.set_Pr5564308138774400199at_nat) tptp.set_Pr4329608150637261639at_nat)
% 3.70/4.02 (declare-fun tptp.field_3145993188331922222at_nat (tptp.set_Pr4329608150637261639at_nat) tptp.set_se7855581050983116737at_nat)
% 3.70/4.02 (declare-fun tptp.total_7429123086324524369_nat_o (tptp.set_Pr4532377907799695533_nat_o tptp.set_Pr2161125870931222855_nat_o) Bool)
% 3.70/4.02 (declare-fun tptp.total_on_o (tptp.set_o tptp.set_Product_prod_o_o) Bool)
% 3.70/4.02 (declare-fun tptp.total_on_int (tptp.set_int tptp.set_Pr958786334691620121nt_int) Bool)
% 3.70/4.02 (declare-fun tptp.total_on_nat (tptp.set_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.total_3592101749530773125at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr8693737435421807431at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.total_1513685709984341995at_nat (tptp.set_Pr4329608150637261639at_nat tptp.set_Pr5564308138774400199at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.total_7212417256332265445at_nat (tptp.set_se7855581050983116737at_nat tptp.set_Pr4329608150637261639at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.algebr932160517623751201me_int (tptp.int tptp.int) Bool)
% 3.70/4.02 (declare-fun tptp.algebr934650988132801477me_nat (tptp.nat tptp.nat) Bool)
% 3.70/4.02 (declare-fun tptp.divide6298287555418463151nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 3.70/4.02 (declare-fun tptp.divide5121882707175180666atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 3.70/4.02 (declare-fun tptp.divide_divide_int (tptp.int tptp.int) tptp.int)
% 3.70/4.02 (declare-fun tptp.divide_divide_nat (tptp.nat tptp.nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.divide_divide_rat (tptp.rat tptp.rat) tptp.rat)
% 3.70/4.02 (declare-fun tptp.dvd_dvd_Code_integer (tptp.code_integer tptp.code_integer) Bool)
% 3.70/4.02 (declare-fun tptp.dvd_dvd_int (tptp.int tptp.int) Bool)
% 3.70/4.02 (declare-fun tptp.dvd_dvd_nat (tptp.nat tptp.nat) Bool)
% 3.70/4.02 (declare-fun tptp.modulo364778990260209775nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 3.70/4.02 (declare-fun tptp.modulo8411746178871703098atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 3.70/4.02 (declare-fun tptp.modulo_modulo_int (tptp.int tptp.int) tptp.int)
% 3.70/4.02 (declare-fun tptp.modulo_modulo_nat (tptp.nat tptp.nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.zero_n2684676970156552555ol_int (Bool) tptp.int)
% 3.70/4.02 (declare-fun tptp.zero_n2687167440665602831ol_nat (Bool) tptp.nat)
% 3.70/4.02 (declare-fun tptp.collec939566748876313656_nat_o ((-> (-> tptp.produc3658429121746597890et_nat Bool) Bool)) tptp.set_Pr4532377907799695533_nat_o)
% 3.70/4.02 (declare-fun tptp.collect_o ((-> Bool Bool)) tptp.set_o)
% 3.70/4.02 (declare-fun tptp.collect_int ((-> tptp.int Bool)) tptp.set_int)
% 3.70/4.02 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 3.70/4.02 (declare-fun tptp.collec3392354462482085612at_nat ((-> tptp.product_prod_nat_nat Bool)) tptp.set_Pr1261947904930325089at_nat)
% 3.70/4.02 (declare-fun tptp.collec6321179662152712658at_nat ((-> tptp.produc3843707927480180839at_nat Bool)) tptp.set_Pr4329608150637261639at_nat)
% 3.70/4.02 (declare-fun tptp.image_4470545334726330049nteger ((-> tptp.code_integer tptp.code_integer) tptp.set_Code_integer) tptp.set_Code_integer)
% 3.70/4.02 (declare-fun tptp.image_1215581382706833972nteger ((-> tptp.nat tptp.code_integer) tptp.set_nat) tptp.set_Code_integer)
% 3.70/4.02 (declare-fun tptp.image_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 3.70/4.02 (declare-fun tptp.image_nat_set_nat ((-> tptp.nat tptp.set_nat) tptp.set_nat) tptp.set_set_nat)
% 3.70/4.02 (declare-fun tptp.insert5175938949040314269_nat_o ((-> tptp.produc3658429121746597890et_nat Bool) tptp.set_Pr4532377907799695533_nat_o) tptp.set_Pr4532377907799695533_nat_o)
% 3.70/4.02 (declare-fun tptp.insert_o2 (Bool tptp.set_o) tptp.set_o)
% 3.70/4.02 (declare-fun tptp.insert_int2 (tptp.int tptp.set_int) tptp.set_int)
% 3.70/4.02 (declare-fun tptp.insert_nat2 (tptp.nat tptp.set_nat) tptp.set_nat)
% 3.70/4.02 (declare-fun tptp.insert6201435330877294327od_o_o (tptp.product_prod_o_o tptp.set_Product_prod_o_o) tptp.set_Product_prod_o_o)
% 3.70/4.02 (declare-fun tptp.insert5290817439147925377n_assn (tptp.produc6575502325842934193n_assn tptp.set_Pr5949110396991348497n_assn) tptp.set_Pr5949110396991348497n_assn)
% 3.70/4.02 (declare-fun tptp.insert5033312907999012233nt_int (tptp.product_prod_int_int tptp.set_Pr958786334691620121nt_int) tptp.set_Pr958786334691620121nt_int)
% 3.70/4.02 (declare-fun tptp.insert8211810215607154385at_nat (tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 3.70/4.02 (declare-fun tptp.insert5050368324300391991at_nat (tptp.produc859450856879609959at_nat tptp.set_Pr8693737435421807431at_nat) tptp.set_Pr8693737435421807431at_nat)
% 3.70/4.02 (declare-fun tptp.insert398606708087465655at_nat (tptp.produc1906917888121415911at_nat tptp.set_Pr5564308138774400199at_nat) tptp.set_Pr5564308138774400199at_nat)
% 3.70/4.02 (declare-fun tptp.insert9069300056098147895at_nat (tptp.produc3843707927480180839at_nat tptp.set_Pr4329608150637261639at_nat) tptp.set_Pr4329608150637261639at_nat)
% 3.70/4.02 (declare-fun tptp.insert9200635055090092081at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_se7855581050983116737at_nat) tptp.set_se7855581050983116737at_nat)
% 3.70/4.02 (declare-fun tptp.insert_c (tptp.c tptp.set_c) tptp.set_c)
% 3.70/4.02 (declare-fun tptp.insert_d (tptp.d tptp.set_d) tptp.set_d)
% 3.70/4.02 (declare-fun tptp.is_empty_o (tptp.set_o) Bool)
% 3.70/4.02 (declare-fun tptp.is_empty_int (tptp.set_int) Bool)
% 3.70/4.02 (declare-fun tptp.is_empty_nat (tptp.set_nat) Bool)
% 3.70/4.02 (declare-fun tptp.is_emp7749065762491207043n_assn (tptp.set_Pr5949110396991348497n_assn) Bool)
% 3.70/4.02 (declare-fun tptp.is_emp1662574758705540307at_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.is_emp7572232645145209145at_nat (tptp.set_Pr4329608150637261639at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.is_sin5180296473474724033_nat_o (tptp.set_Pr4532377907799695533_nat_o) Bool)
% 3.70/4.02 (declare-fun tptp.is_singleton_o (tptp.set_o) Bool)
% 3.70/4.02 (declare-fun tptp.is_singleton_int (tptp.set_int) Bool)
% 3.70/4.02 (declare-fun tptp.is_singleton_nat (tptp.set_nat) Bool)
% 3.70/4.02 (declare-fun tptp.is_sin2850979758926227957at_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.is_sin2937591304547752795at_nat (tptp.set_Pr4329608150637261639at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.pairwi2432143822833250616_nat_o ((-> (-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) Bool) tptp.set_Pr4532377907799695533_nat_o) Bool)
% 3.70/4.02 (declare-fun tptp.pairwise_o ((-> Bool Bool Bool) tptp.set_o) Bool)
% 3.70/4.02 (declare-fun tptp.pairwise_int ((-> tptp.int tptp.int Bool) tptp.set_int) Bool)
% 3.70/4.02 (declare-fun tptp.pairwise_nat ((-> tptp.nat tptp.nat Bool) tptp.set_nat) Bool)
% 3.70/4.02 (declare-fun tptp.pairwi6357175311820755948at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.set_Pr1261947904930325089at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.pairwi3222497012029234898at_nat ((-> tptp.produc3843707927480180839at_nat tptp.produc3843707927480180839at_nat Bool) tptp.set_Pr4329608150637261639at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.remove4651630035290841522_nat_o ((-> tptp.produc3658429121746597890et_nat Bool) tptp.set_Pr4532377907799695533_nat_o) tptp.set_Pr4532377907799695533_nat_o)
% 3.70/4.02 (declare-fun tptp.remove_o (Bool tptp.set_o) tptp.set_o)
% 3.70/4.02 (declare-fun tptp.remove_int (tptp.int tptp.set_int) tptp.set_int)
% 3.70/4.02 (declare-fun tptp.remove_nat (tptp.nat tptp.set_nat) tptp.set_nat)
% 3.70/4.02 (declare-fun tptp.remove6142905432236673558n_assn (tptp.produc6575502325842934193n_assn tptp.set_Pr5949110396991348497n_assn) tptp.set_Pr5949110396991348497n_assn)
% 3.70/4.02 (declare-fun tptp.remove6466555014256735590at_nat (tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 3.70/4.02 (declare-fun tptp.remove5300788332298244428at_nat (tptp.produc3843707927480180839at_nat tptp.set_Pr4329608150637261639at_nat) tptp.set_Pr4329608150637261639at_nat)
% 3.70/4.02 (declare-fun tptp.the_elem_o (tptp.set_o) Bool)
% 3.70/4.02 (declare-fun tptp.the_elem_int (tptp.set_int) tptp.int)
% 3.70/4.02 (declare-fun tptp.the_elem_nat (tptp.set_nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.the_el2281957884133575798at_nat (tptp.set_Pr1261947904930325089at_nat) tptp.product_prod_nat_nat)
% 3.70/4.02 (declare-fun tptp.the_el221668144340439132at_nat (tptp.set_Pr4329608150637261639at_nat) tptp.produc3843707927480180839at_nat)
% 3.70/4.02 (declare-fun tptp.vimage_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 3.70/4.02 (declare-fun tptp.set_fo2584398358068434914at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.nat tptp.nat) tptp.nat)
% 3.70/4.02 (declare-fun tptp.set_or189985376899183464nteger (tptp.code_integer tptp.code_integer) tptp.set_Code_integer)
% 3.70/4.02 (declare-fun tptp.set_or1266510415728281911st_int (tptp.int tptp.int) tptp.set_int)
% 3.70/4.02 (declare-fun tptp.set_or1269000886237332187st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 3.70/4.02 (declare-fun tptp.set_or8404916559141939852nteger (tptp.code_integer tptp.code_integer) tptp.set_Code_integer)
% 3.70/4.02 (declare-fun tptp.set_or4662586982721622107an_int (tptp.int tptp.int) tptp.set_int)
% 3.70/4.02 (declare-fun tptp.set_or4665077453230672383an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 3.70/4.02 (declare-fun tptp.set_ord_atLeast_nat (tptp.nat) tptp.set_nat)
% 3.70/4.02 (declare-fun tptp.set_ord_atMost_nat (tptp.nat) tptp.set_nat)
% 3.70/4.02 (declare-fun tptp.set_or2715278749043346189nteger (tptp.code_integer tptp.code_integer) tptp.set_Code_integer)
% 3.70/4.02 (declare-fun tptp.set_or6656581121297822940st_int (tptp.int tptp.int) tptp.set_int)
% 3.70/4.02 (declare-fun tptp.set_or6659071591806873216st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 3.70/4.02 (declare-fun tptp.set_or4266950643985792945nteger (tptp.code_integer tptp.code_integer) tptp.set_Code_integer)
% 3.70/4.02 (declare-fun tptp.set_or5832277885323065728an_int (tptp.int tptp.int) tptp.set_int)
% 3.70/4.02 (declare-fun tptp.set_or5834768355832116004an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 3.70/4.02 (declare-fun tptp.set_or1210151606488870762an_nat (tptp.nat) tptp.set_nat)
% 3.70/4.02 (declare-fun tptp.set_ord_lessThan_nat (tptp.nat) tptp.set_nat)
% 3.70/4.02 (declare-fun tptp.syntax7398250324933576852n_assn (tptp.assn tptp.assn) Bool)
% 3.70/4.02 (declare-fun tptp.transi2905341329935302413cl_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 3.70/4.02 (declare-fun tptp.transi6261509568448316235cl_int (tptp.set_Pr958786334691620121nt_int) tptp.set_Pr958786334691620121nt_int)
% 3.70/4.02 (declare-fun tptp.transi6264000038957366511cl_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 3.70/4.02 (declare-fun tptp.transi4533545184864474924nt_int (tptp.set_Pr8634505666381077339nt_int) tptp.set_Pr8634505666381077339nt_int)
% 3.70/4.02 (declare-fun tptp.transi6228740973808232501nteger (tptp.set_Pr1722956316086891245nteger) tptp.set_Pr1722956316086891245nteger)
% 3.70/4.02 (declare-fun tptp.transi5221092739591632921et_nat (tptp.set_Pr3444600963470892981et_nat) tptp.set_Pr3444600963470892981et_nat)
% 3.70/4.02 (declare-fun tptp.transi3145040225084697757et_nat (tptp.set_Pr7928877670098842301et_nat) tptp.set_Pr7928877670098842301et_nat)
% 3.70/4.02 (declare-fun tptp.transi7434818091516421410nt_int (tptp.set_Pr4708930517165415495nt_int) tptp.set_Pr4708930517165415495nt_int)
% 3.70/4.02 (declare-fun tptp.transi2703068831062848130at_nat (tptp.set_Pr4329608150637261639at_nat) tptp.set_Pr4329608150637261639at_nat)
% 3.70/4.02 (declare-fun tptp.transitive_trancl_c (tptp.set_Product_prod_c_c) tptp.set_Product_prod_c_c)
% 3.70/4.02 (declare-fun tptp.transitive_trancl_d (tptp.set_Product_prod_d_d) tptp.set_Product_prod_d_d)
% 3.70/4.02 (declare-fun tptp.transi2163837189807498211lp_nat ((-> tptp.nat tptp.nat Bool) tptp.nat tptp.nat) Bool)
% 3.70/4.02 (declare-fun tptp.type_d3909072315231072503_nat_o ((-> tptp.assn tptp.produc3658429121746597890et_nat Bool) (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.assn) tptp.set_Pr4532377907799695533_nat_o) Bool)
% 3.70/4.02 (declare-fun tptp.vEBT_L8888932350013902202nt_int (tptp.set_nat (-> tptp.int tptp.int tptp.assn) tptp.list_int tptp.list_int) tptp.assn)
% 3.70/4.02 (declare-fun tptp.vEBT_L8891422820522952478nt_nat (tptp.set_nat (-> tptp.int tptp.nat tptp.assn) tptp.list_int tptp.list_nat) tptp.assn)
% 3.70/4.02 (declare-fun tptp.vEBT_L7889578638112847646at_int (tptp.set_nat (-> tptp.nat tptp.int tptp.assn) tptp.list_nat tptp.list_int) tptp.assn)
% 3.70/4.02 (declare-fun tptp.vEBT_L7892069108621897922at_nat (tptp.set_nat (-> tptp.nat tptp.nat tptp.assn) tptp.list_nat tptp.list_nat) tptp.assn)
% 3.70/4.02 (declare-fun tptp.vEBT_L8146214880390291086_nat_c (tptp.set_nat (-> tptp.nat tptp.c tptp.assn) tptp.list_nat tptp.list_c) tptp.assn)
% 3.70/4.02 (declare-fun tptp.vEBT_L8146214880390291087_nat_d (tptp.set_nat (-> tptp.nat tptp.d tptp.assn) tptp.list_nat tptp.list_d) tptp.assn)
% 3.70/4.02 (declare-fun tptp.vEBT_L6582681566615743372_c_int (tptp.set_nat (-> tptp.c tptp.int tptp.assn) tptp.list_c tptp.list_int) tptp.assn)
% 3.70/4.02 (declare-fun tptp.vEBT_L6585172037124793648_c_nat (tptp.set_nat (-> tptp.c tptp.nat tptp.assn) tptp.list_c tptp.list_nat) tptp.assn)
% 3.70/4.02 (declare-fun tptp.vEBT_L824818263033719200sn_c_c (tptp.set_nat (-> tptp.c tptp.c tptp.assn) tptp.list_c tptp.list_c) tptp.assn)
% 3.70/4.02 (declare-fun tptp.vEBT_L824818263033719201sn_c_d (tptp.set_nat (-> tptp.c tptp.d tptp.assn) tptp.list_c tptp.list_d) tptp.assn)
% 3.70/4.02 (declare-fun tptp.vEBT_L7818125895572137869_d_int (tptp.set_nat (-> tptp.d tptp.int tptp.assn) tptp.list_d tptp.list_int) tptp.assn)
% 3.70/4.02 (declare-fun tptp.vEBT_L7820616366081188145_d_nat (tptp.set_nat (-> tptp.d tptp.nat tptp.assn) tptp.list_d tptp.list_nat) tptp.assn)
% 3.70/4.02 (declare-fun tptp.vEBT_L7260734717915818975sn_d_c (tptp.set_nat (-> tptp.d tptp.c tptp.assn) tptp.list_d tptp.list_c) tptp.assn)
% 3.70/4.02 (declare-fun tptp.vEBT_L7260734717915818976sn_d_d (tptp.set_nat (-> tptp.d tptp.d tptp.assn) tptp.list_d tptp.list_d) tptp.assn)
% 3.70/4.02 (declare-fun tptp.vEBT_L74593716426352029nt_int ((-> tptp.int tptp.int tptp.assn) tptp.list_int tptp.list_int) tptp.assn)
% 3.70/4.02 (declare-fun tptp.vEBT_L77084186935402305nt_nat ((-> tptp.int tptp.nat tptp.assn) tptp.list_int tptp.list_nat) tptp.assn)
% 3.70/4.02 (declare-fun tptp.vEBT_L1620274777744359680n_assn ((-> tptp.int tptp.produc6575502325842934193n_assn tptp.assn) tptp.list_int tptp.list_P8527749157015355191n_assn) tptp.assn)
% 3.70/4.02 (declare-fun tptp.vEBT_L3472024597287490640at_nat ((-> tptp.int tptp.product_prod_nat_nat tptp.assn) tptp.list_int tptp.list_P6011104703257516679at_nat) tptp.assn)
% 3.70/4.02 (declare-fun tptp.vEBT_L8298612041380073281at_int ((-> tptp.nat tptp.int tptp.assn) tptp.list_nat tptp.list_int) tptp.assn)
% 3.70/4.02 (declare-fun tptp.vEBT_L8301102511889123557at_nat ((-> tptp.nat tptp.nat tptp.assn) tptp.list_nat tptp.list_nat) tptp.assn)
% 3.70/4.02 (declare-fun tptp.vEBT_L9083610150846024284n_assn ((-> tptp.nat tptp.produc6575502325842934193n_assn tptp.assn) tptp.list_nat tptp.list_P8527749157015355191n_assn) tptp.assn)
% 3.70/4.02 (declare-fun tptp.vEBT_L434182512823356844at_nat ((-> tptp.nat tptp.product_prod_nat_nat tptp.assn) tptp.list_nat tptp.list_P6011104703257516679at_nat) tptp.assn)
% 3.70/4.02 (declare-fun tptp.vEBT_L6400351906427472171_nat_c ((-> tptp.nat tptp.c tptp.assn) tptp.list_nat tptp.list_c) tptp.assn)
% 3.70/4.02 (declare-fun tptp.vEBT_L6400351906427472172_nat_d ((-> tptp.nat tptp.d tptp.assn) tptp.list_nat tptp.list_d) tptp.assn)
% 3.70/4.02 (declare-fun tptp.vEBT_L4760345170377931482sn_int ((-> tptp.produc6575502325842934193n_assn tptp.int tptp.assn) tptp.list_P8527749157015355191n_assn tptp.list_int) tptp.assn)
% 3.70/4.02 (declare-fun tptp.vEBT_L4762835640886981758sn_nat ((-> tptp.produc6575502325842934193n_assn tptp.nat tptp.assn) tptp.list_P8527749157015355191n_assn tptp.list_nat) tptp.assn)
% 3.70/4.02 (declare-fun tptp.vEBT_L3108143461992071043n_assn ((-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn tptp.assn) tptp.list_P8527749157015355191n_assn tptp.list_P8527749157015355191n_assn) tptp.assn)
% 3.70/4.02 (declare-fun tptp.vEBT_L6295016686126367274at_int ((-> tptp.product_prod_nat_nat tptp.int tptp.assn) tptp.list_P6011104703257516679at_nat tptp.list_int) tptp.assn)
% 3.70/4.02 (declare-fun tptp.vEBT_L6297507156635417550at_nat ((-> tptp.product_prod_nat_nat tptp.nat tptp.assn) tptp.list_P6011104703257516679at_nat tptp.list_nat) tptp.assn)
% 3.70/4.02 (declare-fun tptp.vEBT_L4836818592652924457_c_int ((-> tptp.c tptp.int tptp.assn) tptp.list_c tptp.list_int) tptp.assn)
% 3.70/4.02 (declare-fun tptp.vEBT_L4839309063161974733_c_nat ((-> tptp.c tptp.nat tptp.assn) tptp.list_c tptp.list_nat) tptp.assn)
% 3.70/4.02 (declare-fun tptp.vEBT_L7968352277243653187sn_c_c ((-> tptp.c tptp.c tptp.assn) tptp.list_c tptp.list_c) tptp.assn)
% 3.70/4.02 (declare-fun tptp.vEBT_L7968352277243653188sn_c_d ((-> tptp.c tptp.d tptp.assn) tptp.list_c tptp.list_d) tptp.assn)
% 3.70/4.02 (declare-fun tptp.vEBT_L6072262921609318954_d_int ((-> tptp.d tptp.int tptp.assn) tptp.list_d tptp.list_int) tptp.assn)
% 3.70/4.02 (declare-fun tptp.vEBT_L6074753392118369230_d_nat ((-> tptp.d tptp.nat tptp.assn) tptp.list_d tptp.list_nat) tptp.assn)
% 3.70/4.02 (declare-fun tptp.vEBT_L5180896695270977154sn_d_c ((-> tptp.d tptp.c tptp.assn) tptp.list_d tptp.list_c) tptp.assn)
% 3.70/4.02 (declare-fun tptp.vEBT_L5180896695270977155sn_d_d ((-> tptp.d tptp.d tptp.assn) tptp.list_d tptp.list_d) tptp.assn)
% 3.70/4.02 (declare-fun tptp.accp_list_nat ((-> tptp.list_nat tptp.list_nat Bool) tptp.list_nat) Bool)
% 3.70/4.02 (declare-fun tptp.accp_P1862375125659990705et_nat ((-> tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat Bool) tptp.produc2732055786443039994et_nat) Bool)
% 3.70/4.02 (declare-fun tptp.accp_P8126237942716283194atural ((-> tptp.produc7822875418678951345atural tptp.produc7822875418678951345atural Bool) tptp.produc7822875418678951345atural) Bool)
% 3.70/4.02 (declare-fun tptp.accp_P1096762738010456898nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 3.70/4.02 (declare-fun tptp.accp_P4275260045618599050at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat) Bool)
% 3.70/4.02 (declare-fun tptp.less_than () tptp.set_Pr1261947904930325089at_nat)
% 3.70/4.02 (declare-fun tptp.max_ex8135407076693332796at_nat (tptp.set_Pr8693737435421807431at_nat) tptp.set_Pr4329608150637261639at_nat)
% 3.70/4.02 (declare-fun tptp.min_ex6901939911449802026at_nat (tptp.set_Pr8693737435421807431at_nat) tptp.set_Pr4329608150637261639at_nat)
% 3.70/4.02 (declare-fun tptp.pred_nat () tptp.set_Pr1261947904930325089at_nat)
% 3.70/4.02 (declare-fun tptp.wf_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.member8845023287901829240e_term ((-> tptp.int tptp.option6357759511663192854e_term) tptp.set_in3461395444621081367e_term) Bool)
% 3.70/4.02 (declare-fun tptp.member4242434998011752849e_term ((-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term) tptp.set_Pr7604974323444597168e_term) Bool)
% 3.70/4.02 (declare-fun tptp.member6576561426505652726_nat_o ((-> tptp.produc3658429121746597890et_nat Bool) tptp.set_Pr4532377907799695533_nat_o) Bool)
% 3.70/4.02 (declare-fun tptp.member3222579708246209666e_term ((-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.set_Pr3642885161833720865e_term) Bool)
% 3.70/4.02 (declare-fun tptp.member_o (Bool tptp.set_o) Bool)
% 3.70/4.02 (declare-fun tptp.member_assn (tptp.assn tptp.set_assn) Bool)
% 3.70/4.02 (declare-fun tptp.member_Code_integer (tptp.code_integer tptp.set_Code_integer) Bool)
% 3.70/4.02 (declare-fun tptp.member_int (tptp.int tptp.set_int) Bool)
% 3.70/4.02 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 3.70/4.02 (declare-fun tptp.member_num (tptp.num tptp.set_num) Bool)
% 3.70/4.02 (declare-fun tptp.member7034335876925520548nt_int (tptp.produc7773217078559923341nt_int tptp.set_Pr1872883991513573699nt_int) Bool)
% 3.70/4.02 (declare-fun tptp.member4164122664394876845nteger (tptp.produc1908205239877642774nteger tptp.set_Pr1281608226676607948nteger) Bool)
% 3.70/4.02 (declare-fun tptp.member8781333585448626064_nat_o (tptp.produc4928098042776334183_nat_o tptp.set_Pr2161125870931222855_nat_o) Bool)
% 3.70/4.02 (declare-fun tptp.member6124377750444531601et_nat (tptp.produc2732055786443039994et_nat tptp.set_Pr8536935166611901872et_nat) Bool)
% 3.70/4.02 (declare-fun tptp.member1996754912294343701et_nat (tptp.produc3925858234332021118et_nat tptp.set_Pr3286484037609594932et_nat) Bool)
% 3.70/4.02 (declare-fun tptp.member7618704894036264090nt_int (tptp.produc2285326912895808259nt_int tptp.set_Pr9222295170931077689nt_int) Bool)
% 3.70/4.02 (declare-fun tptp.member7466972457876170832od_o_o (tptp.product_prod_o_o tptp.set_Product_prod_o_o) Bool)
% 3.70/4.02 (declare-fun tptp.member7957490590177025114n_assn (tptp.produc6575502325842934193n_assn tptp.set_Pr5949110396991348497n_assn) Bool)
% 3.70/4.02 (declare-fun tptp.member157494554546826820nteger (tptp.produc8923325533196201883nteger tptp.set_Pr4811707699266497531nteger) Bool)
% 3.70/4.02 (declare-fun tptp.member6260224972018164377et_nat (tptp.produc3658429121746597890et_nat tptp.set_Pr3948176798113811640et_nat) Bool)
% 3.70/4.02 (declare-fun tptp.member5262025264175285858nt_int (tptp.product_prod_int_int tptp.set_Pr958786334691620121nt_int) Bool)
% 3.70/4.02 (declare-fun tptp.member216504246829706758nt_nat (tptp.product_prod_int_nat tptp.set_Pr3448869479623346877nt_nat) Bool)
% 3.70/4.02 (declare-fun tptp.member241480614033477777n_assn (tptp.produc3167338625816234618n_assn tptp.set_Pr3255386646789011632n_assn) Bool)
% 3.70/4.02 (declare-fun tptp.member5261114234888836065at_nat (tptp.produc1062882101152166346at_nat tptp.set_Pr6620829329807565824at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.member6698963635872716290st_int (tptp.produc1186641810826059865st_int tptp.set_Pr765067013931698361st_int) Bool)
% 3.70/4.02 (declare-fun tptp.member9189046780804443046st_nat (tptp.produc3676724955757786621st_nat tptp.set_Pr5578615432719617117st_nat) Bool)
% 3.70/4.02 (declare-fun tptp.member490958779117458567n_assn (tptp.produc8582807064127716720n_assn tptp.set_Pr4168565316758867366n_assn) Bool)
% 3.70/4.02 (declare-fun tptp.member4850886304473975718st_int (tptp.produc8561936516282095101st_int tptp.set_Pr7861072320784411741st_int) Bool)
% 3.70/4.02 (declare-fun tptp.member7340969449405702474st_nat (tptp.produc1828647624359046049st_nat tptp.set_Pr3451248702717554689st_nat) Bool)
% 3.70/4.02 (declare-fun tptp.member3687432546746012131n_assn (tptp.produc2555908794901494476n_assn tptp.set_Pr7093487733527993602n_assn) Bool)
% 3.70/4.02 (declare-fun tptp.member6074218473364765234list_c (tptp.produc1655478831073744795list_c tptp.set_Pr2380792130361903057list_c) Bool)
% 3.70/4.02 (declare-fun tptp.member6145252513411111219list_d (tptp.produc1726512871120090780list_d tptp.set_Pr9082979648927643218list_d) Bool)
% 3.70/4.02 (declare-fun tptp.member5295696281703116473st_int (tptp.produc4164172529858598818st_int tptp.set_Pr4898238009683259096st_int) Bool)
% 3.70/4.02 (declare-fun tptp.member7785779426634843229st_nat (tptp.produc6654255674790325574st_nat tptp.set_Pr488414391616402044st_nat) Bool)
% 3.70/4.02 (declare-fun tptp.member3994142547374651152n_assn (tptp.produc337509097454979815n_assn tptp.set_Pr6863447823992824007n_assn) Bool)
% 3.70/4.02 (declare-fun tptp.member4080735728053443344at_nat (tptp.produc424102278133772007at_nat tptp.set_Pr4333006031979791559at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.member3694854580982123912st_int (tptp.produc8499486975545879281st_int tptp.set_Pr1946635486513090599st_int) Bool)
% 3.70/4.02 (declare-fun tptp.member6184937725913850668st_nat (tptp.produc1766198083622830229st_nat tptp.set_Pr6760183905301009355st_nat) Bool)
% 3.70/4.02 (declare-fun tptp.member7012247553653173456list_c (tptp.produc7985223085803476903list_c tptp.set_Pr2058341694840537735list_c) Bool)
% 3.70/4.02 (declare-fun tptp.member7083281593699519441list_d (tptp.produc8056257125849822888list_d tptp.set_Pr8760529213406277896list_d) Bool)
% 3.70/4.02 (declare-fun tptp.member4361754056522032265st_int (tptp.produc9166386451085787634st_int tptp.set_Pr7415257249380972200st_int) Bool)
% 3.70/4.02 (declare-fun tptp.member6851837201453759021st_nat (tptp.produc2433097559162738582st_nat tptp.set_Pr3005433631314115148st_nat) Bool)
% 3.70/4.02 (declare-fun tptp.member1739767152416986127list_c (tptp.produc2712742684567289574list_c tptp.set_Pr8195957489705318982list_c) Bool)
% 3.70/4.02 (declare-fun tptp.member1810801192463332112list_d (tptp.produc2783776724613635559list_d tptp.set_Pr5674772971416283335list_d) Bool)
% 3.70/4.02 (declare-fun tptp.member6689249552917799696at_nat (tptp.produc4166570645942440679at_nat tptp.set_Pr8551490117392284871at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.member4262671552274231302at_int (tptp.product_prod_nat_int tptp.set_Pr7995236796853374141at_int) Bool)
% 3.70/4.02 (declare-fun tptp.member8440522571783428010at_nat (tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.member7704815987135142381n_assn (tptp.produc1407301962063123414n_assn tptp.set_Pr247834672394327052n_assn) Bool)
% 3.70/4.02 (declare-fun tptp.member2223272150424702269at_nat (tptp.produc7248412053542808358at_nat tptp.set_Pr7717912310451564380at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.member8962352060716553276_nat_c (tptp.product_prod_nat_c tptp.set_Pr4335409928928841947_nat_c) Bool)
% 3.70/4.02 (declare-fun tptp.member8962352065019782077_nat_d (tptp.product_prod_nat_d tptp.set_Pr4406443968975187932_nat_d) Bool)
% 3.70/4.02 (declare-fun tptp.member4085533954029916580nt_int (tptp.produc2501202720802129403nt_int tptp.set_Pr8634505666381077339nt_int) Bool)
% 3.70/4.02 (declare-fun tptp.member2446009503569356342nteger (tptp.produc824974754969098637nteger tptp.set_Pr1722956316086891245nteger) Bool)
% 3.70/4.02 (declare-fun tptp.member6341495586645257982et_nat (tptp.produc5657529347773406293et_nat tptp.set_Pr3444600963470892981et_nat) Bool)
% 3.70/4.02 (declare-fun tptp.member4763271486408492550et_nat (tptp.produc6830853553727218525et_nat tptp.set_Pr7928877670098842301et_nat) Bool)
% 3.70/4.02 (declare-fun tptp.member6582457606847315088nt_int (tptp.produc2432570611225516007nt_int tptp.set_Pr4708930517165415495nt_int) Bool)
% 3.70/4.02 (declare-fun tptp.member5792320502188913699sn_int (tptp.produc8718178513971670540sn_int tptp.set_Pr2181989527757714242sn_int) Bool)
% 3.70/4.02 (declare-fun tptp.member746799484843334599sn_nat (tptp.produc3672657496626091440sn_nat tptp.set_Pr4672072672689440998sn_nat) Bool)
% 3.70/4.02 (declare-fun tptp.member4743710847862083984n_assn (tptp.produc9053633027152450663n_assn tptp.set_Pr8116311503512020807n_assn) Bool)
% 3.70/4.02 (declare-fun tptp.member8394280151737582451at_int (tptp.produc4196048018000912732at_int tptp.set_Pr49084382684228242at_int) Bool)
% 3.70/4.02 (declare-fun tptp.member3348759134392003351at_nat (tptp.produc8373899037510109440at_nat tptp.set_Pr2539167527615954998at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.member8206827879206165904at_nat (tptp.produc859450856879609959at_nat tptp.set_Pr8693737435421807431at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.member6009668390874684176at_nat (tptp.produc1906917888121415911at_nat tptp.set_Pr5564308138774400199at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.member444158400953824016od_o_o (tptp.produc2934264451710624999od_o_o tptp.set_Pr1932065953672099015od_o_o) Bool)
% 3.70/4.02 (declare-fun tptp.member4095101504841534314at_nat (tptp.produc732395585841259969at_nat tptp.set_Pr457366540195662369at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.member8757157785044589968at_nat (tptp.produc3843707927480180839at_nat tptp.set_Pr4329608150637261639at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.member4017226226790010994_c_int (tptp.product_prod_c_int tptp.set_Pr4413417460947882513_c_int) Bool)
% 3.70/4.02 (declare-fun tptp.member8195077246299207702_c_nat (tptp.product_prod_c_nat tptp.set_Pr6903500605879609269_c_nat) Bool)
% 3.70/4.02 (declare-fun tptp.member5074992359041316560od_c_c (tptp.product_prod_c_c tptp.set_Product_prod_c_c) Bool)
% 3.70/4.02 (declare-fun tptp.member5074992363344545361od_c_d (tptp.product_prod_c_d tptp.set_Product_prod_c_d) Bool)
% 3.70/4.02 (declare-fun tptp.member5252670555746405491_d_int (tptp.product_prod_d_int tptp.set_Pr786264039281237394_d_int) Bool)
% 3.70/4.02 (declare-fun tptp.member207149538400826391_d_nat (tptp.product_prod_d_nat tptp.set_Pr3276347184212964150_d_nat) Bool)
% 3.70/4.02 (declare-fun tptp.member2287536777068640527od_d_c (tptp.product_prod_d_c tptp.set_Product_prod_d_c) Bool)
% 3.70/4.02 (declare-fun tptp.member2287536781371869328od_d_d (tptp.product_prod_d_d tptp.set_Product_prod_d_d) Bool)
% 3.70/4.02 (declare-fun tptp.member2643936169264416010at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_se7855581050983116737at_nat) Bool)
% 3.70/4.02 (declare-fun tptp.member_c (tptp.c tptp.set_c) Bool)
% 3.70/4.02 (declare-fun tptp.member_d (tptp.d tptp.set_d) Bool)
% 3.70/4.02 (declare-fun tptp.a (tptp.c tptp.d) tptp.assn)
% 3.70/4.02 (declare-fun tptp.f () tptp.assn)
% 3.70/4.02 (declare-fun tptp.i () tptp.set_nat)
% 3.70/4.02 (declare-fun tptp.p () tptp.assn)
% 3.70/4.02 (declare-fun tptp.q () tptp.assn)
% 3.70/4.02 (declare-fun tptp.i2 () tptp.nat)
% 3.70/4.02 (declare-fun tptp.x () tptp.c)
% 3.70/4.02 (declare-fun tptp.xi () tptp.d)
% 3.70/4.02 (declare-fun tptp.xs () tptp.list_c)
% 3.70/4.02 (declare-fun tptp.xsi () tptp.list_d)
% 3.70/4.02 (assert (forall ((P tptp.assn) (Q tptp.assn)) (=> (forall ((H tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P) H) (@ (@ tptp.rep_assn Q) H))) (@ (@ tptp.entails P) Q))))
% 3.70/4.02 (assert (@ (@ tptp.entails tptp.p) tptp.bot_bot_assn))
% 3.70/4.02 (assert (@ (@ tptp.member_nat tptp.i2) tptp.i))
% 3.70/4.02 (assert (forall ((A tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.entails A) B) (=> (@ (@ tptp.entails B) A) (= A B)))))
% 3.70/4.02 (assert (forall ((P tptp.assn)) (@ (@ tptp.entails P) P)))
% 3.70/4.02 (assert (forall ((P tptp.assn) (Q tptp.assn) (R tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 Q) (=> (@ (@ tptp.entails Q) R) (@ _let_1 R))))))
% 3.70/4.03 (assert (forall ((P tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ (@ tptp.entails P) Q))) (=> _let_1 _let_1))))
% 3.70/4.03 (assert (forall ((P tptp.assn)) (@ (@ tptp.entails tptp.bot_bot_assn) P)))
% 3.70/4.03 (assert (forall ((P tptp.assn) (H2 tptp.produc3658429121746597890et_nat) (Q tptp.assn)) (=> (@ (@ tptp.rep_assn P) H2) (=> (@ (@ tptp.entails P) Q) (@ (@ tptp.rep_assn Q) H2)))))
% 3.70/4.03 (assert (forall ((P tptp.assn) (Q tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.entails P) Q) (=> (@ (@ tptp.rep_assn P) H2) (@ (@ tptp.rep_assn Q) H2)))))
% 3.70/4.03 (assert (= tptp.entails (lambda ((P2 tptp.assn) (Q2 tptp.assn)) (forall ((H3 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P2) H3) (@ (@ tptp.rep_assn Q2) H3))))))
% 3.70/4.03 (assert (forall ((P tptp.assn)) (= (@ (@ tptp.entails P) tptp.bot_bot_assn) (forall ((H3 tptp.produc3658429121746597890et_nat)) (not (@ (@ tptp.rep_assn P) H3))))))
% 3.70/4.03 (assert (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L824818263033719201sn_c_d tptp.i) tptp.a) (@ (@ (@ tptp.list_update_c tptp.xs) tptp.i2) tptp.x)) (@ (@ (@ tptp.list_update_d tptp.xsi) tptp.i2) tptp.xi))) tptp.f)) tptp.q))
% 3.70/4.03 (assert (forall ((P tptp.assn) (Q tptp.assn)) (=> (@ (@ tptp.entails P) Q) (@ (@ tptp.entailst P) Q))))
% 3.70/4.03 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (= (@ tptp.rep_assn X) (@ tptp.rep_assn Y)) (= X Y))))
% 3.70/4.03 (assert (forall ((A tptp.assn)) (@ (@ tptp.entailst A) A)))
% 3.70/4.03 (assert (forall ((P tptp.assn)) (= (@ (@ tptp.times_times_assn tptp.bot_bot_assn) P) tptp.bot_bot_assn)))
% 3.70/4.03 (assert (forall ((P tptp.assn)) (= (@ (@ tptp.times_times_assn P) tptp.bot_bot_assn) tptp.bot_bot_assn)))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn A2))) (= (@ (@ tptp.times_times_assn (@ _let_1 B2)) C) (@ (@ tptp.times_times_assn (@ _let_1 C)) B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn A2))) (let ((_let_2 (@ tptp.times_times_assn B2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 3.70/4.03 (assert (= tptp.times_times_assn (lambda ((A3 tptp.assn) (B3 tptp.assn)) (@ (@ tptp.times_times_assn B3) A3))))
% 3.70/4.03 (assert (forall ((H2 tptp.produc3658429121746597890et_nat)) (not (@ (@ tptp.rep_assn tptp.bot_bot_assn) H2))))
% 3.70/4.03 (assert (forall ((A tptp.assn) (B tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn A) B)) H2) (exists ((H1 tptp.produc3658429121746597890et_nat) (H22 tptp.produc3658429121746597890et_nat)) (and (@ (@ tptp.rep_assn A) H1) (@ (@ tptp.rep_assn B) H22))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn A2) B2)) H2) (not (=> (exists ((X_1 tptp.produc3658429121746597890et_nat)) (@ (@ tptp.rep_assn A2) X_1)) (forall ((H_2 tptp.produc3658429121746597890et_nat)) (not (@ (@ tptp.rep_assn B2) H_2))))))))
% 3.70/4.03 (assert (forall ((A tptp.assn) (B tptp.assn) (C2 tptp.assn)) (let ((_let_1 (@ tptp.entailst A))) (=> (@ _let_1 B) (=> (@ (@ tptp.entailst B) C2) (@ _let_1 C2))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn A2))) (= (@ (@ tptp.times_times_assn (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_assn B2) C))))))
% 3.70/4.03 (assert (forall ((F tptp.assn) (F2 tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.entailst F) F2) (@ (@ tptp.entailst (@ (@ tptp.times_times_assn F) A)) F2))))
% 3.70/4.03 (assert (forall ((F tptp.assn) (F2 tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.entailst F) F2) (@ (@ tptp.entailst (@ (@ tptp.times_times_assn F) A)) (@ (@ tptp.times_times_assn F2) A)))))
% 3.70/4.03 (assert (forall ((P tptp.assn) (Q tptp.assn) (A tptp.assn) (F tptp.assn) (B tptp.assn)) (let ((_let_1 (@ tptp.entailst A))) (=> (@ (@ tptp.entailst P) Q) (=> (@ _let_1 (@ (@ tptp.times_times_assn P) F)) (=> (@ (@ tptp.entailst (@ (@ tptp.times_times_assn Q) F)) B) (@ _let_1 B)))))))
% 3.70/4.03 (assert (forall ((A tptp.assn) (B tptp.assn) (C2 tptp.assn) (D tptp.assn)) (=> (@ (@ tptp.entailst A) B) (=> (@ (@ tptp.entailst C2) D) (@ (@ tptp.entailst (@ (@ tptp.times_times_assn A) C2)) (@ (@ tptp.times_times_assn B) D))))))
% 3.70/4.03 (assert (= tptp.times_times_assn (lambda ((P2 tptp.assn) (Q2 tptp.assn)) (@ (@ tptp.times_times_assn Q2) P2))))
% 3.70/4.03 (assert (forall ((P tptp.assn) (Q tptp.assn) (R tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn P))) (= (@ (@ tptp.times_times_assn (@ _let_1 Q)) R) (@ _let_1 (@ (@ tptp.times_times_assn Q) R))))))
% 3.70/4.03 (assert (forall ((Ps tptp.assn) (H2 tptp.produc3658429121746597890et_nat) (P tptp.assn) (R tptp.assn) (F tptp.assn)) (=> (@ (@ tptp.rep_assn Ps) H2) (=> (@ (@ tptp.entails P) R) (=> (@ (@ tptp.entails Ps) (@ (@ tptp.times_times_assn P) F)) (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn R) F)) H2))))))
% 3.70/4.03 (assert (forall ((P tptp.assn) (R tptp.assn) (Ps tptp.assn) (F tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails Ps))) (=> (@ (@ tptp.entails P) R) (=> (@ _let_1 (@ (@ tptp.times_times_assn P) F)) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn R) F)) Q) (@ _let_1 Q)))))))
% 3.70/4.03 (assert (forall ((P tptp.assn) (P3 tptp.assn) (Q tptp.assn) (Q3 tptp.assn)) (=> (@ (@ tptp.entails P) P3) (=> (@ (@ tptp.entails Q) Q3) (@ (@ tptp.entails (@ (@ tptp.times_times_assn P) Q)) (@ (@ tptp.times_times_assn P3) Q3))))))
% 3.70/4.03 (assert (forall ((A tptp.assn) (B tptp.assn) (C2 tptp.assn)) (let ((_let_1 (@ tptp.entails A))) (=> (@ _let_1 (@ (@ tptp.times_times_assn B) C2)) (@ _let_1 (@ (@ tptp.times_times_assn C2) B))))))
% 3.70/4.03 (assert (forall ((A tptp.assn) (B tptp.assn) (C2 tptp.assn)) (=> (@ (@ tptp.entails A) B) (@ (@ tptp.entails (@ (@ tptp.times_times_assn A) C2)) (@ (@ tptp.times_times_assn B) C2)))))
% 3.70/4.03 (assert (forall ((A tptp.assn) (B tptp.assn) (C2 tptp.assn)) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn A) B)) C2) (@ (@ tptp.entails (@ (@ tptp.times_times_assn B) A)) C2))))
% 3.70/4.03 (assert (@ (@ tptp.entails tptp.p) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.a tptp.x) tptp.xi)) (@ (@ (@ (@ tptp.vEBT_L824818263033719201sn_c_d (@ (@ tptp.minus_minus_set_nat tptp.i) (@ (@ tptp.insert_nat2 tptp.i2) tptp.bot_bot_set_nat))) tptp.a) tptp.xs) tptp.xsi))) tptp.f)))
% 3.70/4.03 (assert (forall ((Xs tptp.list_c) (I tptp.nat) (X tptp.c) (Y tptp.c)) (let ((_let_1 (@ (@ tptp.list_update_c Xs) I))) (= (@ (@ (@ tptp.list_update_c (@ _let_1 X)) I) Y) (@ _let_1 Y)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_d) (I tptp.nat) (X tptp.d) (Y tptp.d)) (let ((_let_1 (@ (@ tptp.list_update_d Xs) I))) (= (@ (@ (@ tptp.list_update_d (@ _let_1 X)) I) Y) (@ _let_1 Y)))))
% 3.70/4.03 (assert (not (= (@ tptp.size_size_list_c tptp.xs) (@ tptp.size_size_list_d tptp.xsi))))
% 3.70/4.03 (assert (@ (@ tptp.ord_less_nat tptp.i2) (@ tptp.size_size_list_c tptp.xs)))
% 3.70/4.03 (assert (forall ((P tptp.assn) (Q tptp.assn) (F tptp.assn)) (=> (@ (@ (@ tptp.fI_QUERY P) Q) F) (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn Q) F)))))
% 3.70/4.03 (assert (forall ((A2 tptp.produc3843707927480180839at_nat) (P (-> tptp.produc3843707927480180839at_nat Bool))) (= (@ (@ tptp.member8757157785044589968at_nat A2) (@ tptp.collec6321179662152712658at_nat P)) (@ P A2))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (P (-> tptp.int Bool))) (= (@ (@ tptp.member_int A2) (@ tptp.collect_int P)) (@ P A2))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A2) (@ tptp.collect_nat P)) (@ P A2))))
% 3.70/4.03 (assert (forall ((A2 tptp.product_prod_nat_nat) (P (-> tptp.product_prod_nat_nat Bool))) (= (@ (@ tptp.member8440522571783428010at_nat A2) (@ tptp.collec3392354462482085612at_nat P)) (@ P A2))))
% 3.70/4.03 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (P (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (= (@ (@ tptp.member6576561426505652726_nat_o A2) (@ tptp.collec939566748876313656_nat_o P)) (@ P A2))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat)) (= (@ tptp.collec6321179662152712658at_nat (lambda ((X2 tptp.produc3843707927480180839at_nat)) (@ (@ tptp.member8757157785044589968at_nat X2) A))) A)))
% 3.70/4.03 (assert (forall ((A tptp.set_int)) (= (@ tptp.collect_int (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) A))) A)))
% 3.70/4.03 (assert (forall ((A tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) A))) A)))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.collec3392354462482085612at_nat (lambda ((X2 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X2) A))) A)))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (= (@ tptp.collec939566748876313656_nat_o (lambda ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (@ (@ tptp.member6576561426505652726_nat_o X2) A))) A)))
% 3.70/4.03 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_nat P) (@ tptp.collect_nat Q)))))
% 3.70/4.03 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (Q (-> tptp.product_prod_nat_nat Bool))) (=> (forall ((X3 tptp.product_prod_nat_nat)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collec3392354462482085612at_nat P) (@ tptp.collec3392354462482085612at_nat Q)))))
% 3.70/4.03 (assert (forall ((P (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool)) (Q (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (= (@ P X3) (@ Q X3))) (= (@ tptp.collec939566748876313656_nat_o P) (@ tptp.collec939566748876313656_nat_o Q)))))
% 3.70/4.03 (assert (= tptp.fI_QUERY (lambda ((P2 tptp.assn) (Q2 tptp.assn) (F3 tptp.assn)) (@ (@ tptp.entails P2) (@ (@ tptp.times_times_assn Q2) F3)))))
% 3.70/4.03 (assert (forall ((Q tptp.assn) (R tptp.assn) (F tptp.assn) (S tptp.assn) (P tptp.assn) (X4 tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ tptp.wand_assn Q) R)) F)) S) (=> (@ _let_1 (@ (@ tptp.times_times_assn F) X4)) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn Q) X4)) R) (@ _let_1 S)))))))
% 3.70/4.03 (assert (forall ((Q tptp.assn) (P tptp.assn) (R tptp.assn)) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn Q) P)) R) (@ (@ tptp.entails P) (@ (@ tptp.wand_assn Q) R)))))
% 3.70/4.03 (assert (forall ((P tptp.assn) (Q tptp.assn)) (@ (@ tptp.entails (@ (@ tptp.times_times_assn P) (@ (@ tptp.wand_assn P) Q))) Q)))
% 3.70/4.03 (assert (forall ((Xs tptp.list_c) (I tptp.nat) (X tptp.c)) (= (@ tptp.size_size_list_c (@ (@ (@ tptp.list_update_c Xs) I) X)) (@ tptp.size_size_list_c Xs))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_d) (I tptp.nat) (X tptp.d)) (= (@ tptp.size_size_list_d (@ (@ (@ tptp.list_update_d Xs) I) X)) (@ tptp.size_size_list_d Xs))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_nat) (I tptp.nat) (X tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ (@ tptp.list_update_nat Xs) I) X)) (@ tptp.size_size_list_nat Xs))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_int) (I tptp.nat) (X tptp.int)) (= (@ tptp.size_size_list_int (@ (@ (@ tptp.list_update_int Xs) I) X)) (@ tptp.size_size_list_int Xs))))
% 3.70/4.03 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X) Y) (not (@ (@ tptp.ord_le6747313008572928689nteger Y) X)))))
% 3.70/4.03 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_assn X) Y) (not (@ (@ tptp.ord_less_assn Y) X)))))
% 3.70/4.03 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (@ (@ tptp.ord_less_num Y) X)))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (@ (@ tptp.ord_less_int Y) X)))))
% 3.70/4.03 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X) Y) (not (= Y X)))))
% 3.70/4.03 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_assn X) Y) (not (= Y X)))))
% 3.70/4.03 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (= Y X)))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= Y X)))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (= Y X)))))
% 3.70/4.03 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X) Y) (not (= X Y)))))
% 3.70/4.03 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_assn X) Y) (not (= X Y)))))
% 3.70/4.03 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (= X Y)))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= X Y)))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (= X Y)))))
% 3.70/4.03 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (or (@ (@ tptp.ord_le6747313008572928689nteger X) Y) (= X Y) (@ (@ tptp.ord_le6747313008572928689nteger Y) X))))
% 3.70/4.03 (assert (forall ((X tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_num X) Y) (= X Y) (@ (@ tptp.ord_less_num Y) X))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_nat X) Y) (= X Y) (@ (@ tptp.ord_less_nat Y) X))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_int X) Y) (= X Y) (@ (@ tptp.ord_less_int Y) X))))
% 3.70/4.03 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (P Bool)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X) Y) (=> (@ (@ tptp.ord_le6747313008572928689nteger Y) X) P))))
% 3.70/4.03 (assert (forall ((X tptp.assn) (Y tptp.assn) (P Bool)) (=> (@ (@ tptp.ord_less_assn X) Y) (=> (@ (@ tptp.ord_less_assn Y) X) P))))
% 3.70/4.03 (assert (forall ((X tptp.num) (Y tptp.num) (P Bool)) (=> (@ (@ tptp.ord_less_num X) Y) (=> (@ (@ tptp.ord_less_num Y) X) P))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat) (P Bool)) (=> (@ (@ tptp.ord_less_nat X) Y) (=> (@ (@ tptp.ord_less_nat Y) X) P))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int) (P Bool)) (=> (@ (@ tptp.ord_less_int X) Y) (=> (@ (@ tptp.ord_less_int Y) X) P))))
% 3.70/4.03 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X) Y) (not (@ (@ tptp.ord_le6747313008572928689nteger Y) X)))))
% 3.70/4.03 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_assn X) Y) (not (@ (@ tptp.ord_less_assn Y) X)))))
% 3.70/4.03 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (@ (@ tptp.ord_less_num Y) X)))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (@ (@ tptp.ord_less_int Y) X)))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (F4 (-> tptp.code_integer tptp.code_integer)) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 B2)) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (F4 (-> tptp.code_integer tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (@ (@ tptp.ord_less_assn (@ F4 B2)) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_less_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_assn (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (F4 (-> tptp.code_integer tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (@ (@ tptp.ord_less_num (@ F4 B2)) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_num (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (F4 (-> tptp.code_integer tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (@ (@ tptp.ord_less_nat (@ F4 B2)) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_less_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_nat (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (F4 (-> tptp.code_integer tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (@ (@ tptp.ord_less_int (@ F4 B2)) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_less_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_int (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.code_integer)) (C tptp.code_integer)) (=> (@ (@ tptp.ord_less_assn A2) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 B2)) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_assn A2) B2) (=> (@ (@ tptp.ord_less_assn (@ F4 B2)) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_assn (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_assn A2) B2) (=> (@ (@ tptp.ord_less_num (@ F4 B2)) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_num (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_assn A2) B2) (=> (@ (@ tptp.ord_less_nat (@ F4 B2)) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_nat (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_assn A2) B2) (=> (@ (@ tptp.ord_less_int (@ F4 B2)) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_int (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (F4 (-> tptp.code_integer tptp.code_integer)) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (F4 (-> tptp.assn tptp.code_integer)) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_assn B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (F4 (-> tptp.num tptp.code_integer)) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_num B2) C) (=> (forall ((X3 tptp.num) (Y2 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (F4 (-> tptp.nat tptp.code_integer)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_nat B2) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (F4 (-> tptp.int tptp.code_integer)) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_int B2) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (F4 (-> tptp.code_integer tptp.assn)) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_less_assn A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_less_assn (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (F4 (-> tptp.assn tptp.assn)) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_assn B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_assn (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (F4 (-> tptp.num tptp.assn)) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_assn A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_num B2) C) (=> (forall ((X3 tptp.num) (Y2 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y2) (@ (@ tptp.ord_less_assn (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (F4 (-> tptp.nat tptp.assn)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_assn A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_nat B2) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_less_assn (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (F4 (-> tptp.int tptp.assn)) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_assn A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_int B2) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y2) (@ (@ tptp.ord_less_assn (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))))
% 3.70/4.03 (assert (forall ((X tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger X) X))))
% 3.70/4.03 (assert (forall ((X tptp.assn)) (not (@ (@ tptp.ord_less_assn X) X))))
% 3.70/4.03 (assert (forall ((X tptp.num)) (not (@ (@ tptp.ord_less_num X) X))))
% 3.70/4.03 (assert (forall ((X tptp.nat)) (not (@ (@ tptp.ord_less_nat X) X))))
% 3.70/4.03 (assert (forall ((X tptp.int)) (not (@ (@ tptp.ord_less_int X) X))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (F4 (-> tptp.code_integer tptp.code_integer)) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (F4 (-> tptp.code_integer tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_less_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_assn (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (F4 (-> tptp.code_integer tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_num (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (F4 (-> tptp.code_integer tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_less_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_nat (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (F4 (-> tptp.code_integer tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_less_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_int (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.code_integer)) (C tptp.code_integer)) (=> (@ (@ tptp.ord_less_assn A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_assn A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_assn (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_assn A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_num (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_assn A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_nat (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_assn A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_int (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (F4 (-> tptp.code_integer tptp.code_integer)) (B2 tptp.code_integer) (C tptp.code_integer)) (=> (= A2 (@ F4 B2)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger A2) (@ F4 C)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (F4 (-> tptp.code_integer tptp.assn)) (B2 tptp.code_integer) (C tptp.code_integer)) (=> (= A2 (@ F4 B2)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_less_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_assn A2) (@ F4 C)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.num) (F4 (-> tptp.code_integer tptp.num)) (B2 tptp.code_integer) (C tptp.code_integer)) (=> (= A2 (@ F4 B2)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_num A2) (@ F4 C)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (F4 (-> tptp.code_integer tptp.nat)) (B2 tptp.code_integer) (C tptp.code_integer)) (=> (= A2 (@ F4 B2)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_less_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_nat A2) (@ F4 C)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (F4 (-> tptp.code_integer tptp.int)) (B2 tptp.code_integer) (C tptp.code_integer)) (=> (= A2 (@ F4 B2)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_less_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_int A2) (@ F4 C)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (F4 (-> tptp.assn tptp.code_integer)) (B2 tptp.assn) (C tptp.assn)) (=> (= A2 (@ F4 B2)) (=> (@ (@ tptp.ord_less_assn B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger A2) (@ F4 C)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (F4 (-> tptp.assn tptp.assn)) (B2 tptp.assn) (C tptp.assn)) (=> (= A2 (@ F4 B2)) (=> (@ (@ tptp.ord_less_assn B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_assn A2) (@ F4 C)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.num) (F4 (-> tptp.assn tptp.num)) (B2 tptp.assn) (C tptp.assn)) (=> (= A2 (@ F4 B2)) (=> (@ (@ tptp.ord_less_assn B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_num A2) (@ F4 C)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (F4 (-> tptp.assn tptp.nat)) (B2 tptp.assn) (C tptp.assn)) (=> (= A2 (@ F4 B2)) (=> (@ (@ tptp.ord_less_assn B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_nat A2) (@ F4 C)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (F4 (-> tptp.assn tptp.int)) (B2 tptp.assn) (C tptp.assn)) (=> (= A2 (@ F4 B2)) (=> (@ (@ tptp.ord_less_assn B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_int A2) (@ F4 C)))))))
% 3.70/4.03 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_le6747313008572928689nteger Y) Z) (@ _let_1 Z))))))
% 3.70/4.03 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_assn Y) Z) (@ _let_1 Z))))))
% 3.70/4.03 (assert (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_num Y) Z) (@ _let_1 Z))))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_nat Y) Z) (@ _let_1 Z))))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ _let_1 Z))))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (not (@ (@ tptp.ord_le6747313008572928689nteger B2) A2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn A2) B2) (not (@ (@ tptp.ord_less_assn B2) A2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.num) (B2 tptp.num)) (=> (@ (@ tptp.ord_less_num A2) B2) (not (@ (@ tptp.ord_less_num B2) A2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (not (@ (@ tptp.ord_less_nat B2) A2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (not (@ (@ tptp.ord_less_int B2) A2)))))
% 3.70/4.03 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (not (= X Y)) (or (@ (@ tptp.ord_le6747313008572928689nteger X) Y) (@ (@ tptp.ord_le6747313008572928689nteger Y) X)))))
% 3.70/4.03 (assert (forall ((X tptp.num) (Y tptp.num)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_num X) Y) (@ (@ tptp.ord_less_num Y) X)))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_nat Y) X)))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_int X) Y) (@ (@ tptp.ord_less_int Y) X)))))
% 3.70/4.03 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X) Y) (not (@ (@ tptp.ord_le6747313008572928689nteger Y) X)))))
% 3.70/4.03 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_assn X) Y) (not (@ (@ tptp.ord_less_assn Y) X)))))
% 3.70/4.03 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (@ (@ tptp.ord_less_num Y) X)))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (@ (@ tptp.ord_less_int Y) X)))))
% 3.70/4.03 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_le6747313008572928689nteger X) Y)) (@ (@ tptp.ord_le6747313008572928689nteger Y) X)))))
% 3.70/4.03 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (@ (@ tptp.ord_less_num Y) X)))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_int Y) X)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_c)) (=> (not (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_c Ys))) (not (= Xs Ys)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_d) (Ys tptp.list_d)) (=> (not (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_d Ys))) (not (= Xs Ys)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys))) (not (= Xs Ys)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys))) (not (= Xs Ys)))))
% 3.70/4.03 (assert (forall ((N tptp.nat)) (exists ((Xs2 tptp.list_c)) (= (@ tptp.size_size_list_c Xs2) N))))
% 3.70/4.03 (assert (forall ((N tptp.nat)) (exists ((Xs2 tptp.list_d)) (= (@ tptp.size_size_list_d Xs2) N))))
% 3.70/4.03 (assert (forall ((N tptp.nat)) (exists ((Xs2 tptp.list_nat)) (= (@ tptp.size_size_list_nat Xs2) N))))
% 3.70/4.03 (assert (forall ((N tptp.nat)) (exists ((Xs2 tptp.list_int)) (= (@ tptp.size_size_list_int Xs2) N))))
% 3.70/4.03 (assert (forall ((P (-> tptp.list_c Bool)) (Xs tptp.list_c)) (=> (forall ((Xs2 tptp.list_c)) (=> (forall ((Ys2 tptp.list_c)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_c Ys2)) (@ tptp.size_size_list_c Xs2)) (@ P Ys2))) (@ P Xs2))) (@ P Xs))))
% 3.70/4.03 (assert (forall ((P (-> tptp.list_d Bool)) (Xs tptp.list_d)) (=> (forall ((Xs2 tptp.list_d)) (=> (forall ((Ys2 tptp.list_d)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_d Ys2)) (@ tptp.size_size_list_d Xs2)) (@ P Ys2))) (@ P Xs2))) (@ P Xs))))
% 3.70/4.03 (assert (forall ((P (-> tptp.list_nat Bool)) (Xs tptp.list_nat)) (=> (forall ((Xs2 tptp.list_nat)) (=> (forall ((Ys2 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat Ys2)) (@ tptp.size_size_list_nat Xs2)) (@ P Ys2))) (@ P Xs2))) (@ P Xs))))
% 3.70/4.03 (assert (forall ((P (-> tptp.list_int Bool)) (Xs tptp.list_int)) (=> (forall ((Xs2 tptp.list_int)) (=> (forall ((Ys2 tptp.list_int)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_int Ys2)) (@ tptp.size_size_list_int Xs2)) (@ P Ys2))) (@ P Xs2))) (@ P Xs))))
% 3.70/4.03 (assert (forall ((B2 tptp.code_integer) (A2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) A2) (not (= A2 B2)))))
% 3.70/4.03 (assert (forall ((B2 tptp.assn) (A2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn B2) A2) (not (= A2 B2)))))
% 3.70/4.03 (assert (forall ((B2 tptp.num) (A2 tptp.num)) (=> (@ (@ tptp.ord_less_num B2) A2) (not (= A2 B2)))))
% 3.70/4.03 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A2) (not (= A2 B2)))))
% 3.70/4.03 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A2) (not (= A2 B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (not (= A2 B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn A2) B2) (not (= A2 B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.num) (B2 tptp.num)) (=> (@ (@ tptp.ord_less_num A2) B2) (not (= A2 B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (not (= A2 B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (not (= A2 B2)))))
% 3.70/4.03 (assert (forall ((B2 tptp.code_integer) (A2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 3.70/4.03 (assert (forall ((B2 tptp.assn) (A2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn C))) (=> (@ (@ tptp.ord_less_assn B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 3.70/4.03 (assert (forall ((B2 tptp.num) (A2 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ (@ tptp.ord_less_num B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 3.70/4.03 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_nat B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 3.70/4.03 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ (@ tptp.ord_less_int B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 3.70/4.03 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (not (@ (@ tptp.ord_le6747313008572928689nteger X) Y)) (or (@ (@ tptp.ord_le6747313008572928689nteger Y) X) (= X Y)))))
% 3.70/4.03 (assert (forall ((X tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_num X) Y)) (or (@ (@ tptp.ord_less_num Y) X) (= X Y)))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (or (@ (@ tptp.ord_less_nat Y) X) (= X Y)))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_int X) Y)) (or (@ (@ tptp.ord_less_int Y) X) (= X Y)))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) C) (@ _let_1 C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_assn B2) C) (@ _let_1 C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.num) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_num B2) C) (@ _let_1 C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat B2) C) (@ _let_1 C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_int B2) C) (@ _let_1 C))))))
% 3.70/4.03 (assert (forall ((P (-> tptp.code_integer tptp.code_integer Bool)) (A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (forall ((A4 tptp.code_integer) (B4 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A4) B4) (@ (@ P A4) B4))) (=> (forall ((A4 tptp.code_integer)) (@ (@ P A4) A4)) (=> (forall ((A4 tptp.code_integer) (B4 tptp.code_integer)) (=> (@ (@ P B4) A4) (@ (@ P A4) B4))) (@ (@ P A2) B2))))))
% 3.70/4.03 (assert (forall ((P (-> tptp.num tptp.num Bool)) (A2 tptp.num) (B2 tptp.num)) (=> (forall ((A4 tptp.num) (B4 tptp.num)) (=> (@ (@ tptp.ord_less_num A4) B4) (@ (@ P A4) B4))) (=> (forall ((A4 tptp.num)) (@ (@ P A4) A4)) (=> (forall ((A4 tptp.num) (B4 tptp.num)) (=> (@ (@ P B4) A4) (@ (@ P A4) B4))) (@ (@ P A2) B2))))))
% 3.70/4.03 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A2 tptp.nat) (B2 tptp.nat)) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A4) B4) (@ (@ P A4) B4))) (=> (forall ((A4 tptp.nat)) (@ (@ P A4) A4)) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (@ (@ P B4) A4) (@ (@ P A4) B4))) (@ (@ P A2) B2))))))
% 3.70/4.03 (assert (forall ((P (-> tptp.int tptp.int Bool)) (A2 tptp.int) (B2 tptp.int)) (=> (forall ((A4 tptp.int) (B4 tptp.int)) (=> (@ (@ tptp.ord_less_int A4) B4) (@ (@ P A4) B4))) (=> (forall ((A4 tptp.int)) (@ (@ P A4) A4)) (=> (forall ((A4 tptp.int) (B4 tptp.int)) (=> (@ (@ P B4) A4) (@ (@ P A4) B4))) (@ (@ P A2) B2))))))
% 3.70/4.03 (assert (= (lambda ((P4 (-> tptp.nat Bool))) (exists ((X5 tptp.nat)) (@ P4 X5))) (lambda ((P2 (-> tptp.nat Bool))) (exists ((N2 tptp.nat)) (and (@ P2 N2) (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (not (@ P2 M)))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger A2) A2))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn)) (not (@ (@ tptp.ord_less_assn A2) A2))))
% 3.70/4.03 (assert (forall ((A2 tptp.num)) (not (@ (@ tptp.ord_less_num A2) A2))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat)) (not (@ (@ tptp.ord_less_nat A2) A2))))
% 3.70/4.03 (assert (forall ((A2 tptp.int)) (not (@ (@ tptp.ord_less_int A2) A2))))
% 3.70/4.03 (assert (forall ((B2 tptp.code_integer) (A2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) A2) (not (@ (@ tptp.ord_le6747313008572928689nteger A2) B2)))))
% 3.70/4.03 (assert (forall ((B2 tptp.assn) (A2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn B2) A2) (not (@ (@ tptp.ord_less_assn A2) B2)))))
% 3.70/4.03 (assert (forall ((B2 tptp.num) (A2 tptp.num)) (=> (@ (@ tptp.ord_less_num B2) A2) (not (@ (@ tptp.ord_less_num A2) B2)))))
% 3.70/4.03 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A2) (not (@ (@ tptp.ord_less_nat A2) B2)))))
% 3.70/4.03 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A2) (not (@ (@ tptp.ord_less_int A2) B2)))))
% 3.70/4.03 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (not (@ (@ tptp.ord_le6747313008572928689nteger X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_le6747313008572928689nteger Y) X)))))
% 3.70/4.03 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_num Y) X)))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_int Y) X)))))
% 3.70/4.03 (assert (forall ((Y tptp.code_integer) (X tptp.code_integer)) (=> (not (@ (@ tptp.ord_le6747313008572928689nteger Y) X)) (= (not (@ (@ tptp.ord_le6747313008572928689nteger X) Y)) (= X Y)))))
% 3.70/4.03 (assert (forall ((Y tptp.num) (X tptp.num)) (=> (not (@ (@ tptp.ord_less_num Y) X)) (= (not (@ (@ tptp.ord_less_num X) Y)) (= X Y)))))
% 3.70/4.03 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y) X)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (= X Y)))))
% 3.70/4.03 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (not (@ (@ tptp.ord_less_int Y) X)) (= (not (@ (@ tptp.ord_less_int X) Y)) (= X Y)))))
% 3.70/4.03 (assert (forall ((P (-> tptp.nat Bool)) (A2 tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Y3) X3) (@ P Y3))) (@ P X3))) (@ P A2))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A2))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn A2))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.num) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A2))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A2))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (=> (= A2 B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) C) (@ (@ tptp.ord_le6747313008572928689nteger A2) C)))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (C tptp.assn)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_assn B2) C) (@ (@ tptp.ord_less_assn A2) C)))))
% 3.70/4.03 (assert (forall ((A2 tptp.num) (B2 tptp.num) (C tptp.num)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_num B2) C) (@ (@ tptp.ord_less_num A2) C)))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_nat B2) C) (@ (@ tptp.ord_less_nat A2) C)))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_int B2) C) (@ (@ tptp.ord_less_int A2) C)))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (not (@ (@ tptp.ord_le6747313008572928689nteger B2) A2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn A2) B2) (not (@ (@ tptp.ord_less_assn B2) A2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.num) (B2 tptp.num)) (=> (@ (@ tptp.ord_less_num A2) B2) (not (@ (@ tptp.ord_less_num B2) A2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (not (@ (@ tptp.ord_less_nat B2) A2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (not (@ (@ tptp.ord_less_int B2) A2)))))
% 3.70/4.03 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X) Y) (not (= X Y)))))
% 3.70/4.03 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_assn X) Y) (not (= X Y)))))
% 3.70/4.03 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (= X Y)))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= X Y)))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (= X Y)))))
% 3.70/4.03 (assert (forall ((X tptp.nat)) (exists ((X_1 tptp.nat)) (@ (@ tptp.ord_less_nat X) X_1))))
% 3.70/4.03 (assert (forall ((X tptp.int)) (exists ((X_1 tptp.int)) (@ (@ tptp.ord_less_int X) X_1))))
% 3.70/4.03 (assert (forall ((X tptp.int)) (exists ((Y2 tptp.int)) (@ (@ tptp.ord_less_int Y2) X))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_Pr4329608150637261639at_nat)) (= (not (= A2 tptp.bot_bo228742789529271731at_nat)) (@ (@ tptp.ord_le2604355607129572851at_nat tptp.bot_bo228742789529271731at_nat) A2))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (= (not (= A2 tptp.bot_bo2099793752762293965at_nat)) (@ (@ tptp.ord_le7866589430770878221at_nat tptp.bot_bo2099793752762293965at_nat) A2))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_o)) (= (not (= A2 tptp.bot_bot_set_o)) (@ (@ tptp.ord_less_set_o tptp.bot_bot_set_o) A2))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_nat)) (= (not (= A2 tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_set_nat tptp.bot_bot_set_nat) A2))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_int)) (= (not (= A2 tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_set_int tptp.bot_bot_set_int) A2))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn)) (= (not (= A2 tptp.bot_bot_assn)) (@ (@ tptp.ord_less_assn tptp.bot_bot_assn) A2))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat)) (= (not (= A2 tptp.bot_bot_nat)) (@ (@ tptp.ord_less_nat tptp.bot_bot_nat) A2))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_Pr4329608150637261639at_nat)) (not (@ (@ tptp.ord_le2604355607129572851at_nat A2) tptp.bot_bo228742789529271731at_nat))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (not (@ (@ tptp.ord_le7866589430770878221at_nat A2) tptp.bot_bo2099793752762293965at_nat))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_o)) (not (@ (@ tptp.ord_less_set_o A2) tptp.bot_bot_set_o))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_nat)) (not (@ (@ tptp.ord_less_set_nat A2) tptp.bot_bot_set_nat))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_int)) (not (@ (@ tptp.ord_less_set_int A2) tptp.bot_bot_set_int))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn)) (not (@ (@ tptp.ord_less_assn A2) tptp.bot_bot_assn))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat)) (not (@ (@ tptp.ord_less_nat A2) tptp.bot_bot_nat))))
% 3.70/4.03 (assert (forall ((L tptp.list_c) (Li tptp.list_c) (A (-> tptp.c tptp.c tptp.assn))) (=> (not (= (@ tptp.size_size_list_c L) (@ tptp.size_size_list_c Li))) (= (@ (@ (@ tptp.vEBT_L7968352277243653187sn_c_c A) L) Li) tptp.bot_bot_assn))))
% 3.70/4.03 (assert (forall ((L tptp.list_c) (Li tptp.list_d) (A (-> tptp.c tptp.d tptp.assn))) (=> (not (= (@ tptp.size_size_list_c L) (@ tptp.size_size_list_d Li))) (= (@ (@ (@ tptp.vEBT_L7968352277243653188sn_c_d A) L) Li) tptp.bot_bot_assn))))
% 3.70/4.03 (assert (forall ((L tptp.list_c) (Li tptp.list_nat) (A (-> tptp.c tptp.nat tptp.assn))) (=> (not (= (@ tptp.size_size_list_c L) (@ tptp.size_size_list_nat Li))) (= (@ (@ (@ tptp.vEBT_L4839309063161974733_c_nat A) L) Li) tptp.bot_bot_assn))))
% 3.70/4.03 (assert (forall ((L tptp.list_c) (Li tptp.list_int) (A (-> tptp.c tptp.int tptp.assn))) (=> (not (= (@ tptp.size_size_list_c L) (@ tptp.size_size_list_int Li))) (= (@ (@ (@ tptp.vEBT_L4836818592652924457_c_int A) L) Li) tptp.bot_bot_assn))))
% 3.70/4.03 (assert (forall ((L tptp.list_d) (Li tptp.list_c) (A (-> tptp.d tptp.c tptp.assn))) (=> (not (= (@ tptp.size_size_list_d L) (@ tptp.size_size_list_c Li))) (= (@ (@ (@ tptp.vEBT_L5180896695270977154sn_d_c A) L) Li) tptp.bot_bot_assn))))
% 3.70/4.03 (assert (forall ((L tptp.list_d) (Li tptp.list_d) (A (-> tptp.d tptp.d tptp.assn))) (=> (not (= (@ tptp.size_size_list_d L) (@ tptp.size_size_list_d Li))) (= (@ (@ (@ tptp.vEBT_L5180896695270977155sn_d_d A) L) Li) tptp.bot_bot_assn))))
% 3.70/4.03 (assert (forall ((L tptp.list_d) (Li tptp.list_nat) (A (-> tptp.d tptp.nat tptp.assn))) (=> (not (= (@ tptp.size_size_list_d L) (@ tptp.size_size_list_nat Li))) (= (@ (@ (@ tptp.vEBT_L6074753392118369230_d_nat A) L) Li) tptp.bot_bot_assn))))
% 3.70/4.03 (assert (forall ((L tptp.list_d) (Li tptp.list_int) (A (-> tptp.d tptp.int tptp.assn))) (=> (not (= (@ tptp.size_size_list_d L) (@ tptp.size_size_list_int Li))) (= (@ (@ (@ tptp.vEBT_L6072262921609318954_d_int A) L) Li) tptp.bot_bot_assn))))
% 3.70/4.03 (assert (forall ((L tptp.list_nat) (Li tptp.list_c) (A (-> tptp.nat tptp.c tptp.assn))) (=> (not (= (@ tptp.size_size_list_nat L) (@ tptp.size_size_list_c Li))) (= (@ (@ (@ tptp.vEBT_L6400351906427472171_nat_c A) L) Li) tptp.bot_bot_assn))))
% 3.70/4.03 (assert (forall ((L tptp.list_nat) (Li tptp.list_d) (A (-> tptp.nat tptp.d tptp.assn))) (=> (not (= (@ tptp.size_size_list_nat L) (@ tptp.size_size_list_d Li))) (= (@ (@ (@ tptp.vEBT_L6400351906427472172_nat_d A) L) Li) tptp.bot_bot_assn))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (I2 tptp.nat) (Xs tptp.list_c) (X tptp.c) (X6 tptp.c)) (let ((_let_1 (@ tptp.list_update_c Xs))) (=> (not (= I I2)) (= (@ (@ (@ tptp.list_update_c (@ (@ _let_1 I) X)) I2) X6) (@ (@ (@ tptp.list_update_c (@ (@ _let_1 I2) X6)) I) X))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (I2 tptp.nat) (Xs tptp.list_d) (X tptp.d) (X6 tptp.d)) (let ((_let_1 (@ tptp.list_update_d Xs))) (=> (not (= I I2)) (= (@ (@ (@ tptp.list_update_d (@ (@ _let_1 I) X)) I2) X6) (@ (@ (@ tptp.list_update_d (@ (@ _let_1 I2) X6)) I) X))))))
% 3.70/4.03 (assert (forall ((A2 tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.insert9069300056098147895at_nat A2))) (= (@ _let_1 (@ (@ tptp.minus_3314409938677909166at_nat A) (@ _let_1 tptp.bot_bo228742789529271731at_nat))) (@ _let_1 A)))))
% 3.70/4.03 (assert (forall ((A2 tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A2))) (= (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A) (@ _let_1 tptp.bot_bo2099793752762293965at_nat))) (@ _let_1 A)))))
% 3.70/4.03 (assert (forall ((A2 Bool) (A tptp.set_o)) (let ((_let_1 (@ tptp.insert_o2 A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_o A) (@ _let_1 tptp.bot_bot_set_o))) (@ _let_1 A)))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (A tptp.set_int)) (let ((_let_1 (@ tptp.insert_int2 A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A) (@ _let_1 tptp.bot_bot_set_int))) (@ _let_1 A)))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat2 A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) (@ _let_1 tptp.bot_bot_set_nat))) (@ _let_1 A)))))
% 3.70/4.03 (assert (forall ((X Bool) (B tptp.set_o) (A tptp.set_o)) (=> (@ (@ tptp.member_o X) B) (= (@ (@ tptp.minus_minus_set_o (@ (@ tptp.insert_o2 X) A)) B) (@ (@ tptp.minus_minus_set_o A) B)))))
% 3.70/4.03 (assert (forall ((X tptp.produc3843707927480180839at_nat) (B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X) B) (= (@ (@ tptp.minus_3314409938677909166at_nat (@ (@ tptp.insert9069300056098147895at_nat X) A)) B) (@ (@ tptp.minus_3314409938677909166at_nat A) B)))))
% 3.70/4.03 (assert (forall ((X tptp.product_prod_nat_nat) (B tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X) B) (= (@ (@ tptp.minus_1356011639430497352at_nat (@ (@ tptp.insert8211810215607154385at_nat X) A)) B) (@ (@ tptp.minus_1356011639430497352at_nat A) B)))))
% 3.70/4.03 (assert (forall ((X tptp.int) (B tptp.set_int) (A tptp.set_int)) (=> (@ (@ tptp.member_int X) B) (= (@ (@ tptp.minus_minus_set_int (@ (@ tptp.insert_int2 X) A)) B) (@ (@ tptp.minus_minus_set_int A) B)))))
% 3.70/4.03 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.set_Pr4532377907799695533_nat_o) (A tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.member6576561426505652726_nat_o X) B) (= (@ (@ tptp.minus_1801376950450012436_nat_o (@ (@ tptp.insert5175938949040314269_nat_o X) A)) B) (@ (@ tptp.minus_1801376950450012436_nat_o A) B)))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (B tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.member_nat X) B) (= (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.insert_nat2 X) A)) B) (@ (@ tptp.minus_minus_set_nat A) B)))))
% 3.70/4.03 (assert (forall ((X Bool) (A tptp.set_o) (B tptp.set_o)) (let ((_let_1 (@ tptp.minus_minus_set_o A))) (=> (not (@ (@ tptp.member_o X) A)) (= (@ _let_1 (@ (@ tptp.insert_o2 X) B)) (@ _let_1 B))))))
% 3.70/4.03 (assert (forall ((X tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.minus_3314409938677909166at_nat A))) (=> (not (@ (@ tptp.member8757157785044589968at_nat X) A)) (= (@ _let_1 (@ (@ tptp.insert9069300056098147895at_nat X) B)) (@ _let_1 B))))))
% 3.70/4.03 (assert (forall ((X tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat A))) (=> (not (@ (@ tptp.member8440522571783428010at_nat X) A)) (= (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat X) B)) (@ _let_1 B))))))
% 3.70/4.03 (assert (forall ((X tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.minus_minus_set_int A))) (=> (not (@ (@ tptp.member_int X) A)) (= (@ _let_1 (@ (@ tptp.insert_int2 X) B)) (@ _let_1 B))))))
% 3.70/4.03 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.minus_1801376950450012436_nat_o A))) (=> (not (@ (@ tptp.member6576561426505652726_nat_o X) A)) (= (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o X) B)) (@ _let_1 B))))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A))) (=> (not (@ (@ tptp.member_nat X) A)) (= (@ _let_1 (@ (@ tptp.insert_nat2 X) B)) (@ _let_1 B))))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.minus_3314409938677909166at_nat A) tptp.bot_bo228742789529271731at_nat) A)))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.minus_1356011639430497352at_nat A) tptp.bot_bo2099793752762293965at_nat) A)))
% 3.70/4.03 (assert (forall ((A tptp.set_o)) (= (@ (@ tptp.minus_minus_set_o A) tptp.bot_bot_set_o) A)))
% 3.70/4.03 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int A) tptp.bot_bot_set_int) A)))
% 3.70/4.03 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat A) tptp.bot_bot_set_nat) A)))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.minus_3314409938677909166at_nat tptp.bot_bo228742789529271731at_nat) A) tptp.bot_bo228742789529271731at_nat)))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.minus_1356011639430497352at_nat tptp.bot_bo2099793752762293965at_nat) A) tptp.bot_bo2099793752762293965at_nat)))
% 3.70/4.03 (assert (forall ((A tptp.set_o)) (= (@ (@ tptp.minus_minus_set_o tptp.bot_bot_set_o) A) tptp.bot_bot_set_o)))
% 3.70/4.03 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int tptp.bot_bot_set_int) A) tptp.bot_bot_set_int)))
% 3.70/4.03 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat tptp.bot_bot_set_nat) A) tptp.bot_bot_set_nat)))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.minus_3314409938677909166at_nat A) A) tptp.bot_bo228742789529271731at_nat)))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.minus_1356011639430497352at_nat A) A) tptp.bot_bo2099793752762293965at_nat)))
% 3.70/4.03 (assert (forall ((A tptp.set_o)) (= (@ (@ tptp.minus_minus_set_o A) A) tptp.bot_bot_set_o)))
% 3.70/4.03 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int A) A) tptp.bot_bot_set_int)))
% 3.70/4.03 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat A) A) tptp.bot_bot_set_nat)))
% 3.70/4.03 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool))) (@ (@ tptp.member6576561426505652726_nat_o A2) (@ (@ tptp.insert5175938949040314269_nat_o A2) tptp.bot_bo7824918357723582233_nat_o))))
% 3.70/4.03 (assert (forall ((A2 tptp.produc3843707927480180839at_nat)) (@ (@ tptp.member8757157785044589968at_nat A2) (@ (@ tptp.insert9069300056098147895at_nat A2) tptp.bot_bo228742789529271731at_nat))))
% 3.70/4.03 (assert (forall ((A2 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat A2) (@ (@ tptp.insert8211810215607154385at_nat A2) tptp.bot_bo2099793752762293965at_nat))))
% 3.70/4.03 (assert (forall ((A2 Bool)) (@ (@ tptp.member_o A2) (@ (@ tptp.insert_o2 A2) tptp.bot_bot_set_o))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat)) (@ (@ tptp.member_nat A2) (@ (@ tptp.insert_nat2 A2) tptp.bot_bot_set_nat))))
% 3.70/4.03 (assert (forall ((A2 tptp.int)) (@ (@ tptp.member_int A2) (@ (@ tptp.insert_int2 A2) tptp.bot_bot_set_int))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (A2 tptp.produc3843707927480180839at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.insert9069300056098147895at_nat A2))) (let ((_let_2 (@ tptp.minus_3314409938677909166at_nat A))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_3314409938677909166at_nat (@ _let_2 B)) (@ _let_1 tptp.bot_bo228742789529271731at_nat)))))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (A2 tptp.product_prod_nat_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A2))) (let ((_let_2 (@ tptp.minus_1356011639430497352at_nat A))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_2 B)) (@ _let_1 tptp.bot_bo2099793752762293965at_nat)))))))
% 3.70/4.03 (assert (forall ((A tptp.set_o) (A2 Bool) (B tptp.set_o)) (let ((_let_1 (@ tptp.insert_o2 A2))) (let ((_let_2 (@ tptp.minus_minus_set_o A))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_minus_set_o (@ _let_2 B)) (@ _let_1 tptp.bot_bot_set_o)))))))
% 3.70/4.03 (assert (forall ((A tptp.set_int) (A2 tptp.int) (B tptp.set_int)) (let ((_let_1 (@ tptp.insert_int2 A2))) (let ((_let_2 (@ tptp.minus_minus_set_int A))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_minus_set_int (@ _let_2 B)) (@ _let_1 tptp.bot_bot_set_int)))))))
% 3.70/4.03 (assert (forall ((A tptp.set_nat) (A2 tptp.nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat2 A2))) (let ((_let_2 (@ tptp.minus_minus_set_nat A))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_minus_set_nat (@ _let_2 B)) (@ _let_1 tptp.bot_bot_set_nat)))))))
% 3.70/4.03 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.insert5175938949040314269_nat_o A2))) (=> (@ (@ tptp.member6576561426505652726_nat_o A2) A) (= (@ _let_1 (@ (@ tptp.minus_1801376950450012436_nat_o A) (@ _let_1 tptp.bot_bo7824918357723582233_nat_o))) A)))))
% 3.70/4.03 (assert (forall ((A2 tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.insert9069300056098147895at_nat A2))) (=> (@ (@ tptp.member8757157785044589968at_nat A2) A) (= (@ _let_1 (@ (@ tptp.minus_3314409938677909166at_nat A) (@ _let_1 tptp.bot_bo228742789529271731at_nat))) A)))))
% 3.70/4.03 (assert (forall ((A2 tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A2))) (=> (@ (@ tptp.member8440522571783428010at_nat A2) A) (= (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A) (@ _let_1 tptp.bot_bo2099793752762293965at_nat))) A)))))
% 3.70/4.03 (assert (forall ((A2 Bool) (A tptp.set_o)) (let ((_let_1 (@ tptp.insert_o2 A2))) (=> (@ (@ tptp.member_o A2) A) (= (@ _let_1 (@ (@ tptp.minus_minus_set_o A) (@ _let_1 tptp.bot_bot_set_o))) A)))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (A tptp.set_int)) (let ((_let_1 (@ tptp.insert_int2 A2))) (=> (@ (@ tptp.member_int A2) A) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A) (@ _let_1 tptp.bot_bot_set_int))) A)))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat2 A2))) (=> (@ (@ tptp.member_nat A2) A) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) (@ _let_1 tptp.bot_bot_set_nat))) A)))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (A2 tptp.produc3843707927480180839at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.insert9069300056098147895at_nat A2))) (let ((_let_2 (@ tptp.minus_3314409938677909166at_nat A))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_3314409938677909166at_nat (@ _let_2 (@ _let_1 tptp.bot_bo228742789529271731at_nat))) B))))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (A2 tptp.product_prod_nat_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A2))) (let ((_let_2 (@ tptp.minus_1356011639430497352at_nat A))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_2 (@ _let_1 tptp.bot_bo2099793752762293965at_nat))) B))))))
% 3.70/4.03 (assert (forall ((A tptp.set_o) (A2 Bool) (B tptp.set_o)) (let ((_let_1 (@ tptp.insert_o2 A2))) (let ((_let_2 (@ tptp.minus_minus_set_o A))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_minus_set_o (@ _let_2 (@ _let_1 tptp.bot_bot_set_o))) B))))))
% 3.70/4.03 (assert (forall ((A tptp.set_int) (A2 tptp.int) (B tptp.set_int)) (let ((_let_1 (@ tptp.insert_int2 A2))) (let ((_let_2 (@ tptp.minus_minus_set_int A))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_minus_set_int (@ _let_2 (@ _let_1 tptp.bot_bot_set_int))) B))))))
% 3.70/4.03 (assert (forall ((A tptp.set_nat) (A2 tptp.nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat2 A2))) (let ((_let_2 (@ tptp.minus_minus_set_nat A))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_minus_set_nat (@ _let_2 (@ _let_1 tptp.bot_bot_set_nat))) B))))))
% 3.70/4.03 (assert (forall ((X tptp.produc3843707927480180839at_nat) (Y tptp.produc3843707927480180839at_nat) (A 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 A)) _let_1) (@ _let_2 (@ (@ tptp.minus_3314409938677909166at_nat A) _let_1))))))))
% 3.70/4.03 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat) (A 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 A)) _let_1) (@ _let_2 (@ (@ tptp.minus_1356011639430497352at_nat A) _let_1))))))))
% 3.70/4.03 (assert (forall ((X Bool) (Y Bool) (A tptp.set_o)) (let ((_let_1 (@ (@ tptp.insert_o2 Y) tptp.bot_bot_set_o))) (let ((_let_2 (@ tptp.insert_o2 X))) (=> (not (= X Y)) (= (@ (@ tptp.minus_minus_set_o (@ _let_2 A)) _let_1) (@ _let_2 (@ (@ tptp.minus_minus_set_o A) _let_1))))))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int) (A tptp.set_int)) (let ((_let_1 (@ (@ tptp.insert_int2 Y) tptp.bot_bot_set_int))) (let ((_let_2 (@ tptp.insert_int2 X))) (=> (not (= X Y)) (= (@ (@ tptp.minus_minus_set_int (@ _let_2 A)) _let_1) (@ _let_2 (@ (@ tptp.minus_minus_set_int A) _let_1))))))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ (@ tptp.insert_nat2 Y) tptp.bot_bot_set_nat))) (let ((_let_2 (@ tptp.insert_nat2 X))) (=> (not (= X Y)) (= (@ (@ tptp.minus_minus_set_nat (@ _let_2 A)) _let_1) (@ _let_2 (@ (@ tptp.minus_minus_set_nat A) _let_1))))))))
% 3.70/4.03 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.insert5175938949040314269_nat_o X))) (=> (not (@ (@ tptp.member6576561426505652726_nat_o X) A)) (= (@ (@ tptp.minus_1801376950450012436_nat_o (@ _let_1 A)) (@ _let_1 tptp.bot_bo7824918357723582233_nat_o)) A)))))
% 3.70/4.03 (assert (forall ((X tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.insert9069300056098147895at_nat X))) (=> (not (@ (@ tptp.member8757157785044589968at_nat X) A)) (= (@ (@ tptp.minus_3314409938677909166at_nat (@ _let_1 A)) (@ _let_1 tptp.bot_bo228742789529271731at_nat)) A)))))
% 3.70/4.03 (assert (forall ((X tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat X))) (=> (not (@ (@ tptp.member8440522571783428010at_nat X) A)) (= (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_1 A)) (@ _let_1 tptp.bot_bo2099793752762293965at_nat)) A)))))
% 3.70/4.03 (assert (forall ((X Bool) (A tptp.set_o)) (let ((_let_1 (@ tptp.insert_o2 X))) (=> (not (@ (@ tptp.member_o X) A)) (= (@ (@ tptp.minus_minus_set_o (@ _let_1 A)) (@ _let_1 tptp.bot_bot_set_o)) A)))))
% 3.70/4.03 (assert (forall ((X tptp.int) (A tptp.set_int)) (let ((_let_1 (@ tptp.insert_int2 X))) (=> (not (@ (@ tptp.member_int X) A)) (= (@ (@ tptp.minus_minus_set_int (@ _let_1 A)) (@ _let_1 tptp.bot_bot_set_int)) A)))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat2 X))) (=> (not (@ (@ tptp.member_nat X) A)) (= (@ (@ tptp.minus_minus_set_nat (@ _let_1 A)) (@ _let_1 tptp.bot_bot_set_nat)) A)))))
% 3.70/4.03 (assert (forall ((P (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (= (= tptp.bot_bo7824918357723582233_nat_o (@ tptp.collec939566748876313656_nat_o P)) (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (not (@ P X2))))))
% 3.70/4.03 (assert (forall ((P (-> tptp.produc3843707927480180839at_nat Bool))) (= (= tptp.bot_bo228742789529271731at_nat (@ tptp.collec6321179662152712658at_nat P)) (forall ((X2 tptp.produc3843707927480180839at_nat)) (not (@ P X2))))))
% 3.70/4.03 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool))) (= (= tptp.bot_bo2099793752762293965at_nat (@ tptp.collec3392354462482085612at_nat P)) (forall ((X2 tptp.product_prod_nat_nat)) (not (@ P X2))))))
% 3.70/4.03 (assert (forall ((P (-> Bool Bool))) (= (= tptp.bot_bot_set_o (@ tptp.collect_o P)) (forall ((X2 Bool)) (not (@ P X2))))))
% 3.70/4.03 (assert (forall ((P (-> tptp.nat Bool))) (= (= tptp.bot_bot_set_nat (@ tptp.collect_nat P)) (forall ((X2 tptp.nat)) (not (@ P X2))))))
% 3.70/4.03 (assert (forall ((P (-> tptp.int Bool))) (= (= tptp.bot_bot_set_int (@ tptp.collect_int P)) (forall ((X2 tptp.int)) (not (@ P X2))))))
% 3.70/4.03 (assert (forall ((P (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (= (= (@ tptp.collec939566748876313656_nat_o P) tptp.bot_bo7824918357723582233_nat_o) (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (not (@ P X2))))))
% 3.70/4.03 (assert (forall ((P (-> tptp.produc3843707927480180839at_nat Bool))) (= (= (@ tptp.collec6321179662152712658at_nat P) tptp.bot_bo228742789529271731at_nat) (forall ((X2 tptp.produc3843707927480180839at_nat)) (not (@ P X2))))))
% 3.70/4.03 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool))) (= (= (@ tptp.collec3392354462482085612at_nat P) tptp.bot_bo2099793752762293965at_nat) (forall ((X2 tptp.product_prod_nat_nat)) (not (@ P X2))))))
% 3.70/4.03 (assert (forall ((P (-> Bool Bool))) (= (= (@ tptp.collect_o P) tptp.bot_bot_set_o) (forall ((X2 Bool)) (not (@ P X2))))))
% 3.70/4.03 (assert (forall ((P (-> tptp.nat Bool))) (= (= (@ tptp.collect_nat P) tptp.bot_bot_set_nat) (forall ((X2 tptp.nat)) (not (@ P X2))))))
% 3.70/4.03 (assert (forall ((P (-> tptp.int Bool))) (= (= (@ tptp.collect_int P) tptp.bot_bot_set_int) (forall ((X2 tptp.int)) (not (@ P X2))))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (= (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (not (@ (@ tptp.member6576561426505652726_nat_o X2) A))) (= A tptp.bot_bo7824918357723582233_nat_o))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat)) (= (forall ((X2 tptp.produc3843707927480180839at_nat)) (not (@ (@ tptp.member8757157785044589968at_nat X2) A))) (= A tptp.bot_bo228742789529271731at_nat))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat)) (= (forall ((X2 tptp.product_prod_nat_nat)) (not (@ (@ tptp.member8440522571783428010at_nat X2) A))) (= A tptp.bot_bo2099793752762293965at_nat))))
% 3.70/4.03 (assert (forall ((A tptp.set_o)) (= (forall ((X2 Bool)) (not (@ (@ tptp.member_o X2) A))) (= A tptp.bot_bot_set_o))))
% 3.70/4.03 (assert (forall ((A tptp.set_nat)) (= (forall ((X2 tptp.nat)) (not (@ (@ tptp.member_nat X2) A))) (= A tptp.bot_bot_set_nat))))
% 3.70/4.03 (assert (forall ((A tptp.set_int)) (= (forall ((X2 tptp.int)) (not (@ (@ tptp.member_int X2) A))) (= A tptp.bot_bot_set_int))))
% 3.70/4.03 (assert (forall ((C (-> tptp.produc3658429121746597890et_nat Bool))) (not (@ (@ tptp.member6576561426505652726_nat_o C) tptp.bot_bo7824918357723582233_nat_o))))
% 3.70/4.03 (assert (forall ((C tptp.produc3843707927480180839at_nat)) (not (@ (@ tptp.member8757157785044589968at_nat C) tptp.bot_bo228742789529271731at_nat))))
% 3.70/4.03 (assert (forall ((C tptp.product_prod_nat_nat)) (not (@ (@ tptp.member8440522571783428010at_nat C) tptp.bot_bo2099793752762293965at_nat))))
% 3.70/4.03 (assert (forall ((C Bool)) (not (@ (@ tptp.member_o C) tptp.bot_bot_set_o))))
% 3.70/4.03 (assert (forall ((C tptp.nat)) (not (@ (@ tptp.member_nat C) tptp.bot_bot_set_nat))))
% 3.70/4.03 (assert (forall ((C tptp.int)) (not (@ (@ tptp.member_int C) tptp.bot_bot_set_int))))
% 3.70/4.03 (assert (forall ((A2 Bool) (B tptp.set_o) (B2 Bool)) (let ((_let_1 (@ tptp.member_o A2))) (=> (=> (not (@ _let_1 B)) (= A2 B2)) (@ _let_1 (@ (@ tptp.insert_o2 B2) B))))))
% 3.70/4.03 (assert (forall ((A2 tptp.produc3843707927480180839at_nat) (B tptp.set_Pr4329608150637261639at_nat) (B2 tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat A2))) (=> (=> (not (@ _let_1 B)) (= A2 B2)) (@ _let_1 (@ (@ tptp.insert9069300056098147895at_nat B2) B))))))
% 3.70/4.03 (assert (forall ((A2 tptp.product_prod_nat_nat) (B tptp.set_Pr1261947904930325089at_nat) (B2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat A2))) (=> (=> (not (@ _let_1 B)) (= A2 B2)) (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat B2) B))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B tptp.set_nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat A2))) (=> (=> (not (@ _let_1 B)) (= A2 B2)) (@ _let_1 (@ (@ tptp.insert_nat2 B2) B))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B tptp.set_int) (B2 tptp.int)) (let ((_let_1 (@ tptp.member_int A2))) (=> (=> (not (@ _let_1 B)) (= A2 B2)) (@ _let_1 (@ (@ tptp.insert_int2 B2) B))))))
% 3.70/4.03 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.set_Pr4532377907799695533_nat_o) (B2 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o A2))) (=> (=> (not (@ _let_1 B)) (= A2 B2)) (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o B2) B))))))
% 3.70/4.03 (assert (forall ((A2 Bool) (B2 Bool) (A tptp.set_o)) (let ((_let_1 (@ tptp.member_o A2))) (= (@ _let_1 (@ (@ tptp.insert_o2 B2) A)) (or (= A2 B2) (@ _let_1 A))))))
% 3.70/4.03 (assert (forall ((A2 tptp.produc3843707927480180839at_nat) (B2 tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat A2))) (= (@ _let_1 (@ (@ tptp.insert9069300056098147895at_nat B2) A)) (or (= A2 B2) (@ _let_1 A))))))
% 3.70/4.03 (assert (forall ((A2 tptp.product_prod_nat_nat) (B2 tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat A2))) (= (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat B2) A)) (or (= A2 B2) (@ _let_1 A))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A2))) (= (@ _let_1 (@ (@ tptp.insert_nat2 B2) A)) (or (= A2 B2) (@ _let_1 A))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int) (A tptp.set_int)) (let ((_let_1 (@ tptp.member_int A2))) (= (@ _let_1 (@ (@ tptp.insert_int2 B2) A)) (or (= A2 B2) (@ _let_1 A))))))
% 3.70/4.03 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o A2))) (= (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o B2) A)) (or (= A2 B2) (@ _let_1 A))))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat2 X))) (let ((_let_2 (@ _let_1 A))) (= (@ _let_1 _let_2) _let_2)))))
% 3.70/4.03 (assert (forall ((X tptp.int) (A tptp.set_int)) (let ((_let_1 (@ tptp.insert_int2 X))) (let ((_let_2 (@ _let_1 A))) (= (@ _let_1 _let_2) _let_2)))))
% 3.70/4.03 (assert (forall ((X tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat X))) (let ((_let_2 (@ _let_1 A))) (= (@ _let_1 _let_2) _let_2)))))
% 3.70/4.03 (assert (forall ((X tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.insert9069300056098147895at_nat X))) (let ((_let_2 (@ _let_1 A))) (= (@ _let_1 _let_2) _let_2)))))
% 3.70/4.03 (assert (forall ((X Bool) (A tptp.set_o)) (let ((_let_1 (@ tptp.insert_o2 X))) (let ((_let_2 (@ _let_1 A))) (= (@ _let_1 _let_2) _let_2)))))
% 3.70/4.03 (assert (forall ((C tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.minus_3314409938677909166at_nat A) B)))))))
% 3.70/4.03 (assert (forall ((C tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A) B)))))))
% 3.70/4.03 (assert (forall ((C tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A) B)))))))
% 3.70/4.03 (assert (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.minus_1801376950450012436_nat_o A) B)))))))
% 3.70/4.03 (assert (forall ((C tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B)))))))
% 3.70/4.03 (assert (forall ((C tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (= (@ _let_1 (@ (@ tptp.minus_3314409938677909166at_nat A) B)) (and (@ _let_1 A) (not (@ _let_1 B)))))))
% 3.70/4.03 (assert (forall ((C tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (= (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A) B)) (and (@ _let_1 A) (not (@ _let_1 B)))))))
% 3.70/4.03 (assert (forall ((C tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A) B)) (and (@ _let_1 A) (not (@ _let_1 B)))))))
% 3.70/4.03 (assert (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (= (@ _let_1 (@ (@ tptp.minus_1801376950450012436_nat_o A) B)) (and (@ _let_1 A) (not (@ _let_1 B)))))))
% 3.70/4.03 (assert (forall ((C tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B)) (and (@ _let_1 A) (not (@ _let_1 B)))))))
% 3.70/4.03 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ (@ tptp.minus_minus_set_nat A) B))) (= (@ (@ tptp.minus_minus_set_nat _let_1) B) _let_1))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat)) (not (@ (@ tptp.ord_le2604355607129572851at_nat A) tptp.bot_bo228742789529271731at_nat))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat)) (not (@ (@ tptp.ord_le7866589430770878221at_nat A) tptp.bot_bo2099793752762293965at_nat))))
% 3.70/4.03 (assert (forall ((A tptp.set_o)) (not (@ (@ tptp.ord_less_set_o A) tptp.bot_bot_set_o))))
% 3.70/4.03 (assert (forall ((A tptp.set_nat)) (not (@ (@ tptp.ord_less_set_nat A) tptp.bot_bot_set_nat))))
% 3.70/4.03 (assert (forall ((A tptp.set_int)) (not (@ (@ tptp.ord_less_set_int A) tptp.bot_bot_set_int))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le2604355607129572851at_nat A) B) (exists ((B4 tptp.produc3843707927480180839at_nat)) (@ (@ tptp.member8757157785044589968at_nat B4) (@ (@ tptp.minus_3314409938677909166at_nat B) A))))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat A) B) (exists ((B4 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat B4) (@ (@ tptp.minus_1356011639430497352at_nat B) A))))))
% 3.70/4.03 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A) B) (exists ((B4 tptp.int)) (@ (@ tptp.member_int B4) (@ (@ tptp.minus_minus_set_int B) A))))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.ord_le2453136405763929_nat_o A) B) (exists ((B4 (-> tptp.produc3658429121746597890et_nat Bool))) (@ (@ tptp.member6576561426505652726_nat_o B4) (@ (@ tptp.minus_1801376950450012436_nat_o B) A))))))
% 3.70/4.03 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A) B) (exists ((B4 tptp.nat)) (@ (@ tptp.member_nat B4) (@ (@ tptp.minus_minus_set_nat B) A))))))
% 3.70/4.03 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (S tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.member6576561426505652726_nat_o X) S) (@ (@ tptp.ord_le2453136405763929_nat_o (@ (@ tptp.minus_1801376950450012436_nat_o S) (@ (@ tptp.insert5175938949040314269_nat_o X) tptp.bot_bo7824918357723582233_nat_o))) S))))
% 3.70/4.03 (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))))
% 3.70/4.03 (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))))
% 3.70/4.03 (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_o2 X) tptp.bot_bot_set_o))) S))))
% 3.70/4.03 (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_int2 X) tptp.bot_bot_set_int))) S))))
% 3.70/4.03 (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_nat2 X) tptp.bot_bot_set_nat))) S))))
% 3.70/4.03 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (S tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.member6576561426505652726_nat_o X) S) (not (= S tptp.bot_bo7824918357723582233_nat_o)))))
% 3.70/4.03 (assert (forall ((X tptp.produc3843707927480180839at_nat) (S tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X) S) (not (= S tptp.bot_bo228742789529271731at_nat)))))
% 3.70/4.03 (assert (forall ((X tptp.product_prod_nat_nat) (S tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X) S) (not (= S tptp.bot_bo2099793752762293965at_nat)))))
% 3.70/4.03 (assert (forall ((X Bool) (S tptp.set_o)) (=> (@ (@ tptp.member_o X) S) (not (= S tptp.bot_bot_set_o)))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (S tptp.set_nat)) (=> (@ (@ tptp.member_nat X) S) (not (= S tptp.bot_bot_set_nat)))))
% 3.70/4.03 (assert (forall ((X tptp.int) (S tptp.set_int)) (=> (@ (@ tptp.member_int X) S) (not (= S tptp.bot_bot_set_int)))))
% 3.70/4.03 (assert (forall ((S tptp.set_Pr4532377907799695533_nat_o)) (=> (not (= S tptp.bot_bo7824918357723582233_nat_o)) (not (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (not (@ (@ tptp.member6576561426505652726_nat_o X3) S)))))))
% 3.70/4.03 (assert (forall ((S tptp.set_Pr4329608150637261639at_nat)) (=> (not (= S tptp.bot_bo228742789529271731at_nat)) (not (forall ((X3 tptp.produc3843707927480180839at_nat)) (not (@ (@ tptp.member8757157785044589968at_nat X3) S)))))))
% 3.70/4.03 (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)))))))
% 3.70/4.03 (assert (forall ((S tptp.set_o)) (=> (not (= S tptp.bot_bot_set_o)) (not (forall ((X3 Bool)) (not (@ (@ tptp.member_o X3) S)))))))
% 3.70/4.03 (assert (forall ((S tptp.set_nat)) (=> (not (= S tptp.bot_bot_set_nat)) (not (forall ((X3 tptp.nat)) (not (@ (@ tptp.member_nat X3) S)))))))
% 3.70/4.03 (assert (forall ((S tptp.set_int)) (=> (not (= S tptp.bot_bot_set_int)) (not (forall ((X3 tptp.int)) (not (@ (@ tptp.member_int X3) S)))))))
% 3.70/4.03 (assert (= tptp.bot_bo7824918357723582233_nat_o (@ tptp.collec939566748876313656_nat_o tptp.bot_bo7963750851167320836at_o_o)))
% 3.70/4.03 (assert (= tptp.bot_bo228742789529271731at_nat (@ tptp.collec6321179662152712658at_nat tptp.bot_bo6829958733157050602_nat_o)))
% 3.70/4.03 (assert (= tptp.bot_bo2099793752762293965at_nat (@ tptp.collec3392354462482085612at_nat tptp.bot_bo482883023278783056_nat_o)))
% 3.70/4.03 (assert (= tptp.bot_bot_set_o (@ tptp.collect_o tptp.bot_bot_o_o)))
% 3.70/4.03 (assert (= tptp.bot_bot_set_nat (@ tptp.collect_nat tptp.bot_bot_nat_o)))
% 3.70/4.03 (assert (= tptp.bot_bot_set_int (@ tptp.collect_int tptp.bot_bot_int_o)))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (= (exists ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (@ (@ tptp.member6576561426505652726_nat_o X2) A)) (not (= A tptp.bot_bo7824918357723582233_nat_o)))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat)) (= (exists ((X2 tptp.produc3843707927480180839at_nat)) (@ (@ tptp.member8757157785044589968at_nat X2) A)) (not (= A tptp.bot_bo228742789529271731at_nat)))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat)) (= (exists ((X2 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X2) A)) (not (= A tptp.bot_bo2099793752762293965at_nat)))))
% 3.70/4.03 (assert (forall ((A tptp.set_o)) (= (exists ((X2 Bool)) (@ (@ tptp.member_o X2) A)) (not (= A tptp.bot_bot_set_o)))))
% 3.70/4.03 (assert (forall ((A tptp.set_nat)) (= (exists ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) A)) (not (= A tptp.bot_bot_set_nat)))))
% 3.70/4.03 (assert (forall ((A tptp.set_int)) (= (exists ((X2 tptp.int)) (@ (@ tptp.member_int X2) A)) (not (= A tptp.bot_bot_set_int)))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (=> (forall ((Y2 (-> tptp.produc3658429121746597890et_nat Bool))) (not (@ (@ tptp.member6576561426505652726_nat_o Y2) A))) (= A tptp.bot_bo7824918357723582233_nat_o))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat)) (=> (forall ((Y2 tptp.produc3843707927480180839at_nat)) (not (@ (@ tptp.member8757157785044589968at_nat Y2) A))) (= A tptp.bot_bo228742789529271731at_nat))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((Y2 tptp.product_prod_nat_nat)) (not (@ (@ tptp.member8440522571783428010at_nat Y2) A))) (= A tptp.bot_bo2099793752762293965at_nat))))
% 3.70/4.03 (assert (forall ((A tptp.set_o)) (=> (forall ((Y2 Bool)) (not (@ (@ tptp.member_o Y2) A))) (= A tptp.bot_bot_set_o))))
% 3.70/4.03 (assert (forall ((A tptp.set_nat)) (=> (forall ((Y2 tptp.nat)) (not (@ (@ tptp.member_nat Y2) A))) (= A tptp.bot_bot_set_nat))))
% 3.70/4.03 (assert (forall ((A tptp.set_int)) (=> (forall ((Y2 tptp.int)) (not (@ (@ tptp.member_int Y2) A))) (= A tptp.bot_bot_set_int))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (= A tptp.bot_bo7824918357723582233_nat_o) (not (@ (@ tptp.member6576561426505652726_nat_o A2) A)))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (A2 tptp.produc3843707927480180839at_nat)) (=> (= A tptp.bot_bo228742789529271731at_nat) (not (@ (@ tptp.member8757157785044589968at_nat A2) A)))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (A2 tptp.product_prod_nat_nat)) (=> (= A tptp.bot_bo2099793752762293965at_nat) (not (@ (@ tptp.member8440522571783428010at_nat A2) A)))))
% 3.70/4.03 (assert (forall ((A tptp.set_o) (A2 Bool)) (=> (= A tptp.bot_bot_set_o) (not (@ (@ tptp.member_o A2) A)))))
% 3.70/4.03 (assert (forall ((A tptp.set_nat) (A2 tptp.nat)) (=> (= A tptp.bot_bot_set_nat) (not (@ (@ tptp.member_nat A2) A)))))
% 3.70/4.03 (assert (forall ((A tptp.set_int) (A2 tptp.int)) (=> (= A tptp.bot_bot_set_int) (not (@ (@ tptp.member_int A2) A)))))
% 3.70/4.03 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool))) (not (@ (@ tptp.member6576561426505652726_nat_o A2) tptp.bot_bo7824918357723582233_nat_o))))
% 3.70/4.03 (assert (forall ((A2 tptp.produc3843707927480180839at_nat)) (not (@ (@ tptp.member8757157785044589968at_nat A2) tptp.bot_bo228742789529271731at_nat))))
% 3.70/4.03 (assert (forall ((A2 tptp.product_prod_nat_nat)) (not (@ (@ tptp.member8440522571783428010at_nat A2) tptp.bot_bo2099793752762293965at_nat))))
% 3.70/4.03 (assert (forall ((A2 Bool)) (not (@ (@ tptp.member_o A2) tptp.bot_bot_set_o))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat)) (not (@ (@ tptp.member_nat A2) tptp.bot_bot_set_nat))))
% 3.70/4.03 (assert (forall ((A2 tptp.int)) (not (@ (@ tptp.member_int A2) tptp.bot_bot_set_int))))
% 3.70/4.03 (assert (forall ((A2 Bool) (B2 Bool) (A tptp.set_o)) (let ((_let_1 (@ tptp.member_o A2))) (=> (@ _let_1 (@ (@ tptp.insert_o2 B2) A)) (=> (= A2 (not B2)) (@ _let_1 A))))))
% 3.70/4.03 (assert (forall ((A2 tptp.produc3843707927480180839at_nat) (B2 tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat A2))) (=> (@ _let_1 (@ (@ tptp.insert9069300056098147895at_nat B2) A)) (=> (not (= A2 B2)) (@ _let_1 A))))))
% 3.70/4.03 (assert (forall ((A2 tptp.product_prod_nat_nat) (B2 tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat A2))) (=> (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat B2) A)) (=> (not (= A2 B2)) (@ _let_1 A))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A2))) (=> (@ _let_1 (@ (@ tptp.insert_nat2 B2) A)) (=> (not (= A2 B2)) (@ _let_1 A))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int) (A tptp.set_int)) (let ((_let_1 (@ tptp.member_int A2))) (=> (@ _let_1 (@ (@ tptp.insert_int2 B2) A)) (=> (not (= A2 B2)) (@ _let_1 A))))))
% 3.70/4.03 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o A2))) (=> (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o B2) A)) (=> (not (= A2 B2)) (@ _let_1 A))))))
% 3.70/4.03 (assert (forall ((A2 Bool) (B tptp.set_o)) (@ (@ tptp.member_o A2) (@ (@ tptp.insert_o2 A2) B))))
% 3.70/4.03 (assert (forall ((A2 tptp.produc3843707927480180839at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.member8757157785044589968at_nat A2) (@ (@ tptp.insert9069300056098147895at_nat A2) B))))
% 3.70/4.03 (assert (forall ((A2 tptp.product_prod_nat_nat) (B tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.member8440522571783428010at_nat A2) (@ (@ tptp.insert8211810215607154385at_nat A2) B))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B tptp.set_nat)) (@ (@ tptp.member_nat A2) (@ (@ tptp.insert_nat2 A2) B))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B tptp.set_int)) (@ (@ tptp.member_int A2) (@ (@ tptp.insert_int2 A2) B))))
% 3.70/4.03 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.set_Pr4532377907799695533_nat_o)) (@ (@ tptp.member6576561426505652726_nat_o A2) (@ (@ tptp.insert5175938949040314269_nat_o A2) B))))
% 3.70/4.03 (assert (forall ((A2 Bool) (B tptp.set_o) (B2 Bool)) (let ((_let_1 (@ tptp.member_o A2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert_o2 B2) B))))))
% 3.70/4.03 (assert (forall ((A2 tptp.produc3843707927480180839at_nat) (B tptp.set_Pr4329608150637261639at_nat) (B2 tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat A2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert9069300056098147895at_nat B2) B))))))
% 3.70/4.03 (assert (forall ((A2 tptp.product_prod_nat_nat) (B tptp.set_Pr1261947904930325089at_nat) (B2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat A2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat B2) B))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B tptp.set_nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat A2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert_nat2 B2) B))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B tptp.set_int) (B2 tptp.int)) (let ((_let_1 (@ tptp.member_int A2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert_int2 B2) B))))))
% 3.70/4.03 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.set_Pr4532377907799695533_nat_o) (B2 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o A2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o B2) B))))))
% 3.70/4.03 (assert (forall ((X Bool) (A tptp.set_o)) (=> (@ (@ tptp.member_o X) A) (not (forall ((B5 tptp.set_o)) (=> (= A (@ (@ tptp.insert_o2 X) B5)) (@ (@ tptp.member_o X) B5)))))))
% 3.70/4.03 (assert (forall ((X tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X) A) (not (forall ((B5 tptp.set_Pr4329608150637261639at_nat)) (=> (= A (@ (@ tptp.insert9069300056098147895at_nat X) B5)) (@ (@ tptp.member8757157785044589968at_nat X) B5)))))))
% 3.70/4.03 (assert (forall ((X tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X) A) (not (forall ((B5 tptp.set_Pr1261947904930325089at_nat)) (=> (= A (@ (@ tptp.insert8211810215607154385at_nat X) B5)) (@ (@ tptp.member8440522571783428010at_nat X) B5)))))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (A tptp.set_nat)) (=> (@ (@ tptp.member_nat X) A) (not (forall ((B5 tptp.set_nat)) (=> (= A (@ (@ tptp.insert_nat2 X) B5)) (@ (@ tptp.member_nat X) B5)))))))
% 3.70/4.03 (assert (forall ((X tptp.int) (A tptp.set_int)) (=> (@ (@ tptp.member_int X) A) (not (forall ((B5 tptp.set_int)) (=> (= A (@ (@ tptp.insert_int2 X) B5)) (@ (@ tptp.member_int X) B5)))))))
% 3.70/4.03 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.member6576561426505652726_nat_o X) A) (not (forall ((B5 tptp.set_Pr4532377907799695533_nat_o)) (=> (= A (@ (@ tptp.insert5175938949040314269_nat_o X) B5)) (@ (@ tptp.member6576561426505652726_nat_o X) B5)))))))
% 3.70/4.03 (assert (forall ((X Bool) (A tptp.set_o) (B tptp.set_o)) (let ((_let_1 (@ tptp.insert_o2 X))) (let ((_let_2 (@ tptp.member_o X))) (=> (not (@ _let_2 A)) (=> (not (@ _let_2 B)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))))
% 3.70/4.03 (assert (forall ((X tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.insert9069300056098147895at_nat X))) (let ((_let_2 (@ tptp.member8757157785044589968at_nat X))) (=> (not (@ _let_2 A)) (=> (not (@ _let_2 B)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))))
% 3.70/4.03 (assert (forall ((X tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat X))) (let ((_let_2 (@ tptp.member8440522571783428010at_nat X))) (=> (not (@ _let_2 A)) (=> (not (@ _let_2 B)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat2 X))) (let ((_let_2 (@ tptp.member_nat X))) (=> (not (@ _let_2 A)) (=> (not (@ _let_2 B)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))))
% 3.70/4.03 (assert (forall ((X tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.insert_int2 X))) (let ((_let_2 (@ tptp.member_int X))) (=> (not (@ _let_2 A)) (=> (not (@ _let_2 B)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))))
% 3.70/4.03 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.insert5175938949040314269_nat_o X))) (let ((_let_2 (@ tptp.member6576561426505652726_nat_o X))) (=> (not (@ _let_2 A)) (=> (not (@ _let_2 B)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))))
% 3.70/4.03 (assert (forall ((A2 Bool) (A tptp.set_o)) (=> (@ (@ tptp.member_o A2) A) (= (@ (@ tptp.insert_o2 A2) A) A))))
% 3.70/4.03 (assert (forall ((A2 tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat A2) A) (= (@ (@ tptp.insert9069300056098147895at_nat A2) A) A))))
% 3.70/4.03 (assert (forall ((A2 tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat A2) A) (= (@ (@ tptp.insert8211810215607154385at_nat A2) A) A))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (A tptp.set_nat)) (=> (@ (@ tptp.member_nat A2) A) (= (@ (@ tptp.insert_nat2 A2) A) A))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (A tptp.set_int)) (=> (@ (@ tptp.member_int A2) A) (= (@ (@ tptp.insert_int2 A2) A) A))))
% 3.70/4.03 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.member6576561426505652726_nat_o A2) A) (= (@ (@ tptp.insert5175938949040314269_nat_o A2) A) A))))
% 3.70/4.03 (assert (forall ((A2 Bool) (A tptp.set_o) (B2 Bool) (B tptp.set_o)) (=> (not (@ (@ tptp.member_o A2) A)) (=> (not (@ (@ tptp.member_o B2) B)) (= (= (@ (@ tptp.insert_o2 A2) A) (@ (@ tptp.insert_o2 B2) B)) (and (=> (= A2 B2) (= A B)) (=> (= A2 (not B2)) (exists ((C3 tptp.set_o)) (and (= A (@ (@ tptp.insert_o2 B2) C3)) (not (@ (@ tptp.member_o B2) C3)) (= B (@ (@ tptp.insert_o2 A2) C3)) (not (@ (@ tptp.member_o A2) C3)))))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B2 tptp.produc3843707927480180839at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (= A2 B2))) (=> (not (@ (@ tptp.member8757157785044589968at_nat A2) A)) (=> (not (@ (@ tptp.member8757157785044589968at_nat B2) B)) (= (= (@ (@ tptp.insert9069300056098147895at_nat A2) A) (@ (@ tptp.insert9069300056098147895at_nat B2) B)) (and (=> _let_1 (= A B)) (=> (not _let_1) (exists ((C3 tptp.set_Pr4329608150637261639at_nat)) (and (= A (@ (@ tptp.insert9069300056098147895at_nat B2) C3)) (not (@ (@ tptp.member8757157785044589968at_nat B2) C3)) (= B (@ (@ tptp.insert9069300056098147895at_nat A2) C3)) (not (@ (@ tptp.member8757157785044589968at_nat A2) C3))))))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B2 tptp.product_prod_nat_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (= A2 B2))) (=> (not (@ (@ tptp.member8440522571783428010at_nat A2) A)) (=> (not (@ (@ tptp.member8440522571783428010at_nat B2) B)) (= (= (@ (@ tptp.insert8211810215607154385at_nat A2) A) (@ (@ tptp.insert8211810215607154385at_nat B2) B)) (and (=> _let_1 (= A B)) (=> (not _let_1) (exists ((C3 tptp.set_Pr1261947904930325089at_nat)) (and (= A (@ (@ tptp.insert8211810215607154385at_nat B2) C3)) (not (@ (@ tptp.member8440522571783428010at_nat B2) C3)) (= B (@ (@ tptp.insert8211810215607154385at_nat A2) C3)) (not (@ (@ tptp.member8440522571783428010at_nat A2) C3))))))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (A tptp.set_nat) (B2 tptp.nat) (B tptp.set_nat)) (let ((_let_1 (= A2 B2))) (=> (not (@ (@ tptp.member_nat A2) A)) (=> (not (@ (@ tptp.member_nat B2) B)) (= (= (@ (@ tptp.insert_nat2 A2) A) (@ (@ tptp.insert_nat2 B2) B)) (and (=> _let_1 (= A B)) (=> (not _let_1) (exists ((C3 tptp.set_nat)) (and (= A (@ (@ tptp.insert_nat2 B2) C3)) (not (@ (@ tptp.member_nat B2) C3)) (= B (@ (@ tptp.insert_nat2 A2) C3)) (not (@ (@ tptp.member_nat A2) C3))))))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (A tptp.set_int) (B2 tptp.int) (B tptp.set_int)) (let ((_let_1 (= A2 B2))) (=> (not (@ (@ tptp.member_int A2) A)) (=> (not (@ (@ tptp.member_int B2) B)) (= (= (@ (@ tptp.insert_int2 A2) A) (@ (@ tptp.insert_int2 B2) B)) (and (=> _let_1 (= A B)) (=> (not _let_1) (exists ((C3 tptp.set_int)) (and (= A (@ (@ tptp.insert_int2 B2) C3)) (not (@ (@ tptp.member_int B2) C3)) (= B (@ (@ tptp.insert_int2 A2) C3)) (not (@ (@ tptp.member_int A2) C3))))))))))))
% 3.70/4.03 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (= A2 B2))) (=> (not (@ (@ tptp.member6576561426505652726_nat_o A2) A)) (=> (not (@ (@ tptp.member6576561426505652726_nat_o B2) B)) (= (= (@ (@ tptp.insert5175938949040314269_nat_o A2) A) (@ (@ tptp.insert5175938949040314269_nat_o B2) B)) (and (=> _let_1 (= A B)) (=> (not _let_1) (exists ((C3 tptp.set_Pr4532377907799695533_nat_o)) (and (= A (@ (@ tptp.insert5175938949040314269_nat_o B2) C3)) (not (@ (@ tptp.member6576561426505652726_nat_o B2) C3)) (= B (@ (@ tptp.insert5175938949040314269_nat_o A2) C3)) (not (@ (@ tptp.member6576561426505652726_nat_o A2) C3))))))))))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat2 X))) (let ((_let_2 (@ tptp.insert_nat2 Y))) (= (@ _let_1 (@ _let_2 A)) (@ _let_2 (@ _let_1 A)))))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int) (A tptp.set_int)) (let ((_let_1 (@ tptp.insert_int2 X))) (let ((_let_2 (@ tptp.insert_int2 Y))) (= (@ _let_1 (@ _let_2 A)) (@ _let_2 (@ _let_1 A)))))))
% 3.70/4.03 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat X))) (let ((_let_2 (@ tptp.insert8211810215607154385at_nat Y))) (= (@ _let_1 (@ _let_2 A)) (@ _let_2 (@ _let_1 A)))))))
% 3.70/4.03 (assert (forall ((X tptp.produc3843707927480180839at_nat) (Y tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.insert9069300056098147895at_nat X))) (let ((_let_2 (@ tptp.insert9069300056098147895at_nat Y))) (= (@ _let_1 (@ _let_2 A)) (@ _let_2 (@ _let_1 A)))))))
% 3.70/4.03 (assert (forall ((X Bool) (Y Bool) (A tptp.set_o)) (let ((_let_1 (@ tptp.insert_o2 X))) (let ((_let_2 (@ tptp.insert_o2 Y))) (= (@ _let_1 (@ _let_2 A)) (@ _let_2 (@ _let_1 A)))))))
% 3.70/4.03 (assert (forall ((A2 Bool) (A tptp.set_o)) (=> (@ (@ tptp.member_o A2) A) (exists ((B5 tptp.set_o)) (and (= A (@ (@ tptp.insert_o2 A2) B5)) (not (@ (@ tptp.member_o A2) B5)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat A2) A) (exists ((B5 tptp.set_Pr4329608150637261639at_nat)) (and (= A (@ (@ tptp.insert9069300056098147895at_nat A2) B5)) (not (@ (@ tptp.member8757157785044589968at_nat A2) B5)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat A2) A) (exists ((B5 tptp.set_Pr1261947904930325089at_nat)) (and (= A (@ (@ tptp.insert8211810215607154385at_nat A2) B5)) (not (@ (@ tptp.member8440522571783428010at_nat A2) B5)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (A tptp.set_nat)) (=> (@ (@ tptp.member_nat A2) A) (exists ((B5 tptp.set_nat)) (and (= A (@ (@ tptp.insert_nat2 A2) B5)) (not (@ (@ tptp.member_nat A2) B5)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (A tptp.set_int)) (=> (@ (@ tptp.member_int A2) A) (exists ((B5 tptp.set_int)) (and (= A (@ (@ tptp.insert_int2 A2) B5)) (not (@ (@ tptp.member_int A2) B5)))))))
% 3.70/4.03 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.member6576561426505652726_nat_o A2) A) (exists ((B5 tptp.set_Pr4532377907799695533_nat_o)) (and (= A (@ (@ tptp.insert5175938949040314269_nat_o A2) B5)) (not (@ (@ tptp.member6576561426505652726_nat_o A2) B5)))))))
% 3.70/4.03 (assert (forall ((C tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_3314409938677909166at_nat A) B)) (not (=> (@ _let_1 A) (@ _let_1 B)))))))
% 3.70/4.03 (assert (forall ((C tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A) B)) (not (=> (@ _let_1 A) (@ _let_1 B)))))))
% 3.70/4.03 (assert (forall ((C tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A) B)) (not (=> (@ _let_1 A) (@ _let_1 B)))))))
% 3.70/4.03 (assert (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ _let_1 (@ (@ tptp.minus_1801376950450012436_nat_o A) B)) (not (=> (@ _let_1 A) (@ _let_1 B)))))))
% 3.70/4.03 (assert (forall ((C tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B)) (not (=> (@ _let_1 A) (@ _let_1 B)))))))
% 3.70/4.03 (assert (forall ((C tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_3314409938677909166at_nat A) B)) (@ _let_1 A)))))
% 3.70/4.03 (assert (forall ((C tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A) B)) (@ _let_1 A)))))
% 3.70/4.03 (assert (forall ((C tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A) B)) (@ _let_1 A)))))
% 3.70/4.03 (assert (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ _let_1 (@ (@ tptp.minus_1801376950450012436_nat_o A) B)) (@ _let_1 A)))))
% 3.70/4.03 (assert (forall ((C tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B)) (@ _let_1 A)))))
% 3.70/4.03 (assert (forall ((C tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_3314409938677909166at_nat A) B)) (not (@ _let_1 B))))))
% 3.70/4.03 (assert (forall ((C tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A) B)) (not (@ _let_1 B))))))
% 3.70/4.03 (assert (forall ((C tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A) B)) (not (@ _let_1 B))))))
% 3.70/4.03 (assert (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ _let_1 (@ (@ tptp.minus_1801376950450012436_nat_o A) B)) (not (@ _let_1 B))))))
% 3.70/4.03 (assert (forall ((C tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B)) (not (@ _let_1 B))))))
% 3.70/4.03 (assert (forall ((A2 tptp.produc3843707927480180839at_nat) (B2 tptp.produc3843707927480180839at_nat)) (=> (= (@ (@ tptp.insert9069300056098147895at_nat A2) tptp.bot_bo228742789529271731at_nat) (@ (@ tptp.insert9069300056098147895at_nat B2) tptp.bot_bo228742789529271731at_nat)) (= A2 B2))))
% 3.70/4.03 (assert (forall ((A2 tptp.product_prod_nat_nat) (B2 tptp.product_prod_nat_nat)) (=> (= (@ (@ tptp.insert8211810215607154385at_nat A2) tptp.bot_bo2099793752762293965at_nat) (@ (@ tptp.insert8211810215607154385at_nat B2) tptp.bot_bo2099793752762293965at_nat)) (= A2 B2))))
% 3.70/4.03 (assert (forall ((A2 Bool) (B2 Bool)) (=> (= (@ (@ tptp.insert_o2 A2) tptp.bot_bot_set_o) (@ (@ tptp.insert_o2 B2) tptp.bot_bot_set_o)) (= A2 B2))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (= (@ (@ tptp.insert_nat2 A2) tptp.bot_bot_set_nat) (@ (@ tptp.insert_nat2 B2) tptp.bot_bot_set_nat)) (= A2 B2))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (= (@ (@ tptp.insert_int2 A2) tptp.bot_bot_set_int) (@ (@ tptp.insert_int2 B2) tptp.bot_bot_set_int)) (= A2 B2))))
% 3.70/4.03 (assert (forall ((A2 tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (not (= (@ (@ tptp.insert9069300056098147895at_nat A2) A) tptp.bot_bo228742789529271731at_nat))))
% 3.70/4.03 (assert (forall ((A2 tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat)) (not (= (@ (@ tptp.insert8211810215607154385at_nat A2) A) tptp.bot_bo2099793752762293965at_nat))))
% 3.70/4.03 (assert (forall ((A2 Bool) (A tptp.set_o)) (not (= (@ (@ tptp.insert_o2 A2) A) tptp.bot_bot_set_o))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (A tptp.set_nat)) (not (= (@ (@ tptp.insert_nat2 A2) A) tptp.bot_bot_set_nat))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (A tptp.set_int)) (not (= (@ (@ tptp.insert_int2 A2) A) tptp.bot_bot_set_int))))
% 3.70/4.03 (assert (forall ((A2 tptp.produc3843707927480180839at_nat) (B2 tptp.produc3843707927480180839at_nat) (C tptp.produc3843707927480180839at_nat) (D2 tptp.produc3843707927480180839at_nat)) (= (= (@ (@ tptp.insert9069300056098147895at_nat A2) (@ (@ tptp.insert9069300056098147895at_nat B2) tptp.bot_bo228742789529271731at_nat)) (@ (@ tptp.insert9069300056098147895at_nat C) (@ (@ tptp.insert9069300056098147895at_nat D2) tptp.bot_bo228742789529271731at_nat))) (or (and (= A2 C) (= B2 D2)) (and (= A2 D2) (= B2 C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.product_prod_nat_nat) (B2 tptp.product_prod_nat_nat) (C tptp.product_prod_nat_nat) (D2 tptp.product_prod_nat_nat)) (= (= (@ (@ tptp.insert8211810215607154385at_nat A2) (@ (@ tptp.insert8211810215607154385at_nat B2) tptp.bot_bo2099793752762293965at_nat)) (@ (@ tptp.insert8211810215607154385at_nat C) (@ (@ tptp.insert8211810215607154385at_nat D2) tptp.bot_bo2099793752762293965at_nat))) (or (and (= A2 C) (= B2 D2)) (and (= A2 D2) (= B2 C))))))
% 3.70/4.03 (assert (forall ((A2 Bool) (B2 Bool) (C Bool) (D2 Bool)) (= (= (@ (@ tptp.insert_o2 A2) (@ (@ tptp.insert_o2 B2) tptp.bot_bot_set_o)) (@ (@ tptp.insert_o2 C) (@ (@ tptp.insert_o2 D2) tptp.bot_bot_set_o))) (or (and (= A2 C) (= B2 D2)) (and (= A2 D2) (= B2 C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat) (D2 tptp.nat)) (= (= (@ (@ tptp.insert_nat2 A2) (@ (@ tptp.insert_nat2 B2) tptp.bot_bot_set_nat)) (@ (@ tptp.insert_nat2 C) (@ (@ tptp.insert_nat2 D2) tptp.bot_bot_set_nat))) (or (and (= A2 C) (= B2 D2)) (and (= A2 D2) (= B2 C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int) (D2 tptp.int)) (= (= (@ (@ tptp.insert_int2 A2) (@ (@ tptp.insert_int2 B2) tptp.bot_bot_set_int)) (@ (@ tptp.insert_int2 C) (@ (@ tptp.insert_int2 D2) tptp.bot_bot_set_int))) (or (and (= A2 C) (= B2 D2)) (and (= A2 D2) (= B2 C))))))
% 3.70/4.03 (assert (forall ((B2 (-> tptp.produc3658429121746597890et_nat Bool)) (A2 (-> tptp.produc3658429121746597890et_nat Bool))) (= (@ (@ tptp.member6576561426505652726_nat_o B2) (@ (@ tptp.insert5175938949040314269_nat_o A2) tptp.bot_bo7824918357723582233_nat_o)) (= B2 A2))))
% 3.70/4.03 (assert (forall ((B2 tptp.produc3843707927480180839at_nat) (A2 tptp.produc3843707927480180839at_nat)) (= (@ (@ tptp.member8757157785044589968at_nat B2) (@ (@ tptp.insert9069300056098147895at_nat A2) tptp.bot_bo228742789529271731at_nat)) (= B2 A2))))
% 3.70/4.03 (assert (forall ((B2 tptp.product_prod_nat_nat) (A2 tptp.product_prod_nat_nat)) (= (@ (@ tptp.member8440522571783428010at_nat B2) (@ (@ tptp.insert8211810215607154385at_nat A2) tptp.bot_bo2099793752762293965at_nat)) (= B2 A2))))
% 3.70/4.03 (assert (forall ((B2 Bool) (A2 Bool)) (= (@ (@ tptp.member_o B2) (@ (@ tptp.insert_o2 A2) tptp.bot_bot_set_o)) (= B2 A2))))
% 3.70/4.03 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (= (@ (@ tptp.member_nat B2) (@ (@ tptp.insert_nat2 A2) tptp.bot_bot_set_nat)) (= B2 A2))))
% 3.70/4.03 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (= (@ (@ tptp.member_int B2) (@ (@ tptp.insert_int2 A2) tptp.bot_bot_set_int)) (= B2 A2))))
% 3.70/4.03 (assert (forall ((B2 (-> tptp.produc3658429121746597890et_nat Bool)) (A2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o B2) (@ (@ tptp.insert5175938949040314269_nat_o A2) tptp.bot_bo7824918357723582233_nat_o)) (= B2 A2))))
% 3.70/4.03 (assert (forall ((B2 tptp.produc3843707927480180839at_nat) (A2 tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat B2) (@ (@ tptp.insert9069300056098147895at_nat A2) tptp.bot_bo228742789529271731at_nat)) (= B2 A2))))
% 3.70/4.03 (assert (forall ((B2 tptp.product_prod_nat_nat) (A2 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat B2) (@ (@ tptp.insert8211810215607154385at_nat A2) tptp.bot_bo2099793752762293965at_nat)) (= B2 A2))))
% 3.70/4.03 (assert (forall ((B2 Bool) (A2 Bool)) (=> (@ (@ tptp.member_o B2) (@ (@ tptp.insert_o2 A2) tptp.bot_bot_set_o)) (= B2 A2))))
% 3.70/4.03 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.member_nat B2) (@ (@ tptp.insert_nat2 A2) tptp.bot_bot_set_nat)) (= B2 A2))))
% 3.70/4.03 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.insert_int2 A2) tptp.bot_bot_set_int)) (= B2 A2))))
% 3.70/4.03 (assert (forall ((X Bool) (B tptp.set_o) (A tptp.set_o)) (let ((_let_1 (@ (@ tptp.minus_minus_set_o A) B))) (let ((_let_2 (@ tptp.insert_o2 X))) (let ((_let_3 (@ (@ tptp.minus_minus_set_o (@ _let_2 A)) B))) (let ((_let_4 (@ (@ tptp.member_o X) B))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 3.70/4.03 (assert (forall ((X tptp.produc3843707927480180839at_nat) (B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ (@ tptp.minus_3314409938677909166at_nat A) B))) (let ((_let_2 (@ tptp.insert9069300056098147895at_nat X))) (let ((_let_3 (@ (@ tptp.minus_3314409938677909166at_nat (@ _let_2 A)) B))) (let ((_let_4 (@ (@ tptp.member8757157785044589968at_nat X) B))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 3.70/4.03 (assert (forall ((X tptp.product_prod_nat_nat) (B tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ tptp.minus_1356011639430497352at_nat A) B))) (let ((_let_2 (@ tptp.insert8211810215607154385at_nat X))) (let ((_let_3 (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_2 A)) B))) (let ((_let_4 (@ (@ tptp.member8440522571783428010at_nat X) B))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 3.70/4.03 (assert (forall ((X tptp.int) (B tptp.set_int) (A tptp.set_int)) (let ((_let_1 (@ (@ tptp.minus_minus_set_int A) B))) (let ((_let_2 (@ tptp.insert_int2 X))) (let ((_let_3 (@ (@ tptp.minus_minus_set_int (@ _let_2 A)) B))) (let ((_let_4 (@ (@ tptp.member_int X) B))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 3.70/4.03 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.set_Pr4532377907799695533_nat_o) (A tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ (@ tptp.minus_1801376950450012436_nat_o A) B))) (let ((_let_2 (@ tptp.insert5175938949040314269_nat_o X))) (let ((_let_3 (@ (@ tptp.minus_1801376950450012436_nat_o (@ _let_2 A)) B))) (let ((_let_4 (@ (@ tptp.member6576561426505652726_nat_o X) B))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (B tptp.set_nat) (A tptp.set_nat)) (let ((_let_1 (@ (@ tptp.minus_minus_set_nat A) B))) (let ((_let_2 (@ tptp.insert_nat2 X))) (let ((_let_3 (@ (@ tptp.minus_minus_set_nat (@ _let_2 A)) B))) (let ((_let_4 (@ (@ tptp.member_nat X) B))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 3.70/4.03 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (X4 tptp.set_Pr4532377907799695533_nat_o)) (=> (not (@ (@ tptp.member6576561426505652726_nat_o X) X4)) (= (@ (@ tptp.minus_1801376950450012436_nat_o X4) (@ (@ tptp.insert5175938949040314269_nat_o X) tptp.bot_bo7824918357723582233_nat_o)) X4))))
% 3.70/4.03 (assert (forall ((X tptp.produc3843707927480180839at_nat) (X4 tptp.set_Pr4329608150637261639at_nat)) (=> (not (@ (@ tptp.member8757157785044589968at_nat X) X4)) (= (@ (@ tptp.minus_3314409938677909166at_nat X4) (@ (@ tptp.insert9069300056098147895at_nat X) tptp.bot_bo228742789529271731at_nat)) X4))))
% 3.70/4.03 (assert (forall ((X tptp.product_prod_nat_nat) (X4 tptp.set_Pr1261947904930325089at_nat)) (=> (not (@ (@ tptp.member8440522571783428010at_nat X) X4)) (= (@ (@ tptp.minus_1356011639430497352at_nat X4) (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat)) X4))))
% 3.70/4.03 (assert (forall ((X Bool) (X4 tptp.set_o)) (=> (not (@ (@ tptp.member_o X) X4)) (= (@ (@ tptp.minus_minus_set_o X4) (@ (@ tptp.insert_o2 X) tptp.bot_bot_set_o)) X4))))
% 3.70/4.03 (assert (forall ((X tptp.int) (X4 tptp.set_int)) (=> (not (@ (@ tptp.member_int X) X4)) (= (@ (@ tptp.minus_minus_set_int X4) (@ (@ tptp.insert_int2 X) tptp.bot_bot_set_int)) X4))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (X4 tptp.set_nat)) (=> (not (@ (@ tptp.member_nat X) X4)) (= (@ (@ tptp.minus_minus_set_nat X4) (@ (@ tptp.insert_nat2 X) tptp.bot_bot_set_nat)) X4))))
% 3.70/4.03 (assert (forall ((P tptp.assn) (A (-> tptp.c tptp.nat tptp.assn)) (Xs tptp.list_c) (I tptp.nat) (Xsi tptp.list_nat) (I3 tptp.set_nat) (F tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_c Xs) I)) (@ (@ tptp.nth_nat Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L6585172037124793648_c_nat (@ (@ tptp.minus_minus_set_nat I3) (@ (@ tptp.insert_nat2 I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_c Xs)) (=> (@ (@ tptp.member_nat I) I3) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L6585172037124793648_c_nat I3) A) Xs) Xsi)) F)) Q) (@ _let_1 Q))))))))
% 3.70/4.03 (assert (forall ((P tptp.assn) (A (-> tptp.c tptp.int tptp.assn)) (Xs tptp.list_c) (I tptp.nat) (Xsi tptp.list_int) (I3 tptp.set_nat) (F tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_c Xs) I)) (@ (@ tptp.nth_int Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L6582681566615743372_c_int (@ (@ tptp.minus_minus_set_nat I3) (@ (@ tptp.insert_nat2 I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_c Xs)) (=> (@ (@ tptp.member_nat I) I3) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L6582681566615743372_c_int I3) A) Xs) Xsi)) F)) Q) (@ _let_1 Q))))))))
% 3.70/4.03 (assert (forall ((P tptp.assn) (A (-> tptp.d tptp.nat tptp.assn)) (Xs tptp.list_d) (I tptp.nat) (Xsi tptp.list_nat) (I3 tptp.set_nat) (F tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_d Xs) I)) (@ (@ tptp.nth_nat Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7820616366081188145_d_nat (@ (@ tptp.minus_minus_set_nat I3) (@ (@ tptp.insert_nat2 I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_d Xs)) (=> (@ (@ tptp.member_nat I) I3) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L7820616366081188145_d_nat I3) A) Xs) Xsi)) F)) Q) (@ _let_1 Q))))))))
% 3.70/4.03 (assert (forall ((P tptp.assn) (A (-> tptp.d tptp.int tptp.assn)) (Xs tptp.list_d) (I tptp.nat) (Xsi tptp.list_int) (I3 tptp.set_nat) (F tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_d Xs) I)) (@ (@ tptp.nth_int Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7818125895572137869_d_int (@ (@ tptp.minus_minus_set_nat I3) (@ (@ tptp.insert_nat2 I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_d Xs)) (=> (@ (@ tptp.member_nat I) I3) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L7818125895572137869_d_int I3) A) Xs) Xsi)) F)) Q) (@ _let_1 Q))))))))
% 3.70/4.03 (assert (forall ((P tptp.assn) (A (-> tptp.nat tptp.nat tptp.assn)) (Xs tptp.list_nat) (I tptp.nat) (Xsi tptp.list_nat) (I3 tptp.set_nat) (F tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_nat Xs) I)) (@ (@ tptp.nth_nat Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7892069108621897922at_nat (@ (@ tptp.minus_minus_set_nat I3) (@ (@ tptp.insert_nat2 I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs)) (=> (@ (@ tptp.member_nat I) I3) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L7892069108621897922at_nat I3) A) Xs) Xsi)) F)) Q) (@ _let_1 Q))))))))
% 3.70/4.03 (assert (forall ((P tptp.assn) (A (-> tptp.nat tptp.int tptp.assn)) (Xs tptp.list_nat) (I tptp.nat) (Xsi tptp.list_int) (I3 tptp.set_nat) (F tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_nat Xs) I)) (@ (@ tptp.nth_int Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7889578638112847646at_int (@ (@ tptp.minus_minus_set_nat I3) (@ (@ tptp.insert_nat2 I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs)) (=> (@ (@ tptp.member_nat I) I3) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L7889578638112847646at_int I3) A) Xs) Xsi)) F)) Q) (@ _let_1 Q))))))))
% 3.70/4.03 (assert (forall ((P tptp.assn) (A (-> tptp.int tptp.nat tptp.assn)) (Xs tptp.list_int) (I tptp.nat) (Xsi tptp.list_nat) (I3 tptp.set_nat) (F tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_int Xs) I)) (@ (@ tptp.nth_nat Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L8891422820522952478nt_nat (@ (@ tptp.minus_minus_set_nat I3) (@ (@ tptp.insert_nat2 I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs)) (=> (@ (@ tptp.member_nat I) I3) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L8891422820522952478nt_nat I3) A) Xs) Xsi)) F)) Q) (@ _let_1 Q))))))))
% 3.70/4.03 (assert (forall ((P tptp.assn) (A (-> tptp.int tptp.int tptp.assn)) (Xs tptp.list_int) (I tptp.nat) (Xsi tptp.list_int) (I3 tptp.set_nat) (F tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_int Xs) I)) (@ (@ tptp.nth_int Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L8888932350013902202nt_int (@ (@ tptp.minus_minus_set_nat I3) (@ (@ tptp.insert_nat2 I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs)) (=> (@ (@ tptp.member_nat I) I3) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L8888932350013902202nt_int I3) A) Xs) Xsi)) F)) Q) (@ _let_1 Q))))))))
% 3.70/4.03 (assert (forall ((P tptp.assn) (A (-> tptp.c tptp.d tptp.assn)) (Xs tptp.list_c) (I tptp.nat) (Xsi tptp.list_d) (I3 tptp.set_nat) (F tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_c Xs) I)) (@ (@ tptp.nth_d Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L824818263033719201sn_c_d (@ (@ tptp.minus_minus_set_nat I3) (@ (@ tptp.insert_nat2 I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_c Xs)) (=> (@ (@ tptp.member_nat I) I3) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L824818263033719201sn_c_d I3) A) Xs) Xsi)) F)) Q) (@ _let_1 Q))))))))
% 3.70/4.03 (assert (forall ((X tptp.produc3843707927480180839at_nat)) (= (@ tptp.the_el221668144340439132at_nat (@ (@ tptp.insert9069300056098147895at_nat X) tptp.bot_bo228742789529271731at_nat)) X)))
% 3.70/4.03 (assert (forall ((X tptp.product_prod_nat_nat)) (= (@ tptp.the_el2281957884133575798at_nat (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat)) X)))
% 3.70/4.03 (assert (forall ((X Bool)) (= (@ tptp.the_elem_o (@ (@ tptp.insert_o2 X) tptp.bot_bot_set_o)) X)))
% 3.70/4.03 (assert (forall ((X tptp.nat)) (= (@ tptp.the_elem_nat (@ (@ tptp.insert_nat2 X) tptp.bot_bot_set_nat)) X)))
% 3.70/4.03 (assert (forall ((X tptp.int)) (= (@ tptp.the_elem_int (@ (@ tptp.insert_int2 X) tptp.bot_bot_set_int)) X)))
% 3.70/4.03 (assert (forall ((I tptp.nat) (I3 tptp.set_nat) (Xs tptp.list_c) (A (-> tptp.c tptp.nat tptp.assn)) (Xsi tptp.list_nat)) (=> (@ (@ tptp.member_nat I) I3) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_c Xs)) (= (@ (@ (@ (@ tptp.vEBT_L6585172037124793648_c_nat I3) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_c Xs) I)) (@ (@ tptp.nth_nat Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L6585172037124793648_c_nat (@ (@ tptp.minus_minus_set_nat I3) (@ (@ tptp.insert_nat2 I) tptp.bot_bot_set_nat))) A) Xs) Xsi)))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (I3 tptp.set_nat) (Xs tptp.list_c) (A (-> tptp.c tptp.int tptp.assn)) (Xsi tptp.list_int)) (=> (@ (@ tptp.member_nat I) I3) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_c Xs)) (= (@ (@ (@ (@ tptp.vEBT_L6582681566615743372_c_int I3) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_c Xs) I)) (@ (@ tptp.nth_int Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L6582681566615743372_c_int (@ (@ tptp.minus_minus_set_nat I3) (@ (@ tptp.insert_nat2 I) tptp.bot_bot_set_nat))) A) Xs) Xsi)))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (I3 tptp.set_nat) (Xs tptp.list_d) (A (-> tptp.d tptp.nat tptp.assn)) (Xsi tptp.list_nat)) (=> (@ (@ tptp.member_nat I) I3) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_d Xs)) (= (@ (@ (@ (@ tptp.vEBT_L7820616366081188145_d_nat I3) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_d Xs) I)) (@ (@ tptp.nth_nat Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7820616366081188145_d_nat (@ (@ tptp.minus_minus_set_nat I3) (@ (@ tptp.insert_nat2 I) tptp.bot_bot_set_nat))) A) Xs) Xsi)))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (I3 tptp.set_nat) (Xs tptp.list_d) (A (-> tptp.d tptp.int tptp.assn)) (Xsi tptp.list_int)) (=> (@ (@ tptp.member_nat I) I3) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_d Xs)) (= (@ (@ (@ (@ tptp.vEBT_L7818125895572137869_d_int I3) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_d Xs) I)) (@ (@ tptp.nth_int Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7818125895572137869_d_int (@ (@ tptp.minus_minus_set_nat I3) (@ (@ tptp.insert_nat2 I) tptp.bot_bot_set_nat))) A) Xs) Xsi)))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (I3 tptp.set_nat) (Xs tptp.list_nat) (A (-> tptp.nat tptp.nat tptp.assn)) (Xsi tptp.list_nat)) (=> (@ (@ tptp.member_nat I) I3) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs)) (= (@ (@ (@ (@ tptp.vEBT_L7892069108621897922at_nat I3) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_nat Xs) I)) (@ (@ tptp.nth_nat Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7892069108621897922at_nat (@ (@ tptp.minus_minus_set_nat I3) (@ (@ tptp.insert_nat2 I) tptp.bot_bot_set_nat))) A) Xs) Xsi)))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (I3 tptp.set_nat) (Xs tptp.list_nat) (A (-> tptp.nat tptp.int tptp.assn)) (Xsi tptp.list_int)) (=> (@ (@ tptp.member_nat I) I3) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs)) (= (@ (@ (@ (@ tptp.vEBT_L7889578638112847646at_int I3) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_nat Xs) I)) (@ (@ tptp.nth_int Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7889578638112847646at_int (@ (@ tptp.minus_minus_set_nat I3) (@ (@ tptp.insert_nat2 I) tptp.bot_bot_set_nat))) A) Xs) Xsi)))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (I3 tptp.set_nat) (Xs tptp.list_int) (A (-> tptp.int tptp.nat tptp.assn)) (Xsi tptp.list_nat)) (=> (@ (@ tptp.member_nat I) I3) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs)) (= (@ (@ (@ (@ tptp.vEBT_L8891422820522952478nt_nat I3) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_int Xs) I)) (@ (@ tptp.nth_nat Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L8891422820522952478nt_nat (@ (@ tptp.minus_minus_set_nat I3) (@ (@ tptp.insert_nat2 I) tptp.bot_bot_set_nat))) A) Xs) Xsi)))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (I3 tptp.set_nat) (Xs tptp.list_int) (A (-> tptp.int tptp.int tptp.assn)) (Xsi tptp.list_int)) (=> (@ (@ tptp.member_nat I) I3) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs)) (= (@ (@ (@ (@ tptp.vEBT_L8888932350013902202nt_int I3) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_int Xs) I)) (@ (@ tptp.nth_int Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L8888932350013902202nt_int (@ (@ tptp.minus_minus_set_nat I3) (@ (@ tptp.insert_nat2 I) tptp.bot_bot_set_nat))) A) Xs) Xsi)))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (I3 tptp.set_nat) (Xs tptp.list_c) (A (-> tptp.c tptp.d tptp.assn)) (Xsi tptp.list_d)) (=> (@ (@ tptp.member_nat I) I3) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_c Xs)) (= (@ (@ (@ (@ tptp.vEBT_L824818263033719201sn_c_d I3) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_c Xs) I)) (@ (@ tptp.nth_d Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L824818263033719201sn_c_d (@ (@ tptp.minus_minus_set_nat I3) (@ (@ tptp.insert_nat2 I) tptp.bot_bot_set_nat))) A) Xs) Xsi)))))))
% 3.70/4.03 (assert (forall ((X tptp.produc3843707927480180839at_nat)) (@ tptp.is_sin2937591304547752795at_nat (@ (@ tptp.insert9069300056098147895at_nat X) tptp.bot_bo228742789529271731at_nat))))
% 3.70/4.03 (assert (forall ((X tptp.product_prod_nat_nat)) (@ tptp.is_sin2850979758926227957at_nat (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat))))
% 3.70/4.03 (assert (forall ((X Bool)) (@ tptp.is_singleton_o (@ (@ tptp.insert_o2 X) tptp.bot_bot_set_o))))
% 3.70/4.03 (assert (forall ((X tptp.nat)) (@ tptp.is_singleton_nat (@ (@ tptp.insert_nat2 X) tptp.bot_bot_set_nat))))
% 3.70/4.03 (assert (forall ((X tptp.int)) (@ tptp.is_singleton_int (@ (@ tptp.insert_int2 X) tptp.bot_bot_set_int))))
% 3.70/4.03 (assert (forall ((P (-> tptp.code_integer Bool)) (D tptp.code_integer) (Q (-> tptp.code_integer Bool))) (=> (forall ((X3 tptp.code_integer) (K tptp.code_integer)) (= (@ P X3) (@ P (@ (@ tptp.minus_8373710615458151222nteger X3) (@ (@ tptp.times_3573771949741848930nteger K) D))))) (=> (forall ((X3 tptp.code_integer) (K tptp.code_integer)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_8373710615458151222nteger X3) (@ (@ tptp.times_3573771949741848930nteger K) D))))) (forall ((X7 tptp.code_integer) (K2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.minus_8373710615458151222nteger X7) (@ (@ tptp.times_3573771949741848930nteger K2) D)))) (= (or (@ P X7) (@ Q X7)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 3.70/4.03 (assert (forall ((P (-> tptp.rat Bool)) (D tptp.rat) (Q (-> tptp.rat Bool))) (=> (forall ((X3 tptp.rat) (K tptp.rat)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K) D))))) (=> (forall ((X3 tptp.rat) (K tptp.rat)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K) D))))) (forall ((X7 tptp.rat) (K2 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X7) (@ (@ tptp.times_times_rat K2) D)))) (= (or (@ P X7) (@ Q X7)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 3.70/4.03 (assert (forall ((P (-> tptp.int Bool)) (D tptp.int) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D))))) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D))))) (forall ((X7 tptp.int) (K2 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X7) (@ (@ tptp.times_times_int K2) D)))) (= (or (@ P X7) (@ Q X7)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 3.70/4.03 (assert (forall ((P (-> tptp.code_integer Bool)) (D tptp.code_integer) (Q (-> tptp.code_integer Bool))) (=> (forall ((X3 tptp.code_integer) (K tptp.code_integer)) (= (@ P X3) (@ P (@ (@ tptp.minus_8373710615458151222nteger X3) (@ (@ tptp.times_3573771949741848930nteger K) D))))) (=> (forall ((X3 tptp.code_integer) (K tptp.code_integer)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_8373710615458151222nteger X3) (@ (@ tptp.times_3573771949741848930nteger K) D))))) (forall ((X7 tptp.code_integer) (K2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.minus_8373710615458151222nteger X7) (@ (@ tptp.times_3573771949741848930nteger K2) D)))) (= (and (@ P X7) (@ Q X7)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 3.70/4.03 (assert (forall ((P (-> tptp.rat Bool)) (D tptp.rat) (Q (-> tptp.rat Bool))) (=> (forall ((X3 tptp.rat) (K tptp.rat)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K) D))))) (=> (forall ((X3 tptp.rat) (K tptp.rat)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K) D))))) (forall ((X7 tptp.rat) (K2 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X7) (@ (@ tptp.times_times_rat K2) D)))) (= (and (@ P X7) (@ Q X7)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 3.70/4.03 (assert (forall ((P (-> tptp.int Bool)) (D tptp.int) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D))))) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D))))) (forall ((X7 tptp.int) (K2 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X7) (@ (@ tptp.times_times_int K2) D)))) (= (and (@ P X7) (@ Q X7)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger A2) B2)) C) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B2) C)))))
% 3.70/4.03 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A2) B2)) C) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B2) C)))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A2) B2)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B2) C)))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A2))) (= (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger B2) C)) (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 B2)) (@ _let_1 C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B2) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B2)) (@ _let_1 C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B2) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B2)) (@ _let_1 C))))))
% 3.70/4.03 (assert (forall ((B2 tptp.code_integer) (C tptp.code_integer) (A2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger B2) C)) A2) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.times_3573771949741848930nteger B2) A2)) (@ (@ tptp.times_3573771949741848930nteger C) A2)))))
% 3.70/4.03 (assert (forall ((B2 tptp.rat) (C tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B2) C)) A2) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat B2) A2)) (@ (@ tptp.times_times_rat C) A2)))))
% 3.70/4.03 (assert (forall ((B2 tptp.nat) (C tptp.nat) (A2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat B2) C)) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat B2) A2)) (@ (@ tptp.times_times_nat C) A2)))))
% 3.70/4.03 (assert (forall ((B2 tptp.int) (C tptp.int) (A2 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B2) C)) A2) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int B2) A2)) (@ (@ tptp.times_times_int C) A2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A2))) (= (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger B2) C)) (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 B2)) (@ _let_1 C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B2) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B2)) (@ _let_1 C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat B2) C)) (@ (@ tptp.minus_minus_nat (@ _let_1 B2)) (@ _let_1 C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B2) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B2)) (@ _let_1 C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (D2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (@ (@ tptp.ord_less_rat D2) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A2) C)) (@ (@ tptp.minus_minus_rat B2) D2))))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (D2 tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger D2) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.minus_8373710615458151222nteger A2) C)) (@ (@ tptp.minus_8373710615458151222nteger B2) D2))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int) (D2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ (@ tptp.ord_less_int D2) C) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A2) C)) (@ (@ tptp.minus_minus_int B2) D2))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (J tptp.nat) (Xs tptp.list_nat) (X tptp.nat)) (=> (not (= I J)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs) I) X)) J) (@ (@ tptp.nth_nat Xs) J)))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (J tptp.nat) (Xs tptp.list_int) (X tptp.int)) (=> (not (= I J)) (= (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs) I) X)) J) (@ (@ tptp.nth_int Xs) J)))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (J tptp.nat) (Xs tptp.list_c) (X tptp.c)) (=> (not (= I J)) (= (@ (@ tptp.nth_c (@ (@ (@ tptp.list_update_c Xs) I) X)) J) (@ (@ tptp.nth_c Xs) J)))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (J tptp.nat) (Xs tptp.list_d) (X tptp.d)) (=> (not (= I J)) (= (@ (@ tptp.nth_d (@ (@ (@ tptp.list_update_d Xs) I) X)) J) (@ (@ tptp.nth_d Xs) J)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_nat) (I tptp.nat)) (= (@ (@ (@ tptp.list_update_nat Xs) I) (@ (@ tptp.nth_nat Xs) I)) Xs)))
% 3.70/4.03 (assert (forall ((Xs tptp.list_int) (I tptp.nat)) (= (@ (@ (@ tptp.list_update_int Xs) I) (@ (@ tptp.nth_int Xs) I)) Xs)))
% 3.70/4.03 (assert (forall ((Xs tptp.list_c) (I tptp.nat)) (= (@ (@ (@ tptp.list_update_c Xs) I) (@ (@ tptp.nth_c Xs) I)) Xs)))
% 3.70/4.03 (assert (forall ((Xs tptp.list_d) (I tptp.nat)) (= (@ (@ (@ tptp.list_update_d Xs) I) (@ (@ tptp.nth_d Xs) I)) Xs)))
% 3.70/4.03 (assert (forall ((I tptp.nat) (Xs tptp.list_c) (X tptp.c)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_c Xs)) (= (@ (@ tptp.nth_c (@ (@ (@ tptp.list_update_c Xs) I) X)) I) X))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (Xs tptp.list_d) (X tptp.d)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_d Xs)) (= (@ (@ tptp.nth_d (@ (@ (@ tptp.list_update_d Xs) I) X)) I) X))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (Xs tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs) I) X)) I) X))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (Xs tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs) I) X)) I) X))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (L tptp.list_c) (J tptp.nat) (X tptp.c)) (=> (not (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_c L))) (= (@ (@ tptp.nth_c (@ (@ (@ tptp.list_update_c L) J) X)) I) (@ (@ tptp.nth_c L) I)))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (L tptp.list_d) (J tptp.nat) (X tptp.d)) (=> (not (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_d L))) (= (@ (@ tptp.nth_d (@ (@ (@ tptp.list_update_d L) J) X)) I) (@ (@ tptp.nth_d L) I)))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (L tptp.list_nat) (J tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat L))) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat L) J) X)) I) (@ (@ tptp.nth_nat L) I)))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (L tptp.list_int) (J tptp.nat) (X tptp.int)) (=> (not (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int L))) (= (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int L) J) X)) I) (@ (@ tptp.nth_int L) I)))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (C tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (=> (@ (@ tptp.ord_le2604355607129572851at_nat A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ (@ tptp.ord_le7866589430770878221at_nat A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 3.70/4.03 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ (@ tptp.ord_less_set_nat A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 3.70/4.03 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ (@ tptp.ord_less_set_int A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o) (C (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ (@ tptp.ord_le2453136405763929_nat_o A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 3.70/4.03 (assert (= (lambda ((Y4 tptp.list_c) (Z2 tptp.list_c)) (= Y4 Z2)) (lambda ((Xs3 tptp.list_c) (Ys3 tptp.list_c)) (and (= (@ tptp.size_size_list_c Xs3) (@ tptp.size_size_list_c Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_c Xs3)) (= (@ (@ tptp.nth_c Xs3) I4) (@ (@ tptp.nth_c Ys3) I4))))))))
% 3.70/4.03 (assert (= (lambda ((Y4 tptp.list_d) (Z2 tptp.list_d)) (= Y4 Z2)) (lambda ((Xs3 tptp.list_d) (Ys3 tptp.list_d)) (and (= (@ tptp.size_size_list_d Xs3) (@ tptp.size_size_list_d Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_d Xs3)) (= (@ (@ tptp.nth_d Xs3) I4) (@ (@ tptp.nth_d Ys3) I4))))))))
% 3.70/4.03 (assert (= (lambda ((Y4 tptp.list_nat) (Z2 tptp.list_nat)) (= Y4 Z2)) (lambda ((Xs3 tptp.list_nat) (Ys3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs3) (@ tptp.size_size_list_nat Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs3)) (= (@ (@ tptp.nth_nat Xs3) I4) (@ (@ tptp.nth_nat Ys3) I4))))))))
% 3.70/4.03 (assert (= (lambda ((Y4 tptp.list_int) (Z2 tptp.list_int)) (= Y4 Z2)) (lambda ((Xs3 tptp.list_int) (Ys3 tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs3) (@ tptp.size_size_list_int Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs3)) (= (@ (@ tptp.nth_int Xs3) I4) (@ (@ tptp.nth_int Ys3) I4))))))))
% 3.70/4.03 (assert (forall ((K3 tptp.nat) (P (-> tptp.nat tptp.c Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K3) (exists ((X8 tptp.c)) (@ (@ P I4) X8)))) (exists ((Xs3 tptp.list_c)) (and (= (@ tptp.size_size_list_c Xs3) K3) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K3) (@ (@ P I4) (@ (@ tptp.nth_c Xs3) I4)))))))))
% 3.70/4.03 (assert (forall ((K3 tptp.nat) (P (-> tptp.nat tptp.d Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K3) (exists ((X8 tptp.d)) (@ (@ P I4) X8)))) (exists ((Xs3 tptp.list_d)) (and (= (@ tptp.size_size_list_d Xs3) K3) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K3) (@ (@ P I4) (@ (@ tptp.nth_d Xs3) I4)))))))))
% 3.70/4.03 (assert (forall ((K3 tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K3) (exists ((X8 tptp.nat)) (@ (@ P I4) X8)))) (exists ((Xs3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs3) K3) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K3) (@ (@ P I4) (@ (@ tptp.nth_nat Xs3) I4)))))))))
% 3.70/4.03 (assert (forall ((K3 tptp.nat) (P (-> tptp.nat tptp.int Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K3) (exists ((X8 tptp.int)) (@ (@ P I4) X8)))) (exists ((Xs3 tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs3) K3) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K3) (@ (@ P I4) (@ (@ tptp.nth_int Xs3) I4)))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_c)) (=> (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_c Ys)) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_c Xs)) (= (@ (@ tptp.nth_c Xs) I5) (@ (@ tptp.nth_c Ys) I5)))) (= Xs Ys)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_d) (Ys tptp.list_d)) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_d Ys)) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_d Xs)) (= (@ (@ tptp.nth_d Xs) I5) (@ (@ tptp.nth_d Ys) I5)))) (= Xs Ys)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys)) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I5) (@ (@ tptp.nth_nat Ys) I5)))) (= Xs Ys)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (=> (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys)) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int Xs) I5) (@ (@ tptp.nth_int Ys) I5)))) (= Xs Ys)))))
% 3.70/4.03 (assert (forall ((N tptp.nat) (P (-> tptp.c tptp.nat Bool))) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) N) (exists ((Li2 tptp.c)) (@ (@ P Li2) I5)))) (not (forall ((L2 tptp.list_c)) (=> (= (@ tptp.size_size_list_c L2) N) (not (forall ((I6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I6) N) (@ (@ P (@ (@ tptp.nth_c L2) I6)) I6))))))))))
% 3.70/4.03 (assert (forall ((N tptp.nat) (P (-> tptp.d tptp.nat Bool))) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) N) (exists ((Li2 tptp.d)) (@ (@ P Li2) I5)))) (not (forall ((L2 tptp.list_d)) (=> (= (@ tptp.size_size_list_d L2) N) (not (forall ((I6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I6) N) (@ (@ P (@ (@ tptp.nth_d L2) I6)) I6))))))))))
% 3.70/4.03 (assert (forall ((N tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) N) (exists ((Li2 tptp.nat)) (@ (@ P Li2) I5)))) (not (forall ((L2 tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat L2) N) (not (forall ((I6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I6) N) (@ (@ P (@ (@ tptp.nth_nat L2) I6)) I6))))))))))
% 3.70/4.03 (assert (forall ((N tptp.nat) (P (-> tptp.int tptp.nat Bool))) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) N) (exists ((Li2 tptp.int)) (@ (@ P Li2) I5)))) (not (forall ((L2 tptp.list_int)) (=> (= (@ tptp.size_size_list_int L2) N) (not (forall ((I6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I6) N) (@ (@ P (@ (@ tptp.nth_int L2) I6)) I6))))))))))
% 3.70/4.03 (assert (= tptp.is_sin2937591304547752795at_nat (lambda ((A5 tptp.set_Pr4329608150637261639at_nat)) (= A5 (@ (@ tptp.insert9069300056098147895at_nat (@ tptp.the_el221668144340439132at_nat A5)) tptp.bot_bo228742789529271731at_nat)))))
% 3.70/4.03 (assert (= tptp.is_sin2850979758926227957at_nat (lambda ((A5 tptp.set_Pr1261947904930325089at_nat)) (= A5 (@ (@ tptp.insert8211810215607154385at_nat (@ tptp.the_el2281957884133575798at_nat A5)) tptp.bot_bo2099793752762293965at_nat)))))
% 3.70/4.03 (assert (= tptp.is_singleton_o (lambda ((A5 tptp.set_o)) (= A5 (@ (@ tptp.insert_o2 (@ tptp.the_elem_o A5)) tptp.bot_bot_set_o)))))
% 3.70/4.03 (assert (= tptp.is_singleton_nat (lambda ((A5 tptp.set_nat)) (= A5 (@ (@ tptp.insert_nat2 (@ tptp.the_elem_nat A5)) tptp.bot_bot_set_nat)))))
% 3.70/4.03 (assert (= tptp.is_singleton_int (lambda ((A5 tptp.set_int)) (= A5 (@ (@ tptp.insert_int2 (@ tptp.the_elem_int A5)) tptp.bot_bot_set_int)))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (=> (not (= A tptp.bot_bo7824918357723582233_nat_o)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X3) A) (=> (@ (@ tptp.member6576561426505652726_nat_o Y2) A) (= X3 Y2)))) (@ tptp.is_sin5180296473474724033_nat_o A)))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat)) (=> (not (= A tptp.bot_bo228742789529271731at_nat)) (=> (forall ((X3 tptp.produc3843707927480180839at_nat) (Y2 tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X3) A) (=> (@ (@ tptp.member8757157785044589968at_nat Y2) A) (= X3 Y2)))) (@ tptp.is_sin2937591304547752795at_nat A)))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat)) (=> (not (= A tptp.bot_bo2099793752762293965at_nat)) (=> (forall ((X3 tptp.product_prod_nat_nat) (Y2 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) A) (=> (@ (@ tptp.member8440522571783428010at_nat Y2) A) (= X3 Y2)))) (@ tptp.is_sin2850979758926227957at_nat A)))))
% 3.70/4.03 (assert (forall ((A tptp.set_o)) (=> (not (= A tptp.bot_bot_set_o)) (=> (forall ((X3 Bool) (Y2 Bool)) (=> (@ (@ tptp.member_o X3) A) (=> (@ (@ tptp.member_o Y2) A) (= X3 Y2)))) (@ tptp.is_singleton_o A)))))
% 3.70/4.03 (assert (forall ((A tptp.set_nat)) (=> (not (= A tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A) (=> (@ (@ tptp.member_nat Y2) A) (= X3 Y2)))) (@ tptp.is_singleton_nat A)))))
% 3.70/4.03 (assert (forall ((A tptp.set_int)) (=> (not (= A tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.member_int X3) A) (=> (@ (@ tptp.member_int Y2) A) (= X3 Y2)))) (@ tptp.is_singleton_int A)))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (Xs tptp.list_c) (J tptp.nat) (X tptp.c)) (let ((_let_1 (@ (@ tptp.nth_c (@ (@ (@ tptp.list_update_c Xs) I) X)) J))) (let ((_let_2 (= I J))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_c Xs)) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_c Xs) J)))))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (Xs tptp.list_d) (J tptp.nat) (X tptp.d)) (let ((_let_1 (@ (@ tptp.nth_d (@ (@ (@ tptp.list_update_d Xs) I) X)) J))) (let ((_let_2 (= I J))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_d Xs)) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_d Xs) J)))))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (Xs tptp.list_nat) (J tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs) I) X)) J))) (let ((_let_2 (= I J))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs)) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_nat Xs) J)))))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (Xs tptp.list_int) (J tptp.nat) (X tptp.int)) (let ((_let_1 (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs) I) X)) J))) (let ((_let_2 (= I J))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs)) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_int Xs) J)))))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (Xs tptp.list_c) (X tptp.c)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_c Xs)) (= (= (@ (@ (@ tptp.list_update_c Xs) I) X) Xs) (= (@ (@ tptp.nth_c Xs) I) X)))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (Xs tptp.list_d) (X tptp.d)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_d Xs)) (= (= (@ (@ (@ tptp.list_update_d Xs) I) X) Xs) (= (@ (@ tptp.nth_d Xs) I) X)))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (Xs tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs)) (= (= (@ (@ (@ tptp.list_update_nat Xs) I) X) Xs) (= (@ (@ tptp.nth_nat Xs) I) X)))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (Xs tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs)) (= (= (@ (@ (@ tptp.list_update_int Xs) I) X) Xs) (= (@ (@ tptp.nth_int Xs) I) X)))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (J tptp.nat) (L tptp.list_c) (X tptp.c)) (let ((_let_1 (@ (@ tptp.nth_c (@ (@ (@ tptp.list_update_c L) I) X)) J))) (let ((_let_2 (and (= I J) (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_c L))))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_c L) J))))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (J tptp.nat) (L tptp.list_d) (X tptp.d)) (let ((_let_1 (@ (@ tptp.nth_d (@ (@ (@ tptp.list_update_d L) I) X)) J))) (let ((_let_2 (and (= I J) (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_d L))))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_d L) J))))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (J tptp.nat) (L tptp.list_nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat L) I) X)) J))) (let ((_let_2 (and (= I J) (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat L))))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_nat L) J))))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (J tptp.nat) (L tptp.list_int) (X tptp.int)) (let ((_let_1 (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int L) I) X)) J))) (let ((_let_2 (and (= I J) (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int L))))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_int L) J))))))))
% 3.70/4.03 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_le6747313008572928689nteger X) Y)) (@ (@ tptp.ord_le6747313008572928689nteger Y) X)))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_int Y) X)))))
% 3.70/4.03 (assert (forall ((P (-> tptp.code_integer Bool)) (P3 (-> tptp.code_integer Bool)) (Q (-> tptp.code_integer Bool)) (Q3 (-> tptp.code_integer Bool))) (=> (exists ((Z3 tptp.code_integer)) (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z3) X3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z3 tptp.code_integer)) (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z3) X3) (= (@ Q X3) (@ Q3 X3))))) (exists ((Z4 tptp.code_integer)) (forall ((X7 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z4) X7) (= (and (@ P X7) (@ Q X7)) (and (@ P3 X7) (@ Q3 X7))))))))))
% 3.70/4.03 (assert (forall ((P (-> tptp.num Bool)) (P3 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q3 (-> tptp.num Bool))) (=> (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X3) (= (@ Q X3) (@ Q3 X3))))) (exists ((Z4 tptp.num)) (forall ((X7 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X7) (= (and (@ P X7) (@ Q X7)) (and (@ P3 X7) (@ Q3 X7))))))))))
% 3.70/4.03 (assert (forall ((P (-> tptp.nat Bool)) (P3 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q3 (-> tptp.nat Bool))) (=> (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X3) (= (@ Q X3) (@ Q3 X3))))) (exists ((Z4 tptp.nat)) (forall ((X7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X7) (= (and (@ P X7) (@ Q X7)) (and (@ P3 X7) (@ Q3 X7))))))))))
% 3.70/4.03 (assert (forall ((P (-> tptp.int Bool)) (P3 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q3 (-> tptp.int Bool))) (=> (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X3) (= (@ Q X3) (@ Q3 X3))))) (exists ((Z4 tptp.int)) (forall ((X7 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X7) (= (and (@ P X7) (@ Q X7)) (and (@ P3 X7) (@ Q3 X7))))))))))
% 3.70/4.03 (assert (forall ((P (-> tptp.code_integer Bool)) (P3 (-> tptp.code_integer Bool)) (Q (-> tptp.code_integer Bool)) (Q3 (-> tptp.code_integer Bool))) (=> (exists ((Z3 tptp.code_integer)) (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z3) X3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z3 tptp.code_integer)) (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z3) X3) (= (@ Q X3) (@ Q3 X3))))) (exists ((Z4 tptp.code_integer)) (forall ((X7 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z4) X7) (= (or (@ P X7) (@ Q X7)) (or (@ P3 X7) (@ Q3 X7))))))))))
% 3.70/4.03 (assert (forall ((P (-> tptp.num Bool)) (P3 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q3 (-> tptp.num Bool))) (=> (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X3) (= (@ Q X3) (@ Q3 X3))))) (exists ((Z4 tptp.num)) (forall ((X7 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X7) (= (or (@ P X7) (@ Q X7)) (or (@ P3 X7) (@ Q3 X7))))))))))
% 3.70/4.03 (assert (forall ((P (-> tptp.nat Bool)) (P3 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q3 (-> tptp.nat Bool))) (=> (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X3) (= (@ Q X3) (@ Q3 X3))))) (exists ((Z4 tptp.nat)) (forall ((X7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X7) (= (or (@ P X7) (@ Q X7)) (or (@ P3 X7) (@ Q3 X7))))))))))
% 3.70/4.03 (assert (forall ((P (-> tptp.int Bool)) (P3 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q3 (-> tptp.int Bool))) (=> (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X3) (= (@ Q X3) (@ Q3 X3))))) (exists ((Z4 tptp.int)) (forall ((X7 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X7) (= (or (@ P X7) (@ Q X7)) (or (@ P3 X7) (@ Q3 X7))))))))))
% 3.70/4.03 (assert (forall ((T tptp.code_integer)) (exists ((Z4 tptp.code_integer)) (forall ((X7 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z4) X7) (not (= X7 T)))))))
% 3.70/4.03 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X7 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X7) (not (= X7 T)))))))
% 3.70/4.03 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X7) (not (= X7 T)))))))
% 3.70/4.03 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X7 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X7) (not (= X7 T)))))))
% 3.70/4.03 (assert (forall ((T tptp.code_integer)) (exists ((Z4 tptp.code_integer)) (forall ((X7 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z4) X7) (not (= X7 T)))))))
% 3.70/4.03 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X7 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X7) (not (= X7 T)))))))
% 3.70/4.03 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X7) (not (= X7 T)))))))
% 3.70/4.03 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X7 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X7) (not (= X7 T)))))))
% 3.70/4.03 (assert (forall ((T tptp.code_integer)) (exists ((Z4 tptp.code_integer)) (forall ((X7 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z4) X7) (not (@ (@ tptp.ord_le6747313008572928689nteger X7) T)))))))
% 3.70/4.03 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X7 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X7) (not (@ (@ tptp.ord_less_num X7) T)))))))
% 3.70/4.03 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X7) (not (@ (@ tptp.ord_less_nat X7) T)))))))
% 3.70/4.03 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X7 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X7) (not (@ (@ tptp.ord_less_int X7) T)))))))
% 3.70/4.03 (assert (forall ((T tptp.code_integer)) (exists ((Z4 tptp.code_integer)) (forall ((X7 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z4) X7) (@ (@ tptp.ord_le6747313008572928689nteger T) X7))))))
% 3.70/4.03 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X7 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X7) (@ (@ tptp.ord_less_num T) X7))))))
% 3.70/4.03 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X7) (@ (@ tptp.ord_less_nat T) X7))))))
% 3.70/4.03 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X7 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X7) (@ (@ tptp.ord_less_int T) X7))))))
% 3.70/4.03 (assert (forall ((P (-> tptp.code_integer Bool)) (P3 (-> tptp.code_integer Bool)) (Q (-> tptp.code_integer Bool)) (Q3 (-> tptp.code_integer Bool))) (=> (exists ((Z3 tptp.code_integer)) (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Z3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z3 tptp.code_integer)) (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Z3) (= (@ Q X3) (@ Q3 X3))))) (exists ((Z4 tptp.code_integer)) (forall ((X7 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X7) Z4) (= (and (@ P X7) (@ Q X7)) (and (@ P3 X7) (@ Q3 X7))))))))))
% 3.70/4.03 (assert (forall ((P (-> tptp.num Bool)) (P3 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q3 (-> tptp.num Bool))) (=> (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z3) (= (@ Q X3) (@ Q3 X3))))) (exists ((Z4 tptp.num)) (forall ((X7 tptp.num)) (=> (@ (@ tptp.ord_less_num X7) Z4) (= (and (@ P X7) (@ Q X7)) (and (@ P3 X7) (@ Q3 X7))))))))))
% 3.70/4.03 (assert (forall ((P (-> tptp.nat Bool)) (P3 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q3 (-> tptp.nat Bool))) (=> (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z3) (= (@ Q X3) (@ Q3 X3))))) (exists ((Z4 tptp.nat)) (forall ((X7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X7) Z4) (= (and (@ P X7) (@ Q X7)) (and (@ P3 X7) (@ Q3 X7))))))))))
% 3.70/4.03 (assert (forall ((P (-> tptp.int Bool)) (P3 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q3 (-> tptp.int Bool))) (=> (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z3) (= (@ Q X3) (@ Q3 X3))))) (exists ((Z4 tptp.int)) (forall ((X7 tptp.int)) (=> (@ (@ tptp.ord_less_int X7) Z4) (= (and (@ P X7) (@ Q X7)) (and (@ P3 X7) (@ Q3 X7))))))))))
% 3.70/4.03 (assert (forall ((P (-> tptp.code_integer Bool)) (P3 (-> tptp.code_integer Bool)) (Q (-> tptp.code_integer Bool)) (Q3 (-> tptp.code_integer Bool))) (=> (exists ((Z3 tptp.code_integer)) (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Z3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z3 tptp.code_integer)) (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Z3) (= (@ Q X3) (@ Q3 X3))))) (exists ((Z4 tptp.code_integer)) (forall ((X7 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X7) Z4) (= (or (@ P X7) (@ Q X7)) (or (@ P3 X7) (@ Q3 X7))))))))))
% 3.70/4.03 (assert (forall ((P (-> tptp.num Bool)) (P3 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q3 (-> tptp.num Bool))) (=> (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z3) (= (@ Q X3) (@ Q3 X3))))) (exists ((Z4 tptp.num)) (forall ((X7 tptp.num)) (=> (@ (@ tptp.ord_less_num X7) Z4) (= (or (@ P X7) (@ Q X7)) (or (@ P3 X7) (@ Q3 X7))))))))))
% 3.70/4.03 (assert (forall ((P (-> tptp.nat Bool)) (P3 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q3 (-> tptp.nat Bool))) (=> (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z3) (= (@ Q X3) (@ Q3 X3))))) (exists ((Z4 tptp.nat)) (forall ((X7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X7) Z4) (= (or (@ P X7) (@ Q X7)) (or (@ P3 X7) (@ Q3 X7))))))))))
% 3.70/4.03 (assert (forall ((P (-> tptp.int Bool)) (P3 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q3 (-> tptp.int Bool))) (=> (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z3) (= (@ Q X3) (@ Q3 X3))))) (exists ((Z4 tptp.int)) (forall ((X7 tptp.int)) (=> (@ (@ tptp.ord_less_int X7) Z4) (= (or (@ P X7) (@ Q X7)) (or (@ P3 X7) (@ Q3 X7))))))))))
% 3.70/4.03 (assert (forall ((T tptp.code_integer)) (exists ((Z4 tptp.code_integer)) (forall ((X7 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X7) Z4) (not (= X7 T)))))))
% 3.70/4.03 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X7 tptp.num)) (=> (@ (@ tptp.ord_less_num X7) Z4) (not (= X7 T)))))))
% 3.70/4.03 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X7) Z4) (not (= X7 T)))))))
% 3.70/4.03 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X7 tptp.int)) (=> (@ (@ tptp.ord_less_int X7) Z4) (not (= X7 T)))))))
% 3.70/4.03 (assert (forall ((T tptp.code_integer)) (exists ((Z4 tptp.code_integer)) (forall ((X7 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X7) Z4) (not (= X7 T)))))))
% 3.70/4.03 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X7 tptp.num)) (=> (@ (@ tptp.ord_less_num X7) Z4) (not (= X7 T)))))))
% 3.70/4.03 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X7) Z4) (not (= X7 T)))))))
% 3.70/4.03 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X7 tptp.int)) (=> (@ (@ tptp.ord_less_int X7) Z4) (not (= X7 T)))))))
% 3.70/4.03 (assert (forall ((T tptp.code_integer)) (exists ((Z4 tptp.code_integer)) (forall ((X7 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger X7))) (=> (@ _let_1 Z4) (@ _let_1 T)))))))
% 3.70/4.03 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X7 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X7))) (=> (@ _let_1 Z4) (@ _let_1 T)))))))
% 3.70/4.03 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X7 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X7))) (=> (@ _let_1 Z4) (@ _let_1 T)))))))
% 3.70/4.03 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X7 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X7))) (=> (@ _let_1 Z4) (@ _let_1 T)))))))
% 3.70/4.03 (assert (forall ((T tptp.code_integer)) (exists ((Z4 tptp.code_integer)) (forall ((X7 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X7) Z4) (not (@ (@ tptp.ord_le6747313008572928689nteger T) X7)))))))
% 3.70/4.03 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X7 tptp.num)) (=> (@ (@ tptp.ord_less_num X7) Z4) (not (@ (@ tptp.ord_less_num T) X7)))))))
% 3.70/4.03 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X7) Z4) (not (@ (@ tptp.ord_less_nat T) X7)))))))
% 3.70/4.03 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X7 tptp.int)) (=> (@ (@ tptp.ord_less_int X7) Z4) (not (@ (@ tptp.ord_less_int T) X7)))))))
% 3.70/4.03 (assert (forall ((B2 tptp.code_integer) (A2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger B2))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 3.70/4.03 (assert (forall ((B2 tptp.assn) (A2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn B2))) (let ((_let_2 (@ tptp.times_times_assn A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 3.70/4.03 (assert (forall ((B2 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat B2))) (let ((_let_2 (@ tptp.times_times_rat A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 3.70/4.03 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B2))) (let ((_let_2 (@ tptp.times_times_nat A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 3.70/4.03 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int B2))) (let ((_let_2 (@ tptp.times_times_int A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 3.70/4.03 (assert (= tptp.times_3573771949741848930nteger (lambda ((A3 tptp.code_integer) (B3 tptp.code_integer)) (@ (@ tptp.times_3573771949741848930nteger B3) A3))))
% 3.70/4.03 (assert (= tptp.times_times_assn (lambda ((A3 tptp.assn) (B3 tptp.assn)) (@ (@ tptp.times_times_assn B3) A3))))
% 3.70/4.03 (assert (= tptp.times_times_rat (lambda ((A3 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.times_times_rat B3) A3))))
% 3.70/4.03 (assert (= tptp.times_times_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.times_times_nat B3) A3))))
% 3.70/4.03 (assert (= tptp.times_times_int (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ tptp.times_times_int B3) A3))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A2))) (= (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B2) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn A2))) (= (@ (@ tptp.times_times_assn (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_assn B2) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A2))) (= (@ (@ tptp.times_times_rat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_rat B2) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A2))) (= (@ (@ tptp.times_times_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_nat B2) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A2))) (= (@ (@ tptp.times_times_int (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_int B2) C))))))
% 3.70/4.03 (assert (forall ((I3 tptp.set_nat) (I7 tptp.set_nat) (Xs tptp.list_c) (Xs4 tptp.list_c) (Xsi tptp.list_c) (Xsi2 tptp.list_c) (A (-> tptp.c tptp.c tptp.assn)) (A6 (-> tptp.c tptp.c tptp.assn))) (=> (= I3 I7) (=> (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_c Xs4)) (=> (= (@ tptp.size_size_list_c Xsi) (@ tptp.size_size_list_c Xsi2)) (=> (forall ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_c Xsi2) I5))) (let ((_let_2 (@ (@ tptp.nth_c Xs4) I5))) (let ((_let_3 (@ (@ tptp.nth_c Xsi) I5))) (let ((_let_4 (@ (@ tptp.nth_c Xs) I5))) (let ((_let_5 (@ tptp.size_size_list_c Xs))) (=> (@ (@ tptp.member_nat I5) I3) (=> (@ (@ tptp.ord_less_nat I5) _let_5) (=> (= _let_5 (@ tptp.size_size_list_c Xsi)) (and (= _let_4 _let_2) (= _let_3 _let_1) (= (@ (@ A _let_4) _let_3) (@ (@ A6 _let_2) _let_1)))))))))))) (= (@ (@ (@ (@ tptp.vEBT_L824818263033719200sn_c_c I3) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L824818263033719200sn_c_c I7) A6) Xs4) Xsi2))))))))
% 3.70/4.03 (assert (forall ((I3 tptp.set_nat) (I7 tptp.set_nat) (Xs tptp.list_c) (Xs4 tptp.list_c) (Xsi tptp.list_nat) (Xsi2 tptp.list_nat) (A (-> tptp.c tptp.nat tptp.assn)) (A6 (-> tptp.c tptp.nat tptp.assn))) (=> (= I3 I7) (=> (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_c Xs4)) (=> (= (@ tptp.size_size_list_nat Xsi) (@ tptp.size_size_list_nat Xsi2)) (=> (forall ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat Xsi2) I5))) (let ((_let_2 (@ (@ tptp.nth_c Xs4) I5))) (let ((_let_3 (@ (@ tptp.nth_nat Xsi) I5))) (let ((_let_4 (@ (@ tptp.nth_c Xs) I5))) (let ((_let_5 (@ tptp.size_size_list_c Xs))) (=> (@ (@ tptp.member_nat I5) I3) (=> (@ (@ tptp.ord_less_nat I5) _let_5) (=> (= _let_5 (@ tptp.size_size_list_nat Xsi)) (and (= _let_4 _let_2) (= _let_3 _let_1) (= (@ (@ A _let_4) _let_3) (@ (@ A6 _let_2) _let_1)))))))))))) (= (@ (@ (@ (@ tptp.vEBT_L6585172037124793648_c_nat I3) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L6585172037124793648_c_nat I7) A6) Xs4) Xsi2))))))))
% 3.70/4.03 (assert (forall ((I3 tptp.set_nat) (I7 tptp.set_nat) (Xs tptp.list_c) (Xs4 tptp.list_c) (Xsi tptp.list_int) (Xsi2 tptp.list_int) (A (-> tptp.c tptp.int tptp.assn)) (A6 (-> tptp.c tptp.int tptp.assn))) (=> (= I3 I7) (=> (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_c Xs4)) (=> (= (@ tptp.size_size_list_int Xsi) (@ tptp.size_size_list_int Xsi2)) (=> (forall ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_int Xsi2) I5))) (let ((_let_2 (@ (@ tptp.nth_c Xs4) I5))) (let ((_let_3 (@ (@ tptp.nth_int Xsi) I5))) (let ((_let_4 (@ (@ tptp.nth_c Xs) I5))) (let ((_let_5 (@ tptp.size_size_list_c Xs))) (=> (@ (@ tptp.member_nat I5) I3) (=> (@ (@ tptp.ord_less_nat I5) _let_5) (=> (= _let_5 (@ tptp.size_size_list_int Xsi)) (and (= _let_4 _let_2) (= _let_3 _let_1) (= (@ (@ A _let_4) _let_3) (@ (@ A6 _let_2) _let_1)))))))))))) (= (@ (@ (@ (@ tptp.vEBT_L6582681566615743372_c_int I3) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L6582681566615743372_c_int I7) A6) Xs4) Xsi2))))))))
% 3.70/4.03 (assert (forall ((I3 tptp.set_nat) (I7 tptp.set_nat) (Xs tptp.list_d) (Xs4 tptp.list_d) (Xsi tptp.list_c) (Xsi2 tptp.list_c) (A (-> tptp.d tptp.c tptp.assn)) (A6 (-> tptp.d tptp.c tptp.assn))) (=> (= I3 I7) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_d Xs4)) (=> (= (@ tptp.size_size_list_c Xsi) (@ tptp.size_size_list_c Xsi2)) (=> (forall ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_c Xsi2) I5))) (let ((_let_2 (@ (@ tptp.nth_d Xs4) I5))) (let ((_let_3 (@ (@ tptp.nth_c Xsi) I5))) (let ((_let_4 (@ (@ tptp.nth_d Xs) I5))) (let ((_let_5 (@ tptp.size_size_list_d Xs))) (=> (@ (@ tptp.member_nat I5) I3) (=> (@ (@ tptp.ord_less_nat I5) _let_5) (=> (= _let_5 (@ tptp.size_size_list_c Xsi)) (and (= _let_4 _let_2) (= _let_3 _let_1) (= (@ (@ A _let_4) _let_3) (@ (@ A6 _let_2) _let_1)))))))))))) (= (@ (@ (@ (@ tptp.vEBT_L7260734717915818975sn_d_c I3) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L7260734717915818975sn_d_c I7) A6) Xs4) Xsi2))))))))
% 3.70/4.03 (assert (forall ((I3 tptp.set_nat) (I7 tptp.set_nat) (Xs tptp.list_d) (Xs4 tptp.list_d) (Xsi tptp.list_d) (Xsi2 tptp.list_d) (A (-> tptp.d tptp.d tptp.assn)) (A6 (-> tptp.d tptp.d tptp.assn))) (=> (= I3 I7) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_d Xs4)) (=> (= (@ tptp.size_size_list_d Xsi) (@ tptp.size_size_list_d Xsi2)) (=> (forall ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_d Xsi2) I5))) (let ((_let_2 (@ (@ tptp.nth_d Xs4) I5))) (let ((_let_3 (@ (@ tptp.nth_d Xsi) I5))) (let ((_let_4 (@ (@ tptp.nth_d Xs) I5))) (let ((_let_5 (@ tptp.size_size_list_d Xs))) (=> (@ (@ tptp.member_nat I5) I3) (=> (@ (@ tptp.ord_less_nat I5) _let_5) (=> (= _let_5 (@ tptp.size_size_list_d Xsi)) (and (= _let_4 _let_2) (= _let_3 _let_1) (= (@ (@ A _let_4) _let_3) (@ (@ A6 _let_2) _let_1)))))))))))) (= (@ (@ (@ (@ tptp.vEBT_L7260734717915818976sn_d_d I3) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L7260734717915818976sn_d_d I7) A6) Xs4) Xsi2))))))))
% 3.70/4.03 (assert (forall ((I3 tptp.set_nat) (I7 tptp.set_nat) (Xs tptp.list_d) (Xs4 tptp.list_d) (Xsi tptp.list_nat) (Xsi2 tptp.list_nat) (A (-> tptp.d tptp.nat tptp.assn)) (A6 (-> tptp.d tptp.nat tptp.assn))) (=> (= I3 I7) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_d Xs4)) (=> (= (@ tptp.size_size_list_nat Xsi) (@ tptp.size_size_list_nat Xsi2)) (=> (forall ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat Xsi2) I5))) (let ((_let_2 (@ (@ tptp.nth_d Xs4) I5))) (let ((_let_3 (@ (@ tptp.nth_nat Xsi) I5))) (let ((_let_4 (@ (@ tptp.nth_d Xs) I5))) (let ((_let_5 (@ tptp.size_size_list_d Xs))) (=> (@ (@ tptp.member_nat I5) I3) (=> (@ (@ tptp.ord_less_nat I5) _let_5) (=> (= _let_5 (@ tptp.size_size_list_nat Xsi)) (and (= _let_4 _let_2) (= _let_3 _let_1) (= (@ (@ A _let_4) _let_3) (@ (@ A6 _let_2) _let_1)))))))))))) (= (@ (@ (@ (@ tptp.vEBT_L7820616366081188145_d_nat I3) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L7820616366081188145_d_nat I7) A6) Xs4) Xsi2))))))))
% 3.70/4.03 (assert (forall ((I3 tptp.set_nat) (I7 tptp.set_nat) (Xs tptp.list_d) (Xs4 tptp.list_d) (Xsi tptp.list_int) (Xsi2 tptp.list_int) (A (-> tptp.d tptp.int tptp.assn)) (A6 (-> tptp.d tptp.int tptp.assn))) (=> (= I3 I7) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_d Xs4)) (=> (= (@ tptp.size_size_list_int Xsi) (@ tptp.size_size_list_int Xsi2)) (=> (forall ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_int Xsi2) I5))) (let ((_let_2 (@ (@ tptp.nth_d Xs4) I5))) (let ((_let_3 (@ (@ tptp.nth_int Xsi) I5))) (let ((_let_4 (@ (@ tptp.nth_d Xs) I5))) (let ((_let_5 (@ tptp.size_size_list_d Xs))) (=> (@ (@ tptp.member_nat I5) I3) (=> (@ (@ tptp.ord_less_nat I5) _let_5) (=> (= _let_5 (@ tptp.size_size_list_int Xsi)) (and (= _let_4 _let_2) (= _let_3 _let_1) (= (@ (@ A _let_4) _let_3) (@ (@ A6 _let_2) _let_1)))))))))))) (= (@ (@ (@ (@ tptp.vEBT_L7818125895572137869_d_int I3) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L7818125895572137869_d_int I7) A6) Xs4) Xsi2))))))))
% 3.70/4.03 (assert (forall ((I3 tptp.set_nat) (I7 tptp.set_nat) (Xs tptp.list_nat) (Xs4 tptp.list_nat) (Xsi tptp.list_c) (Xsi2 tptp.list_c) (A (-> tptp.nat tptp.c tptp.assn)) (A6 (-> tptp.nat tptp.c tptp.assn))) (=> (= I3 I7) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Xs4)) (=> (= (@ tptp.size_size_list_c Xsi) (@ tptp.size_size_list_c Xsi2)) (=> (forall ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_c Xsi2) I5))) (let ((_let_2 (@ (@ tptp.nth_nat Xs4) I5))) (let ((_let_3 (@ (@ tptp.nth_c Xsi) I5))) (let ((_let_4 (@ (@ tptp.nth_nat Xs) I5))) (let ((_let_5 (@ tptp.size_size_list_nat Xs))) (=> (@ (@ tptp.member_nat I5) I3) (=> (@ (@ tptp.ord_less_nat I5) _let_5) (=> (= _let_5 (@ tptp.size_size_list_c Xsi)) (and (= _let_4 _let_2) (= _let_3 _let_1) (= (@ (@ A _let_4) _let_3) (@ (@ A6 _let_2) _let_1)))))))))))) (= (@ (@ (@ (@ tptp.vEBT_L8146214880390291086_nat_c I3) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L8146214880390291086_nat_c I7) A6) Xs4) Xsi2))))))))
% 3.70/4.03 (assert (forall ((I3 tptp.set_nat) (I7 tptp.set_nat) (Xs tptp.list_nat) (Xs4 tptp.list_nat) (Xsi tptp.list_d) (Xsi2 tptp.list_d) (A (-> tptp.nat tptp.d tptp.assn)) (A6 (-> tptp.nat tptp.d tptp.assn))) (=> (= I3 I7) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Xs4)) (=> (= (@ tptp.size_size_list_d Xsi) (@ tptp.size_size_list_d Xsi2)) (=> (forall ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_d Xsi2) I5))) (let ((_let_2 (@ (@ tptp.nth_nat Xs4) I5))) (let ((_let_3 (@ (@ tptp.nth_d Xsi) I5))) (let ((_let_4 (@ (@ tptp.nth_nat Xs) I5))) (let ((_let_5 (@ tptp.size_size_list_nat Xs))) (=> (@ (@ tptp.member_nat I5) I3) (=> (@ (@ tptp.ord_less_nat I5) _let_5) (=> (= _let_5 (@ tptp.size_size_list_d Xsi)) (and (= _let_4 _let_2) (= _let_3 _let_1) (= (@ (@ A _let_4) _let_3) (@ (@ A6 _let_2) _let_1)))))))))))) (= (@ (@ (@ (@ tptp.vEBT_L8146214880390291087_nat_d I3) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L8146214880390291087_nat_d I7) A6) Xs4) Xsi2))))))))
% 3.70/4.03 (assert (forall ((I3 tptp.set_nat) (I7 tptp.set_nat) (Xs tptp.list_nat) (Xs4 tptp.list_nat) (Xsi tptp.list_nat) (Xsi2 tptp.list_nat) (A (-> tptp.nat tptp.nat tptp.assn)) (A6 (-> tptp.nat tptp.nat tptp.assn))) (=> (= I3 I7) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Xs4)) (=> (= (@ tptp.size_size_list_nat Xsi) (@ tptp.size_size_list_nat Xsi2)) (=> (forall ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat Xsi2) I5))) (let ((_let_2 (@ (@ tptp.nth_nat Xs4) I5))) (let ((_let_3 (@ (@ tptp.nth_nat Xsi) I5))) (let ((_let_4 (@ (@ tptp.nth_nat Xs) I5))) (let ((_let_5 (@ tptp.size_size_list_nat Xs))) (=> (@ (@ tptp.member_nat I5) I3) (=> (@ (@ tptp.ord_less_nat I5) _let_5) (=> (= _let_5 (@ tptp.size_size_list_nat Xsi)) (and (= _let_4 _let_2) (= _let_3 _let_1) (= (@ (@ A _let_4) _let_3) (@ (@ A6 _let_2) _let_1)))))))))))) (= (@ (@ (@ (@ tptp.vEBT_L7892069108621897922at_nat I3) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L7892069108621897922at_nat I7) A6) Xs4) Xsi2))))))))
% 3.70/4.03 (assert (forall ((I3 tptp.set_nat) (I7 tptp.set_nat) (A (-> tptp.c tptp.c tptp.assn)) (A6 (-> tptp.c tptp.c tptp.assn)) (Xs tptp.list_c) (Xs4 tptp.list_c) (Xsi tptp.list_c) (Xsi2 tptp.list_c)) (=> (= I3 I7) (=> (= A A6) (=> (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_c Xs4)) (=> (= (@ tptp.size_size_list_c Xsi) (@ tptp.size_size_list_c Xsi2)) (=> (forall ((I5 tptp.nat)) (let ((_let_1 (@ tptp.size_size_list_c Xs))) (=> (@ (@ tptp.member_nat I5) I3) (=> (@ (@ tptp.ord_less_nat I5) _let_1) (=> (= _let_1 (@ tptp.size_size_list_c Xsi)) (and (= (@ (@ tptp.nth_c Xs) I5) (@ (@ tptp.nth_c Xs4) I5)) (= (@ (@ tptp.nth_c Xsi) I5) (@ (@ tptp.nth_c Xsi2) I5)))))))) (= (@ (@ (@ (@ tptp.vEBT_L824818263033719200sn_c_c I3) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L824818263033719200sn_c_c I7) A6) Xs4) Xsi2)))))))))
% 3.70/4.03 (assert (forall ((I3 tptp.set_nat) (I7 tptp.set_nat) (A (-> tptp.c tptp.nat tptp.assn)) (A6 (-> tptp.c tptp.nat tptp.assn)) (Xs tptp.list_c) (Xs4 tptp.list_c) (Xsi tptp.list_nat) (Xsi2 tptp.list_nat)) (=> (= I3 I7) (=> (= A A6) (=> (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_c Xs4)) (=> (= (@ tptp.size_size_list_nat Xsi) (@ tptp.size_size_list_nat Xsi2)) (=> (forall ((I5 tptp.nat)) (let ((_let_1 (@ tptp.size_size_list_c Xs))) (=> (@ (@ tptp.member_nat I5) I3) (=> (@ (@ tptp.ord_less_nat I5) _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Xsi)) (and (= (@ (@ tptp.nth_c Xs) I5) (@ (@ tptp.nth_c Xs4) I5)) (= (@ (@ tptp.nth_nat Xsi) I5) (@ (@ tptp.nth_nat Xsi2) I5)))))))) (= (@ (@ (@ (@ tptp.vEBT_L6585172037124793648_c_nat I3) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L6585172037124793648_c_nat I7) A6) Xs4) Xsi2)))))))))
% 3.70/4.03 (assert (forall ((I3 tptp.set_nat) (I7 tptp.set_nat) (A (-> tptp.c tptp.int tptp.assn)) (A6 (-> tptp.c tptp.int tptp.assn)) (Xs tptp.list_c) (Xs4 tptp.list_c) (Xsi tptp.list_int) (Xsi2 tptp.list_int)) (=> (= I3 I7) (=> (= A A6) (=> (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_c Xs4)) (=> (= (@ tptp.size_size_list_int Xsi) (@ tptp.size_size_list_int Xsi2)) (=> (forall ((I5 tptp.nat)) (let ((_let_1 (@ tptp.size_size_list_c Xs))) (=> (@ (@ tptp.member_nat I5) I3) (=> (@ (@ tptp.ord_less_nat I5) _let_1) (=> (= _let_1 (@ tptp.size_size_list_int Xsi)) (and (= (@ (@ tptp.nth_c Xs) I5) (@ (@ tptp.nth_c Xs4) I5)) (= (@ (@ tptp.nth_int Xsi) I5) (@ (@ tptp.nth_int Xsi2) I5)))))))) (= (@ (@ (@ (@ tptp.vEBT_L6582681566615743372_c_int I3) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L6582681566615743372_c_int I7) A6) Xs4) Xsi2)))))))))
% 3.70/4.03 (assert (forall ((I3 tptp.set_nat) (I7 tptp.set_nat) (A (-> tptp.d tptp.c tptp.assn)) (A6 (-> tptp.d tptp.c tptp.assn)) (Xs tptp.list_d) (Xs4 tptp.list_d) (Xsi tptp.list_c) (Xsi2 tptp.list_c)) (=> (= I3 I7) (=> (= A A6) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_d Xs4)) (=> (= (@ tptp.size_size_list_c Xsi) (@ tptp.size_size_list_c Xsi2)) (=> (forall ((I5 tptp.nat)) (let ((_let_1 (@ tptp.size_size_list_d Xs))) (=> (@ (@ tptp.member_nat I5) I3) (=> (@ (@ tptp.ord_less_nat I5) _let_1) (=> (= _let_1 (@ tptp.size_size_list_c Xsi)) (and (= (@ (@ tptp.nth_d Xs) I5) (@ (@ tptp.nth_d Xs4) I5)) (= (@ (@ tptp.nth_c Xsi) I5) (@ (@ tptp.nth_c Xsi2) I5)))))))) (= (@ (@ (@ (@ tptp.vEBT_L7260734717915818975sn_d_c I3) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L7260734717915818975sn_d_c I7) A6) Xs4) Xsi2)))))))))
% 3.70/4.03 (assert (forall ((I3 tptp.set_nat) (I7 tptp.set_nat) (A (-> tptp.d tptp.d tptp.assn)) (A6 (-> tptp.d tptp.d tptp.assn)) (Xs tptp.list_d) (Xs4 tptp.list_d) (Xsi tptp.list_d) (Xsi2 tptp.list_d)) (=> (= I3 I7) (=> (= A A6) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_d Xs4)) (=> (= (@ tptp.size_size_list_d Xsi) (@ tptp.size_size_list_d Xsi2)) (=> (forall ((I5 tptp.nat)) (let ((_let_1 (@ tptp.size_size_list_d Xs))) (=> (@ (@ tptp.member_nat I5) I3) (=> (@ (@ tptp.ord_less_nat I5) _let_1) (=> (= _let_1 (@ tptp.size_size_list_d Xsi)) (and (= (@ (@ tptp.nth_d Xs) I5) (@ (@ tptp.nth_d Xs4) I5)) (= (@ (@ tptp.nth_d Xsi) I5) (@ (@ tptp.nth_d Xsi2) I5)))))))) (= (@ (@ (@ (@ tptp.vEBT_L7260734717915818976sn_d_d I3) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L7260734717915818976sn_d_d I7) A6) Xs4) Xsi2)))))))))
% 3.70/4.03 (assert (forall ((I3 tptp.set_nat) (I7 tptp.set_nat) (A (-> tptp.d tptp.nat tptp.assn)) (A6 (-> tptp.d tptp.nat tptp.assn)) (Xs tptp.list_d) (Xs4 tptp.list_d) (Xsi tptp.list_nat) (Xsi2 tptp.list_nat)) (=> (= I3 I7) (=> (= A A6) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_d Xs4)) (=> (= (@ tptp.size_size_list_nat Xsi) (@ tptp.size_size_list_nat Xsi2)) (=> (forall ((I5 tptp.nat)) (let ((_let_1 (@ tptp.size_size_list_d Xs))) (=> (@ (@ tptp.member_nat I5) I3) (=> (@ (@ tptp.ord_less_nat I5) _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Xsi)) (and (= (@ (@ tptp.nth_d Xs) I5) (@ (@ tptp.nth_d Xs4) I5)) (= (@ (@ tptp.nth_nat Xsi) I5) (@ (@ tptp.nth_nat Xsi2) I5)))))))) (= (@ (@ (@ (@ tptp.vEBT_L7820616366081188145_d_nat I3) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L7820616366081188145_d_nat I7) A6) Xs4) Xsi2)))))))))
% 3.70/4.03 (assert (forall ((I3 tptp.set_nat) (I7 tptp.set_nat) (A (-> tptp.d tptp.int tptp.assn)) (A6 (-> tptp.d tptp.int tptp.assn)) (Xs tptp.list_d) (Xs4 tptp.list_d) (Xsi tptp.list_int) (Xsi2 tptp.list_int)) (=> (= I3 I7) (=> (= A A6) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_d Xs4)) (=> (= (@ tptp.size_size_list_int Xsi) (@ tptp.size_size_list_int Xsi2)) (=> (forall ((I5 tptp.nat)) (let ((_let_1 (@ tptp.size_size_list_d Xs))) (=> (@ (@ tptp.member_nat I5) I3) (=> (@ (@ tptp.ord_less_nat I5) _let_1) (=> (= _let_1 (@ tptp.size_size_list_int Xsi)) (and (= (@ (@ tptp.nth_d Xs) I5) (@ (@ tptp.nth_d Xs4) I5)) (= (@ (@ tptp.nth_int Xsi) I5) (@ (@ tptp.nth_int Xsi2) I5)))))))) (= (@ (@ (@ (@ tptp.vEBT_L7818125895572137869_d_int I3) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L7818125895572137869_d_int I7) A6) Xs4) Xsi2)))))))))
% 3.70/4.03 (assert (forall ((I3 tptp.set_nat) (I7 tptp.set_nat) (A (-> tptp.nat tptp.c tptp.assn)) (A6 (-> tptp.nat tptp.c tptp.assn)) (Xs tptp.list_nat) (Xs4 tptp.list_nat) (Xsi tptp.list_c) (Xsi2 tptp.list_c)) (=> (= I3 I7) (=> (= A A6) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Xs4)) (=> (= (@ tptp.size_size_list_c Xsi) (@ tptp.size_size_list_c Xsi2)) (=> (forall ((I5 tptp.nat)) (let ((_let_1 (@ tptp.size_size_list_nat Xs))) (=> (@ (@ tptp.member_nat I5) I3) (=> (@ (@ tptp.ord_less_nat I5) _let_1) (=> (= _let_1 (@ tptp.size_size_list_c Xsi)) (and (= (@ (@ tptp.nth_nat Xs) I5) (@ (@ tptp.nth_nat Xs4) I5)) (= (@ (@ tptp.nth_c Xsi) I5) (@ (@ tptp.nth_c Xsi2) I5)))))))) (= (@ (@ (@ (@ tptp.vEBT_L8146214880390291086_nat_c I3) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L8146214880390291086_nat_c I7) A6) Xs4) Xsi2)))))))))
% 3.70/4.03 (assert (forall ((I3 tptp.set_nat) (I7 tptp.set_nat) (A (-> tptp.nat tptp.d tptp.assn)) (A6 (-> tptp.nat tptp.d tptp.assn)) (Xs tptp.list_nat) (Xs4 tptp.list_nat) (Xsi tptp.list_d) (Xsi2 tptp.list_d)) (=> (= I3 I7) (=> (= A A6) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Xs4)) (=> (= (@ tptp.size_size_list_d Xsi) (@ tptp.size_size_list_d Xsi2)) (=> (forall ((I5 tptp.nat)) (let ((_let_1 (@ tptp.size_size_list_nat Xs))) (=> (@ (@ tptp.member_nat I5) I3) (=> (@ (@ tptp.ord_less_nat I5) _let_1) (=> (= _let_1 (@ tptp.size_size_list_d Xsi)) (and (= (@ (@ tptp.nth_nat Xs) I5) (@ (@ tptp.nth_nat Xs4) I5)) (= (@ (@ tptp.nth_d Xsi) I5) (@ (@ tptp.nth_d Xsi2) I5)))))))) (= (@ (@ (@ (@ tptp.vEBT_L8146214880390291087_nat_d I3) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L8146214880390291087_nat_d I7) A6) Xs4) Xsi2)))))))))
% 3.70/4.03 (assert (forall ((I3 tptp.set_nat) (I7 tptp.set_nat) (A (-> tptp.nat tptp.nat tptp.assn)) (A6 (-> tptp.nat tptp.nat tptp.assn)) (Xs tptp.list_nat) (Xs4 tptp.list_nat) (Xsi tptp.list_nat) (Xsi2 tptp.list_nat)) (=> (= I3 I7) (=> (= A A6) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Xs4)) (=> (= (@ tptp.size_size_list_nat Xsi) (@ tptp.size_size_list_nat Xsi2)) (=> (forall ((I5 tptp.nat)) (let ((_let_1 (@ tptp.size_size_list_nat Xs))) (=> (@ (@ tptp.member_nat I5) I3) (=> (@ (@ tptp.ord_less_nat I5) _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Xsi)) (and (= (@ (@ tptp.nth_nat Xs) I5) (@ (@ tptp.nth_nat Xs4) I5)) (= (@ (@ tptp.nth_nat Xsi) I5) (@ (@ tptp.nth_nat Xsi2) I5)))))))) (= (@ (@ (@ (@ tptp.vEBT_L7892069108621897922at_nat I3) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L7892069108621897922at_nat I7) A6) Xs4) Xsi2)))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A2))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 C)) B2) (@ (@ tptp.minus_minus_rat (@ _let_1 B2)) C)))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 C)) B2) (@ (@ tptp.minus_minus_nat (@ _let_1 B2)) C)))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A2))) (= (@ (@ tptp.minus_minus_int (@ _let_1 C)) B2) (@ (@ tptp.minus_minus_int (@ _let_1 B2)) C)))))
% 3.70/4.03 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A2) B2) (@ (@ tptp.minus_minus_rat C) D2)) (= (= A2 B2) (= C D2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int) (D2 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A2) B2) (@ (@ tptp.minus_minus_int C) D2)) (= (= A2 B2) (= C D2)))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat)) (=> (@ tptp.is_sin2937591304547752795at_nat A) (not (forall ((X3 tptp.produc3843707927480180839at_nat)) (not (= A (@ (@ tptp.insert9069300056098147895at_nat X3) tptp.bot_bo228742789529271731at_nat))))))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.is_sin2850979758926227957at_nat A) (not (forall ((X3 tptp.product_prod_nat_nat)) (not (= A (@ (@ tptp.insert8211810215607154385at_nat X3) tptp.bot_bo2099793752762293965at_nat))))))))
% 3.70/4.03 (assert (forall ((A tptp.set_o)) (=> (@ tptp.is_singleton_o A) (not (forall ((X3 Bool)) (not (= A (@ (@ tptp.insert_o2 X3) tptp.bot_bot_set_o))))))))
% 3.70/4.03 (assert (forall ((A tptp.set_nat)) (=> (@ tptp.is_singleton_nat A) (not (forall ((X3 tptp.nat)) (not (= A (@ (@ tptp.insert_nat2 X3) tptp.bot_bot_set_nat))))))))
% 3.70/4.03 (assert (forall ((A tptp.set_int)) (=> (@ tptp.is_singleton_int A) (not (forall ((X3 tptp.int)) (not (= A (@ (@ tptp.insert_int2 X3) tptp.bot_bot_set_int))))))))
% 3.70/4.03 (assert (= tptp.is_sin2937591304547752795at_nat (lambda ((A5 tptp.set_Pr4329608150637261639at_nat)) (exists ((X2 tptp.produc3843707927480180839at_nat)) (= A5 (@ (@ tptp.insert9069300056098147895at_nat X2) tptp.bot_bo228742789529271731at_nat))))))
% 3.70/4.03 (assert (= tptp.is_sin2850979758926227957at_nat (lambda ((A5 tptp.set_Pr1261947904930325089at_nat)) (exists ((X2 tptp.product_prod_nat_nat)) (= A5 (@ (@ tptp.insert8211810215607154385at_nat X2) tptp.bot_bo2099793752762293965at_nat))))))
% 3.70/4.03 (assert (= tptp.is_singleton_o (lambda ((A5 tptp.set_o)) (exists ((X2 Bool)) (= A5 (@ (@ tptp.insert_o2 X2) tptp.bot_bot_set_o))))))
% 3.70/4.03 (assert (= tptp.is_singleton_nat (lambda ((A5 tptp.set_nat)) (exists ((X2 tptp.nat)) (= A5 (@ (@ tptp.insert_nat2 X2) tptp.bot_bot_set_nat))))))
% 3.70/4.03 (assert (= tptp.is_singleton_int (lambda ((A5 tptp.set_int)) (exists ((X2 tptp.int)) (= A5 (@ (@ tptp.insert_int2 X2) tptp.bot_bot_set_int))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (I3 tptp.set_nat) (Xs tptp.list_c) (A (-> tptp.c tptp.nat tptp.assn)) (Xsi tptp.list_nat)) (=> (not (@ (@ tptp.member_nat I) I3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_c Xs)) (= (@ (@ (@ (@ tptp.vEBT_L6585172037124793648_c_nat (@ (@ tptp.insert_nat2 I) I3)) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_c Xs) I)) (@ (@ tptp.nth_nat Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L6585172037124793648_c_nat I3) A) Xs) Xsi)))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (I3 tptp.set_nat) (Xs tptp.list_c) (A (-> tptp.c tptp.int tptp.assn)) (Xsi tptp.list_int)) (=> (not (@ (@ tptp.member_nat I) I3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_c Xs)) (= (@ (@ (@ (@ tptp.vEBT_L6582681566615743372_c_int (@ (@ tptp.insert_nat2 I) I3)) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_c Xs) I)) (@ (@ tptp.nth_int Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L6582681566615743372_c_int I3) A) Xs) Xsi)))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (I3 tptp.set_nat) (Xs tptp.list_d) (A (-> tptp.d tptp.nat tptp.assn)) (Xsi tptp.list_nat)) (=> (not (@ (@ tptp.member_nat I) I3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_d Xs)) (= (@ (@ (@ (@ tptp.vEBT_L7820616366081188145_d_nat (@ (@ tptp.insert_nat2 I) I3)) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_d Xs) I)) (@ (@ tptp.nth_nat Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7820616366081188145_d_nat I3) A) Xs) Xsi)))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (I3 tptp.set_nat) (Xs tptp.list_d) (A (-> tptp.d tptp.int tptp.assn)) (Xsi tptp.list_int)) (=> (not (@ (@ tptp.member_nat I) I3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_d Xs)) (= (@ (@ (@ (@ tptp.vEBT_L7818125895572137869_d_int (@ (@ tptp.insert_nat2 I) I3)) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_d Xs) I)) (@ (@ tptp.nth_int Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7818125895572137869_d_int I3) A) Xs) Xsi)))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (I3 tptp.set_nat) (Xs tptp.list_nat) (A (-> tptp.nat tptp.nat tptp.assn)) (Xsi tptp.list_nat)) (=> (not (@ (@ tptp.member_nat I) I3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs)) (= (@ (@ (@ (@ tptp.vEBT_L7892069108621897922at_nat (@ (@ tptp.insert_nat2 I) I3)) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_nat Xs) I)) (@ (@ tptp.nth_nat Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7892069108621897922at_nat I3) A) Xs) Xsi)))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (I3 tptp.set_nat) (Xs tptp.list_nat) (A (-> tptp.nat tptp.int tptp.assn)) (Xsi tptp.list_int)) (=> (not (@ (@ tptp.member_nat I) I3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs)) (= (@ (@ (@ (@ tptp.vEBT_L7889578638112847646at_int (@ (@ tptp.insert_nat2 I) I3)) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_nat Xs) I)) (@ (@ tptp.nth_int Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7889578638112847646at_int I3) A) Xs) Xsi)))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (I3 tptp.set_nat) (Xs tptp.list_int) (A (-> tptp.int tptp.nat tptp.assn)) (Xsi tptp.list_nat)) (=> (not (@ (@ tptp.member_nat I) I3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs)) (= (@ (@ (@ (@ tptp.vEBT_L8891422820522952478nt_nat (@ (@ tptp.insert_nat2 I) I3)) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_int Xs) I)) (@ (@ tptp.nth_nat Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L8891422820522952478nt_nat I3) A) Xs) Xsi)))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (I3 tptp.set_nat) (Xs tptp.list_int) (A (-> tptp.int tptp.int tptp.assn)) (Xsi tptp.list_int)) (=> (not (@ (@ tptp.member_nat I) I3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs)) (= (@ (@ (@ (@ tptp.vEBT_L8888932350013902202nt_int (@ (@ tptp.insert_nat2 I) I3)) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_int Xs) I)) (@ (@ tptp.nth_int Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L8888932350013902202nt_int I3) A) Xs) Xsi)))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (I3 tptp.set_nat) (Xs tptp.list_c) (A (-> tptp.c tptp.d tptp.assn)) (Xsi tptp.list_d)) (=> (not (@ (@ tptp.member_nat I) I3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_c Xs)) (= (@ (@ (@ (@ tptp.vEBT_L824818263033719201sn_c_d (@ (@ tptp.insert_nat2 I) I3)) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_c Xs) I)) (@ (@ tptp.nth_d Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L824818263033719201sn_c_d I3) A) Xs) Xsi)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A2) C)) (@ (@ tptp.minus_minus_rat B2) C)))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.minus_8373710615458151222nteger A2) C)) (@ (@ tptp.minus_8373710615458151222nteger B2) C)))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A2) C)) (@ (@ tptp.minus_minus_int B2) C)))))
% 3.70/4.03 (assert (forall ((B2 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat C))) (=> (@ (@ tptp.ord_less_rat B2) A2) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B2))))))
% 3.70/4.03 (assert (forall ((B2 tptp.code_integer) (A2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) A2) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B2))))))
% 3.70/4.03 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int C))) (=> (@ (@ tptp.ord_less_int B2) A2) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2))))))
% 3.70/4.03 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A2) B2) (@ (@ tptp.minus_minus_rat C) D2)) (= (@ (@ tptp.ord_less_rat A2) B2) (@ (@ tptp.ord_less_rat C) D2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (= (@ (@ tptp.minus_8373710615458151222nteger A2) B2) (@ (@ tptp.minus_8373710615458151222nteger C) D2)) (= (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (@ (@ tptp.ord_le6747313008572928689nteger C) D2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int) (D2 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A2) B2) (@ (@ tptp.minus_minus_int C) D2)) (= (@ (@ tptp.ord_less_int A2) B2) (@ (@ tptp.ord_less_int C) D2)))))
% 3.70/4.03 (assert (= tptp.bot_bo7963750851167320836at_o_o (lambda ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (@ (@ tptp.member6576561426505652726_nat_o X2) tptp.bot_bo7824918357723582233_nat_o))))
% 3.70/4.03 (assert (= tptp.bot_bo6829958733157050602_nat_o (lambda ((X2 tptp.produc3843707927480180839at_nat)) (@ (@ tptp.member8757157785044589968at_nat X2) tptp.bot_bo228742789529271731at_nat))))
% 3.70/4.03 (assert (= tptp.bot_bo482883023278783056_nat_o (lambda ((X2 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X2) tptp.bot_bo2099793752762293965at_nat))))
% 3.70/4.03 (assert (= tptp.bot_bot_o_o (lambda ((X2 Bool)) (@ (@ tptp.member_o X2) tptp.bot_bot_set_o))))
% 3.70/4.03 (assert (= tptp.bot_bot_nat_o (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) tptp.bot_bot_set_nat))))
% 3.70/4.03 (assert (= tptp.bot_bot_int_o (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) tptp.bot_bot_set_int))))
% 3.70/4.03 (assert (forall ((P (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (= (= (@ tptp.collec939566748876313656_nat_o P) tptp.bot_bo7824918357723582233_nat_o) (= P tptp.bot_bo7963750851167320836at_o_o))))
% 3.70/4.03 (assert (forall ((P (-> tptp.produc3843707927480180839at_nat Bool))) (= (= (@ tptp.collec6321179662152712658at_nat P) tptp.bot_bo228742789529271731at_nat) (= P tptp.bot_bo6829958733157050602_nat_o))))
% 3.70/4.03 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool))) (= (= (@ tptp.collec3392354462482085612at_nat P) tptp.bot_bo2099793752762293965at_nat) (= P tptp.bot_bo482883023278783056_nat_o))))
% 3.70/4.03 (assert (forall ((P (-> Bool Bool))) (= (= (@ tptp.collect_o P) tptp.bot_bot_set_o) (= P tptp.bot_bot_o_o))))
% 3.70/4.03 (assert (forall ((P (-> tptp.nat Bool))) (= (= (@ tptp.collect_nat P) tptp.bot_bot_set_nat) (= P tptp.bot_bot_nat_o))))
% 3.70/4.03 (assert (forall ((P (-> tptp.int Bool))) (= (= (@ tptp.collect_int P) tptp.bot_bot_set_int) (= P tptp.bot_bot_int_o))))
% 3.70/4.03 (assert (= tptp.remove5300788332298244428at_nat (lambda ((X2 tptp.produc3843707927480180839at_nat) (A5 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.minus_3314409938677909166at_nat A5) (@ (@ tptp.insert9069300056098147895at_nat X2) tptp.bot_bo228742789529271731at_nat)))))
% 3.70/4.03 (assert (= tptp.remove6466555014256735590at_nat (lambda ((X2 tptp.product_prod_nat_nat) (A5 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.minus_1356011639430497352at_nat A5) (@ (@ tptp.insert8211810215607154385at_nat X2) tptp.bot_bo2099793752762293965at_nat)))))
% 3.70/4.03 (assert (= tptp.remove_o (lambda ((X2 Bool) (A5 tptp.set_o)) (@ (@ tptp.minus_minus_set_o A5) (@ (@ tptp.insert_o2 X2) tptp.bot_bot_set_o)))))
% 3.70/4.03 (assert (= tptp.remove_int (lambda ((X2 tptp.int) (A5 tptp.set_int)) (@ (@ tptp.minus_minus_set_int A5) (@ (@ tptp.insert_int2 X2) tptp.bot_bot_set_int)))))
% 3.70/4.03 (assert (= tptp.remove_nat (lambda ((X2 tptp.nat) (A5 tptp.set_nat)) (@ (@ tptp.minus_minus_set_nat A5) (@ (@ tptp.insert_nat2 X2) tptp.bot_bot_set_nat)))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (L tptp.list_P6011104703257516679at_nat) (X tptp.product_prod_nat_nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s5460976970255530739at_nat L)) (= (@ (@ tptp.insert8211810215607154385at_nat (@ (@ tptp.nth_Pr7617993195940197384at_nat L) I)) (@ tptp.set_Pr5648618587558075414at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat L) I) X))) (@ (@ tptp.insert8211810215607154385at_nat X) (@ tptp.set_Pr5648618587558075414at_nat L))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (L tptp.list_P5464809261938338413at_nat) (X tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s1588839187904960729at_nat L)) (= (@ (@ tptp.insert9069300056098147895at_nat (@ (@ tptp.nth_Pr1239524528086697198at_nat L) I)) (@ tptp.set_Pr3765526544606949372at_nat (@ (@ (@ tptp.list_u4696772448584712917at_nat L) I) X))) (@ (@ tptp.insert9069300056098147895at_nat X) (@ tptp.set_Pr3765526544606949372at_nat L))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (L tptp.list_o) (X Bool)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o L)) (= (@ (@ tptp.insert_o2 (@ (@ tptp.nth_o L) I)) (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o L) I) X))) (@ (@ tptp.insert_o2 X) (@ tptp.set_o2 L))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (L tptp.list_P8527749157015355191n_assn) (X tptp.produc6575502325842934193n_assn)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6829681357464350627n_assn L)) (= (@ (@ tptp.insert5290817439147925377n_assn (@ (@ tptp.nth_Pr1769885009046257848n_assn L) I)) (@ tptp.set_Pr1139785259514867910n_assn (@ (@ (@ tptp.list_u4534839942911652127n_assn L) I) X))) (@ (@ tptp.insert5290817439147925377n_assn X) (@ tptp.set_Pr1139785259514867910n_assn L))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (L tptp.list_c) (X tptp.c)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_c L)) (= (@ (@ tptp.insert_c (@ (@ tptp.nth_c L) I)) (@ tptp.set_c2 (@ (@ (@ tptp.list_update_c L) I) X))) (@ (@ tptp.insert_c X) (@ tptp.set_c2 L))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (L tptp.list_d) (X tptp.d)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_d L)) (= (@ (@ tptp.insert_d (@ (@ tptp.nth_d L) I)) (@ tptp.set_d2 (@ (@ (@ tptp.list_update_d L) I) X))) (@ (@ tptp.insert_d X) (@ tptp.set_d2 L))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (L tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat L)) (= (@ (@ tptp.insert_nat2 (@ (@ tptp.nth_nat L) I)) (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat L) I) X))) (@ (@ tptp.insert_nat2 X) (@ tptp.set_nat2 L))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (L tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int L)) (= (@ (@ tptp.insert_int2 (@ (@ tptp.nth_int L) I)) (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int L) I) X))) (@ (@ tptp.insert_int2 X) (@ tptp.set_int2 L))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (Xs tptp.list_P8527749157015355191n_assn) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_Pr1769885009046257848n_assn Xs))) (let ((_let_2 (@ tptp.size_s6829681357464350627n_assn Xs))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_Pr1139785259514867910n_assn (@ (@ (@ tptp.list_u4534839942911652127n_assn (@ (@ (@ tptp.list_u4534839942911652127n_assn Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.set_Pr1139785259514867910n_assn Xs))))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (Xs tptp.list_c) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_c Xs))) (let ((_let_2 (@ tptp.size_size_list_c Xs))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_c2 (@ (@ (@ tptp.list_update_c (@ (@ (@ tptp.list_update_c Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.set_c2 Xs))))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (Xs tptp.list_d) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_d Xs))) (let ((_let_2 (@ tptp.size_size_list_d Xs))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_d2 (@ (@ (@ tptp.list_update_d (@ (@ (@ tptp.list_update_d Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.set_d2 Xs))))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (Xs tptp.list_nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (let ((_let_2 (@ tptp.size_size_list_nat Xs))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat (@ (@ (@ tptp.list_update_nat Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.set_nat2 Xs))))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (Xs tptp.list_int) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs))) (let ((_let_2 (@ tptp.size_size_list_int Xs))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int (@ (@ (@ tptp.list_update_int Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.set_int2 Xs))))))))
% 3.70/4.03 (assert (= tptp.is_emp7572232645145209145at_nat (lambda ((A5 tptp.set_Pr4329608150637261639at_nat)) (= A5 tptp.bot_bo228742789529271731at_nat))))
% 3.70/4.03 (assert (= tptp.is_emp1662574758705540307at_nat (lambda ((A5 tptp.set_Pr1261947904930325089at_nat)) (= A5 tptp.bot_bo2099793752762293965at_nat))))
% 3.70/4.03 (assert (= tptp.is_empty_o (lambda ((A5 tptp.set_o)) (= A5 tptp.bot_bot_set_o))))
% 3.70/4.03 (assert (= tptp.is_empty_nat (lambda ((A5 tptp.set_nat)) (= A5 tptp.bot_bot_set_nat))))
% 3.70/4.03 (assert (= tptp.is_empty_int (lambda ((A5 tptp.set_int)) (= A5 tptp.bot_bot_set_int))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (Xs tptp.list_c) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_c Xs))) (let ((_let_2 (@ tptp.size_size_list_c Xs))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.distinct_c (@ (@ (@ tptp.list_update_c (@ (@ (@ tptp.list_update_c Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.distinct_c Xs))))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (Xs tptp.list_d) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_d Xs))) (let ((_let_2 (@ tptp.size_size_list_d Xs))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.distinct_d (@ (@ (@ tptp.list_update_d (@ (@ (@ tptp.list_update_d Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.distinct_d Xs))))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (Xs tptp.list_nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (let ((_let_2 (@ tptp.size_size_list_nat Xs))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.distinct_nat (@ (@ (@ tptp.list_update_nat (@ (@ (@ tptp.list_update_nat Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.distinct_nat Xs))))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (Xs tptp.list_int) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs))) (let ((_let_2 (@ tptp.size_size_list_int Xs))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.distinct_int (@ (@ (@ tptp.list_update_int (@ (@ (@ tptp.list_update_int Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.distinct_int Xs))))))))
% 3.70/4.03 (assert (= tptp.list_ex_c (lambda ((P2 (-> tptp.c Bool)) (Xs3 tptp.list_c)) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_c Xs3)) (@ P2 (@ (@ tptp.nth_c Xs3) N2)))))))
% 3.70/4.03 (assert (= tptp.list_ex_d (lambda ((P2 (-> tptp.d Bool)) (Xs3 tptp.list_d)) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_d Xs3)) (@ P2 (@ (@ tptp.nth_d Xs3) N2)))))))
% 3.70/4.03 (assert (= tptp.list_ex_nat (lambda ((P2 (-> tptp.nat Bool)) (Xs3 tptp.list_nat)) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs3)) (@ P2 (@ (@ tptp.nth_nat Xs3) N2)))))))
% 3.70/4.03 (assert (= tptp.list_ex_int (lambda ((P2 (-> tptp.int Bool)) (Xs3 tptp.list_int)) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_int Xs3)) (@ P2 (@ (@ tptp.nth_int Xs3) N2)))))))
% 3.70/4.03 (assert (forall ((P tptp.assn) (Q tptp.assn) (B2 Bool)) (let ((_let_1 (@ tptp.entails P))) (= (@ _let_1 (@ (@ tptp.times_times_assn Q) (@ tptp.pure_assn B2))) (and (forall ((H3 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P) H3) B2)) (@ _let_1 Q))))))
% 3.70/4.03 (assert (forall ((P Bool) (Q Bool)) (= (= (@ tptp.pure_assn P) (@ tptp.pure_assn Q)) (= P Q))))
% 3.70/4.03 (assert (forall ((X tptp.produc3843707927480180839at_nat) (Y tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat X))) (= (@ _let_1 (@ (@ tptp.remove5300788332298244428at_nat Y) A)) (and (@ _let_1 A) (not (= X Y)))))))
% 3.70/4.03 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X))) (= (@ _let_1 (@ (@ tptp.remove6466555014256735590at_nat Y) A)) (and (@ _let_1 A) (not (= X Y)))))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat X))) (= (@ _let_1 (@ (@ tptp.remove_nat Y) A)) (and (@ _let_1 A) (not (= X Y)))))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int) (A tptp.set_int)) (let ((_let_1 (@ tptp.member_int X))) (= (@ _let_1 (@ (@ tptp.remove_int Y) A)) (and (@ _let_1 A) (not (= X Y)))))))
% 3.70/4.03 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Y (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o X))) (= (@ _let_1 (@ (@ tptp.remove4651630035290841522_nat_o Y) A)) (and (@ _let_1 A) (not (= X Y)))))))
% 3.70/4.03 (assert (forall ((A2 Bool) (B2 Bool)) (= (@ (@ tptp.times_times_assn (@ tptp.pure_assn A2)) (@ tptp.pure_assn B2)) (@ tptp.pure_assn (and A2 B2)))))
% 3.70/4.03 (assert (= (@ tptp.pure_assn false) tptp.bot_bot_assn))
% 3.70/4.03 (assert (forall ((P Bool)) (= (= (@ tptp.pure_assn P) tptp.bot_bot_assn) (not P))))
% 3.70/4.03 (assert (forall ((P tptp.assn) (B2 Bool) (H2 tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn P) (@ tptp.pure_assn B2))) H2) (and (@ (@ tptp.rep_assn P) H2) B2))))
% 3.70/4.03 (assert (forall ((P tptp.assn) (B2 Bool) (Q tptp.assn)) (= (@ (@ tptp.entails (@ (@ tptp.times_times_assn P) (@ tptp.pure_assn B2))) Q) (=> B2 (@ (@ tptp.entails P) Q)))))
% 3.70/4.03 (assert (forall ((P tptp.assn) (Q tptp.assn) (H2 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) tptp.bot_bot_set_nat))) (= (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn P) Q)) _let_1) (and (@ (@ tptp.rep_assn P) _let_1) (@ (@ tptp.rep_assn Q) _let_1))))))
% 3.70/4.03 (assert (forall ((B2 Bool) (H2 tptp.heap_e7401611519738050253t_unit)) (= (@ (@ tptp.rep_assn (@ tptp.pure_assn B2)) (@ (@ tptp.produc7507926704131184380et_nat H2) tptp.bot_bot_set_nat)) B2)))
% 3.70/4.03 (assert (forall ((Xs tptp.list_P5464809261938338413at_nat) (Ys tptp.list_P5464809261938338413at_nat) (F4 (-> tptp.produc3843707927480180839at_nat Bool)) (G (-> tptp.produc3843707927480180839at_nat Bool))) (=> (= Xs Ys) (=> (forall ((X3 tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X3) (@ tptp.set_Pr3765526544606949372at_nat Ys)) (= (@ F4 X3) (@ G X3)))) (= (@ (@ tptp.list_e5181628221095382443at_nat F4) Xs) (@ (@ tptp.list_e5181628221095382443at_nat G) Ys))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_P6011104703257516679at_nat) (Ys tptp.list_P6011104703257516679at_nat) (F4 (-> tptp.product_prod_nat_nat Bool)) (G (-> tptp.product_prod_nat_nat Bool))) (=> (= Xs Ys) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) (@ tptp.set_Pr5648618587558075414at_nat Ys)) (= (@ F4 X3) (@ G X3)))) (= (@ (@ tptp.list_e7689525607045846085at_nat F4) Xs) (@ (@ tptp.list_e7689525607045846085at_nat G) Ys))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_P7985473006766602707_nat_o) (Ys tptp.list_P7985473006766602707_nat_o) (F4 (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool)) (G (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (=> (= Xs Ys) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X3) (@ tptp.set_Pr400311997697478754_nat_o Ys)) (= (@ F4 X3) (@ G X3)))) (= (@ (@ tptp.list_e4587384546317177617_nat_o F4) Xs) (@ (@ tptp.list_e4587384546317177617_nat_o G) Ys))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int) (F4 (-> tptp.int Bool)) (G (-> tptp.int Bool))) (=> (= Xs Ys) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Ys)) (= (@ F4 X3) (@ G X3)))) (= (@ (@ tptp.list_ex_int F4) Xs) (@ (@ tptp.list_ex_int G) Ys))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (F4 (-> tptp.nat Bool)) (G (-> tptp.nat Bool))) (=> (= Xs Ys) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Ys)) (= (@ F4 X3) (@ G X3)))) (= (@ (@ tptp.list_ex_nat F4) Xs) (@ (@ tptp.list_ex_nat G) Ys))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_P8527749157015355191n_assn) (F4 (-> tptp.produc6575502325842934193n_assn Bool)) (G (-> tptp.produc6575502325842934193n_assn Bool))) (=> (= Xs Ys) (=> (forall ((X3 tptp.produc6575502325842934193n_assn)) (=> (@ (@ tptp.member7957490590177025114n_assn X3) (@ tptp.set_Pr1139785259514867910n_assn Ys)) (= (@ F4 X3) (@ G X3)))) (= (@ (@ tptp.list_e1087220904399170805n_assn F4) Xs) (@ (@ tptp.list_e1087220904399170805n_assn G) Ys))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_int)) (let ((_let_1 (@ tptp.distinct_int Xs))) (=> _let_1 _let_1))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_nat)) (let ((_let_1 (@ tptp.distinct_nat Xs))) (=> _let_1 _let_1))))
% 3.70/4.03 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (not (= X (@ (@ tptp.produc7507926704131184380et_nat H) As)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (S tptp.set_Pr4329608150637261639at_nat) (P (-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool))) (let ((_let_1 (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat A2) B2)) S))) (=> _let_1 (=> (=> _let_1 (@ (@ P A2) B2)) (exists ((A4 tptp.set_Pr1261947904930325089at_nat) (B4 tptp.set_Pr1261947904930325089at_nat)) (and (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat A4) B4)) S) (@ (@ P A4) B4))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (S tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.nat tptp.nat Bool))) (let ((_let_1 (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B2)) S))) (=> _let_1 (=> (=> _let_1 (@ (@ P A2) B2)) (exists ((A4 tptp.nat) (B4 tptp.nat)) (and (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A4) B4)) S) (@ (@ P A4) B4))))))))
% 3.70/4.03 (assert (forall ((A2 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B2 tptp.produc8923325533196201883nteger) (S tptp.set_Pr1281608226676607948nteger) (P (-> (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger Bool))) (let ((_let_1 (@ (@ tptp.member4164122664394876845nteger (@ (@ tptp.produc8603105652947943368nteger A2) B2)) S))) (=> _let_1 (=> (=> _let_1 (@ (@ P A2) B2)) (exists ((A4 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B4 tptp.produc8923325533196201883nteger)) (and (@ (@ tptp.member4164122664394876845nteger (@ (@ tptp.produc8603105652947943368nteger A4) B4)) S) (@ (@ P A4) B4))))))))
% 3.70/4.03 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.produc3658429121746597890et_nat) (S tptp.set_Pr3286484037609594932et_nat) (P (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A2) B2)) S))) (=> _let_1 (=> (=> _let_1 (@ (@ P A2) B2)) (exists ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.produc3658429121746597890et_nat)) (and (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A4) B4)) S) (@ (@ P A4) B4))))))))
% 3.70/4.03 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.produc3925858234332021118et_nat) (S tptp.set_Pr8536935166611901872et_nat) (P (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat Bool))) (let ((_let_1 (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A2) B2)) S))) (=> _let_1 (=> (=> _let_1 (@ (@ P A2) B2)) (exists ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.produc3925858234332021118et_nat)) (and (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A4) B4)) S) (@ (@ P A4) B4))))))))
% 3.70/4.03 (assert (forall ((A2 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B2 tptp.product_prod_int_int) (S tptp.set_Pr9222295170931077689nt_int) (P (-> (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool))) (let ((_let_1 (@ (@ tptp.member7618704894036264090nt_int (@ (@ tptp.produc5700946648718959541nt_int A2) B2)) S))) (=> _let_1 (=> (=> _let_1 (@ (@ P A2) B2)) (exists ((A4 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B4 tptp.product_prod_int_int)) (and (@ (@ tptp.member7618704894036264090nt_int (@ (@ tptp.produc5700946648718959541nt_int A4) B4)) S) (@ (@ P A4) B4))))))))
% 3.70/4.03 (assert (forall ((A2 (-> tptp.int tptp.option6357759511663192854e_term)) (B2 tptp.product_prod_int_int) (S tptp.set_Pr1872883991513573699nt_int) (P (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool))) (let ((_let_1 (@ (@ tptp.member7034335876925520548nt_int (@ (@ tptp.produc4305682042979456191nt_int A2) B2)) S))) (=> _let_1 (=> (=> _let_1 (@ (@ P A2) B2)) (exists ((A4 (-> tptp.int tptp.option6357759511663192854e_term)) (B4 tptp.product_prod_int_int)) (and (@ (@ tptp.member7034335876925520548nt_int (@ (@ tptp.produc4305682042979456191nt_int A4) B4)) S) (@ (@ P A4) B4))))))))
% 3.70/4.03 (assert (forall ((X tptp.produc7773217078559923341nt_int)) (not (forall ((F5 (-> tptp.int tptp.option6357759511663192854e_term)) (A4 tptp.int) (B4 tptp.int)) (not (= X (@ (@ tptp.produc4305682042979456191nt_int F5) (@ (@ tptp.product_Pair_int_int A4) B4))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_int) (Xs4 tptp.list_int) (Xsi tptp.list_int) (Xsi2 tptp.list_int) (A (-> tptp.int tptp.int tptp.assn)) (A6 (-> tptp.int tptp.int tptp.assn))) (=> (= Xs Xs4) (=> (= Xsi Xsi2) (=> (forall ((X3 tptp.int) (Xi tptp.int)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs4)) (=> (@ (@ tptp.member_int Xi) (@ tptp.set_int2 Xsi2)) (= (@ (@ A X3) Xi) (@ (@ A6 X3) Xi))))) (= (@ (@ (@ tptp.vEBT_L74593716426352029nt_int A) Xs) Xsi) (@ (@ (@ tptp.vEBT_L74593716426352029nt_int A6) Xs4) Xsi2)))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_int) (Xs4 tptp.list_int) (Xsi tptp.list_nat) (Xsi2 tptp.list_nat) (A (-> tptp.int tptp.nat tptp.assn)) (A6 (-> tptp.int tptp.nat tptp.assn))) (=> (= Xs Xs4) (=> (= Xsi Xsi2) (=> (forall ((X3 tptp.int) (Xi tptp.nat)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs4)) (=> (@ (@ tptp.member_nat Xi) (@ tptp.set_nat2 Xsi2)) (= (@ (@ A X3) Xi) (@ (@ A6 X3) Xi))))) (= (@ (@ (@ tptp.vEBT_L77084186935402305nt_nat A) Xs) Xsi) (@ (@ (@ tptp.vEBT_L77084186935402305nt_nat A6) Xs4) Xsi2)))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_nat) (Xs4 tptp.list_nat) (Xsi tptp.list_int) (Xsi2 tptp.list_int) (A (-> tptp.nat tptp.int tptp.assn)) (A6 (-> tptp.nat tptp.int tptp.assn))) (=> (= Xs Xs4) (=> (= Xsi Xsi2) (=> (forall ((X3 tptp.nat) (Xi tptp.int)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs4)) (=> (@ (@ tptp.member_int Xi) (@ tptp.set_int2 Xsi2)) (= (@ (@ A X3) Xi) (@ (@ A6 X3) Xi))))) (= (@ (@ (@ tptp.vEBT_L8298612041380073281at_int A) Xs) Xsi) (@ (@ (@ tptp.vEBT_L8298612041380073281at_int A6) Xs4) Xsi2)))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_nat) (Xs4 tptp.list_nat) (Xsi tptp.list_nat) (Xsi2 tptp.list_nat) (A (-> tptp.nat tptp.nat tptp.assn)) (A6 (-> tptp.nat tptp.nat tptp.assn))) (=> (= Xs Xs4) (=> (= Xsi Xsi2) (=> (forall ((X3 tptp.nat) (Xi tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs4)) (=> (@ (@ tptp.member_nat Xi) (@ tptp.set_nat2 Xsi2)) (= (@ (@ A X3) Xi) (@ (@ A6 X3) Xi))))) (= (@ (@ (@ tptp.vEBT_L8301102511889123557at_nat A) Xs) Xsi) (@ (@ (@ tptp.vEBT_L8301102511889123557at_nat A6) Xs4) Xsi2)))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_P6011104703257516679at_nat) (Xs4 tptp.list_P6011104703257516679at_nat) (Xsi tptp.list_int) (Xsi2 tptp.list_int) (A (-> tptp.product_prod_nat_nat tptp.int tptp.assn)) (A6 (-> tptp.product_prod_nat_nat tptp.int tptp.assn))) (=> (= Xs Xs4) (=> (= Xsi Xsi2) (=> (forall ((X3 tptp.product_prod_nat_nat) (Xi tptp.int)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) (@ tptp.set_Pr5648618587558075414at_nat Xs4)) (=> (@ (@ tptp.member_int Xi) (@ tptp.set_int2 Xsi2)) (= (@ (@ A X3) Xi) (@ (@ A6 X3) Xi))))) (= (@ (@ (@ tptp.vEBT_L6295016686126367274at_int A) Xs) Xsi) (@ (@ (@ tptp.vEBT_L6295016686126367274at_int A6) Xs4) Xsi2)))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_P6011104703257516679at_nat) (Xs4 tptp.list_P6011104703257516679at_nat) (Xsi tptp.list_nat) (Xsi2 tptp.list_nat) (A (-> tptp.product_prod_nat_nat tptp.nat tptp.assn)) (A6 (-> tptp.product_prod_nat_nat tptp.nat tptp.assn))) (=> (= Xs Xs4) (=> (= Xsi Xsi2) (=> (forall ((X3 tptp.product_prod_nat_nat) (Xi tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) (@ tptp.set_Pr5648618587558075414at_nat Xs4)) (=> (@ (@ tptp.member_nat Xi) (@ tptp.set_nat2 Xsi2)) (= (@ (@ A X3) Xi) (@ (@ A6 X3) Xi))))) (= (@ (@ (@ tptp.vEBT_L6297507156635417550at_nat A) Xs) Xsi) (@ (@ (@ tptp.vEBT_L6297507156635417550at_nat A6) Xs4) Xsi2)))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_int) (Xs4 tptp.list_int) (Xsi tptp.list_P6011104703257516679at_nat) (Xsi2 tptp.list_P6011104703257516679at_nat) (A (-> tptp.int tptp.product_prod_nat_nat tptp.assn)) (A6 (-> tptp.int tptp.product_prod_nat_nat tptp.assn))) (=> (= Xs Xs4) (=> (= Xsi Xsi2) (=> (forall ((X3 tptp.int) (Xi tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs4)) (=> (@ (@ tptp.member8440522571783428010at_nat Xi) (@ tptp.set_Pr5648618587558075414at_nat Xsi2)) (= (@ (@ A X3) Xi) (@ (@ A6 X3) Xi))))) (= (@ (@ (@ tptp.vEBT_L3472024597287490640at_nat A) Xs) Xsi) (@ (@ (@ tptp.vEBT_L3472024597287490640at_nat A6) Xs4) Xsi2)))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_int) (Xs4 tptp.list_int) (Xsi tptp.list_P8527749157015355191n_assn) (Xsi2 tptp.list_P8527749157015355191n_assn) (A (-> tptp.int tptp.produc6575502325842934193n_assn tptp.assn)) (A6 (-> tptp.int tptp.produc6575502325842934193n_assn tptp.assn))) (=> (= Xs Xs4) (=> (= Xsi Xsi2) (=> (forall ((X3 tptp.int) (Xi tptp.produc6575502325842934193n_assn)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs4)) (=> (@ (@ tptp.member7957490590177025114n_assn Xi) (@ tptp.set_Pr1139785259514867910n_assn Xsi2)) (= (@ (@ A X3) Xi) (@ (@ A6 X3) Xi))))) (= (@ (@ (@ tptp.vEBT_L1620274777744359680n_assn A) Xs) Xsi) (@ (@ (@ tptp.vEBT_L1620274777744359680n_assn A6) Xs4) Xsi2)))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_nat) (Xs4 tptp.list_nat) (Xsi tptp.list_P6011104703257516679at_nat) (Xsi2 tptp.list_P6011104703257516679at_nat) (A (-> tptp.nat tptp.product_prod_nat_nat tptp.assn)) (A6 (-> tptp.nat tptp.product_prod_nat_nat tptp.assn))) (=> (= Xs Xs4) (=> (= Xsi Xsi2) (=> (forall ((X3 tptp.nat) (Xi tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs4)) (=> (@ (@ tptp.member8440522571783428010at_nat Xi) (@ tptp.set_Pr5648618587558075414at_nat Xsi2)) (= (@ (@ A X3) Xi) (@ (@ A6 X3) Xi))))) (= (@ (@ (@ tptp.vEBT_L434182512823356844at_nat A) Xs) Xsi) (@ (@ (@ tptp.vEBT_L434182512823356844at_nat A6) Xs4) Xsi2)))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_nat) (Xs4 tptp.list_nat) (Xsi tptp.list_P8527749157015355191n_assn) (Xsi2 tptp.list_P8527749157015355191n_assn) (A (-> tptp.nat tptp.produc6575502325842934193n_assn tptp.assn)) (A6 (-> tptp.nat tptp.produc6575502325842934193n_assn tptp.assn))) (=> (= Xs Xs4) (=> (= Xsi Xsi2) (=> (forall ((X3 tptp.nat) (Xi tptp.produc6575502325842934193n_assn)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs4)) (=> (@ (@ tptp.member7957490590177025114n_assn Xi) (@ tptp.set_Pr1139785259514867910n_assn Xsi2)) (= (@ (@ A X3) Xi) (@ (@ A6 X3) Xi))))) (= (@ (@ (@ tptp.vEBT_L9083610150846024284n_assn A) Xs) Xsi) (@ (@ (@ tptp.vEBT_L9083610150846024284n_assn A6) Xs4) Xsi2)))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_P5464809261938338413at_nat) (X tptp.produc3843707927480180839at_nat)) (=> (@ tptp.distin5355857245021852384at_nat Xs) (=> (@ (@ tptp.member8757157785044589968at_nat X) (@ tptp.set_Pr3765526544606949372at_nat Xs)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.ord_less_nat X3) (@ tptp.size_s1588839187904960729at_nat Xs)) (= (@ (@ tptp.nth_Pr1239524528086697198at_nat Xs) X3) X) (forall ((Y3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat Y3) (@ tptp.size_s1588839187904960729at_nat Xs)) (= (@ (@ tptp.nth_Pr1239524528086697198at_nat Xs) Y3) X)) (= Y3 X3)))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_P6011104703257516679at_nat) (X tptp.product_prod_nat_nat)) (=> (@ tptp.distin6923225563576452346at_nat Xs) (=> (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.ord_less_nat X3) (@ tptp.size_s5460976970255530739at_nat Xs)) (= (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) X3) X) (forall ((Y3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat Y3) (@ tptp.size_s5460976970255530739at_nat Xs)) (= (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) Y3) X)) (= Y3 X3)))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_P7985473006766602707_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.distin299582740263731014_nat_o Xs) (=> (@ (@ tptp.member6576561426505652726_nat_o X) (@ tptp.set_Pr400311997697478754_nat_o Xs)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.ord_less_nat X3) (@ tptp.size_s8908918004648414271_nat_o Xs)) (= (@ (@ tptp.nth_Pr6840583978799713108_nat_o Xs) X3) X) (forall ((Y3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat Y3) (@ tptp.size_s8908918004648414271_nat_o Xs)) (= (@ (@ tptp.nth_Pr6840583978799713108_nat_o Xs) Y3) X)) (= Y3 X3)))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (X tptp.produc6575502325842934193n_assn)) (=> (@ tptp.distin4809818325527169450n_assn Xs) (=> (@ (@ tptp.member7957490590177025114n_assn X) (@ tptp.set_Pr1139785259514867910n_assn Xs)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.ord_less_nat X3) (@ tptp.size_s6829681357464350627n_assn Xs)) (= (@ (@ tptp.nth_Pr1769885009046257848n_assn Xs) X3) X) (forall ((Y3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat Y3) (@ tptp.size_s6829681357464350627n_assn Xs)) (= (@ (@ tptp.nth_Pr1769885009046257848n_assn Xs) Y3) X)) (= Y3 X3)))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_c) (X tptp.c)) (=> (@ tptp.distinct_c Xs) (=> (@ (@ tptp.member_c X) (@ tptp.set_c2 Xs)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.ord_less_nat X3) (@ tptp.size_size_list_c Xs)) (= (@ (@ tptp.nth_c Xs) X3) X) (forall ((Y3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat Y3) (@ tptp.size_size_list_c Xs)) (= (@ (@ tptp.nth_c Xs) Y3) X)) (= Y3 X3)))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_d) (X tptp.d)) (=> (@ tptp.distinct_d Xs) (=> (@ (@ tptp.member_d X) (@ tptp.set_d2 Xs)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.ord_less_nat X3) (@ tptp.size_size_list_d Xs)) (= (@ (@ tptp.nth_d Xs) X3) X) (forall ((Y3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat Y3) (@ tptp.size_size_list_d Xs)) (= (@ (@ tptp.nth_d Xs) Y3) X)) (= Y3 X3)))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_nat) (X tptp.nat)) (=> (@ tptp.distinct_nat Xs) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.ord_less_nat X3) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) X3) X) (forall ((Y3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat Y3) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) Y3) X)) (= Y3 X3)))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_int) (X tptp.int)) (=> (@ tptp.distinct_int Xs) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.ord_less_nat X3) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int Xs) X3) X) (forall ((Y3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat Y3) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int Xs) Y3) X)) (= Y3 X3)))))))))
% 3.70/4.03 (assert (forall ((P tptp.assn) (H2 tptp.heap_e7401611519738050253t_unit) (H4 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ tptp.rep_assn P))) (= (@ _let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) tptp.bot_bot_set_nat)) (@ _let_1 (@ (@ tptp.produc7507926704131184380et_nat H4) tptp.bot_bot_set_nat))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_P7985473006766602707_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (I tptp.nat)) (=> (@ tptp.distin299582740263731014_nat_o Xs) (=> (not (@ (@ tptp.member6576561426505652726_nat_o A2) (@ (@ tptp.minus_1801376950450012436_nat_o (@ tptp.set_Pr400311997697478754_nat_o Xs)) (@ (@ tptp.insert5175938949040314269_nat_o (@ (@ tptp.nth_Pr6840583978799713108_nat_o Xs) I)) tptp.bot_bo7824918357723582233_nat_o)))) (@ tptp.distin299582740263731014_nat_o (@ (@ (@ tptp.list_u6943956310655620667_nat_o Xs) I) A2))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (A2 tptp.produc6575502325842934193n_assn) (I tptp.nat)) (=> (@ tptp.distin4809818325527169450n_assn Xs) (=> (not (@ (@ tptp.member7957490590177025114n_assn A2) (@ (@ tptp.minus_2301194108115264760n_assn (@ tptp.set_Pr1139785259514867910n_assn Xs)) (@ (@ tptp.insert5290817439147925377n_assn (@ (@ tptp.nth_Pr1769885009046257848n_assn Xs) I)) tptp.bot_bo1176836662018730877n_assn)))) (@ tptp.distin4809818325527169450n_assn (@ (@ (@ tptp.list_u4534839942911652127n_assn Xs) I) A2))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_c) (A2 tptp.c) (I tptp.nat)) (=> (@ tptp.distinct_c Xs) (=> (not (@ (@ tptp.member_c A2) (@ (@ tptp.minus_minus_set_c (@ tptp.set_c2 Xs)) (@ (@ tptp.insert_c (@ (@ tptp.nth_c Xs) I)) tptp.bot_bot_set_c)))) (@ tptp.distinct_c (@ (@ (@ tptp.list_update_c Xs) I) A2))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_d) (A2 tptp.d) (I tptp.nat)) (=> (@ tptp.distinct_d Xs) (=> (not (@ (@ tptp.member_d A2) (@ (@ tptp.minus_minus_set_d (@ tptp.set_d2 Xs)) (@ (@ tptp.insert_d (@ (@ tptp.nth_d Xs) I)) tptp.bot_bot_set_d)))) (@ tptp.distinct_d (@ (@ (@ tptp.list_update_d Xs) I) A2))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_P5464809261938338413at_nat) (A2 tptp.produc3843707927480180839at_nat) (I tptp.nat)) (=> (@ tptp.distin5355857245021852384at_nat Xs) (=> (not (@ (@ tptp.member8757157785044589968at_nat A2) (@ (@ tptp.minus_3314409938677909166at_nat (@ tptp.set_Pr3765526544606949372at_nat Xs)) (@ (@ tptp.insert9069300056098147895at_nat (@ (@ tptp.nth_Pr1239524528086697198at_nat Xs) I)) tptp.bot_bo228742789529271731at_nat)))) (@ tptp.distin5355857245021852384at_nat (@ (@ (@ tptp.list_u4696772448584712917at_nat Xs) I) A2))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_P6011104703257516679at_nat) (A2 tptp.product_prod_nat_nat) (I tptp.nat)) (=> (@ tptp.distin6923225563576452346at_nat Xs) (=> (not (@ (@ tptp.member8440522571783428010at_nat A2) (@ (@ tptp.minus_1356011639430497352at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs)) (@ (@ tptp.insert8211810215607154385at_nat (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) I)) tptp.bot_bo2099793752762293965at_nat)))) (@ tptp.distin6923225563576452346at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat Xs) I) A2))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_o) (A2 Bool) (I tptp.nat)) (=> (@ tptp.distinct_o Xs) (=> (not (@ (@ tptp.member_o A2) (@ (@ tptp.minus_minus_set_o (@ tptp.set_o2 Xs)) (@ (@ tptp.insert_o2 (@ (@ tptp.nth_o Xs) I)) tptp.bot_bot_set_o)))) (@ tptp.distinct_o (@ (@ (@ tptp.list_update_o Xs) I) A2))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_int) (A2 tptp.int) (I tptp.nat)) (=> (@ tptp.distinct_int Xs) (=> (not (@ (@ tptp.member_int A2) (@ (@ tptp.minus_minus_set_int (@ tptp.set_int2 Xs)) (@ (@ tptp.insert_int2 (@ (@ tptp.nth_int Xs) I)) tptp.bot_bot_set_int)))) (@ tptp.distinct_int (@ (@ (@ tptp.list_update_int Xs) I) A2))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_nat) (A2 tptp.nat) (I tptp.nat)) (=> (@ tptp.distinct_nat Xs) (=> (not (@ (@ tptp.member_nat A2) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_nat2 Xs)) (@ (@ tptp.insert_nat2 (@ (@ tptp.nth_nat Xs) I)) tptp.bot_bot_set_nat)))) (@ tptp.distinct_nat (@ (@ (@ tptp.list_update_nat Xs) I) A2))))))
% 3.70/4.03 (assert (= tptp.distinct_c (lambda ((Xs3 tptp.list_c)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_c Xs3)) (forall ((J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_c Xs3))) (=> (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_c Xs3)) (=> (not (= I4 J2)) (not (= (@ _let_1 I4) (@ _let_1 J2))))))))))))
% 3.70/4.03 (assert (= tptp.distinct_d (lambda ((Xs3 tptp.list_d)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_d Xs3)) (forall ((J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_d Xs3))) (=> (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_d Xs3)) (=> (not (= I4 J2)) (not (= (@ _let_1 I4) (@ _let_1 J2))))))))))))
% 3.70/4.03 (assert (= tptp.distinct_nat (lambda ((Xs3 tptp.list_nat)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs3)) (forall ((J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs3))) (=> (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_nat Xs3)) (=> (not (= I4 J2)) (not (= (@ _let_1 I4) (@ _let_1 J2))))))))))))
% 3.70/4.03 (assert (= tptp.distinct_int (lambda ((Xs3 tptp.list_int)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs3)) (forall ((J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs3))) (=> (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_int Xs3)) (=> (not (= I4 J2)) (not (= (@ _let_1 I4) (@ _let_1 J2))))))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_c) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_c Xs))) (let ((_let_2 (@ tptp.size_size_list_c Xs))) (=> (@ tptp.distinct_c Xs) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (= (@ _let_1 I) (@ _let_1 J)) (= I J)))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_d) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_d Xs))) (let ((_let_2 (@ tptp.size_size_list_d Xs))) (=> (@ tptp.distinct_d Xs) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (= (@ _let_1 I) (@ _let_1 J)) (= I J)))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_nat) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (let ((_let_2 (@ tptp.size_size_list_nat Xs))) (=> (@ tptp.distinct_nat Xs) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (= (@ _let_1 I) (@ _let_1 J)) (= I J)))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_int) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs))) (let ((_let_2 (@ tptp.size_size_list_int Xs))) (=> (@ tptp.distinct_int Xs) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (= (@ _let_1 I) (@ _let_1 J)) (= I J)))))))))
% 3.70/4.03 (assert (forall ((L tptp.list_P8527749157015355191n_assn) (P (-> tptp.produc6575502325842934193n_assn Bool))) (= (forall ((X2 tptp.produc6575502325842934193n_assn)) (=> (@ (@ tptp.member7957490590177025114n_assn X2) (@ tptp.set_Pr1139785259514867910n_assn L)) (@ P X2))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6829681357464350627n_assn L)) (@ P (@ (@ tptp.nth_Pr1769885009046257848n_assn L) I4)))))))
% 3.70/4.03 (assert (forall ((L tptp.list_c) (P (-> tptp.c Bool))) (= (forall ((X2 tptp.c)) (=> (@ (@ tptp.member_c X2) (@ tptp.set_c2 L)) (@ P X2))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_c L)) (@ P (@ (@ tptp.nth_c L) I4)))))))
% 3.70/4.03 (assert (forall ((L tptp.list_d) (P (-> tptp.d Bool))) (= (forall ((X2 tptp.d)) (=> (@ (@ tptp.member_d X2) (@ tptp.set_d2 L)) (@ P X2))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_d L)) (@ P (@ (@ tptp.nth_d L) I4)))))))
% 3.70/4.03 (assert (forall ((L tptp.list_nat) (P (-> tptp.nat Bool))) (= (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 L)) (@ P X2))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat L)) (@ P (@ (@ tptp.nth_nat L) I4)))))))
% 3.70/4.03 (assert (forall ((L tptp.list_int) (P (-> tptp.int Bool))) (= (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) (@ tptp.set_int2 L)) (@ P X2))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int L)) (@ P (@ (@ tptp.nth_int L) I4)))))))
% 3.70/4.03 (assert (forall ((N tptp.nat) (Xs tptp.list_P5464809261938338413at_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s1588839187904960729at_nat Xs)) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.nth_Pr1239524528086697198at_nat Xs) N)) (@ tptp.set_Pr3765526544606949372at_nat Xs)))))
% 3.70/4.03 (assert (forall ((N tptp.nat) (Xs tptp.list_P6011104703257516679at_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s5460976970255530739at_nat Xs)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) N)) (@ tptp.set_Pr5648618587558075414at_nat Xs)))))
% 3.70/4.03 (assert (forall ((N tptp.nat) (Xs tptp.list_P7985473006766602707_nat_o)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s8908918004648414271_nat_o Xs)) (@ (@ tptp.member6576561426505652726_nat_o (@ (@ tptp.nth_Pr6840583978799713108_nat_o Xs) N)) (@ tptp.set_Pr400311997697478754_nat_o Xs)))))
% 3.70/4.03 (assert (forall ((N tptp.nat) (Xs tptp.list_P8527749157015355191n_assn)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6829681357464350627n_assn Xs)) (@ (@ tptp.member7957490590177025114n_assn (@ (@ tptp.nth_Pr1769885009046257848n_assn Xs) N)) (@ tptp.set_Pr1139785259514867910n_assn Xs)))))
% 3.70/4.03 (assert (forall ((N tptp.nat) (Xs tptp.list_c)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_c Xs)) (@ (@ tptp.member_c (@ (@ tptp.nth_c Xs) N)) (@ tptp.set_c2 Xs)))))
% 3.70/4.03 (assert (forall ((N tptp.nat) (Xs tptp.list_d)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_d Xs)) (@ (@ tptp.member_d (@ (@ tptp.nth_d Xs) N)) (@ tptp.set_d2 Xs)))))
% 3.70/4.03 (assert (forall ((N tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.member_nat (@ (@ tptp.nth_nat Xs) N)) (@ tptp.set_nat2 Xs)))))
% 3.70/4.03 (assert (forall ((N tptp.nat) (Xs tptp.list_int)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs)) (@ (@ tptp.member_int (@ (@ tptp.nth_int Xs) N)) (@ tptp.set_int2 Xs)))))
% 3.70/4.03 (assert (forall ((N tptp.nat) (Xs tptp.list_P8527749157015355191n_assn) (P (-> tptp.produc6575502325842934193n_assn Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6829681357464350627n_assn Xs)) (=> (forall ((X3 tptp.produc6575502325842934193n_assn)) (=> (@ (@ tptp.member7957490590177025114n_assn X3) (@ tptp.set_Pr1139785259514867910n_assn Xs)) (@ P X3))) (@ P (@ (@ tptp.nth_Pr1769885009046257848n_assn Xs) N))))))
% 3.70/4.03 (assert (forall ((N tptp.nat) (Xs tptp.list_c) (P (-> tptp.c Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_c Xs)) (=> (forall ((X3 tptp.c)) (=> (@ (@ tptp.member_c X3) (@ tptp.set_c2 Xs)) (@ P X3))) (@ P (@ (@ tptp.nth_c Xs) N))))))
% 3.70/4.03 (assert (forall ((N tptp.nat) (Xs tptp.list_d) (P (-> tptp.d Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_d Xs)) (=> (forall ((X3 tptp.d)) (=> (@ (@ tptp.member_d X3) (@ tptp.set_d2 Xs)) (@ P X3))) (@ P (@ (@ tptp.nth_d Xs) N))))))
% 3.70/4.03 (assert (forall ((N tptp.nat) (Xs tptp.list_nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs)) (@ P X3))) (@ P (@ (@ tptp.nth_nat Xs) N))))))
% 3.70/4.03 (assert (forall ((N tptp.nat) (Xs tptp.list_int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs)) (@ P X3))) (@ P (@ (@ tptp.nth_int Xs) N))))))
% 3.70/4.03 (assert (forall ((X tptp.produc3843707927480180839at_nat) (Xs tptp.list_P5464809261938338413at_nat)) (= (@ (@ tptp.member8757157785044589968at_nat X) (@ tptp.set_Pr3765526544606949372at_nat Xs)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s1588839187904960729at_nat Xs)) (= (@ (@ tptp.nth_Pr1239524528086697198at_nat Xs) I4) X))))))
% 3.70/4.03 (assert (forall ((X tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (= (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s5460976970255530739at_nat Xs)) (= (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) I4) X))))))
% 3.70/4.03 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xs tptp.list_P7985473006766602707_nat_o)) (= (@ (@ tptp.member6576561426505652726_nat_o X) (@ tptp.set_Pr400311997697478754_nat_o Xs)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s8908918004648414271_nat_o Xs)) (= (@ (@ tptp.nth_Pr6840583978799713108_nat_o Xs) I4) X))))))
% 3.70/4.03 (assert (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (= (@ (@ tptp.member7957490590177025114n_assn X) (@ tptp.set_Pr1139785259514867910n_assn Xs)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6829681357464350627n_assn Xs)) (= (@ (@ tptp.nth_Pr1769885009046257848n_assn Xs) I4) X))))))
% 3.70/4.03 (assert (forall ((X tptp.c) (Xs tptp.list_c)) (= (@ (@ tptp.member_c X) (@ tptp.set_c2 Xs)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_c Xs)) (= (@ (@ tptp.nth_c Xs) I4) X))))))
% 3.70/4.03 (assert (forall ((X tptp.d) (Xs tptp.list_d)) (= (@ (@ tptp.member_d X) (@ tptp.set_d2 Xs)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_d Xs)) (= (@ (@ tptp.nth_d Xs) I4) X))))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (= (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I4) X))))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Xs tptp.list_int)) (= (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int Xs) I4) X))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_P5464809261938338413at_nat) (P (-> tptp.produc3843707927480180839at_nat Bool)) (X tptp.produc3843707927480180839at_nat)) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_s1588839187904960729at_nat Xs)) (@ P (@ (@ tptp.nth_Pr1239524528086697198at_nat Xs) I5)))) (=> (@ (@ tptp.member8757157785044589968at_nat X) (@ tptp.set_Pr3765526544606949372at_nat Xs)) (@ P X)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_P6011104703257516679at_nat) (P (-> tptp.product_prod_nat_nat Bool)) (X tptp.product_prod_nat_nat)) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_s5460976970255530739at_nat Xs)) (@ P (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) I5)))) (=> (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs)) (@ P X)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_P7985473006766602707_nat_o) (P (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool)) (X (-> tptp.produc3658429121746597890et_nat Bool))) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_s8908918004648414271_nat_o Xs)) (@ P (@ (@ tptp.nth_Pr6840583978799713108_nat_o Xs) I5)))) (=> (@ (@ tptp.member6576561426505652726_nat_o X) (@ tptp.set_Pr400311997697478754_nat_o Xs)) (@ P X)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (P (-> tptp.produc6575502325842934193n_assn Bool)) (X tptp.produc6575502325842934193n_assn)) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_s6829681357464350627n_assn Xs)) (@ P (@ (@ tptp.nth_Pr1769885009046257848n_assn Xs) I5)))) (=> (@ (@ tptp.member7957490590177025114n_assn X) (@ tptp.set_Pr1139785259514867910n_assn Xs)) (@ P X)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_c) (P (-> tptp.c Bool)) (X tptp.c)) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_c Xs)) (@ P (@ (@ tptp.nth_c Xs) I5)))) (=> (@ (@ tptp.member_c X) (@ tptp.set_c2 Xs)) (@ P X)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_d) (P (-> tptp.d Bool)) (X tptp.d)) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_d Xs)) (@ P (@ (@ tptp.nth_d Xs) I5)))) (=> (@ (@ tptp.member_d X) (@ tptp.set_d2 Xs)) (@ P X)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_nat) (P (-> tptp.nat Bool)) (X tptp.nat)) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_nat Xs)) (@ P (@ (@ tptp.nth_nat Xs) I5)))) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs)) (@ P X)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_int) (P (-> tptp.int Bool)) (X tptp.int)) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_int Xs)) (@ P (@ (@ tptp.nth_int Xs) I5)))) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs)) (@ P X)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (P (-> tptp.produc6575502325842934193n_assn Bool))) (= (forall ((X2 tptp.produc6575502325842934193n_assn)) (=> (@ (@ tptp.member7957490590177025114n_assn X2) (@ tptp.set_Pr1139785259514867910n_assn Xs)) (@ P X2))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6829681357464350627n_assn Xs)) (@ P (@ (@ tptp.nth_Pr1769885009046257848n_assn Xs) I4)))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_c) (P (-> tptp.c Bool))) (= (forall ((X2 tptp.c)) (=> (@ (@ tptp.member_c X2) (@ tptp.set_c2 Xs)) (@ P X2))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_c Xs)) (@ P (@ (@ tptp.nth_c Xs) I4)))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_d) (P (-> tptp.d Bool))) (= (forall ((X2 tptp.d)) (=> (@ (@ tptp.member_d X2) (@ tptp.set_d2 Xs)) (@ P X2))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_d Xs)) (@ P (@ (@ tptp.nth_d Xs) I4)))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_nat) (P (-> tptp.nat Bool))) (= (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Xs)) (@ P X2))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs)) (@ P (@ (@ tptp.nth_nat Xs) I4)))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_int) (P (-> tptp.int Bool))) (= (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) (@ tptp.set_int2 Xs)) (@ P X2))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs)) (@ P (@ (@ tptp.nth_int Xs) I4)))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (L tptp.list_P5464809261938338413at_nat) (X tptp.produc3843707927480180839at_nat) (Y tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s1588839187904960729at_nat L)) (= (@ (@ tptp.member8757157785044589968at_nat X) (@ tptp.set_Pr3765526544606949372at_nat (@ (@ (@ tptp.list_u4696772448584712917at_nat L) I) Y))) (or (= X Y) (forall ((Y5 tptp.produc3843707927480180839at_nat)) (@ (@ tptp.member8757157785044589968at_nat X) (@ tptp.set_Pr3765526544606949372at_nat (@ (@ (@ tptp.list_u4696772448584712917at_nat L) I) Y5)))))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (L tptp.list_P6011104703257516679at_nat) (X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s5460976970255530739at_nat L)) (= (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat L) I) Y))) (or (= X Y) (forall ((Y5 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat L) I) Y5)))))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (L tptp.list_P7985473006766602707_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Y (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s8908918004648414271_nat_o L)) (= (@ (@ tptp.member6576561426505652726_nat_o X) (@ tptp.set_Pr400311997697478754_nat_o (@ (@ (@ tptp.list_u6943956310655620667_nat_o L) I) Y))) (or (= X Y) (forall ((Y5 (-> tptp.produc3658429121746597890et_nat Bool))) (@ (@ tptp.member6576561426505652726_nat_o X) (@ tptp.set_Pr400311997697478754_nat_o (@ (@ (@ tptp.list_u6943956310655620667_nat_o L) I) Y5)))))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (L tptp.list_P8527749157015355191n_assn) (X tptp.produc6575502325842934193n_assn) (Y tptp.produc6575502325842934193n_assn)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6829681357464350627n_assn L)) (= (@ (@ tptp.member7957490590177025114n_assn X) (@ tptp.set_Pr1139785259514867910n_assn (@ (@ (@ tptp.list_u4534839942911652127n_assn L) I) Y))) (or (= X Y) (forall ((Y5 tptp.produc6575502325842934193n_assn)) (@ (@ tptp.member7957490590177025114n_assn X) (@ tptp.set_Pr1139785259514867910n_assn (@ (@ (@ tptp.list_u4534839942911652127n_assn L) I) Y5)))))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (L tptp.list_c) (X tptp.c) (Y tptp.c)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_c L)) (= (@ (@ tptp.member_c X) (@ tptp.set_c2 (@ (@ (@ tptp.list_update_c L) I) Y))) (or (= X Y) (forall ((Y5 tptp.c)) (@ (@ tptp.member_c X) (@ tptp.set_c2 (@ (@ (@ tptp.list_update_c L) I) Y5)))))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (L tptp.list_d) (X tptp.d) (Y tptp.d)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_d L)) (= (@ (@ tptp.member_d X) (@ tptp.set_d2 (@ (@ (@ tptp.list_update_d L) I) Y))) (or (= X Y) (forall ((Y5 tptp.d)) (@ (@ tptp.member_d X) (@ tptp.set_d2 (@ (@ (@ tptp.list_update_d L) I) Y5)))))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (L tptp.list_nat) (X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat L)) (= (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat L) I) Y))) (or (= X Y) (forall ((Y5 tptp.nat)) (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat L) I) Y5)))))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (L tptp.list_int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int L)) (= (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int L) I) Y))) (or (= X Y) (forall ((Y5 tptp.int)) (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int L) I) Y5)))))))))
% 3.70/4.03 (assert (forall ((X tptp.produc3843707927480180839at_nat) (L tptp.list_P5464809261938338413at_nat) (I tptp.nat) (Y tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat X))) (=> (@ _let_1 (@ tptp.set_Pr3765526544606949372at_nat (@ (@ (@ tptp.list_u4696772448584712917at_nat L) I) Y))) (=> (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s1588839187904960729at_nat L)) (not (= X Y))) (@ _let_1 (@ tptp.set_Pr3765526544606949372at_nat L)))))))
% 3.70/4.03 (assert (forall ((X tptp.product_prod_nat_nat) (L tptp.list_P6011104703257516679at_nat) (I tptp.nat) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X))) (=> (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat L) I) Y))) (=> (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s5460976970255530739at_nat L)) (not (= X Y))) (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat L)))))))
% 3.70/4.03 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (L tptp.list_P7985473006766602707_nat_o) (I tptp.nat) (Y (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o X))) (=> (@ _let_1 (@ tptp.set_Pr400311997697478754_nat_o (@ (@ (@ tptp.list_u6943956310655620667_nat_o L) I) Y))) (=> (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s8908918004648414271_nat_o L)) (not (= X Y))) (@ _let_1 (@ tptp.set_Pr400311997697478754_nat_o L)))))))
% 3.70/4.03 (assert (forall ((X tptp.produc6575502325842934193n_assn) (L tptp.list_P8527749157015355191n_assn) (I tptp.nat) (Y tptp.produc6575502325842934193n_assn)) (let ((_let_1 (@ tptp.member7957490590177025114n_assn X))) (=> (@ _let_1 (@ tptp.set_Pr1139785259514867910n_assn (@ (@ (@ tptp.list_u4534839942911652127n_assn L) I) Y))) (=> (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6829681357464350627n_assn L)) (not (= X Y))) (@ _let_1 (@ tptp.set_Pr1139785259514867910n_assn L)))))))
% 3.70/4.03 (assert (forall ((X tptp.c) (L tptp.list_c) (I tptp.nat) (Y tptp.c)) (let ((_let_1 (@ tptp.member_c X))) (=> (@ _let_1 (@ tptp.set_c2 (@ (@ (@ tptp.list_update_c L) I) Y))) (=> (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_c L)) (not (= X Y))) (@ _let_1 (@ tptp.set_c2 L)))))))
% 3.70/4.03 (assert (forall ((X tptp.d) (L tptp.list_d) (I tptp.nat) (Y tptp.d)) (let ((_let_1 (@ tptp.member_d X))) (=> (@ _let_1 (@ tptp.set_d2 (@ (@ (@ tptp.list_update_d L) I) Y))) (=> (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_d L)) (not (= X Y))) (@ _let_1 (@ tptp.set_d2 L)))))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (L tptp.list_nat) (I tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (=> (@ _let_1 (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat L) I) Y))) (=> (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat L)) (not (= X Y))) (@ _let_1 (@ tptp.set_nat2 L)))))))
% 3.70/4.03 (assert (forall ((X tptp.int) (L tptp.list_int) (I tptp.nat) (Y tptp.int)) (let ((_let_1 (@ tptp.member_int X))) (=> (@ _let_1 (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int L) I) Y))) (=> (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int L)) (not (= X Y))) (@ _let_1 (@ tptp.set_int2 L)))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (L tptp.list_P5464809261938338413at_nat) (X tptp.produc3843707927480180839at_nat) (Y tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat X))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s1588839187904960729at_nat L)) (= (@ _let_1 (@ tptp.set_Pr3765526544606949372at_nat (@ (@ (@ tptp.list_u4696772448584712917at_nat L) I) Y))) (or (= X Y) (and (@ _let_1 (@ tptp.set_Pr3765526544606949372at_nat L)) (forall ((Y5 tptp.produc3843707927480180839at_nat)) (@ (@ tptp.member8757157785044589968at_nat X) (@ tptp.set_Pr3765526544606949372at_nat (@ (@ (@ tptp.list_u4696772448584712917at_nat L) I) Y5)))))))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (L tptp.list_P6011104703257516679at_nat) (X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s5460976970255530739at_nat L)) (= (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat L) I) Y))) (or (= X Y) (and (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat L)) (forall ((Y5 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat L) I) Y5)))))))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (L tptp.list_P7985473006766602707_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Y (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o X))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s8908918004648414271_nat_o L)) (= (@ _let_1 (@ tptp.set_Pr400311997697478754_nat_o (@ (@ (@ tptp.list_u6943956310655620667_nat_o L) I) Y))) (or (= X Y) (and (@ _let_1 (@ tptp.set_Pr400311997697478754_nat_o L)) (forall ((Y5 (-> tptp.produc3658429121746597890et_nat Bool))) (@ (@ tptp.member6576561426505652726_nat_o X) (@ tptp.set_Pr400311997697478754_nat_o (@ (@ (@ tptp.list_u6943956310655620667_nat_o L) I) Y5)))))))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (L tptp.list_P8527749157015355191n_assn) (X tptp.produc6575502325842934193n_assn) (Y tptp.produc6575502325842934193n_assn)) (let ((_let_1 (@ tptp.member7957490590177025114n_assn X))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6829681357464350627n_assn L)) (= (@ _let_1 (@ tptp.set_Pr1139785259514867910n_assn (@ (@ (@ tptp.list_u4534839942911652127n_assn L) I) Y))) (or (= X Y) (and (@ _let_1 (@ tptp.set_Pr1139785259514867910n_assn L)) (forall ((Y5 tptp.produc6575502325842934193n_assn)) (@ (@ tptp.member7957490590177025114n_assn X) (@ tptp.set_Pr1139785259514867910n_assn (@ (@ (@ tptp.list_u4534839942911652127n_assn L) I) Y5)))))))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (L tptp.list_c) (X tptp.c) (Y tptp.c)) (let ((_let_1 (@ tptp.member_c X))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_c L)) (= (@ _let_1 (@ tptp.set_c2 (@ (@ (@ tptp.list_update_c L) I) Y))) (or (= X Y) (and (@ _let_1 (@ tptp.set_c2 L)) (forall ((Y5 tptp.c)) (@ (@ tptp.member_c X) (@ tptp.set_c2 (@ (@ (@ tptp.list_update_c L) I) Y5)))))))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (L tptp.list_d) (X tptp.d) (Y tptp.d)) (let ((_let_1 (@ tptp.member_d X))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_d L)) (= (@ _let_1 (@ tptp.set_d2 (@ (@ (@ tptp.list_update_d L) I) Y))) (or (= X Y) (and (@ _let_1 (@ tptp.set_d2 L)) (forall ((Y5 tptp.d)) (@ (@ tptp.member_d X) (@ tptp.set_d2 (@ (@ (@ tptp.list_update_d L) I) Y5)))))))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (L tptp.list_nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat L)) (= (@ _let_1 (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat L) I) Y))) (or (= X Y) (and (@ _let_1 (@ tptp.set_nat2 L)) (forall ((Y5 tptp.nat)) (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat L) I) Y5)))))))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (L tptp.list_int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.member_int X))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int L)) (= (@ _let_1 (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int L) I) Y))) (or (= X Y) (and (@ _let_1 (@ tptp.set_int2 L)) (forall ((Y5 tptp.int)) (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int L) I) Y5)))))))))))
% 3.70/4.03 (assert (forall ((N tptp.nat) (Xs tptp.list_P5464809261938338413at_nat) (X tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s1588839187904960729at_nat Xs)) (@ (@ tptp.member8757157785044589968at_nat X) (@ tptp.set_Pr3765526544606949372at_nat (@ (@ (@ tptp.list_u4696772448584712917at_nat Xs) N) X))))))
% 3.70/4.03 (assert (forall ((N tptp.nat) (Xs tptp.list_P6011104703257516679at_nat) (X tptp.product_prod_nat_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s5460976970255530739at_nat Xs)) (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat Xs) N) X))))))
% 3.70/4.03 (assert (forall ((N tptp.nat) (Xs tptp.list_P7985473006766602707_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s8908918004648414271_nat_o Xs)) (@ (@ tptp.member6576561426505652726_nat_o X) (@ tptp.set_Pr400311997697478754_nat_o (@ (@ (@ tptp.list_u6943956310655620667_nat_o Xs) N) X))))))
% 3.70/4.03 (assert (forall ((N tptp.nat) (Xs tptp.list_P8527749157015355191n_assn) (X tptp.produc6575502325842934193n_assn)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6829681357464350627n_assn Xs)) (@ (@ tptp.member7957490590177025114n_assn X) (@ tptp.set_Pr1139785259514867910n_assn (@ (@ (@ tptp.list_u4534839942911652127n_assn Xs) N) X))))))
% 3.70/4.03 (assert (forall ((N tptp.nat) (Xs tptp.list_c) (X tptp.c)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_c Xs)) (@ (@ tptp.member_c X) (@ tptp.set_c2 (@ (@ (@ tptp.list_update_c Xs) N) X))))))
% 3.70/4.03 (assert (forall ((N tptp.nat) (Xs tptp.list_d) (X tptp.d)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_d Xs)) (@ (@ tptp.member_d X) (@ tptp.set_d2 (@ (@ (@ tptp.list_update_d Xs) N) X))))))
% 3.70/4.03 (assert (forall ((N tptp.nat) (Xs tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs) N) X))))))
% 3.70/4.03 (assert (forall ((N tptp.nat) (Xs tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs)) (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs) N) X))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (N tptp.nat) (X tptp.produc6575502325842934193n_assn)) (=> (@ tptp.distin4809818325527169450n_assn Xs) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6829681357464350627n_assn Xs)) (= (@ tptp.set_Pr1139785259514867910n_assn (@ (@ (@ tptp.list_u4534839942911652127n_assn Xs) N) X)) (@ (@ tptp.insert5290817439147925377n_assn X) (@ (@ tptp.minus_2301194108115264760n_assn (@ tptp.set_Pr1139785259514867910n_assn Xs)) (@ (@ tptp.insert5290817439147925377n_assn (@ (@ tptp.nth_Pr1769885009046257848n_assn Xs) N)) tptp.bot_bo1176836662018730877n_assn))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_c) (N tptp.nat) (X tptp.c)) (=> (@ tptp.distinct_c Xs) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_c Xs)) (= (@ tptp.set_c2 (@ (@ (@ tptp.list_update_c Xs) N) X)) (@ (@ tptp.insert_c X) (@ (@ tptp.minus_minus_set_c (@ tptp.set_c2 Xs)) (@ (@ tptp.insert_c (@ (@ tptp.nth_c Xs) N)) tptp.bot_bot_set_c))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_d) (N tptp.nat) (X tptp.d)) (=> (@ tptp.distinct_d Xs) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_d Xs)) (= (@ tptp.set_d2 (@ (@ (@ tptp.list_update_d Xs) N) X)) (@ (@ tptp.insert_d X) (@ (@ tptp.minus_minus_set_d (@ tptp.set_d2 Xs)) (@ (@ tptp.insert_d (@ (@ tptp.nth_d Xs) N)) tptp.bot_bot_set_d))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_P5464809261938338413at_nat) (N tptp.nat) (X tptp.produc3843707927480180839at_nat)) (=> (@ tptp.distin5355857245021852384at_nat Xs) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s1588839187904960729at_nat Xs)) (= (@ tptp.set_Pr3765526544606949372at_nat (@ (@ (@ tptp.list_u4696772448584712917at_nat Xs) N) X)) (@ (@ tptp.insert9069300056098147895at_nat X) (@ (@ tptp.minus_3314409938677909166at_nat (@ tptp.set_Pr3765526544606949372at_nat Xs)) (@ (@ tptp.insert9069300056098147895at_nat (@ (@ tptp.nth_Pr1239524528086697198at_nat Xs) N)) tptp.bot_bo228742789529271731at_nat))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_P6011104703257516679at_nat) (N tptp.nat) (X tptp.product_prod_nat_nat)) (=> (@ tptp.distin6923225563576452346at_nat Xs) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s5460976970255530739at_nat Xs)) (= (@ tptp.set_Pr5648618587558075414at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat Xs) N) X)) (@ (@ tptp.insert8211810215607154385at_nat X) (@ (@ tptp.minus_1356011639430497352at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs)) (@ (@ tptp.insert8211810215607154385at_nat (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) N)) tptp.bot_bo2099793752762293965at_nat))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_o) (N tptp.nat) (X Bool)) (=> (@ tptp.distinct_o Xs) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs)) (= (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o Xs) N) X)) (@ (@ tptp.insert_o2 X) (@ (@ tptp.minus_minus_set_o (@ tptp.set_o2 Xs)) (@ (@ tptp.insert_o2 (@ (@ tptp.nth_o Xs) N)) tptp.bot_bot_set_o))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_int) (N tptp.nat) (X tptp.int)) (=> (@ tptp.distinct_int Xs) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs)) (= (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs) N) X)) (@ (@ tptp.insert_int2 X) (@ (@ tptp.minus_minus_set_int (@ tptp.set_int2 Xs)) (@ (@ tptp.insert_int2 (@ (@ tptp.nth_int Xs) N)) tptp.bot_bot_set_int))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_nat) (N tptp.nat) (X tptp.nat)) (=> (@ tptp.distinct_nat Xs) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (= (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs) N) X)) (@ (@ tptp.insert_nat2 X) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_nat2 Xs)) (@ (@ tptp.insert_nat2 (@ (@ tptp.nth_nat Xs) N)) tptp.bot_bot_set_nat))))))))
% 3.70/4.03 (assert (forall ((X1 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (X22 tptp.produc8923325533196201883nteger) (Y1 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (Y22 tptp.produc8923325533196201883nteger)) (= (= (@ (@ tptp.produc8603105652947943368nteger X1) X22) (@ (@ tptp.produc8603105652947943368nteger Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 3.70/4.03 (assert (forall ((X1 (-> tptp.produc3658429121746597890et_nat Bool)) (X22 tptp.produc3658429121746597890et_nat) (Y1 (-> tptp.produc3658429121746597890et_nat Bool)) (Y22 tptp.produc3658429121746597890et_nat)) (= (= (@ (@ tptp.produc5001842942810119800et_nat X1) X22) (@ (@ tptp.produc5001842942810119800et_nat Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 3.70/4.03 (assert (forall ((X1 (-> tptp.produc3658429121746597890et_nat Bool)) (X22 tptp.produc3925858234332021118et_nat) (Y1 (-> tptp.produc3658429121746597890et_nat Bool)) (Y22 tptp.produc3925858234332021118et_nat)) (= (= (@ (@ tptp.produc2245416461498447860et_nat X1) X22) (@ (@ tptp.produc2245416461498447860et_nat Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 3.70/4.03 (assert (forall ((X1 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (X22 tptp.product_prod_int_int) (Y1 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y22 tptp.product_prod_int_int)) (= (= (@ (@ tptp.produc5700946648718959541nt_int X1) X22) (@ (@ tptp.produc5700946648718959541nt_int Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 3.70/4.03 (assert (forall ((X1 (-> tptp.int tptp.option6357759511663192854e_term)) (X22 tptp.product_prod_int_int) (Y1 (-> tptp.int tptp.option6357759511663192854e_term)) (Y22 tptp.product_prod_int_int)) (= (= (@ (@ tptp.produc4305682042979456191nt_int X1) X22) (@ (@ tptp.produc4305682042979456191nt_int Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 3.70/4.03 (assert (forall ((A2 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B2 tptp.produc8923325533196201883nteger) (A7 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B6 tptp.produc8923325533196201883nteger)) (= (= (@ (@ tptp.produc8603105652947943368nteger A2) B2) (@ (@ tptp.produc8603105652947943368nteger A7) B6)) (and (= A2 A7) (= B2 B6)))))
% 3.70/4.03 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.produc3658429121746597890et_nat) (A7 (-> tptp.produc3658429121746597890et_nat Bool)) (B6 tptp.produc3658429121746597890et_nat)) (= (= (@ (@ tptp.produc5001842942810119800et_nat A2) B2) (@ (@ tptp.produc5001842942810119800et_nat A7) B6)) (and (= A2 A7) (= B2 B6)))))
% 3.70/4.03 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.produc3925858234332021118et_nat) (A7 (-> tptp.produc3658429121746597890et_nat Bool)) (B6 tptp.produc3925858234332021118et_nat)) (= (= (@ (@ tptp.produc2245416461498447860et_nat A2) B2) (@ (@ tptp.produc2245416461498447860et_nat A7) B6)) (and (= A2 A7) (= B2 B6)))))
% 3.70/4.03 (assert (forall ((A2 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B2 tptp.product_prod_int_int) (A7 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B6 tptp.product_prod_int_int)) (= (= (@ (@ tptp.produc5700946648718959541nt_int A2) B2) (@ (@ tptp.produc5700946648718959541nt_int A7) B6)) (and (= A2 A7) (= B2 B6)))))
% 3.70/4.03 (assert (forall ((A2 (-> tptp.int tptp.option6357759511663192854e_term)) (B2 tptp.product_prod_int_int) (A7 (-> tptp.int tptp.option6357759511663192854e_term)) (B6 tptp.product_prod_int_int)) (= (= (@ (@ tptp.produc4305682042979456191nt_int A2) B2) (@ (@ tptp.produc4305682042979456191nt_int A7) B6)) (and (= A2 A7) (= B2 B6)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (= (@ tptp.distinct_int (@ (@ tptp.union_int Xs) Ys)) (@ tptp.distinct_int Ys))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (= (@ tptp.distinct_nat (@ (@ tptp.union_nat Xs) Ys)) (@ tptp.distinct_nat Ys))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (X tptp.produc6575502325842934193n_assn)) (=> (@ tptp.distin4809818325527169450n_assn Xs) (= (@ tptp.set_Pr1139785259514867910n_assn (@ (@ tptp.remove1670527618125605709n_assn X) Xs)) (@ (@ tptp.minus_2301194108115264760n_assn (@ tptp.set_Pr1139785259514867910n_assn Xs)) (@ (@ tptp.insert5290817439147925377n_assn X) tptp.bot_bo1176836662018730877n_assn))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_P5464809261938338413at_nat) (X tptp.produc3843707927480180839at_nat)) (=> (@ tptp.distin5355857245021852384at_nat Xs) (= (@ tptp.set_Pr3765526544606949372at_nat (@ (@ tptp.remove8895909992688781315at_nat X) Xs)) (@ (@ tptp.minus_3314409938677909166at_nat (@ tptp.set_Pr3765526544606949372at_nat Xs)) (@ (@ tptp.insert9069300056098147895at_nat X) tptp.bot_bo228742789529271731at_nat))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_P6011104703257516679at_nat) (X tptp.product_prod_nat_nat)) (=> (@ tptp.distin6923225563576452346at_nat Xs) (= (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.remove5766854097993331357at_nat X) Xs)) (@ (@ tptp.minus_1356011639430497352at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs)) (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_o) (X Bool)) (=> (@ tptp.distinct_o Xs) (= (@ tptp.set_o2 (@ (@ tptp.remove1_o X) Xs)) (@ (@ tptp.minus_minus_set_o (@ tptp.set_o2 Xs)) (@ (@ tptp.insert_o2 X) tptp.bot_bot_set_o))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_int) (X tptp.int)) (=> (@ tptp.distinct_int Xs) (= (@ tptp.set_int2 (@ (@ tptp.remove1_int X) Xs)) (@ (@ tptp.minus_minus_set_int (@ tptp.set_int2 Xs)) (@ (@ tptp.insert_int2 X) tptp.bot_bot_set_int))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_nat) (X tptp.nat)) (=> (@ tptp.distinct_nat Xs) (= (@ tptp.set_nat2 (@ (@ tptp.remove1_nat X) Xs)) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_nat2 Xs)) (@ (@ tptp.insert_nat2 X) tptp.bot_bot_set_nat))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_int)) (= (@ tptp.is_empty_int (@ tptp.set_int2 Xs)) (@ tptp.null_int Xs))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_nat)) (= (@ tptp.is_empty_nat (@ tptp.set_nat2 Xs)) (@ tptp.null_nat Xs))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn)) (= (@ tptp.is_emp7749065762491207043n_assn (@ tptp.set_Pr1139785259514867910n_assn Xs)) (@ tptp.null_P7596217980778516671n_assn Xs))))
% 3.70/4.03 (assert (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (= (@ tptp.set_Pr1139785259514867910n_assn (@ (@ tptp.remove1763081955827946941n_assn X) Xs)) (@ (@ tptp.minus_2301194108115264760n_assn (@ tptp.set_Pr1139785259514867910n_assn Xs)) (@ (@ tptp.insert5290817439147925377n_assn X) tptp.bot_bo1176836662018730877n_assn)))))
% 3.70/4.03 (assert (forall ((X tptp.produc3843707927480180839at_nat) (Xs tptp.list_P5464809261938338413at_nat)) (= (@ tptp.set_Pr3765526544606949372at_nat (@ (@ tptp.remove4908499291543849587at_nat X) Xs)) (@ (@ tptp.minus_3314409938677909166at_nat (@ tptp.set_Pr3765526544606949372at_nat Xs)) (@ (@ tptp.insert9069300056098147895at_nat X) tptp.bot_bo228742789529271731at_nat)))))
% 3.70/4.03 (assert (forall ((X tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (= (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.remove3673390508374433037at_nat X) Xs)) (@ (@ tptp.minus_1356011639430497352at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs)) (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat)))))
% 3.70/4.03 (assert (forall ((X Bool) (Xs tptp.list_o)) (= (@ tptp.set_o2 (@ (@ tptp.removeAll_o X) Xs)) (@ (@ tptp.minus_minus_set_o (@ tptp.set_o2 Xs)) (@ (@ tptp.insert_o2 X) tptp.bot_bot_set_o)))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Xs tptp.list_int)) (= (@ tptp.set_int2 (@ (@ tptp.removeAll_int X) Xs)) (@ (@ tptp.minus_minus_set_int (@ tptp.set_int2 Xs)) (@ (@ tptp.insert_int2 X) tptp.bot_bot_set_int)))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (= (@ tptp.set_nat2 (@ (@ tptp.removeAll_nat X) Xs)) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_nat2 Xs)) (@ (@ tptp.insert_nat2 X) tptp.bot_bot_set_nat)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_s1210847774152347623at_nat) (Ys tptp.list_s1210847774152347623at_nat) (R2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat Xs) Ys)) (@ tptp.listre8180072825634266816at_nat R2)) (exists ((Y5 tptp.set_Pr1261947904930325089at_nat) (N2 tptp.nat)) (and (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ (@ tptp.nth_se5679702624988424552at_nat Xs) N2)) Y5)) R2) (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s8736152011456118867at_nat Xs)) (= Ys (@ (@ (@ tptp.list_u8444657558853818831at_nat Xs) N2) Y5)))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_c) (R2 tptp.set_Product_prod_c_c)) (= (@ (@ tptp.member7012247553653173456list_c (@ (@ tptp.produc5515445818230282391list_c Xs) Ys)) (@ tptp.listrel1_c R2)) (exists ((Y5 tptp.c) (N2 tptp.nat)) (and (@ (@ tptp.member5074992359041316560od_c_c (@ (@ tptp.product_Pair_c_c (@ (@ tptp.nth_c Xs) N2)) Y5)) R2) (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_c Xs)) (= Ys (@ (@ (@ tptp.list_update_c Xs) N2) Y5)))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_d) (Ys tptp.list_d) (R2 tptp.set_Product_prod_d_d)) (= (@ (@ tptp.member1810801192463332112list_d (@ (@ tptp.produc242965421297323863list_d Xs) Ys)) (@ tptp.listrel1_d R2)) (exists ((Y5 tptp.d) (N2 tptp.nat)) (and (@ (@ tptp.member2287536781371869328od_d_d (@ (@ tptp.product_Pair_d_d (@ (@ tptp.nth_d Xs) N2)) Y5)) R2) (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_d Xs)) (= Ys (@ (@ (@ tptp.list_update_d Xs) N2) Y5)))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Xs) Ys)) (@ tptp.listrel1_nat R2)) (exists ((Y5 tptp.nat) (N2 tptp.nat)) (and (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.nth_nat Xs) N2)) Y5)) R2) (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs)) (= Ys (@ (@ (@ tptp.list_update_nat Xs) N2) Y5)))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int) (R2 tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Xs) Ys)) (@ tptp.listrel1_int R2)) (exists ((Y5 tptp.int) (N2 tptp.nat)) (and (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int (@ (@ tptp.nth_int Xs) N2)) Y5)) R2) (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_int Xs)) (= Ys (@ (@ (@ tptp.list_update_int Xs) N2) Y5)))))))
% 3.70/4.03 (assert (forall ((X tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (= (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.insert8944034826898310173at_nat X) Xs)) (@ (@ tptp.insert8211810215607154385at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs)))))
% 3.70/4.03 (assert (forall ((X tptp.produc3843707927480180839at_nat) (Xs tptp.list_P5464809261938338413at_nat)) (= (@ tptp.set_Pr3765526544606949372at_nat (@ (@ tptp.insert4149901806602606979at_nat X) Xs)) (@ (@ tptp.insert9069300056098147895at_nat X) (@ tptp.set_Pr3765526544606949372at_nat Xs)))))
% 3.70/4.03 (assert (forall ((X Bool) (Xs tptp.list_o)) (= (@ tptp.set_o2 (@ (@ tptp.insert_o X) Xs)) (@ (@ tptp.insert_o2 X) (@ tptp.set_o2 Xs)))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Xs tptp.list_int)) (= (@ tptp.set_int2 (@ (@ tptp.insert_int X) Xs)) (@ (@ tptp.insert_int2 X) (@ tptp.set_int2 Xs)))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (= (@ tptp.set_nat2 (@ (@ tptp.insert_nat X) Xs)) (@ (@ tptp.insert_nat2 X) (@ tptp.set_nat2 Xs)))))
% 3.70/4.03 (assert (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (= (@ tptp.set_Pr1139785259514867910n_assn (@ (@ tptp.insert3246601298802261197n_assn X) Xs)) (@ (@ tptp.insert5290817439147925377n_assn X) (@ tptp.set_Pr1139785259514867910n_assn Xs)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_c) (R2 tptp.set_Product_prod_c_c)) (= (@ (@ tptp.member7012247553653173456list_c (@ (@ tptp.produc5515445818230282391list_c Xs) Ys)) (@ tptp.listrel_c_c R2)) (and (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_c Ys)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_c Xs)) (@ (@ tptp.member5074992359041316560od_c_c (@ (@ tptp.product_Pair_c_c (@ (@ tptp.nth_c Xs) N2)) (@ (@ tptp.nth_c Ys) N2))) R2)))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_d) (R2 tptp.set_Product_prod_c_d)) (= (@ (@ tptp.member7083281593699519441list_d (@ (@ tptp.produc5515445822533511192list_d Xs) Ys)) (@ tptp.listrel_c_d R2)) (and (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_d Ys)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_c Xs)) (@ (@ tptp.member5074992363344545361od_c_d (@ (@ tptp.product_Pair_c_d (@ (@ tptp.nth_c Xs) N2)) (@ (@ tptp.nth_d Ys) N2))) R2)))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_nat) (R2 tptp.set_Pr6903500605879609269_c_nat)) (= (@ (@ tptp.member6184937725913850668st_nat (@ (@ tptp.produc6126748735280710287st_nat Xs) Ys)) (@ tptp.listrel_c_nat R2)) (and (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_nat Ys)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_c Xs)) (@ (@ tptp.member8195077246299207702_c_nat (@ (@ tptp.product_Pair_c_nat (@ (@ tptp.nth_c Xs) N2)) (@ (@ tptp.nth_nat Ys) N2))) R2)))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_int) (R2 tptp.set_Pr4413417460947882513_c_int)) (= (@ (@ tptp.member3694854580982123912st_int (@ (@ tptp.produc1948897715771513579st_int Xs) Ys)) (@ tptp.listrel_c_int R2)) (and (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_int Ys)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_c Xs)) (@ (@ tptp.member4017226226790010994_c_int (@ (@ tptp.product_Pair_c_int (@ (@ tptp.nth_c Xs) N2)) (@ (@ tptp.nth_int Ys) N2))) R2)))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_d) (Ys tptp.list_c) (R2 tptp.set_Product_prod_d_c)) (= (@ (@ tptp.member1739767152416986127list_c (@ (@ tptp.produc242965416994095062list_c Xs) Ys)) (@ tptp.listrel_d_c R2)) (and (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_c Ys)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_d Xs)) (@ (@ tptp.member2287536777068640527od_d_c (@ (@ tptp.product_Pair_d_c (@ (@ tptp.nth_d Xs) N2)) (@ (@ tptp.nth_c Ys) N2))) R2)))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_d) (Ys tptp.list_d) (R2 tptp.set_Product_prod_d_d)) (= (@ (@ tptp.member1810801192463332112list_d (@ (@ tptp.produc242965421297323863list_d Xs) Ys)) (@ tptp.listrel_d_d R2)) (and (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_d Ys)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_d Xs)) (@ (@ tptp.member2287536781371869328od_d_d (@ (@ tptp.product_Pair_d_d (@ (@ tptp.nth_d Xs) N2)) (@ (@ tptp.nth_d Ys) N2))) R2)))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_d) (Ys tptp.list_nat) (R2 tptp.set_Pr3276347184212964150_d_nat)) (= (@ (@ tptp.member6851837201453759021st_nat (@ (@ tptp.produc6793648210820618640st_nat Xs) Ys)) (@ tptp.listrel_d_nat R2)) (and (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_nat Ys)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_d Xs)) (@ (@ tptp.member207149538400826391_d_nat (@ (@ tptp.product_Pair_d_nat (@ (@ tptp.nth_d Xs) N2)) (@ (@ tptp.nth_nat Ys) N2))) R2)))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_d) (Ys tptp.list_int) (R2 tptp.set_Pr786264039281237394_d_int)) (= (@ (@ tptp.member4361754056522032265st_int (@ (@ tptp.produc2615797191311421932st_int Xs) Ys)) (@ tptp.listrel_d_int R2)) (and (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_int Ys)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_d Xs)) (@ (@ tptp.member5252670555746405491_d_int (@ (@ tptp.product_Pair_d_int (@ (@ tptp.nth_d Xs) N2)) (@ (@ tptp.nth_int Ys) N2))) R2)))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_c) (R2 tptp.set_Pr4335409928928841947_nat_c)) (= (@ (@ tptp.member6074218473364765234list_c (@ (@ tptp.produc7723716018658481613list_c Xs) Ys)) (@ tptp.listrel_nat_c R2)) (and (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_c Ys)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.member8962352060716553276_nat_c (@ (@ tptp.product_Pair_nat_c (@ (@ tptp.nth_nat Xs) N2)) (@ (@ tptp.nth_c Ys) N2))) R2)))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_d) (R2 tptp.set_Pr4406443968975187932_nat_d)) (= (@ (@ tptp.member6145252513411111219list_d (@ (@ tptp.produc7723716022961710414list_d Xs) Ys)) (@ tptp.listrel_nat_d R2)) (and (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_d Ys)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.member8962352065019782077_nat_d (@ (@ tptp.product_Pair_nat_d (@ (@ tptp.nth_nat Xs) N2)) (@ (@ tptp.nth_d Ys) N2))) R2)))))))
% 3.70/4.03 (assert (forall ((P tptp.assn) (B2 Bool)) (let ((_let_1 (@ tptp.entails P))) (= (@ _let_1 (@ tptp.pure_assn B2)) (and (forall ((H3 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P) H3) B2)) (@ _let_1 tptp.one_one_assn))))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger tptp.one_one_Code_integer) A2) A2)))
% 3.70/4.03 (assert (forall ((A2 tptp.assn)) (= (@ (@ tptp.times_times_assn tptp.one_one_assn) A2) A2)))
% 3.70/4.03 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A2) A2)))
% 3.70/4.03 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A2) A2)))
% 3.70/4.03 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A2) A2)))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger A2) tptp.one_one_Code_integer) A2)))
% 3.70/4.03 (assert (forall ((A2 tptp.assn)) (= (@ (@ tptp.times_times_assn A2) tptp.one_one_assn) A2)))
% 3.70/4.03 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.times_times_rat A2) tptp.one_one_rat) A2)))
% 3.70/4.03 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.times_times_nat A2) tptp.one_one_nat) A2)))
% 3.70/4.03 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.times_times_int A2) tptp.one_one_int) A2)))
% 3.70/4.03 (assert (forall ((A2 tptp.produc3843707927480180839at_nat) (B2 tptp.produc3843707927480180839at_nat) (Xs tptp.list_P5464809261938338413at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat A2))) (=> (not (= A2 B2)) (= (@ _let_1 (@ tptp.set_Pr3765526544606949372at_nat (@ (@ tptp.remove8895909992688781315at_nat B2) Xs))) (@ _let_1 (@ tptp.set_Pr3765526544606949372at_nat Xs)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.product_prod_nat_nat) (B2 tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat A2))) (=> (not (= A2 B2)) (= (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.remove5766854097993331357at_nat B2) Xs))) (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat Xs)))))))
% 3.70/4.03 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 (-> tptp.produc3658429121746597890et_nat Bool)) (Xs tptp.list_P7985473006766602707_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o A2))) (=> (not (= A2 B2)) (= (@ _let_1 (@ tptp.set_Pr400311997697478754_nat_o (@ (@ tptp.remove4235003712227595625_nat_o B2) Xs))) (@ _let_1 (@ tptp.set_Pr400311997697478754_nat_o Xs)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int) (Xs tptp.list_int)) (let ((_let_1 (@ tptp.member_int A2))) (=> (not (= A2 B2)) (= (@ _let_1 (@ tptp.set_int2 (@ (@ tptp.remove1_int B2) Xs))) (@ _let_1 (@ tptp.set_int2 Xs)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ tptp.member_nat A2))) (=> (not (= A2 B2)) (= (@ _let_1 (@ tptp.set_nat2 (@ (@ tptp.remove1_nat B2) Xs))) (@ _let_1 (@ tptp.set_nat2 Xs)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.produc6575502325842934193n_assn) (B2 tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ tptp.member7957490590177025114n_assn A2))) (=> (not (= A2 B2)) (= (@ _let_1 (@ tptp.set_Pr1139785259514867910n_assn (@ (@ tptp.remove1670527618125605709n_assn B2) Xs))) (@ _let_1 (@ tptp.set_Pr1139785259514867910n_assn Xs)))))))
% 3.70/4.03 (assert (forall ((X tptp.produc3843707927480180839at_nat) (Xs tptp.list_P5464809261938338413at_nat)) (=> (not (@ (@ tptp.member8757157785044589968at_nat X) (@ tptp.set_Pr3765526544606949372at_nat Xs))) (= (@ (@ tptp.remove4908499291543849587at_nat X) Xs) Xs))))
% 3.70/4.03 (assert (forall ((X tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (=> (not (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs))) (= (@ (@ tptp.remove3673390508374433037at_nat X) Xs) Xs))))
% 3.70/4.03 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xs tptp.list_P7985473006766602707_nat_o)) (=> (not (@ (@ tptp.member6576561426505652726_nat_o X) (@ tptp.set_Pr400311997697478754_nat_o Xs))) (= (@ (@ tptp.remove7604696131425036249_nat_o X) Xs) Xs))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Xs tptp.list_int)) (=> (not (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs))) (= (@ (@ tptp.removeAll_int X) Xs) Xs))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (=> (not (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs))) (= (@ (@ tptp.removeAll_nat X) Xs) Xs))))
% 3.70/4.03 (assert (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (=> (not (@ (@ tptp.member7957490590177025114n_assn X) (@ tptp.set_Pr1139785259514867910n_assn Xs))) (= (@ (@ tptp.remove1763081955827946941n_assn X) Xs) Xs))))
% 3.70/4.03 (assert (= (@ tptp.pure_assn true) tptp.one_one_assn))
% 3.70/4.03 (assert (forall ((P Bool)) (= (= (@ tptp.pure_assn P) tptp.one_one_assn) P)))
% 3.70/4.03 (assert (forall ((A tptp.assn)) (@ (@ tptp.entailst A) tptp.one_one_assn)))
% 3.70/4.03 (assert (forall ((X tptp.produc3843707927480180839at_nat) (Xs tptp.list_P5464809261938338413at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X) (@ tptp.set_Pr3765526544606949372at_nat Xs)) (= (@ (@ tptp.insert4149901806602606979at_nat X) Xs) Xs))))
% 3.70/4.03 (assert (forall ((X tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs)) (= (@ (@ tptp.insert8944034826898310173at_nat X) Xs) Xs))))
% 3.70/4.03 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xs tptp.list_P7985473006766602707_nat_o)) (=> (@ (@ tptp.member6576561426505652726_nat_o X) (@ tptp.set_Pr400311997697478754_nat_o Xs)) (= (@ (@ tptp.insert8021100735160035049_nat_o X) Xs) Xs))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Xs tptp.list_int)) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs)) (= (@ (@ tptp.insert_int X) Xs) Xs))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs)) (= (@ (@ tptp.insert_nat X) Xs) Xs))))
% 3.70/4.03 (assert (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (=> (@ (@ tptp.member7957490590177025114n_assn X) (@ tptp.set_Pr1139785259514867910n_assn Xs)) (= (@ (@ tptp.insert3246601298802261197n_assn X) Xs) Xs))))
% 3.70/4.03 (assert (not (= tptp.bot_bot_assn tptp.one_one_assn)))
% 3.70/4.03 (assert (forall ((X tptp.int) (Xs tptp.list_int)) (= (@ tptp.distinct_int (@ (@ tptp.insert_int X) Xs)) (@ tptp.distinct_int Xs))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (= (@ tptp.distinct_nat (@ (@ tptp.insert_nat X) Xs)) (@ tptp.distinct_nat Xs))))
% 3.70/4.03 (assert (forall ((B2 Bool) (Q tptp.assn)) (= (@ (@ tptp.entails (@ tptp.pure_assn B2)) Q) (=> B2 (@ (@ tptp.entails tptp.one_one_assn) Q)))))
% 3.70/4.03 (assert (forall ((X tptp.code_integer)) (= (= tptp.one_one_Code_integer X) (= X tptp.one_one_Code_integer))))
% 3.70/4.03 (assert (forall ((X tptp.assn)) (= (= tptp.one_one_assn X) (= X tptp.one_one_assn))))
% 3.70/4.03 (assert (forall ((X tptp.rat)) (= (= tptp.one_one_rat X) (= X tptp.one_one_rat))))
% 3.70/4.03 (assert (forall ((X tptp.nat)) (= (= tptp.one_one_nat X) (= X tptp.one_one_nat))))
% 3.70/4.03 (assert (forall ((X tptp.int)) (= (= tptp.one_one_int X) (= X tptp.one_one_int))))
% 3.70/4.03 (assert (forall ((X tptp.produc2732055786443039994et_nat)) (not (forall ((P5 (-> tptp.produc3658429121746597890et_nat Bool)) (Q4 (-> tptp.produc3658429121746597890et_nat Bool)) (H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (not (= X (@ (@ tptp.produc2245416461498447860et_nat P5) (@ (@ tptp.produc5001842942810119800et_nat Q4) (@ (@ tptp.produc7507926704131184380et_nat H) As)))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_c) (R2 tptp.set_Product_prod_c_c)) (=> (@ (@ tptp.member7012247553653173456list_c (@ (@ tptp.produc5515445818230282391list_c Xs) Ys)) (@ tptp.listrel1_c R2)) (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_c Ys)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_d) (Ys tptp.list_d) (R2 tptp.set_Product_prod_d_d)) (=> (@ (@ tptp.member1810801192463332112list_d (@ (@ tptp.produc242965421297323863list_d Xs) Ys)) (@ tptp.listrel1_d R2)) (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_d Ys)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Xs) Ys)) (@ tptp.listrel1_nat R2)) (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int) (R2 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Xs) Ys)) (@ tptp.listrel1_int R2)) (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_c) (R2 tptp.set_Product_prod_c_c)) (=> (@ (@ tptp.member7012247553653173456list_c (@ (@ tptp.produc5515445818230282391list_c Xs) Ys)) (@ tptp.listrel_c_c R2)) (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_c Ys)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_d) (R2 tptp.set_Product_prod_c_d)) (=> (@ (@ tptp.member7083281593699519441list_d (@ (@ tptp.produc5515445822533511192list_d Xs) Ys)) (@ tptp.listrel_c_d R2)) (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_d Ys)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_nat) (R2 tptp.set_Pr6903500605879609269_c_nat)) (=> (@ (@ tptp.member6184937725913850668st_nat (@ (@ tptp.produc6126748735280710287st_nat Xs) Ys)) (@ tptp.listrel_c_nat R2)) (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_nat Ys)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_int) (R2 tptp.set_Pr4413417460947882513_c_int)) (=> (@ (@ tptp.member3694854580982123912st_int (@ (@ tptp.produc1948897715771513579st_int Xs) Ys)) (@ tptp.listrel_c_int R2)) (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_int Ys)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_d) (Ys tptp.list_c) (R2 tptp.set_Product_prod_d_c)) (=> (@ (@ tptp.member1739767152416986127list_c (@ (@ tptp.produc242965416994095062list_c Xs) Ys)) (@ tptp.listrel_d_c R2)) (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_c Ys)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_d) (Ys tptp.list_d) (R2 tptp.set_Product_prod_d_d)) (=> (@ (@ tptp.member1810801192463332112list_d (@ (@ tptp.produc242965421297323863list_d Xs) Ys)) (@ tptp.listrel_d_d R2)) (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_d Ys)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_d) (Ys tptp.list_nat) (R2 tptp.set_Pr3276347184212964150_d_nat)) (=> (@ (@ tptp.member6851837201453759021st_nat (@ (@ tptp.produc6793648210820618640st_nat Xs) Ys)) (@ tptp.listrel_d_nat R2)) (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_nat Ys)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_d) (Ys tptp.list_int) (R2 tptp.set_Pr786264039281237394_d_int)) (=> (@ (@ tptp.member4361754056522032265st_int (@ (@ tptp.produc2615797191311421932st_int Xs) Ys)) (@ tptp.listrel_d_int R2)) (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_int Ys)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_c) (R2 tptp.set_Pr4335409928928841947_nat_c)) (=> (@ (@ tptp.member6074218473364765234list_c (@ (@ tptp.produc7723716018658481613list_c Xs) Ys)) (@ tptp.listrel_nat_c R2)) (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_c Ys)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_d) (R2 tptp.set_Pr4406443968975187932_nat_d)) (=> (@ (@ tptp.member6145252513411111219list_d (@ (@ tptp.produc7723716022961710414list_d Xs) Ys)) (@ tptp.listrel_nat_d R2)) (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_d Ys)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_int) (X tptp.int)) (=> (@ tptp.distinct_int Xs) (= (@ (@ tptp.remove1_int X) Xs) (@ (@ tptp.removeAll_int X) Xs)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_nat) (X tptp.nat)) (=> (@ tptp.distinct_nat Xs) (= (@ (@ tptp.remove1_nat X) Xs) (@ (@ tptp.removeAll_nat X) Xs)))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger A2) tptp.one_one_Code_integer) A2)))
% 3.70/4.03 (assert (forall ((A2 tptp.assn)) (= (@ (@ tptp.times_times_assn A2) tptp.one_one_assn) A2)))
% 3.70/4.03 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.times_times_rat A2) tptp.one_one_rat) A2)))
% 3.70/4.03 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.times_times_nat A2) tptp.one_one_nat) A2)))
% 3.70/4.03 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.times_times_int A2) tptp.one_one_int) A2)))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger tptp.one_one_Code_integer) A2) A2)))
% 3.70/4.03 (assert (forall ((A2 tptp.assn)) (= (@ (@ tptp.times_times_assn tptp.one_one_assn) A2) A2)))
% 3.70/4.03 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A2) A2)))
% 3.70/4.03 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A2) A2)))
% 3.70/4.03 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A2) A2)))
% 3.70/4.03 (assert (forall ((P tptp.assn)) (= (@ (@ tptp.times_times_assn tptp.one_one_assn) P) P)))
% 3.70/4.03 (assert (forall ((A2 tptp.assn)) (= (@ (@ tptp.times_times_assn tptp.one_one_assn) A2) A2)))
% 3.70/4.03 (assert (forall ((A2 tptp.assn)) (= (@ (@ tptp.times_times_assn A2) tptp.one_one_assn) A2)))
% 3.70/4.03 (assert (forall ((X tptp.produc3843707927480180839at_nat) (Xs tptp.list_P5464809261938338413at_nat)) (=> (not (@ (@ tptp.member8757157785044589968at_nat X) (@ tptp.set_Pr3765526544606949372at_nat Xs))) (= (@ (@ tptp.remove8895909992688781315at_nat X) Xs) Xs))))
% 3.70/4.03 (assert (forall ((X tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (=> (not (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs))) (= (@ (@ tptp.remove5766854097993331357at_nat X) Xs) Xs))))
% 3.70/4.03 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xs tptp.list_P7985473006766602707_nat_o)) (=> (not (@ (@ tptp.member6576561426505652726_nat_o X) (@ tptp.set_Pr400311997697478754_nat_o Xs))) (= (@ (@ tptp.remove4235003712227595625_nat_o X) Xs) Xs))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Xs tptp.list_int)) (=> (not (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs))) (= (@ (@ tptp.remove1_int X) Xs) Xs))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (=> (not (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs))) (= (@ (@ tptp.remove1_nat X) Xs) Xs))))
% 3.70/4.03 (assert (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (=> (not (@ (@ tptp.member7957490590177025114n_assn X) (@ tptp.set_Pr1139785259514867910n_assn Xs))) (= (@ (@ tptp.remove1670527618125605709n_assn X) Xs) Xs))))
% 3.70/4.03 (assert (forall ((X tptp.produc3843707927480180839at_nat) (Xs tptp.list_P5464809261938338413at_nat) (Y tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat X))) (=> (not (@ _let_1 (@ tptp.set_Pr3765526544606949372at_nat Xs))) (not (@ _let_1 (@ tptp.set_Pr3765526544606949372at_nat (@ (@ tptp.remove8895909992688781315at_nat Y) Xs))))))))
% 3.70/4.03 (assert (forall ((X tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X))) (=> (not (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat Xs))) (not (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.remove5766854097993331357at_nat Y) Xs))))))))
% 3.70/4.03 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xs tptp.list_P7985473006766602707_nat_o) (Y (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o X))) (=> (not (@ _let_1 (@ tptp.set_Pr400311997697478754_nat_o Xs))) (not (@ _let_1 (@ tptp.set_Pr400311997697478754_nat_o (@ (@ tptp.remove4235003712227595625_nat_o Y) Xs))))))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Xs tptp.list_int) (Y tptp.int)) (let ((_let_1 (@ tptp.member_int X))) (=> (not (@ _let_1 (@ tptp.set_int2 Xs))) (not (@ _let_1 (@ tptp.set_int2 (@ (@ tptp.remove1_int Y) Xs))))))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Xs tptp.list_nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (=> (not (@ _let_1 (@ tptp.set_nat2 Xs))) (not (@ _let_1 (@ tptp.set_nat2 (@ (@ tptp.remove1_nat Y) Xs))))))))
% 3.70/4.03 (assert (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn) (Y tptp.produc6575502325842934193n_assn)) (let ((_let_1 (@ tptp.member7957490590177025114n_assn X))) (=> (not (@ _let_1 (@ tptp.set_Pr1139785259514867910n_assn Xs))) (not (@ _let_1 (@ tptp.set_Pr1139785259514867910n_assn (@ (@ tptp.remove1670527618125605709n_assn Y) Xs))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_int) (X tptp.int)) (=> (@ tptp.distinct_int Xs) (@ tptp.distinct_int (@ (@ tptp.remove1_int X) Xs)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_nat) (X tptp.nat)) (=> (@ tptp.distinct_nat Xs) (@ tptp.distinct_nat (@ (@ tptp.remove1_nat X) Xs)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_int) (X tptp.int)) (=> (@ tptp.distinct_int Xs) (@ tptp.distinct_int (@ (@ tptp.removeAll_int X) Xs)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_nat) (X tptp.nat)) (=> (@ tptp.distinct_nat Xs) (@ tptp.distinct_nat (@ (@ tptp.removeAll_nat X) Xs)))))
% 3.70/4.03 (assert (forall ((M2 tptp.rat) (N tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_rat M2) N)))))))
% 3.70/4.03 (assert (forall ((M2 tptp.code_integer) (N tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger M2) N)))))))
% 3.70/4.03 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_nat M2) N)))))))
% 3.70/4.03 (assert (forall ((M2 tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_int M2) N)))))))
% 3.70/4.03 (assert (forall ((P tptp.assn) (Q tptp.assn)) (=> (@ (@ (@ tptp.fI_QUERY P) Q) tptp.one_one_assn) (@ (@ tptp.entails P) Q))))
% 3.70/4.03 (assert (forall ((P (-> tptp.produc2732055786443039994et_nat Bool)) (X tptp.produc2732055786443039994et_nat)) (=> (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 (-> tptp.produc3658429121746597890et_nat Bool)) (C4 tptp.heap_e7401611519738050253t_unit) (D3 tptp.set_nat)) (@ P (@ (@ tptp.produc2245416461498447860et_nat A4) (@ (@ tptp.produc5001842942810119800et_nat B4) (@ (@ tptp.produc7507926704131184380et_nat C4) D3))))) (@ P X))))
% 3.70/4.03 (assert (forall ((P (-> tptp.produc1908205239877642774nteger Bool)) (X tptp.produc1908205239877642774nteger)) (=> (forall ((A4 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B4 tptp.code_integer) (C4 tptp.code_integer)) (@ P (@ (@ tptp.produc8603105652947943368nteger A4) (@ (@ tptp.produc1086072967326762835nteger B4) C4)))) (@ P X))))
% 3.70/4.03 (assert (forall ((P (-> tptp.produc3925858234332021118et_nat Bool)) (X tptp.produc3925858234332021118et_nat)) (=> (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.heap_e7401611519738050253t_unit) (C4 tptp.set_nat)) (@ P (@ (@ tptp.produc5001842942810119800et_nat A4) (@ (@ tptp.produc7507926704131184380et_nat B4) C4)))) (@ P X))))
% 3.70/4.03 (assert (forall ((P (-> tptp.produc2732055786443039994et_nat Bool)) (X tptp.produc2732055786443039994et_nat)) (=> (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 (-> tptp.produc3658429121746597890et_nat Bool)) (C4 tptp.produc3658429121746597890et_nat)) (@ P (@ (@ tptp.produc2245416461498447860et_nat A4) (@ (@ tptp.produc5001842942810119800et_nat B4) C4)))) (@ P X))))
% 3.70/4.03 (assert (forall ((P (-> tptp.produc2285326912895808259nt_int Bool)) (X tptp.produc2285326912895808259nt_int)) (=> (forall ((A4 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B4 tptp.int) (C4 tptp.int)) (@ P (@ (@ tptp.produc5700946648718959541nt_int A4) (@ (@ tptp.product_Pair_int_int B4) C4)))) (@ P X))))
% 3.70/4.03 (assert (forall ((P (-> tptp.produc7773217078559923341nt_int Bool)) (X tptp.produc7773217078559923341nt_int)) (=> (forall ((A4 (-> tptp.int tptp.option6357759511663192854e_term)) (B4 tptp.int) (C4 tptp.int)) (@ P (@ (@ tptp.produc4305682042979456191nt_int A4) (@ (@ tptp.product_Pair_int_int B4) C4)))) (@ P X))))
% 3.70/4.03 (assert (forall ((Y tptp.produc2732055786443039994et_nat)) (not (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 (-> tptp.produc3658429121746597890et_nat Bool)) (C4 tptp.heap_e7401611519738050253t_unit) (D3 tptp.set_nat)) (not (= Y (@ (@ tptp.produc2245416461498447860et_nat A4) (@ (@ tptp.produc5001842942810119800et_nat B4) (@ (@ tptp.produc7507926704131184380et_nat C4) D3)))))))))
% 3.70/4.03 (assert (forall ((Y tptp.produc1908205239877642774nteger)) (not (forall ((A4 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B4 tptp.code_integer) (C4 tptp.code_integer)) (not (= Y (@ (@ tptp.produc8603105652947943368nteger A4) (@ (@ tptp.produc1086072967326762835nteger B4) C4))))))))
% 3.70/4.03 (assert (forall ((Y tptp.produc3925858234332021118et_nat)) (not (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.heap_e7401611519738050253t_unit) (C4 tptp.set_nat)) (not (= Y (@ (@ tptp.produc5001842942810119800et_nat A4) (@ (@ tptp.produc7507926704131184380et_nat B4) C4))))))))
% 3.70/4.03 (assert (forall ((Y tptp.produc2732055786443039994et_nat)) (not (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 (-> tptp.produc3658429121746597890et_nat Bool)) (C4 tptp.produc3658429121746597890et_nat)) (not (= Y (@ (@ tptp.produc2245416461498447860et_nat A4) (@ (@ tptp.produc5001842942810119800et_nat B4) C4))))))))
% 3.70/4.03 (assert (forall ((Y tptp.produc2285326912895808259nt_int)) (not (forall ((A4 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B4 tptp.int) (C4 tptp.int)) (not (= Y (@ (@ tptp.produc5700946648718959541nt_int A4) (@ (@ tptp.product_Pair_int_int B4) C4))))))))
% 3.70/4.03 (assert (forall ((Y tptp.produc7773217078559923341nt_int)) (not (forall ((A4 (-> tptp.int tptp.option6357759511663192854e_term)) (B4 tptp.int) (C4 tptp.int)) (not (= Y (@ (@ tptp.produc4305682042979456191nt_int A4) (@ (@ tptp.product_Pair_int_int B4) C4))))))))
% 3.70/4.03 (assert (forall ((A2 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B2 tptp.produc8923325533196201883nteger) (A7 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B6 tptp.produc8923325533196201883nteger)) (=> (= (@ (@ tptp.produc8603105652947943368nteger A2) B2) (@ (@ tptp.produc8603105652947943368nteger A7) B6)) (not (=> (= A2 A7) (not (= B2 B6)))))))
% 3.70/4.03 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.produc3658429121746597890et_nat) (A7 (-> tptp.produc3658429121746597890et_nat Bool)) (B6 tptp.produc3658429121746597890et_nat)) (=> (= (@ (@ tptp.produc5001842942810119800et_nat A2) B2) (@ (@ tptp.produc5001842942810119800et_nat A7) B6)) (not (=> (= A2 A7) (not (= B2 B6)))))))
% 3.70/4.03 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.produc3925858234332021118et_nat) (A7 (-> tptp.produc3658429121746597890et_nat Bool)) (B6 tptp.produc3925858234332021118et_nat)) (=> (= (@ (@ tptp.produc2245416461498447860et_nat A2) B2) (@ (@ tptp.produc2245416461498447860et_nat A7) B6)) (not (=> (= A2 A7) (not (= B2 B6)))))))
% 3.70/4.03 (assert (forall ((A2 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B2 tptp.product_prod_int_int) (A7 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B6 tptp.product_prod_int_int)) (=> (= (@ (@ tptp.produc5700946648718959541nt_int A2) B2) (@ (@ tptp.produc5700946648718959541nt_int A7) B6)) (not (=> (= A2 A7) (not (= B2 B6)))))))
% 3.70/4.03 (assert (forall ((A2 (-> tptp.int tptp.option6357759511663192854e_term)) (B2 tptp.product_prod_int_int) (A7 (-> tptp.int tptp.option6357759511663192854e_term)) (B6 tptp.product_prod_int_int)) (=> (= (@ (@ tptp.produc4305682042979456191nt_int A2) B2) (@ (@ tptp.produc4305682042979456191nt_int A7) B6)) (not (=> (= A2 A7) (not (= B2 B6)))))))
% 3.70/4.03 (assert (forall ((P (-> tptp.produc1908205239877642774nteger Bool)) (P6 tptp.produc1908205239877642774nteger)) (=> (forall ((A4 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B4 tptp.produc8923325533196201883nteger)) (@ P (@ (@ tptp.produc8603105652947943368nteger A4) B4))) (@ P P6))))
% 3.70/4.03 (assert (forall ((P (-> tptp.produc3925858234332021118et_nat Bool)) (P6 tptp.produc3925858234332021118et_nat)) (=> (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.produc3658429121746597890et_nat)) (@ P (@ (@ tptp.produc5001842942810119800et_nat A4) B4))) (@ P P6))))
% 3.70/4.03 (assert (forall ((P (-> tptp.produc2732055786443039994et_nat Bool)) (P6 tptp.produc2732055786443039994et_nat)) (=> (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.produc3925858234332021118et_nat)) (@ P (@ (@ tptp.produc2245416461498447860et_nat A4) B4))) (@ P P6))))
% 3.70/4.03 (assert (forall ((P (-> tptp.produc2285326912895808259nt_int Bool)) (P6 tptp.produc2285326912895808259nt_int)) (=> (forall ((A4 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B4 tptp.product_prod_int_int)) (@ P (@ (@ tptp.produc5700946648718959541nt_int A4) B4))) (@ P P6))))
% 3.70/4.03 (assert (forall ((P (-> tptp.produc7773217078559923341nt_int Bool)) (P6 tptp.produc7773217078559923341nt_int)) (=> (forall ((A4 (-> tptp.int tptp.option6357759511663192854e_term)) (B4 tptp.product_prod_int_int)) (@ P (@ (@ tptp.produc4305682042979456191nt_int A4) B4))) (@ P P6))))
% 3.70/4.03 (assert (forall ((P6 tptp.produc1908205239877642774nteger)) (exists ((X3 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (Y2 tptp.produc8923325533196201883nteger)) (= P6 (@ (@ tptp.produc8603105652947943368nteger X3) Y2)))))
% 3.70/4.03 (assert (forall ((P6 tptp.produc3925858234332021118et_nat)) (exists ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 tptp.produc3658429121746597890et_nat)) (= P6 (@ (@ tptp.produc5001842942810119800et_nat X3) Y2)))))
% 3.70/4.03 (assert (forall ((P6 tptp.produc2732055786443039994et_nat)) (exists ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 tptp.produc3925858234332021118et_nat)) (= P6 (@ (@ tptp.produc2245416461498447860et_nat X3) Y2)))))
% 3.70/4.03 (assert (forall ((P6 tptp.produc2285326912895808259nt_int)) (exists ((X3 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y2 tptp.product_prod_int_int)) (= P6 (@ (@ tptp.produc5700946648718959541nt_int X3) Y2)))))
% 3.70/4.03 (assert (forall ((P6 tptp.produc7773217078559923341nt_int)) (exists ((X3 (-> tptp.int tptp.option6357759511663192854e_term)) (Y2 tptp.product_prod_int_int)) (= P6 (@ (@ tptp.produc4305682042979456191nt_int X3) Y2)))))
% 3.70/4.03 (assert (forall ((Y tptp.produc1908205239877642774nteger)) (not (forall ((A4 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B4 tptp.produc8923325533196201883nteger)) (not (= Y (@ (@ tptp.produc8603105652947943368nteger A4) B4)))))))
% 3.70/4.03 (assert (forall ((Y tptp.produc3925858234332021118et_nat)) (not (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.produc3658429121746597890et_nat)) (not (= Y (@ (@ tptp.produc5001842942810119800et_nat A4) B4)))))))
% 3.70/4.03 (assert (forall ((Y tptp.produc2732055786443039994et_nat)) (not (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.produc3925858234332021118et_nat)) (not (= Y (@ (@ tptp.produc2245416461498447860et_nat A4) B4)))))))
% 3.70/4.03 (assert (forall ((Y tptp.produc2285326912895808259nt_int)) (not (forall ((A4 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B4 tptp.product_prod_int_int)) (not (= Y (@ (@ tptp.produc5700946648718959541nt_int A4) B4)))))))
% 3.70/4.03 (assert (forall ((Y tptp.produc7773217078559923341nt_int)) (not (forall ((A4 (-> tptp.int tptp.option6357759511663192854e_term)) (B4 tptp.product_prod_int_int)) (not (= Y (@ (@ tptp.produc4305682042979456191nt_int A4) B4)))))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Xs tptp.list_int)) (= (@ (@ tptp.remove_int X) (@ tptp.set_int2 Xs)) (@ tptp.set_int2 (@ (@ tptp.removeAll_int X) Xs)))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (= (@ (@ tptp.remove_nat X) (@ tptp.set_nat2 Xs)) (@ tptp.set_nat2 (@ (@ tptp.removeAll_nat X) Xs)))))
% 3.70/4.03 (assert (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (= (@ (@ tptp.remove6142905432236673558n_assn X) (@ tptp.set_Pr1139785259514867910n_assn Xs)) (@ tptp.set_Pr1139785259514867910n_assn (@ (@ tptp.remove1763081955827946941n_assn X) Xs)))))
% 3.70/4.03 (assert (forall ((H2 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.rep_assn tptp.one_one_assn) (@ (@ tptp.produc7507926704131184380et_nat H2) tptp.bot_bot_set_nat))))
% 3.70/4.03 (assert (forall ((X tptp.produc3843707927480180839at_nat) (Xs tptp.list_P5464809261938338413at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X) (@ tptp.set_Pr3765526544606949372at_nat Xs)) (@ (@ tptp.ord_less_nat (@ tptp.size_s1588839187904960729at_nat (@ (@ tptp.remove4908499291543849587at_nat X) Xs))) (@ tptp.size_s1588839187904960729at_nat Xs)))))
% 3.70/4.03 (assert (forall ((X tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs)) (@ (@ tptp.ord_less_nat (@ tptp.size_s5460976970255530739at_nat (@ (@ tptp.remove3673390508374433037at_nat X) Xs))) (@ tptp.size_s5460976970255530739at_nat Xs)))))
% 3.70/4.03 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xs tptp.list_P7985473006766602707_nat_o)) (=> (@ (@ tptp.member6576561426505652726_nat_o X) (@ tptp.set_Pr400311997697478754_nat_o Xs)) (@ (@ tptp.ord_less_nat (@ tptp.size_s8908918004648414271_nat_o (@ (@ tptp.remove7604696131425036249_nat_o X) Xs))) (@ tptp.size_s8908918004648414271_nat_o Xs)))))
% 3.70/4.03 (assert (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (=> (@ (@ tptp.member7957490590177025114n_assn X) (@ tptp.set_Pr1139785259514867910n_assn Xs)) (@ (@ tptp.ord_less_nat (@ tptp.size_s6829681357464350627n_assn (@ (@ tptp.remove1763081955827946941n_assn X) Xs))) (@ tptp.size_s6829681357464350627n_assn Xs)))))
% 3.70/4.03 (assert (forall ((X tptp.c) (Xs tptp.list_c)) (=> (@ (@ tptp.member_c X) (@ tptp.set_c2 Xs)) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_c (@ (@ tptp.removeAll_c X) Xs))) (@ tptp.size_size_list_c Xs)))))
% 3.70/4.03 (assert (forall ((X tptp.d) (Xs tptp.list_d)) (=> (@ (@ tptp.member_d X) (@ tptp.set_d2 Xs)) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_d (@ (@ tptp.removeAll_d X) Xs))) (@ tptp.size_size_list_d Xs)))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs)) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat (@ (@ tptp.removeAll_nat X) Xs))) (@ tptp.size_size_list_nat Xs)))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Xs tptp.list_int)) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs)) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_int (@ (@ tptp.removeAll_int X) Xs))) (@ tptp.size_size_list_int Xs)))))
% 3.70/4.03 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.one_one_rat)))
% 3.70/4.03 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) tptp.one_one_Code_integer)))
% 3.70/4.03 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.one_one_nat)))
% 3.70/4.03 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.one_one_int)))
% 3.70/4.03 (assert (forall ((X Bool) (Xa tptp.produc3658429121746597890et_nat)) (=> (not (@ (@ tptp.pure_a825153325127701367it_nat X) Xa)) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (= Xa (@ (@ tptp.produc7507926704131184380et_nat H) As)) (and (= As tptp.bot_bot_set_nat) X)))))))
% 3.70/4.03 (assert (forall ((X Bool) (Xa tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.pure_a825153325127701367it_nat X) Xa) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (= Xa (@ (@ tptp.produc7507926704131184380et_nat H) As)) (not (and (= As tptp.bot_bot_set_nat) X))))))))
% 3.70/4.03 (assert (forall ((X Bool) (Xa tptp.produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ (@ tptp.pure_a825153325127701367it_nat X) Xa) Y) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (= Xa (@ (@ tptp.produc7507926704131184380et_nat H) As)) (= Y (not (and (= As tptp.bot_bot_set_nat) X)))))))))
% 3.70/4.03 (assert (forall ((B2 Bool) (H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (= (@ (@ tptp.pure_a825153325127701367it_nat B2) (@ (@ tptp.produc7507926704131184380et_nat H2) As2)) (and (= As2 tptp.bot_bot_set_nat) B2))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (Xs tptp.list_c) (Ys tptp.list_c)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 (@ tptp.size_size_list_c Xs)) (=> (@ _let_1 (@ tptp.size_size_list_c Ys)) (= (@ (@ tptp.nth_Product_prod_c_c (@ (@ tptp.zip_c_c Xs) Ys)) I) (@ (@ tptp.product_Pair_c_c (@ (@ tptp.nth_c Xs) I)) (@ (@ tptp.nth_c Ys) I))))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (Xs tptp.list_c) (Ys tptp.list_d)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 (@ tptp.size_size_list_c Xs)) (=> (@ _let_1 (@ tptp.size_size_list_d Ys)) (= (@ (@ tptp.nth_Product_prod_c_d (@ (@ tptp.zip_c_d Xs) Ys)) I) (@ (@ tptp.product_Pair_c_d (@ (@ tptp.nth_c Xs) I)) (@ (@ tptp.nth_d Ys) I))))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (Xs tptp.list_c) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 (@ tptp.size_size_list_c Xs)) (=> (@ _let_1 (@ tptp.size_size_list_nat Ys)) (= (@ (@ tptp.nth_Pr1708982275578427192_c_nat (@ (@ tptp.zip_c_nat Xs) Ys)) I) (@ (@ tptp.product_Pair_c_nat (@ (@ tptp.nth_c Xs) I)) (@ (@ tptp.nth_nat Ys) I))))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (Xs tptp.list_c) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 (@ tptp.size_size_list_c Xs)) (=> (@ _let_1 (@ tptp.size_size_list_int Ys)) (= (@ (@ tptp.nth_Pr6754503292924006292_c_int (@ (@ tptp.zip_c_int Xs) Ys)) I) (@ (@ tptp.product_Pair_c_int (@ (@ tptp.nth_c Xs) I)) (@ (@ tptp.nth_int Ys) I))))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (Xs tptp.list_d) (Ys tptp.list_c)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 (@ tptp.size_size_list_d Xs)) (=> (@ _let_1 (@ tptp.size_size_list_c Ys)) (= (@ (@ tptp.nth_Product_prod_d_c (@ (@ tptp.zip_d_c Xs) Ys)) I) (@ (@ tptp.product_Pair_d_c (@ (@ tptp.nth_d Xs) I)) (@ (@ tptp.nth_c Ys) I))))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (Xs tptp.list_d) (Ys tptp.list_d)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 (@ tptp.size_size_list_d Xs)) (=> (@ _let_1 (@ tptp.size_size_list_d Ys)) (= (@ (@ tptp.nth_Product_prod_d_d (@ (@ tptp.zip_d_d Xs) Ys)) I) (@ (@ tptp.product_Pair_d_d (@ (@ tptp.nth_d Xs) I)) (@ (@ tptp.nth_d Ys) I))))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (Xs tptp.list_d) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 (@ tptp.size_size_list_d Xs)) (=> (@ _let_1 (@ tptp.size_size_list_nat Ys)) (= (@ (@ tptp.nth_Pr2944426604534821689_d_nat (@ (@ tptp.zip_d_nat Xs) Ys)) I) (@ (@ tptp.product_Pair_d_nat (@ (@ tptp.nth_d Xs) I)) (@ (@ tptp.nth_nat Ys) I))))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (Xs tptp.list_d) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 (@ tptp.size_size_list_d Xs)) (=> (@ _let_1 (@ tptp.size_size_list_int Ys)) (= (@ (@ tptp.nth_Pr7989947621880400789_d_int (@ (@ tptp.zip_d_int Xs) Ys)) I) (@ (@ tptp.product_Pair_d_int (@ (@ tptp.nth_d Xs) I)) (@ (@ tptp.nth_int Ys) I))))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (Xs tptp.list_nat) (Ys tptp.list_c)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 (@ tptp.size_size_list_nat Xs)) (=> (@ _let_1 (@ tptp.size_size_list_c Ys)) (= (@ (@ tptp.nth_Pr2476257089995772766_nat_c (@ (@ tptp.zip_nat_c Xs) Ys)) I) (@ (@ tptp.product_Pair_nat_c (@ (@ tptp.nth_nat Xs) I)) (@ (@ tptp.nth_c Ys) I))))))))
% 3.70/4.03 (assert (forall ((I tptp.nat) (Xs tptp.list_nat) (Ys tptp.list_d)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 (@ tptp.size_size_list_nat Xs)) (=> (@ _let_1 (@ tptp.size_size_list_d Ys)) (= (@ (@ tptp.nth_Pr2476257094299001567_nat_d (@ (@ tptp.zip_nat_d Xs) Ys)) I) (@ (@ tptp.product_Pair_nat_d (@ (@ tptp.nth_nat Xs) I)) (@ (@ tptp.nth_d Ys) I))))))))
% 3.70/4.03 (assert (forall ((F4 (-> tptp.produc1908205239877642774nteger Bool)) (A2 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B2 tptp.produc8923325533196201883nteger)) (=> (@ F4 (@ (@ tptp.produc8603105652947943368nteger A2) B2)) (@ (@ (@ tptp.produc1217013493180205570eger_o F4) A2) B2))))
% 3.70/4.03 (assert (forall ((F4 (-> tptp.produc3925858234332021118et_nat Bool)) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.produc3658429121746597890et_nat)) (=> (@ F4 (@ (@ tptp.produc5001842942810119800et_nat A2) B2)) (@ (@ (@ tptp.produc6216949301066131538_nat_o F4) A2) B2))))
% 3.70/4.03 (assert (forall ((F4 (-> tptp.produc2732055786443039994et_nat Bool)) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.produc3925858234332021118et_nat)) (=> (@ F4 (@ (@ tptp.produc2245416461498447860et_nat A2) B2)) (@ (@ (@ tptp.produc5101573711933517782_nat_o F4) A2) B2))))
% 3.70/4.03 (assert (forall ((F4 (-> tptp.produc2285326912895808259nt_int Bool)) (A2 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B2 tptp.product_prod_int_int)) (=> (@ F4 (@ (@ tptp.produc5700946648718959541nt_int A2) B2)) (@ (@ (@ tptp.produc730925184835016917_int_o F4) A2) B2))))
% 3.70/4.03 (assert (forall ((F4 (-> tptp.produc7773217078559923341nt_int Bool)) (A2 (-> tptp.int tptp.option6357759511663192854e_term)) (B2 tptp.product_prod_int_int)) (=> (@ F4 (@ (@ tptp.produc4305682042979456191nt_int A2) B2)) (@ (@ (@ tptp.produc9098658269643458507_int_o F4) A2) B2))))
% 3.70/4.03 (assert (forall ((A2 tptp.list_c) (B2 tptp.list_c) (A7 tptp.list_c) (B6 tptp.list_c)) (=> (= (@ tptp.size_size_list_c A2) (@ tptp.size_size_list_c B2)) (=> (= (@ tptp.size_size_list_c A7) (@ tptp.size_size_list_c B6)) (= (= (@ (@ tptp.zip_c_c A2) B2) (@ (@ tptp.zip_c_c A7) B6)) (and (= A2 A7) (= B2 B6)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.list_c) (B2 tptp.list_d) (A7 tptp.list_c) (B6 tptp.list_d)) (=> (= (@ tptp.size_size_list_c A2) (@ tptp.size_size_list_d B2)) (=> (= (@ tptp.size_size_list_c A7) (@ tptp.size_size_list_d B6)) (= (= (@ (@ tptp.zip_c_d A2) B2) (@ (@ tptp.zip_c_d A7) B6)) (and (= A2 A7) (= B2 B6)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.list_c) (B2 tptp.list_nat) (A7 tptp.list_c) (B6 tptp.list_nat)) (=> (= (@ tptp.size_size_list_c A2) (@ tptp.size_size_list_nat B2)) (=> (= (@ tptp.size_size_list_c A7) (@ tptp.size_size_list_nat B6)) (= (= (@ (@ tptp.zip_c_nat A2) B2) (@ (@ tptp.zip_c_nat A7) B6)) (and (= A2 A7) (= B2 B6)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.list_c) (B2 tptp.list_int) (A7 tptp.list_c) (B6 tptp.list_int)) (=> (= (@ tptp.size_size_list_c A2) (@ tptp.size_size_list_int B2)) (=> (= (@ tptp.size_size_list_c A7) (@ tptp.size_size_list_int B6)) (= (= (@ (@ tptp.zip_c_int A2) B2) (@ (@ tptp.zip_c_int A7) B6)) (and (= A2 A7) (= B2 B6)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.list_d) (B2 tptp.list_c) (A7 tptp.list_d) (B6 tptp.list_c)) (=> (= (@ tptp.size_size_list_d A2) (@ tptp.size_size_list_c B2)) (=> (= (@ tptp.size_size_list_d A7) (@ tptp.size_size_list_c B6)) (= (= (@ (@ tptp.zip_d_c A2) B2) (@ (@ tptp.zip_d_c A7) B6)) (and (= A2 A7) (= B2 B6)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.list_d) (B2 tptp.list_d) (A7 tptp.list_d) (B6 tptp.list_d)) (=> (= (@ tptp.size_size_list_d A2) (@ tptp.size_size_list_d B2)) (=> (= (@ tptp.size_size_list_d A7) (@ tptp.size_size_list_d B6)) (= (= (@ (@ tptp.zip_d_d A2) B2) (@ (@ tptp.zip_d_d A7) B6)) (and (= A2 A7) (= B2 B6)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.list_d) (B2 tptp.list_nat) (A7 tptp.list_d) (B6 tptp.list_nat)) (=> (= (@ tptp.size_size_list_d A2) (@ tptp.size_size_list_nat B2)) (=> (= (@ tptp.size_size_list_d A7) (@ tptp.size_size_list_nat B6)) (= (= (@ (@ tptp.zip_d_nat A2) B2) (@ (@ tptp.zip_d_nat A7) B6)) (and (= A2 A7) (= B2 B6)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.list_d) (B2 tptp.list_int) (A7 tptp.list_d) (B6 tptp.list_int)) (=> (= (@ tptp.size_size_list_d A2) (@ tptp.size_size_list_int B2)) (=> (= (@ tptp.size_size_list_d A7) (@ tptp.size_size_list_int B6)) (= (= (@ (@ tptp.zip_d_int A2) B2) (@ (@ tptp.zip_d_int A7) B6)) (and (= A2 A7) (= B2 B6)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.list_nat) (B2 tptp.list_c) (A7 tptp.list_nat) (B6 tptp.list_c)) (=> (= (@ tptp.size_size_list_nat A2) (@ tptp.size_size_list_c B2)) (=> (= (@ tptp.size_size_list_nat A7) (@ tptp.size_size_list_c B6)) (= (= (@ (@ tptp.zip_nat_c A2) B2) (@ (@ tptp.zip_nat_c A7) B6)) (and (= A2 A7) (= B2 B6)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.list_nat) (B2 tptp.list_d) (A7 tptp.list_nat) (B6 tptp.list_d)) (=> (= (@ tptp.size_size_list_nat A2) (@ tptp.size_size_list_d B2)) (=> (= (@ tptp.size_size_list_nat A7) (@ tptp.size_size_list_d B6)) (= (= (@ (@ tptp.zip_nat_d A2) B2) (@ (@ tptp.zip_nat_d A7) B6)) (and (= A2 A7) (= B2 B6)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.list_c) (B2 tptp.list_c) (A7 tptp.list_c) (B6 tptp.list_c)) (=> (= (@ tptp.size_size_list_c A2) (@ tptp.size_size_list_c B2)) (=> (= (@ tptp.size_size_list_c A7) (@ tptp.size_size_list_c B6)) (=> (= (@ (@ tptp.zip_c_c A2) B2) (@ (@ tptp.zip_c_c A7) B6)) (and (= A2 A7) (= B2 B6)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.list_c) (B2 tptp.list_d) (A7 tptp.list_c) (B6 tptp.list_d)) (=> (= (@ tptp.size_size_list_c A2) (@ tptp.size_size_list_d B2)) (=> (= (@ tptp.size_size_list_c A7) (@ tptp.size_size_list_d B6)) (=> (= (@ (@ tptp.zip_c_d A2) B2) (@ (@ tptp.zip_c_d A7) B6)) (and (= A2 A7) (= B2 B6)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.list_c) (B2 tptp.list_nat) (A7 tptp.list_c) (B6 tptp.list_nat)) (=> (= (@ tptp.size_size_list_c A2) (@ tptp.size_size_list_nat B2)) (=> (= (@ tptp.size_size_list_c A7) (@ tptp.size_size_list_nat B6)) (=> (= (@ (@ tptp.zip_c_nat A2) B2) (@ (@ tptp.zip_c_nat A7) B6)) (and (= A2 A7) (= B2 B6)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.list_c) (B2 tptp.list_int) (A7 tptp.list_c) (B6 tptp.list_int)) (=> (= (@ tptp.size_size_list_c A2) (@ tptp.size_size_list_int B2)) (=> (= (@ tptp.size_size_list_c A7) (@ tptp.size_size_list_int B6)) (=> (= (@ (@ tptp.zip_c_int A2) B2) (@ (@ tptp.zip_c_int A7) B6)) (and (= A2 A7) (= B2 B6)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.list_d) (B2 tptp.list_c) (A7 tptp.list_d) (B6 tptp.list_c)) (=> (= (@ tptp.size_size_list_d A2) (@ tptp.size_size_list_c B2)) (=> (= (@ tptp.size_size_list_d A7) (@ tptp.size_size_list_c B6)) (=> (= (@ (@ tptp.zip_d_c A2) B2) (@ (@ tptp.zip_d_c A7) B6)) (and (= A2 A7) (= B2 B6)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.list_d) (B2 tptp.list_d) (A7 tptp.list_d) (B6 tptp.list_d)) (=> (= (@ tptp.size_size_list_d A2) (@ tptp.size_size_list_d B2)) (=> (= (@ tptp.size_size_list_d A7) (@ tptp.size_size_list_d B6)) (=> (= (@ (@ tptp.zip_d_d A2) B2) (@ (@ tptp.zip_d_d A7) B6)) (and (= A2 A7) (= B2 B6)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.list_d) (B2 tptp.list_nat) (A7 tptp.list_d) (B6 tptp.list_nat)) (=> (= (@ tptp.size_size_list_d A2) (@ tptp.size_size_list_nat B2)) (=> (= (@ tptp.size_size_list_d A7) (@ tptp.size_size_list_nat B6)) (=> (= (@ (@ tptp.zip_d_nat A2) B2) (@ (@ tptp.zip_d_nat A7) B6)) (and (= A2 A7) (= B2 B6)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.list_d) (B2 tptp.list_int) (A7 tptp.list_d) (B6 tptp.list_int)) (=> (= (@ tptp.size_size_list_d A2) (@ tptp.size_size_list_int B2)) (=> (= (@ tptp.size_size_list_d A7) (@ tptp.size_size_list_int B6)) (=> (= (@ (@ tptp.zip_d_int A2) B2) (@ (@ tptp.zip_d_int A7) B6)) (and (= A2 A7) (= B2 B6)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.list_nat) (B2 tptp.list_c) (A7 tptp.list_nat) (B6 tptp.list_c)) (=> (= (@ tptp.size_size_list_nat A2) (@ tptp.size_size_list_c B2)) (=> (= (@ tptp.size_size_list_nat A7) (@ tptp.size_size_list_c B6)) (=> (= (@ (@ tptp.zip_nat_c A2) B2) (@ (@ tptp.zip_nat_c A7) B6)) (and (= A2 A7) (= B2 B6)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.list_nat) (B2 tptp.list_d) (A7 tptp.list_nat) (B6 tptp.list_d)) (=> (= (@ tptp.size_size_list_nat A2) (@ tptp.size_size_list_d B2)) (=> (= (@ tptp.size_size_list_nat A7) (@ tptp.size_size_list_d B6)) (=> (= (@ (@ tptp.zip_nat_d A2) B2) (@ (@ tptp.zip_nat_d A7) B6)) (and (= A2 A7) (= B2 B6)))))))
% 3.70/4.03 (assert (forall ((L tptp.list_P267710562049004973od_c_c)) (not (forall ((L1 tptp.list_c) (L22 tptp.list_c)) (let ((_let_1 (@ tptp.size_size_list_c L22))) (=> (= L (@ (@ tptp.zip_c_c L1) L22)) (=> (= (@ tptp.size_size_list_c L1) _let_1) (not (= (@ tptp.size_s2756448709718749209od_c_c L) _let_1)))))))))
% 3.70/4.03 (assert (forall ((L tptp.list_P338744602095350958od_c_d)) (not (forall ((L1 tptp.list_c) (L22 tptp.list_d)) (let ((_let_1 (@ tptp.size_size_list_d L22))) (=> (= L (@ (@ tptp.zip_c_d L1) L22)) (=> (= (@ tptp.size_size_list_c L1) _let_1) (not (= (@ tptp.size_s2827482749765095194od_c_d L) _let_1)))))))))
% 3.70/4.03 (assert (forall ((L tptp.list_P5561950507774946575_c_nat)) (not (forall ((L1 tptp.list_c) (L22 tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat L22))) (=> (= L (@ (@ tptp.zip_c_nat L1) L22)) (=> (= (@ tptp.size_size_list_c L1) _let_1) (not (= (@ tptp.size_s2954062820725854115_c_nat L) _let_1)))))))))
% 3.70/4.03 (assert (forall ((L tptp.list_P3071867362843219819_c_int)) (not (forall ((L1 tptp.list_c) (L22 tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int L22))) (=> (= L (@ (@ tptp.zip_c_int L1) L22)) (=> (= (@ tptp.size_size_list_c L1) _let_1) (not (= (@ tptp.size_s463979675794127359_c_int L) _let_1)))))))))
% 3.70/4.03 (assert (forall ((L tptp.list_P8855433598298794092od_d_c)) (not (forall ((L1 tptp.list_d) (L22 tptp.list_c)) (let ((_let_1 (@ tptp.size_size_list_c L22))) (=> (= L (@ (@ tptp.zip_d_c L1) L22)) (=> (= (@ tptp.size_size_list_d L1) _let_1) (not (= (@ tptp.size_s2120799709113762520od_d_c L) _let_1)))))))))
% 3.70/4.03 (assert (forall ((L tptp.list_P8926467638345140077od_d_d)) (not (forall ((L1 tptp.list_d) (L22 tptp.list_d)) (let ((_let_1 (@ tptp.size_size_list_d L22))) (=> (= L (@ (@ tptp.zip_d_d L1) L22)) (=> (= (@ tptp.size_size_list_d L1) _let_1) (not (= (@ tptp.size_s2191833749160108505od_d_d L) _let_1)))))))))
% 3.70/4.03 (assert (forall ((L tptp.list_P1934797086108301456_d_nat)) (not (forall ((L1 tptp.list_d) (L22 tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat L22))) (=> (= L (@ (@ tptp.zip_d_nat L1) L22)) (=> (= (@ tptp.size_size_list_d L1) _let_1) (not (= (@ tptp.size_s8550281435913984804_d_nat L) _let_1)))))))))
% 3.70/4.03 (assert (forall ((L tptp.list_P8668085978031350508_d_int)) (not (forall ((L1 tptp.list_d) (L22 tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int L22))) (=> (= L (@ (@ tptp.zip_d_int L1) L22)) (=> (= (@ tptp.size_size_list_d L1) _let_1) (not (= (@ tptp.size_s6060198290982258048_d_int L) _let_1)))))))))
% 3.70/4.03 (assert (forall ((L tptp.list_P2993859830824179253_nat_c)) (not (forall ((L1 tptp.list_nat) (L22 tptp.list_c)) (let ((_let_1 (@ tptp.size_size_list_c L22))) (=> (= L (@ (@ tptp.zip_nat_c L1) L22)) (=> (= (@ tptp.size_size_list_nat L1) _let_1) (not (= (@ tptp.size_s385972143775086793_nat_c L) _let_1)))))))))
% 3.70/4.03 (assert (forall ((L tptp.list_P3064893870870525238_nat_d)) (not (forall ((L1 tptp.list_nat) (L22 tptp.list_d)) (let ((_let_1 (@ tptp.size_size_list_d L22))) (=> (= L (@ (@ tptp.zip_nat_d L1) L22)) (=> (= (@ tptp.size_size_list_nat L1) _let_1) (not (= (@ tptp.size_s457006183821432778_nat_d L) _let_1)))))))))
% 3.70/4.03 (assert (forall ((F4 (-> tptp.produc1908205239877642774nteger Bool)) (A2 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B2 tptp.produc8923325533196201883nteger)) (=> (@ (@ (@ tptp.produc1217013493180205570eger_o F4) A2) B2) (@ F4 (@ (@ tptp.produc8603105652947943368nteger A2) B2)))))
% 3.70/4.03 (assert (forall ((F4 (-> tptp.produc3925858234332021118et_nat Bool)) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ (@ tptp.produc6216949301066131538_nat_o F4) A2) B2) (@ F4 (@ (@ tptp.produc5001842942810119800et_nat A2) B2)))))
% 3.70/4.03 (assert (forall ((F4 (-> tptp.produc2732055786443039994et_nat Bool)) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.produc3925858234332021118et_nat)) (=> (@ (@ (@ tptp.produc5101573711933517782_nat_o F4) A2) B2) (@ F4 (@ (@ tptp.produc2245416461498447860et_nat A2) B2)))))
% 3.70/4.03 (assert (forall ((F4 (-> tptp.produc2285326912895808259nt_int Bool)) (A2 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B2 tptp.product_prod_int_int)) (=> (@ (@ (@ tptp.produc730925184835016917_int_o F4) A2) B2) (@ F4 (@ (@ tptp.produc5700946648718959541nt_int A2) B2)))))
% 3.70/4.03 (assert (forall ((F4 (-> tptp.produc7773217078559923341nt_int Bool)) (A2 (-> tptp.int tptp.option6357759511663192854e_term)) (B2 tptp.product_prod_int_int)) (=> (@ (@ (@ tptp.produc9098658269643458507_int_o F4) A2) B2) (@ F4 (@ (@ tptp.produc4305682042979456191nt_int A2) B2)))))
% 3.70/4.03 (assert (forall ((F4 (-> tptp.produc1908205239877642774nteger Bool)) (A2 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B2 tptp.produc8923325533196201883nteger)) (=> (@ (@ (@ tptp.produc1217013493180205570eger_o F4) A2) B2) (@ F4 (@ (@ tptp.produc8603105652947943368nteger A2) B2)))))
% 3.70/4.03 (assert (forall ((F4 (-> tptp.produc3925858234332021118et_nat Bool)) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ (@ tptp.produc6216949301066131538_nat_o F4) A2) B2) (@ F4 (@ (@ tptp.produc5001842942810119800et_nat A2) B2)))))
% 3.70/4.03 (assert (forall ((F4 (-> tptp.produc2732055786443039994et_nat Bool)) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.produc3925858234332021118et_nat)) (=> (@ (@ (@ tptp.produc5101573711933517782_nat_o F4) A2) B2) (@ F4 (@ (@ tptp.produc2245416461498447860et_nat A2) B2)))))
% 3.70/4.03 (assert (forall ((F4 (-> tptp.produc2285326912895808259nt_int Bool)) (A2 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B2 tptp.product_prod_int_int)) (=> (@ (@ (@ tptp.produc730925184835016917_int_o F4) A2) B2) (@ F4 (@ (@ tptp.produc5700946648718959541nt_int A2) B2)))))
% 3.70/4.03 (assert (forall ((F4 (-> tptp.produc7773217078559923341nt_int Bool)) (A2 (-> tptp.int tptp.option6357759511663192854e_term)) (B2 tptp.product_prod_int_int)) (=> (@ (@ (@ tptp.produc9098658269643458507_int_o F4) A2) B2) (@ F4 (@ (@ tptp.produc4305682042979456191nt_int A2) B2)))))
% 3.70/4.03 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Xs tptp.list_s1210847774152347623at_nat) (Ys tptp.list_s1210847774152347623at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Y)) (@ tptp.set_Pr3765526544606949372at_nat (@ (@ tptp.zip_se5600341670672612855at_nat Xs) Ys))) (@ (@ tptp.member2643936169264416010at_nat Y) (@ tptp.set_se5049602875457034614at_nat Ys)))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat) (Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.zip_nat_nat Xs) Ys))) (@ (@ tptp.member_nat Y) (@ tptp.set_nat2 Ys)))))
% 3.70/4.03 (assert (forall ((X tptp.assn) (Y tptp.assn) (Xs tptp.list_assn) (Ys tptp.list_assn)) (=> (@ (@ tptp.member7957490590177025114n_assn (@ (@ tptp.produc118845697133431529n_assn X) Y)) (@ tptp.set_Pr1139785259514867910n_assn (@ (@ tptp.zip_assn_assn Xs) Ys))) (@ (@ tptp.member_assn Y) (@ tptp.set_assn2 Ys)))))
% 3.70/4.03 (assert (forall ((X (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (Y tptp.produc8923325533196201883nteger) (Xs tptp.list_P1316552470764441098e_term) (Ys tptp.list_P5578671422887162913nteger)) (=> (@ (@ tptp.member4164122664394876845nteger (@ (@ tptp.produc8603105652947943368nteger X) Y)) (@ tptp.set_Pr2135590979564877377nteger (@ (@ tptp.zip_Pr8292346330294042792nteger Xs) Ys))) (@ (@ tptp.member157494554546826820nteger Y) (@ tptp.set_Pr920681315882439344nteger Ys)))))
% 3.70/4.03 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Y tptp.produc3658429121746597890et_nat) (Xs tptp.list_P7985473006766602707_nat_o) (Ys tptp.list_P9062070895058802706et_nat)) (=> (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat X) Y)) (@ tptp.set_Pr364071364088684201et_nat (@ (@ tptp.zip_Pr7134870689397686104et_nat Xs) Ys))) (@ (@ tptp.member6260224972018164377et_nat Y) (@ tptp.set_Pr3864771053587467565et_nat Ys)))))
% 3.70/4.03 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Y tptp.produc3925858234332021118et_nat) (Xs tptp.list_P7985473006766602707_nat_o) (Ys tptp.list_P2321686559999237006et_nat)) (=> (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat X) Y)) (@ tptp.set_Pr7458301993993767461et_nat (@ (@ tptp.zip_Pr8136144321567152340et_nat Xs) Ys))) (@ (@ tptp.member1996754912294343701et_nat Y) (@ tptp.set_Pr364071364088684201et_nat Ys)))))
% 3.70/4.03 (assert (forall ((X (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y tptp.product_prod_int_int) (Xs tptp.list_P1743416141875011707e_term) (Ys tptp.list_P5707943133018811711nt_int)) (=> (@ (@ tptp.member7618704894036264090nt_int (@ (@ tptp.produc5700946648718959541nt_int X) Y)) (@ tptp.set_Pr4943052134776177454nt_int (@ (@ tptp.zip_Pr4168994715204986005nt_int Xs) Ys))) (@ (@ tptp.member5262025264175285858nt_int Y) (@ tptp.set_Pr2470121279949933262nt_int Ys)))))
% 3.70/4.03 (assert (forall ((X (-> tptp.int tptp.option6357759511663192854e_term)) (Y tptp.product_prod_int_int) (Xs tptp.list_i8448526496819171953e_term) (Ys tptp.list_P5707943133018811711nt_int)) (=> (@ (@ tptp.member7034335876925520548nt_int (@ (@ tptp.produc4305682042979456191nt_int X) Y)) (@ tptp.set_Pr1633835384712236856nt_int (@ (@ tptp.zip_in8766932505889695135nt_int Xs) Ys))) (@ (@ tptp.member5262025264175285858nt_int Y) (@ tptp.set_Pr2470121279949933262nt_int Ys)))))
% 3.70/4.03 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Xs tptp.list_s1210847774152347623at_nat) (Ys tptp.list_s1210847774152347623at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Y)) (@ tptp.set_Pr3765526544606949372at_nat (@ (@ tptp.zip_se5600341670672612855at_nat Xs) Ys))) (@ (@ tptp.member2643936169264416010at_nat X) (@ tptp.set_se5049602875457034614at_nat Xs)))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat) (Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.zip_nat_nat Xs) Ys))) (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs)))))
% 3.70/4.03 (assert (forall ((X tptp.assn) (Y tptp.assn) (Xs tptp.list_assn) (Ys tptp.list_assn)) (=> (@ (@ tptp.member7957490590177025114n_assn (@ (@ tptp.produc118845697133431529n_assn X) Y)) (@ tptp.set_Pr1139785259514867910n_assn (@ (@ tptp.zip_assn_assn Xs) Ys))) (@ (@ tptp.member_assn X) (@ tptp.set_assn2 Xs)))))
% 3.70/4.03 (assert (forall ((X (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (Y tptp.produc8923325533196201883nteger) (Xs tptp.list_P1316552470764441098e_term) (Ys tptp.list_P5578671422887162913nteger)) (=> (@ (@ tptp.member4164122664394876845nteger (@ (@ tptp.produc8603105652947943368nteger X) Y)) (@ tptp.set_Pr2135590979564877377nteger (@ (@ tptp.zip_Pr8292346330294042792nteger Xs) Ys))) (@ (@ tptp.member4242434998011752849e_term X) (@ tptp.set_Pr8342322266483756581e_term Xs)))))
% 3.70/4.03 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Y tptp.produc3658429121746597890et_nat) (Xs tptp.list_P7985473006766602707_nat_o) (Ys tptp.list_P9062070895058802706et_nat)) (=> (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat X) Y)) (@ tptp.set_Pr364071364088684201et_nat (@ (@ tptp.zip_Pr7134870689397686104et_nat Xs) Ys))) (@ (@ tptp.member6576561426505652726_nat_o X) (@ tptp.set_Pr400311997697478754_nat_o Xs)))))
% 3.70/4.03 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Y tptp.produc3925858234332021118et_nat) (Xs tptp.list_P7985473006766602707_nat_o) (Ys tptp.list_P2321686559999237006et_nat)) (=> (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat X) Y)) (@ tptp.set_Pr7458301993993767461et_nat (@ (@ tptp.zip_Pr8136144321567152340et_nat Xs) Ys))) (@ (@ tptp.member6576561426505652726_nat_o X) (@ tptp.set_Pr400311997697478754_nat_o Xs)))))
% 3.70/4.03 (assert (forall ((X (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y tptp.product_prod_int_int) (Xs tptp.list_P1743416141875011707e_term) (Ys tptp.list_P5707943133018811711nt_int)) (=> (@ (@ tptp.member7618704894036264090nt_int (@ (@ tptp.produc5700946648718959541nt_int X) Y)) (@ tptp.set_Pr4943052134776177454nt_int (@ (@ tptp.zip_Pr4168994715204986005nt_int Xs) Ys))) (@ (@ tptp.member3222579708246209666e_term X) (@ tptp.set_Pr16608062948090134e_term Xs)))))
% 3.70/4.03 (assert (forall ((X (-> tptp.int tptp.option6357759511663192854e_term)) (Y tptp.product_prod_int_int) (Xs tptp.list_i8448526496819171953e_term) (Ys tptp.list_P5707943133018811711nt_int)) (=> (@ (@ tptp.member7034335876925520548nt_int (@ (@ tptp.produc4305682042979456191nt_int X) Y)) (@ tptp.set_Pr1633835384712236856nt_int (@ (@ tptp.zip_in8766932505889695135nt_int Xs) Ys))) (@ (@ tptp.member8845023287901829240e_term X) (@ tptp.set_in5217446777445088012e_term Xs)))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int) (Xs tptp.list_int) (Ys tptp.list_int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) (@ tptp.set_Pr2470121279949933262nt_int (@ (@ tptp.zip_int_int Xs) Ys))) (not (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs)) (not (@ (@ tptp.member_int Y) (@ tptp.set_int2 Ys))))))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.nat) (Xs tptp.list_int) (Ys tptp.list_nat)) (=> (@ (@ tptp.member216504246829706758nt_nat (@ (@ tptp.product_Pair_int_nat X) Y)) (@ tptp.set_Pr6647972299459129970nt_nat (@ (@ tptp.zip_int_nat Xs) Ys))) (not (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs)) (not (@ (@ tptp.member_nat Y) (@ tptp.set_nat2 Ys))))))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.int) (Xs tptp.list_nat) (Ys tptp.list_int)) (=> (@ (@ tptp.member4262671552274231302at_int (@ (@ tptp.product_Pair_nat_int X) Y)) (@ tptp.set_Pr1470767568048878706at_int (@ (@ tptp.zip_nat_int Xs) Ys))) (not (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs)) (not (@ (@ tptp.member_int Y) (@ tptp.set_int2 Ys))))))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat) (Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.zip_nat_nat Xs) Ys))) (not (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs)) (not (@ (@ tptp.member_nat Y) (@ tptp.set_nat2 Ys))))))))
% 3.70/4.03 (assert (forall ((X tptp.assn) (Y tptp.assn) (Xs tptp.list_assn) (Ys tptp.list_assn)) (=> (@ (@ tptp.member7957490590177025114n_assn (@ (@ tptp.produc118845697133431529n_assn X) Y)) (@ tptp.set_Pr1139785259514867910n_assn (@ (@ tptp.zip_assn_assn Xs) Ys))) (not (=> (@ (@ tptp.member_assn X) (@ tptp.set_assn2 Xs)) (not (@ (@ tptp.member_assn Y) (@ tptp.set_assn2 Ys))))))))
% 3.70/4.03 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.int) (Xs tptp.list_P6011104703257516679at_nat) (Ys tptp.list_int)) (=> (@ (@ tptp.member8394280151737582451at_int (@ (@ tptp.produc6348220600061155286at_int X) Y)) (@ tptp.set_Pr3658594827066574855at_int (@ (@ tptp.zip_Pr6866960147343648950at_int Xs) Ys))) (not (=> (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs)) (not (@ (@ tptp.member_int Y) (@ tptp.set_int2 Ys))))))))
% 3.70/4.03 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.nat) (Xs tptp.list_P6011104703257516679at_nat) (Ys tptp.list_nat)) (=> (@ (@ tptp.member3348759134392003351at_nat (@ (@ tptp.produc6350711070570205562at_nat X) Y)) (@ tptp.set_Pr7836445846575771563at_nat (@ (@ tptp.zip_Pr6869450617852699226at_nat Xs) Ys))) (not (=> (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs)) (not (@ (@ tptp.member_nat Y) (@ tptp.set_nat2 Ys))))))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.product_prod_nat_nat) (Xs tptp.list_int) (Ys tptp.list_P6011104703257516679at_nat)) (=> (@ (@ tptp.member5261114234888836065at_nat (@ (@ tptp.produc3525228511222278652at_nat X) Y)) (@ tptp.set_Pr525428910217828469at_nat (@ (@ tptp.zip_in4043968058504772316at_nat Xs) Ys))) (not (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs)) (not (@ (@ tptp.member8440522571783428010at_nat Y) (@ tptp.set_Pr5648618587558075414at_nat Ys))))))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.produc6575502325842934193n_assn) (Xs tptp.list_int) (Ys tptp.list_P8527749157015355191n_assn)) (=> (@ (@ tptp.member241480614033477777n_assn (@ (@ tptp.produc3313821056773121708n_assn X) Y)) (@ tptp.set_Pr4510407026980144421n_assn (@ (@ tptp.zip_in7098856637274830732n_assn Xs) Ys))) (not (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs)) (not (@ (@ tptp.member7957490590177025114n_assn Y) (@ tptp.set_Pr1139785259514867910n_assn Ys))))))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.product_prod_nat_nat) (Xs tptp.list_nat) (Ys tptp.list_P6011104703257516679at_nat)) (=> (@ (@ tptp.member2223272150424702269at_nat (@ (@ tptp.produc487386426758144856at_nat X) Y)) (@ tptp.set_Pr6710958862608470481at_nat (@ (@ tptp.zip_na1006125974040638520at_nat Xs) Ys))) (not (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs)) (not (@ (@ tptp.member8440522571783428010at_nat Y) (@ tptp.set_Pr5648618587558075414at_nat Ys))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.produc3843707927480180839at_nat) (B2 tptp.produc3843707927480180839at_nat) (Xs tptp.list_P5464809261938338413at_nat)) (= (@ (@ tptp.member6009668390874684176at_nat (@ (@ tptp.produc2335810615602371415at_nat A2) B2)) (@ tptp.set_Pr4552580085251402108at_nat (@ (@ tptp.zip_Pr2522280425463452279at_nat Xs) Xs))) (and (@ (@ tptp.member8757157785044589968at_nat A2) (@ tptp.set_Pr3765526544606949372at_nat Xs)) (= A2 B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.product_prod_nat_nat) (B2 tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (= (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat A2) B2)) (@ tptp.set_Pr5518436109238095868at_nat (@ (@ tptp.zip_Pr4664179122662387191at_nat Xs) Xs))) (and (@ (@ tptp.member8440522571783428010at_nat A2) (@ tptp.set_Pr5648618587558075414at_nat Xs)) (= A2 B2)))))
% 3.70/4.03 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 (-> tptp.produc3658429121746597890et_nat Bool)) (Xs tptp.list_P7985473006766602707_nat_o)) (= (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o A2) B2)) (@ tptp.set_Pr8666615595052072444_nat_o (@ (@ tptp.zip_Pr2849639184604596727_nat_o Xs) Xs))) (and (@ (@ tptp.member6576561426505652726_nat_o A2) (@ tptp.set_Pr400311997697478754_nat_o Xs)) (= A2 B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (Xs tptp.list_s1210847774152347623at_nat)) (= (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat A2) B2)) (@ tptp.set_Pr3765526544606949372at_nat (@ (@ tptp.zip_se5600341670672612855at_nat Xs) Xs))) (and (@ (@ tptp.member2643936169264416010at_nat A2) (@ tptp.set_se5049602875457034614at_nat Xs)) (= A2 B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int) (Xs tptp.list_int)) (= (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B2)) (@ tptp.set_Pr2470121279949933262nt_int (@ (@ tptp.zip_int_int Xs) Xs))) (and (@ (@ tptp.member_int A2) (@ tptp.set_int2 Xs)) (= A2 B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (Xs tptp.list_nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B2)) (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.zip_nat_nat Xs) Xs))) (and (@ (@ tptp.member_nat A2) (@ tptp.set_nat2 Xs)) (= A2 B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.produc6575502325842934193n_assn) (B2 tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (= (@ (@ tptp.member4743710847862083984n_assn (@ (@ tptp.produc6128706242671166167n_assn A2) B2)) (@ tptp.set_Pr8975451644279219196n_assn (@ (@ tptp.zip_Pr8806919808394484215n_assn Xs) Xs))) (and (@ (@ tptp.member7957490590177025114n_assn A2) (@ tptp.set_Pr1139785259514867910n_assn Xs)) (= A2 B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (Xs tptp.list_assn)) (= (@ (@ tptp.member7957490590177025114n_assn (@ (@ tptp.produc118845697133431529n_assn A2) B2)) (@ tptp.set_Pr1139785259514867910n_assn (@ (@ tptp.zip_assn_assn Xs) Xs))) (and (@ (@ tptp.member_assn A2) (@ tptp.set_assn2 Xs)) (= A2 B2)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_c) (I tptp.nat) (X tptp.c) (Ys tptp.list_c) (Y tptp.c)) (= (@ (@ tptp.zip_c_c (@ (@ (@ tptp.list_update_c Xs) I) X)) (@ (@ (@ tptp.list_update_c Ys) I) Y)) (@ (@ (@ tptp.list_u8616212504517173525od_c_c (@ (@ tptp.zip_c_c Xs) Ys)) I) (@ (@ tptp.product_Pair_c_c X) Y)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_c) (I tptp.nat) (X tptp.c) (Ys tptp.list_d) (Y tptp.d)) (= (@ (@ tptp.zip_c_d (@ (@ (@ tptp.list_update_c Xs) I) X)) (@ (@ (@ tptp.list_update_d Ys) I) Y)) (@ (@ (@ tptp.list_u8616212508820402326od_c_d (@ (@ tptp.zip_c_d Xs) Ys)) I) (@ (@ tptp.product_Pair_c_d X) Y)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_d) (I tptp.nat) (X tptp.d) (Ys tptp.list_c) (Y tptp.c)) (= (@ (@ tptp.zip_d_c (@ (@ (@ tptp.list_update_d Xs) I) X)) (@ (@ (@ tptp.list_update_c Ys) I) Y)) (@ (@ (@ tptp.list_u5828756922544497492od_d_c (@ (@ tptp.zip_d_c Xs) Ys)) I) (@ (@ tptp.product_Pair_d_c X) Y)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_d) (I tptp.nat) (X tptp.d) (Ys tptp.list_d) (Y tptp.d)) (= (@ (@ tptp.zip_d_d (@ (@ (@ tptp.list_update_d Xs) I) X)) (@ (@ (@ tptp.list_update_d Ys) I) Y)) (@ (@ (@ tptp.list_u5828756926847726293od_d_d (@ (@ tptp.zip_d_d Xs) Ys)) I) (@ (@ tptp.product_Pair_d_d X) Y)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_P1316552470764441098e_term) (I tptp.nat) (X (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (Ys tptp.list_P5578671422887162913nteger) (Y tptp.produc8923325533196201883nteger)) (= (@ (@ tptp.zip_Pr8292346330294042792nteger (@ (@ (@ tptp.list_u877304756163299468e_term Xs) I) X)) (@ (@ (@ tptp.list_u2254550707601501961nteger Ys) I) Y)) (@ (@ (@ tptp.list_u234853988314817064nteger (@ (@ tptp.zip_Pr8292346330294042792nteger Xs) Ys)) I) (@ (@ tptp.produc8603105652947943368nteger X) Y)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_P7985473006766602707_nat_o) (I tptp.nat) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Ys tptp.list_P9062070895058802706et_nat) (Y tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.zip_Pr7134870689397686104et_nat (@ (@ (@ tptp.list_u6943956310655620667_nat_o Xs) I) X)) (@ (@ (@ tptp.list_u9060326803697358356et_nat Ys) I) Y)) (@ (@ (@ tptp.list_u1866171116859985808et_nat (@ (@ tptp.zip_Pr7134870689397686104et_nat Xs) Ys)) I) (@ (@ tptp.produc5001842942810119800et_nat X) Y)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_P7985473006766602707_nat_o) (I tptp.nat) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Ys tptp.list_P2321686559999237006et_nat) (Y tptp.produc3925858234332021118et_nat)) (= (@ (@ tptp.zip_Pr8136144321567152340et_nat (@ (@ (@ tptp.list_u6943956310655620667_nat_o Xs) I) X)) (@ (@ (@ tptp.list_u1866171116859985808et_nat Ys) I) Y)) (@ (@ (@ tptp.list_u1913845194572276492et_nat (@ (@ tptp.zip_Pr8136144321567152340et_nat Xs) Ys)) I) (@ (@ tptp.produc2245416461498447860et_nat X) Y)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_P1743416141875011707e_term) (I tptp.nat) (X (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Ys tptp.list_P5707943133018811711nt_int) (Y tptp.product_prod_int_int)) (= (@ (@ tptp.zip_Pr4168994715204986005nt_int (@ (@ (@ tptp.list_u3533491785856317309e_term Xs) I) X)) (@ (@ (@ tptp.list_u3002344382305578791nt_int Ys) I) Y)) (@ (@ (@ tptp.list_u7736365598306452245nt_int (@ (@ tptp.zip_Pr4168994715204986005nt_int Xs) Ys)) I) (@ (@ tptp.produc5700946648718959541nt_int X) Y)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_i8448526496819171953e_term) (I tptp.nat) (X (-> tptp.int tptp.option6357759511663192854e_term)) (Ys tptp.list_P5707943133018811711nt_int) (Y tptp.product_prod_int_int)) (= (@ (@ tptp.zip_in8766932505889695135nt_int (@ (@ (@ tptp.list_u8946639151299769843e_term Xs) I) X)) (@ (@ (@ tptp.list_u3002344382305578791nt_int Ys) I) Y)) (@ (@ (@ tptp.list_u4780935413889332127nt_int (@ (@ tptp.zip_in8766932505889695135nt_int Xs) Ys)) I) (@ (@ tptp.produc4305682042979456191nt_int X) Y)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_assn) (Ys tptp.list_assn) (X tptp.assn)) (=> (= (@ tptp.size_size_list_assn Xs) (@ tptp.size_size_list_assn Ys)) (=> (@ (@ tptp.member_assn X) (@ tptp.set_assn2 Xs)) (not (forall ((Y2 tptp.assn)) (not (@ (@ tptp.member7957490590177025114n_assn (@ (@ tptp.produc118845697133431529n_assn X) Y2)) (@ tptp.set_Pr1139785259514867910n_assn (@ (@ tptp.zip_assn_assn Xs) Ys))))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_c) (X tptp.c)) (=> (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_c Ys)) (=> (@ (@ tptp.member_c X) (@ tptp.set_c2 Xs)) (not (forall ((Y2 tptp.c)) (not (@ (@ tptp.member5074992359041316560od_c_c (@ (@ tptp.product_Pair_c_c X) Y2)) (@ tptp.set_Product_prod_c_c2 (@ (@ tptp.zip_c_c Xs) Ys))))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_d) (X tptp.c)) (=> (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_d Ys)) (=> (@ (@ tptp.member_c X) (@ tptp.set_c2 Xs)) (not (forall ((Y2 tptp.d)) (not (@ (@ tptp.member5074992363344545361od_c_d (@ (@ tptp.product_Pair_c_d X) Y2)) (@ tptp.set_Product_prod_c_d2 (@ (@ tptp.zip_c_d Xs) Ys))))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_nat) (X tptp.c)) (=> (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_nat Ys)) (=> (@ (@ tptp.member_c X) (@ tptp.set_c2 Xs)) (not (forall ((Y2 tptp.nat)) (not (@ (@ tptp.member8195077246299207702_c_nat (@ (@ tptp.product_Pair_c_nat X) Y2)) (@ tptp.set_Pr3395872032415823530_c_nat (@ (@ tptp.zip_c_nat Xs) Ys))))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_int) (X tptp.c)) (=> (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_int Ys)) (=> (@ (@ tptp.member_c X) (@ tptp.set_c2 Xs)) (not (forall ((Y2 tptp.int)) (not (@ (@ tptp.member4017226226790010994_c_int (@ (@ tptp.product_Pair_c_int X) Y2)) (@ tptp.set_Pr8441393049761402630_c_int (@ (@ tptp.zip_c_int Xs) Ys))))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_d) (Ys tptp.list_c) (X tptp.d)) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_c Ys)) (=> (@ (@ tptp.member_d X) (@ tptp.set_d2 Xs)) (not (forall ((Y2 tptp.c)) (not (@ (@ tptp.member2287536777068640527od_d_c (@ (@ tptp.product_Pair_d_c X) Y2)) (@ tptp.set_Product_prod_d_c2 (@ (@ tptp.zip_d_c Xs) Ys))))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_d) (Ys tptp.list_d) (X tptp.d)) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_d Ys)) (=> (@ (@ tptp.member_d X) (@ tptp.set_d2 Xs)) (not (forall ((Y2 tptp.d)) (not (@ (@ tptp.member2287536781371869328od_d_d (@ (@ tptp.product_Pair_d_d X) Y2)) (@ tptp.set_Product_prod_d_d2 (@ (@ tptp.zip_d_d Xs) Ys))))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_d) (Ys tptp.list_nat) (X tptp.d)) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_nat Ys)) (=> (@ (@ tptp.member_d X) (@ tptp.set_d2 Xs)) (not (forall ((Y2 tptp.nat)) (not (@ (@ tptp.member207149538400826391_d_nat (@ (@ tptp.product_Pair_d_nat X) Y2)) (@ tptp.set_Pr4631316361372218027_d_nat (@ (@ tptp.zip_d_nat Xs) Ys))))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_d) (Ys tptp.list_int) (X tptp.d)) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_int Ys)) (=> (@ (@ tptp.member_d X) (@ tptp.set_d2 Xs)) (not (forall ((Y2 tptp.int)) (not (@ (@ tptp.member5252670555746405491_d_int (@ (@ tptp.product_Pair_d_int X) Y2)) (@ tptp.set_Pr453465341863021319_d_int (@ (@ tptp.zip_d_int Xs) Ys))))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_c) (X tptp.nat)) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_c Ys)) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs)) (not (forall ((Y2 tptp.c)) (not (@ (@ tptp.member8962352060716553276_nat_c (@ (@ tptp.product_Pair_nat_c X) Y2)) (@ tptp.set_Pr4163146846833169104_nat_c (@ (@ tptp.zip_nat_c Xs) Ys))))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_assn) (Ys tptp.list_assn) (Y tptp.assn)) (=> (= (@ tptp.size_size_list_assn Xs) (@ tptp.size_size_list_assn Ys)) (=> (@ (@ tptp.member_assn Y) (@ tptp.set_assn2 Ys)) (not (forall ((X3 tptp.assn)) (not (@ (@ tptp.member7957490590177025114n_assn (@ (@ tptp.produc118845697133431529n_assn X3) Y)) (@ tptp.set_Pr1139785259514867910n_assn (@ (@ tptp.zip_assn_assn Xs) Ys))))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_c) (Y tptp.c)) (=> (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_c Ys)) (=> (@ (@ tptp.member_c Y) (@ tptp.set_c2 Ys)) (not (forall ((X3 tptp.c)) (not (@ (@ tptp.member5074992359041316560od_c_c (@ (@ tptp.product_Pair_c_c X3) Y)) (@ tptp.set_Product_prod_c_c2 (@ (@ tptp.zip_c_c Xs) Ys))))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_d) (Y tptp.d)) (=> (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_d Ys)) (=> (@ (@ tptp.member_d Y) (@ tptp.set_d2 Ys)) (not (forall ((X3 tptp.c)) (not (@ (@ tptp.member5074992363344545361od_c_d (@ (@ tptp.product_Pair_c_d X3) Y)) (@ tptp.set_Product_prod_c_d2 (@ (@ tptp.zip_c_d Xs) Ys))))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_nat) (Y tptp.nat)) (=> (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_nat Ys)) (=> (@ (@ tptp.member_nat Y) (@ tptp.set_nat2 Ys)) (not (forall ((X3 tptp.c)) (not (@ (@ tptp.member8195077246299207702_c_nat (@ (@ tptp.product_Pair_c_nat X3) Y)) (@ tptp.set_Pr3395872032415823530_c_nat (@ (@ tptp.zip_c_nat Xs) Ys))))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_int) (Y tptp.int)) (=> (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_int Ys)) (=> (@ (@ tptp.member_int Y) (@ tptp.set_int2 Ys)) (not (forall ((X3 tptp.c)) (not (@ (@ tptp.member4017226226790010994_c_int (@ (@ tptp.product_Pair_c_int X3) Y)) (@ tptp.set_Pr8441393049761402630_c_int (@ (@ tptp.zip_c_int Xs) Ys))))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_d) (Ys tptp.list_c) (Y tptp.c)) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_c Ys)) (=> (@ (@ tptp.member_c Y) (@ tptp.set_c2 Ys)) (not (forall ((X3 tptp.d)) (not (@ (@ tptp.member2287536777068640527od_d_c (@ (@ tptp.product_Pair_d_c X3) Y)) (@ tptp.set_Product_prod_d_c2 (@ (@ tptp.zip_d_c Xs) Ys))))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_d) (Ys tptp.list_d) (Y tptp.d)) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_d Ys)) (=> (@ (@ tptp.member_d Y) (@ tptp.set_d2 Ys)) (not (forall ((X3 tptp.d)) (not (@ (@ tptp.member2287536781371869328od_d_d (@ (@ tptp.product_Pair_d_d X3) Y)) (@ tptp.set_Product_prod_d_d2 (@ (@ tptp.zip_d_d Xs) Ys))))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_d) (Ys tptp.list_nat) (Y tptp.nat)) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_nat Ys)) (=> (@ (@ tptp.member_nat Y) (@ tptp.set_nat2 Ys)) (not (forall ((X3 tptp.d)) (not (@ (@ tptp.member207149538400826391_d_nat (@ (@ tptp.product_Pair_d_nat X3) Y)) (@ tptp.set_Pr4631316361372218027_d_nat (@ (@ tptp.zip_d_nat Xs) Ys))))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_d) (Ys tptp.list_int) (Y tptp.int)) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_int Ys)) (=> (@ (@ tptp.member_int Y) (@ tptp.set_int2 Ys)) (not (forall ((X3 tptp.d)) (not (@ (@ tptp.member5252670555746405491_d_int (@ (@ tptp.product_Pair_d_int X3) Y)) (@ tptp.set_Pr453465341863021319_d_int (@ (@ tptp.zip_d_int Xs) Ys))))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_c) (Y tptp.c)) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_c Ys)) (=> (@ (@ tptp.member_c Y) (@ tptp.set_c2 Ys)) (not (forall ((X3 tptp.nat)) (not (@ (@ tptp.member8962352060716553276_nat_c (@ (@ tptp.product_Pair_nat_c X3) Y)) (@ tptp.set_Pr4163146846833169104_nat_c (@ (@ tptp.zip_nat_c Xs) Ys))))))))))
% 3.70/4.03 (assert (forall ((X tptp.produc3843707927480180839at_nat) (Xs tptp.list_P5464809261938338413at_nat)) (let ((_let_1 (@ tptp.size_s1588839187904960729at_nat Xs))) (let ((_let_2 (@ tptp.size_s1588839187904960729at_nat (@ (@ tptp.remove8895909992688781315at_nat X) Xs)))) (let ((_let_3 (@ (@ tptp.member8757157785044589968at_nat X) (@ tptp.set_Pr3765526544606949372at_nat Xs)))) (and (=> _let_3 (= _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))))
% 3.70/4.03 (assert (forall ((X tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (let ((_let_1 (@ tptp.size_s5460976970255530739at_nat Xs))) (let ((_let_2 (@ tptp.size_s5460976970255530739at_nat (@ (@ tptp.remove5766854097993331357at_nat X) Xs)))) (let ((_let_3 (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs)))) (and (=> _let_3 (= _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))))
% 3.70/4.03 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xs tptp.list_P7985473006766602707_nat_o)) (let ((_let_1 (@ tptp.size_s8908918004648414271_nat_o Xs))) (let ((_let_2 (@ tptp.size_s8908918004648414271_nat_o (@ (@ tptp.remove4235003712227595625_nat_o X) Xs)))) (let ((_let_3 (@ (@ tptp.member6576561426505652726_nat_o X) (@ tptp.set_Pr400311997697478754_nat_o Xs)))) (and (=> _let_3 (= _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))))
% 3.70/4.03 (assert (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ tptp.size_s6829681357464350627n_assn Xs))) (let ((_let_2 (@ tptp.size_s6829681357464350627n_assn (@ (@ tptp.remove1670527618125605709n_assn X) Xs)))) (let ((_let_3 (@ (@ tptp.member7957490590177025114n_assn X) (@ tptp.set_Pr1139785259514867910n_assn Xs)))) (and (=> _let_3 (= _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))))
% 3.70/4.03 (assert (forall ((X tptp.c) (Xs tptp.list_c)) (let ((_let_1 (@ tptp.size_size_list_c Xs))) (let ((_let_2 (@ tptp.size_size_list_c (@ (@ tptp.remove1_c X) Xs)))) (let ((_let_3 (@ (@ tptp.member_c X) (@ tptp.set_c2 Xs)))) (and (=> _let_3 (= _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))))
% 3.70/4.03 (assert (forall ((X tptp.d) (Xs tptp.list_d)) (let ((_let_1 (@ tptp.size_size_list_d Xs))) (let ((_let_2 (@ tptp.size_size_list_d (@ (@ tptp.remove1_d X) Xs)))) (let ((_let_3 (@ (@ tptp.member_d X) (@ tptp.set_d2 Xs)))) (and (=> _let_3 (= _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Xs))) (let ((_let_2 (@ tptp.size_size_list_nat (@ (@ tptp.remove1_nat X) Xs)))) (let ((_let_3 (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs)))) (and (=> _let_3 (= _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Xs tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Xs))) (let ((_let_2 (@ tptp.size_size_list_int (@ (@ tptp.remove1_int X) Xs)))) (let ((_let_3 (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs)))) (and (=> _let_3 (= _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (= (@ (@ tptp.insert_nat2 X) (@ tptp.coset_nat Xs)) (@ tptp.coset_nat (@ (@ tptp.removeAll_nat X) Xs)))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Xs tptp.list_int)) (= (@ (@ tptp.insert_int2 X) (@ tptp.coset_int Xs)) (@ tptp.coset_int (@ (@ tptp.removeAll_int X) Xs)))))
% 3.70/4.03 (assert (forall ((X tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (= (@ (@ tptp.insert8211810215607154385at_nat X) (@ tptp.coset_6809516720700967924at_nat Xs)) (@ tptp.coset_6809516720700967924at_nat (@ (@ tptp.remove3673390508374433037at_nat X) Xs)))))
% 3.70/4.03 (assert (forall ((X tptp.produc3843707927480180839at_nat) (Xs tptp.list_P5464809261938338413at_nat)) (= (@ (@ tptp.insert9069300056098147895at_nat X) (@ tptp.coset_5307619257043544794at_nat Xs)) (@ tptp.coset_5307619257043544794at_nat (@ (@ tptp.remove4908499291543849587at_nat X) Xs)))))
% 3.70/4.03 (assert (forall ((X Bool) (Xs tptp.list_o)) (= (@ (@ tptp.insert_o2 X) (@ tptp.coset_o Xs)) (@ tptp.coset_o (@ (@ tptp.removeAll_o X) Xs)))))
% 3.70/4.03 (assert (forall ((L12 tptp.list_c) (L23 tptp.list_c)) (=> (= (@ tptp.size_size_list_c L12) (@ tptp.size_size_list_c L23)) (= (@ (@ (@ tptp.zipf_c684006316856269033od_c_c tptp.product_Pair_c_c) L12) L23) (@ (@ tptp.zip_c_c L12) L23)))))
% 3.70/4.03 (assert (forall ((L12 tptp.list_c) (L23 tptp.list_d)) (=> (= (@ tptp.size_size_list_c L12) (@ tptp.size_size_list_d L23)) (= (@ (@ (@ tptp.zipf_c44566020827681705od_c_d tptp.product_Pair_c_d) L12) L23) (@ (@ tptp.zip_c_d L12) L23)))))
% 3.70/4.03 (assert (forall ((L12 tptp.list_c) (L23 tptp.list_nat)) (=> (= (@ tptp.size_size_list_c L12) (@ tptp.size_size_list_nat L23)) (= (@ (@ (@ tptp.zipf_c7084520048314076179_c_nat tptp.product_Pair_c_nat) L12) L23) (@ (@ tptp.zip_c_nat L12) L23)))))
% 3.70/4.03 (assert (forall ((L12 tptp.list_c) (L23 tptp.list_int)) (=> (= (@ tptp.size_size_list_c L12) (@ tptp.size_size_list_int L23)) (= (@ (@ (@ tptp.zipf_c230841880303976139_c_int tptp.product_Pair_c_int) L12) L23) (@ (@ tptp.zip_c_int L12) L23)))))
% 3.70/4.03 (assert (forall ((L12 tptp.list_d) (L23 tptp.list_c)) (=> (= (@ tptp.size_size_list_d L12) (@ tptp.size_size_list_c L23)) (= (@ (@ (@ tptp.zipf_d1836499321508429225od_d_c tptp.product_Pair_d_c) L12) L23) (@ (@ tptp.zip_d_c L12) L23)))))
% 3.70/4.03 (assert (forall ((L12 tptp.list_d) (L23 tptp.list_d)) (=> (= (@ tptp.size_size_list_d L12) (@ tptp.size_size_list_d L23)) (= (@ (@ (@ tptp.zipf_d1197059025479841897od_d_d tptp.product_Pair_d_d) L12) L23) (@ (@ tptp.zip_d_d L12) L23)))))
% 3.70/4.03 (assert (forall ((L12 tptp.list_d) (L23 tptp.list_nat)) (=> (= (@ tptp.size_size_list_d L12) (@ tptp.size_size_list_nat L23)) (= (@ (@ (@ tptp.zipf_d7851395264309270293_d_nat tptp.product_Pair_d_nat) L12) L23) (@ (@ tptp.zip_d_nat L12) L23)))))
% 3.70/4.03 (assert (forall ((L12 tptp.list_d) (L23 tptp.list_int)) (=> (= (@ tptp.size_size_list_d L12) (@ tptp.size_size_list_int L23)) (= (@ (@ (@ tptp.zipf_d997717096299170253_d_int tptp.product_Pair_d_int) L12) L23) (@ (@ tptp.zip_d_int L12) L23)))))
% 3.70/4.03 (assert (forall ((L12 tptp.list_nat) (L23 tptp.list_c)) (=> (= (@ tptp.size_size_list_nat L12) (@ tptp.size_size_list_c L23)) (= (@ (@ (@ tptp.zipf_n5773672615478942615_nat_c tptp.product_Pair_nat_c) L12) L23) (@ (@ tptp.zip_nat_c L12) L23)))))
% 3.70/4.03 (assert (forall ((L12 tptp.list_nat) (L23 tptp.list_d)) (=> (= (@ tptp.size_size_list_nat L12) (@ tptp.size_size_list_d L23)) (= (@ (@ (@ tptp.zipf_n3657244561791696409_nat_d tptp.product_Pair_nat_d) L12) L23) (@ (@ tptp.zip_nat_d L12) L23)))))
% 3.70/4.03 (assert (forall ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (= (@ tptp.one_assn_raw (@ (@ tptp.produc7507926704131184380et_nat H2) As2)) (= As2 tptp.bot_bot_set_nat))))
% 3.70/4.03 (assert (forall ((X tptp.produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ tptp.one_assn_raw X) Y) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (= X (@ (@ tptp.produc7507926704131184380et_nat H) As)) (= Y (not (= As tptp.bot_bot_set_nat)))))))))
% 3.70/4.03 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (=> (@ tptp.one_assn_raw X) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (= X (@ (@ tptp.produc7507926704131184380et_nat H) As)) (not (= As tptp.bot_bot_set_nat))))))))
% 3.70/4.03 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (=> (not (@ tptp.one_assn_raw X)) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (= X (@ (@ tptp.produc7507926704131184380et_nat H) As)) (= As tptp.bot_bot_set_nat)))))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o X))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.insert5175938949040314269_nat_o X))) (let ((_let_4 (@ _let_1 B))) (let ((_let_5 (@ tptp.ord_le2453136405763929_nat_o A))) (= (@ _let_5 (@ _let_3 B)) (and (=> _let_4 (@ _let_5 B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_le2453136405763929_nat_o (@ (@ tptp.minus_1801376950450012436_nat_o A) (@ _let_3 tptp.bot_bo7824918357723582233_nat_o))) B)) (=> (not _let_2) (@ (@ tptp.ord_le2965882846123202637_nat_o A) B)))))))))))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (X tptp.produc3843707927480180839at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat X))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.insert9069300056098147895at_nat X))) (let ((_let_4 (@ _let_1 B))) (let ((_let_5 (@ tptp.ord_le2604355607129572851at_nat A))) (= (@ _let_5 (@ _let_3 B)) (and (=> _let_4 (@ _let_5 B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_le2604355607129572851at_nat (@ (@ tptp.minus_3314409938677909166at_nat A) (@ _let_3 tptp.bot_bo228742789529271731at_nat))) B)) (=> (not _let_2) (@ (@ tptp.ord_le1268244103169919719at_nat A) B)))))))))))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.insert8211810215607154385at_nat X))) (let ((_let_4 (@ _let_1 B))) (let ((_let_5 (@ tptp.ord_le7866589430770878221at_nat A))) (= (@ _let_5 (@ _let_3 B)) (and (=> _let_4 (@ _let_5 B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_le7866589430770878221at_nat (@ (@ tptp.minus_1356011639430497352at_nat A) (@ _let_3 tptp.bot_bo2099793752762293965at_nat))) B)) (=> (not _let_2) (@ (@ tptp.ord_le3146513528884898305at_nat A) B)))))))))))))
% 3.70/4.03 (assert (forall ((A tptp.set_o) (X Bool) (B tptp.set_o)) (let ((_let_1 (@ tptp.member_o X))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.insert_o2 X))) (let ((_let_4 (@ _let_1 B))) (let ((_let_5 (@ tptp.ord_less_set_o A))) (= (@ _let_5 (@ _let_3 B)) (and (=> _let_4 (@ _let_5 B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_o (@ (@ tptp.minus_minus_set_o A) (@ _let_3 tptp.bot_bot_set_o))) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_o A) B)))))))))))))
% 3.70/4.03 (assert (forall ((A tptp.set_int) (X tptp.int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int X))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.insert_int2 X))) (let ((_let_4 (@ _let_1 B))) (let ((_let_5 (@ tptp.ord_less_set_int A))) (= (@ _let_5 (@ _let_3 B)) (and (=> _let_4 (@ _let_5 B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_int (@ (@ tptp.minus_minus_set_int A) (@ _let_3 tptp.bot_bot_set_int))) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_int A) B)))))))))))))
% 3.70/4.03 (assert (forall ((A tptp.set_nat) (X tptp.nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat X))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.insert_nat2 X))) (let ((_let_4 (@ _let_1 B))) (let ((_let_5 (@ tptp.ord_less_set_nat A))) (= (@ _let_5 (@ _let_3 B)) (and (=> _let_4 (@ _let_5 B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_nat (@ (@ tptp.minus_minus_set_nat A) (@ _let_3 tptp.bot_bot_set_nat))) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_nat A) B)))))))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_c) (R2 tptp.set_Product_prod_c_c) (N tptp.nat)) (=> (@ (@ tptp.member7012247553653173456list_c (@ (@ tptp.produc5515445818230282391list_c Xs) Ys)) (@ (@ tptp.lexn_c R2) N)) (and (= (@ tptp.size_size_list_c Xs) N) (= (@ tptp.size_size_list_c Ys) N)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_d) (Ys tptp.list_d) (R2 tptp.set_Product_prod_d_d) (N tptp.nat)) (=> (@ (@ tptp.member1810801192463332112list_d (@ (@ tptp.produc242965421297323863list_d Xs) Ys)) (@ (@ tptp.lexn_d R2) N)) (and (= (@ tptp.size_size_list_d Xs) N) (= (@ tptp.size_size_list_d Ys) N)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (R2 tptp.set_Pr1261947904930325089at_nat) (N tptp.nat)) (=> (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Xs) Ys)) (@ (@ tptp.lexn_nat R2) N)) (and (= (@ tptp.size_size_list_nat Xs) N) (= (@ tptp.size_size_list_nat Ys) N)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int) (R2 tptp.set_Pr958786334691620121nt_int) (N tptp.nat)) (=> (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Xs) Ys)) (@ (@ tptp.lexn_int R2) N)) (and (= (@ tptp.size_size_list_int Xs) N) (= (@ tptp.size_size_list_int Ys) N)))))
% 3.70/4.03 (assert (= tptp.pairwi3222497012029234898at_nat (lambda ((R3 (-> tptp.produc3843707927480180839at_nat tptp.produc3843707927480180839at_nat Bool)) (S2 tptp.set_Pr4329608150637261639at_nat)) (forall ((X2 tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X2) S2) (forall ((Y5 tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat Y5) (@ (@ tptp.minus_3314409938677909166at_nat S2) (@ (@ tptp.insert9069300056098147895at_nat X2) tptp.bot_bo228742789529271731at_nat))) (@ (@ R3 X2) Y5))))))))
% 3.70/4.03 (assert (= tptp.pairwi6357175311820755948at_nat (lambda ((R3 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (S2 tptp.set_Pr1261947904930325089at_nat)) (forall ((X2 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X2) S2) (forall ((Y5 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat Y5) (@ (@ tptp.minus_1356011639430497352at_nat S2) (@ (@ tptp.insert8211810215607154385at_nat X2) tptp.bot_bo2099793752762293965at_nat))) (@ (@ R3 X2) Y5))))))))
% 3.70/4.03 (assert (= tptp.pairwise_o (lambda ((R3 (-> Bool Bool Bool)) (S2 tptp.set_o)) (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) S2) (forall ((Y5 Bool)) (=> (@ (@ tptp.member_o Y5) (@ (@ tptp.minus_minus_set_o S2) (@ (@ tptp.insert_o2 X2) tptp.bot_bot_set_o))) (@ (@ R3 X2) Y5))))))))
% 3.70/4.03 (assert (= tptp.pairwise_int (lambda ((R3 (-> tptp.int tptp.int Bool)) (S2 tptp.set_int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) S2) (forall ((Y5 tptp.int)) (=> (@ (@ tptp.member_int Y5) (@ (@ tptp.minus_minus_set_int S2) (@ (@ tptp.insert_int2 X2) tptp.bot_bot_set_int))) (@ (@ R3 X2) Y5))))))))
% 3.70/4.03 (assert (= tptp.pairwise_nat (lambda ((R3 (-> tptp.nat tptp.nat Bool)) (S2 tptp.set_nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) S2) (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.member_nat Y5) (@ (@ tptp.minus_minus_set_nat S2) (@ (@ tptp.insert_nat2 X2) tptp.bot_bot_set_nat))) (@ (@ R3 X2) Y5))))))))
% 3.70/4.03 (assert (forall ((B2 Bool) (Q tptp.assn)) (let ((_let_1 (@ tptp.pure_assn B2))) (= (@ (@ tptp.inf_inf_assn _let_1) Q) (@ (@ tptp.times_times_assn (@ (@ tptp.inf_inf_assn tptp.one_one_assn) Q)) _let_1)))))
% 3.70/4.03 (assert (forall ((P tptp.assn) (B2 Bool)) (let ((_let_1 (@ tptp.pure_assn B2))) (= (@ (@ tptp.inf_inf_assn P) _let_1) (@ (@ tptp.times_times_assn (@ (@ tptp.inf_inf_assn tptp.one_one_assn) P)) _let_1)))))
% 3.70/4.03 (assert (forall ((X tptp.assn)) (@ (@ tptp.ord_less_eq_assn X) X)))
% 3.70/4.03 (assert (forall ((X tptp.filter_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat X) X)))
% 3.70/4.03 (assert (forall ((X tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X) X)))
% 3.70/4.03 (assert (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) X)))
% 3.70/4.03 (assert (forall ((X tptp.int)) (@ (@ tptp.ord_less_eq_int X) X)))
% 3.70/4.03 (assert (forall ((A2 tptp.assn)) (@ (@ tptp.ord_less_eq_assn A2) A2)))
% 3.70/4.03 (assert (forall ((A2 tptp.filter_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat A2) A2)))
% 3.70/4.03 (assert (forall ((A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A2) A2)))
% 3.70/4.03 (assert (forall ((A2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat A2) A2)))
% 3.70/4.03 (assert (forall ((A2 tptp.int)) (@ (@ tptp.ord_less_eq_int A2) A2)))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (=> (forall ((X3 tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat X3))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_le1268244103169919719at_nat A) B))))
% 3.70/4.03 (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) (@ _let_1 B)))) (@ (@ tptp.ord_le3146513528884898305at_nat A) B))))
% 3.70/4.03 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (forall ((X3 tptp.int)) (let ((_let_1 (@ tptp.member_int X3))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_less_eq_set_int A) B))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o X3))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_le2965882846123202637_nat_o A) B))))
% 3.70/4.03 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X3))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.ord_less_eq_set_nat A) B))))
% 3.70/4.03 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (= A B)))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn)) (= (@ (@ tptp.inf_inf_assn A2) A2) A2)))
% 3.70/4.03 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A2) A2) A2)))
% 3.70/4.03 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A2) A2) A2)))
% 3.70/4.03 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn X) X) X)))
% 3.70/4.03 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X) X) X)))
% 3.70/4.03 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat X) X) X)))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn A2))) (let ((_let_2 (@ _let_1 B2))) (= (@ _let_1 _let_2) _let_2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A2))) (let ((_let_2 (@ _let_1 B2))) (= (@ _let_1 _let_2) _let_2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A2))) (let ((_let_2 (@ _let_1 B2))) (= (@ _let_1 _let_2) _let_2)))))
% 3.70/4.03 (assert (forall ((X tptp.assn) (Y tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 3.70/4.03 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 3.70/4.03 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn)) (let ((_let_1 (@ (@ tptp.inf_inf_assn A2) B2))) (= (@ (@ tptp.inf_inf_assn _let_1) B2) _let_1))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.inf_inf_set_nat A2) B2))) (= (@ (@ tptp.inf_inf_set_nat _let_1) B2) _let_1))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2))) (= (@ (@ tptp.inf_in2572325071724192079at_nat _let_1) B2) _let_1))))
% 3.70/4.03 (assert (forall ((X tptp.assn) (Y tptp.assn)) (let ((_let_1 (@ (@ tptp.inf_inf_assn X) Y))) (= (@ (@ tptp.inf_inf_assn _let_1) Y) _let_1))))
% 3.70/4.03 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (let ((_let_1 (@ (@ tptp.inf_inf_set_nat X) Y))) (= (@ (@ tptp.inf_inf_set_nat _let_1) Y) _let_1))))
% 3.70/4.03 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ tptp.inf_in2572325071724192079at_nat X) Y))) (= (@ (@ tptp.inf_in2572325071724192079at_nat _let_1) Y) _let_1))))
% 3.70/4.03 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat X))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z)) (and (@ _let_1 Y) (@ _let_1 Z))))))
% 3.70/4.03 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn X))) (= (@ _let_1 (@ (@ tptp.inf_inf_assn Y) Z)) (and (@ _let_1 Y) (@ _let_1 Z))))))
% 3.70/4.03 (assert (forall ((X tptp.filter_nat) (Y tptp.filter_nat) (Z tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_le2510731241096832064er_nat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_filter_nat Y) Z)) (and (@ _let_1 Y) (@ _let_1 Z))))))
% 3.70/4.03 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y) Z)) (and (@ _let_1 Y) (@ _let_1 Z))))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z)) (and (@ _let_1 Y) (@ _let_1 Z))))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (= (@ _let_1 (@ (@ tptp.inf_inf_int Y) Z)) (and (@ _let_1 Y) (@ _let_1 Z))))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A2))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B2) C)) (and (@ _let_1 B2) (@ _let_1 C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn A2))) (= (@ _let_1 (@ (@ tptp.inf_inf_assn B2) C)) (and (@ _let_1 B2) (@ _let_1 C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat) (C tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_le2510731241096832064er_nat A2))) (= (@ _let_1 (@ (@ tptp.inf_inf_filter_nat B2) C)) (and (@ _let_1 B2) (@ _let_1 C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat B2) C)) (and (@ _let_1 B2) (@ _let_1 C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (= (@ _let_1 (@ (@ tptp.inf_inf_nat B2) C)) (and (@ _let_1 B2) (@ _let_1 C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A2))) (= (@ _let_1 (@ (@ tptp.inf_inf_int B2) C)) (and (@ _let_1 B2) (@ _let_1 C))))))
% 3.70/4.03 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn X) tptp.bot_bot_assn) tptp.bot_bot_assn)))
% 3.70/4.03 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat X) tptp.bot_bo228742789529271731at_nat) tptp.bot_bo228742789529271731at_nat)))
% 3.70/4.03 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat X) tptp.bot_bo2099793752762293965at_nat) tptp.bot_bo2099793752762293965at_nat)))
% 3.70/4.03 (assert (forall ((X tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o X) tptp.bot_bot_set_o) tptp.bot_bot_set_o)))
% 3.70/4.03 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X) tptp.bot_bot_set_nat) tptp.bot_bot_set_nat)))
% 3.70/4.03 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int X) tptp.bot_bot_set_int) tptp.bot_bot_set_int)))
% 3.70/4.03 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn tptp.bot_bot_assn) X) tptp.bot_bot_assn)))
% 3.70/4.03 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat tptp.bot_bo228742789529271731at_nat) X) tptp.bot_bo228742789529271731at_nat)))
% 3.70/4.03 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bot_bo2099793752762293965at_nat) X) tptp.bot_bo2099793752762293965at_nat)))
% 3.70/4.03 (assert (forall ((X tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o tptp.bot_bot_set_o) X) tptp.bot_bot_set_o)))
% 3.70/4.03 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat tptp.bot_bot_set_nat) X) tptp.bot_bot_set_nat)))
% 3.70/4.03 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int tptp.bot_bot_set_int) X) tptp.bot_bot_set_int)))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat A) tptp.bot_bo228742789529271731at_nat) (= A tptp.bot_bo228742789529271731at_nat))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat A) tptp.bot_bo2099793752762293965at_nat) (= A tptp.bot_bo2099793752762293965at_nat))))
% 3.70/4.03 (assert (forall ((A tptp.set_o)) (= (@ (@ tptp.ord_less_eq_set_o A) tptp.bot_bot_set_o) (= A tptp.bot_bot_set_o))))
% 3.70/4.03 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))))
% 3.70/4.03 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat) (= A tptp.bot_bot_set_nat))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat tptp.bot_bo228742789529271731at_nat) A)))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat tptp.bot_bo2099793752762293965at_nat) A)))
% 3.70/4.03 (assert (forall ((A tptp.set_o)) (@ (@ tptp.ord_less_eq_set_o tptp.bot_bot_set_o) A)))
% 3.70/4.03 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A)))
% 3.70/4.03 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A)))
% 3.70/4.03 (assert (forall ((X Bool) (A tptp.set_o) (B tptp.set_o)) (= (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.insert_o2 X) A)) B) (and (@ (@ tptp.member_o X) B) (@ (@ tptp.ord_less_eq_set_o A) B)))))
% 3.70/4.03 (assert (forall ((X tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.insert9069300056098147895at_nat X) A)) B) (and (@ (@ tptp.member8757157785044589968at_nat X) B) (@ (@ tptp.ord_le1268244103169919719at_nat A) B)))))
% 3.70/4.03 (assert (forall ((X tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.insert8211810215607154385at_nat X) A)) B) (and (@ (@ tptp.member8440522571783428010at_nat X) B) (@ (@ tptp.ord_le3146513528884898305at_nat A) B)))))
% 3.70/4.03 (assert (forall ((X tptp.int) (A tptp.set_int) (B tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.insert_int2 X) A)) B) (and (@ (@ tptp.member_int X) B) (@ (@ tptp.ord_less_eq_set_int A) B)))))
% 3.70/4.03 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.ord_le2965882846123202637_nat_o (@ (@ tptp.insert5175938949040314269_nat_o X) A)) B) (and (@ (@ tptp.member6576561426505652726_nat_o X) B) (@ (@ tptp.ord_le2965882846123202637_nat_o A) B)))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.insert_nat2 X) A)) B) (and (@ (@ tptp.member_nat X) B) (@ (@ tptp.ord_less_eq_set_nat A) B)))))
% 3.70/4.03 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_set_nat A) B)))))
% 3.70/4.03 (assert (forall ((A2 Bool) (B2 Bool)) (= (@ (@ tptp.inf_inf_assn (@ tptp.pure_assn A2)) (@ tptp.pure_assn B2)) (@ tptp.pure_assn (and A2 B2)))))
% 3.70/4.03 (assert (forall ((B2 tptp.produc3843707927480180839at_nat) (A2 tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ (@ tptp.insert9069300056098147895at_nat B2) tptp.bot_bo228742789529271731at_nat))) (= (= _let_1 (@ (@ tptp.insert9069300056098147895at_nat A2) A)) (and (= A2 B2) (@ (@ tptp.ord_le1268244103169919719at_nat A) _let_1))))))
% 3.70/4.03 (assert (forall ((B2 tptp.product_prod_nat_nat) (A2 tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ tptp.insert8211810215607154385at_nat B2) tptp.bot_bo2099793752762293965at_nat))) (= (= _let_1 (@ (@ tptp.insert8211810215607154385at_nat A2) A)) (and (= A2 B2) (@ (@ tptp.ord_le3146513528884898305at_nat A) _let_1))))))
% 3.70/4.03 (assert (forall ((B2 Bool) (A2 Bool) (A tptp.set_o)) (let ((_let_1 (@ (@ tptp.insert_o2 B2) tptp.bot_bot_set_o))) (= (= _let_1 (@ (@ tptp.insert_o2 A2) A)) (and (= A2 B2) (@ (@ tptp.ord_less_eq_set_o A) _let_1))))))
% 3.70/4.03 (assert (forall ((B2 tptp.int) (A2 tptp.int) (A tptp.set_int)) (let ((_let_1 (@ (@ tptp.insert_int2 B2) tptp.bot_bot_set_int))) (= (= _let_1 (@ (@ tptp.insert_int2 A2) A)) (and (= A2 B2) (@ (@ tptp.ord_less_eq_set_int A) _let_1))))))
% 3.70/4.03 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ (@ tptp.insert_nat2 B2) tptp.bot_bot_set_nat))) (= (= _let_1 (@ (@ tptp.insert_nat2 A2) A)) (and (= A2 B2) (@ (@ tptp.ord_less_eq_set_nat A) _let_1))))))
% 3.70/4.03 (assert (forall ((A2 tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B2 tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ (@ tptp.insert9069300056098147895at_nat B2) tptp.bot_bo228742789529271731at_nat))) (= (= (@ (@ tptp.insert9069300056098147895at_nat A2) A) _let_1) (and (= A2 B2) (@ (@ tptp.ord_le1268244103169919719at_nat A) _let_1))))))
% 3.70/4.03 (assert (forall ((A2 tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.insert8211810215607154385at_nat B2) tptp.bot_bo2099793752762293965at_nat))) (= (= (@ (@ tptp.insert8211810215607154385at_nat A2) A) _let_1) (and (= A2 B2) (@ (@ tptp.ord_le3146513528884898305at_nat A) _let_1))))))
% 3.70/4.03 (assert (forall ((A2 Bool) (A tptp.set_o) (B2 Bool)) (let ((_let_1 (@ (@ tptp.insert_o2 B2) tptp.bot_bot_set_o))) (= (= (@ (@ tptp.insert_o2 A2) A) _let_1) (and (= A2 B2) (@ (@ tptp.ord_less_eq_set_o A) _let_1))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (A tptp.set_int) (B2 tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int2 B2) tptp.bot_bot_set_int))) (= (= (@ (@ tptp.insert_int2 A2) A) _let_1) (and (= A2 B2) (@ (@ tptp.ord_less_eq_set_int A) _let_1))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (A tptp.set_nat) (B2 tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat2 B2) tptp.bot_bot_set_nat))) (= (= (@ (@ tptp.insert_nat2 A2) A) _let_1) (and (= A2 B2) (@ (@ tptp.ord_less_eq_set_nat A) _let_1))))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (= (= (@ (@ tptp.minus_3314409938677909166at_nat A) B) tptp.bot_bo228742789529271731at_nat) (@ (@ tptp.ord_le1268244103169919719at_nat A) B))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.minus_1356011639430497352at_nat A) B) tptp.bot_bo2099793752762293965at_nat) (@ (@ tptp.ord_le3146513528884898305at_nat A) B))))
% 3.70/4.03 (assert (forall ((A tptp.set_o) (B tptp.set_o)) (= (= (@ (@ tptp.minus_minus_set_o A) B) tptp.bot_bot_set_o) (@ (@ tptp.ord_less_eq_set_o A) B))))
% 3.70/4.03 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int A) B) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int A) B))))
% 3.70/4.03 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat A) B) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat A) B))))
% 3.70/4.03 (assert (forall ((P tptp.assn) (Q tptp.assn) (B2 Bool)) (let ((_let_1 (@ tptp.pure_assn B2))) (let ((_let_2 (@ tptp.inf_inf_assn P))) (= (@ _let_2 (@ (@ tptp.times_times_assn Q) _let_1)) (@ (@ tptp.times_times_assn (@ _let_2 Q)) _let_1))))))
% 3.70/4.03 (assert (forall ((P tptp.assn) (B2 Bool) (Q tptp.assn)) (let ((_let_1 (@ tptp.pure_assn B2))) (= (@ (@ tptp.inf_inf_assn (@ (@ tptp.times_times_assn P) _let_1)) Q) (@ (@ tptp.times_times_assn (@ (@ tptp.inf_inf_assn P) Q)) _let_1)))))
% 3.70/4.03 (assert (forall ((P tptp.assn) (Q tptp.assn) (H2 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) tptp.bot_bot_set_nat))) (= (@ (@ tptp.rep_assn (@ (@ tptp.inf_inf_assn P) Q)) _let_1) (and (@ (@ tptp.rep_assn P) _let_1) (@ (@ tptp.rep_assn Q) _let_1))))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (X tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat X))) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 3.70/4.03 (assert (forall ((A tptp.set_int) (B tptp.set_int) (X tptp.int)) (let ((_let_1 (@ tptp.member_int X))) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o X))) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 3.70/4.03 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (C tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 3.70/4.03 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o) (C (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 3.70/4.03 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (@ _let_1 A) (@ _let_1 B))))))
% 3.70/4.03 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (= A B) (not (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (not (@ (@ tptp.ord_less_eq_set_nat B) A)))))))
% 3.70/4.03 (assert (forall ((R (-> tptp.produc3843707927480180839at_nat tptp.produc3843707927480180839at_nat Bool)) (S tptp.set_Pr4329608150637261639at_nat) (X tptp.produc3843707927480180839at_nat) (Y tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.pairwi3222497012029234898at_nat R) S) (=> (@ (@ tptp.member8757157785044589968at_nat X) S) (=> (@ (@ tptp.member8757157785044589968at_nat Y) S) (=> (not (= X Y)) (@ (@ R X) Y)))))))
% 3.70/4.03 (assert (forall ((R (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (S tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (=> (@ (@ tptp.pairwi6357175311820755948at_nat R) S) (=> (@ (@ tptp.member8440522571783428010at_nat X) S) (=> (@ (@ tptp.member8440522571783428010at_nat Y) S) (=> (not (= X Y)) (@ (@ R X) Y)))))))
% 3.70/4.03 (assert (forall ((R (-> tptp.nat tptp.nat Bool)) (S tptp.set_nat) (X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.pairwise_nat R) S) (=> (@ (@ tptp.member_nat X) S) (=> (@ (@ tptp.member_nat Y) S) (=> (not (= X Y)) (@ (@ R X) Y)))))))
% 3.70/4.03 (assert (forall ((R (-> tptp.int tptp.int Bool)) (S tptp.set_int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.pairwise_int R) S) (=> (@ (@ tptp.member_int X) S) (=> (@ (@ tptp.member_int Y) S) (=> (not (= X Y)) (@ (@ R X) Y)))))))
% 3.70/4.03 (assert (forall ((R (-> (-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) Bool)) (S tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Y (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.pairwi2432143822833250616_nat_o R) S) (=> (@ (@ tptp.member6576561426505652726_nat_o X) S) (=> (@ (@ tptp.member6576561426505652726_nat_o Y) S) (=> (not (= X Y)) (@ (@ R X) Y)))))))
% 3.70/4.03 (assert (forall ((S tptp.set_Pr4329608150637261639at_nat) (R (-> tptp.produc3843707927480180839at_nat tptp.produc3843707927480180839at_nat Bool))) (=> (forall ((X3 tptp.produc3843707927480180839at_nat) (Y2 tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X3) S) (=> (@ (@ tptp.member8757157785044589968at_nat Y2) S) (=> (not (= X3 Y2)) (@ (@ R X3) Y2))))) (@ (@ tptp.pairwi3222497012029234898at_nat R) S))))
% 3.70/4.03 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (R (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool))) (=> (forall ((X3 tptp.product_prod_nat_nat) (Y2 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) S) (=> (@ (@ tptp.member8440522571783428010at_nat Y2) S) (=> (not (= X3 Y2)) (@ (@ R X3) Y2))))) (@ (@ tptp.pairwi6357175311820755948at_nat R) S))))
% 3.70/4.03 (assert (forall ((S tptp.set_nat) (R (-> tptp.nat tptp.nat Bool))) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (=> (@ (@ tptp.member_nat Y2) S) (=> (not (= X3 Y2)) (@ (@ R X3) Y2))))) (@ (@ tptp.pairwise_nat R) S))))
% 3.70/4.03 (assert (forall ((S tptp.set_int) (R (-> tptp.int tptp.int Bool))) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.member_int X3) S) (=> (@ (@ tptp.member_int Y2) S) (=> (not (= X3 Y2)) (@ (@ R X3) Y2))))) (@ (@ tptp.pairwise_int R) S))))
% 3.70/4.03 (assert (forall ((S tptp.set_Pr4532377907799695533_nat_o) (R (-> (-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X3) S) (=> (@ (@ tptp.member6576561426505652726_nat_o Y2) S) (=> (not (= X3 Y2)) (@ (@ R X3) Y2))))) (@ (@ tptp.pairwi2432143822833250616_nat_o R) S))))
% 3.70/4.03 (assert (= tptp.ord_le1268244103169919719at_nat (lambda ((A5 tptp.set_Pr4329608150637261639at_nat) (B7 tptp.set_Pr4329608150637261639at_nat)) (forall ((X2 tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat X2))) (=> (@ _let_1 A5) (@ _let_1 B7)))))))
% 3.70/4.03 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((A5 tptp.set_Pr1261947904930325089at_nat) (B7 tptp.set_Pr1261947904930325089at_nat)) (forall ((X2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X2))) (=> (@ _let_1 A5) (@ _let_1 B7)))))))
% 3.70/4.03 (assert (= tptp.ord_less_eq_set_int (lambda ((A5 tptp.set_int) (B7 tptp.set_int)) (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.member_int X2))) (=> (@ _let_1 A5) (@ _let_1 B7)))))))
% 3.70/4.03 (assert (= tptp.ord_le2965882846123202637_nat_o (lambda ((A5 tptp.set_Pr4532377907799695533_nat_o) (B7 tptp.set_Pr4532377907799695533_nat_o)) (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o X2))) (=> (@ _let_1 A5) (@ _let_1 B7)))))))
% 3.70/4.03 (assert (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B7 tptp.set_nat)) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X2))) (=> (@ _let_1 A5) (@ _let_1 B7)))))))
% 3.70/4.03 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (= A B) (@ (@ tptp.ord_less_eq_set_nat A) B))))
% 3.70/4.03 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (= A B) (@ (@ tptp.ord_less_eq_set_nat B) A))))
% 3.70/4.03 (assert (= tptp.ord_le1268244103169919719at_nat (lambda ((A5 tptp.set_Pr4329608150637261639at_nat) (B7 tptp.set_Pr4329608150637261639at_nat)) (forall ((T2 tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat T2))) (=> (@ _let_1 A5) (@ _let_1 B7)))))))
% 3.70/4.03 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((A5 tptp.set_Pr1261947904930325089at_nat) (B7 tptp.set_Pr1261947904930325089at_nat)) (forall ((T2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat T2))) (=> (@ _let_1 A5) (@ _let_1 B7)))))))
% 3.70/4.03 (assert (= tptp.ord_less_eq_set_int (lambda ((A5 tptp.set_int) (B7 tptp.set_int)) (forall ((T2 tptp.int)) (let ((_let_1 (@ tptp.member_int T2))) (=> (@ _let_1 A5) (@ _let_1 B7)))))))
% 3.70/4.03 (assert (= tptp.ord_le2965882846123202637_nat_o (lambda ((A5 tptp.set_Pr4532377907799695533_nat_o) (B7 tptp.set_Pr4532377907799695533_nat_o)) (forall ((T2 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o T2))) (=> (@ _let_1 A5) (@ _let_1 B7)))))))
% 3.70/4.03 (assert (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B7 tptp.set_nat)) (forall ((T2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat T2))) (=> (@ _let_1 A5) (@ _let_1 B7)))))))
% 3.70/4.03 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A) A)))
% 3.70/4.03 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (Q (-> tptp.product_prod_nat_nat Bool))) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ P X3) (@ Q X3))) (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.collec3392354462482085612at_nat P)) (@ tptp.collec3392354462482085612at_nat Q)))))
% 3.70/4.03 (assert (forall ((P (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool)) (Q (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ P X3) (@ Q X3))) (@ (@ tptp.ord_le2965882846123202637_nat_o (@ tptp.collec939566748876313656_nat_o P)) (@ tptp.collec939566748876313656_nat_o Q)))))
% 3.70/4.03 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (=> (@ P X3) (@ Q X3))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat P)) (@ tptp.collect_nat Q)))))
% 3.70/4.03 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_nat B) C2) (@ _let_1 C2))))))
% 3.70/4.03 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.set_nat) (Q (-> tptp.nat tptp.nat Bool)) (B tptp.set_nat)) (=> (@ (@ tptp.pairwise_nat P) A) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ P X3) Y2) (@ (@ Q X3) Y2))) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (@ (@ tptp.pairwise_nat Q) B))))))
% 3.70/4.03 (assert (= (lambda ((Y4 tptp.set_nat) (Z2 tptp.set_nat)) (= Y4 Z2)) (lambda ((A5 tptp.set_nat) (B7 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A5) B7) (@ (@ tptp.ord_less_eq_set_nat B7) A5)))))
% 3.70/4.03 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (S tptp.set_nat) (T3 tptp.set_nat)) (let ((_let_1 (@ tptp.pairwise_nat P))) (=> (@ _let_1 S) (=> (@ (@ tptp.ord_less_eq_set_nat T3) S) (@ _let_1 T3))))))
% 3.70/4.03 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (Q (-> tptp.product_prod_nat_nat Bool))) (= (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.collec3392354462482085612at_nat P)) (@ tptp.collec3392354462482085612at_nat Q)) (forall ((X2 tptp.product_prod_nat_nat)) (=> (@ P X2) (@ Q X2))))))
% 3.70/4.03 (assert (forall ((P (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool)) (Q (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (= (@ (@ tptp.ord_le2965882846123202637_nat_o (@ tptp.collec939566748876313656_nat_o P)) (@ tptp.collec939566748876313656_nat_o Q)) (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ P X2) (@ Q X2))))))
% 3.70/4.03 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat P)) (@ tptp.collect_nat Q)) (forall ((X2 tptp.nat)) (=> (@ P X2) (@ Q X2))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (C tptp.assn) (D2 tptp.assn)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_eq_assn B2) C) (=> (= C D2) (@ (@ tptp.ord_less_eq_assn A2) D2))))))
% 3.70/4.03 (assert (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat) (C tptp.filter_nat) (D2 tptp.filter_nat)) (=> (= A2 B2) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B2) C) (=> (= C D2) (@ (@ tptp.ord_le2510731241096832064er_nat A2) D2))))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (C tptp.set_nat) (D2 tptp.set_nat)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) C) (=> (= C D2) (@ (@ tptp.ord_less_eq_set_nat A2) D2))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (= C D2) (@ (@ tptp.ord_less_eq_nat A2) D2))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int) (D2 tptp.int)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_eq_int B2) C) (=> (= C D2) (@ (@ tptp.ord_less_eq_int A2) D2))))))
% 3.70/4.03 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.product_prod_nat_nat Bool))) (= (@ (@ tptp.ord_le3146513528884898305at_nat S) (@ tptp.collec3392354462482085612at_nat P)) (forall ((X2 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X2) S) (@ P X2))))))
% 3.70/4.03 (assert (forall ((S tptp.set_Pr4532377907799695533_nat_o) (P (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (= (@ (@ tptp.ord_le2965882846123202637_nat_o S) (@ tptp.collec939566748876313656_nat_o P)) (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X2) S) (@ P X2))))))
% 3.70/4.03 (assert (forall ((S tptp.set_nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_set_nat S) (@ tptp.collect_nat P)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) S) (@ P X2))))))
% 3.70/4.03 (assert (forall ((X tptp.assn) (Y tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 3.70/4.03 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (let ((_let_2 (@ tptp.inf_inf_assn Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 3.70/4.03 (assert (= tptp.inf_inf_assn (lambda ((X2 tptp.assn) (Y5 tptp.assn)) (@ (@ tptp.inf_inf_assn Y5) X2))))
% 3.70/4.03 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn X) X) X)))
% 3.70/4.03 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (= (@ (@ tptp.inf_inf_assn (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_inf_assn Y) Z))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat A2) B2)) (and (@ (@ tptp.ord_less_eq_nat B2) A2) (not (= B2 A2))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int A2) B2)) (and (@ (@ tptp.ord_less_eq_int B2) A2) (not (= B2 A2))))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_int Z))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_int Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 3.70/4.03 (assert (= (lambda ((Y4 tptp.assn) (Z2 tptp.assn)) (= Y4 Z2)) (lambda ((X2 tptp.assn) (Y5 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn X2) Y5) (@ (@ tptp.ord_less_eq_assn Y5) X2)))))
% 3.70/4.03 (assert (= (lambda ((Y4 tptp.filter_nat) (Z2 tptp.filter_nat)) (= Y4 Z2)) (lambda ((X2 tptp.filter_nat) (Y5 tptp.filter_nat)) (and (@ (@ tptp.ord_le2510731241096832064er_nat X2) Y5) (@ (@ tptp.ord_le2510731241096832064er_nat Y5) X2)))))
% 3.70/4.03 (assert (= (lambda ((Y4 tptp.set_nat) (Z2 tptp.set_nat)) (= Y4 Z2)) (lambda ((X2 tptp.set_nat) (Y5 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat X2) Y5) (@ (@ tptp.ord_less_eq_set_nat Y5) X2)))))
% 3.70/4.03 (assert (= (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2)) (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X2) Y5) (@ (@ tptp.ord_less_eq_nat Y5) X2)))))
% 3.70/4.03 (assert (= (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2)) (lambda ((X2 tptp.int) (Y5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X2) Y5) (@ (@ tptp.ord_less_eq_int Y5) X2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (C tptp.assn)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_eq_assn B2) C) (@ (@ tptp.ord_less_eq_assn A2) C)))))
% 3.70/4.03 (assert (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat) (C tptp.filter_nat)) (=> (= A2 B2) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B2) C) (@ (@ tptp.ord_le2510731241096832064er_nat A2) C)))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (C tptp.set_nat)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) C) (@ (@ tptp.ord_less_eq_set_nat A2) C)))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (@ (@ tptp.ord_less_eq_nat A2) C)))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_eq_int B2) C) (@ (@ tptp.ord_less_eq_int A2) C)))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn A2))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat) (C tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_le2510731241096832064er_nat A2))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A2))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))))
% 3.70/4.03 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X) Y) (=> (@ (@ tptp.ord_less_eq_assn Y) X) (= X Y)))))
% 3.70/4.03 (assert (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat X) Y) (=> (@ (@ tptp.ord_le2510731241096832064er_nat Y) X) (= X Y)))))
% 3.70/4.03 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (= X Y)))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= X Y)))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= X Y)))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_assn B2) C) (@ _let_1 C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat) (C tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_le2510731241096832064er_nat A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B2) C) (@ _let_1 C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) C) (@ _let_1 C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (@ _let_1 C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_int B2) C) (@ _let_1 C))))))
% 3.70/4.03 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_assn Y) Z) (@ _let_1 Z))))))
% 3.70/4.03 (assert (forall ((X tptp.filter_nat) (Y tptp.filter_nat) (Z tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_le2510731241096832064er_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_le2510731241096832064er_nat Y) Z) (@ _let_1 Z))))))
% 3.70/4.03 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_nat Y) Z) (@ _let_1 Z))))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z) (@ _let_1 Z))))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ _let_1 Z))))))
% 3.70/4.03 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A2 tptp.nat) (B2 tptp.nat)) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A4) B4) (@ (@ P A4) B4))) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (@ (@ P B4) A4) (@ (@ P A4) B4))) (@ (@ P A2) B2)))))
% 3.70/4.03 (assert (forall ((P (-> tptp.int tptp.int Bool)) (A2 tptp.int) (B2 tptp.int)) (=> (forall ((A4 tptp.int) (B4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A4) B4) (@ (@ P A4) B4))) (=> (forall ((A4 tptp.int) (B4 tptp.int)) (=> (@ (@ P B4) A4) (@ (@ P A4) B4))) (@ (@ P A2) B2)))))
% 3.70/4.03 (assert (= (lambda ((Y4 tptp.assn) (Z2 tptp.assn)) (= Y4 Z2)) (lambda ((A3 tptp.assn) (B3 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn B3) A3) (@ (@ tptp.ord_less_eq_assn A3) B3)))))
% 3.70/4.03 (assert (= (lambda ((Y4 tptp.filter_nat) (Z2 tptp.filter_nat)) (= Y4 Z2)) (lambda ((A3 tptp.filter_nat) (B3 tptp.filter_nat)) (and (@ (@ tptp.ord_le2510731241096832064er_nat B3) A3) (@ (@ tptp.ord_le2510731241096832064er_nat A3) B3)))))
% 3.70/4.03 (assert (= (lambda ((Y4 tptp.set_nat) (Z2 tptp.set_nat)) (= Y4 Z2)) (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B3) A3) (@ (@ tptp.ord_less_eq_set_nat A3) B3)))))
% 3.70/4.03 (assert (= (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2)) (lambda ((A3 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B3) A3) (@ (@ tptp.ord_less_eq_nat A3) B3)))))
% 3.70/4.03 (assert (= (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2)) (lambda ((A3 tptp.int) (B3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B3) A3) (@ (@ tptp.ord_less_eq_int A3) B3)))))
% 3.70/4.03 (assert (forall ((B2 tptp.assn) (A2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn B2) A2) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (= A2 B2)))))
% 3.70/4.03 (assert (forall ((B2 tptp.filter_nat) (A2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B2) A2) (=> (@ (@ tptp.ord_le2510731241096832064er_nat A2) B2) (= A2 B2)))))
% 3.70/4.03 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A2) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (= A2 B2)))))
% 3.70/4.03 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= A2 B2)))))
% 3.70/4.03 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (= A2 B2)))))
% 3.70/4.03 (assert (forall ((B2 tptp.assn) (A2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn C))) (=> (@ (@ tptp.ord_less_eq_assn B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 3.70/4.03 (assert (forall ((B2 tptp.filter_nat) (A2 tptp.filter_nat) (C tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_le2510731241096832064er_nat C))) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 3.70/4.03 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C))) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 3.70/4.03 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 3.70/4.03 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (=> (@ (@ tptp.ord_less_eq_assn B2) A2) (= A2 B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat A2) B2) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B2) A2) (= A2 B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A2) (= A2 B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (= A2 B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (= A2 B2)))))
% 3.70/4.03 (assert (= (lambda ((Y4 tptp.assn) (Z2 tptp.assn)) (= Y4 Z2)) (lambda ((A3 tptp.assn) (B3 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn A3) B3) (@ (@ tptp.ord_less_eq_assn B3) A3)))))
% 3.70/4.03 (assert (= (lambda ((Y4 tptp.filter_nat) (Z2 tptp.filter_nat)) (= Y4 Z2)) (lambda ((A3 tptp.filter_nat) (B3 tptp.filter_nat)) (and (@ (@ tptp.ord_le2510731241096832064er_nat A3) B3) (@ (@ tptp.ord_le2510731241096832064er_nat B3) A3)))))
% 3.70/4.03 (assert (= (lambda ((Y4 tptp.set_nat) (Z2 tptp.set_nat)) (= Y4 Z2)) (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A3) B3) (@ (@ tptp.ord_less_eq_set_nat B3) A3)))))
% 3.70/4.03 (assert (= (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2)) (lambda ((A3 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B3) (@ (@ tptp.ord_less_eq_nat B3) A3)))))
% 3.70/4.03 (assert (= (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2)) (lambda ((A3 tptp.int) (B3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A3) B3) (@ (@ tptp.ord_less_eq_int B3) A3)))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (F4 (-> tptp.assn tptp.assn)) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_assn B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (F4 (-> tptp.nat tptp.assn)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_assn A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (F4 (-> tptp.int tptp.assn)) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_assn A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_int B2) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y2) (@ (@ tptp.ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (F4 (-> tptp.assn tptp.nat)) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_assn B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (F4 (-> tptp.nat tptp.nat)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (F4 (-> tptp.int tptp.nat)) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_int B2) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (F4 (-> tptp.assn tptp.int)) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_int A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_assn B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (F4 (-> tptp.nat tptp.int)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (F4 (-> tptp.int tptp.int)) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_int B2) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (F4 (-> tptp.filter_nat tptp.assn)) (B2 tptp.filter_nat) (C tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_less_eq_assn A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B2) C) (=> (forall ((X3 tptp.filter_nat) (Y2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat X3) Y2) (@ (@ tptp.ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (=> (@ (@ tptp.ord_less_eq_assn (@ F4 B2)) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_assn (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (=> (@ (@ tptp.ord_less_eq_nat (@ F4 B2)) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_nat (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (=> (@ (@ tptp.ord_less_eq_int (@ F4 B2)) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_int (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (F4 (-> tptp.nat tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_assn (@ F4 B2)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_assn (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (F4 (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat (@ F4 B2)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_nat (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (F4 (-> tptp.nat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_int (@ F4 B2)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_int (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int) (F4 (-> tptp.int tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_eq_assn (@ F4 B2)) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y2) (@ (@ tptp.ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_assn (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int) (F4 (-> tptp.int tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_eq_nat (@ F4 B2)) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_nat (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int) (F4 (-> tptp.int tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_eq_int (@ F4 B2)) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_int (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.filter_nat)) (C tptp.filter_nat)) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (=> (@ (@ tptp.ord_le2510731241096832064er_nat (@ F4 B2)) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_le2510731241096832064er_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le2510731241096832064er_nat (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (= X Y) (@ (@ tptp.ord_less_eq_assn X) Y))))
% 3.70/4.03 (assert (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (=> (= X Y) (@ (@ tptp.ord_le2510731241096832064er_nat X) Y))))
% 3.70/4.03 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (= X Y) (@ (@ tptp.ord_less_eq_set_nat X) Y))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (= X Y) (@ (@ tptp.ord_less_eq_nat X) Y))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (= X Y) (@ (@ tptp.ord_less_eq_int X) Y))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_eq_int X) Y) (@ (@ tptp.ord_less_eq_int Y) X))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (F4 (-> tptp.assn tptp.assn)) (B2 tptp.assn) (C tptp.assn)) (=> (= A2 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_assn B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_assn A2) (@ F4 C)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (F4 (-> tptp.assn tptp.nat)) (B2 tptp.assn) (C tptp.assn)) (=> (= A2 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_assn B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_nat A2) (@ F4 C)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (F4 (-> tptp.assn tptp.int)) (B2 tptp.assn) (C tptp.assn)) (=> (= A2 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_assn B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_int A2) (@ F4 C)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (F4 (-> tptp.nat tptp.assn)) (B2 tptp.nat) (C tptp.nat)) (=> (= A2 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_assn A2) (@ F4 C)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (F4 (-> tptp.nat tptp.nat)) (B2 tptp.nat) (C tptp.nat)) (=> (= A2 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_nat A2) (@ F4 C)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (F4 (-> tptp.nat tptp.int)) (B2 tptp.nat) (C tptp.nat)) (=> (= A2 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_int A2) (@ F4 C)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (F4 (-> tptp.int tptp.assn)) (B2 tptp.int) (C tptp.int)) (=> (= A2 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_int B2) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y2) (@ (@ tptp.ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_assn A2) (@ F4 C)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (F4 (-> tptp.int tptp.nat)) (B2 tptp.int) (C tptp.int)) (=> (= A2 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_int B2) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_nat A2) (@ F4 C)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (F4 (-> tptp.int tptp.int)) (B2 tptp.int) (C tptp.int)) (=> (= A2 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_int B2) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_int A2) (@ F4 C)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.filter_nat) (F4 (-> tptp.assn tptp.filter_nat)) (B2 tptp.assn) (C tptp.assn)) (=> (= A2 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_assn B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_le2510731241096832064er_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le2510731241096832064er_nat A2) (@ F4 C)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_assn (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_nat (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_int (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (F4 (-> tptp.nat tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_assn (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (F4 (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_nat (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (F4 (-> tptp.nat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_int (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int) (F4 (-> tptp.int tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y2) (@ (@ tptp.ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_assn (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int) (F4 (-> tptp.int tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_nat (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int) (F4 (-> tptp.int tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_int (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.filter_nat)) (C tptp.filter_nat)) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_le2510731241096832064er_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le2510731241096832064er_nat (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))))
% 3.70/4.03 (assert (forall ((Y tptp.assn) (X tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn Y) X) (= (@ (@ tptp.ord_less_eq_assn X) Y) (= X Y)))))
% 3.70/4.03 (assert (forall ((Y tptp.filter_nat) (X tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat Y) X) (= (@ (@ tptp.ord_le2510731241096832064er_nat X) Y) (= X Y)))))
% 3.70/4.03 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (= (@ (@ tptp.ord_less_eq_set_nat X) Y) (= X Y)))))
% 3.70/4.03 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.ord_less_eq_nat X) Y) (= X Y)))))
% 3.70/4.03 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.ord_less_eq_int X) Y) (= X Y)))))
% 3.70/4.03 (assert (forall ((X tptp.assn) (Y tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 3.70/4.03 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 3.70/4.03 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 3.70/4.03 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (let ((_let_2 (@ tptp.inf_inf_assn Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 3.70/4.03 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (let ((_let_2 (@ tptp.inf_inf_set_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 3.70/4.03 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (let ((_let_2 (@ tptp.inf_in2572325071724192079at_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 3.70/4.03 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (= (@ (@ tptp.inf_inf_assn (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_inf_assn Y) Z))))))
% 3.70/4.03 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (= (@ (@ tptp.inf_inf_set_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y) Z))))))
% 3.70/4.03 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z))))))
% 3.70/4.03 (assert (= tptp.inf_inf_assn (lambda ((X2 tptp.assn) (Y5 tptp.assn)) (@ (@ tptp.inf_inf_assn Y5) X2))))
% 3.70/4.03 (assert (= tptp.inf_inf_set_nat (lambda ((X2 tptp.set_nat) (Y5 tptp.set_nat)) (@ (@ tptp.inf_inf_set_nat Y5) X2))))
% 3.70/4.03 (assert (= tptp.inf_in2572325071724192079at_nat (lambda ((X2 tptp.set_Pr1261947904930325089at_nat) (Y5 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.inf_in2572325071724192079at_nat Y5) X2))))
% 3.70/4.03 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) Y)))
% 3.70/4.03 (assert (forall ((X tptp.assn) (Y tptp.assn)) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn X) Y)) Y)))
% 3.70/4.03 (assert (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.inf_inf_filter_nat X) Y)) Y)))
% 3.70/4.03 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X) Y)) Y)))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat X) Y)) Y)))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int X) Y)) Y)))
% 3.70/4.03 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) X)))
% 3.70/4.03 (assert (forall ((X tptp.assn) (Y tptp.assn)) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn X) Y)) X)))
% 3.70/4.03 (assert (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.inf_inf_filter_nat X) Y)) X)))
% 3.70/4.03 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X) Y)) X)))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat X) Y)) X)))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int X) Y)) X)))
% 3.70/4.03 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) X)))
% 3.70/4.03 (assert (forall ((X tptp.assn) (Y tptp.assn)) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn X) Y)) X)))
% 3.70/4.03 (assert (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.inf_inf_filter_nat X) Y)) X)))
% 3.70/4.03 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X) Y)) X)))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat X) Y)) X)))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int X) Y)) X)))
% 3.70/4.03 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) Y)))
% 3.70/4.03 (assert (forall ((X tptp.assn) (Y tptp.assn)) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn X) Y)) Y)))
% 3.70/4.03 (assert (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.inf_inf_filter_nat X) Y)) Y)))
% 3.70/4.03 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X) Y)) Y)))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat X) Y)) Y)))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int X) Y)) Y)))
% 3.70/4.03 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat X))) (=> (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2)) (not (=> (@ _let_1 A2) (not (@ _let_1 B2))))))))
% 3.70/4.03 (assert (forall ((X tptp.assn) (A2 tptp.assn) (B2 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn X))) (=> (@ _let_1 (@ (@ tptp.inf_inf_assn A2) B2)) (not (=> (@ _let_1 A2) (not (@ _let_1 B2))))))))
% 3.70/4.03 (assert (forall ((X tptp.filter_nat) (A2 tptp.filter_nat) (B2 tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_le2510731241096832064er_nat X))) (=> (@ _let_1 (@ (@ tptp.inf_inf_filter_nat A2) B2)) (not (=> (@ _let_1 A2) (not (@ _let_1 B2))))))))
% 3.70/4.03 (assert (forall ((X tptp.set_nat) (A2 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat A2) B2)) (not (=> (@ _let_1 A2) (not (@ _let_1 B2))))))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 (@ (@ tptp.inf_inf_nat A2) B2)) (not (=> (@ _let_1 A2) (not (@ _let_1 B2))))))))
% 3.70/4.03 (assert (forall ((X tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 (@ (@ tptp.inf_inf_int A2) B2)) (not (=> (@ _let_1 A2) (not (@ _let_1 B2))))))))
% 3.70/4.03 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat X))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2)))))))
% 3.70/4.03 (assert (forall ((X tptp.assn) (A2 tptp.assn) (B2 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn X))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.inf_inf_assn A2) B2)))))))
% 3.70/4.03 (assert (forall ((X tptp.filter_nat) (A2 tptp.filter_nat) (B2 tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_le2510731241096832064er_nat X))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.inf_inf_filter_nat A2) B2)))))))
% 3.70/4.03 (assert (forall ((X tptp.set_nat) (A2 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A2) B2)))))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.inf_inf_nat A2) B2)))))))
% 3.70/4.03 (assert (forall ((X tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.inf_inf_int A2) B2)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (D2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) C) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B2) D2) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2)) (@ (@ tptp.inf_in2572325071724192079at_nat C) D2))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (C tptp.assn) (B2 tptp.assn) (D2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A2) C) (=> (@ (@ tptp.ord_less_eq_assn B2) D2) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn A2) B2)) (@ (@ tptp.inf_inf_assn C) D2))))))
% 3.70/4.03 (assert (forall ((A2 tptp.filter_nat) (C tptp.filter_nat) (B2 tptp.filter_nat) (D2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat A2) C) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B2) D2) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.inf_inf_filter_nat A2) B2)) (@ (@ tptp.inf_inf_filter_nat C) D2))))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_nat) (C tptp.set_nat) (B2 tptp.set_nat) (D2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) C) (=> (@ (@ tptp.ord_less_eq_set_nat B2) D2) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A2) B2)) (@ (@ tptp.inf_inf_set_nat C) D2))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B2 tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) C) (=> (@ (@ tptp.ord_less_eq_nat B2) D2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A2) B2)) (@ (@ tptp.inf_inf_nat C) D2))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) C) (=> (@ (@ tptp.ord_less_eq_int B2) D2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A2) B2)) (@ (@ tptp.inf_inf_int C) D2))))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) X) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2)) X))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (X tptp.assn) (B2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A2) X) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn A2) B2)) X))))
% 3.70/4.03 (assert (forall ((A2 tptp.filter_nat) (X tptp.filter_nat) (B2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat A2) X) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.inf_inf_filter_nat A2) B2)) X))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_nat) (X tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) X) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A2) B2)) X))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (X tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) X) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A2) B2)) X))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (X tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) X) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A2) B2)) X))))
% 3.70/4.03 (assert (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B2) X) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2)) X))))
% 3.70/4.03 (assert (forall ((B2 tptp.assn) (X tptp.assn) (A2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn B2) X) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn A2) B2)) X))))
% 3.70/4.03 (assert (forall ((B2 tptp.filter_nat) (X tptp.filter_nat) (A2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B2) X) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.inf_inf_filter_nat A2) B2)) X))))
% 3.70/4.03 (assert (forall ((B2 tptp.set_nat) (X tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B2) X) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A2) B2)) X))))
% 3.70/4.03 (assert (forall ((B2 tptp.nat) (X tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) X) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A2) B2)) X))))
% 3.70/4.03 (assert (forall ((B2 tptp.int) (X tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) X) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A2) B2)) X))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn A2))) (= (@ (@ tptp.inf_inf_assn (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.inf_inf_assn B2) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A2))) (= (@ (@ tptp.inf_inf_set_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.inf_inf_set_nat B2) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A2))) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B2) C))))))
% 3.70/4.03 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (= (@ (@ tptp.inf_inf_assn (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_inf_assn Y) Z))))))
% 3.70/4.03 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (= (@ (@ tptp.inf_inf_set_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y) Z))))))
% 3.70/4.03 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z))))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) B2) (= A2 (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (= A2 (@ (@ tptp.inf_inf_assn A2) B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat A2) B2) (= A2 (@ (@ tptp.inf_inf_filter_nat A2) B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (= A2 (@ (@ tptp.inf_inf_set_nat A2) B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= A2 (@ (@ tptp.inf_inf_nat A2) B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (= A2 (@ (@ tptp.inf_inf_int A2) B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (=> (= A2 (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2)) (@ (@ tptp.ord_le3146513528884898305at_nat A2) B2))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn)) (=> (= A2 (@ (@ tptp.inf_inf_assn A2) B2)) (@ (@ tptp.ord_less_eq_assn A2) B2))))
% 3.70/4.03 (assert (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat)) (=> (= A2 (@ (@ tptp.inf_inf_filter_nat A2) B2)) (@ (@ tptp.ord_le2510731241096832064er_nat A2) B2))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (= A2 (@ (@ tptp.inf_inf_set_nat A2) B2)) (@ (@ tptp.ord_less_eq_set_nat A2) B2))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (= A2 (@ (@ tptp.inf_inf_nat A2) B2)) (@ (@ tptp.ord_less_eq_nat A2) B2))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (= A2 (@ (@ tptp.inf_inf_int A2) B2)) (@ (@ tptp.ord_less_eq_int A2) B2))))
% 3.70/4.03 (assert (forall ((F4 (-> 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) (Y2 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ F4 X3) Y2)) X3)) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat) (Y2 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ F4 X3) Y2)) Y2)) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat) (Y2 tptp.set_Pr1261947904930325089at_nat) (Z4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat X3))) (=> (@ _let_1 Y2) (=> (@ _let_1 Z4) (@ _let_1 (@ (@ F4 Y2) Z4)))))) (= (@ (@ tptp.inf_in2572325071724192079at_nat X) Y) (@ (@ F4 X) Y)))))))
% 3.70/4.03 (assert (forall ((F4 (-> tptp.assn tptp.assn tptp.assn)) (X tptp.assn) (Y tptp.assn)) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (@ (@ tptp.ord_less_eq_assn (@ (@ F4 X3) Y2)) X3)) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (@ (@ tptp.ord_less_eq_assn (@ (@ F4 X3) Y2)) Y2)) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn) (Z4 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn X3))) (=> (@ _let_1 Y2) (=> (@ _let_1 Z4) (@ _let_1 (@ (@ F4 Y2) Z4)))))) (= (@ (@ tptp.inf_inf_assn X) Y) (@ (@ F4 X) Y)))))))
% 3.70/4.03 (assert (forall ((F4 (-> tptp.filter_nat tptp.filter_nat tptp.filter_nat)) (X tptp.filter_nat) (Y tptp.filter_nat)) (=> (forall ((X3 tptp.filter_nat) (Y2 tptp.filter_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ F4 X3) Y2)) X3)) (=> (forall ((X3 tptp.filter_nat) (Y2 tptp.filter_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ F4 X3) Y2)) Y2)) (=> (forall ((X3 tptp.filter_nat) (Y2 tptp.filter_nat) (Z4 tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_le2510731241096832064er_nat X3))) (=> (@ _let_1 Y2) (=> (@ _let_1 Z4) (@ _let_1 (@ (@ F4 Y2) Z4)))))) (= (@ (@ tptp.inf_inf_filter_nat X) Y) (@ (@ F4 X) Y)))))))
% 3.70/4.03 (assert (forall ((F4 (-> tptp.set_nat tptp.set_nat tptp.set_nat)) (X tptp.set_nat) (Y tptp.set_nat)) (=> (forall ((X3 tptp.set_nat) (Y2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ F4 X3) Y2)) X3)) (=> (forall ((X3 tptp.set_nat) (Y2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ F4 X3) Y2)) Y2)) (=> (forall ((X3 tptp.set_nat) (Y2 tptp.set_nat) (Z4 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X3))) (=> (@ _let_1 Y2) (=> (@ _let_1 Z4) (@ _let_1 (@ (@ F4 Y2) Z4)))))) (= (@ (@ tptp.inf_inf_set_nat X) Y) (@ (@ F4 X) Y)))))))
% 3.70/4.03 (assert (forall ((F4 (-> tptp.nat tptp.nat tptp.nat)) (X tptp.nat) (Y tptp.nat)) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ F4 X3) Y2)) X3)) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ F4 X3) Y2)) Y2)) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat) (Z4 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X3))) (=> (@ _let_1 Y2) (=> (@ _let_1 Z4) (@ _let_1 (@ (@ F4 Y2) Z4)))))) (= (@ (@ tptp.inf_inf_nat X) Y) (@ (@ F4 X) Y)))))))
% 3.70/4.03 (assert (forall ((F4 (-> tptp.int tptp.int tptp.int)) (X tptp.int) (Y tptp.int)) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ F4 X3) Y2)) X3)) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ F4 X3) Y2)) Y2)) (=> (forall ((X3 tptp.int) (Y2 tptp.int) (Z4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X3))) (=> (@ _let_1 Y2) (=> (@ _let_1 Z4) (@ _let_1 (@ (@ F4 Y2) Z4)))))) (= (@ (@ tptp.inf_inf_int X) Y) (@ (@ F4 X) Y)))))))
% 3.70/4.03 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((X2 tptp.set_Pr1261947904930325089at_nat) (Y5 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat X2) Y5) X2))))
% 3.70/4.03 (assert (= tptp.ord_less_eq_assn (lambda ((X2 tptp.assn) (Y5 tptp.assn)) (= (@ (@ tptp.inf_inf_assn X2) Y5) X2))))
% 3.70/4.03 (assert (= tptp.ord_le2510731241096832064er_nat (lambda ((X2 tptp.filter_nat) (Y5 tptp.filter_nat)) (= (@ (@ tptp.inf_inf_filter_nat X2) Y5) X2))))
% 3.70/4.03 (assert (= tptp.ord_less_eq_set_nat (lambda ((X2 tptp.set_nat) (Y5 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X2) Y5) X2))))
% 3.70/4.03 (assert (= tptp.ord_less_eq_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (= (@ (@ tptp.inf_inf_nat X2) Y5) X2))))
% 3.70/4.03 (assert (= tptp.ord_less_eq_int (lambda ((X2 tptp.int) (Y5 tptp.int)) (= (@ (@ tptp.inf_inf_int X2) Y5) X2))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) B2) (= (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2) A2))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (= (@ (@ tptp.inf_inf_assn A2) B2) A2))))
% 3.70/4.03 (assert (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat A2) B2) (= (@ (@ tptp.inf_inf_filter_nat A2) B2) A2))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (= (@ (@ tptp.inf_inf_set_nat A2) B2) A2))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= (@ (@ tptp.inf_inf_nat A2) B2) A2))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (= (@ (@ tptp.inf_inf_int A2) B2) A2))))
% 3.70/4.03 (assert (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B2) A2) (= (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2) B2))))
% 3.70/4.03 (assert (forall ((B2 tptp.assn) (A2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn B2) A2) (= (@ (@ tptp.inf_inf_assn A2) B2) B2))))
% 3.70/4.03 (assert (forall ((B2 tptp.filter_nat) (A2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B2) A2) (= (@ (@ tptp.inf_inf_filter_nat A2) B2) B2))))
% 3.70/4.03 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A2) (= (@ (@ tptp.inf_inf_set_nat A2) B2) B2))))
% 3.70/4.03 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (= (@ (@ tptp.inf_inf_nat A2) B2) B2))))
% 3.70/4.03 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (= (@ (@ tptp.inf_inf_int A2) B2) B2))))
% 3.70/4.03 (assert (= tptp.inf_inf_assn (lambda ((A3 tptp.assn) (B3 tptp.assn)) (@ (@ tptp.inf_inf_assn B3) A3))))
% 3.70/4.03 (assert (= tptp.inf_inf_set_nat (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (@ (@ tptp.inf_inf_set_nat B3) A3))))
% 3.70/4.03 (assert (= tptp.inf_in2572325071724192079at_nat (lambda ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.inf_in2572325071724192079at_nat B3) A3))))
% 3.70/4.03 (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))))
% 3.70/4.03 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X) Y) (= (@ (@ tptp.inf_inf_assn X) Y) X))))
% 3.70/4.03 (assert (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat X) Y) (= (@ (@ tptp.inf_inf_filter_nat X) Y) X))))
% 3.70/4.03 (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))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (@ (@ tptp.inf_inf_nat X) Y) X))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (@ (@ tptp.inf_inf_int X) Y) X))))
% 3.70/4.03 (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))))
% 3.70/4.03 (assert (forall ((Y tptp.assn) (X tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn Y) X) (= (@ (@ tptp.inf_inf_assn X) Y) Y))))
% 3.70/4.03 (assert (forall ((Y tptp.filter_nat) (X tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat Y) X) (= (@ (@ tptp.inf_inf_filter_nat X) Y) Y))))
% 3.70/4.03 (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))))
% 3.70/4.03 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.inf_inf_nat X) Y) Y))))
% 3.70/4.03 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.inf_inf_int X) Y) Y))))
% 3.70/4.03 (assert (= tptp.inf_inf_assn (lambda ((X2 tptp.assn) (Y5 tptp.assn)) (@ (@ tptp.inf_inf_assn Y5) X2))))
% 3.70/4.03 (assert (= tptp.inf_inf_set_nat (lambda ((X2 tptp.set_nat) (Y5 tptp.set_nat)) (@ (@ tptp.inf_inf_set_nat Y5) X2))))
% 3.70/4.03 (assert (= tptp.inf_in2572325071724192079at_nat (lambda ((X2 tptp.set_Pr1261947904930325089at_nat) (Y5 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.inf_in2572325071724192079at_nat Y5) X2))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A2))) (=> (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B2) C)) (not (=> (@ _let_1 B2) (not (@ _let_1 C))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn A2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_assn B2) C)) (not (=> (@ _let_1 B2) (not (@ _let_1 C))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat) (C tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_le2510731241096832064er_nat A2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_filter_nat B2) C)) (not (=> (@ _let_1 B2) (not (@ _let_1 C))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat B2) C)) (not (=> (@ _let_1 B2) (not (@ _let_1 C))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_nat B2) C)) (not (=> (@ _let_1 B2) (not (@ _let_1 C))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_int B2) C)) (not (=> (@ _let_1 B2) (not (@ _let_1 C))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A2))) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B2) C)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn A2))) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.inf_inf_assn B2) C)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat) (C tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_le2510731241096832064er_nat A2))) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.inf_inf_filter_nat B2) C)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.inf_inf_set_nat B2) C)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.inf_inf_nat B2) C)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A2))) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.inf_inf_int B2) C)))))))
% 3.70/4.03 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z)))))))
% 3.70/4.03 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.inf_inf_assn Y) Z)))))))
% 3.70/4.03 (assert (forall ((X tptp.filter_nat) (Y tptp.filter_nat) (Z tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_le2510731241096832064er_nat X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.inf_inf_filter_nat Y) Z)))))))
% 3.70/4.03 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y) Z)))))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z)))))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.inf_inf_int Y) Z)))))))
% 3.70/4.03 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= A3 (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)))))
% 3.70/4.03 (assert (= tptp.ord_less_eq_assn (lambda ((A3 tptp.assn) (B3 tptp.assn)) (= A3 (@ (@ tptp.inf_inf_assn A3) B3)))))
% 3.70/4.03 (assert (= tptp.ord_le2510731241096832064er_nat (lambda ((A3 tptp.filter_nat) (B3 tptp.filter_nat)) (= A3 (@ (@ tptp.inf_inf_filter_nat A3) B3)))))
% 3.70/4.03 (assert (= tptp.ord_less_eq_set_nat (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= A3 (@ (@ tptp.inf_inf_set_nat A3) B3)))))
% 3.70/4.03 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (= A3 (@ (@ tptp.inf_inf_nat A3) B3)))))
% 3.70/4.03 (assert (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B3 tptp.int)) (= A3 (@ (@ tptp.inf_inf_int A3) B3)))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2)) A2)))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn)) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn A2) B2)) A2)))
% 3.70/4.03 (assert (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.inf_inf_filter_nat A2) B2)) A2)))
% 3.70/4.03 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A2) B2)) A2)))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A2) B2)) A2)))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A2) B2)) A2)))
% 3.70/4.03 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2)) B2)))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn)) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn A2) B2)) B2)))
% 3.70/4.03 (assert (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.inf_inf_filter_nat A2) B2)) B2)))
% 3.70/4.03 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A2) B2)) B2)))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A2) B2)) B2)))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A2) B2)) B2)))
% 3.70/4.03 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3) A3))))
% 3.70/4.03 (assert (= tptp.ord_less_eq_assn (lambda ((A3 tptp.assn) (B3 tptp.assn)) (= (@ (@ tptp.inf_inf_assn A3) B3) A3))))
% 3.70/4.03 (assert (= tptp.ord_le2510731241096832064er_nat (lambda ((A3 tptp.filter_nat) (B3 tptp.filter_nat)) (= (@ (@ tptp.inf_inf_filter_nat A3) B3) A3))))
% 3.70/4.03 (assert (= tptp.ord_less_eq_set_nat (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A3) B3) A3))))
% 3.70/4.03 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.inf_inf_nat A3) B3) A3))))
% 3.70/4.03 (assert (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.inf_inf_int A3) B3) A3))))
% 3.70/4.03 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((B3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3) B3))))
% 3.70/4.03 (assert (= tptp.ord_less_eq_assn (lambda ((B3 tptp.assn) (A3 tptp.assn)) (= (@ (@ tptp.inf_inf_assn A3) B3) B3))))
% 3.70/4.03 (assert (= tptp.ord_le2510731241096832064er_nat (lambda ((B3 tptp.filter_nat) (A3 tptp.filter_nat)) (= (@ (@ tptp.inf_inf_filter_nat A3) B3) B3))))
% 3.70/4.03 (assert (= tptp.ord_less_eq_set_nat (lambda ((B3 tptp.set_nat) (A3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A3) B3) B3))))
% 3.70/4.03 (assert (= tptp.ord_less_eq_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (= (@ (@ tptp.inf_inf_nat A3) B3) B3))))
% 3.70/4.03 (assert (= tptp.ord_less_eq_int (lambda ((B3 tptp.int) (A3 tptp.int)) (= (@ (@ tptp.inf_inf_int A3) B3) B3))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) C) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2)) C))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (C tptp.assn) (B2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A2) C) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn A2) B2)) C))))
% 3.70/4.03 (assert (forall ((A2 tptp.filter_nat) (C tptp.filter_nat) (B2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat A2) C) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.inf_inf_filter_nat A2) B2)) C))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_nat) (C tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) C) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A2) B2)) C))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A2) B2)) C))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A2) B2)) C))))
% 3.70/4.03 (assert (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B2) C) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2)) C))))
% 3.70/4.03 (assert (forall ((B2 tptp.assn) (C tptp.assn) (A2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn B2) C) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn A2) B2)) C))))
% 3.70/4.03 (assert (forall ((B2 tptp.filter_nat) (C tptp.filter_nat) (A2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B2) C) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.inf_inf_filter_nat A2) B2)) C))))
% 3.70/4.03 (assert (forall ((B2 tptp.set_nat) (C tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B2) C) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A2) B2)) C))))
% 3.70/4.03 (assert (forall ((B2 tptp.nat) (C tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A2) B2)) C))))
% 3.70/4.03 (assert (forall ((B2 tptp.int) (C tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A2) B2)) C))))
% 3.70/4.03 (assert (forall ((B2 tptp.assn) (A2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn B2))) (let ((_let_2 (@ tptp.inf_inf_assn A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 3.70/4.03 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat B2))) (let ((_let_2 (@ tptp.inf_inf_set_nat A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 3.70/4.03 (assert (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat B2))) (let ((_let_2 (@ tptp.inf_in2572325071724192079at_nat A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 3.70/4.03 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (let ((_let_2 (@ tptp.inf_inf_assn Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 3.70/4.03 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (let ((_let_2 (@ tptp.inf_inf_set_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 3.70/4.03 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (let ((_let_2 (@ tptp.inf_in2572325071724192079at_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 3.70/4.03 (assert (forall ((B2 tptp.set_nat) (C tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B2) C) (@ (@ tptp.ord_less_set_nat (@ (@ tptp.inf_inf_set_nat A2) B2)) C))))
% 3.70/4.03 (assert (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat B2) C) (@ (@ tptp.ord_le7866589430770878221at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2)) C))))
% 3.70/4.03 (assert (forall ((B2 tptp.assn) (C tptp.assn) (A2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn B2) C) (@ (@ tptp.ord_less_assn (@ (@ tptp.inf_inf_assn A2) B2)) C))))
% 3.70/4.03 (assert (forall ((B2 tptp.nat) (C tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.inf_inf_nat A2) B2)) C))))
% 3.70/4.03 (assert (forall ((B2 tptp.int) (C tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int B2) C) (@ (@ tptp.ord_less_int (@ (@ tptp.inf_inf_int A2) B2)) C))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_nat) (C tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) C) (@ (@ tptp.ord_less_set_nat (@ (@ tptp.inf_inf_set_nat A2) B2)) C))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat A2) C) (@ (@ tptp.ord_le7866589430770878221at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2)) C))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (C tptp.assn) (B2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn A2) C) (@ (@ tptp.ord_less_assn (@ (@ tptp.inf_inf_assn A2) B2)) C))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.inf_inf_nat A2) B2)) C))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) C) (@ (@ tptp.ord_less_int (@ (@ tptp.inf_inf_int A2) B2)) C))))
% 3.70/4.03 (assert (= tptp.ord_less_set_nat (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (and (= A3 (@ (@ tptp.inf_inf_set_nat A3) B3)) (not (= A3 B3))))))
% 3.70/4.03 (assert (= tptp.ord_le7866589430770878221at_nat (lambda ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (and (= A3 (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)) (not (= A3 B3))))))
% 3.70/4.03 (assert (= tptp.ord_less_assn (lambda ((A3 tptp.assn) (B3 tptp.assn)) (and (= A3 (@ (@ tptp.inf_inf_assn A3) B3)) (not (= A3 B3))))))
% 3.70/4.03 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (and (= A3 (@ (@ tptp.inf_inf_nat A3) B3)) (not (= A3 B3))))))
% 3.70/4.03 (assert (= tptp.ord_less_int (lambda ((A3 tptp.int) (B3 tptp.int)) (and (= A3 (@ (@ tptp.inf_inf_int A3) B3)) (not (= A3 B3))))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat A2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat B2) C)) (not (=> (@ _let_1 B2) (not (@ _let_1 C))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le7866589430770878221at_nat A2))) (=> (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B2) C)) (not (=> (@ _let_1 B2) (not (@ _let_1 C))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn A2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_assn B2) C)) (not (=> (@ _let_1 B2) (not (@ _let_1 C))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_nat B2) C)) (not (=> (@ _let_1 B2) (not (@ _let_1 C))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_int B2) C)) (not (=> (@ _let_1 B2) (not (@ _let_1 C))))))))
% 3.70/4.03 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B2) A2) (= (@ (@ tptp.inf_inf_set_nat A2) B2) B2))))
% 3.70/4.03 (assert (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat B2) A2) (= (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2) B2))))
% 3.70/4.03 (assert (forall ((B2 tptp.assn) (A2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn B2) A2) (= (@ (@ tptp.inf_inf_assn A2) B2) B2))))
% 3.70/4.03 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A2) (= (@ (@ tptp.inf_inf_nat A2) B2) B2))))
% 3.70/4.03 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A2) (= (@ (@ tptp.inf_inf_int A2) B2) B2))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) B2) (= (@ (@ tptp.inf_inf_set_nat A2) B2) A2))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat A2) B2) (= (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2) A2))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn A2) B2) (= (@ (@ tptp.inf_inf_assn A2) B2) A2))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (= (@ (@ tptp.inf_inf_nat A2) B2) A2))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (= (@ (@ tptp.inf_inf_int A2) B2) A2))))
% 3.70/4.03 (assert (forall ((B2 tptp.set_nat) (X tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B2) X) (@ (@ tptp.ord_less_set_nat (@ (@ tptp.inf_inf_set_nat A2) B2)) X))))
% 3.70/4.03 (assert (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat B2) X) (@ (@ tptp.ord_le7866589430770878221at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2)) X))))
% 3.70/4.03 (assert (forall ((B2 tptp.assn) (X tptp.assn) (A2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn B2) X) (@ (@ tptp.ord_less_assn (@ (@ tptp.inf_inf_assn A2) B2)) X))))
% 3.70/4.03 (assert (forall ((B2 tptp.nat) (X tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) X) (@ (@ tptp.ord_less_nat (@ (@ tptp.inf_inf_nat A2) B2)) X))))
% 3.70/4.03 (assert (forall ((B2 tptp.int) (X tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int B2) X) (@ (@ tptp.ord_less_int (@ (@ tptp.inf_inf_int A2) B2)) X))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_nat) (X tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) X) (@ (@ tptp.ord_less_set_nat (@ (@ tptp.inf_inf_set_nat A2) B2)) X))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat A2) X) (@ (@ tptp.ord_le7866589430770878221at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2)) X))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (X tptp.assn) (B2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn A2) X) (@ (@ tptp.ord_less_assn (@ (@ tptp.inf_inf_assn A2) B2)) X))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (X tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) X) (@ (@ tptp.ord_less_nat (@ (@ tptp.inf_inf_nat A2) B2)) X))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (X tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) X) (@ (@ tptp.ord_less_int (@ (@ tptp.inf_inf_int A2) B2)) X))))
% 3.70/4.03 (assert (forall ((T tptp.code_integer)) (exists ((Z4 tptp.code_integer)) (forall ((X7 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z4) X7) (not (@ (@ tptp.ord_le3102999989581377725nteger X7) T)))))))
% 3.70/4.03 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X7 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X7) (not (@ (@ tptp.ord_less_eq_num X7) T)))))))
% 3.70/4.03 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X7) (not (@ (@ tptp.ord_less_eq_nat X7) T)))))))
% 3.70/4.03 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X7 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X7) (not (@ (@ tptp.ord_less_eq_int X7) T)))))))
% 3.70/4.03 (assert (forall ((T tptp.code_integer)) (exists ((Z4 tptp.code_integer)) (forall ((X7 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z4) X7) (@ (@ tptp.ord_le3102999989581377725nteger T) X7))))))
% 3.70/4.03 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X7 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X7) (@ (@ tptp.ord_less_eq_num T) X7))))))
% 3.70/4.03 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X7) (@ (@ tptp.ord_less_eq_nat T) X7))))))
% 3.70/4.03 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X7 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X7) (@ (@ tptp.ord_less_eq_int T) X7))))))
% 3.70/4.03 (assert (forall ((T tptp.code_integer)) (exists ((Z4 tptp.code_integer)) (forall ((X7 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X7) Z4) (@ (@ tptp.ord_le3102999989581377725nteger X7) T))))))
% 3.70/4.03 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X7 tptp.num)) (=> (@ (@ tptp.ord_less_num X7) Z4) (@ (@ tptp.ord_less_eq_num X7) T))))))
% 3.70/4.03 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X7) Z4) (@ (@ tptp.ord_less_eq_nat X7) T))))))
% 3.70/4.03 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X7 tptp.int)) (=> (@ (@ tptp.ord_less_int X7) Z4) (@ (@ tptp.ord_less_eq_int X7) T))))))
% 3.70/4.03 (assert (forall ((T tptp.code_integer)) (exists ((Z4 tptp.code_integer)) (forall ((X7 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X7) Z4) (not (@ (@ tptp.ord_le3102999989581377725nteger T) X7)))))))
% 3.70/4.03 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X7 tptp.num)) (=> (@ (@ tptp.ord_less_num X7) Z4) (not (@ (@ tptp.ord_less_eq_num T) X7)))))))
% 3.70/4.03 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X7) Z4) (not (@ (@ tptp.ord_less_eq_nat T) X7)))))))
% 3.70/4.03 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X7 tptp.int)) (=> (@ (@ tptp.ord_less_int X7) Z4) (not (@ (@ tptp.ord_less_eq_int T) X7)))))))
% 3.70/4.03 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger X) Y) (or (@ (@ tptp.ord_le6747313008572928689nteger X) Y) (= X Y)))))
% 3.70/4.03 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (or (@ (@ tptp.ord_less_num X) Y) (= X Y)))))
% 3.70/4.03 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X) Y) (or (@ (@ tptp.ord_less_assn X) Y) (= X Y)))))
% 3.70/4.03 (assert (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat X) Y) (or (@ (@ tptp.ord_less_filter_nat X) Y) (= X Y)))))
% 3.70/4.03 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (or (@ (@ tptp.ord_less_set_nat X) Y) (= X Y)))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (or (@ (@ tptp.ord_less_nat X) Y) (= X Y)))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (or (@ (@ tptp.ord_less_int X) Y) (= X Y)))))
% 3.70/4.03 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (or (@ (@ tptp.ord_le3102999989581377725nteger X) Y) (@ (@ tptp.ord_le6747313008572928689nteger Y) X))))
% 3.70/4.03 (assert (forall ((X tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_eq_num X) Y) (@ (@ tptp.ord_less_num Y) X))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_nat Y) X))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_eq_int X) Y) (@ (@ tptp.ord_less_int Y) X))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (F4 (-> tptp.code_integer tptp.code_integer)) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ F4 B2)) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (F4 (-> tptp.code_integer tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (@ (@ tptp.ord_less_eq_num (@ F4 B2)) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_num (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.code_integer)) (C tptp.code_integer)) (=> (@ (@ tptp.ord_less_assn A2) B2) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ F4 B2)) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_assn A2) B2) (=> (@ (@ tptp.ord_less_eq_num (@ F4 B2)) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_num (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.num) (B2 tptp.num) (F4 (-> tptp.num tptp.code_integer)) (C tptp.code_integer)) (=> (@ (@ tptp.ord_less_num A2) B2) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ F4 B2)) C) (=> (forall ((X3 tptp.num) (Y2 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.num) (B2 tptp.num) (F4 (-> tptp.num tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_num A2) B2) (=> (@ (@ tptp.ord_less_eq_num (@ F4 B2)) C) (=> (forall ((X3 tptp.num) (Y2 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y2) (@ (@ tptp.ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_num (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (F4 (-> tptp.nat tptp.code_integer)) (C tptp.code_integer)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ F4 B2)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (F4 (-> tptp.nat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_num (@ F4 B2)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_num (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int) (F4 (-> tptp.int tptp.code_integer)) (C tptp.code_integer)) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ F4 B2)) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int) (F4 (-> tptp.int tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ (@ tptp.ord_less_eq_num (@ F4 B2)) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y2) (@ (@ tptp.ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_num (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (F4 (-> tptp.assn tptp.code_integer)) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_assn B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_le3102999989581377725nteger (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.num) (F4 (-> tptp.assn tptp.num)) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_num A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_assn B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_less_eq_num (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (F4 (-> tptp.assn tptp.assn)) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_assn B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (F4 (-> tptp.assn tptp.nat)) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_assn B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (F4 (-> tptp.assn tptp.int)) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_int A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_assn B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (F4 (-> tptp.nat tptp.code_integer)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_le3102999989581377725nteger (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.num) (F4 (-> tptp.nat tptp.num)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_num A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_num (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (F4 (-> tptp.nat tptp.assn)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_assn A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (F4 (-> tptp.nat tptp.nat)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (F4 (-> tptp.nat tptp.int)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.code_integer)) (C tptp.code_integer)) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 B2)) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_le3102999989581377725nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (=> (@ (@ tptp.ord_less_num (@ F4 B2)) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_less_eq_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_num (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (=> (@ (@ tptp.ord_less_assn (@ F4 B2)) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_assn (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (=> (@ (@ tptp.ord_less_nat (@ F4 B2)) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_nat (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (=> (@ (@ tptp.ord_less_int (@ F4 B2)) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_int (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (F4 (-> tptp.nat tptp.code_integer)) (C tptp.code_integer)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 B2)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_le3102999989581377725nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (F4 (-> tptp.nat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_num (@ F4 B2)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_num (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (F4 (-> tptp.nat tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_assn (@ F4 B2)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_assn (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (F4 (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_nat (@ F4 B2)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_nat (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (F4 (-> tptp.nat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_int (@ F4 B2)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_int (@ F4 A2)) C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (F4 (-> tptp.code_integer tptp.code_integer)) (B2 tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) (@ F4 B2)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger A2) (@ F4 C)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.num) (F4 (-> tptp.code_integer tptp.num)) (B2 tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_less_eq_num A2) (@ F4 B2)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_num A2) (@ F4 C)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (F4 (-> tptp.assn tptp.code_integer)) (B2 tptp.assn) (C tptp.assn)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) (@ F4 B2)) (=> (@ (@ tptp.ord_less_assn B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger A2) (@ F4 C)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.num) (F4 (-> tptp.assn tptp.num)) (B2 tptp.assn) (C tptp.assn)) (=> (@ (@ tptp.ord_less_eq_num A2) (@ F4 B2)) (=> (@ (@ tptp.ord_less_assn B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_num A2) (@ F4 C)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (F4 (-> tptp.num tptp.code_integer)) (B2 tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) (@ F4 B2)) (=> (@ (@ tptp.ord_less_num B2) C) (=> (forall ((X3 tptp.num) (Y2 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger A2) (@ F4 C)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.num) (F4 (-> tptp.num tptp.num)) (B2 tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A2) (@ F4 B2)) (=> (@ (@ tptp.ord_less_num B2) C) (=> (forall ((X3 tptp.num) (Y2 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y2) (@ (@ tptp.ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_num A2) (@ F4 C)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (F4 (-> tptp.nat tptp.code_integer)) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) (@ F4 B2)) (=> (@ (@ tptp.ord_less_nat B2) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger A2) (@ F4 C)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.num) (F4 (-> tptp.nat tptp.num)) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A2) (@ F4 B2)) (=> (@ (@ tptp.ord_less_nat B2) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_num A2) (@ F4 C)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (F4 (-> tptp.int tptp.code_integer)) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) (@ F4 B2)) (=> (@ (@ tptp.ord_less_int B2) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger A2) (@ F4 C)))))))
% 3.70/4.03 (assert (forall ((A2 tptp.num) (F4 (-> tptp.int tptp.num)) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A2) (@ F4 B2)) (=> (@ (@ tptp.ord_less_int B2) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y2) (@ (@ tptp.ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_num A2) (@ F4 C)))))))
% 3.70/4.03 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_le3102999989581377725nteger Y) Z) (@ _let_1 Z))))))
% 3.70/4.03 (assert (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_num Y) Z) (@ _let_1 Z))))))
% 3.70/4.03 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_assn Y) Z) (@ _let_1 Z))))))
% 3.70/4.03 (assert (forall ((X tptp.filter_nat) (Y tptp.filter_nat) (Z tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_less_filter_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_le2510731241096832064er_nat Y) Z) (@ _let_1 Z))))))
% 3.70/4.03 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_nat Y) Z) (@ _let_1 Z))))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z) (@ _let_1 Z))))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ _let_1 Z))))))
% 3.70/4.03 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger X) Y) (=> (@ (@ tptp.ord_le6747313008572928689nteger Y) Z) (@ (@ tptp.ord_le6747313008572928689nteger X) Z)))))
% 3.70/4.03 (assert (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (=> (@ (@ tptp.ord_less_num Y) Z) (@ (@ tptp.ord_less_num X) Z)))))
% 3.70/4.03 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X) Y) (=> (@ (@ tptp.ord_less_assn Y) Z) (@ (@ tptp.ord_less_assn X) Z)))))
% 3.70/4.03 (assert (forall ((X tptp.filter_nat) (Y tptp.filter_nat) (Z tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat X) Y) (=> (@ (@ tptp.ord_less_filter_nat Y) Z) (@ (@ tptp.ord_less_filter_nat X) Z)))))
% 3.70/4.03 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (=> (@ (@ tptp.ord_less_set_nat Y) Z) (@ (@ tptp.ord_less_set_nat X) Z)))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (=> (@ (@ tptp.ord_less_nat Y) Z) (@ (@ tptp.ord_less_nat X) Z)))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ (@ tptp.ord_less_int X) Z)))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (not (= A2 B2)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B2) (@ (@ tptp.ord_le6747313008572928689nteger A2) B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.num) (B2 tptp.num)) (=> (not (= A2 B2)) (=> (@ (@ tptp.ord_less_eq_num A2) B2) (@ (@ tptp.ord_less_num A2) B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn)) (=> (not (= A2 B2)) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (@ (@ tptp.ord_less_assn A2) B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat)) (=> (not (= A2 B2)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat A2) B2) (@ (@ tptp.ord_less_filter_nat A2) B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (not (= A2 B2)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (@ (@ tptp.ord_less_set_nat A2) B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (not (= A2 B2)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (@ (@ tptp.ord_less_nat A2) B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (not (= A2 B2)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (@ (@ tptp.ord_less_int A2) B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B2) (=> (not (= A2 B2)) (@ (@ tptp.ord_le6747313008572928689nteger A2) B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.num) (B2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A2) B2) (=> (not (= A2 B2)) (@ (@ tptp.ord_less_num A2) B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (=> (not (= A2 B2)) (@ (@ tptp.ord_less_assn A2) B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat A2) B2) (=> (not (= A2 B2)) (@ (@ tptp.ord_less_filter_nat A2) B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (=> (not (= A2 B2)) (@ (@ tptp.ord_less_set_nat A2) B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (not (= A2 B2)) (@ (@ tptp.ord_less_nat A2) B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (not (= A2 B2)) (@ (@ tptp.ord_less_int A2) B2)))))
% 3.70/4.03 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X) Y) (@ (@ tptp.ord_le3102999989581377725nteger X) Y))))
% 3.70/4.03 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (@ (@ tptp.ord_less_eq_num X) Y))))
% 3.70/4.03 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_assn X) Y) (@ (@ tptp.ord_less_eq_assn X) Y))))
% 3.70/4.03 (assert (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (=> (@ (@ tptp.ord_less_filter_nat X) Y) (@ (@ tptp.ord_le2510731241096832064er_nat X) Y))))
% 3.70/4.03 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat X) Y) (@ (@ tptp.ord_less_eq_set_nat X) Y))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_eq_nat X) Y))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (@ (@ tptp.ord_less_eq_int X) Y))))
% 3.70/4.03 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (not (@ (@ tptp.ord_le6747313008572928689nteger X) Y)) (@ (@ tptp.ord_le3102999989581377725nteger Y) X))))
% 3.70/4.03 (assert (forall ((X tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_num X) Y)) (@ (@ tptp.ord_less_eq_num Y) X))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))))
% 3.70/4.03 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (not (@ (@ tptp.ord_le3102999989581377725nteger X) Y)) (@ (@ tptp.ord_le6747313008572928689nteger Y) X))))
% 3.70/4.03 (assert (forall ((X tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num X) Y)) (@ (@ tptp.ord_less_num Y) X))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int X) Y)) (@ (@ tptp.ord_less_int Y) X))))
% 3.70/4.03 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((X2 tptp.code_integer) (Y5 tptp.code_integer)) (and (@ (@ tptp.ord_le3102999989581377725nteger X2) Y5) (not (= X2 Y5))))))
% 3.70/4.03 (assert (= tptp.ord_less_num (lambda ((X2 tptp.num) (Y5 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X2) Y5) (not (= X2 Y5))))))
% 3.70/4.03 (assert (= tptp.ord_less_assn (lambda ((X2 tptp.assn) (Y5 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn X2) Y5) (not (= X2 Y5))))))
% 3.70/4.03 (assert (= tptp.ord_less_filter_nat (lambda ((X2 tptp.filter_nat) (Y5 tptp.filter_nat)) (and (@ (@ tptp.ord_le2510731241096832064er_nat X2) Y5) (not (= X2 Y5))))))
% 3.70/4.03 (assert (= tptp.ord_less_set_nat (lambda ((X2 tptp.set_nat) (Y5 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat X2) Y5) (not (= X2 Y5))))))
% 3.70/4.03 (assert (= tptp.ord_less_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X2) Y5) (not (= X2 Y5))))))
% 3.70/4.03 (assert (= tptp.ord_less_int (lambda ((X2 tptp.int) (Y5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X2) Y5) (not (= X2 Y5))))))
% 3.70/4.03 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((X2 tptp.code_integer) (Y5 tptp.code_integer)) (or (@ (@ tptp.ord_le6747313008572928689nteger X2) Y5) (= X2 Y5)))))
% 3.70/4.03 (assert (= tptp.ord_less_eq_num (lambda ((X2 tptp.num) (Y5 tptp.num)) (or (@ (@ tptp.ord_less_num X2) Y5) (= X2 Y5)))))
% 3.70/4.03 (assert (= tptp.ord_less_eq_assn (lambda ((X2 tptp.assn) (Y5 tptp.assn)) (or (@ (@ tptp.ord_less_assn X2) Y5) (= X2 Y5)))))
% 3.70/4.03 (assert (= tptp.ord_le2510731241096832064er_nat (lambda ((X2 tptp.filter_nat) (Y5 tptp.filter_nat)) (or (@ (@ tptp.ord_less_filter_nat X2) Y5) (= X2 Y5)))))
% 3.70/4.03 (assert (= tptp.ord_less_eq_set_nat (lambda ((X2 tptp.set_nat) (Y5 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat X2) Y5) (= X2 Y5)))))
% 3.70/4.03 (assert (= tptp.ord_less_eq_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (or (@ (@ tptp.ord_less_nat X2) Y5) (= X2 Y5)))))
% 3.70/4.03 (assert (= tptp.ord_less_eq_int (lambda ((X2 tptp.int) (Y5 tptp.int)) (or (@ (@ tptp.ord_less_int X2) Y5) (= X2 Y5)))))
% 3.70/4.03 (assert (forall ((B2 tptp.code_integer) (A2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) A2) (@ (@ tptp.ord_le3102999989581377725nteger B2) A2))))
% 3.70/4.03 (assert (forall ((B2 tptp.num) (A2 tptp.num)) (=> (@ (@ tptp.ord_less_num B2) A2) (@ (@ tptp.ord_less_eq_num B2) A2))))
% 3.70/4.03 (assert (forall ((B2 tptp.assn) (A2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn B2) A2) (@ (@ tptp.ord_less_eq_assn B2) A2))))
% 3.70/4.03 (assert (forall ((B2 tptp.filter_nat) (A2 tptp.filter_nat)) (=> (@ (@ tptp.ord_less_filter_nat B2) A2) (@ (@ tptp.ord_le2510731241096832064er_nat B2) A2))))
% 3.70/4.03 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B2) A2) (@ (@ tptp.ord_less_eq_set_nat B2) A2))))
% 3.70/4.03 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A2) (@ (@ tptp.ord_less_eq_nat B2) A2))))
% 3.70/4.03 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A2) (@ (@ tptp.ord_less_eq_int B2) A2))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (@ (@ tptp.ord_le3102999989581377725nteger A2) B2))))
% 3.70/4.03 (assert (forall ((A2 tptp.num) (B2 tptp.num)) (=> (@ (@ tptp.ord_less_num A2) B2) (@ (@ tptp.ord_less_eq_num A2) B2))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn A2) B2) (@ (@ tptp.ord_less_eq_assn A2) B2))))
% 3.70/4.03 (assert (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat)) (=> (@ (@ tptp.ord_less_filter_nat A2) B2) (@ (@ tptp.ord_le2510731241096832064er_nat A2) B2))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) B2) (@ (@ tptp.ord_less_eq_set_nat A2) B2))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (@ (@ tptp.ord_less_eq_nat A2) B2))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (@ (@ tptp.ord_less_eq_int A2) B2))))
% 3.70/4.03 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((B3 tptp.code_integer) (A3 tptp.code_integer)) (and (@ (@ tptp.ord_le3102999989581377725nteger B3) A3) (not (@ (@ tptp.ord_le3102999989581377725nteger A3) B3))))))
% 3.70/4.03 (assert (= tptp.ord_less_num (lambda ((B3 tptp.num) (A3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B3) A3) (not (@ (@ tptp.ord_less_eq_num A3) B3))))))
% 3.70/4.03 (assert (= tptp.ord_less_assn (lambda ((B3 tptp.assn) (A3 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn B3) A3) (not (@ (@ tptp.ord_less_eq_assn A3) B3))))))
% 3.70/4.03 (assert (= tptp.ord_less_filter_nat (lambda ((B3 tptp.filter_nat) (A3 tptp.filter_nat)) (and (@ (@ tptp.ord_le2510731241096832064er_nat B3) A3) (not (@ (@ tptp.ord_le2510731241096832064er_nat A3) B3))))))
% 3.70/4.03 (assert (= tptp.ord_less_set_nat (lambda ((B3 tptp.set_nat) (A3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B3) A3) (not (@ (@ tptp.ord_less_eq_set_nat A3) B3))))))
% 3.70/4.03 (assert (= tptp.ord_less_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B3) A3) (not (@ (@ tptp.ord_less_eq_nat A3) B3))))))
% 3.70/4.03 (assert (= tptp.ord_less_int (lambda ((B3 tptp.int) (A3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B3) A3) (not (@ (@ tptp.ord_less_eq_int A3) B3))))))
% 3.70/4.03 (assert (forall ((B2 tptp.code_integer) (A2 tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) A2) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) B2) (@ (@ tptp.ord_le6747313008572928689nteger C) A2)))))
% 3.70/4.03 (assert (forall ((B2 tptp.num) (A2 tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_num B2) A2) (=> (@ (@ tptp.ord_less_eq_num C) B2) (@ (@ tptp.ord_less_num C) A2)))))
% 3.70/4.03 (assert (forall ((B2 tptp.assn) (A2 tptp.assn) (C tptp.assn)) (=> (@ (@ tptp.ord_less_assn B2) A2) (=> (@ (@ tptp.ord_less_eq_assn C) B2) (@ (@ tptp.ord_less_assn C) A2)))))
% 3.70/4.03 (assert (forall ((B2 tptp.filter_nat) (A2 tptp.filter_nat) (C tptp.filter_nat)) (=> (@ (@ tptp.ord_less_filter_nat B2) A2) (=> (@ (@ tptp.ord_le2510731241096832064er_nat C) B2) (@ (@ tptp.ord_less_filter_nat C) A2)))))
% 3.70/4.03 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat) (C tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B2) A2) (=> (@ (@ tptp.ord_less_eq_set_nat C) B2) (@ (@ tptp.ord_less_set_nat C) A2)))))
% 3.70/4.03 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A2) (=> (@ (@ tptp.ord_less_eq_nat C) B2) (@ (@ tptp.ord_less_nat C) A2)))))
% 3.70/4.03 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A2) (=> (@ (@ tptp.ord_less_eq_int C) B2) (@ (@ tptp.ord_less_int C) A2)))))
% 3.70/4.03 (assert (forall ((B2 tptp.code_integer) (A2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger C))) (=> (@ (@ tptp.ord_le3102999989581377725nteger B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 3.70/4.03 (assert (forall ((B2 tptp.num) (A2 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ (@ tptp.ord_less_eq_num B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 3.70/4.03 (assert (forall ((B2 tptp.assn) (A2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn C))) (=> (@ (@ tptp.ord_less_eq_assn B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 3.70/4.03 (assert (forall ((B2 tptp.filter_nat) (A2 tptp.filter_nat) (C tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_less_filter_nat C))) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 3.70/4.03 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat C))) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 3.70/4.03 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 3.70/4.03 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 3.70/4.03 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((B3 tptp.code_integer) (A3 tptp.code_integer)) (and (@ (@ tptp.ord_le3102999989581377725nteger B3) A3) (not (= A3 B3))))))
% 3.70/4.03 (assert (= tptp.ord_less_num (lambda ((B3 tptp.num) (A3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B3) A3) (not (= A3 B3))))))
% 3.70/4.03 (assert (= tptp.ord_less_assn (lambda ((B3 tptp.assn) (A3 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn B3) A3) (not (= A3 B3))))))
% 3.70/4.03 (assert (= tptp.ord_less_filter_nat (lambda ((B3 tptp.filter_nat) (A3 tptp.filter_nat)) (and (@ (@ tptp.ord_le2510731241096832064er_nat B3) A3) (not (= A3 B3))))))
% 3.70/4.03 (assert (= tptp.ord_less_set_nat (lambda ((B3 tptp.set_nat) (A3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B3) A3) (not (= A3 B3))))))
% 3.70/4.03 (assert (= tptp.ord_less_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B3) A3) (not (= A3 B3))))))
% 3.70/4.03 (assert (= tptp.ord_less_int (lambda ((B3 tptp.int) (A3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B3) A3) (not (= A3 B3))))))
% 3.70/4.03 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((B3 tptp.code_integer) (A3 tptp.code_integer)) (or (@ (@ tptp.ord_le6747313008572928689nteger B3) A3) (= A3 B3)))))
% 3.70/4.03 (assert (= tptp.ord_less_eq_num (lambda ((B3 tptp.num) (A3 tptp.num)) (or (@ (@ tptp.ord_less_num B3) A3) (= A3 B3)))))
% 3.70/4.03 (assert (= tptp.ord_less_eq_assn (lambda ((B3 tptp.assn) (A3 tptp.assn)) (or (@ (@ tptp.ord_less_assn B3) A3) (= A3 B3)))))
% 3.70/4.03 (assert (= tptp.ord_le2510731241096832064er_nat (lambda ((B3 tptp.filter_nat) (A3 tptp.filter_nat)) (or (@ (@ tptp.ord_less_filter_nat B3) A3) (= A3 B3)))))
% 3.70/4.03 (assert (= tptp.ord_less_eq_set_nat (lambda ((B3 tptp.set_nat) (A3 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat B3) A3) (= A3 B3)))))
% 3.70/4.03 (assert (= tptp.ord_less_eq_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (or (@ (@ tptp.ord_less_nat B3) A3) (= A3 B3)))))
% 3.70/4.03 (assert (= tptp.ord_less_eq_int (lambda ((B3 tptp.int) (A3 tptp.int)) (or (@ (@ tptp.ord_less_int B3) A3) (= A3 B3)))))
% 3.70/4.03 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((A3 tptp.code_integer) (B3 tptp.code_integer)) (and (@ (@ tptp.ord_le3102999989581377725nteger A3) B3) (not (@ (@ tptp.ord_le3102999989581377725nteger B3) A3))))))
% 3.70/4.03 (assert (= tptp.ord_less_num (lambda ((A3 tptp.num) (B3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A3) B3) (not (@ (@ tptp.ord_less_eq_num B3) A3))))))
% 3.70/4.03 (assert (= tptp.ord_less_assn (lambda ((A3 tptp.assn) (B3 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn A3) B3) (not (@ (@ tptp.ord_less_eq_assn B3) A3))))))
% 3.70/4.03 (assert (= tptp.ord_less_filter_nat (lambda ((A3 tptp.filter_nat) (B3 tptp.filter_nat)) (and (@ (@ tptp.ord_le2510731241096832064er_nat A3) B3) (not (@ (@ tptp.ord_le2510731241096832064er_nat B3) A3))))))
% 3.70/4.03 (assert (= tptp.ord_less_set_nat (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A3) B3) (not (@ (@ tptp.ord_less_eq_set_nat B3) A3))))))
% 3.70/4.03 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B3) (not (@ (@ tptp.ord_less_eq_nat B3) A3))))))
% 3.70/4.03 (assert (= tptp.ord_less_int (lambda ((A3 tptp.int) (B3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A3) B3) (not (@ (@ tptp.ord_less_eq_int B3) A3))))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_le3102999989581377725nteger B2) C) (@ _let_1 C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.num) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_num B2) C) (@ _let_1 C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_assn B2) C) (@ _let_1 C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat) (C tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_less_filter_nat A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B2) C) (@ _let_1 C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) C) (@ _let_1 C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (@ _let_1 C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_int B2) C) (@ _let_1 C))))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) C) (@ (@ tptp.ord_le6747313008572928689nteger A2) C)))))
% 3.70/4.03 (assert (forall ((A2 tptp.num) (B2 tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A2) B2) (=> (@ (@ tptp.ord_less_num B2) C) (@ (@ tptp.ord_less_num A2) C)))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (C tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (=> (@ (@ tptp.ord_less_assn B2) C) (@ (@ tptp.ord_less_assn A2) C)))))
% 3.70/4.03 (assert (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat) (C tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat A2) B2) (=> (@ (@ tptp.ord_less_filter_nat B2) C) (@ (@ tptp.ord_less_filter_nat A2) C)))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (C tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (=> (@ (@ tptp.ord_less_set_nat B2) C) (@ (@ tptp.ord_less_set_nat A2) C)))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_nat B2) C) (@ (@ tptp.ord_less_nat A2) C)))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_int B2) C) (@ (@ tptp.ord_less_int A2) C)))))
% 3.70/4.03 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((A3 tptp.code_integer) (B3 tptp.code_integer)) (and (@ (@ tptp.ord_le3102999989581377725nteger A3) B3) (not (= A3 B3))))))
% 3.70/4.03 (assert (= tptp.ord_less_num (lambda ((A3 tptp.num) (B3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A3) B3) (not (= A3 B3))))))
% 3.70/4.03 (assert (= tptp.ord_less_assn (lambda ((A3 tptp.assn) (B3 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn A3) B3) (not (= A3 B3))))))
% 3.70/4.03 (assert (= tptp.ord_less_filter_nat (lambda ((A3 tptp.filter_nat) (B3 tptp.filter_nat)) (and (@ (@ tptp.ord_le2510731241096832064er_nat A3) B3) (not (= A3 B3))))))
% 3.70/4.03 (assert (= tptp.ord_less_set_nat (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A3) B3) (not (= A3 B3))))))
% 3.70/4.03 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B3) (not (= A3 B3))))))
% 3.70/4.03 (assert (= tptp.ord_less_int (lambda ((A3 tptp.int) (B3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A3) B3) (not (= A3 B3))))))
% 3.70/4.03 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((A3 tptp.code_integer) (B3 tptp.code_integer)) (or (@ (@ tptp.ord_le6747313008572928689nteger A3) B3) (= A3 B3)))))
% 3.70/4.03 (assert (= tptp.ord_less_eq_num (lambda ((A3 tptp.num) (B3 tptp.num)) (or (@ (@ tptp.ord_less_num A3) B3) (= A3 B3)))))
% 3.70/4.03 (assert (= tptp.ord_less_eq_assn (lambda ((A3 tptp.assn) (B3 tptp.assn)) (or (@ (@ tptp.ord_less_assn A3) B3) (= A3 B3)))))
% 3.70/4.03 (assert (= tptp.ord_le2510731241096832064er_nat (lambda ((A3 tptp.filter_nat) (B3 tptp.filter_nat)) (or (@ (@ tptp.ord_less_filter_nat A3) B3) (= A3 B3)))))
% 3.70/4.03 (assert (= tptp.ord_less_eq_set_nat (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat A3) B3) (= A3 B3)))))
% 3.70/4.03 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (or (@ (@ tptp.ord_less_nat A3) B3) (= A3 B3)))))
% 3.70/4.03 (assert (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B3 tptp.int)) (or (@ (@ tptp.ord_less_int A3) B3) (= A3 B3)))))
% 3.70/4.03 (assert (forall ((Y tptp.code_integer) (X tptp.code_integer)) (=> (not (@ (@ tptp.ord_le3102999989581377725nteger Y) X)) (@ (@ tptp.ord_le6747313008572928689nteger X) Y))))
% 3.70/4.03 (assert (forall ((Y tptp.num) (X tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num Y) X)) (@ (@ tptp.ord_less_num X) Y))))
% 3.70/4.03 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat Y) X)) (@ (@ tptp.ord_less_nat X) Y))))
% 3.70/4.03 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int Y) X)) (@ (@ tptp.ord_less_int X) Y))))
% 3.70/4.03 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((X2 tptp.code_integer) (Y5 tptp.code_integer)) (and (@ (@ tptp.ord_le3102999989581377725nteger X2) Y5) (not (@ (@ tptp.ord_le3102999989581377725nteger Y5) X2))))))
% 3.70/4.03 (assert (= tptp.ord_less_num (lambda ((X2 tptp.num) (Y5 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X2) Y5) (not (@ (@ tptp.ord_less_eq_num Y5) X2))))))
% 3.70/4.03 (assert (= tptp.ord_less_assn (lambda ((X2 tptp.assn) (Y5 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn X2) Y5) (not (@ (@ tptp.ord_less_eq_assn Y5) X2))))))
% 3.70/4.03 (assert (= tptp.ord_less_filter_nat (lambda ((X2 tptp.filter_nat) (Y5 tptp.filter_nat)) (and (@ (@ tptp.ord_le2510731241096832064er_nat X2) Y5) (not (@ (@ tptp.ord_le2510731241096832064er_nat Y5) X2))))))
% 3.70/4.03 (assert (= tptp.ord_less_set_nat (lambda ((X2 tptp.set_nat) (Y5 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat X2) Y5) (not (@ (@ tptp.ord_less_eq_set_nat Y5) X2))))))
% 3.70/4.03 (assert (= tptp.ord_less_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X2) Y5) (not (@ (@ tptp.ord_less_eq_nat Y5) X2))))))
% 3.70/4.03 (assert (= tptp.ord_less_int (lambda ((X2 tptp.int) (Y5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X2) Y5) (not (@ (@ tptp.ord_less_eq_int Y5) X2))))))
% 3.70/4.03 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger X) Y) (= (not (@ (@ tptp.ord_le6747313008572928689nteger X) Y)) (= X Y)))))
% 3.70/4.03 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (= (not (@ (@ tptp.ord_less_num X) Y)) (= X Y)))))
% 3.70/4.03 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X) Y) (= (not (@ (@ tptp.ord_less_assn X) Y)) (= X Y)))))
% 3.70/4.03 (assert (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat X) Y) (= (not (@ (@ tptp.ord_less_filter_nat X) Y)) (= X Y)))))
% 3.70/4.03 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (= (not (@ (@ tptp.ord_less_set_nat X) Y)) (= X Y)))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (not (@ (@ tptp.ord_less_nat X) Y)) (= X Y)))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (not (@ (@ tptp.ord_less_int X) Y)) (= X Y)))))
% 3.70/4.03 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (not (@ (@ tptp.ord_le6747313008572928689nteger X) Y)) (= (@ (@ tptp.ord_le3102999989581377725nteger X) Y) (= X Y)))))
% 3.70/4.03 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (= (@ (@ tptp.ord_less_eq_num X) Y) (= X Y)))))
% 3.70/4.03 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (not (@ (@ tptp.ord_less_assn X) Y)) (= (@ (@ tptp.ord_less_eq_assn X) Y) (= X Y)))))
% 3.70/4.03 (assert (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (=> (not (@ (@ tptp.ord_less_filter_nat X) Y)) (= (@ (@ tptp.ord_le2510731241096832064er_nat X) Y) (= X Y)))))
% 3.70/4.03 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (not (@ (@ tptp.ord_less_set_nat X) Y)) (= (@ (@ tptp.ord_less_eq_set_nat X) Y) (= X Y)))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (= (@ (@ tptp.ord_less_eq_nat X) Y) (= X Y)))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (= (@ (@ tptp.ord_less_eq_int X) Y) (= X Y)))))
% 3.70/4.03 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (not (@ (@ tptp.ord_le6747313008572928689nteger A2) B2)) (or (not (@ (@ tptp.ord_le3102999989581377725nteger A2) B2)) (= A2 B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.num) (B2 tptp.num)) (= (not (@ (@ tptp.ord_less_num A2) B2)) (or (not (@ (@ tptp.ord_less_eq_num A2) B2)) (= A2 B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn) (B2 tptp.assn)) (= (not (@ (@ tptp.ord_less_assn A2) B2)) (or (not (@ (@ tptp.ord_less_eq_assn A2) B2)) (= A2 B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat)) (= (not (@ (@ tptp.ord_less_filter_nat A2) B2)) (or (not (@ (@ tptp.ord_le2510731241096832064er_nat A2) B2)) (= A2 B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (= (not (@ (@ tptp.ord_less_set_nat A2) B2)) (or (not (@ (@ tptp.ord_less_eq_set_nat A2) B2)) (= A2 B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat A2) B2)) (or (not (@ (@ tptp.ord_less_eq_nat A2) B2)) (= A2 B2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (not (@ (@ tptp.ord_less_int A2) B2)) (or (not (@ (@ tptp.ord_less_eq_int A2) B2)) (= A2 B2)))))
% 3.70/4.03 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (not (@ (@ tptp.ord_le6747313008572928689nteger X) Y)) (@ (@ tptp.ord_le3102999989581377725nteger Y) X))))
% 3.70/4.03 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (@ (@ tptp.ord_less_eq_num Y) X))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))))
% 3.70/4.03 (assert (forall ((Y tptp.code_integer) (X tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger Y) X) (not (@ (@ tptp.ord_le6747313008572928689nteger X) Y)))))
% 3.70/4.03 (assert (forall ((Y tptp.num) (X tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X) (not (@ (@ tptp.ord_less_num X) Y)))))
% 3.70/4.03 (assert (forall ((Y tptp.assn) (X tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn Y) X) (not (@ (@ tptp.ord_less_assn X) Y)))))
% 3.70/4.03 (assert (forall ((Y tptp.filter_nat) (X tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat Y) X) (not (@ (@ tptp.ord_less_filter_nat X) Y)))))
% 3.70/4.03 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (not (@ (@ tptp.ord_less_set_nat X) Y)))))
% 3.70/4.03 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (not (@ (@ tptp.ord_less_nat X) Y)))))
% 3.70/4.03 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (not (@ (@ tptp.ord_less_int X) Y)))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A2) tptp.bot_bo228742789529271731at_nat) (= A2 tptp.bot_bo228742789529271731at_nat))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) tptp.bot_bo2099793752762293965at_nat) (= A2 tptp.bot_bo2099793752762293965at_nat))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_o)) (=> (@ (@ tptp.ord_less_eq_set_o A2) tptp.bot_bot_set_o) (= A2 tptp.bot_bot_set_o))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) tptp.bot_bot_set_int) (= A2 tptp.bot_bot_set_int))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A2) tptp.bot_bot_assn) (= A2 tptp.bot_bot_assn))))
% 3.70/4.03 (assert (forall ((A2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat A2) tptp.bot_bot_filter_nat) (= A2 tptp.bot_bot_filter_nat))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) tptp.bot_bot_set_nat) (= A2 tptp.bot_bot_set_nat))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.bot_bot_nat) (= A2 tptp.bot_bot_nat))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat A2) tptp.bot_bo228742789529271731at_nat) (= A2 tptp.bot_bo228742789529271731at_nat))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat A2) tptp.bot_bo2099793752762293965at_nat) (= A2 tptp.bot_bo2099793752762293965at_nat))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_o)) (= (@ (@ tptp.ord_less_eq_set_o A2) tptp.bot_bot_set_o) (= A2 tptp.bot_bot_set_o))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A2) tptp.bot_bot_set_int) (= A2 tptp.bot_bot_set_int))))
% 3.70/4.03 (assert (forall ((A2 tptp.assn)) (= (@ (@ tptp.ord_less_eq_assn A2) tptp.bot_bot_assn) (= A2 tptp.bot_bot_assn))))
% 3.70/4.03 (assert (forall ((A2 tptp.filter_nat)) (= (@ (@ tptp.ord_le2510731241096832064er_nat A2) tptp.bot_bot_filter_nat) (= A2 tptp.bot_bot_filter_nat))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A2) tptp.bot_bot_set_nat) (= A2 tptp.bot_bot_set_nat))))
% 3.70/4.03 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A2) tptp.bot_bot_nat) (= A2 tptp.bot_bot_nat))))
% 3.70/4.03 (assert (forall ((A2 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat tptp.bot_bo228742789529271731at_nat) A2)))
% 3.70/4.03 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat tptp.bot_bo2099793752762293965at_nat) A2)))
% 3.70/4.03 (assert (forall ((A2 tptp.set_o)) (@ (@ tptp.ord_less_eq_set_o tptp.bot_bot_set_o) A2)))
% 3.70/4.03 (assert (forall ((A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A2)))
% 3.70/4.03 (assert (forall ((A2 tptp.assn)) (@ (@ tptp.ord_less_eq_assn tptp.bot_bot_assn) A2)))
% 3.70/4.03 (assert (forall ((A2 tptp.filter_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat tptp.bot_bot_filter_nat) A2)))
% 3.70/4.03 (assert (forall ((A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A2)))
% 3.70/4.03 (assert (forall ((A2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.bot_bot_nat) A2)))
% 3.70/4.03 (assert (forall ((R2 tptp.set_Pr4329608150637261639at_nat) (S3 tptp.set_Pr4329608150637261639at_nat)) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat) (Y2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X3) Y2)))) (=> (@ _let_1 R2) (@ _let_1 S3)))) (@ (@ tptp.ord_le1268244103169919719at_nat R2) S3))))
% 3.70/4.03 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (S3 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) Y2)))) (=> (@ _let_1 R2) (@ _let_1 S3)))) (@ (@ tptp.ord_le3146513528884898305at_nat R2) S3))))
% 3.70/4.03 (assert (forall ((R2 tptp.set_Pr1281608226676607948nteger) (S3 tptp.set_Pr1281608226676607948nteger)) (=> (forall ((X3 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (Y2 tptp.produc8923325533196201883nteger)) (let ((_let_1 (@ tptp.member4164122664394876845nteger (@ (@ tptp.produc8603105652947943368nteger X3) Y2)))) (=> (@ _let_1 R2) (@ _let_1 S3)))) (@ (@ tptp.ord_le653643898420964396nteger R2) S3))))
% 3.70/4.03 (assert (forall ((R2 tptp.set_Pr3286484037609594932et_nat) (S3 tptp.set_Pr3286484037609594932et_nat)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 tptp.produc3658429121746597890et_nat)) (let ((_let_1 (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat X3) Y2)))) (=> (@ _let_1 R2) (@ _let_1 S3)))) (@ (@ tptp.ord_le5966269811547037844et_nat R2) S3))))
% 3.70/4.03 (assert (forall ((R2 tptp.set_Pr8536935166611901872et_nat) (S3 tptp.set_Pr8536935166611901872et_nat)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 tptp.produc3925858234332021118et_nat)) (let ((_let_1 (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat X3) Y2)))) (=> (@ _let_1 R2) (@ _let_1 S3)))) (@ (@ tptp.ord_le4763372923235995152et_nat R2) S3))))
% 3.70/4.03 (assert (forall ((R2 tptp.set_Pr9222295170931077689nt_int) (S3 tptp.set_Pr9222295170931077689nt_int)) (=> (forall ((X3 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y2 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.member7618704894036264090nt_int (@ (@ tptp.produc5700946648718959541nt_int X3) Y2)))) (=> (@ _let_1 R2) (@ _let_1 S3)))) (@ (@ tptp.ord_le8725513860283290265nt_int R2) S3))))
% 3.70/4.03 (assert (forall ((R2 tptp.set_Pr1872883991513573699nt_int) (S3 tptp.set_Pr1872883991513573699nt_int)) (=> (forall ((X3 (-> tptp.int tptp.option6357759511663192854e_term)) (Y2 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.member7034335876925520548nt_int (@ (@ tptp.produc4305682042979456191nt_int X3) Y2)))) (=> (@ _let_1 R2) (@ _let_1 S3)))) (@ (@ tptp.ord_le135402666524580259nt_int R2) S3))))
% 3.70/4.03 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A2) B2) (@ (@ tptp.minus_minus_rat C) D2)) (= (@ (@ tptp.ord_less_eq_rat A2) B2) (@ (@ tptp.ord_less_eq_rat C) D2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int) (D2 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A2) B2) (@ (@ tptp.minus_minus_int C) D2)) (= (@ (@ tptp.ord_less_eq_int A2) B2) (@ (@ tptp.ord_less_eq_int C) D2)))))
% 3.70/4.03 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A2) C)) (@ (@ tptp.minus_minus_rat B2) C)))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A2) C)) (@ (@ tptp.minus_minus_int B2) C)))))
% 3.70/4.03 (assert (forall ((B2 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B2) A2) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2))))))
% 3.70/4.03 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int C))) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2))))))
% 3.70/4.03 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (D2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_eq_rat D2) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A2) C)) (@ (@ tptp.minus_minus_rat B2) D2))))))
% 3.70/4.03 (assert (forall ((A2 tptp.int) (B2 tptp.int) (D2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_eq_int D2) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A2) C)) (@ (@ tptp.minus_minus_int B2) D2))))))
% 3.70/4.03 (assert (forall ((P tptp.assn) (Q tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn (@ (@ tptp.inf_inf_assn P) Q)) H2) (and (@ (@ tptp.rep_assn P) H2) (@ (@ tptp.rep_assn Q) H2)))))
% 3.70/4.03 (assert (forall ((A tptp.assn) (B tptp.assn) (C2 tptp.assn)) (let ((_let_1 (@ tptp.entails A))) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.inf_inf_assn B) C2)))))))
% 3.70/4.03 (assert (forall ((A tptp.assn) (C2 tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.entails A) C2) (@ (@ tptp.entails (@ (@ tptp.inf_inf_assn A) B)) C2))))
% 3.70/4.03 (assert (forall ((B tptp.assn) (C2 tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.entails B) C2) (@ (@ tptp.entails (@ (@ tptp.inf_inf_assn A) B)) C2))))
% 3.70/4.03 (assert (forall ((A tptp.set_int) (B tptp.set_int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert_int2 B2) B))))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (B2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat B2) B))))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (B2 tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.ord_le1268244103169919719at_nat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert9069300056098147895at_nat B2) B))))))
% 3.70/4.03 (assert (forall ((A tptp.set_o) (B tptp.set_o) (B2 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_set_o A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert_o2 B2) B))))))
% 3.70/4.03 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert_nat2 B2) B))))))
% 3.70/4.03 (assert (forall ((B tptp.set_int) (A2 tptp.int)) (@ (@ tptp.ord_less_eq_set_int B) (@ (@ tptp.insert_int2 A2) B))))
% 3.70/4.03 (assert (forall ((B tptp.set_Pr1261947904930325089at_nat) (A2 tptp.product_prod_nat_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat B) (@ (@ tptp.insert8211810215607154385at_nat A2) B))))
% 3.70/4.03 (assert (forall ((B tptp.set_Pr4329608150637261639at_nat) (A2 tptp.produc3843707927480180839at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat B) (@ (@ tptp.insert9069300056098147895at_nat A2) B))))
% 3.70/4.03 (assert (forall ((B tptp.set_o) (A2 Bool)) (@ (@ tptp.ord_less_eq_set_o B) (@ (@ tptp.insert_o2 A2) B))))
% 3.70/4.03 (assert (forall ((B tptp.set_nat) (A2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat B) (@ (@ tptp.insert_nat2 A2) B))))
% 3.70/4.03 (assert (forall ((X Bool) (A tptp.set_o) (B tptp.set_o)) (let ((_let_1 (@ tptp.ord_less_eq_set_o A))) (=> (not (@ (@ tptp.member_o X) A)) (= (@ _let_1 (@ (@ tptp.insert_o2 X) B)) (@ _let_1 B))))))
% 3.70/4.03 (assert (forall ((X tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le1268244103169919719at_nat A))) (=> (not (@ (@ tptp.member8757157785044589968at_nat X) A)) (= (@ _let_1 (@ (@ tptp.insert9069300056098147895at_nat X) B)) (@ _let_1 B))))))
% 3.70/4.03 (assert (forall ((X tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A))) (=> (not (@ (@ tptp.member8440522571783428010at_nat X) A)) (= (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat X) B)) (@ _let_1 B))))))
% 3.70/4.03 (assert (forall ((X tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A))) (=> (not (@ (@ tptp.member_int X) A)) (= (@ _let_1 (@ (@ tptp.insert_int2 X) B)) (@ _let_1 B))))))
% 3.70/4.03 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.ord_le2965882846123202637_nat_o A))) (=> (not (@ (@ tptp.member6576561426505652726_nat_o X) A)) (= (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o X) B)) (@ _let_1 B))))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (=> (not (@ (@ tptp.member_nat X) A)) (= (@ _let_1 (@ (@ tptp.insert_nat2 X) B)) (@ _let_1 B))))))
% 3.70/4.03 (assert (forall ((C2 tptp.set_int) (D tptp.set_int) (A2 tptp.int)) (let ((_let_1 (@ tptp.insert_int2 A2))) (=> (@ (@ tptp.ord_less_eq_set_int C2) D) (@ (@ tptp.ord_less_eq_set_int (@ _let_1 C2)) (@ _let_1 D))))))
% 3.70/4.03 (assert (forall ((C2 tptp.set_Pr1261947904930325089at_nat) (D tptp.set_Pr1261947904930325089at_nat) (A2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A2))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat C2) D) (@ (@ tptp.ord_le3146513528884898305at_nat (@ _let_1 C2)) (@ _let_1 D))))))
% 3.70/4.03 (assert (forall ((C2 tptp.set_Pr4329608150637261639at_nat) (D tptp.set_Pr4329608150637261639at_nat) (A2 tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.insert9069300056098147895at_nat A2))) (=> (@ (@ tptp.ord_le1268244103169919719at_nat C2) D) (@ (@ tptp.ord_le1268244103169919719at_nat (@ _let_1 C2)) (@ _let_1 D))))))
% 3.70/4.03 (assert (forall ((C2 tptp.set_o) (D tptp.set_o) (A2 Bool)) (let ((_let_1 (@ tptp.insert_o2 A2))) (=> (@ (@ tptp.ord_less_eq_set_o C2) D) (@ (@ tptp.ord_less_eq_set_o (@ _let_1 C2)) (@ _let_1 D))))))
% 3.70/4.03 (assert (forall ((C2 tptp.set_nat) (D tptp.set_nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.insert_nat2 A2))) (=> (@ (@ tptp.ord_less_eq_set_nat C2) D) (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 C2)) (@ _let_1 D))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_P5464809261938338413at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat (@ tptp.set_Pr3765526544606949372at_nat Xs)) B) (forall ((X2 tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat X2))) (=> (@ _let_1 (@ tptp.set_Pr3765526544606949372at_nat Xs)) (@ _let_1 B)))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_P6011104703257516679at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs)) B) (forall ((X2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X2))) (=> (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat Xs)) (@ _let_1 B)))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_P7985473006766602707_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.ord_le2965882846123202637_nat_o (@ tptp.set_Pr400311997697478754_nat_o Xs)) B) (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o X2))) (=> (@ _let_1 (@ tptp.set_Pr400311997697478754_nat_o Xs)) (@ _let_1 B)))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_int) (B tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) B) (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.member_int X2))) (=> (@ _let_1 (@ tptp.set_int2 Xs)) (@ _let_1 B)))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (B tptp.set_Pr5949110396991348497n_assn)) (= (@ (@ tptp.ord_le171416862856029873n_assn (@ tptp.set_Pr1139785259514867910n_assn Xs)) B) (forall ((X2 tptp.produc6575502325842934193n_assn)) (let ((_let_1 (@ tptp.member7957490590177025114n_assn X2))) (=> (@ _let_1 (@ tptp.set_Pr1139785259514867910n_assn Xs)) (@ _let_1 B)))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_nat) (B tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) B) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X2))) (=> (@ _let_1 (@ tptp.set_nat2 Xs)) (@ _let_1 B)))))))
% 3.70/4.03 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (@ (@ tptp.ord_less_eq_set_nat B) C2) (= (@ (@ tptp.minus_minus_set_nat B) (@ (@ tptp.minus_minus_set_nat C2) A)) A)))))
% 3.70/4.03 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A) B)) A)))
% 3.70/4.03 (assert (forall ((A tptp.set_nat) (C2 tptp.set_nat) (D tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) C2) (=> (@ (@ tptp.ord_less_eq_set_nat D) B) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A) B)) (@ (@ tptp.minus_minus_set_nat C2) D))))))
% 3.70/4.03 (assert (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B7 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat A5) B7) (= A5 B7)))))
% 3.70/4.03 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (@ (@ tptp.ord_less_set_nat B) C2) (@ (@ tptp.ord_less_set_nat A) C2)))))
% 3.70/4.03 (assert (= tptp.ord_less_set_nat (lambda ((A5 tptp.set_nat) (B7 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A5) B7) (not (@ (@ tptp.ord_less_eq_set_nat B7) A5))))))
% 3.70/4.03 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_nat B) C2) (@ _let_1 C2))))))
% 3.70/4.03 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A) B) (@ (@ tptp.ord_less_eq_set_nat A) B))))
% 3.70/4.03 (assert (= tptp.ord_less_set_nat (lambda ((A5 tptp.set_nat) (B7 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A5) B7) (not (= A5 B7))))))
% 3.70/4.03 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A) B) (not (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (@ (@ tptp.ord_less_eq_set_nat B) A))))))
% 3.70/4.03 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn tptp.bot_bot_assn) X) tptp.bot_bot_assn)))
% 3.70/4.03 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn X) tptp.bot_bot_assn) tptp.bot_bot_assn)))
% 3.70/4.03 (assert (forall ((P (-> tptp.produc3843707927480180839at_nat tptp.produc3843707927480180839at_nat Bool))) (@ (@ tptp.pairwi3222497012029234898at_nat P) tptp.bot_bo228742789529271731at_nat)))
% 3.70/4.03 (assert (forall ((P (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool))) (@ (@ tptp.pairwi6357175311820755948at_nat P) tptp.bot_bo2099793752762293965at_nat)))
% 3.70/4.03 (assert (forall ((P (-> Bool Bool Bool))) (@ (@ tptp.pairwise_o P) tptp.bot_bot_set_o)))
% 3.70/4.03 (assert (forall ((P (-> tptp.nat tptp.nat Bool))) (@ (@ tptp.pairwise_nat P) tptp.bot_bot_set_nat)))
% 3.70/4.03 (assert (forall ((P (-> tptp.int tptp.int Bool))) (@ (@ tptp.pairwise_int P) tptp.bot_bot_set_int)))
% 3.70/4.03 (assert (forall ((R2 (-> Bool Bool Bool)) (X Bool) (S3 tptp.set_o)) (let ((_let_1 (@ tptp.pairwise_o R2))) (= (@ _let_1 (@ (@ tptp.insert_o2 X) S3)) (and (forall ((Y5 Bool)) (=> (and (@ (@ tptp.member_o Y5) S3) (not (= Y5 X))) (and (@ (@ R2 X) Y5) (@ (@ R2 Y5) X)))) (@ _let_1 S3))))))
% 3.70/4.03 (assert (forall ((R2 (-> tptp.produc3843707927480180839at_nat tptp.produc3843707927480180839at_nat Bool)) (X tptp.produc3843707927480180839at_nat) (S3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.pairwi3222497012029234898at_nat R2))) (= (@ _let_1 (@ (@ tptp.insert9069300056098147895at_nat X) S3)) (and (forall ((Y5 tptp.produc3843707927480180839at_nat)) (=> (and (@ (@ tptp.member8757157785044589968at_nat Y5) S3) (not (= Y5 X))) (and (@ (@ R2 X) Y5) (@ (@ R2 Y5) X)))) (@ _let_1 S3))))))
% 3.70/4.03 (assert (forall ((R2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (X tptp.product_prod_nat_nat) (S3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.pairwi6357175311820755948at_nat R2))) (= (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat X) S3)) (and (forall ((Y5 tptp.product_prod_nat_nat)) (=> (and (@ (@ tptp.member8440522571783428010at_nat Y5) S3) (not (= Y5 X))) (and (@ (@ R2 X) Y5) (@ (@ R2 Y5) X)))) (@ _let_1 S3))))))
% 3.70/4.03 (assert (forall ((R2 (-> tptp.nat tptp.nat Bool)) (X tptp.nat) (S3 tptp.set_nat)) (let ((_let_1 (@ tptp.pairwise_nat R2))) (= (@ _let_1 (@ (@ tptp.insert_nat2 X) S3)) (and (forall ((Y5 tptp.nat)) (=> (and (@ (@ tptp.member_nat Y5) S3) (not (= Y5 X))) (and (@ (@ R2 X) Y5) (@ (@ R2 Y5) X)))) (@ _let_1 S3))))))
% 3.70/4.03 (assert (forall ((R2 (-> tptp.int tptp.int Bool)) (X tptp.int) (S3 tptp.set_int)) (let ((_let_1 (@ tptp.pairwise_int R2))) (= (@ _let_1 (@ (@ tptp.insert_int2 X) S3)) (and (forall ((Y5 tptp.int)) (=> (and (@ (@ tptp.member_int Y5) S3) (not (= Y5 X))) (and (@ (@ R2 X) Y5) (@ (@ R2 Y5) X)))) (@ _let_1 S3))))))
% 3.70/4.03 (assert (forall ((R2 (-> (-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) Bool)) (X (-> tptp.produc3658429121746597890et_nat Bool)) (S3 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.pairwi2432143822833250616_nat_o R2))) (= (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o X) S3)) (and (forall ((Y5 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (and (@ (@ tptp.member6576561426505652726_nat_o Y5) S3) (not (= Y5 X))) (and (@ (@ R2 X) Y5) (@ (@ R2 Y5) X)))) (@ _let_1 S3))))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (X tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ (@ tptp.insert9069300056098147895at_nat X) tptp.bot_bo228742789529271731at_nat))) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A) _let_1) (or (= A tptp.bot_bo228742789529271731at_nat) (= A _let_1))))))
% 3.70/4.03 (assert (forall ((A 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 A) _let_1) (or (= A tptp.bot_bo2099793752762293965at_nat) (= A _let_1))))))
% 3.70/4.03 (assert (forall ((A tptp.set_o) (X Bool)) (let ((_let_1 (@ (@ tptp.insert_o2 X) tptp.bot_bot_set_o))) (=> (@ (@ tptp.ord_less_eq_set_o A) _let_1) (or (= A tptp.bot_bot_set_o) (= A _let_1))))))
% 3.70/4.03 (assert (forall ((A tptp.set_int) (X tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int2 X) tptp.bot_bot_set_int))) (=> (@ (@ tptp.ord_less_eq_set_int A) _let_1) (or (= A tptp.bot_bot_set_int) (= A _let_1))))))
% 3.70/4.03 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat2 X) tptp.bot_bot_set_nat))) (=> (@ (@ tptp.ord_less_eq_set_nat A) _let_1) (or (= A tptp.bot_bot_set_nat) (= A _let_1))))))
% 3.70/4.03 (assert (forall ((X4 tptp.set_Pr4329608150637261639at_nat) (A2 tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ (@ tptp.insert9069300056098147895at_nat A2) tptp.bot_bo228742789529271731at_nat))) (= (@ (@ tptp.ord_le1268244103169919719at_nat X4) _let_1) (or (= X4 tptp.bot_bo228742789529271731at_nat) (= X4 _let_1))))))
% 3.70/4.03 (assert (forall ((X4 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.insert8211810215607154385at_nat A2) tptp.bot_bo2099793752762293965at_nat))) (= (@ (@ tptp.ord_le3146513528884898305at_nat X4) _let_1) (or (= X4 tptp.bot_bo2099793752762293965at_nat) (= X4 _let_1))))))
% 3.70/4.03 (assert (forall ((X4 tptp.set_o) (A2 Bool)) (let ((_let_1 (@ (@ tptp.insert_o2 A2) tptp.bot_bot_set_o))) (= (@ (@ tptp.ord_less_eq_set_o X4) _let_1) (or (= X4 tptp.bot_bot_set_o) (= X4 _let_1))))))
% 3.70/4.03 (assert (forall ((X4 tptp.set_int) (A2 tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int2 A2) tptp.bot_bot_set_int))) (= (@ (@ tptp.ord_less_eq_set_int X4) _let_1) (or (= X4 tptp.bot_bot_set_int) (= X4 _let_1))))))
% 3.70/4.03 (assert (forall ((X4 tptp.set_nat) (A2 tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat2 A2) tptp.bot_bot_set_nat))) (= (@ (@ tptp.ord_less_eq_set_nat X4) _let_1) (or (= X4 tptp.bot_bot_set_nat) (= X4 _let_1))))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A) B) (= (@ (@ tptp.minus_3314409938677909166at_nat A) B) tptp.bot_bo228742789529271731at_nat))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A) B) (= (@ (@ tptp.minus_1356011639430497352at_nat A) B) tptp.bot_bo2099793752762293965at_nat))))
% 3.70/4.03 (assert (forall ((A tptp.set_o) (B tptp.set_o)) (=> (@ (@ tptp.ord_less_eq_set_o A) B) (= (@ (@ tptp.minus_minus_set_o A) B) tptp.bot_bot_set_o))))
% 3.70/4.03 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (= (@ (@ tptp.minus_minus_set_int A) B) tptp.bot_bot_set_int))))
% 3.70/4.03 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (= (@ (@ tptp.minus_minus_set_nat A) B) tptp.bot_bot_set_nat))))
% 3.70/4.03 (assert (forall ((A tptp.set_o) (B tptp.set_o) (X Bool) (C2 tptp.set_o)) (let ((_let_1 (@ tptp.minus_minus_set_o B))) (let ((_let_2 (@ tptp.ord_less_eq_set_o A))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_o2 X) C2))) (and (@ _let_2 (@ _let_1 C2)) (not (@ (@ tptp.member_o X) A))))))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (X tptp.produc3843707927480180839at_nat) (C2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.minus_3314409938677909166at_nat B))) (let ((_let_2 (@ tptp.ord_le1268244103169919719at_nat A))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert9069300056098147895at_nat X) C2))) (and (@ _let_2 (@ _let_1 C2)) (not (@ (@ tptp.member8757157785044589968at_nat X) A))))))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat B))) (let ((_let_2 (@ tptp.ord_le3146513528884898305at_nat A))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat X) C2))) (and (@ _let_2 (@ _let_1 C2)) (not (@ (@ tptp.member8440522571783428010at_nat X) A))))))))
% 3.70/4.03 (assert (forall ((A tptp.set_int) (B tptp.set_int) (X tptp.int) (C2 tptp.set_int)) (let ((_let_1 (@ tptp.minus_minus_set_int B))) (let ((_let_2 (@ tptp.ord_less_eq_set_int A))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_int2 X) C2))) (and (@ _let_2 (@ _let_1 C2)) (not (@ (@ tptp.member_int X) A))))))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool)) (C2 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.minus_1801376950450012436_nat_o B))) (let ((_let_2 (@ tptp.ord_le2965882846123202637_nat_o A))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o X) C2))) (and (@ _let_2 (@ _let_1 C2)) (not (@ (@ tptp.member6576561426505652726_nat_o X) A))))))))
% 3.70/4.03 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (X tptp.nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat B))) (let ((_let_2 (@ tptp.ord_less_eq_set_nat A))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_nat2 X) C2))) (and (@ _let_2 (@ _let_1 C2)) (not (@ (@ tptp.member_nat X) A))))))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_P5464809261938338413at_nat) (A tptp.set_Pr4329608150637261639at_nat) (X tptp.produc3843707927480180839at_nat) (I tptp.nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat (@ tptp.set_Pr3765526544606949372at_nat Xs)) A) (=> (@ (@ tptp.member8757157785044589968at_nat X) A) (@ (@ tptp.ord_le1268244103169919719at_nat (@ tptp.set_Pr3765526544606949372at_nat (@ (@ (@ tptp.list_u4696772448584712917at_nat Xs) I) X))) A)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_P6011104703257516679at_nat) (A tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (I tptp.nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs)) A) (=> (@ (@ tptp.member8440522571783428010at_nat X) A) (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat Xs) I) X))) A)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_P7985473006766602707_nat_o) (A tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool)) (I tptp.nat)) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o (@ tptp.set_Pr400311997697478754_nat_o Xs)) A) (=> (@ (@ tptp.member6576561426505652726_nat_o X) A) (@ (@ tptp.ord_le2965882846123202637_nat_o (@ tptp.set_Pr400311997697478754_nat_o (@ (@ (@ tptp.list_u6943956310655620667_nat_o Xs) I) X))) A)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_int) (A tptp.set_int) (X tptp.int) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) A) (=> (@ (@ tptp.member_int X) A) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs) I) X))) A)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (A tptp.set_Pr5949110396991348497n_assn) (X tptp.produc6575502325842934193n_assn) (I tptp.nat)) (=> (@ (@ tptp.ord_le171416862856029873n_assn (@ tptp.set_Pr1139785259514867910n_assn Xs)) A) (=> (@ (@ tptp.member7957490590177025114n_assn X) A) (@ (@ tptp.ord_le171416862856029873n_assn (@ tptp.set_Pr1139785259514867910n_assn (@ (@ (@ tptp.list_u4534839942911652127n_assn Xs) I) X))) A)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_c) (A tptp.set_c) (X tptp.c) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_c (@ tptp.set_c2 Xs)) A) (=> (@ (@ tptp.member_c X) A) (@ (@ tptp.ord_less_eq_set_c (@ tptp.set_c2 (@ (@ (@ tptp.list_update_c Xs) I) X))) A)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_d) (A tptp.set_d) (X tptp.d) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_d (@ tptp.set_d2 Xs)) A) (=> (@ (@ tptp.member_d X) A) (@ (@ tptp.ord_less_eq_set_d (@ tptp.set_d2 (@ (@ (@ tptp.list_update_d Xs) I) X))) A)))))
% 3.70/4.03 (assert (forall ((Xs tptp.list_nat) (A tptp.set_nat) (X tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) A) (=> (@ (@ tptp.member_nat X) A) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs) I) X))) A)))))
% 3.70/4.03 (assert (forall ((X tptp.int) (Xs tptp.list_int)) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 (@ (@ tptp.remove1_int X) Xs))) (@ tptp.set_int2 Xs))))
% 3.70/4.03 (assert (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (@ (@ tptp.ord_le171416862856029873n_assn (@ tptp.set_Pr1139785259514867910n_assn (@ (@ tptp.remove1670527618125605709n_assn X) Xs))) (@ tptp.set_Pr1139785259514867910n_assn Xs))))
% 3.70/4.03 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 (@ (@ tptp.remove1_nat X) Xs))) (@ tptp.set_nat2 Xs))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (Ys tptp.list_P5464809261938338413at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat A) (@ tptp.coset_5307619257043544794at_nat Ys)) (forall ((X2 tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat X2))) (=> (@ _let_1 (@ tptp.set_Pr3765526544606949372at_nat Ys)) (not (@ _let_1 A))))))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (Ys tptp.list_P6011104703257516679at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat A) (@ tptp.coset_6809516720700967924at_nat Ys)) (forall ((X2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X2))) (=> (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat Ys)) (not (@ _let_1 A))))))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (Ys tptp.list_P7985473006766602707_nat_o)) (= (@ (@ tptp.ord_le2965882846123202637_nat_o A) (@ tptp.coset_9017067850271954240_nat_o Ys)) (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o X2))) (=> (@ _let_1 (@ tptp.set_Pr400311997697478754_nat_o Ys)) (not (@ _let_1 A))))))))
% 3.70/4.03 (assert (forall ((A tptp.set_int) (Ys tptp.list_int)) (= (@ (@ tptp.ord_less_eq_set_int A) (@ tptp.coset_int Ys)) (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.member_int X2))) (=> (@ _let_1 (@ tptp.set_int2 Ys)) (not (@ _let_1 A))))))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr5949110396991348497n_assn) (Ys tptp.list_P8527749157015355191n_assn)) (= (@ (@ tptp.ord_le171416862856029873n_assn A) (@ tptp.coset_703488708621576356n_assn Ys)) (forall ((X2 tptp.produc6575502325842934193n_assn)) (let ((_let_1 (@ tptp.member7957490590177025114n_assn X2))) (=> (@ _let_1 (@ tptp.set_Pr1139785259514867910n_assn Ys)) (not (@ _let_1 A))))))))
% 3.70/4.03 (assert (forall ((A tptp.set_nat) (Ys tptp.list_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A) (@ tptp.coset_nat Ys)) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X2))) (=> (@ _let_1 (@ tptp.set_nat2 Ys)) (not (@ _let_1 A))))))))
% 3.70/4.03 (assert (forall ((P (-> tptp.produc3843707927480180839at_nat tptp.produc3843707927480180839at_nat Bool)) (A tptp.produc3843707927480180839at_nat)) (@ (@ tptp.pairwi3222497012029234898at_nat P) (@ (@ tptp.insert9069300056098147895at_nat A) tptp.bot_bo228742789529271731at_nat))))
% 3.70/4.03 (assert (forall ((P (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (A tptp.product_prod_nat_nat)) (@ (@ tptp.pairwi6357175311820755948at_nat P) (@ (@ tptp.insert8211810215607154385at_nat A) tptp.bot_bo2099793752762293965at_nat))))
% 3.70/4.03 (assert (forall ((P (-> Bool Bool Bool)) (A Bool)) (@ (@ tptp.pairwise_o P) (@ (@ tptp.insert_o2 A) tptp.bot_bot_set_o))))
% 3.70/4.03 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat)) (@ (@ tptp.pairwise_nat P) (@ (@ tptp.insert_nat2 A) tptp.bot_bot_set_nat))))
% 3.70/4.03 (assert (forall ((P (-> tptp.int tptp.int Bool)) (A tptp.int)) (@ (@ tptp.pairwise_int P) (@ (@ tptp.insert_int2 A) tptp.bot_bot_set_int))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.ord_le2965882846123202637_nat_o A))) (let ((_let_2 (@ (@ tptp.member6576561426505652726_nat_o X) A))) (let ((_let_3 (@ tptp.insert5175938949040314269_nat_o X))) (= (@ _let_1 (@ _let_3 B)) (and (=> _let_2 (@ (@ tptp.ord_le2965882846123202637_nat_o (@ (@ tptp.minus_1801376950450012436_nat_o A) (@ _let_3 tptp.bot_bo7824918357723582233_nat_o))) B)) (=> (not _let_2) (@ _let_1 B)))))))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (X tptp.produc3843707927480180839at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le1268244103169919719at_nat A))) (let ((_let_2 (@ (@ tptp.member8757157785044589968at_nat X) A))) (let ((_let_3 (@ tptp.insert9069300056098147895at_nat X))) (= (@ _let_1 (@ _let_3 B)) (and (=> _let_2 (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.minus_3314409938677909166at_nat A) (@ _let_3 tptp.bot_bo228742789529271731at_nat))) B)) (=> (not _let_2) (@ _let_1 B)))))))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A))) (let ((_let_2 (@ (@ tptp.member8440522571783428010at_nat X) A))) (let ((_let_3 (@ tptp.insert8211810215607154385at_nat X))) (= (@ _let_1 (@ _let_3 B)) (and (=> _let_2 (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.minus_1356011639430497352at_nat A) (@ _let_3 tptp.bot_bo2099793752762293965at_nat))) B)) (=> (not _let_2) (@ _let_1 B)))))))))
% 3.70/4.03 (assert (forall ((A tptp.set_o) (X Bool) (B tptp.set_o)) (let ((_let_1 (@ tptp.ord_less_eq_set_o A))) (let ((_let_2 (@ (@ tptp.member_o X) A))) (let ((_let_3 (@ tptp.insert_o2 X))) (= (@ _let_1 (@ _let_3 B)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.minus_minus_set_o A) (@ _let_3 tptp.bot_bot_set_o))) B)) (=> (not _let_2) (@ _let_1 B)))))))))
% 3.70/4.03 (assert (forall ((A tptp.set_int) (X tptp.int) (B tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A))) (let ((_let_2 (@ (@ tptp.member_int X) A))) (let ((_let_3 (@ tptp.insert_int2 X))) (= (@ _let_1 (@ _let_3 B)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A) (@ _let_3 tptp.bot_bot_set_int))) B)) (=> (not _let_2) (@ _let_1 B)))))))))
% 3.70/4.03 (assert (forall ((A tptp.set_nat) (X tptp.nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (let ((_let_2 (@ (@ tptp.member_nat X) A))) (let ((_let_3 (@ tptp.insert_nat2 X))) (= (@ _let_1 (@ _let_3 B)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A) (@ _let_3 tptp.bot_bot_set_nat))) B)) (=> (not _let_2) (@ _let_1 B)))))))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (X tptp.produc3843707927480180839at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.insert9069300056098147895at_nat X))) (=> (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.minus_3314409938677909166at_nat A) (@ _let_1 tptp.bot_bo228742789529271731at_nat))) B) (@ (@ tptp.ord_le1268244103169919719at_nat A) (@ _let_1 B))))))
% 3.70/4.03 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat X))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.minus_1356011639430497352at_nat A) (@ _let_1 tptp.bot_bo2099793752762293965at_nat))) B) (@ (@ tptp.ord_le3146513528884898305at_nat A) (@ _let_1 B))))))
% 3.70/4.03 (assert (forall ((A tptp.set_o) (X Bool) (B tptp.set_o)) (let ((_let_1 (@ tptp.insert_o2 X))) (=> (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.minus_minus_set_o A) (@ _let_1 tptp.bot_bot_set_o))) B) (@ (@ tptp.ord_less_eq_set_o A) (@ _let_1 B))))))
% 3.70/4.04 (assert (forall ((A tptp.set_int) (X tptp.int) (B tptp.set_int)) (let ((_let_1 (@ tptp.insert_int2 X))) (=> (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A) (@ _let_1 tptp.bot_bot_set_int))) B) (@ (@ tptp.ord_less_eq_set_int A) (@ _let_1 B))))))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (X tptp.nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat2 X))) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A) (@ _let_1 tptp.bot_bot_set_nat))) B) (@ (@ tptp.ord_less_eq_set_nat A) (@ _let_1 B))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_P6011104703257516679at_nat) (I tptp.nat) (X tptp.product_prod_nat_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat Xs) I) X))) (@ (@ tptp.insert8211810215607154385at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs)))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_P5464809261938338413at_nat) (I tptp.nat) (X tptp.produc3843707927480180839at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat (@ tptp.set_Pr3765526544606949372at_nat (@ (@ (@ tptp.list_u4696772448584712917at_nat Xs) I) X))) (@ (@ tptp.insert9069300056098147895at_nat X) (@ tptp.set_Pr3765526544606949372at_nat Xs)))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_o) (I tptp.nat) (X Bool)) (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o Xs) I) X))) (@ (@ tptp.insert_o2 X) (@ tptp.set_o2 Xs)))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_int) (I tptp.nat) (X tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs) I) X))) (@ (@ tptp.insert_int2 X) (@ tptp.set_int2 Xs)))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (I tptp.nat) (X tptp.produc6575502325842934193n_assn)) (@ (@ tptp.ord_le171416862856029873n_assn (@ tptp.set_Pr1139785259514867910n_assn (@ (@ (@ tptp.list_u4534839942911652127n_assn Xs) I) X))) (@ (@ tptp.insert5290817439147925377n_assn X) (@ tptp.set_Pr1139785259514867910n_assn Xs)))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_c) (I tptp.nat) (X tptp.c)) (@ (@ tptp.ord_less_eq_set_c (@ tptp.set_c2 (@ (@ (@ tptp.list_update_c Xs) I) X))) (@ (@ tptp.insert_c X) (@ tptp.set_c2 Xs)))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_d) (I tptp.nat) (X tptp.d)) (@ (@ tptp.ord_less_eq_set_d (@ tptp.set_d2 (@ (@ (@ tptp.list_update_d Xs) I) X))) (@ (@ tptp.insert_d X) (@ tptp.set_d2 Xs)))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_nat) (I tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs) I) X))) (@ (@ tptp.insert_nat2 X) (@ tptp.set_nat2 Xs)))))
% 3.70/4.04 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn X) tptp.bot_bot_assn) tptp.bot_bot_assn)))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat X) tptp.bot_bo228742789529271731at_nat) tptp.bot_bo228742789529271731at_nat)))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat X) tptp.bot_bo2099793752762293965at_nat) tptp.bot_bo2099793752762293965at_nat)))
% 3.70/4.04 (assert (forall ((X tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o X) tptp.bot_bot_set_o) tptp.bot_bot_set_o)))
% 3.70/4.04 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X) tptp.bot_bot_set_nat) tptp.bot_bot_set_nat)))
% 3.70/4.04 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int X) tptp.bot_bot_set_int) tptp.bot_bot_set_int)))
% 3.70/4.04 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn tptp.bot_bot_assn) X) tptp.bot_bot_assn)))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat tptp.bot_bo228742789529271731at_nat) X) tptp.bot_bo228742789529271731at_nat)))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bot_bo2099793752762293965at_nat) X) tptp.bot_bo2099793752762293965at_nat)))
% 3.70/4.04 (assert (forall ((X tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o tptp.bot_bot_set_o) X) tptp.bot_bot_set_o)))
% 3.70/4.04 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat tptp.bot_bot_set_nat) X) tptp.bot_bot_set_nat)))
% 3.70/4.04 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int tptp.bot_bot_set_int) X) tptp.bot_bot_set_int)))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (= (= (@ (@ tptp.minus_3314409938677909166at_nat X) Y) tptp.bot_bo228742789529271731at_nat) (@ (@ tptp.ord_le1268244103169919719at_nat X) Y))))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.minus_1356011639430497352at_nat X) Y) tptp.bot_bo2099793752762293965at_nat) (@ (@ tptp.ord_le3146513528884898305at_nat X) Y))))
% 3.70/4.04 (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))))
% 3.70/4.04 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int X) Y) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int X) Y))))
% 3.70/4.04 (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))))
% 3.70/4.04 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat X) Y) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat X) Y))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_c)) (= (@ tptp.size_s2756448709718749209od_c_c (@ (@ tptp.product_c_c Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_c Xs)) (@ tptp.size_size_list_c Ys)))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_d)) (= (@ tptp.size_s2827482749765095194od_c_d (@ (@ tptp.product_c_d Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_c Xs)) (@ tptp.size_size_list_d Ys)))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_nat)) (= (@ tptp.size_s2954062820725854115_c_nat (@ (@ tptp.product_c_nat Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_c Xs)) (@ tptp.size_size_list_nat Ys)))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_int)) (= (@ tptp.size_s463979675794127359_c_int (@ (@ tptp.product_c_int Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_c Xs)) (@ tptp.size_size_list_int Ys)))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_d) (Ys tptp.list_c)) (= (@ tptp.size_s2120799709113762520od_d_c (@ (@ tptp.product_d_c Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_d Xs)) (@ tptp.size_size_list_c Ys)))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_d) (Ys tptp.list_d)) (= (@ tptp.size_s2191833749160108505od_d_d (@ (@ tptp.product_d_d Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_d Xs)) (@ tptp.size_size_list_d Ys)))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_d) (Ys tptp.list_nat)) (= (@ tptp.size_s8550281435913984804_d_nat (@ (@ tptp.product_d_nat Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_d Xs)) (@ tptp.size_size_list_nat Ys)))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_d) (Ys tptp.list_int)) (= (@ tptp.size_s6060198290982258048_d_int (@ (@ tptp.product_d_int Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_d Xs)) (@ tptp.size_size_list_int Ys)))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_c)) (= (@ tptp.size_s385972143775086793_nat_c (@ (@ tptp.product_nat_c Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs)) (@ tptp.size_size_list_c Ys)))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_d)) (= (@ tptp.size_s457006183821432778_nat_d (@ (@ tptp.product_nat_d Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs)) (@ tptp.size_size_list_d Ys)))))
% 3.70/4.04 (assert (forall ((J tptp.nat) (K3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) K3) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J) N)) K3))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (N tptp.nat) (L tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (let ((_let_2 (@ tptp.ord_less_nat M2))) (=> (@ _let_2 N) (=> (@ _let_2 L) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 M2))))))))
% 3.70/4.04 (assert (forall ((X Bool) (A tptp.set_o) (X4 tptp.set_o)) (=> (@ (@ tptp.member_o X) A) (=> (@ (@ tptp.ord_less_eq_set_o X4) A) (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.insert_o2 X) X4)) A)))))
% 3.70/4.04 (assert (forall ((X tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (X4 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X) A) (=> (@ (@ tptp.ord_le1268244103169919719at_nat X4) A) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.insert9069300056098147895at_nat X) X4)) A)))))
% 3.70/4.04 (assert (forall ((X tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (X4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X) A) (=> (@ (@ tptp.ord_le3146513528884898305at_nat X4) A) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.insert8211810215607154385at_nat X) X4)) A)))))
% 3.70/4.04 (assert (forall ((X tptp.int) (A tptp.set_int) (X4 tptp.set_int)) (=> (@ (@ tptp.member_int X) A) (=> (@ (@ tptp.ord_less_eq_set_int X4) A) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.insert_int2 X) X4)) A)))))
% 3.70/4.04 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (X4 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.member6576561426505652726_nat_o X) A) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o X4) A) (@ (@ tptp.ord_le2965882846123202637_nat_o (@ (@ tptp.insert5175938949040314269_nat_o X) X4)) A)))))
% 3.70/4.04 (assert (forall ((X tptp.nat) (A tptp.set_nat) (X4 tptp.set_nat)) (=> (@ (@ tptp.member_nat X) A) (=> (@ (@ tptp.ord_less_eq_set_nat X4) A) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.insert_nat2 X) X4)) A)))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (not (@ (@ tptp.member6576561426505652726_nat_o X3) A))) (@ (@ tptp.ord_le2965882846123202637_nat_o A) tptp.bot_bo7824918357723582233_nat_o))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat)) (=> (forall ((X3 tptp.produc3843707927480180839at_nat)) (not (@ (@ tptp.member8757157785044589968at_nat X3) A))) (@ (@ tptp.ord_le1268244103169919719at_nat A) tptp.bot_bo228742789529271731at_nat))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X3 tptp.product_prod_nat_nat)) (not (@ (@ tptp.member8440522571783428010at_nat X3) A))) (@ (@ tptp.ord_le3146513528884898305at_nat A) tptp.bot_bo2099793752762293965at_nat))))
% 3.70/4.04 (assert (forall ((A tptp.set_o)) (=> (forall ((X3 Bool)) (not (@ (@ tptp.member_o X3) A))) (@ (@ tptp.ord_less_eq_set_o A) tptp.bot_bot_set_o))))
% 3.70/4.04 (assert (forall ((A tptp.set_int)) (=> (forall ((X3 tptp.int)) (not (@ (@ tptp.member_int X3) A))) (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int))))
% 3.70/4.04 (assert (forall ((A tptp.set_nat)) (=> (forall ((X3 tptp.nat)) (not (@ (@ tptp.member_nat X3) A))) (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ P A2) (=> (not (@ P B2)) (exists ((C4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A2) C4) (@ (@ tptp.ord_less_eq_nat C4) B2) (forall ((X7 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat A2) X7) (@ (@ tptp.ord_less_nat X7) C4)) (@ P X7))) (forall ((D4 tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat A2) X3) (@ (@ tptp.ord_less_nat X3) D4)) (@ P X3))) (@ (@ tptp.ord_less_eq_nat D4) C4))))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ P A2) (=> (not (@ P B2)) (exists ((C4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A2) C4) (@ (@ tptp.ord_less_eq_int C4) B2) (forall ((X7 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int A2) X7) (@ (@ tptp.ord_less_int X7) C4)) (@ P X7))) (forall ((D4 tptp.int)) (=> (forall ((X3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int A2) X3) (@ (@ tptp.ord_less_int X3) D4)) (@ P X3))) (@ (@ tptp.ord_less_eq_int D4) C4))))))))))
% 3.70/4.04 (assert (forall ((B6 tptp.code_integer) (A7 tptp.code_integer)) (= (not (@ (@ tptp.ord_le3102999989581377725nteger B6) A7)) (@ (@ tptp.ord_le6747313008572928689nteger A7) B6))))
% 3.70/4.04 (assert (forall ((B6 tptp.num) (A7 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num B6) A7)) (@ (@ tptp.ord_less_num A7) B6))))
% 3.70/4.04 (assert (forall ((B6 tptp.nat) (A7 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat B6) A7)) (@ (@ tptp.ord_less_nat A7) B6))))
% 3.70/4.04 (assert (forall ((B6 tptp.int) (A7 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int B6) A7)) (@ (@ tptp.ord_less_int A7) B6))))
% 3.70/4.04 (assert (forall ((C2 tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat C2))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) (and (@ _let_1 A) (@ _let_1 B))))))
% 3.70/4.04 (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 (@ (@ tptp.inf_inf_set_nat A) B)) (and (@ _let_1 A) (@ _let_1 B))))))
% 3.70/4.04 (assert (forall ((A2 Bool) (C2 tptp.set_o) (B tptp.set_o)) (=> (not (@ (@ tptp.member_o A2) C2)) (= (@ (@ tptp.inf_inf_set_o (@ (@ tptp.insert_o2 A2) B)) C2) (@ (@ tptp.inf_inf_set_o B) C2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.produc3843707927480180839at_nat) (C2 tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (=> (not (@ (@ tptp.member8757157785044589968at_nat A2) C2)) (= (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.insert9069300056098147895at_nat A2) B)) C2) (@ (@ tptp.inf_in7913087082777306421at_nat B) C2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (C2 tptp.set_int) (B tptp.set_int)) (=> (not (@ (@ tptp.member_int A2) C2)) (= (@ (@ tptp.inf_inf_set_int (@ (@ tptp.insert_int2 A2) B)) C2) (@ (@ tptp.inf_inf_set_int B) C2)))))
% 3.70/4.04 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (C2 tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (=> (not (@ (@ tptp.member6576561426505652726_nat_o A2) C2)) (= (@ (@ tptp.inf_in1906310914598751387_nat_o (@ (@ tptp.insert5175938949040314269_nat_o A2) B)) C2) (@ (@ tptp.inf_in1906310914598751387_nat_o B) C2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (C2 tptp.set_nat) (B tptp.set_nat)) (=> (not (@ (@ tptp.member_nat A2) C2)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.insert_nat2 A2) B)) C2) (@ (@ tptp.inf_inf_set_nat B) C2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.product_prod_nat_nat) (C2 tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (=> (not (@ (@ tptp.member8440522571783428010at_nat A2) C2)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.insert8211810215607154385at_nat A2) B)) C2) (@ (@ tptp.inf_in2572325071724192079at_nat B) C2)))))
% 3.70/4.04 (assert (forall ((A2 Bool) (C2 tptp.set_o) (B tptp.set_o)) (let ((_let_1 (@ tptp.insert_o2 A2))) (=> (@ (@ tptp.member_o A2) C2) (= (@ (@ tptp.inf_inf_set_o (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.inf_inf_set_o B) C2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.produc3843707927480180839at_nat) (C2 tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.insert9069300056098147895at_nat A2))) (=> (@ (@ tptp.member8757157785044589968at_nat A2) C2) (= (@ (@ tptp.inf_in7913087082777306421at_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat B) C2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (C2 tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.insert_int2 A2))) (=> (@ (@ tptp.member_int A2) C2) (= (@ (@ tptp.inf_inf_set_int (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.inf_inf_set_int B) C2)))))))
% 3.70/4.04 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (C2 tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.insert5175938949040314269_nat_o A2))) (=> (@ (@ tptp.member6576561426505652726_nat_o A2) C2) (= (@ (@ tptp.inf_in1906310914598751387_nat_o (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.inf_in1906310914598751387_nat_o B) C2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (C2 tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat2 A2))) (=> (@ (@ tptp.member_nat A2) C2) (= (@ (@ tptp.inf_inf_set_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.inf_inf_set_nat B) C2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.product_prod_nat_nat) (C2 tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A2))) (=> (@ (@ tptp.member8440522571783428010at_nat A2) C2) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B) C2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.insert_int2 A2))) (= (@ (@ tptp.inf_inf_set_int (@ _let_1 A)) (@ _let_1 B)) (@ _let_1 (@ (@ tptp.inf_inf_set_int A) B))))))
% 3.70/4.04 (assert (forall ((A2 tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.insert9069300056098147895at_nat A2))) (= (@ (@ tptp.inf_in7913087082777306421at_nat (@ _let_1 A)) (@ _let_1 B)) (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat A) B))))))
% 3.70/4.04 (assert (forall ((A2 Bool) (A tptp.set_o) (B tptp.set_o)) (let ((_let_1 (@ tptp.insert_o2 A2))) (= (@ (@ tptp.inf_inf_set_o (@ _let_1 A)) (@ _let_1 B)) (@ _let_1 (@ (@ tptp.inf_inf_set_o A) B))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat2 A2))) (= (@ (@ tptp.inf_inf_set_nat (@ _let_1 A)) (@ _let_1 B)) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B))))))
% 3.70/4.04 (assert (forall ((A2 tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A2))) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 A)) (@ _let_1 B)) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A) B))))))
% 3.70/4.04 (assert (forall ((A2 Bool) (A tptp.set_o) (B tptp.set_o)) (let ((_let_1 (@ tptp.inf_inf_set_o A))) (=> (not (@ (@ tptp.member_o A2) A)) (= (@ _let_1 (@ (@ tptp.insert_o2 A2) B)) (@ _let_1 B))))))
% 3.70/4.04 (assert (forall ((A2 tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.inf_in7913087082777306421at_nat A))) (=> (not (@ (@ tptp.member8757157785044589968at_nat A2) A)) (= (@ _let_1 (@ (@ tptp.insert9069300056098147895at_nat A2) B)) (@ _let_1 B))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.inf_inf_set_int A))) (=> (not (@ (@ tptp.member_int A2) A)) (= (@ _let_1 (@ (@ tptp.insert_int2 A2) B)) (@ _let_1 B))))))
% 3.70/4.04 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.inf_in1906310914598751387_nat_o A))) (=> (not (@ (@ tptp.member6576561426505652726_nat_o A2) A)) (= (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o A2) B)) (@ _let_1 B))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (=> (not (@ (@ tptp.member_nat A2) A)) (= (@ _let_1 (@ (@ tptp.insert_nat2 A2) B)) (@ _let_1 B))))))
% 3.70/4.04 (assert (forall ((A2 tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A))) (=> (not (@ (@ tptp.member8440522571783428010at_nat A2) A)) (= (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat A2) B)) (@ _let_1 B))))))
% 3.70/4.04 (assert (forall ((A2 Bool) (A tptp.set_o) (B tptp.set_o)) (let ((_let_1 (@ tptp.inf_inf_set_o A))) (let ((_let_2 (@ tptp.insert_o2 A2))) (=> (@ (@ tptp.member_o A2) A) (= (@ _let_1 (@ _let_2 B)) (@ _let_2 (@ _let_1 B))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.inf_in7913087082777306421at_nat A))) (let ((_let_2 (@ tptp.insert9069300056098147895at_nat A2))) (=> (@ (@ tptp.member8757157785044589968at_nat A2) A) (= (@ _let_1 (@ _let_2 B)) (@ _let_2 (@ _let_1 B))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.inf_inf_set_int A))) (let ((_let_2 (@ tptp.insert_int2 A2))) (=> (@ (@ tptp.member_int A2) A) (= (@ _let_1 (@ _let_2 B)) (@ _let_2 (@ _let_1 B))))))))
% 3.70/4.04 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.inf_in1906310914598751387_nat_o A))) (let ((_let_2 (@ tptp.insert5175938949040314269_nat_o A2))) (=> (@ (@ tptp.member6576561426505652726_nat_o A2) A) (= (@ _let_1 (@ _let_2 B)) (@ _let_2 (@ _let_1 B))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (let ((_let_2 (@ tptp.insert_nat2 A2))) (=> (@ (@ tptp.member_nat A2) A) (= (@ _let_1 (@ _let_2 B)) (@ _let_2 (@ _let_1 B))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A))) (let ((_let_2 (@ tptp.insert8211810215607154385at_nat A2))) (=> (@ (@ tptp.member8440522571783428010at_nat A2) A) (= (@ _let_1 (@ _let_2 B)) (@ _let_2 (@ _let_1 B))))))))
% 3.70/4.04 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (= (= (@ (@ tptp.inf_in1906310914598751387_nat_o (@ (@ tptp.insert5175938949040314269_nat_o A2) A)) B) tptp.bot_bo7824918357723582233_nat_o) (and (not (@ (@ tptp.member6576561426505652726_nat_o A2) B)) (= (@ (@ tptp.inf_in1906310914598751387_nat_o A) B) tptp.bot_bo7824918357723582233_nat_o)))))
% 3.70/4.04 (assert (forall ((A2 tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (= (= (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.insert9069300056098147895at_nat A2) A)) B) tptp.bot_bo228742789529271731at_nat) (and (not (@ (@ tptp.member8757157785044589968at_nat A2) B)) (= (@ (@ tptp.inf_in7913087082777306421at_nat A) B) tptp.bot_bo228742789529271731at_nat)))))
% 3.70/4.04 (assert (forall ((A2 tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.insert8211810215607154385at_nat A2) A)) B) tptp.bot_bo2099793752762293965at_nat) (and (not (@ (@ tptp.member8440522571783428010at_nat A2) B)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A) B) tptp.bot_bo2099793752762293965at_nat)))))
% 3.70/4.04 (assert (forall ((A2 Bool) (A tptp.set_o) (B tptp.set_o)) (= (= (@ (@ tptp.inf_inf_set_o (@ (@ tptp.insert_o2 A2) A)) B) tptp.bot_bot_set_o) (and (not (@ (@ tptp.member_o A2) B)) (= (@ (@ tptp.inf_inf_set_o A) B) tptp.bot_bot_set_o)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.insert_nat2 A2) A)) B) tptp.bot_bot_set_nat) (and (not (@ (@ tptp.member_nat A2) B)) (= (@ (@ tptp.inf_inf_set_nat A) B) tptp.bot_bot_set_nat)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (A tptp.set_int) (B tptp.set_int)) (= (= (@ (@ tptp.inf_inf_set_int (@ (@ tptp.insert_int2 A2) A)) B) tptp.bot_bot_set_int) (and (not (@ (@ tptp.member_int A2) B)) (= (@ (@ tptp.inf_inf_set_int A) B) tptp.bot_bot_set_int)))))
% 3.70/4.04 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (= (= tptp.bot_bo7824918357723582233_nat_o (@ (@ tptp.inf_in1906310914598751387_nat_o (@ (@ tptp.insert5175938949040314269_nat_o A2) A)) B)) (and (not (@ (@ tptp.member6576561426505652726_nat_o A2) B)) (= tptp.bot_bo7824918357723582233_nat_o (@ (@ tptp.inf_in1906310914598751387_nat_o A) B))))))
% 3.70/4.04 (assert (forall ((A2 tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (= (= tptp.bot_bo228742789529271731at_nat (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.insert9069300056098147895at_nat A2) A)) B)) (and (not (@ (@ tptp.member8757157785044589968at_nat A2) B)) (= tptp.bot_bo228742789529271731at_nat (@ (@ tptp.inf_in7913087082777306421at_nat A) B))))))
% 3.70/4.04 (assert (forall ((A2 tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (= tptp.bot_bo2099793752762293965at_nat (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.insert8211810215607154385at_nat A2) A)) B)) (and (not (@ (@ tptp.member8440522571783428010at_nat A2) B)) (= tptp.bot_bo2099793752762293965at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B))))))
% 3.70/4.04 (assert (forall ((A2 Bool) (A tptp.set_o) (B tptp.set_o)) (= (= tptp.bot_bot_set_o (@ (@ tptp.inf_inf_set_o (@ (@ tptp.insert_o2 A2) A)) B)) (and (not (@ (@ tptp.member_o A2) B)) (= tptp.bot_bot_set_o (@ (@ tptp.inf_inf_set_o A) B))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (= (= tptp.bot_bot_set_nat (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.insert_nat2 A2) A)) B)) (and (not (@ (@ tptp.member_nat A2) B)) (= tptp.bot_bot_set_nat (@ (@ tptp.inf_inf_set_nat A) B))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (A tptp.set_int) (B tptp.set_int)) (= (= tptp.bot_bot_set_int (@ (@ tptp.inf_inf_set_int (@ (@ tptp.insert_int2 A2) A)) B)) (and (not (@ (@ tptp.member_int A2) B)) (= tptp.bot_bot_set_int (@ (@ tptp.inf_inf_set_int A) B))))))
% 3.70/4.04 (assert (forall ((B tptp.set_Pr4532377907799695533_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.inf_in1906310914598751387_nat_o B))) (= (= (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o A2) A)) tptp.bot_bo7824918357723582233_nat_o) (and (not (@ (@ tptp.member6576561426505652726_nat_o A2) B)) (= (@ _let_1 A) tptp.bot_bo7824918357723582233_nat_o))))))
% 3.70/4.04 (assert (forall ((B tptp.set_Pr4329608150637261639at_nat) (A2 tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.inf_in7913087082777306421at_nat B))) (= (= (@ _let_1 (@ (@ tptp.insert9069300056098147895at_nat A2) A)) tptp.bot_bo228742789529271731at_nat) (and (not (@ (@ tptp.member8757157785044589968at_nat A2) B)) (= (@ _let_1 A) tptp.bot_bo228742789529271731at_nat))))))
% 3.70/4.04 (assert (forall ((B tptp.set_Pr1261947904930325089at_nat) (A2 tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat B))) (= (= (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat A2) A)) tptp.bot_bo2099793752762293965at_nat) (and (not (@ (@ tptp.member8440522571783428010at_nat A2) B)) (= (@ _let_1 A) tptp.bot_bo2099793752762293965at_nat))))))
% 3.70/4.04 (assert (forall ((B tptp.set_o) (A2 Bool) (A tptp.set_o)) (let ((_let_1 (@ tptp.inf_inf_set_o B))) (= (= (@ _let_1 (@ (@ tptp.insert_o2 A2) A)) tptp.bot_bot_set_o) (and (not (@ (@ tptp.member_o A2) B)) (= (@ _let_1 A) tptp.bot_bot_set_o))))))
% 3.70/4.04 (assert (forall ((B tptp.set_nat) (A2 tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat B))) (= (= (@ _let_1 (@ (@ tptp.insert_nat2 A2) A)) tptp.bot_bot_set_nat) (and (not (@ (@ tptp.member_nat A2) B)) (= (@ _let_1 A) tptp.bot_bot_set_nat))))))
% 3.70/4.04 (assert (forall ((B tptp.set_int) (A2 tptp.int) (A tptp.set_int)) (let ((_let_1 (@ tptp.inf_inf_set_int B))) (= (= (@ _let_1 (@ (@ tptp.insert_int2 A2) A)) tptp.bot_bot_set_int) (and (not (@ (@ tptp.member_int A2) B)) (= (@ _let_1 A) tptp.bot_bot_set_int))))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.inf_in1906310914598751387_nat_o A))) (= (= tptp.bot_bo7824918357723582233_nat_o (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o B2) B))) (and (not (@ (@ tptp.member6576561426505652726_nat_o B2) A)) (= tptp.bot_bo7824918357723582233_nat_o (@ _let_1 B)))))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B2 tptp.produc3843707927480180839at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.inf_in7913087082777306421at_nat A))) (= (= tptp.bot_bo228742789529271731at_nat (@ _let_1 (@ (@ tptp.insert9069300056098147895at_nat B2) B))) (and (not (@ (@ tptp.member8757157785044589968at_nat B2) A)) (= tptp.bot_bo228742789529271731at_nat (@ _let_1 B)))))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B2 tptp.product_prod_nat_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A))) (= (= tptp.bot_bo2099793752762293965at_nat (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat B2) B))) (and (not (@ (@ tptp.member8440522571783428010at_nat B2) A)) (= tptp.bot_bo2099793752762293965at_nat (@ _let_1 B)))))))
% 3.70/4.04 (assert (forall ((A tptp.set_o) (B2 Bool) (B tptp.set_o)) (let ((_let_1 (@ tptp.inf_inf_set_o A))) (= (= tptp.bot_bot_set_o (@ _let_1 (@ (@ tptp.insert_o2 B2) B))) (and (not (@ (@ tptp.member_o B2) A)) (= tptp.bot_bot_set_o (@ _let_1 B)))))))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (B2 tptp.nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (= (= tptp.bot_bot_set_nat (@ _let_1 (@ (@ tptp.insert_nat2 B2) B))) (and (not (@ (@ tptp.member_nat B2) A)) (= tptp.bot_bot_set_nat (@ _let_1 B)))))))
% 3.70/4.04 (assert (forall ((A tptp.set_int) (B2 tptp.int) (B tptp.set_int)) (let ((_let_1 (@ tptp.inf_inf_set_int A))) (= (= tptp.bot_bot_set_int (@ _let_1 (@ (@ tptp.insert_int2 B2) B))) (and (not (@ (@ tptp.member_int B2) A)) (= tptp.bot_bot_set_int (@ _let_1 B)))))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat A) (@ (@ tptp.minus_3314409938677909166at_nat B) A)) tptp.bot_bo228742789529271731at_nat)))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A) (@ (@ tptp.minus_1356011639430497352at_nat B) A)) tptp.bot_bo2099793752762293965at_nat)))
% 3.70/4.04 (assert (forall ((A tptp.set_o) (B tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o A) (@ (@ tptp.minus_minus_set_o B) A)) tptp.bot_bot_set_o)))
% 3.70/4.04 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int A) (@ (@ tptp.minus_minus_set_int B) A)) tptp.bot_bot_set_int)))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A) (@ (@ tptp.minus_minus_set_nat B) A)) tptp.bot_bot_set_nat)))
% 3.70/4.04 (assert (forall ((Xs tptp.list_c) (I tptp.nat) (X tptp.c)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_c Xs)) I) (= (@ (@ (@ tptp.list_update_c Xs) I) X) Xs))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_d) (I tptp.nat) (X tptp.d)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_d Xs)) I) (= (@ (@ (@ tptp.list_update_d Xs) I) X) Xs))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_nat) (I tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) I) (= (@ (@ (@ tptp.list_update_nat Xs) I) X) Xs))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_int) (I tptp.nat) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs)) I) (= (@ (@ (@ tptp.list_update_int Xs) I) X) Xs))))
% 3.70/4.04 (assert (= tptp.ord_less_nat (lambda ((M tptp.nat) (N2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M) N2) (not (= M N2))))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 3.70/4.04 (assert (= tptp.ord_less_eq_nat (lambda ((M tptp.nat) (N2 tptp.nat)) (or (@ (@ tptp.ord_less_nat M) N2) (= M N2)))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M2) N) (= M2 N)) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (=> (not (= M2 N)) (@ (@ tptp.ord_less_nat M2) N)))))
% 3.70/4.04 (assert (forall ((F4 (-> tptp.nat tptp.nat)) (I tptp.nat) (J tptp.nat)) (=> (forall ((I5 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) J3) (@ (@ tptp.ord_less_nat (@ F4 I5)) (@ F4 J3)))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ F4 I)) (@ F4 J))))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (= (= (@ (@ tptp.inf_in7913087082777306421at_nat A) B) tptp.bot_bo228742789529271731at_nat) (forall ((X2 tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X2) A) (forall ((Y5 tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat Y5) B) (not (= X2 Y5)))))))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.inf_in2572325071724192079at_nat A) B) tptp.bot_bo2099793752762293965at_nat) (forall ((X2 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X2) A) (forall ((Y5 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat Y5) B) (not (= X2 Y5)))))))))
% 3.70/4.04 (assert (forall ((A tptp.set_o) (B tptp.set_o)) (= (= (@ (@ tptp.inf_inf_set_o A) B) tptp.bot_bot_set_o) (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) A) (forall ((Y5 Bool)) (=> (@ (@ tptp.member_o Y5) B) (= X2 (not Y5)))))))))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat A) B) tptp.bot_bot_set_nat) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A) (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.member_nat Y5) B) (not (= X2 Y5)))))))))
% 3.70/4.04 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (= (= (@ (@ tptp.inf_inf_set_int A) B) tptp.bot_bot_set_int) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A) (forall ((Y5 tptp.int)) (=> (@ (@ tptp.member_int Y5) B) (not (= X2 Y5)))))))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat A) tptp.bot_bo228742789529271731at_nat) tptp.bot_bo228742789529271731at_nat)))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A) tptp.bot_bo2099793752762293965at_nat) tptp.bot_bo2099793752762293965at_nat)))
% 3.70/4.04 (assert (forall ((A tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o A) tptp.bot_bot_set_o) tptp.bot_bot_set_o)))
% 3.70/4.04 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A) tptp.bot_bot_set_nat) tptp.bot_bot_set_nat)))
% 3.70/4.04 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int A) tptp.bot_bot_set_int) tptp.bot_bot_set_int)))
% 3.70/4.04 (assert (forall ((B tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat tptp.bot_bo228742789529271731at_nat) B) tptp.bot_bo228742789529271731at_nat)))
% 3.70/4.04 (assert (forall ((B tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bot_bo2099793752762293965at_nat) B) tptp.bot_bo2099793752762293965at_nat)))
% 3.70/4.04 (assert (forall ((B tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o tptp.bot_bot_set_o) B) tptp.bot_bot_set_o)))
% 3.70/4.04 (assert (forall ((B tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat tptp.bot_bot_set_nat) B) tptp.bot_bot_set_nat)))
% 3.70/4.04 (assert (forall ((B tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int tptp.bot_bot_set_int) B) tptp.bot_bot_set_int)))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (= (= (@ (@ tptp.inf_in1906310914598751387_nat_o A) B) tptp.bot_bo7824918357723582233_nat_o) (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o X2))) (=> (@ _let_1 A) (not (@ _let_1 B))))))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (= (= (@ (@ tptp.inf_in7913087082777306421at_nat A) B) tptp.bot_bo228742789529271731at_nat) (forall ((X2 tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat X2))) (=> (@ _let_1 A) (not (@ _let_1 B))))))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.inf_in2572325071724192079at_nat A) B) tptp.bot_bo2099793752762293965at_nat) (forall ((X2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X2))) (=> (@ _let_1 A) (not (@ _let_1 B))))))))
% 3.70/4.04 (assert (forall ((A tptp.set_o) (B tptp.set_o)) (= (= (@ (@ tptp.inf_inf_set_o A) B) tptp.bot_bot_set_o) (forall ((X2 Bool)) (let ((_let_1 (@ tptp.member_o X2))) (=> (@ _let_1 A) (not (@ _let_1 B))))))))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat A) B) tptp.bot_bot_set_nat) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X2))) (=> (@ _let_1 A) (not (@ _let_1 B))))))))
% 3.70/4.04 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (= (= (@ (@ tptp.inf_inf_set_int A) B) tptp.bot_bot_set_int) (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.member_int X2))) (=> (@ _let_1 A) (not (@ _let_1 B))))))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o X3))) (=> (@ _let_1 A) (not (@ _let_1 B))))) (= (@ (@ tptp.inf_in1906310914598751387_nat_o A) B) tptp.bot_bo7824918357723582233_nat_o))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (=> (forall ((X3 tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat X3))) (=> (@ _let_1 A) (not (@ _let_1 B))))) (= (@ (@ tptp.inf_in7913087082777306421at_nat A) B) tptp.bot_bo228742789529271731at_nat))))
% 3.70/4.04 (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))))
% 3.70/4.04 (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))))
% 3.70/4.04 (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))))
% 3.70/4.04 (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))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_Pr4532377907799695533_nat_o) (B2 tptp.set_Pr4532377907799695533_nat_o)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o X3))) (=> (@ _let_1 A2) (not (@ _let_1 B2))))) (= (@ (@ tptp.inf_in1906310914598751387_nat_o A2) B2) tptp.bot_bo7824918357723582233_nat_o))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (=> (forall ((X3 tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat X3))) (=> (@ _let_1 A2) (not (@ _let_1 B2))))) (= (@ (@ tptp.inf_in7913087082777306421at_nat A2) B2) tptp.bot_bo228742789529271731at_nat))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X3 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X3))) (=> (@ _let_1 A2) (not (@ _let_1 B2))))) (= (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2) tptp.bot_bo2099793752762293965at_nat))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_o) (B2 tptp.set_o)) (=> (forall ((X3 Bool)) (let ((_let_1 (@ tptp.member_o X3))) (=> (@ _let_1 A2) (not (@ _let_1 B2))))) (= (@ (@ tptp.inf_inf_set_o A2) B2) tptp.bot_bot_set_o))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X3))) (=> (@ _let_1 A2) (not (@ _let_1 B2))))) (= (@ (@ tptp.inf_inf_set_nat A2) B2) tptp.bot_bot_set_nat))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int)) (=> (forall ((X3 tptp.int)) (let ((_let_1 (@ tptp.member_int X3))) (=> (@ _let_1 A2) (not (@ _let_1 B2))))) (= (@ (@ tptp.inf_inf_set_int A2) B2) tptp.bot_bot_set_int))))
% 3.70/4.04 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (S4 tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat B))) (let ((_let_2 (@ tptp.inf_in2572325071724192079at_nat A))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat S) S4) (=> (= (@ _let_2 S4) (@ _let_1 S4)) (= (@ _let_2 S) (@ _let_1 S))))))))
% 3.70/4.04 (assert (forall ((S tptp.set_nat) (S4 tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat B))) (let ((_let_2 (@ tptp.inf_inf_set_nat A))) (=> (@ (@ tptp.ord_less_eq_set_nat S) S4) (=> (= (@ _let_2 S4) (@ _let_1 S4)) (= (@ _let_2 S) (@ _let_1 S))))))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (P (-> tptp.produc3843707927480180839at_nat Bool)) (Q (-> tptp.produc3843707927480180839at_nat Bool))) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A) B) (=> (forall ((X3 tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X3) A) (=> (@ P X3) (@ Q X3)))) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.inf_in7913087082777306421at_nat A) (@ tptp.collec6321179662152712658at_nat P))) (@ (@ tptp.inf_in7913087082777306421at_nat B) (@ tptp.collec6321179662152712658at_nat Q)))))))
% 3.70/4.04 (assert (forall ((A tptp.set_int) (B tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A) (=> (@ P X3) (@ Q X3)))) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int A) (@ tptp.collect_int P))) (@ (@ tptp.inf_inf_set_int B) (@ tptp.collect_int Q)))))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o) (P (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool)) (Q (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o A) B) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X3) A) (=> (@ P X3) (@ Q X3)))) (@ (@ tptp.ord_le2965882846123202637_nat_o (@ (@ tptp.inf_in1906310914598751387_nat_o A) (@ tptp.collec939566748876313656_nat_o P))) (@ (@ tptp.inf_in1906310914598751387_nat_o B) (@ tptp.collec939566748876313656_nat_o Q)))))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.product_prod_nat_nat Bool)) (Q (-> tptp.product_prod_nat_nat Bool))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A) B) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) A) (=> (@ P X3) (@ Q X3)))) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) (@ tptp.collec3392354462482085612at_nat P))) (@ (@ tptp.inf_in2572325071724192079at_nat B) (@ tptp.collec3392354462482085612at_nat Q)))))))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A) (=> (@ P X3) (@ Q X3)))) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A) (@ tptp.collect_nat P))) (@ (@ tptp.inf_inf_set_nat B) (@ tptp.collect_nat Q)))))))
% 3.70/4.04 (assert (forall ((C2 tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat C2))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A) B)))))))
% 3.70/4.04 (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 B) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B)))))))
% 3.70/4.04 (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))))
% 3.70/4.04 (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))))
% 3.70/4.04 (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))))
% 3.70/4.04 (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))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) B)))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) B)))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) A)))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) A)))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (D tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A) C2) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B) D) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) (@ (@ tptp.inf_in2572325071724192079at_nat C2) D))))))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (C2 tptp.set_nat) (B tptp.set_nat) (D tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) C2) (=> (@ (@ tptp.ord_less_eq_set_nat B) D) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) (@ (@ tptp.inf_inf_set_nat C2) D))))))
% 3.70/4.04 (assert (forall ((A2 Bool) (C2 tptp.set_o) (B tptp.set_o)) (let ((_let_1 (@ (@ tptp.inf_inf_set_o B) C2))) (let ((_let_2 (@ tptp.insert_o2 A2))) (let ((_let_3 (@ (@ tptp.inf_inf_set_o (@ _let_2 B)) C2))) (let ((_let_4 (@ (@ tptp.member_o A2) C2))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.produc3843707927480180839at_nat) (C2 tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ (@ tptp.inf_in7913087082777306421at_nat B) C2))) (let ((_let_2 (@ tptp.insert9069300056098147895at_nat A2))) (let ((_let_3 (@ (@ tptp.inf_in7913087082777306421at_nat (@ _let_2 B)) C2))) (let ((_let_4 (@ (@ tptp.member8757157785044589968at_nat A2) C2))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (C2 tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ (@ tptp.inf_inf_set_int B) C2))) (let ((_let_2 (@ tptp.insert_int2 A2))) (let ((_let_3 (@ (@ tptp.inf_inf_set_int (@ _let_2 B)) C2))) (let ((_let_4 (@ (@ tptp.member_int A2) C2))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 3.70/4.04 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (C2 tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ (@ tptp.inf_in1906310914598751387_nat_o B) C2))) (let ((_let_2 (@ tptp.insert5175938949040314269_nat_o A2))) (let ((_let_3 (@ (@ tptp.inf_in1906310914598751387_nat_o (@ _let_2 B)) C2))) (let ((_let_4 (@ (@ tptp.member6576561426505652726_nat_o A2) C2))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (C2 tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ (@ tptp.inf_inf_set_nat B) C2))) (let ((_let_2 (@ tptp.insert_nat2 A2))) (let ((_let_3 (@ (@ tptp.inf_inf_set_nat (@ _let_2 B)) C2))) (let ((_let_4 (@ (@ tptp.member_nat A2) C2))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.product_prod_nat_nat) (C2 tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B) C2))) (let ((_let_2 (@ tptp.insert8211810215607154385at_nat A2))) (let ((_let_3 (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_2 B)) C2))) (let ((_let_4 (@ (@ tptp.member8440522571783428010at_nat A2) C2))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 3.70/4.04 (assert (forall ((A2 Bool) (A tptp.set_o) (B tptp.set_o)) (let ((_let_1 (@ tptp.inf_inf_set_o A))) (let ((_let_2 (@ _let_1 B))) (let ((_let_3 (@ tptp.insert_o2 A2))) (let ((_let_4 (@ _let_1 (@ _let_3 B)))) (let ((_let_5 (@ (@ tptp.member_o A2) A))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.inf_in7913087082777306421at_nat A))) (let ((_let_2 (@ _let_1 B))) (let ((_let_3 (@ tptp.insert9069300056098147895at_nat A2))) (let ((_let_4 (@ _let_1 (@ _let_3 B)))) (let ((_let_5 (@ (@ tptp.member8757157785044589968at_nat A2) A))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.inf_inf_set_int A))) (let ((_let_2 (@ _let_1 B))) (let ((_let_3 (@ tptp.insert_int2 A2))) (let ((_let_4 (@ _let_1 (@ _let_3 B)))) (let ((_let_5 (@ (@ tptp.member_int A2) A))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))))
% 3.70/4.04 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.inf_in1906310914598751387_nat_o A))) (let ((_let_2 (@ _let_1 B))) (let ((_let_3 (@ tptp.insert5175938949040314269_nat_o A2))) (let ((_let_4 (@ _let_1 (@ _let_3 B)))) (let ((_let_5 (@ (@ tptp.member6576561426505652726_nat_o A2) A))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (let ((_let_2 (@ _let_1 B))) (let ((_let_3 (@ tptp.insert_nat2 A2))) (let ((_let_4 (@ _let_1 (@ _let_3 B)))) (let ((_let_5 (@ (@ tptp.member_nat A2) A))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A))) (let ((_let_2 (@ _let_1 B))) (let ((_let_3 (@ tptp.insert8211810215607154385at_nat A2))) (let ((_let_4 (@ _let_1 (@ _let_3 B)))) (let ((_let_5 (@ (@ tptp.member8440522571783428010at_nat A2) A))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A))) (= (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat B) C2))))))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (= (@ (@ tptp.minus_minus_set_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B) C2))))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) C2)))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B) C2)) (@ _let_1 B)))))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (C2 tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat (@ (@ tptp.inf_inf_set_nat A) C2)))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat B) C2)) (@ _let_1 B)))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.inf_in2572325071724192079at_nat A) B)))))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.inf_inf_set_nat A) B)))))
% 3.70/4.04 (assert (forall ((C2 tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat C2))) (= (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A) B)) (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_1 A)) (@ _let_1 B))))))
% 3.70/4.04 (assert (forall ((C2 tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat C2))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B)) (@ (@ tptp.minus_minus_set_nat (@ _let_1 A)) (@ _let_1 B))))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.minus_1356011639430497352at_nat A) B)) C2) (@ (@ tptp.minus_1356011639430497352at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) C2)) (@ (@ tptp.inf_in2572325071724192079at_nat B) C2)))))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.minus_minus_set_nat A) B)) C2) (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.inf_inf_set_nat A) C2)) (@ (@ tptp.inf_inf_set_nat B) C2)))))
% 3.70/4.04 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (=> (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N3) N) (not (@ P N3)))) (@ P N)) (exists ((N4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat N4) N) (@ P N4))))))
% 3.70/4.04 (assert (= tptp.ord_less_eq_assn (lambda ((A3 tptp.assn) (B3 tptp.assn)) (= A3 (@ (@ tptp.inf_inf_assn A3) B3)))))
% 3.70/4.04 (assert (forall ((K3 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K3))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M2) K3)) (@ (@ tptp.minus_minus_nat N) K3)) (@ (@ tptp.ord_less_nat M2) N)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat C) A2) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat A2) C)) (@ (@ tptp.minus_minus_nat B2) C))))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_Pr4329608150637261639at_nat) (A7 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat) (B6 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A2) A7) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B2) B6) (=> (= (@ (@ tptp.inf_in7913087082777306421at_nat A7) B6) tptp.bot_bo228742789529271731at_nat) (= (@ (@ tptp.inf_in7913087082777306421at_nat A2) B2) tptp.bot_bo228742789529271731at_nat))))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (A7 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) A7) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B2) B6) (=> (= (@ (@ tptp.inf_in2572325071724192079at_nat A7) B6) tptp.bot_bo2099793752762293965at_nat) (= (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2) tptp.bot_bo2099793752762293965at_nat))))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_o) (A7 tptp.set_o) (B2 tptp.set_o) (B6 tptp.set_o)) (=> (@ (@ tptp.ord_less_eq_set_o A2) A7) (=> (@ (@ tptp.ord_less_eq_set_o B2) B6) (=> (= (@ (@ tptp.inf_inf_set_o A7) B6) tptp.bot_bot_set_o) (= (@ (@ tptp.inf_inf_set_o A2) B2) tptp.bot_bot_set_o))))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_int) (A7 tptp.set_int) (B2 tptp.set_int) (B6 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) A7) (=> (@ (@ tptp.ord_less_eq_set_int B2) B6) (=> (= (@ (@ tptp.inf_inf_set_int A7) B6) tptp.bot_bot_set_int) (= (@ (@ tptp.inf_inf_set_int A2) B2) tptp.bot_bot_set_int))))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_nat) (A7 tptp.set_nat) (B2 tptp.set_nat) (B6 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) A7) (=> (@ (@ tptp.ord_less_eq_set_nat B2) B6) (=> (= (@ (@ tptp.inf_inf_set_nat A7) B6) tptp.bot_bot_set_nat) (= (@ (@ tptp.inf_inf_set_nat A2) B2) tptp.bot_bot_set_nat))))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (= (not (= (@ (@ tptp.minus_3314409938677909166at_nat A) B) A)) (not (= (@ (@ tptp.inf_in7913087082777306421at_nat A) B) tptp.bot_bo228742789529271731at_nat)))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (not (= (@ (@ tptp.minus_1356011639430497352at_nat A) B) A)) (not (= (@ (@ tptp.inf_in2572325071724192079at_nat A) B) tptp.bot_bo2099793752762293965at_nat)))))
% 3.70/4.04 (assert (forall ((A tptp.set_o) (B tptp.set_o)) (= (not (= (@ (@ tptp.minus_minus_set_o A) B) A)) (not (= (@ (@ tptp.inf_inf_set_o A) B) tptp.bot_bot_set_o)))))
% 3.70/4.04 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (= (not (= (@ (@ tptp.minus_minus_set_int A) B) A)) (not (= (@ (@ tptp.inf_inf_set_int A) B) tptp.bot_bot_set_int)))))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (not (= (@ (@ tptp.minus_minus_set_nat A) B) A)) (not (= (@ (@ tptp.inf_inf_set_nat A) B) tptp.bot_bot_set_nat)))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (= (= (@ (@ tptp.minus_3314409938677909166at_nat A) B) A) (= (@ (@ tptp.inf_in7913087082777306421at_nat A) B) tptp.bot_bo228742789529271731at_nat))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.minus_1356011639430497352at_nat A) B) A) (= (@ (@ tptp.inf_in2572325071724192079at_nat A) B) tptp.bot_bo2099793752762293965at_nat))))
% 3.70/4.04 (assert (forall ((A tptp.set_o) (B tptp.set_o)) (= (= (@ (@ tptp.minus_minus_set_o A) B) A) (= (@ (@ tptp.inf_inf_set_o A) B) tptp.bot_bot_set_o))))
% 3.70/4.04 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int A) B) A) (= (@ (@ tptp.inf_inf_set_int A) B) tptp.bot_bot_set_int))))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat A) B) A) (= (@ (@ tptp.inf_inf_set_nat A) B) tptp.bot_bot_set_nat))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.inf_in7913087082777306421at_nat A) B)) (@ (@ tptp.minus_3314409938677909166at_nat A) B)) tptp.bot_bo228742789529271731at_nat)))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) (@ (@ tptp.minus_1356011639430497352at_nat A) B)) tptp.bot_bo2099793752762293965at_nat)))
% 3.70/4.04 (assert (forall ((A tptp.set_o) (B tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o (@ (@ tptp.inf_inf_set_o A) B)) (@ (@ tptp.minus_minus_set_o A) B)) tptp.bot_bot_set_o)))
% 3.70/4.04 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int (@ (@ tptp.inf_inf_set_int A) B)) (@ (@ tptp.minus_minus_set_int A) B)) tptp.bot_bot_set_int)))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) (@ (@ tptp.minus_minus_set_nat A) B)) tptp.bot_bot_set_nat)))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (=> (= (@ (@ tptp.inf_in7913087082777306421at_nat A) B) tptp.bot_bo228742789529271731at_nat) (= (@ (@ tptp.minus_3314409938677909166at_nat A) B) A))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (=> (= (@ (@ tptp.inf_in2572325071724192079at_nat A) B) tptp.bot_bo2099793752762293965at_nat) (= (@ (@ tptp.minus_1356011639430497352at_nat A) B) A))))
% 3.70/4.04 (assert (forall ((A tptp.set_o) (B tptp.set_o)) (=> (= (@ (@ tptp.inf_inf_set_o A) B) tptp.bot_bot_set_o) (= (@ (@ tptp.minus_minus_set_o A) B) A))))
% 3.70/4.04 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (= (@ (@ tptp.inf_inf_set_int A) B) tptp.bot_bot_set_int) (= (@ (@ tptp.minus_minus_set_int A) B) A))))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (= (@ (@ tptp.inf_inf_set_nat A) B) tptp.bot_bot_set_nat) (= (@ (@ tptp.minus_minus_set_nat A) B) A))))
% 3.70/4.04 (assert (forall ((X tptp.code_integer) (Zs tptp.list_Code_integer)) (let ((_let_1 (@ tptp.foldl_1542389171486570077nteger tptp.times_3573771949741848930nteger))) (= (@ (@ tptp.times_3573771949741848930nteger X) (@ (@ _let_1 tptp.one_one_Code_integer) Zs)) (@ (@ _let_1 X) Zs)))))
% 3.70/4.04 (assert (forall ((X tptp.assn) (Zs tptp.list_assn)) (let ((_let_1 (@ tptp.foldl_assn_assn tptp.times_times_assn))) (= (@ (@ tptp.times_times_assn X) (@ (@ _let_1 tptp.one_one_assn) Zs)) (@ (@ _let_1 X) Zs)))))
% 3.70/4.04 (assert (forall ((X tptp.rat) (Zs tptp.list_rat)) (let ((_let_1 (@ tptp.foldl_rat_rat tptp.times_times_rat))) (= (@ (@ tptp.times_times_rat X) (@ (@ _let_1 tptp.one_one_rat) Zs)) (@ (@ _let_1 X) Zs)))))
% 3.70/4.04 (assert (forall ((X tptp.nat) (Zs tptp.list_nat)) (let ((_let_1 (@ tptp.foldl_nat_nat tptp.times_times_nat))) (= (@ (@ tptp.times_times_nat X) (@ (@ _let_1 tptp.one_one_nat) Zs)) (@ (@ _let_1 X) Zs)))))
% 3.70/4.04 (assert (forall ((X tptp.int) (Zs tptp.list_int)) (let ((_let_1 (@ tptp.foldl_int_int tptp.times_times_int))) (= (@ (@ tptp.times_times_int X) (@ (@ _let_1 tptp.one_one_int) Zs)) (@ (@ _let_1 X) Zs)))))
% 3.70/4.04 (assert (forall ((X tptp.c) (Xs tptp.list_c)) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_c (@ (@ tptp.removeAll_c X) Xs))) (@ tptp.size_size_list_c Xs))))
% 3.70/4.04 (assert (forall ((X tptp.d) (Xs tptp.list_d)) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_d (@ (@ tptp.removeAll_d X) Xs))) (@ tptp.size_size_list_d Xs))))
% 3.70/4.04 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat (@ (@ tptp.removeAll_nat X) Xs))) (@ tptp.size_size_list_nat Xs))))
% 3.70/4.04 (assert (forall ((X tptp.int) (Xs tptp.list_int)) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int (@ (@ tptp.removeAll_int X) Xs))) (@ tptp.size_size_list_int Xs))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le2604355607129572851at_nat (@ (@ tptp.minus_3314409938677909166at_nat A) B)) A) (not (= (@ (@ tptp.inf_in7913087082777306421at_nat A) B) tptp.bot_bo228742789529271731at_nat)))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le7866589430770878221at_nat (@ (@ tptp.minus_1356011639430497352at_nat A) B)) A) (not (= (@ (@ tptp.inf_in2572325071724192079at_nat A) B) tptp.bot_bo2099793752762293965at_nat)))))
% 3.70/4.04 (assert (forall ((A tptp.set_o) (B tptp.set_o)) (= (@ (@ tptp.ord_less_set_o (@ (@ tptp.minus_minus_set_o A) B)) A) (not (= (@ (@ tptp.inf_inf_set_o A) B) tptp.bot_bot_set_o)))))
% 3.70/4.04 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (= (@ (@ tptp.ord_less_set_int (@ (@ tptp.minus_minus_set_int A) B)) A) (not (= (@ (@ tptp.inf_inf_set_int A) B) tptp.bot_bot_set_int)))))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (@ (@ tptp.ord_less_set_nat (@ (@ tptp.minus_minus_set_nat A) B)) A) (not (= (@ (@ tptp.inf_inf_set_nat A) B) tptp.bot_bot_set_nat)))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger A2) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.assn)) (not (@ (@ tptp.ord_less_assn A2) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.num)) (not (@ (@ tptp.ord_less_num A2) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat)) (not (@ (@ tptp.ord_less_nat A2) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.int)) (not (@ (@ tptp.ord_less_int A2) A2))))
% 3.70/4.04 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (S3 tptp.set_Pr1261947904930325089at_nat) (R tptp.set_Pr4329608150637261639at_nat) (S5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.produc2922128104949294807at_nat R2))) (=> (@ (@ tptp.member8757157785044589968at_nat (@ _let_1 S3)) R) (=> (= S5 S3) (@ (@ tptp.member8757157785044589968at_nat (@ _let_1 S5)) R))))))
% 3.70/4.04 (assert (forall ((R2 tptp.nat) (S3 tptp.nat) (R tptp.set_Pr1261947904930325089at_nat) (S5 tptp.nat)) (let ((_let_1 (@ tptp.product_Pair_nat_nat R2))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 S3)) R) (=> (= S5 S3) (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 S5)) R))))))
% 3.70/4.04 (assert (forall ((R2 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (S3 tptp.produc8923325533196201883nteger) (R tptp.set_Pr1281608226676607948nteger) (S5 tptp.produc8923325533196201883nteger)) (let ((_let_1 (@ tptp.produc8603105652947943368nteger R2))) (=> (@ (@ tptp.member4164122664394876845nteger (@ _let_1 S3)) R) (=> (= S5 S3) (@ (@ tptp.member4164122664394876845nteger (@ _let_1 S5)) R))))))
% 3.70/4.04 (assert (forall ((R2 (-> tptp.produc3658429121746597890et_nat Bool)) (S3 tptp.produc3658429121746597890et_nat) (R tptp.set_Pr3286484037609594932et_nat) (S5 tptp.produc3658429121746597890et_nat)) (let ((_let_1 (@ tptp.produc5001842942810119800et_nat R2))) (=> (@ (@ tptp.member1996754912294343701et_nat (@ _let_1 S3)) R) (=> (= S5 S3) (@ (@ tptp.member1996754912294343701et_nat (@ _let_1 S5)) R))))))
% 3.70/4.04 (assert (forall ((R2 (-> tptp.produc3658429121746597890et_nat Bool)) (S3 tptp.produc3925858234332021118et_nat) (R tptp.set_Pr8536935166611901872et_nat) (S5 tptp.produc3925858234332021118et_nat)) (let ((_let_1 (@ tptp.produc2245416461498447860et_nat R2))) (=> (@ (@ tptp.member6124377750444531601et_nat (@ _let_1 S3)) R) (=> (= S5 S3) (@ (@ tptp.member6124377750444531601et_nat (@ _let_1 S5)) R))))))
% 3.70/4.04 (assert (forall ((R2 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (S3 tptp.product_prod_int_int) (R tptp.set_Pr9222295170931077689nt_int) (S5 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.produc5700946648718959541nt_int R2))) (=> (@ (@ tptp.member7618704894036264090nt_int (@ _let_1 S3)) R) (=> (= S5 S3) (@ (@ tptp.member7618704894036264090nt_int (@ _let_1 S5)) R))))))
% 3.70/4.04 (assert (forall ((R2 (-> tptp.int tptp.option6357759511663192854e_term)) (S3 tptp.product_prod_int_int) (R tptp.set_Pr1872883991513573699nt_int) (S5 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.produc4305682042979456191nt_int R2))) (=> (@ (@ tptp.member7034335876925520548nt_int (@ _let_1 S3)) R) (=> (= S5 S3) (@ (@ tptp.member7034335876925520548nt_int (@ _let_1 S5)) R))))))
% 3.70/4.04 (assert (forall ((Ys tptp.list_P8527749157015355191n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (=> (@ tptp.distin4809818325527169450n_assn Ys) (=> (= (@ tptp.set_Pr1139785259514867910n_assn Ys) (@ tptp.set_Pr1139785259514867910n_assn Xs)) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6829681357464350627n_assn Ys)) (@ tptp.size_s6829681357464350627n_assn Xs))))))
% 3.70/4.04 (assert (forall ((Ys tptp.list_c) (Xs tptp.list_c)) (=> (@ tptp.distinct_c Ys) (=> (= (@ tptp.set_c2 Ys) (@ tptp.set_c2 Xs)) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_c Ys)) (@ tptp.size_size_list_c Xs))))))
% 3.70/4.04 (assert (forall ((Ys tptp.list_d) (Xs tptp.list_d)) (=> (@ tptp.distinct_d Ys) (=> (= (@ tptp.set_d2 Ys) (@ tptp.set_d2 Xs)) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_d Ys)) (@ tptp.size_size_list_d Xs))))))
% 3.70/4.04 (assert (forall ((Ys tptp.list_nat) (Xs tptp.list_nat)) (=> (@ tptp.distinct_nat Ys) (=> (= (@ tptp.set_nat2 Ys) (@ tptp.set_nat2 Xs)) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Ys)) (@ tptp.size_size_list_nat Xs))))))
% 3.70/4.04 (assert (forall ((Ys tptp.list_int) (Xs tptp.list_int)) (=> (@ tptp.distinct_int Ys) (=> (= (@ tptp.set_int2 Ys) (@ tptp.set_int2 Xs)) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Ys)) (@ tptp.size_size_list_int Xs))))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (not (= M2 N)) (or (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_nat N) M2)))))
% 3.70/4.04 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 3.70/4.04 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M2) (not (= M2 N)))))
% 3.70/4.04 (assert (forall ((S3 tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S3) T) (not (= S3 T)))))
% 3.70/4.04 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 3.70/4.04 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N5 tptp.nat)) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M3) N5) (@ P M3))) (@ P N5))) (@ P N))))
% 3.70/4.04 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N5 tptp.nat)) (=> (not (@ P N5)) (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N5) (not (@ P M3)))))) (@ P N))))
% 3.70/4.04 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 3.70/4.04 (assert (forall ((X tptp.list_c) (Y tptp.list_c)) (=> (not (= (@ tptp.size_size_list_c X) (@ tptp.size_size_list_c Y))) (not (= X Y)))))
% 3.70/4.04 (assert (forall ((X tptp.list_d) (Y tptp.list_d)) (=> (not (= (@ tptp.size_size_list_d X) (@ tptp.size_size_list_d Y))) (not (= X Y)))))
% 3.70/4.04 (assert (forall ((X tptp.list_nat) (Y tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat X) (@ tptp.size_size_list_nat Y))) (not (= X Y)))))
% 3.70/4.04 (assert (forall ((X tptp.list_int) (Y tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int X) (@ tptp.size_size_list_int Y))) (not (= X Y)))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (=> (@ tptp.distinct_int Xs) (=> (@ tptp.distinct_int Ys) (@ tptp.distin3744728255968310194nt_int (@ (@ tptp.product_int_int Xs) Ys))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_nat)) (=> (@ tptp.distinct_int Xs) (=> (@ tptp.distinct_nat Ys) (@ tptp.distin7922579275477506902nt_nat (@ (@ tptp.product_int_nat Xs) Ys))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_int)) (=> (@ tptp.distinct_nat Xs) (=> (@ tptp.distinct_int Ys) (@ tptp.distin2745374544067255638at_int (@ (@ tptp.product_nat_int Xs) Ys))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (@ tptp.distinct_nat Xs) (=> (@ tptp.distinct_nat Ys) (@ tptp.distin6923225563576452346at_nat (@ (@ tptp.product_nat_nat Xs) Ys))))))
% 3.70/4.04 (assert (forall ((L tptp.list_Code_integer) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_Code_integer L))) (=> (@ (@ tptp.sorted710888440204495920nteger tptp.ord_le3102999989581377725nteger) L) (=> (@ tptp.distin1543349897113766820nteger L) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_s3445333598471063425nteger L)) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 I)) (@ _let_1 J)))))))))
% 3.70/4.04 (assert (forall ((L tptp.list_num) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_num L))) (=> (@ (@ tptp.sorted_wrt_num tptp.ord_less_eq_num) L) (=> (@ tptp.distinct_num L) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_num L)) (@ (@ tptp.ord_less_num (@ _let_1 I)) (@ _let_1 J)))))))))
% 3.70/4.04 (assert (forall ((L tptp.list_nat) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat L))) (=> (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) L) (=> (@ tptp.distinct_nat L) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat L)) (@ (@ tptp.ord_less_nat (@ _let_1 I)) (@ _let_1 J)))))))))
% 3.70/4.04 (assert (forall ((L tptp.list_int) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_int L))) (=> (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) L) (=> (@ tptp.distinct_int L) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_int L)) (@ (@ tptp.ord_less_int (@ _let_1 I)) (@ _let_1 J)))))))))
% 3.70/4.04 (assert (forall ((L tptp.list_Code_integer) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (let ((_let_2 (@ tptp.nth_Code_integer L))) (let ((_let_3 (@ tptp.size_s3445333598471063425nteger L))) (=> (@ tptp.distin1543349897113766820nteger L) (=> (@ (@ tptp.sorted710888440204495920nteger tptp.ord_le3102999989581377725nteger) L) (=> (@ _let_1 _let_3) (=> (@ (@ tptp.ord_less_nat J) _let_3) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_2 I)) (@ _let_2 J)) (@ _let_1 J)))))))))))
% 3.70/4.04 (assert (forall ((L tptp.list_num) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (let ((_let_2 (@ tptp.nth_num L))) (let ((_let_3 (@ tptp.size_size_list_num L))) (=> (@ tptp.distinct_num L) (=> (@ (@ tptp.sorted_wrt_num tptp.ord_less_eq_num) L) (=> (@ _let_1 _let_3) (=> (@ (@ tptp.ord_less_nat J) _let_3) (= (@ (@ tptp.ord_less_num (@ _let_2 I)) (@ _let_2 J)) (@ _let_1 J)))))))))))
% 3.70/4.04 (assert (forall ((L tptp.list_nat) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (let ((_let_2 (@ tptp.nth_nat L))) (let ((_let_3 (@ tptp.size_size_list_nat L))) (=> (@ tptp.distinct_nat L) (=> (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) L) (=> (@ _let_1 _let_3) (=> (@ (@ tptp.ord_less_nat J) _let_3) (= (@ (@ tptp.ord_less_nat (@ _let_2 I)) (@ _let_2 J)) (@ _let_1 J)))))))))))
% 3.70/4.04 (assert (forall ((L tptp.list_int) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (let ((_let_2 (@ tptp.nth_int L))) (let ((_let_3 (@ tptp.size_size_list_int L))) (=> (@ tptp.distinct_int L) (=> (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) L) (=> (@ _let_1 _let_3) (=> (@ (@ tptp.ord_less_nat J) _let_3) (= (@ (@ tptp.ord_less_int (@ _let_2 I)) (@ _let_2 J)) (@ _let_1 J)))))))))))
% 3.70/4.04 (assert (forall ((From tptp.nat) (To tptp.nat) (Xs tptp.list_c)) (=> (@ (@ tptp.ord_less_eq_nat From) To) (=> (@ (@ tptp.ord_less_eq_nat To) (@ tptp.size_size_list_c Xs)) (= (@ tptp.size_size_list_c (@ (@ (@ tptp.slice_c From) To) Xs)) (@ (@ tptp.minus_minus_nat To) From))))))
% 3.70/4.04 (assert (forall ((From tptp.nat) (To tptp.nat) (Xs tptp.list_d)) (=> (@ (@ tptp.ord_less_eq_nat From) To) (=> (@ (@ tptp.ord_less_eq_nat To) (@ tptp.size_size_list_d Xs)) (= (@ tptp.size_size_list_d (@ (@ (@ tptp.slice_d From) To) Xs)) (@ (@ tptp.minus_minus_nat To) From))))))
% 3.70/4.04 (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))))))
% 3.70/4.04 (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))))))
% 3.70/4.04 (assert (forall ((K3 tptp.nat) (Xs tptp.list_c) (Y tptp.c)) (let ((_let_1 (@ tptp.size_size_list_c Xs))) (=> (@ (@ tptp.ord_less_nat K3) _let_1) (= (@ tptp.rev_c (@ (@ (@ tptp.list_update_c Xs) K3) Y)) (@ (@ (@ tptp.list_update_c (@ tptp.rev_c Xs)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat _let_1) K3)) tptp.one_one_nat)) Y))))))
% 3.70/4.04 (assert (forall ((K3 tptp.nat) (Xs tptp.list_d) (Y tptp.d)) (let ((_let_1 (@ tptp.size_size_list_d Xs))) (=> (@ (@ tptp.ord_less_nat K3) _let_1) (= (@ tptp.rev_d (@ (@ (@ tptp.list_update_d Xs) K3) Y)) (@ (@ (@ tptp.list_update_d (@ tptp.rev_d Xs)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat _let_1) K3)) tptp.one_one_nat)) Y))))))
% 3.70/4.04 (assert (forall ((K3 tptp.nat) (Xs tptp.list_nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.size_size_list_nat Xs))) (=> (@ (@ tptp.ord_less_nat K3) _let_1) (= (@ tptp.rev_nat (@ (@ (@ tptp.list_update_nat Xs) K3) Y)) (@ (@ (@ tptp.list_update_nat (@ tptp.rev_nat Xs)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat _let_1) K3)) tptp.one_one_nat)) Y))))))
% 3.70/4.04 (assert (forall ((K3 tptp.nat) (Xs tptp.list_int) (Y tptp.int)) (let ((_let_1 (@ tptp.size_size_list_int Xs))) (=> (@ (@ tptp.ord_less_nat K3) _let_1) (= (@ tptp.rev_int (@ (@ (@ tptp.list_update_int Xs) K3) Y)) (@ (@ (@ tptp.list_update_int (@ tptp.rev_int Xs)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat _let_1) K3)) tptp.one_one_nat)) Y))))))
% 3.70/4.04 (assert (forall ((K3 tptp.nat) (Xs tptp.list_c) (X tptp.c)) (let ((_let_1 (@ tptp.butlast_c Xs))) (let ((_let_2 (@ tptp.butlast_c (@ (@ (@ tptp.list_update_c Xs) K3) X)))) (let ((_let_3 (= K3 (@ (@ tptp.minus_minus_nat (@ tptp.size_size_list_c Xs)) tptp.one_one_nat)))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ (@ tptp.list_update_c _let_1) K3) X)))))))))
% 3.70/4.04 (assert (forall ((K3 tptp.nat) (Xs tptp.list_d) (X tptp.d)) (let ((_let_1 (@ tptp.butlast_d Xs))) (let ((_let_2 (@ tptp.butlast_d (@ (@ (@ tptp.list_update_d Xs) K3) X)))) (let ((_let_3 (= K3 (@ (@ tptp.minus_minus_nat (@ tptp.size_size_list_d Xs)) tptp.one_one_nat)))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ (@ tptp.list_update_d _let_1) K3) X)))))))))
% 3.70/4.04 (assert (forall ((K3 tptp.nat) (Xs tptp.list_nat) (X tptp.nat)) (let ((_let_1 (@ tptp.butlast_nat Xs))) (let ((_let_2 (@ tptp.butlast_nat (@ (@ (@ tptp.list_update_nat Xs) K3) X)))) (let ((_let_3 (= K3 (@ (@ tptp.minus_minus_nat (@ tptp.size_size_list_nat Xs)) tptp.one_one_nat)))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ (@ tptp.list_update_nat _let_1) K3) X)))))))))
% 3.70/4.04 (assert (forall ((K3 tptp.nat) (Xs tptp.list_int) (X tptp.int)) (let ((_let_1 (@ tptp.butlast_int Xs))) (let ((_let_2 (@ tptp.butlast_int (@ (@ (@ tptp.list_update_int Xs) K3) X)))) (let ((_let_3 (= K3 (@ (@ tptp.minus_minus_nat (@ tptp.size_size_list_int Xs)) tptp.one_one_nat)))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ (@ tptp.list_update_int _let_1) K3) X)))))))))
% 3.70/4.04 (assert (forall ((L tptp.list_nat) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat L))) (let ((_let_2 (@ tptp.size_size_list_nat L))) (=> (@ tptp.distinct_nat L) (=> (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) L) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 I)) (@ _let_1 J)) (@ (@ tptp.ord_less_eq_nat I) J))))))))))
% 3.70/4.04 (assert (forall ((L tptp.list_int) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_int L))) (let ((_let_2 (@ tptp.size_size_list_int L))) (=> (@ tptp.distinct_int L) (=> (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) L) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 I)) (@ _let_1 J)) (@ (@ tptp.ord_less_eq_nat I) J))))))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_c)) (= (@ tptp.size_s2756448709718749209od_c_c (@ (@ tptp.zip_c_c Xs) Ys)) (@ (@ tptp.ord_min_nat (@ tptp.size_size_list_c Xs)) (@ tptp.size_size_list_c Ys)))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_d)) (= (@ tptp.size_s2827482749765095194od_c_d (@ (@ tptp.zip_c_d Xs) Ys)) (@ (@ tptp.ord_min_nat (@ tptp.size_size_list_c Xs)) (@ tptp.size_size_list_d Ys)))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_nat)) (= (@ tptp.size_s2954062820725854115_c_nat (@ (@ tptp.zip_c_nat Xs) Ys)) (@ (@ tptp.ord_min_nat (@ tptp.size_size_list_c Xs)) (@ tptp.size_size_list_nat Ys)))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_int)) (= (@ tptp.size_s463979675794127359_c_int (@ (@ tptp.zip_c_int Xs) Ys)) (@ (@ tptp.ord_min_nat (@ tptp.size_size_list_c Xs)) (@ tptp.size_size_list_int Ys)))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_d) (Ys tptp.list_c)) (= (@ tptp.size_s2120799709113762520od_d_c (@ (@ tptp.zip_d_c Xs) Ys)) (@ (@ tptp.ord_min_nat (@ tptp.size_size_list_d Xs)) (@ tptp.size_size_list_c Ys)))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_d) (Ys tptp.list_d)) (= (@ tptp.size_s2191833749160108505od_d_d (@ (@ tptp.zip_d_d Xs) Ys)) (@ (@ tptp.ord_min_nat (@ tptp.size_size_list_d Xs)) (@ tptp.size_size_list_d Ys)))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_d) (Ys tptp.list_nat)) (= (@ tptp.size_s8550281435913984804_d_nat (@ (@ tptp.zip_d_nat Xs) Ys)) (@ (@ tptp.ord_min_nat (@ tptp.size_size_list_d Xs)) (@ tptp.size_size_list_nat Ys)))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_d) (Ys tptp.list_int)) (= (@ tptp.size_s6060198290982258048_d_int (@ (@ tptp.zip_d_int Xs) Ys)) (@ (@ tptp.ord_min_nat (@ tptp.size_size_list_d Xs)) (@ tptp.size_size_list_int Ys)))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_c)) (= (@ tptp.size_s385972143775086793_nat_c (@ (@ tptp.zip_nat_c Xs) Ys)) (@ (@ tptp.ord_min_nat (@ tptp.size_size_list_nat Xs)) (@ tptp.size_size_list_c Ys)))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_d)) (= (@ tptp.size_s457006183821432778_nat_d (@ (@ tptp.zip_nat_d Xs) Ys)) (@ (@ tptp.ord_min_nat (@ tptp.size_size_list_nat Xs)) (@ tptp.size_size_list_d Ys)))))
% 3.70/4.04 (assert (forall ((P tptp.assn) (H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat) (Q tptp.assn) (As3 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H2))) (=> (@ (@ tptp.rep_assn P) (@ _let_1 As2)) (=> (@ (@ tptp.rep_assn Q) (@ _let_1 As3)) (=> (= (@ (@ tptp.inf_inf_set_nat As2) As3) tptp.bot_bot_set_nat) (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn P) Q)) (@ _let_1 (@ (@ tptp.sup_sup_set_nat As2) As3)))))))))
% 3.70/4.04 (assert (forall ((A tptp.assn) (B tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn A) B)) H2) (exists ((Hr tptp.heap_e7401611519738050253t_unit) (As1 tptp.set_nat) (As22 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat Hr))) (and (= H2 (@ _let_1 (@ (@ tptp.sup_sup_set_nat As1) As22))) (= (@ (@ tptp.inf_inf_set_nat As1) As22) tptp.bot_bot_set_nat) (@ (@ tptp.rep_assn A) (@ _let_1 As1)) (@ (@ tptp.rep_assn B) (@ _let_1 As22))))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_c)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_c Xs)) tptp.one_one_nat) (= (@ tptp.rotate1_c Xs) Xs))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_d)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_d Xs)) tptp.one_one_nat) (= (@ tptp.rotate1_d Xs) Xs))))
% 3.70/4.04 (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))))
% 3.70/4.04 (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))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A2) A2) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.assn)) (= (@ (@ tptp.sup_sup_assn A2) A2) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat A2) A2) A2)))
% 3.70/4.04 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat X) X) X)))
% 3.70/4.04 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.sup_sup_assn X) X) X)))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat X) X) X)))
% 3.70/4.04 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A2))) (let ((_let_2 (@ _let_1 B2))) (= (@ _let_1 _let_2) _let_2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.assn) (B2 tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn A2))) (let ((_let_2 (@ _let_1 B2))) (= (@ _let_1 _let_2) _let_2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat A2))) (let ((_let_2 (@ _let_1 B2))) (= (@ _let_1 _let_2) _let_2)))))
% 3.70/4.04 (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)))))
% 3.70/4.04 (assert (forall ((X tptp.assn) (Y tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 3.70/4.04 (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)))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.sup_sup_set_nat A2) B2))) (= (@ (@ tptp.sup_sup_set_nat _let_1) B2) _let_1))))
% 3.70/4.04 (assert (forall ((A2 tptp.assn) (B2 tptp.assn)) (let ((_let_1 (@ (@ tptp.sup_sup_assn A2) B2))) (= (@ (@ tptp.sup_sup_assn _let_1) B2) _let_1))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2))) (= (@ (@ tptp.sup_su5525570899277871387at_nat _let_1) B2) _let_1))))
% 3.70/4.04 (assert (forall ((C tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat A) B)))))))
% 3.70/4.04 (assert (forall ((C tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.inf_inf_set_int A) B)))))))
% 3.70/4.04 (assert (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.inf_in1906310914598751387_nat_o A) B)))))))
% 3.70/4.04 (assert (forall ((C tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B)))))))
% 3.70/4.04 (assert (forall ((C tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A) B)))))))
% 3.70/4.04 (assert (forall ((C tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (= (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat A) B)) (and (@ _let_1 A) (@ _let_1 B))))))
% 3.70/4.04 (assert (forall ((C tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_int A) B)) (and (@ _let_1 A) (@ _let_1 B))))))
% 3.70/4.04 (assert (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (= (@ _let_1 (@ (@ tptp.inf_in1906310914598751387_nat_o A) B)) (and (@ _let_1 A) (@ _let_1 B))))))
% 3.70/4.04 (assert (forall ((C tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B)) (and (@ _let_1 A) (@ _let_1 B))))))
% 3.70/4.04 (assert (forall ((C tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) (and (@ _let_1 A) (@ _let_1 B))))))
% 3.70/4.04 (assert (forall ((C tptp.product_prod_nat_nat) (B tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (=> (not (@ _let_1 B)) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat A) B))))))
% 3.70/4.04 (assert (forall ((C tptp.int) (B tptp.set_int) (A tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (=> (not (@ _let_1 B)) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.sup_sup_set_int A) B))))))
% 3.70/4.04 (assert (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.set_Pr4532377907799695533_nat_o) (A tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (=> (not (@ _let_1 B)) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.sup_su5209123915105501825_nat_o A) B))))))
% 3.70/4.04 (assert (forall ((C tptp.nat) (B tptp.set_nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (=> (not (@ _let_1 B)) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B))))))
% 3.70/4.04 (assert (forall ((C tptp.produc3843707927480180839at_nat) (B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (=> (=> (not (@ _let_1 B)) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A) B))))))
% 3.70/4.04 (assert (forall ((C tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 3.70/4.04 (assert (forall ((C tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 3.70/4.04 (assert (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (= (@ _let_1 (@ (@ tptp.sup_su5209123915105501825_nat_o A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 3.70/4.04 (assert (forall ((C tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 3.70/4.04 (assert (forall ((C tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (= (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.ord_min_nat A2) A2) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_min_nat A2))) (let ((_let_2 (@ _let_1 B2))) (= (@ _let_1 _let_2) _let_2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_min_nat A2) B2))) (= (@ (@ tptp.ord_min_nat _let_1) B2) _let_1))))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat X) Y)) Z) (and (@ (@ tptp.ord_le1268244103169919719at_nat X) Z) (@ (@ tptp.ord_le1268244103169919719at_nat Y) Z)))))
% 3.70/4.04 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (= (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.sup_sup_assn X) Y)) Z) (and (@ (@ tptp.ord_less_eq_assn X) Z) (@ (@ tptp.ord_less_eq_assn Y) Z)))))
% 3.70/4.04 (assert (forall ((X tptp.filter_nat) (Y tptp.filter_nat) (Z tptp.filter_nat)) (= (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.sup_sup_filter_nat X) Y)) Z) (and (@ (@ tptp.ord_le2510731241096832064er_nat X) Z) (@ (@ tptp.ord_le2510731241096832064er_nat Y) Z)))))
% 3.70/4.04 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat X) Y)) Z) (and (@ (@ tptp.ord_less_eq_set_nat X) Z) (@ (@ tptp.ord_less_eq_set_nat Y) Z)))))
% 3.70/4.04 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat X) Y)) Z) (and (@ (@ tptp.ord_less_eq_nat X) Z) (@ (@ tptp.ord_less_eq_nat Y) Z)))))
% 3.70/4.04 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int X) Y)) Z) (and (@ (@ tptp.ord_less_eq_int X) Z) (@ (@ tptp.ord_less_eq_int Y) Z)))))
% 3.70/4.04 (assert (forall ((B2 tptp.set_Pr4329608150637261639at_nat) (C tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat B2) C)) A2) (and (@ (@ tptp.ord_le1268244103169919719at_nat B2) A2) (@ (@ tptp.ord_le1268244103169919719at_nat C) A2)))))
% 3.70/4.04 (assert (forall ((B2 tptp.assn) (C tptp.assn) (A2 tptp.assn)) (= (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.sup_sup_assn B2) C)) A2) (and (@ (@ tptp.ord_less_eq_assn B2) A2) (@ (@ tptp.ord_less_eq_assn C) A2)))))
% 3.70/4.04 (assert (forall ((B2 tptp.filter_nat) (C tptp.filter_nat) (A2 tptp.filter_nat)) (= (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.sup_sup_filter_nat B2) C)) A2) (and (@ (@ tptp.ord_le2510731241096832064er_nat B2) A2) (@ (@ tptp.ord_le2510731241096832064er_nat C) A2)))))
% 3.70/4.04 (assert (forall ((B2 tptp.set_nat) (C tptp.set_nat) (A2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat B2) C)) A2) (and (@ (@ tptp.ord_less_eq_set_nat B2) A2) (@ (@ tptp.ord_less_eq_set_nat C) A2)))))
% 3.70/4.04 (assert (forall ((B2 tptp.nat) (C tptp.nat) (A2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat B2) C)) A2) (and (@ (@ tptp.ord_less_eq_nat B2) A2) (@ (@ tptp.ord_less_eq_nat C) A2)))))
% 3.70/4.04 (assert (forall ((B2 tptp.int) (C tptp.int) (A2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int B2) C)) A2) (and (@ (@ tptp.ord_less_eq_int B2) A2) (@ (@ tptp.ord_less_eq_int C) A2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.assn)) (= (@ (@ tptp.sup_sup_assn A2) tptp.bot_bot_assn) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat A2) tptp.bot_bo228742789529271731at_nat) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat A2) tptp.bot_bo2099793752762293965at_nat) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o A2) tptp.bot_bot_set_o) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A2) tptp.bot_bot_set_nat) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int A2) tptp.bot_bot_set_int) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.assn) (B2 tptp.assn)) (= (= tptp.bot_bot_assn (@ (@ tptp.sup_sup_assn A2) B2)) (and (= A2 tptp.bot_bot_assn) (= B2 tptp.bot_bot_assn)))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (= (= tptp.bot_bo228742789529271731at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2)) (and (= A2 tptp.bot_bo228742789529271731at_nat) (= B2 tptp.bot_bo228742789529271731at_nat)))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (= (= tptp.bot_bo2099793752762293965at_nat (@ (@ tptp.sup_su6327502436637775413at_nat A2) B2)) (and (= A2 tptp.bot_bo2099793752762293965at_nat) (= B2 tptp.bot_bo2099793752762293965at_nat)))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_o) (B2 tptp.set_o)) (= (= tptp.bot_bot_set_o (@ (@ tptp.sup_sup_set_o A2) B2)) (and (= A2 tptp.bot_bot_set_o) (= B2 tptp.bot_bot_set_o)))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (= (= tptp.bot_bot_set_nat (@ (@ tptp.sup_sup_set_nat A2) B2)) (and (= A2 tptp.bot_bot_set_nat) (= B2 tptp.bot_bot_set_nat)))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int)) (= (= tptp.bot_bot_set_int (@ (@ tptp.sup_sup_set_int A2) B2)) (and (= A2 tptp.bot_bot_set_int) (= B2 tptp.bot_bot_set_int)))))
% 3.70/4.04 (assert (forall ((A2 tptp.assn)) (= (@ (@ tptp.sup_sup_assn tptp.bot_bot_assn) A2) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat tptp.bot_bo228742789529271731at_nat) A2) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat tptp.bot_bo2099793752762293965at_nat) A2) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o tptp.bot_bot_set_o) A2) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat tptp.bot_bot_set_nat) A2) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int tptp.bot_bot_set_int) A2) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.assn) (B2 tptp.assn)) (= (= (@ (@ tptp.sup_sup_assn A2) B2) tptp.bot_bot_assn) (and (= A2 tptp.bot_bot_assn) (= B2 tptp.bot_bot_assn)))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (= (= (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2) tptp.bot_bo228742789529271731at_nat) (and (= A2 tptp.bot_bo228742789529271731at_nat) (= B2 tptp.bot_bo228742789529271731at_nat)))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.sup_su6327502436637775413at_nat A2) B2) tptp.bot_bo2099793752762293965at_nat) (and (= A2 tptp.bot_bo2099793752762293965at_nat) (= B2 tptp.bot_bo2099793752762293965at_nat)))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_o) (B2 tptp.set_o)) (= (= (@ (@ tptp.sup_sup_set_o A2) B2) tptp.bot_bot_set_o) (and (= A2 tptp.bot_bot_set_o) (= B2 tptp.bot_bot_set_o)))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (= (= (@ (@ tptp.sup_sup_set_nat A2) B2) tptp.bot_bot_set_nat) (and (= A2 tptp.bot_bot_set_nat) (= B2 tptp.bot_bot_set_nat)))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int)) (= (= (@ (@ tptp.sup_sup_set_int A2) B2) tptp.bot_bot_set_int) (and (= A2 tptp.bot_bot_set_int) (= B2 tptp.bot_bot_set_int)))))
% 3.70/4.04 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (= (@ (@ tptp.sup_sup_assn X) Y) tptp.bot_bot_assn) (and (= X tptp.bot_bot_assn) (= Y tptp.bot_bot_assn)))))
% 3.70/4.04 (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)))))
% 3.70/4.04 (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)))))
% 3.70/4.04 (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)))))
% 3.70/4.04 (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)))))
% 3.70/4.04 (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)))))
% 3.70/4.04 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (= tptp.bot_bot_assn (@ (@ tptp.sup_sup_assn X) Y)) (and (= X tptp.bot_bot_assn) (= Y tptp.bot_bot_assn)))))
% 3.70/4.04 (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)))))
% 3.70/4.04 (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)))))
% 3.70/4.04 (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)))))
% 3.70/4.04 (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)))))
% 3.70/4.04 (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)))))
% 3.70/4.04 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.sup_sup_assn X) tptp.bot_bot_assn) X)))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat X) tptp.bot_bo228742789529271731at_nat) X)))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat X) tptp.bot_bo2099793752762293965at_nat) X)))
% 3.70/4.04 (assert (forall ((X tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o X) tptp.bot_bot_set_o) X)))
% 3.70/4.04 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat X) tptp.bot_bot_set_nat) X)))
% 3.70/4.04 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int X) tptp.bot_bot_set_int) X)))
% 3.70/4.04 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.sup_sup_assn tptp.bot_bot_assn) X) X)))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat tptp.bot_bo228742789529271731at_nat) X) X)))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat tptp.bot_bo2099793752762293965at_nat) X) X)))
% 3.70/4.04 (assert (forall ((X tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o tptp.bot_bot_set_o) X) X)))
% 3.70/4.04 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat tptp.bot_bot_set_nat) X) X)))
% 3.70/4.04 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int tptp.bot_bot_set_int) X) X)))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat X) (@ (@ tptp.sup_su6327502436637775413at_nat X) Y)) X)))
% 3.70/4.04 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X) (@ (@ tptp.sup_sup_set_nat X) Y)) X)))
% 3.70/4.04 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (@ (@ tptp.inf_inf_assn X) (@ (@ tptp.sup_sup_assn X) Y)) X)))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat X) (@ (@ tptp.sup_su5525570899277871387at_nat X) Y)) X)))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat X) (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) X)))
% 3.70/4.04 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat X) (@ (@ tptp.inf_inf_set_nat X) Y)) X)))
% 3.70/4.04 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (@ (@ tptp.sup_sup_assn X) (@ (@ tptp.inf_inf_assn X) Y)) X)))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat X) (@ (@ tptp.inf_in7913087082777306421at_nat X) Y)) X)))
% 3.70/4.04 (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)))))
% 3.70/4.04 (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)))))
% 3.70/4.04 (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)))))
% 3.70/4.04 (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)))))
% 3.70/4.04 (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)))))
% 3.70/4.04 (assert (forall ((M2 tptp.assn) (N tptp.assn)) (let ((_let_1 (@ (@ tptp.ord_min_assn M2) N))) (= (@ (@ tptp.ord_less_eq_assn M2) _let_1) (= _let_1 M2)))))
% 3.70/4.04 (assert (forall ((M2 tptp.filter_nat) (N tptp.filter_nat)) (let ((_let_1 (@ (@ tptp.ord_min_filter_nat M2) N))) (= (@ (@ tptp.ord_le2510731241096832064er_nat M2) _let_1) (= _let_1 M2)))))
% 3.70/4.04 (assert (forall ((M2 tptp.set_nat) (N tptp.set_nat)) (let ((_let_1 (@ (@ tptp.ord_min_set_nat M2) N))) (= (@ (@ tptp.ord_less_eq_set_nat M2) _let_1) (= _let_1 M2)))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_min_nat M2) N))) (= (@ (@ tptp.ord_less_eq_nat M2) _let_1) (= _let_1 M2)))))
% 3.70/4.04 (assert (forall ((M2 tptp.int) (N tptp.int)) (let ((_let_1 (@ (@ tptp.ord_min_int M2) N))) (= (@ (@ tptp.ord_less_eq_int M2) _let_1) (= _let_1 M2)))))
% 3.70/4.04 (assert (forall ((N tptp.assn) (M2 tptp.assn)) (let ((_let_1 (@ (@ tptp.ord_min_assn M2) N))) (= (@ (@ tptp.ord_less_eq_assn N) _let_1) (= _let_1 N)))))
% 3.70/4.04 (assert (forall ((N tptp.filter_nat) (M2 tptp.filter_nat)) (let ((_let_1 (@ (@ tptp.ord_min_filter_nat M2) N))) (= (@ (@ tptp.ord_le2510731241096832064er_nat N) _let_1) (= _let_1 N)))))
% 3.70/4.04 (assert (forall ((N tptp.set_nat) (M2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.ord_min_set_nat M2) N))) (= (@ (@ tptp.ord_less_eq_set_nat N) _let_1) (= _let_1 N)))))
% 3.70/4.04 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_min_nat M2) N))) (= (@ (@ tptp.ord_less_eq_nat N) _let_1) (= _let_1 N)))))
% 3.70/4.04 (assert (forall ((N tptp.int) (M2 tptp.int)) (let ((_let_1 (@ (@ tptp.ord_min_int M2) N))) (= (@ (@ tptp.ord_less_eq_int N) _let_1) (= _let_1 N)))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.ord_min_nat M2) N) N) (@ (@ tptp.ord_less_eq_nat N) M2))))
% 3.70/4.04 (assert (forall ((M2 tptp.int) (N tptp.int)) (= (= (@ (@ tptp.ord_min_int M2) N) N) (@ (@ tptp.ord_less_eq_int N) M2))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.ord_min_nat M2) N) M2) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 3.70/4.04 (assert (forall ((M2 tptp.int) (N tptp.int)) (= (= (@ (@ tptp.ord_min_int M2) N) M2) (@ (@ tptp.ord_less_eq_int M2) N))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= (@ (@ tptp.ord_min_nat A2) B2) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (= (@ (@ tptp.ord_min_int A2) B2) A2))))
% 3.70/4.04 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (= (@ (@ tptp.ord_min_nat A2) B2) B2))))
% 3.70/4.04 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (= (@ (@ tptp.ord_min_int A2) B2) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (= (@ _let_1 (@ (@ tptp.ord_min_nat B2) C)) (and (@ _let_1 B2) (@ _let_1 C))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A2))) (= (@ _let_1 (@ (@ tptp.ord_min_int B2) C)) (and (@ _let_1 B2) (@ _let_1 C))))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A) B)) C2) (and (@ (@ tptp.ord_le1268244103169919719at_nat A) C2) (@ (@ tptp.ord_le1268244103169919719at_nat B) C2)))))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat A) B)) C2) (and (@ (@ tptp.ord_less_eq_set_nat A) C2) (@ (@ tptp.ord_less_eq_set_nat B) C2)))))
% 3.70/4.04 (assert (forall ((A tptp.set_int) (A2 tptp.int) (B tptp.set_int)) (let ((_let_1 (@ tptp.sup_sup_set_int A))) (let ((_let_2 (@ tptp.insert_int2 A2))) (= (@ _let_1 (@ _let_2 B)) (@ _let_2 (@ _let_1 B)))))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (A2 tptp.product_prod_nat_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.sup_su6327502436637775413at_nat A))) (let ((_let_2 (@ tptp.insert8211810215607154385at_nat A2))) (= (@ _let_1 (@ _let_2 B)) (@ _let_2 (@ _let_1 B)))))))
% 3.70/4.04 (assert (forall ((A tptp.set_o) (A2 Bool) (B tptp.set_o)) (let ((_let_1 (@ tptp.sup_sup_set_o A))) (let ((_let_2 (@ tptp.insert_o2 A2))) (= (@ _let_1 (@ _let_2 B)) (@ _let_2 (@ _let_1 B)))))))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (A2 tptp.nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A))) (let ((_let_2 (@ tptp.insert_nat2 A2))) (= (@ _let_1 (@ _let_2 B)) (@ _let_2 (@ _let_1 B)))))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (A2 tptp.produc3843707927480180839at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat A))) (let ((_let_2 (@ tptp.insert9069300056098147895at_nat A2))) (= (@ _let_1 (@ _let_2 B)) (@ _let_2 (@ _let_1 B)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B tptp.set_int) (C2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int2 A2))) (= (@ (@ tptp.sup_sup_set_int (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.sup_sup_set_int B) C2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.product_prod_nat_nat) (B tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A2))) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat B) C2))))))
% 3.70/4.04 (assert (forall ((A2 Bool) (B tptp.set_o) (C2 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o2 A2))) (= (@ (@ tptp.sup_sup_set_o (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.sup_sup_set_o B) C2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat2 A2))) (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.sup_sup_set_nat B) C2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.produc3843707927480180839at_nat) (B tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.insert9069300056098147895at_nat A2))) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat B) C2))))))
% 3.70/4.04 (assert (forall ((Z tptp.code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger Z))) (= (@ _let_1 (@ (@ tptp.ord_min_Code_integer X) Y)) (and (@ _let_1 X) (@ _let_1 Y))))))
% 3.70/4.04 (assert (forall ((Z tptp.num) (X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.ord_less_num Z))) (= (@ _let_1 (@ (@ tptp.ord_min_num X) Y)) (and (@ _let_1 X) (@ _let_1 Y))))))
% 3.70/4.04 (assert (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat Z))) (= (@ _let_1 (@ (@ tptp.ord_min_nat X) Y)) (and (@ _let_1 X) (@ _let_1 Y))))))
% 3.70/4.04 (assert (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_int Z))) (= (@ _let_1 (@ (@ tptp.ord_min_int X) Y)) (and (@ _let_1 X) (@ _let_1 Y))))))
% 3.70/4.04 (assert (forall ((B2 tptp.code_integer) (A2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) A2) (= (@ (@ tptp.ord_min_Code_integer A2) B2) B2))))
% 3.70/4.04 (assert (forall ((B2 tptp.num) (A2 tptp.num)) (=> (@ (@ tptp.ord_less_num B2) A2) (= (@ (@ tptp.ord_min_num A2) B2) B2))))
% 3.70/4.04 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A2) (= (@ (@ tptp.ord_min_nat A2) B2) B2))))
% 3.70/4.04 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A2) (= (@ (@ tptp.ord_min_int A2) B2) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (= (@ (@ tptp.ord_min_Code_integer A2) B2) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.num) (B2 tptp.num)) (=> (@ (@ tptp.ord_less_num A2) B2) (= (@ (@ tptp.ord_min_num A2) B2) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (= (@ (@ tptp.ord_min_nat A2) B2) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (= (@ (@ tptp.ord_min_int A2) B2) A2))))
% 3.70/4.04 (assert (forall ((M2 tptp.code_integer) (N tptp.code_integer)) (let ((_let_1 (@ (@ tptp.ord_min_Code_integer M2) N))) (= (not (@ (@ tptp.ord_le6747313008572928689nteger _let_1) M2)) (= _let_1 M2)))))
% 3.70/4.04 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ (@ tptp.ord_min_num M2) N))) (= (not (@ (@ tptp.ord_less_num _let_1) M2)) (= _let_1 M2)))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_min_nat M2) N))) (= (not (@ (@ tptp.ord_less_nat _let_1) M2)) (= _let_1 M2)))))
% 3.70/4.04 (assert (forall ((M2 tptp.int) (N tptp.int)) (let ((_let_1 (@ (@ tptp.ord_min_int M2) N))) (= (not (@ (@ tptp.ord_less_int _let_1) M2)) (= _let_1 M2)))))
% 3.70/4.04 (assert (forall ((M2 tptp.code_integer) (N tptp.code_integer)) (let ((_let_1 (@ (@ tptp.ord_min_Code_integer M2) N))) (= (not (@ (@ tptp.ord_le6747313008572928689nteger _let_1) N)) (= _let_1 N)))))
% 3.70/4.04 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ (@ tptp.ord_min_num M2) N))) (= (not (@ (@ tptp.ord_less_num _let_1) N)) (= _let_1 N)))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_min_nat M2) N))) (= (not (@ (@ tptp.ord_less_nat _let_1) N)) (= _let_1 N)))))
% 3.70/4.04 (assert (forall ((M2 tptp.int) (N tptp.int)) (let ((_let_1 (@ (@ tptp.ord_min_int M2) N))) (= (not (@ (@ tptp.ord_less_int _let_1) N)) (= _let_1 N)))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.ord_min_Code_integer A2) B2)) A2) (@ (@ tptp.ord_le6747313008572928689nteger B2) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.num) (B2 tptp.num)) (= (@ (@ tptp.ord_less_num (@ (@ tptp.ord_min_num A2) B2)) A2) (@ (@ tptp.ord_less_num B2) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_min_nat A2) B2)) A2) (@ (@ tptp.ord_less_nat B2) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.ord_min_int A2) B2)) A2) (@ (@ tptp.ord_less_int B2) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.ord_min_Code_integer A2) B2)) B2) (@ (@ tptp.ord_le6747313008572928689nteger A2) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.num) (B2 tptp.num)) (= (@ (@ tptp.ord_less_num (@ (@ tptp.ord_min_num A2) B2)) B2) (@ (@ tptp.ord_less_num A2) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_min_nat A2) B2)) B2) (@ (@ tptp.ord_less_nat A2) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.ord_min_int A2) B2)) B2) (@ (@ tptp.ord_less_int A2) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (= (@ (@ tptp.ord_min_Code_integer A2) B2) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.assn) (B2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn A2) B2) (= (@ (@ tptp.ord_min_assn A2) B2) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.num) (B2 tptp.num)) (=> (@ (@ tptp.ord_less_num A2) B2) (= (@ (@ tptp.ord_min_num A2) B2) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (= (@ (@ tptp.ord_min_nat A2) B2) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (= (@ (@ tptp.ord_min_int A2) B2) A2))))
% 3.70/4.04 (assert (forall ((B2 tptp.code_integer) (A2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) A2) (= (@ (@ tptp.ord_min_Code_integer A2) B2) B2))))
% 3.70/4.04 (assert (forall ((B2 tptp.assn) (A2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn B2) A2) (= (@ (@ tptp.ord_min_assn A2) B2) B2))))
% 3.70/4.04 (assert (forall ((B2 tptp.num) (A2 tptp.num)) (=> (@ (@ tptp.ord_less_num B2) A2) (= (@ (@ tptp.ord_min_num A2) B2) B2))))
% 3.70/4.04 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A2) (= (@ (@ tptp.ord_min_nat A2) B2) B2))))
% 3.70/4.04 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A2) (= (@ (@ tptp.ord_min_int A2) B2) B2))))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_mi6693596345299712430at_nat X) tptp.bot_bo228742789529271731at_nat) tptp.bot_bo228742789529271731at_nat)))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_mi4194197829855655752at_nat X) tptp.bot_bo2099793752762293965at_nat) tptp.bot_bo2099793752762293965at_nat)))
% 3.70/4.04 (assert (forall ((X tptp.set_o)) (= (@ (@ tptp.ord_min_set_o X) tptp.bot_bot_set_o) tptp.bot_bot_set_o)))
% 3.70/4.04 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.ord_min_set_nat X) tptp.bot_bot_set_nat) tptp.bot_bot_set_nat)))
% 3.70/4.04 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.ord_min_set_int X) tptp.bot_bot_set_int) tptp.bot_bot_set_int)))
% 3.70/4.04 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.ord_min_nat X) tptp.bot_bot_nat) tptp.bot_bot_nat)))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_mi6693596345299712430at_nat tptp.bot_bo228742789529271731at_nat) X) tptp.bot_bo228742789529271731at_nat)))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_mi4194197829855655752at_nat tptp.bot_bo2099793752762293965at_nat) X) tptp.bot_bo2099793752762293965at_nat)))
% 3.70/4.04 (assert (forall ((X tptp.set_o)) (= (@ (@ tptp.ord_min_set_o tptp.bot_bot_set_o) X) tptp.bot_bot_set_o)))
% 3.70/4.04 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.ord_min_set_nat tptp.bot_bot_set_nat) X) tptp.bot_bot_set_nat)))
% 3.70/4.04 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.ord_min_set_int tptp.bot_bot_set_int) X) tptp.bot_bot_set_int)))
% 3.70/4.04 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.ord_min_nat tptp.bot_bot_nat) X) tptp.bot_bot_nat)))
% 3.70/4.04 (assert (forall ((T3 tptp.set_Pr1261947904930325089at_nat) (S tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat T3) (@ (@ tptp.inf_in2572325071724192079at_nat S) T3)) T3)))
% 3.70/4.04 (assert (forall ((T3 tptp.set_nat) (S tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat T3) (@ (@ tptp.inf_inf_set_nat S) T3)) T3)))
% 3.70/4.04 (assert (forall ((T3 tptp.set_Pr4329608150637261639at_nat) (S tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat T3) (@ (@ tptp.inf_in7913087082777306421at_nat S) T3)) T3)))
% 3.70/4.04 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat S) (@ (@ tptp.inf_in2572325071724192079at_nat S) T3)) S)))
% 3.70/4.04 (assert (forall ((S tptp.set_nat) (T3 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat S) (@ (@ tptp.inf_inf_set_nat S) T3)) S)))
% 3.70/4.04 (assert (forall ((S tptp.set_Pr4329608150637261639at_nat) (T3 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat S) (@ (@ tptp.inf_in7913087082777306421at_nat S) T3)) S)))
% 3.70/4.04 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat S) T3)) T3) T3)))
% 3.70/4.04 (assert (forall ((S tptp.set_nat) (T3 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat S) T3)) T3) T3)))
% 3.70/4.04 (assert (forall ((S tptp.set_Pr4329608150637261639at_nat) (T3 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat S) T3)) T3) T3)))
% 3.70/4.04 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat S) T3)) S) S)))
% 3.70/4.04 (assert (forall ((S tptp.set_nat) (T3 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat S) T3)) S) S)))
% 3.70/4.04 (assert (forall ((S tptp.set_Pr4329608150637261639at_nat) (T3 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat S) T3)) S) S)))
% 3.70/4.04 (assert (forall ((T3 tptp.set_Pr1261947904930325089at_nat) (S tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat T3) (@ (@ tptp.sup_su6327502436637775413at_nat S) T3)) T3)))
% 3.70/4.04 (assert (forall ((T3 tptp.set_nat) (S tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat T3) (@ (@ tptp.sup_sup_set_nat S) T3)) T3)))
% 3.70/4.04 (assert (forall ((T3 tptp.set_Pr4329608150637261639at_nat) (S tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat T3) (@ (@ tptp.sup_su5525570899277871387at_nat S) T3)) T3)))
% 3.70/4.04 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat S) (@ (@ tptp.sup_su6327502436637775413at_nat S) T3)) S)))
% 3.70/4.04 (assert (forall ((S tptp.set_nat) (T3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat S) (@ (@ tptp.sup_sup_set_nat S) T3)) S)))
% 3.70/4.04 (assert (forall ((S tptp.set_Pr4329608150637261639at_nat) (T3 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat S) (@ (@ tptp.sup_su5525570899277871387at_nat S) T3)) S)))
% 3.70/4.04 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat S) T3)) T3) T3)))
% 3.70/4.04 (assert (forall ((S tptp.set_nat) (T3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat S) T3)) T3) T3)))
% 3.70/4.04 (assert (forall ((S tptp.set_Pr4329608150637261639at_nat) (T3 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.sup_su5525570899277871387at_nat S) T3)) T3) T3)))
% 3.70/4.04 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat S) T3)) S) S)))
% 3.70/4.04 (assert (forall ((S tptp.set_nat) (T3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat S) T3)) S) S)))
% 3.70/4.04 (assert (forall ((S tptp.set_Pr4329608150637261639at_nat) (T3 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.sup_su5525570899277871387at_nat S) T3)) S) S)))
% 3.70/4.04 (assert (forall ((B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.minus_3314409938677909166at_nat B) A)) A) (@ (@ tptp.sup_su5525570899277871387at_nat B) A))))
% 3.70/4.04 (assert (forall ((B tptp.set_nat) (A tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.minus_minus_set_nat B) A)) A) (@ (@ tptp.sup_sup_set_nat B) A))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat A))) (= (@ _let_1 (@ (@ tptp.minus_3314409938677909166at_nat B) A)) (@ _let_1 B)))))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat B) A)) (@ _let_1 B)))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_int)) (= (@ tptp.set_int2 (@ tptp.rev_int Xs)) (@ tptp.set_int2 Xs))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_nat)) (= (@ tptp.set_nat2 (@ tptp.rev_nat Xs)) (@ tptp.set_nat2 Xs))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn)) (= (@ tptp.set_Pr1139785259514867910n_assn (@ tptp.rev_Pr4855572775806611735n_assn Xs)) (@ tptp.set_Pr1139785259514867910n_assn Xs))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_c)) (= (@ tptp.size_size_list_c (@ tptp.rev_c Xs)) (@ tptp.size_size_list_c Xs))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_d)) (= (@ tptp.size_size_list_d (@ tptp.rev_d Xs)) (@ tptp.size_size_list_d Xs))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_nat)) (= (@ tptp.size_size_list_nat (@ tptp.rev_nat Xs)) (@ tptp.size_size_list_nat Xs))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_int)) (= (@ tptp.size_size_list_int (@ tptp.rev_int Xs)) (@ tptp.size_size_list_int Xs))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_int)) (= (@ tptp.distinct_int (@ tptp.rev_int Xs)) (@ tptp.distinct_int Xs))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_nat)) (= (@ tptp.distinct_nat (@ tptp.rev_nat Xs)) (@ tptp.distinct_nat Xs))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_int)) (= (@ tptp.set_int2 (@ tptp.rotate1_int Xs)) (@ tptp.set_int2 Xs))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_nat)) (= (@ tptp.set_nat2 (@ tptp.rotate1_nat Xs)) (@ tptp.set_nat2 Xs))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn)) (= (@ tptp.set_Pr1139785259514867910n_assn (@ tptp.rotate328796349445179396n_assn Xs)) (@ tptp.set_Pr1139785259514867910n_assn Xs))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_c)) (= (@ tptp.size_size_list_c (@ tptp.rotate1_c Xs)) (@ tptp.size_size_list_c Xs))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_d)) (= (@ tptp.size_size_list_d (@ tptp.rotate1_d Xs)) (@ tptp.size_size_list_d Xs))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_nat)) (= (@ tptp.size_size_list_nat (@ tptp.rotate1_nat Xs)) (@ tptp.size_size_list_nat Xs))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_int)) (= (@ tptp.size_size_list_int (@ tptp.rotate1_int Xs)) (@ tptp.size_size_list_int Xs))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_int)) (= (@ tptp.distinct_int (@ tptp.rotate1_int Xs)) (@ tptp.distinct_int Xs))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_nat)) (= (@ tptp.distinct_nat (@ tptp.rotate1_nat Xs)) (@ tptp.distinct_nat Xs))))
% 3.70/4.04 (assert (forall ((P (-> tptp.int Bool)) (Xs tptp.list_int)) (let ((_let_1 (@ tptp.list_ex_int P))) (= (@ _let_1 (@ tptp.rev_int Xs)) (@ _let_1 Xs)))))
% 3.70/4.04 (assert (forall ((P (-> tptp.nat Bool)) (Xs tptp.list_nat)) (let ((_let_1 (@ tptp.list_ex_nat P))) (= (@ _let_1 (@ tptp.rev_nat Xs)) (@ _let_1 Xs)))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (= (@ tptp.set_int2 (@ (@ tptp.union_int Xs) Ys)) (@ (@ tptp.sup_sup_set_int (@ tptp.set_int2 Xs)) (@ tptp.set_int2 Ys)))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_P8527749157015355191n_assn)) (= (@ tptp.set_Pr1139785259514867910n_assn (@ (@ tptp.union_944050417204428971n_assn Xs) Ys)) (@ (@ tptp.sup_su1735938885662425829n_assn (@ tptp.set_Pr1139785259514867910n_assn Xs)) (@ tptp.set_Pr1139785259514867910n_assn Ys)))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (= (@ tptp.set_nat2 (@ (@ tptp.union_nat Xs) Ys)) (@ (@ tptp.sup_sup_set_nat (@ tptp.set_nat2 Xs)) (@ tptp.set_nat2 Ys)))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_P5464809261938338413at_nat) (Ys tptp.list_P5464809261938338413at_nat)) (= (@ tptp.set_Pr3765526544606949372at_nat (@ (@ tptp.union_4462254032241401953at_nat Xs) Ys)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ tptp.set_Pr3765526544606949372at_nat Xs)) (@ tptp.set_Pr3765526544606949372at_nat Ys)))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_c)) (= (@ tptp.size_size_list_c (@ tptp.butlast_c Xs)) (@ (@ tptp.minus_minus_nat (@ tptp.size_size_list_c Xs)) tptp.one_one_nat))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_d)) (= (@ tptp.size_size_list_d (@ tptp.butlast_d Xs)) (@ (@ tptp.minus_minus_nat (@ tptp.size_size_list_d Xs)) tptp.one_one_nat))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_nat)) (= (@ tptp.size_size_list_nat (@ tptp.butlast_nat Xs)) (@ (@ tptp.minus_minus_nat (@ tptp.size_size_list_nat Xs)) tptp.one_one_nat))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_int)) (= (@ tptp.size_size_list_int (@ tptp.butlast_int Xs)) (@ (@ tptp.minus_minus_nat (@ tptp.size_size_list_int Xs)) tptp.one_one_nat))))
% 3.70/4.04 (assert (forall ((C tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat A) B)) (not (=> (@ _let_1 A) (not (@ _let_1 B))))))))
% 3.70/4.04 (assert (forall ((C tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_int A) B)) (not (=> (@ _let_1 A) (not (@ _let_1 B))))))))
% 3.70/4.04 (assert (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ _let_1 (@ (@ tptp.inf_in1906310914598751387_nat_o A) B)) (not (=> (@ _let_1 A) (not (@ _let_1 B))))))))
% 3.70/4.04 (assert (forall ((C tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B)) (not (=> (@ _let_1 A) (not (@ _let_1 B))))))))
% 3.70/4.04 (assert (forall ((C tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) (not (=> (@ _let_1 A) (not (@ _let_1 B))))))))
% 3.70/4.04 (assert (forall ((C tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat A) B)) (@ _let_1 A)))))
% 3.70/4.04 (assert (forall ((C tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_int A) B)) (@ _let_1 A)))))
% 3.70/4.04 (assert (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ _let_1 (@ (@ tptp.inf_in1906310914598751387_nat_o A) B)) (@ _let_1 A)))))
% 3.70/4.04 (assert (forall ((C tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B)) (@ _let_1 A)))))
% 3.70/4.04 (assert (forall ((C tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) (@ _let_1 A)))))
% 3.70/4.04 (assert (forall ((C tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat A) B)) (@ _let_1 B)))))
% 3.70/4.04 (assert (forall ((C tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_int A) B)) (@ _let_1 B)))))
% 3.70/4.04 (assert (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ _let_1 (@ (@ tptp.inf_in1906310914598751387_nat_o A) B)) (@ _let_1 B)))))
% 3.70/4.04 (assert (forall ((C tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B)) (@ _let_1 B)))))
% 3.70/4.04 (assert (forall ((C tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) (@ _let_1 B)))))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (= (@ (@ tptp.inf_inf_set_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.inf_inf_set_nat B) C2))))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A))) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B) C2))))))
% 3.70/4.04 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A) A) A)))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A) A) A)))
% 3.70/4.04 (assert (= tptp.inf_inf_set_nat (lambda ((A5 tptp.set_nat) (B7 tptp.set_nat)) (@ (@ tptp.inf_inf_set_nat B7) A5))))
% 3.70/4.04 (assert (= tptp.inf_in2572325071724192079at_nat (lambda ((A5 tptp.set_Pr1261947904930325089at_nat) (B7 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.inf_in2572325071724192079at_nat B7) A5))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) (@ (@ tptp.inf_in2572325071724192079at_nat B) C2))) (@ (@ tptp.inf_in2572325071724192079at_nat C2) A)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat A) B)) (@ (@ tptp.sup_su6327502436637775413at_nat B) C2))) (@ (@ tptp.sup_su6327502436637775413at_nat C2) A)))))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) (@ (@ tptp.inf_inf_set_nat B) C2))) (@ (@ tptp.inf_inf_set_nat C2) A)) (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat A) B)) (@ (@ tptp.sup_sup_set_nat B) C2))) (@ (@ tptp.sup_sup_set_nat C2) A)))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat A) B)) (@ (@ tptp.inf_in7913087082777306421at_nat B) C2))) (@ (@ tptp.inf_in7913087082777306421at_nat C2) A)) (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A) B)) (@ (@ tptp.sup_su5525570899277871387at_nat B) C2))) (@ (@ tptp.sup_su5525570899277871387at_nat C2) A)))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A))) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat B) C2)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 B)) (@ _let_1 C2))))))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat B) C2)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 B)) (@ _let_1 C2))))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.inf_in7913087082777306421at_nat A))) (= (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat B) C2)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 B)) (@ _let_1 C2))))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.sup_su6327502436637775413at_nat A))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B) C2)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 B)) (@ _let_1 C2))))))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat B) C2)) (@ (@ tptp.inf_inf_set_nat (@ _let_1 B)) (@ _let_1 C2))))))
% 3.70/4.04 (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))) (= (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat B) C2)) (@ (@ tptp.inf_in7913087082777306421at_nat (@ _let_1 B)) (@ _let_1 C2))))))
% 3.70/4.04 (assert (forall ((B tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat B) C2)) A) (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat B) A)) (@ (@ tptp.inf_in2572325071724192079at_nat C2) A)))))
% 3.70/4.04 (assert (forall ((B tptp.set_nat) (C2 tptp.set_nat) (A tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat B) C2)) A) (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat B) A)) (@ (@ tptp.inf_inf_set_nat C2) A)))))
% 3.70/4.04 (assert (forall ((B tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.sup_su5525570899277871387at_nat B) C2)) A) (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat B) A)) (@ (@ tptp.inf_in7913087082777306421at_nat C2) A)))))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 3.70/4.04 (assert (forall ((B tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat B) C2)) A) (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat B) A)) (@ (@ tptp.sup_su6327502436637775413at_nat C2) A)))))
% 3.70/4.04 (assert (forall ((B tptp.set_nat) (C2 tptp.set_nat) (A tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat B) C2)) A) (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat B) A)) (@ (@ tptp.sup_sup_set_nat C2) A)))))
% 3.70/4.04 (assert (forall ((B tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat B) C2)) A) (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.sup_su5525570899277871387at_nat B) A)) (@ (@ tptp.sup_su5525570899277871387at_nat C2) A)))))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (let ((_let_2 (@ tptp.inf_inf_set_nat B))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A))) (let ((_let_2 (@ tptp.inf_in2572325071724192079at_nat B))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 3.70/4.04 (assert (= tptp.ord_less_assn (lambda ((A3 tptp.assn) (B3 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn A3) B3) (not (= A3 B3))))))
% 3.70/4.04 (assert (forall ((C tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat A) B)) (=> (not (@ _let_1 A)) (@ _let_1 B))))))
% 3.70/4.04 (assert (forall ((C tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.sup_sup_set_int A) B)) (=> (not (@ _let_1 A)) (@ _let_1 B))))))
% 3.70/4.04 (assert (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ _let_1 (@ (@ tptp.sup_su5209123915105501825_nat_o A) B)) (=> (not (@ _let_1 A)) (@ _let_1 B))))))
% 3.70/4.04 (assert (forall ((C tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B)) (=> (not (@ _let_1 A)) (@ _let_1 B))))))
% 3.70/4.04 (assert (forall ((C tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (=> (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A) B)) (=> (not (@ _let_1 A)) (@ _let_1 B))))))
% 3.70/4.04 (assert (forall ((C tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat A) B))))))
% 3.70/4.04 (assert (forall ((C tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_set_int A) B))))))
% 3.70/4.04 (assert (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su5209123915105501825_nat_o A) B))))))
% 3.70/4.04 (assert (forall ((C tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B))))))
% 3.70/4.04 (assert (forall ((C tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A) B))))))
% 3.70/4.04 (assert (forall ((C tptp.product_prod_nat_nat) (B tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat A) B))))))
% 3.70/4.04 (assert (forall ((C tptp.int) (B tptp.set_int) (A tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_set_int A) B))))))
% 3.70/4.04 (assert (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.set_Pr4532377907799695533_nat_o) (A tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su5209123915105501825_nat_o A) B))))))
% 3.70/4.04 (assert (forall ((C tptp.nat) (B tptp.set_nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B))))))
% 3.70/4.04 (assert (forall ((C tptp.produc3843707927480180839at_nat) (B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A) B))))))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (P (-> tptp.nat Bool))) (= (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) (@ (@ tptp.sup_sup_set_nat A) B)) (@ P X2))) (or (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A) (@ P X2))) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) B) (@ P X2)))))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (P (-> tptp.produc3843707927480180839at_nat Bool))) (= (exists ((X2 tptp.produc3843707927480180839at_nat)) (and (@ (@ tptp.member8757157785044589968at_nat X2) (@ (@ tptp.sup_su5525570899277871387at_nat A) B)) (@ P X2))) (or (exists ((X2 tptp.produc3843707927480180839at_nat)) (and (@ (@ tptp.member8757157785044589968at_nat X2) A) (@ P X2))) (exists ((X2 tptp.produc3843707927480180839at_nat)) (and (@ (@ tptp.member8757157785044589968at_nat X2) B) (@ P X2)))))))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (P (-> tptp.nat Bool))) (= (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.sup_sup_set_nat A) B)) (@ P X2))) (and (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A) (@ P X2))) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) B) (@ P X2)))))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (P (-> tptp.produc3843707927480180839at_nat Bool))) (= (forall ((X2 tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X2) (@ (@ tptp.sup_su5525570899277871387at_nat A) B)) (@ P X2))) (and (forall ((X2 tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X2) A) (@ P X2))) (forall ((X2 tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X2) B) (@ P X2)))))))
% 3.70/4.04 (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))))))
% 3.70/4.04 (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))))))
% 3.70/4.04 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A) A) A)))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat A) A) A)))
% 3.70/4.04 (assert (= tptp.sup_sup_set_nat (lambda ((A5 tptp.set_nat) (B7 tptp.set_nat)) (@ (@ tptp.sup_sup_set_nat B7) A5))))
% 3.70/4.04 (assert (= tptp.sup_su5525570899277871387at_nat (lambda ((A5 tptp.set_Pr4329608150637261639at_nat) (B7 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.sup_su5525570899277871387at_nat B7) A5))))
% 3.70/4.04 (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)))))
% 3.70/4.04 (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)))))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A))) (let ((_let_2 (@ tptp.sup_sup_set_nat B))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 3.70/4.04 (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))) (let ((_let_2 (@ tptp.sup_su5525570899277871387at_nat B))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 3.70/4.04 (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)))))
% 3.70/4.04 (assert (forall ((X tptp.assn) (Y tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 3.70/4.04 (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)))))
% 3.70/4.04 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (let ((_let_2 (@ tptp.sup_sup_set_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 3.70/4.04 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (let ((_let_2 (@ tptp.sup_sup_assn Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat X))) (let ((_let_2 (@ tptp.sup_su5525570899277871387at_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 3.70/4.04 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_sup_set_nat Y) Z))))))
% 3.70/4.04 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (= (@ (@ tptp.sup_sup_assn (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_sup_assn Y) Z))))))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat X))) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat Y) Z))))))
% 3.70/4.04 (assert (= tptp.sup_sup_set_nat (lambda ((X2 tptp.set_nat) (Y5 tptp.set_nat)) (@ (@ tptp.sup_sup_set_nat Y5) X2))))
% 3.70/4.04 (assert (= tptp.sup_sup_assn (lambda ((X2 tptp.assn) (Y5 tptp.assn)) (@ (@ tptp.sup_sup_assn Y5) X2))))
% 3.70/4.04 (assert (= tptp.sup_su5525570899277871387at_nat (lambda ((X2 tptp.set_Pr4329608150637261639at_nat) (Y5 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.sup_su5525570899277871387at_nat Y5) X2))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_min_nat A2))) (= (@ (@ tptp.ord_min_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.ord_min_nat B2) C))))))
% 3.70/4.04 (assert (= tptp.ord_min_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.ord_min_nat B3) A3))))
% 3.70/4.04 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_min_nat B2))) (let ((_let_2 (@ tptp.ord_min_nat A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A2))) (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.sup_sup_set_nat B2) C))))))
% 3.70/4.04 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn A2))) (= (@ (@ tptp.sup_sup_assn (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.sup_sup_assn B2) C))))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat) (C tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat A2))) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat B2) C))))))
% 3.70/4.04 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_sup_set_nat Y) Z))))))
% 3.70/4.04 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (= (@ (@ tptp.sup_sup_assn (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_sup_assn Y) Z))))))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat X))) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat Y) Z))))))
% 3.70/4.04 (assert (= tptp.sup_sup_set_nat (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (@ (@ tptp.sup_sup_set_nat B3) A3))))
% 3.70/4.04 (assert (= tptp.sup_sup_assn (lambda ((A3 tptp.assn) (B3 tptp.assn)) (@ (@ tptp.sup_sup_assn B3) A3))))
% 3.70/4.04 (assert (= tptp.sup_su5525570899277871387at_nat (lambda ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.sup_su5525570899277871387at_nat B3) A3))))
% 3.70/4.04 (assert (= tptp.sup_sup_set_nat (lambda ((X2 tptp.set_nat) (Y5 tptp.set_nat)) (@ (@ tptp.sup_sup_set_nat Y5) X2))))
% 3.70/4.04 (assert (= tptp.sup_sup_assn (lambda ((X2 tptp.assn) (Y5 tptp.assn)) (@ (@ tptp.sup_sup_assn Y5) X2))))
% 3.70/4.04 (assert (= tptp.sup_su5525570899277871387at_nat (lambda ((X2 tptp.set_Pr4329608150637261639at_nat) (Y5 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.sup_su5525570899277871387at_nat Y5) X2))))
% 3.70/4.04 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat B2))) (let ((_let_2 (@ tptp.sup_sup_set_nat A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 3.70/4.04 (assert (forall ((B2 tptp.assn) (A2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn B2))) (let ((_let_2 (@ tptp.sup_sup_assn A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 3.70/4.04 (assert (forall ((B2 tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat) (C tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat B2))) (let ((_let_2 (@ tptp.sup_su5525570899277871387at_nat A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 3.70/4.04 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (let ((_let_2 (@ tptp.sup_sup_set_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 3.70/4.04 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (let ((_let_2 (@ tptp.sup_sup_assn Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat X))) (let ((_let_2 (@ tptp.sup_su5525570899277871387at_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_c)) (=> (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_c Ys)) (= (@ (@ tptp.zip_c_c (@ tptp.rev_c Xs)) (@ tptp.rev_c Ys)) (@ tptp.rev_Product_prod_c_c (@ (@ tptp.zip_c_c Xs) Ys))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_d)) (=> (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_d Ys)) (= (@ (@ tptp.zip_c_d (@ tptp.rev_c Xs)) (@ tptp.rev_d Ys)) (@ tptp.rev_Product_prod_c_d (@ (@ tptp.zip_c_d Xs) Ys))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_nat)) (=> (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_nat Ys)) (= (@ (@ tptp.zip_c_nat (@ tptp.rev_c Xs)) (@ tptp.rev_nat Ys)) (@ tptp.rev_Pr3799340238495523993_c_nat (@ (@ tptp.zip_c_nat Xs) Ys))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_int)) (=> (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_int Ys)) (= (@ (@ tptp.zip_c_int (@ tptp.rev_c Xs)) (@ tptp.rev_int Ys)) (@ tptp.rev_Pr8844861255841103093_c_int (@ (@ tptp.zip_c_int Xs) Ys))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_d) (Ys tptp.list_c)) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_c Ys)) (= (@ (@ tptp.zip_d_c (@ tptp.rev_d Xs)) (@ tptp.rev_c Ys)) (@ tptp.rev_Product_prod_d_c (@ (@ tptp.zip_d_c Xs) Ys))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_d) (Ys tptp.list_d)) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_d Ys)) (= (@ (@ tptp.zip_d_d (@ tptp.rev_d Xs)) (@ tptp.rev_d Ys)) (@ tptp.rev_Product_prod_d_d (@ (@ tptp.zip_d_d Xs) Ys))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_d) (Ys tptp.list_nat)) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_nat Ys)) (= (@ (@ tptp.zip_d_nat (@ tptp.rev_d Xs)) (@ tptp.rev_nat Ys)) (@ tptp.rev_Pr5034784567451918490_d_nat (@ (@ tptp.zip_d_nat Xs) Ys))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_d) (Ys tptp.list_int)) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_int Ys)) (= (@ (@ tptp.zip_d_int (@ tptp.rev_d Xs)) (@ tptp.rev_int Ys)) (@ tptp.rev_Pr856933547942721782_d_int (@ (@ tptp.zip_d_int Xs) Ys))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_c)) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_c Ys)) (= (@ (@ tptp.zip_nat_c (@ tptp.rev_nat Xs)) (@ tptp.rev_c Ys)) (@ tptp.rev_Pr4566615052912869567_nat_c (@ (@ tptp.zip_nat_c Xs) Ys))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_d)) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_d Ys)) (= (@ (@ tptp.zip_nat_d (@ tptp.rev_nat Xs)) (@ tptp.rev_d Ys)) (@ tptp.rev_Pr4566615057216098368_nat_d (@ (@ tptp.zip_nat_d Xs) Ys))))))
% 3.70/4.04 (assert (forall ((Ns tptp.list_nat) (I tptp.nat)) (=> (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) Ns) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Ns)) (@ (@ tptp.ord_less_eq_nat I) (@ (@ tptp.nth_nat Ns) I))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_P5464809261938338413at_nat) (P (-> tptp.produc3843707927480180839at_nat tptp.produc3843707927480180839at_nat Bool)) (Q (-> tptp.produc3843707927480180839at_nat tptp.produc3843707927480180839at_nat Bool))) (=> (forall ((X3 tptp.produc3843707927480180839at_nat) (Y2 tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.set_Pr3765526544606949372at_nat Xs))) (=> (@ (@ tptp.member8757157785044589968at_nat X3) _let_1) (=> (@ (@ tptp.member8757157785044589968at_nat Y2) _let_1) (=> (@ (@ P X3) Y2) (@ (@ Q X3) Y2)))))) (=> (@ (@ tptp.sorted8831241538929206612at_nat P) Xs) (@ (@ tptp.sorted8831241538929206612at_nat Q) Xs)))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_P6011104703257516679at_nat) (P (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (Q (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool))) (=> (forall ((X3 tptp.product_prod_nat_nat) (Y2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.set_Pr5648618587558075414at_nat Xs))) (=> (@ (@ tptp.member8440522571783428010at_nat X3) _let_1) (=> (@ (@ tptp.member8440522571783428010at_nat Y2) _let_1) (=> (@ (@ P X3) Y2) (@ (@ Q X3) Y2)))))) (=> (@ (@ tptp.sorted5214655850825725294at_nat P) Xs) (@ (@ tptp.sorted5214655850825725294at_nat Q) Xs)))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_P7985473006766602707_nat_o) (P (-> (-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) Bool)) (Q (-> (-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.set_Pr400311997697478754_nat_o Xs))) (=> (@ (@ tptp.member6576561426505652726_nat_o X3) _let_1) (=> (@ (@ tptp.member6576561426505652726_nat_o Y2) _let_1) (=> (@ (@ P X3) Y2) (@ (@ Q X3) Y2)))))) (=> (@ (@ tptp.sorted9199660237762088378_nat_o P) Xs) (@ (@ tptp.sorted9199660237762088378_nat_o Q) Xs)))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (P (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn Bool)) (Q (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn Bool))) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Y2 tptp.produc6575502325842934193n_assn)) (let ((_let_1 (@ tptp.set_Pr1139785259514867910n_assn Xs))) (=> (@ (@ tptp.member7957490590177025114n_assn X3) _let_1) (=> (@ (@ tptp.member7957490590177025114n_assn Y2) _let_1) (=> (@ (@ P X3) Y2) (@ (@ Q X3) Y2)))))) (=> (@ (@ tptp.sorted3986126766855596574n_assn P) Xs) (@ (@ tptp.sorted3986126766855596574n_assn Q) Xs)))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_nat) (P (-> tptp.nat tptp.nat Bool)) (Q (-> tptp.nat tptp.nat Bool))) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.set_nat2 Xs))) (=> (@ (@ tptp.member_nat X3) _let_1) (=> (@ (@ tptp.member_nat Y2) _let_1) (=> (@ (@ P X3) Y2) (@ (@ Q X3) Y2)))))) (=> (@ (@ tptp.sorted_wrt_nat P) Xs) (@ (@ tptp.sorted_wrt_nat Q) Xs)))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_int) (P (-> tptp.int tptp.int Bool)) (Q (-> tptp.int tptp.int Bool))) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.set_int2 Xs))) (=> (@ (@ tptp.member_int X3) _let_1) (=> (@ (@ tptp.member_int Y2) _let_1) (=> (@ (@ P X3) Y2) (@ (@ Q X3) Y2)))))) (=> (@ (@ tptp.sorted_wrt_int P) Xs) (@ (@ tptp.sorted_wrt_int Q) Xs)))))
% 3.70/4.04 (assert (= tptp.ord_min_assn (lambda ((A3 tptp.assn) (B3 tptp.assn)) (@ (@ (@ tptp.if_assn (@ (@ tptp.ord_less_eq_assn A3) B3)) A3) B3))))
% 3.70/4.04 (assert (= tptp.ord_min_filter_nat (lambda ((A3 tptp.filter_nat) (B3 tptp.filter_nat)) (@ (@ (@ tptp.if_filter_nat (@ (@ tptp.ord_le2510731241096832064er_nat A3) B3)) A3) B3))))
% 3.70/4.04 (assert (= tptp.ord_min_set_nat (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (@ (@ (@ tptp.if_set_nat (@ (@ tptp.ord_less_eq_set_nat A3) B3)) A3) B3))))
% 3.70/4.04 (assert (= tptp.ord_min_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A3) B3)) A3) B3))))
% 3.70/4.04 (assert (= tptp.ord_min_int (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A3) B3)) A3) B3))))
% 3.70/4.04 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X) Y) (= (@ (@ tptp.ord_min_assn X) Y) X))))
% 3.70/4.04 (assert (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat X) Y) (= (@ (@ tptp.ord_min_filter_nat X) Y) X))))
% 3.70/4.04 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (= (@ (@ tptp.ord_min_set_nat X) Y) X))))
% 3.70/4.04 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (@ (@ tptp.ord_min_nat X) Y) X))))
% 3.70/4.04 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (@ (@ tptp.ord_min_int X) Y) X))))
% 3.70/4.04 (assert (forall ((Y tptp.assn) (X tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn Y) X) (= (@ (@ tptp.ord_min_assn X) Y) Y))))
% 3.70/4.04 (assert (forall ((Y tptp.filter_nat) (X tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat Y) X) (= (@ (@ tptp.ord_min_filter_nat X) Y) Y))))
% 3.70/4.04 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (= (@ (@ tptp.ord_min_set_nat X) Y) Y))))
% 3.70/4.04 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.ord_min_nat X) Y) Y))))
% 3.70/4.04 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.ord_min_int X) Y) Y))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B2 tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) C) (=> (@ (@ tptp.ord_less_eq_nat B2) D2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_min_nat A2) B2)) (@ (@ tptp.ord_min_nat C) D2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) C) (=> (@ (@ tptp.ord_less_eq_int B2) D2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_min_int A2) B2)) (@ (@ tptp.ord_min_int C) D2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= A2 (@ (@ tptp.ord_min_nat A2) B2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (= A2 (@ (@ tptp.ord_min_int A2) B2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (= A2 (@ (@ tptp.ord_min_nat A2) B2)) (@ (@ tptp.ord_less_eq_nat A2) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (= A2 (@ (@ tptp.ord_min_int A2) B2)) (@ (@ tptp.ord_less_eq_int A2) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 (@ (@ tptp.ord_min_nat B2) C)) (not (=> (@ _let_1 B2) (not (@ _let_1 C))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A2))) (=> (@ _let_1 (@ (@ tptp.ord_min_int B2) C)) (not (=> (@ _let_1 B2) (not (@ _let_1 C))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.ord_min_nat B2) C)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A2))) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.ord_min_int B2) C)))))))
% 3.70/4.04 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (= A3 (@ (@ tptp.ord_min_nat A3) B3)))))
% 3.70/4.04 (assert (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B3 tptp.int)) (= A3 (@ (@ tptp.ord_min_int A3) B3)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_min_nat A2) B2)) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_min_int A2) B2)) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_min_nat A2) B2)) B2)))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_min_int A2) B2)) B2)))
% 3.70/4.04 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.ord_min_nat A3) B3) A3))))
% 3.70/4.04 (assert (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.ord_min_int A3) B3) A3))))
% 3.70/4.04 (assert (= tptp.ord_less_eq_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (= (@ (@ tptp.ord_min_nat A3) B3) B3))))
% 3.70/4.04 (assert (= tptp.ord_less_eq_int (lambda ((B3 tptp.int) (A3 tptp.int)) (= (@ (@ tptp.ord_min_int A3) B3) B3))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_min_nat A2) B2)) C))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_min_int A2) B2)) C))))
% 3.70/4.04 (assert (forall ((B2 tptp.nat) (C tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_min_nat A2) B2)) C))))
% 3.70/4.04 (assert (forall ((B2 tptp.int) (C tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_min_int A2) B2)) C))))
% 3.70/4.04 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_min_nat X) Y)) Z) (or (@ (@ tptp.ord_less_eq_nat X) Z) (@ (@ tptp.ord_less_eq_nat Y) Z)))))
% 3.70/4.04 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_min_int X) Y)) Z) (or (@ (@ tptp.ord_less_eq_int X) Z) (@ (@ tptp.ord_less_eq_int Y) Z)))))
% 3.70/4.04 (assert (forall ((B2 tptp.code_integer) (C tptp.code_integer) (A2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.ord_min_Code_integer A2) B2)) C))))
% 3.70/4.04 (assert (forall ((B2 tptp.num) (C tptp.num) (A2 tptp.num)) (=> (@ (@ tptp.ord_less_num B2) C) (@ (@ tptp.ord_less_num (@ (@ tptp.ord_min_num A2) B2)) C))))
% 3.70/4.04 (assert (forall ((B2 tptp.nat) (C tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_min_nat A2) B2)) C))))
% 3.70/4.04 (assert (forall ((B2 tptp.int) (C tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int B2) C) (@ (@ tptp.ord_less_int (@ (@ tptp.ord_min_int A2) B2)) C))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.ord_min_Code_integer A2) B2)) C))))
% 3.70/4.04 (assert (forall ((A2 tptp.num) (C tptp.num) (B2 tptp.num)) (=> (@ (@ tptp.ord_less_num A2) C) (@ (@ tptp.ord_less_num (@ (@ tptp.ord_min_num A2) B2)) C))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_min_nat A2) B2)) C))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) C) (@ (@ tptp.ord_less_int (@ (@ tptp.ord_min_int A2) B2)) C))))
% 3.70/4.04 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((A3 tptp.code_integer) (B3 tptp.code_integer)) (and (= A3 (@ (@ tptp.ord_min_Code_integer A3) B3)) (not (= A3 B3))))))
% 3.70/4.04 (assert (= tptp.ord_less_num (lambda ((A3 tptp.num) (B3 tptp.num)) (and (= A3 (@ (@ tptp.ord_min_num A3) B3)) (not (= A3 B3))))))
% 3.70/4.04 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (and (= A3 (@ (@ tptp.ord_min_nat A3) B3)) (not (= A3 B3))))))
% 3.70/4.04 (assert (= tptp.ord_less_int (lambda ((A3 tptp.int) (B3 tptp.int)) (and (= A3 (@ (@ tptp.ord_min_int A3) B3)) (not (= A3 B3))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A2))) (=> (@ _let_1 (@ (@ tptp.ord_min_Code_integer B2) C)) (not (=> (@ _let_1 B2) (not (@ _let_1 C))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.num) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A2))) (=> (@ _let_1 (@ (@ tptp.ord_min_num B2) C)) (not (=> (@ _let_1 B2) (not (@ _let_1 C))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 (@ (@ tptp.ord_min_nat B2) C)) (not (=> (@ _let_1 B2) (not (@ _let_1 C))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A2))) (=> (@ _let_1 (@ (@ tptp.ord_min_int B2) C)) (not (=> (@ _let_1 B2) (not (@ _let_1 C))))))))
% 3.70/4.04 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.ord_min_Code_integer X) Y)) Z) (or (@ (@ tptp.ord_le6747313008572928689nteger X) Z) (@ (@ tptp.ord_le6747313008572928689nteger Y) Z)))))
% 3.70/4.04 (assert (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (= (@ (@ tptp.ord_less_num (@ (@ tptp.ord_min_num X) Y)) Z) (or (@ (@ tptp.ord_less_num X) Z) (@ (@ tptp.ord_less_num Y) Z)))))
% 3.70/4.04 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_min_nat X) Y)) Z) (or (@ (@ tptp.ord_less_nat X) Z) (@ (@ tptp.ord_less_nat Y) Z)))))
% 3.70/4.04 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.ord_min_int X) Y)) Z) (or (@ (@ tptp.ord_less_int X) Z) (@ (@ tptp.ord_less_int Y) Z)))))
% 3.70/4.04 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.ord_min_rat X) Y)) Z) (@ (@ tptp.ord_min_rat (@ (@ tptp.minus_minus_rat X) Z)) (@ (@ tptp.minus_minus_rat Y) Z)))))
% 3.70/4.04 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.ord_min_int X) Y)) Z) (@ (@ tptp.ord_min_int (@ (@ tptp.minus_minus_int X) Z)) (@ (@ tptp.minus_minus_int Y) Z)))))
% 3.70/4.04 (assert (forall ((Y tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat Y) (@ (@ tptp.sup_su5525570899277871387at_nat X) Y))))
% 3.70/4.04 (assert (forall ((Y tptp.assn) (X tptp.assn)) (@ (@ tptp.ord_less_eq_assn Y) (@ (@ tptp.sup_sup_assn X) Y))))
% 3.70/4.04 (assert (forall ((Y tptp.filter_nat) (X tptp.filter_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat Y) (@ (@ tptp.sup_sup_filter_nat X) Y))))
% 3.70/4.04 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat Y) (@ (@ tptp.sup_sup_set_nat X) Y))))
% 3.70/4.04 (assert (forall ((Y tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y) (@ (@ tptp.sup_sup_nat X) Y))))
% 3.70/4.04 (assert (forall ((Y tptp.int) (X tptp.int)) (@ (@ tptp.ord_less_eq_int Y) (@ (@ tptp.sup_sup_int X) Y))))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat X) (@ (@ tptp.sup_su5525570899277871387at_nat X) Y))))
% 3.70/4.04 (assert (forall ((X tptp.assn) (Y tptp.assn)) (@ (@ tptp.ord_less_eq_assn X) (@ (@ tptp.sup_sup_assn X) Y))))
% 3.70/4.04 (assert (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat X) (@ (@ tptp.sup_sup_filter_nat X) Y))))
% 3.70/4.04 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X) (@ (@ tptp.sup_sup_set_nat X) Y))))
% 3.70/4.04 (assert (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.sup_sup_nat X) Y))))
% 3.70/4.04 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.sup_sup_int X) Y))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2)) X) (not (=> (@ (@ tptp.ord_le1268244103169919719at_nat A2) X) (not (@ (@ tptp.ord_le1268244103169919719at_nat B2) X)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (X tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.sup_sup_assn A2) B2)) X) (not (=> (@ (@ tptp.ord_less_eq_assn A2) X) (not (@ (@ tptp.ord_less_eq_assn B2) X)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat) (X tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.sup_sup_filter_nat A2) B2)) X) (not (=> (@ (@ tptp.ord_le2510731241096832064er_nat A2) X) (not (@ (@ tptp.ord_le2510731241096832064er_nat B2) X)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat A2) B2)) X) (not (=> (@ (@ tptp.ord_less_eq_set_nat A2) X) (not (@ (@ tptp.ord_less_eq_set_nat B2) X)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat A2) B2)) X) (not (=> (@ (@ tptp.ord_less_eq_nat A2) X) (not (@ (@ tptp.ord_less_eq_nat B2) X)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int A2) B2)) X) (not (=> (@ (@ tptp.ord_less_eq_int A2) X) (not (@ (@ tptp.ord_less_eq_int B2) X)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A2) X) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B2) X) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2)) X)))))
% 3.70/4.04 (assert (forall ((A2 tptp.assn) (X tptp.assn) (B2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A2) X) (=> (@ (@ tptp.ord_less_eq_assn B2) X) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.sup_sup_assn A2) B2)) X)))))
% 3.70/4.04 (assert (forall ((A2 tptp.filter_nat) (X tptp.filter_nat) (B2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat A2) X) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B2) X) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.sup_sup_filter_nat A2) B2)) X)))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_nat) (X tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) X) (=> (@ (@ tptp.ord_less_eq_set_nat B2) X) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat A2) B2)) X)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (X tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) X) (=> (@ (@ tptp.ord_less_eq_nat B2) X) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat A2) B2)) X)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (X tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) X) (=> (@ (@ tptp.ord_less_eq_int B2) X) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int A2) B2)) X)))))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat X) (@ (@ tptp.sup_su5525570899277871387at_nat X) Y))))
% 3.70/4.04 (assert (forall ((X tptp.assn) (Y tptp.assn)) (@ (@ tptp.ord_less_eq_assn X) (@ (@ tptp.sup_sup_assn X) Y))))
% 3.70/4.04 (assert (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat X) (@ (@ tptp.sup_sup_filter_nat X) Y))))
% 3.70/4.04 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X) (@ (@ tptp.sup_sup_set_nat X) Y))))
% 3.70/4.04 (assert (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.sup_sup_nat X) Y))))
% 3.70/4.04 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.sup_sup_int X) Y))))
% 3.70/4.04 (assert (forall ((Y tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat Y) (@ (@ tptp.sup_su5525570899277871387at_nat X) Y))))
% 3.70/4.04 (assert (forall ((Y tptp.assn) (X tptp.assn)) (@ (@ tptp.ord_less_eq_assn Y) (@ (@ tptp.sup_sup_assn X) Y))))
% 3.70/4.04 (assert (forall ((Y tptp.filter_nat) (X tptp.filter_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat Y) (@ (@ tptp.sup_sup_filter_nat X) Y))))
% 3.70/4.04 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat Y) (@ (@ tptp.sup_sup_set_nat X) Y))))
% 3.70/4.04 (assert (forall ((Y tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y) (@ (@ tptp.sup_sup_nat X) Y))))
% 3.70/4.04 (assert (forall ((Y tptp.int) (X tptp.int)) (@ (@ tptp.ord_less_eq_int Y) (@ (@ tptp.sup_sup_int X) Y))))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le1268244103169919719at_nat X))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2))))))
% 3.70/4.04 (assert (forall ((X tptp.assn) (A2 tptp.assn) (B2 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn X))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_assn A2) B2))))))
% 3.70/4.04 (assert (forall ((X tptp.filter_nat) (A2 tptp.filter_nat) (B2 tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_le2510731241096832064er_nat X))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_filter_nat A2) B2))))))
% 3.70/4.04 (assert (forall ((X tptp.set_nat) (A2 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A2) B2))))))
% 3.70/4.04 (assert (forall ((X tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_nat A2) B2))))))
% 3.70/4.04 (assert (forall ((X tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_int A2) B2))))))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le1268244103169919719at_nat X))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2))))))
% 3.70/4.04 (assert (forall ((X tptp.assn) (B2 tptp.assn) (A2 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn X))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_assn A2) B2))))))
% 3.70/4.04 (assert (forall ((X tptp.filter_nat) (B2 tptp.filter_nat) (A2 tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_le2510731241096832064er_nat X))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_filter_nat A2) B2))))))
% 3.70/4.04 (assert (forall ((X tptp.set_nat) (B2 tptp.set_nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A2) B2))))))
% 3.70/4.04 (assert (forall ((X tptp.nat) (B2 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_nat A2) B2))))))
% 3.70/4.04 (assert (forall ((X tptp.int) (B2 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_int A2) B2))))))
% 3.70/4.04 (assert (forall ((C tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat) (D2 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat C) A2) (=> (@ (@ tptp.ord_le1268244103169919719at_nat D2) B2) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat C) D2)) (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2))))))
% 3.70/4.04 (assert (forall ((C tptp.assn) (A2 tptp.assn) (D2 tptp.assn) (B2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn C) A2) (=> (@ (@ tptp.ord_less_eq_assn D2) B2) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.sup_sup_assn C) D2)) (@ (@ tptp.sup_sup_assn A2) B2))))))
% 3.70/4.04 (assert (forall ((C tptp.filter_nat) (A2 tptp.filter_nat) (D2 tptp.filter_nat) (B2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat C) A2) (=> (@ (@ tptp.ord_le2510731241096832064er_nat D2) B2) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.sup_sup_filter_nat C) D2)) (@ (@ tptp.sup_sup_filter_nat A2) B2))))))
% 3.70/4.04 (assert (forall ((C tptp.set_nat) (A2 tptp.set_nat) (D2 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat C) A2) (=> (@ (@ tptp.ord_less_eq_set_nat D2) B2) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat C) D2)) (@ (@ tptp.sup_sup_set_nat A2) B2))))))
% 3.70/4.04 (assert (forall ((C tptp.nat) (A2 tptp.nat) (D2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) A2) (=> (@ (@ tptp.ord_less_eq_nat D2) B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat C) D2)) (@ (@ tptp.sup_sup_nat A2) B2))))))
% 3.70/4.04 (assert (forall ((C tptp.int) (A2 tptp.int) (D2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) A2) (=> (@ (@ tptp.ord_less_eq_int D2) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int C) D2)) (@ (@ tptp.sup_sup_int A2) B2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_Pr4329608150637261639at_nat) (C tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat) (D2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A2) C) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B2) D2) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2)) (@ (@ tptp.sup_su5525570899277871387at_nat C) D2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.assn) (C tptp.assn) (B2 tptp.assn) (D2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A2) C) (=> (@ (@ tptp.ord_less_eq_assn B2) D2) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.sup_sup_assn A2) B2)) (@ (@ tptp.sup_sup_assn C) D2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.filter_nat) (C tptp.filter_nat) (B2 tptp.filter_nat) (D2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat A2) C) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B2) D2) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.sup_sup_filter_nat A2) B2)) (@ (@ tptp.sup_sup_filter_nat C) D2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_nat) (C tptp.set_nat) (B2 tptp.set_nat) (D2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) C) (=> (@ (@ tptp.ord_less_eq_set_nat B2) D2) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat A2) B2)) (@ (@ tptp.sup_sup_set_nat C) D2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B2 tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) C) (=> (@ (@ tptp.ord_less_eq_nat B2) D2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat A2) B2)) (@ (@ tptp.sup_sup_nat C) D2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) C) (=> (@ (@ tptp.ord_less_eq_int B2) D2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int A2) B2)) (@ (@ tptp.sup_sup_int C) D2))))))
% 3.70/4.04 (assert (forall ((Y tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat Y) X) (=> (@ (@ tptp.ord_le1268244103169919719at_nat Z) X) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat Y) Z)) X)))))
% 3.70/4.04 (assert (forall ((Y tptp.assn) (X tptp.assn) (Z tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn Y) X) (=> (@ (@ tptp.ord_less_eq_assn Z) X) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.sup_sup_assn Y) Z)) X)))))
% 3.70/4.04 (assert (forall ((Y tptp.filter_nat) (X tptp.filter_nat) (Z tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat Y) X) (=> (@ (@ tptp.ord_le2510731241096832064er_nat Z) X) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.sup_sup_filter_nat Y) Z)) X)))))
% 3.70/4.04 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat) (Z tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (=> (@ (@ tptp.ord_less_eq_set_nat Z) X) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat Y) Z)) X)))))
% 3.70/4.04 (assert (forall ((Y tptp.nat) (X tptp.nat) (Z tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (=> (@ (@ tptp.ord_less_eq_nat Z) X) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat Y) Z)) X)))))
% 3.70/4.04 (assert (forall ((Y tptp.int) (X tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (=> (@ (@ tptp.ord_less_eq_int Z) X) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int Y) Z)) X)))))
% 3.70/4.04 (assert (= tptp.ord_le1268244103169919719at_nat (lambda ((X2 tptp.set_Pr4329608150637261639at_nat) (Y5 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat X2) Y5) Y5))))
% 3.70/4.04 (assert (= tptp.ord_less_eq_assn (lambda ((X2 tptp.assn) (Y5 tptp.assn)) (= (@ (@ tptp.sup_sup_assn X2) Y5) Y5))))
% 3.70/4.04 (assert (= tptp.ord_le2510731241096832064er_nat (lambda ((X2 tptp.filter_nat) (Y5 tptp.filter_nat)) (= (@ (@ tptp.sup_sup_filter_nat X2) Y5) Y5))))
% 3.70/4.04 (assert (= tptp.ord_less_eq_set_nat (lambda ((X2 tptp.set_nat) (Y5 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat X2) Y5) Y5))))
% 3.70/4.04 (assert (= tptp.ord_less_eq_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (= (@ (@ tptp.sup_sup_nat X2) Y5) Y5))))
% 3.70/4.04 (assert (= tptp.ord_less_eq_int (lambda ((X2 tptp.int) (Y5 tptp.int)) (= (@ (@ tptp.sup_sup_int X2) Y5) Y5))))
% 3.70/4.04 (assert (forall ((B2 tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B2) A2) (= A2 (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2)))))
% 3.70/4.04 (assert (forall ((B2 tptp.assn) (A2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn B2) A2) (= A2 (@ (@ tptp.sup_sup_assn A2) B2)))))
% 3.70/4.04 (assert (forall ((B2 tptp.filter_nat) (A2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B2) A2) (= A2 (@ (@ tptp.sup_sup_filter_nat A2) B2)))))
% 3.70/4.04 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A2) (= A2 (@ (@ tptp.sup_sup_set_nat A2) B2)))))
% 3.70/4.04 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (= A2 (@ (@ tptp.sup_sup_nat A2) B2)))))
% 3.70/4.04 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (= A2 (@ (@ tptp.sup_sup_int A2) B2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (=> (= A2 (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2)) (@ (@ tptp.ord_le1268244103169919719at_nat B2) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.assn) (B2 tptp.assn)) (=> (= A2 (@ (@ tptp.sup_sup_assn A2) B2)) (@ (@ tptp.ord_less_eq_assn B2) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat)) (=> (= A2 (@ (@ tptp.sup_sup_filter_nat A2) B2)) (@ (@ tptp.ord_le2510731241096832064er_nat B2) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (= A2 (@ (@ tptp.sup_sup_set_nat A2) B2)) (@ (@ tptp.ord_less_eq_set_nat B2) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (= A2 (@ (@ tptp.sup_sup_nat A2) B2)) (@ (@ tptp.ord_less_eq_nat B2) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (= A2 (@ (@ tptp.sup_sup_int A2) B2)) (@ (@ tptp.ord_less_eq_int B2) A2))))
% 3.70/4.04 (assert (forall ((F4 (-> 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) (Y2 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat X3) (@ (@ F4 X3) Y2))) (=> (forall ((X3 tptp.set_Pr4329608150637261639at_nat) (Y2 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat Y2) (@ (@ F4 X3) Y2))) (=> (forall ((X3 tptp.set_Pr4329608150637261639at_nat) (Y2 tptp.set_Pr4329608150637261639at_nat) (Z4 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat Y2) X3) (=> (@ (@ tptp.ord_le1268244103169919719at_nat Z4) X3) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ F4 Y2) Z4)) X3)))) (= (@ (@ tptp.sup_su5525570899277871387at_nat X) Y) (@ (@ F4 X) Y)))))))
% 3.70/4.04 (assert (forall ((F4 (-> tptp.assn tptp.assn tptp.assn)) (X tptp.assn) (Y tptp.assn)) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (@ (@ tptp.ord_less_eq_assn X3) (@ (@ F4 X3) Y2))) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (@ (@ tptp.ord_less_eq_assn Y2) (@ (@ F4 X3) Y2))) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn) (Z4 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn Y2) X3) (=> (@ (@ tptp.ord_less_eq_assn Z4) X3) (@ (@ tptp.ord_less_eq_assn (@ (@ F4 Y2) Z4)) X3)))) (= (@ (@ tptp.sup_sup_assn X) Y) (@ (@ F4 X) Y)))))))
% 3.70/4.04 (assert (forall ((F4 (-> tptp.filter_nat tptp.filter_nat tptp.filter_nat)) (X tptp.filter_nat) (Y tptp.filter_nat)) (=> (forall ((X3 tptp.filter_nat) (Y2 tptp.filter_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat X3) (@ (@ F4 X3) Y2))) (=> (forall ((X3 tptp.filter_nat) (Y2 tptp.filter_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat Y2) (@ (@ F4 X3) Y2))) (=> (forall ((X3 tptp.filter_nat) (Y2 tptp.filter_nat) (Z4 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat Y2) X3) (=> (@ (@ tptp.ord_le2510731241096832064er_nat Z4) X3) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ F4 Y2) Z4)) X3)))) (= (@ (@ tptp.sup_sup_filter_nat X) Y) (@ (@ F4 X) Y)))))))
% 3.70/4.04 (assert (forall ((F4 (-> tptp.set_nat tptp.set_nat tptp.set_nat)) (X tptp.set_nat) (Y tptp.set_nat)) (=> (forall ((X3 tptp.set_nat) (Y2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X3) (@ (@ F4 X3) Y2))) (=> (forall ((X3 tptp.set_nat) (Y2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat Y2) (@ (@ F4 X3) Y2))) (=> (forall ((X3 tptp.set_nat) (Y2 tptp.set_nat) (Z4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y2) X3) (=> (@ (@ tptp.ord_less_eq_set_nat Z4) X3) (@ (@ tptp.ord_less_eq_set_nat (@ (@ F4 Y2) Z4)) X3)))) (= (@ (@ tptp.sup_sup_set_nat X) Y) (@ (@ F4 X) Y)))))))
% 3.70/4.04 (assert (forall ((F4 (-> tptp.nat tptp.nat tptp.nat)) (X tptp.nat) (Y tptp.nat)) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X3) (@ (@ F4 X3) Y2))) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y2) (@ (@ F4 X3) Y2))) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat) (Z4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y2) X3) (=> (@ (@ tptp.ord_less_eq_nat Z4) X3) (@ (@ tptp.ord_less_eq_nat (@ (@ F4 Y2) Z4)) X3)))) (= (@ (@ tptp.sup_sup_nat X) Y) (@ (@ F4 X) Y)))))))
% 3.70/4.04 (assert (forall ((F4 (-> tptp.int tptp.int tptp.int)) (X tptp.int) (Y tptp.int)) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (@ (@ tptp.ord_less_eq_int X3) (@ (@ F4 X3) Y2))) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (@ (@ tptp.ord_less_eq_int Y2) (@ (@ F4 X3) Y2))) (=> (forall ((X3 tptp.int) (Y2 tptp.int) (Z4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y2) X3) (=> (@ (@ tptp.ord_less_eq_int Z4) X3) (@ (@ tptp.ord_less_eq_int (@ (@ F4 Y2) Z4)) X3)))) (= (@ (@ tptp.sup_sup_int X) Y) (@ (@ F4 X) Y)))))))
% 3.70/4.04 (assert (forall ((B2 tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B2) A2) (= (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2) A2))))
% 3.70/4.04 (assert (forall ((B2 tptp.assn) (A2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn B2) A2) (= (@ (@ tptp.sup_sup_assn A2) B2) A2))))
% 3.70/4.04 (assert (forall ((B2 tptp.filter_nat) (A2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B2) A2) (= (@ (@ tptp.sup_sup_filter_nat A2) B2) A2))))
% 3.70/4.04 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A2) (= (@ (@ tptp.sup_sup_set_nat A2) B2) A2))))
% 3.70/4.04 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (= (@ (@ tptp.sup_sup_nat A2) B2) A2))))
% 3.70/4.04 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (= (@ (@ tptp.sup_sup_int A2) B2) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A2) B2) (= (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.assn) (B2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (= (@ (@ tptp.sup_sup_assn A2) B2) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat A2) B2) (= (@ (@ tptp.sup_sup_filter_nat A2) B2) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (= (@ (@ tptp.sup_sup_set_nat A2) B2) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= (@ (@ tptp.sup_sup_nat A2) B2) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (= (@ (@ tptp.sup_sup_int A2) B2) B2))))
% 3.70/4.04 (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))))
% 3.70/4.04 (assert (forall ((Y tptp.assn) (X tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn Y) X) (= (@ (@ tptp.sup_sup_assn X) Y) X))))
% 3.70/4.04 (assert (forall ((Y tptp.filter_nat) (X tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat Y) X) (= (@ (@ tptp.sup_sup_filter_nat X) Y) X))))
% 3.70/4.04 (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))))
% 3.70/4.04 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.sup_sup_nat X) Y) X))))
% 3.70/4.04 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.sup_sup_int X) Y) X))))
% 3.70/4.04 (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))))
% 3.70/4.04 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X) Y) (= (@ (@ tptp.sup_sup_assn X) Y) Y))))
% 3.70/4.04 (assert (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat X) Y) (= (@ (@ tptp.sup_sup_filter_nat X) Y) Y))))
% 3.70/4.04 (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))))
% 3.70/4.04 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (@ (@ tptp.sup_sup_nat X) Y) Y))))
% 3.70/4.04 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (@ (@ tptp.sup_sup_int X) Y) Y))))
% 3.70/4.04 (assert (forall ((B2 tptp.set_Pr4329608150637261639at_nat) (C tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat B2) C)) A2) (not (=> (@ (@ tptp.ord_le1268244103169919719at_nat B2) A2) (not (@ (@ tptp.ord_le1268244103169919719at_nat C) A2)))))))
% 3.70/4.04 (assert (forall ((B2 tptp.assn) (C tptp.assn) (A2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.sup_sup_assn B2) C)) A2) (not (=> (@ (@ tptp.ord_less_eq_assn B2) A2) (not (@ (@ tptp.ord_less_eq_assn C) A2)))))))
% 3.70/4.04 (assert (forall ((B2 tptp.filter_nat) (C tptp.filter_nat) (A2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.sup_sup_filter_nat B2) C)) A2) (not (=> (@ (@ tptp.ord_le2510731241096832064er_nat B2) A2) (not (@ (@ tptp.ord_le2510731241096832064er_nat C) A2)))))))
% 3.70/4.04 (assert (forall ((B2 tptp.set_nat) (C tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat B2) C)) A2) (not (=> (@ (@ tptp.ord_less_eq_set_nat B2) A2) (not (@ (@ tptp.ord_less_eq_set_nat C) A2)))))))
% 3.70/4.04 (assert (forall ((B2 tptp.nat) (C tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat B2) C)) A2) (not (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (not (@ (@ tptp.ord_less_eq_nat C) A2)))))))
% 3.70/4.04 (assert (forall ((B2 tptp.int) (C tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int B2) C)) A2) (not (=> (@ (@ tptp.ord_less_eq_int B2) A2) (not (@ (@ tptp.ord_less_eq_int C) A2)))))))
% 3.70/4.04 (assert (forall ((B2 tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat) (C tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B2) A2) (=> (@ (@ tptp.ord_le1268244103169919719at_nat C) A2) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat B2) C)) A2)))))
% 3.70/4.04 (assert (forall ((B2 tptp.assn) (A2 tptp.assn) (C tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn B2) A2) (=> (@ (@ tptp.ord_less_eq_assn C) A2) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.sup_sup_assn B2) C)) A2)))))
% 3.70/4.04 (assert (forall ((B2 tptp.filter_nat) (A2 tptp.filter_nat) (C tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B2) A2) (=> (@ (@ tptp.ord_le2510731241096832064er_nat C) A2) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.sup_sup_filter_nat B2) C)) A2)))))
% 3.70/4.04 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat) (C tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A2) (=> (@ (@ tptp.ord_less_eq_set_nat C) A2) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat B2) C)) A2)))))
% 3.70/4.04 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (=> (@ (@ tptp.ord_less_eq_nat C) A2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat B2) C)) A2)))))
% 3.70/4.04 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (=> (@ (@ tptp.ord_less_eq_int C) A2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int B2) C)) A2)))))
% 3.70/4.04 (assert (= tptp.ord_le1268244103169919719at_nat (lambda ((B3 tptp.set_Pr4329608150637261639at_nat) (A3 tptp.set_Pr4329608150637261639at_nat)) (= A3 (@ (@ tptp.sup_su5525570899277871387at_nat A3) B3)))))
% 3.70/4.04 (assert (= tptp.ord_less_eq_assn (lambda ((B3 tptp.assn) (A3 tptp.assn)) (= A3 (@ (@ tptp.sup_sup_assn A3) B3)))))
% 3.70/4.04 (assert (= tptp.ord_le2510731241096832064er_nat (lambda ((B3 tptp.filter_nat) (A3 tptp.filter_nat)) (= A3 (@ (@ tptp.sup_sup_filter_nat A3) B3)))))
% 3.70/4.04 (assert (= tptp.ord_less_eq_set_nat (lambda ((B3 tptp.set_nat) (A3 tptp.set_nat)) (= A3 (@ (@ tptp.sup_sup_set_nat A3) B3)))))
% 3.70/4.04 (assert (= tptp.ord_less_eq_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (= A3 (@ (@ tptp.sup_sup_nat A3) B3)))))
% 3.70/4.04 (assert (= tptp.ord_less_eq_int (lambda ((B3 tptp.int) (A3 tptp.int)) (= A3 (@ (@ tptp.sup_sup_int A3) B3)))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat A2) (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.assn) (B2 tptp.assn)) (@ (@ tptp.ord_less_eq_assn A2) (@ (@ tptp.sup_sup_assn A2) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat A2) (@ (@ tptp.sup_sup_filter_nat A2) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A2) (@ (@ tptp.sup_sup_set_nat A2) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat A2) (@ (@ tptp.sup_sup_nat A2) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_eq_int A2) (@ (@ tptp.sup_sup_int A2) B2))))
% 3.70/4.04 (assert (forall ((B2 tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat B2) (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2))))
% 3.70/4.04 (assert (forall ((B2 tptp.assn) (A2 tptp.assn)) (@ (@ tptp.ord_less_eq_assn B2) (@ (@ tptp.sup_sup_assn A2) B2))))
% 3.70/4.04 (assert (forall ((B2 tptp.filter_nat) (A2 tptp.filter_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat B2) (@ (@ tptp.sup_sup_filter_nat A2) B2))))
% 3.70/4.04 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat B2) (@ (@ tptp.sup_sup_set_nat A2) B2))))
% 3.70/4.04 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat B2) (@ (@ tptp.sup_sup_nat A2) B2))))
% 3.70/4.04 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (@ (@ tptp.ord_less_eq_int B2) (@ (@ tptp.sup_sup_int A2) B2))))
% 3.70/4.04 (assert (= tptp.ord_le1268244103169919719at_nat (lambda ((B3 tptp.set_Pr4329608150637261639at_nat) (A3 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat A3) B3) A3))))
% 3.70/4.04 (assert (= tptp.ord_less_eq_assn (lambda ((B3 tptp.assn) (A3 tptp.assn)) (= (@ (@ tptp.sup_sup_assn A3) B3) A3))))
% 3.70/4.04 (assert (= tptp.ord_le2510731241096832064er_nat (lambda ((B3 tptp.filter_nat) (A3 tptp.filter_nat)) (= (@ (@ tptp.sup_sup_filter_nat A3) B3) A3))))
% 3.70/4.04 (assert (= tptp.ord_less_eq_set_nat (lambda ((B3 tptp.set_nat) (A3 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A3) B3) A3))))
% 3.70/4.04 (assert (= tptp.ord_less_eq_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (= (@ (@ tptp.sup_sup_nat A3) B3) A3))))
% 3.70/4.04 (assert (= tptp.ord_less_eq_int (lambda ((B3 tptp.int) (A3 tptp.int)) (= (@ (@ tptp.sup_sup_int A3) B3) A3))))
% 3.70/4.04 (assert (= tptp.ord_le1268244103169919719at_nat (lambda ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat A3) B3) B3))))
% 3.70/4.04 (assert (= tptp.ord_less_eq_assn (lambda ((A3 tptp.assn) (B3 tptp.assn)) (= (@ (@ tptp.sup_sup_assn A3) B3) B3))))
% 3.70/4.04 (assert (= tptp.ord_le2510731241096832064er_nat (lambda ((A3 tptp.filter_nat) (B3 tptp.filter_nat)) (= (@ (@ tptp.sup_sup_filter_nat A3) B3) B3))))
% 3.70/4.04 (assert (= tptp.ord_less_eq_set_nat (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A3) B3) B3))))
% 3.70/4.04 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.sup_sup_nat A3) B3) B3))))
% 3.70/4.04 (assert (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.sup_sup_int A3) B3) B3))))
% 3.70/4.04 (assert (forall ((C tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le1268244103169919719at_nat C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2))))))
% 3.70/4.04 (assert (forall ((C tptp.assn) (A2 tptp.assn) (B2 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_assn A2) B2))))))
% 3.70/4.04 (assert (forall ((C tptp.filter_nat) (A2 tptp.filter_nat) (B2 tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_le2510731241096832064er_nat C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_filter_nat A2) B2))))))
% 3.70/4.04 (assert (forall ((C tptp.set_nat) (A2 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A2) B2))))))
% 3.70/4.04 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_nat A2) B2))))))
% 3.70/4.04 (assert (forall ((C tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_int A2) B2))))))
% 3.70/4.04 (assert (forall ((C tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le1268244103169919719at_nat C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2))))))
% 3.70/4.04 (assert (forall ((C tptp.assn) (B2 tptp.assn) (A2 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_assn A2) B2))))))
% 3.70/4.04 (assert (forall ((C tptp.filter_nat) (B2 tptp.filter_nat) (A2 tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_le2510731241096832064er_nat C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_filter_nat A2) B2))))))
% 3.70/4.04 (assert (forall ((C tptp.set_nat) (B2 tptp.set_nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A2) B2))))))
% 3.70/4.04 (assert (forall ((C tptp.nat) (B2 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_nat A2) B2))))))
% 3.70/4.04 (assert (forall ((C tptp.int) (B2 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_int A2) B2))))))
% 3.70/4.04 (assert (= tptp.inf_inf_nat tptp.ord_min_nat))
% 3.70/4.04 (assert (forall ((C tptp.set_nat) (B2 tptp.set_nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A2) B2))))))
% 3.70/4.04 (assert (forall ((C tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le2604355607129572851at_nat C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2))))))
% 3.70/4.04 (assert (forall ((C tptp.assn) (B2 tptp.assn) (A2 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_assn A2) B2))))))
% 3.70/4.04 (assert (forall ((C tptp.nat) (B2 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_nat A2) B2))))))
% 3.70/4.04 (assert (forall ((C tptp.int) (B2 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_int A2) B2))))))
% 3.70/4.04 (assert (forall ((C tptp.set_nat) (A2 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A2) B2))))))
% 3.70/4.04 (assert (forall ((C tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le2604355607129572851at_nat C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2))))))
% 3.70/4.04 (assert (forall ((C tptp.assn) (A2 tptp.assn) (B2 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_assn A2) B2))))))
% 3.70/4.04 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_nat A2) B2))))))
% 3.70/4.04 (assert (forall ((C tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_int A2) B2))))))
% 3.70/4.04 (assert (= tptp.ord_less_set_nat (lambda ((B3 tptp.set_nat) (A3 tptp.set_nat)) (and (= A3 (@ (@ tptp.sup_sup_set_nat A3) B3)) (not (= A3 B3))))))
% 3.70/4.04 (assert (= tptp.ord_le2604355607129572851at_nat (lambda ((B3 tptp.set_Pr4329608150637261639at_nat) (A3 tptp.set_Pr4329608150637261639at_nat)) (and (= A3 (@ (@ tptp.sup_su5525570899277871387at_nat A3) B3)) (not (= A3 B3))))))
% 3.70/4.04 (assert (= tptp.ord_less_assn (lambda ((B3 tptp.assn) (A3 tptp.assn)) (and (= A3 (@ (@ tptp.sup_sup_assn A3) B3)) (not (= A3 B3))))))
% 3.70/4.04 (assert (= tptp.ord_less_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (and (= A3 (@ (@ tptp.sup_sup_nat A3) B3)) (not (= A3 B3))))))
% 3.70/4.04 (assert (= tptp.ord_less_int (lambda ((B3 tptp.int) (A3 tptp.int)) (and (= A3 (@ (@ tptp.sup_sup_int A3) B3)) (not (= A3 B3))))))
% 3.70/4.04 (assert (forall ((B2 tptp.set_nat) (C tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat (@ (@ tptp.sup_sup_set_nat B2) C)) A2) (not (=> (@ (@ tptp.ord_less_set_nat B2) A2) (not (@ (@ tptp.ord_less_set_nat C) A2)))))))
% 3.70/4.04 (assert (forall ((B2 tptp.set_Pr4329608150637261639at_nat) (C tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le2604355607129572851at_nat (@ (@ tptp.sup_su5525570899277871387at_nat B2) C)) A2) (not (=> (@ (@ tptp.ord_le2604355607129572851at_nat B2) A2) (not (@ (@ tptp.ord_le2604355607129572851at_nat C) A2)))))))
% 3.70/4.04 (assert (forall ((B2 tptp.assn) (C tptp.assn) (A2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn (@ (@ tptp.sup_sup_assn B2) C)) A2) (not (=> (@ (@ tptp.ord_less_assn B2) A2) (not (@ (@ tptp.ord_less_assn C) A2)))))))
% 3.70/4.04 (assert (forall ((B2 tptp.nat) (C tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.sup_sup_nat B2) C)) A2) (not (=> (@ (@ tptp.ord_less_nat B2) A2) (not (@ (@ tptp.ord_less_nat C) A2)))))))
% 3.70/4.04 (assert (forall ((B2 tptp.int) (C tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.sup_sup_int B2) C)) A2) (not (=> (@ (@ tptp.ord_less_int B2) A2) (not (@ (@ tptp.ord_less_int C) A2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) B2) (= (@ (@ tptp.sup_sup_set_nat A2) B2) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le2604355607129572851at_nat A2) B2) (= (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.assn) (B2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn A2) B2) (= (@ (@ tptp.sup_sup_assn A2) B2) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (= (@ (@ tptp.sup_sup_nat A2) B2) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (= (@ (@ tptp.sup_sup_int A2) B2) B2))))
% 3.70/4.04 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B2) A2) (= (@ (@ tptp.sup_sup_set_nat A2) B2) A2))))
% 3.70/4.04 (assert (forall ((B2 tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le2604355607129572851at_nat B2) A2) (= (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2) A2))))
% 3.70/4.04 (assert (forall ((B2 tptp.assn) (A2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn B2) A2) (= (@ (@ tptp.sup_sup_assn A2) B2) A2))))
% 3.70/4.04 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A2) (= (@ (@ tptp.sup_sup_nat A2) B2) A2))))
% 3.70/4.04 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A2) (= (@ (@ tptp.sup_sup_int A2) B2) A2))))
% 3.70/4.04 (assert (forall ((X tptp.set_nat) (B2 tptp.set_nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat X))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A2) B2))))))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le2604355607129572851at_nat X))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2))))))
% 3.70/4.04 (assert (forall ((X tptp.assn) (B2 tptp.assn) (A2 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn X))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_assn A2) B2))))))
% 3.70/4.04 (assert (forall ((X tptp.nat) (B2 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_nat A2) B2))))))
% 3.70/4.04 (assert (forall ((X tptp.int) (B2 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_int A2) B2))))))
% 3.70/4.04 (assert (forall ((X tptp.set_nat) (A2 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat X))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A2) B2))))))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le2604355607129572851at_nat X))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2))))))
% 3.70/4.04 (assert (forall ((X tptp.assn) (A2 tptp.assn) (B2 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn X))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_assn A2) B2))))))
% 3.70/4.04 (assert (forall ((X tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_nat A2) B2))))))
% 3.70/4.04 (assert (forall ((X tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_int A2) B2))))))
% 3.70/4.04 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.sup_sup_assn X) tptp.bot_bot_assn) X)))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat X) tptp.bot_bo228742789529271731at_nat) X)))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat X) tptp.bot_bo2099793752762293965at_nat) X)))
% 3.70/4.04 (assert (forall ((X tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o X) tptp.bot_bot_set_o) X)))
% 3.70/4.04 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat X) tptp.bot_bot_set_nat) X)))
% 3.70/4.04 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int X) tptp.bot_bot_set_int) X)))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.sup_su6327502436637775413at_nat X))) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat) (Y2 tptp.set_Pr1261947904930325089at_nat) (Z4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X3))) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat Y2) Z4)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 Y2)) (@ _let_1 Z4))))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 Y)) (@ _let_1 Z)))))))
% 3.70/4.04 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (=> (forall ((X3 tptp.set_nat) (Y2 tptp.set_nat) (Z4 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X3))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat Y2) Z4)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 Y2)) (@ _let_1 Z4))))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y) Z)) (@ (@ tptp.inf_inf_set_nat (@ _let_1 Y)) (@ _let_1 Z)))))))
% 3.70/4.04 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn) (Z4 tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X3))) (= (@ _let_1 (@ (@ tptp.sup_sup_assn Y2) Z4)) (@ (@ tptp.sup_sup_assn (@ _let_1 Y2)) (@ _let_1 Z4))))) (= (@ _let_1 (@ (@ tptp.inf_inf_assn Y) Z)) (@ (@ tptp.inf_inf_assn (@ _let_1 Y)) (@ _let_1 Z)))))))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat X))) (=> (forall ((X3 tptp.set_Pr4329608150637261639at_nat) (Y2 tptp.set_Pr4329608150637261639at_nat) (Z4 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.inf_in7913087082777306421at_nat X3))) (= (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat Y2) Z4)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 Y2)) (@ _let_1 Z4))))) (= (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat Y) Z)) (@ (@ tptp.inf_in7913087082777306421at_nat (@ _let_1 Y)) (@ _let_1 Z)))))))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat) (Y2 tptp.set_Pr1261947904930325089at_nat) (Z4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.sup_su6327502436637775413at_nat X3))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y2) Z4)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 Y2)) (@ _let_1 Z4))))) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat Y) Z)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 Y)) (@ _let_1 Z)))))))
% 3.70/4.04 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (=> (forall ((X3 tptp.set_nat) (Y2 tptp.set_nat) (Z4 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X3))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y2) Z4)) (@ (@ tptp.inf_inf_set_nat (@ _let_1 Y2)) (@ _let_1 Z4))))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat Y) Z)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 Y)) (@ _let_1 Z)))))))
% 3.70/4.04 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn) (Z4 tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X3))) (= (@ _let_1 (@ (@ tptp.inf_inf_assn Y2) Z4)) (@ (@ tptp.inf_inf_assn (@ _let_1 Y2)) (@ _let_1 Z4))))) (= (@ _let_1 (@ (@ tptp.sup_sup_assn Y) Z)) (@ (@ tptp.sup_sup_assn (@ _let_1 Y)) (@ _let_1 Z)))))))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.inf_in7913087082777306421at_nat X))) (=> (forall ((X3 tptp.set_Pr4329608150637261639at_nat) (Y2 tptp.set_Pr4329608150637261639at_nat) (Z4 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat X3))) (= (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat Y2) Z4)) (@ (@ tptp.inf_in7913087082777306421at_nat (@ _let_1 Y2)) (@ _let_1 Z4))))) (= (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat Y) Z)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 Y)) (@ _let_1 Z)))))))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat Y) Z)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 3.70/4.04 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat Y) Z)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 3.70/4.04 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (= (@ _let_1 (@ (@ tptp.sup_sup_assn Y) Z)) (@ (@ tptp.sup_sup_assn (@ _let_1 Y)) (@ _let_1 Z))))))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.inf_in7913087082777306421at_nat X))) (= (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat Y) Z)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 3.70/4.04 (assert (forall ((Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat Y) Z)) X) (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat Y) X)) (@ (@ tptp.inf_in2572325071724192079at_nat Z) X)))))
% 3.70/4.04 (assert (forall ((Y tptp.set_nat) (Z tptp.set_nat) (X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat Y) Z)) X) (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat Y) X)) (@ (@ tptp.inf_inf_set_nat Z) X)))))
% 3.70/4.04 (assert (forall ((Y tptp.assn) (Z tptp.assn) (X tptp.assn)) (= (@ (@ tptp.inf_inf_assn (@ (@ tptp.sup_sup_assn Y) Z)) X) (@ (@ tptp.sup_sup_assn (@ (@ tptp.inf_inf_assn Y) X)) (@ (@ tptp.inf_inf_assn Z) X)))))
% 3.70/4.04 (assert (forall ((Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.sup_su5525570899277871387at_nat Y) Z)) X) (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat Y) X)) (@ (@ tptp.inf_in7913087082777306421at_nat Z) X)))))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.sup_su6327502436637775413at_nat X))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 3.70/4.04 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y) Z)) (@ (@ tptp.inf_inf_set_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 3.70/4.04 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (= (@ _let_1 (@ (@ tptp.inf_inf_assn Y) Z)) (@ (@ tptp.inf_inf_assn (@ _let_1 Y)) (@ _let_1 Z))))))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat X))) (= (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat Y) Z)) (@ (@ tptp.inf_in7913087082777306421at_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 3.70/4.04 (assert (forall ((Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z)) X) (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat Y) X)) (@ (@ tptp.sup_su6327502436637775413at_nat Z) X)))))
% 3.70/4.04 (assert (forall ((Y tptp.set_nat) (Z tptp.set_nat) (X tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat Y) Z)) X) (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat Y) X)) (@ (@ tptp.sup_sup_set_nat Z) X)))))
% 3.70/4.04 (assert (forall ((Y tptp.assn) (Z tptp.assn) (X tptp.assn)) (= (@ (@ tptp.sup_sup_assn (@ (@ tptp.inf_inf_assn Y) Z)) X) (@ (@ tptp.inf_inf_assn (@ (@ tptp.sup_sup_assn Y) X)) (@ (@ tptp.sup_sup_assn Z) X)))))
% 3.70/4.04 (assert (forall ((Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat Y) Z)) X) (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.sup_su5525570899277871387at_nat Y) X)) (@ (@ tptp.sup_su5525570899277871387at_nat Z) X)))))
% 3.70/4.04 (assert (forall ((B tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat tptp.bot_bo228742789529271731at_nat) B) B)))
% 3.70/4.04 (assert (forall ((B tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat tptp.bot_bo2099793752762293965at_nat) B) B)))
% 3.70/4.04 (assert (forall ((B tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o tptp.bot_bot_set_o) B) B)))
% 3.70/4.04 (assert (forall ((B tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat tptp.bot_bot_set_nat) B) B)))
% 3.70/4.04 (assert (forall ((B tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int tptp.bot_bot_set_int) B) B)))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat A) tptp.bot_bo228742789529271731at_nat) A)))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat A) tptp.bot_bo2099793752762293965at_nat) A)))
% 3.70/4.04 (assert (forall ((A tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o A) tptp.bot_bot_set_o) A)))
% 3.70/4.04 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A) tptp.bot_bot_set_nat) A)))
% 3.70/4.04 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int A) tptp.bot_bot_set_int) A)))
% 3.70/4.04 (assert (forall ((I tptp.set_Pr4329608150637261639at_nat) (Ww tptp.list_s4242580248156217677at_nat)) (let ((_let_1 (@ tptp.foldl_4541198706405875041at_nat tptp.sup_su5525570899277871387at_nat))) (= (@ (@ _let_1 I) Ww) (@ (@ tptp.sup_su5525570899277871387at_nat I) (@ (@ _let_1 tptp.bot_bo228742789529271731at_nat) Ww))))))
% 3.70/4.04 (assert (forall ((I tptp.set_Pr1261947904930325089at_nat) (Ww tptp.list_s1210847774152347623at_nat)) (let ((_let_1 (@ tptp.foldl_5307762784932486881at_nat tptp.sup_su6327502436637775413at_nat))) (= (@ (@ _let_1 I) Ww) (@ (@ tptp.sup_su6327502436637775413at_nat I) (@ (@ _let_1 tptp.bot_bo2099793752762293965at_nat) Ww))))))
% 3.70/4.04 (assert (forall ((I tptp.set_o) (Ww tptp.list_set_o)) (let ((_let_1 (@ tptp.foldl_set_o_set_o tptp.sup_sup_set_o))) (= (@ (@ _let_1 I) Ww) (@ (@ tptp.sup_sup_set_o I) (@ (@ _let_1 tptp.bot_bot_set_o) Ww))))))
% 3.70/4.04 (assert (forall ((I tptp.set_nat) (Ww tptp.list_set_nat)) (let ((_let_1 (@ tptp.foldl_4988731653086973103et_nat tptp.sup_sup_set_nat))) (= (@ (@ _let_1 I) Ww) (@ (@ tptp.sup_sup_set_nat I) (@ (@ _let_1 tptp.bot_bot_set_nat) Ww))))))
% 3.70/4.04 (assert (forall ((I tptp.set_int) (Ww tptp.list_set_int)) (let ((_let_1 (@ tptp.foldl_6819690284573351271et_int tptp.sup_sup_set_int))) (= (@ (@ _let_1 I) Ww) (@ (@ tptp.sup_sup_set_int I) (@ (@ _let_1 tptp.bot_bot_set_int) Ww))))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (D tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A) C2) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B) D) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A) B)) (@ (@ tptp.sup_su5525570899277871387at_nat C2) D))))))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (C2 tptp.set_nat) (B tptp.set_nat) (D tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) C2) (=> (@ (@ tptp.ord_less_eq_set_nat B) D) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat A) B)) (@ (@ tptp.sup_sup_set_nat C2) D))))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A) C2) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B) C2) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A) B)) C2)))))
% 3.70/4.04 (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 B) C2) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat A) B)) C2)))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat A) (@ (@ tptp.sup_su5525570899277871387at_nat A) B))))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A) (@ (@ tptp.sup_sup_set_nat A) B))))
% 3.70/4.04 (assert (forall ((B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat B) (@ (@ tptp.sup_su5525570899277871387at_nat A) B))))
% 3.70/4.04 (assert (forall ((B tptp.set_nat) (A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat B) (@ (@ tptp.sup_sup_set_nat A) B))))
% 3.70/4.04 (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))))
% 3.70/4.04 (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))))
% 3.70/4.04 (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))))
% 3.70/4.04 (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))))
% 3.70/4.04 (assert (forall ((C2 tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat C2) (@ (@ tptp.sup_su5525570899277871387at_nat A) B)) (not (forall ((A8 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A8) A) (forall ((B8 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B8) B) (not (= C2 (@ (@ tptp.sup_su5525570899277871387at_nat A8) B8)))))))))))
% 3.70/4.04 (assert (forall ((C2 tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat C2) (@ (@ tptp.sup_sup_set_nat A) B)) (not (forall ((A8 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A8) A) (forall ((B8 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B8) B) (not (= C2 (@ (@ tptp.sup_sup_set_nat A8) B8)))))))))))
% 3.70/4.04 (assert (= tptp.ord_le1268244103169919719at_nat (lambda ((A5 tptp.set_Pr4329608150637261639at_nat) (B7 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat A5) B7) B7))))
% 3.70/4.04 (assert (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B7 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A5) B7) B7))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A))) (= (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat B) C2))) (@ (@ tptp.ord_le3146513528884898305at_nat C2) A)))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.inf_in7913087082777306421at_nat A))) (= (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat B) C2))) (@ (@ tptp.ord_le1268244103169919719at_nat C2) A)))))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (= (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.sup_sup_set_nat B) C2))) (@ (@ tptp.ord_less_eq_set_nat C2) A)))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.minus_3314409938677909166at_nat A))) (= (@ (@ tptp.minus_3314409938677909166at_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat B) C2))))))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A))) (= (@ (@ tptp.minus_minus_set_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.sup_sup_set_nat B) C2))))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.minus_3314409938677909166at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A) B)) C2) (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.minus_3314409938677909166at_nat A) C2)) (@ (@ tptp.minus_3314409938677909166at_nat B) C2)))))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.sup_sup_set_nat A) B)) C2) (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.minus_minus_set_nat A) C2)) (@ (@ tptp.minus_minus_set_nat B) C2)))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat A))) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat B) C2)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 B)) (@ _let_1 C2))))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.minus_3314409938677909166at_nat A))) (= (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat B) C2)) (@ (@ tptp.inf_in7913087082777306421at_nat (@ _let_1 B)) (@ _let_1 C2))))))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat B) C2)) (@ (@ tptp.inf_inf_set_nat (@ _let_1 B)) (@ _let_1 C2))))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat A))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B) C2)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 B)) (@ _let_1 C2))))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.minus_3314409938677909166at_nat A))) (= (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat B) C2)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 B)) (@ _let_1 C2))))))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat B) C2)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 B)) (@ _let_1 C2))))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) (@ (@ tptp.minus_1356011639430497352at_nat A) B)) A)))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat A) B)) (@ (@ tptp.minus_3314409938677909166at_nat A) B)) A)))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) (@ (@ tptp.minus_minus_set_nat A) B)) A)))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.minus_1356011639430497352at_nat A) B)) (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) A)))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.minus_3314409938677909166at_nat A) B)) (@ (@ tptp.inf_in7913087082777306421at_nat A) B)) A)))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.minus_minus_set_nat A) B)) (@ (@ tptp.inf_inf_set_nat A) B)) A)))
% 3.70/4.04 (assert (forall ((X tptp.produc3843707927480180839at_nat) (Xs tptp.list_P5464809261938338413at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat X))) (=> (@ _let_1 (@ tptp.set_Pr3765526544606949372at_nat (@ tptp.butlas2561766218336428473at_nat Xs))) (@ _let_1 (@ tptp.set_Pr3765526544606949372at_nat Xs))))))
% 3.70/4.04 (assert (forall ((X tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X))) (=> (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat (@ tptp.butlas5569151904373679443at_nat Xs))) (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat Xs))))))
% 3.70/4.04 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xs tptp.list_P7985473006766602707_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o X))) (=> (@ _let_1 (@ tptp.set_Pr400311997697478754_nat_o (@ tptp.butlas8287983287669047583_nat_o Xs))) (@ _let_1 (@ tptp.set_Pr400311997697478754_nat_o Xs))))))
% 3.70/4.04 (assert (forall ((X tptp.int) (Xs tptp.list_int)) (let ((_let_1 (@ tptp.member_int X))) (=> (@ _let_1 (@ tptp.set_int2 (@ tptp.butlast_int Xs))) (@ _let_1 (@ tptp.set_int2 Xs))))))
% 3.70/4.04 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ tptp.member_nat X))) (=> (@ _let_1 (@ tptp.set_nat2 (@ tptp.butlast_nat Xs))) (@ _let_1 (@ tptp.set_nat2 Xs))))))
% 3.70/4.04 (assert (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ tptp.member7957490590177025114n_assn X))) (=> (@ _let_1 (@ tptp.set_Pr1139785259514867910n_assn (@ tptp.butlas3012047794866324995n_assn Xs))) (@ _let_1 (@ tptp.set_Pr1139785259514867910n_assn Xs))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_int)) (=> (@ tptp.distinct_int Xs) (@ tptp.distinct_int (@ tptp.butlast_int Xs)))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_nat)) (=> (@ tptp.distinct_nat Xs) (@ tptp.distinct_nat (@ tptp.butlast_nat Xs)))))
% 3.70/4.04 (assert (forall ((L tptp.list_nat) (I tptp.nat) (X tptp.nat)) (= (@ (@ (@ tptp.list_update_nat (@ tptp.butlast_nat L)) I) X) (@ tptp.butlast_nat (@ (@ (@ tptp.list_update_nat L) I) X)))))
% 3.70/4.04 (assert (forall ((L tptp.list_c) (I tptp.nat) (X tptp.c)) (= (@ (@ (@ tptp.list_update_c (@ tptp.butlast_c L)) I) X) (@ tptp.butlast_c (@ (@ (@ tptp.list_update_c L) I) X)))))
% 3.70/4.04 (assert (forall ((L tptp.list_d) (I tptp.nat) (X tptp.d)) (= (@ (@ (@ tptp.list_update_d (@ tptp.butlast_d L)) I) X) (@ tptp.butlast_d (@ (@ (@ tptp.list_update_d L) I) X)))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_nat)) (= (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) (@ tptp.rev_nat Xs)) (forall ((I4 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (=> (@ (@ tptp.ord_less_eq_nat I4) J2) (=> (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.ord_less_eq_nat (@ _let_1 J2)) (@ _let_1 I4)))))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_int)) (= (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) (@ tptp.rev_int Xs)) (forall ((I4 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs))) (=> (@ (@ tptp.ord_less_eq_nat I4) J2) (=> (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_int Xs)) (@ (@ tptp.ord_less_eq_int (@ _let_1 J2)) (@ _let_1 I4)))))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_nat) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (=> (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) (@ tptp.rev_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 J)) (@ _let_1 I))))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_int) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs))) (=> (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) (@ tptp.rev_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 J)) (@ _let_1 I))))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_Code_integer)) (=> (@ (@ tptp.sorted710888440204495920nteger tptp.ord_le6747313008572928689nteger) Xs) (@ (@ tptp.sorted710888440204495920nteger tptp.ord_le3102999989581377725nteger) Xs))))
% 3.70/4.04 (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))))
% 3.70/4.04 (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))))
% 3.70/4.04 (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))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_Code_integer) (Ys tptp.list_Code_integer)) (let ((_let_1 (@ tptp.sorted710888440204495920nteger tptp.ord_le6747313008572928689nteger))) (=> (@ _let_1 Xs) (=> (@ _let_1 Ys) (=> (= (@ tptp.set_Code_integer2 Ys) (@ tptp.set_Code_integer2 Xs)) (= Ys Xs)))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_num) (Ys tptp.list_num)) (let ((_let_1 (@ tptp.sorted_wrt_num tptp.ord_less_num))) (=> (@ _let_1 Xs) (=> (@ _let_1 Ys) (=> (= (@ tptp.set_num2 Ys) (@ tptp.set_num2 Xs)) (= Ys Xs)))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.sorted_wrt_nat tptp.ord_less_nat))) (=> (@ _let_1 Xs) (=> (@ _let_1 Ys) (=> (= (@ tptp.set_nat2 Ys) (@ tptp.set_nat2 Xs)) (= Ys Xs)))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.sorted_wrt_int tptp.ord_less_int))) (=> (@ _let_1 Xs) (=> (@ _let_1 Ys) (=> (= (@ tptp.set_int2 Ys) (@ tptp.set_int2 Xs)) (= Ys Xs)))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_c) (P (-> tptp.c tptp.c Bool))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_c Xs)) tptp.one_one_nat) (@ (@ tptp.sorted_wrt_c P) Xs))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_d) (P (-> tptp.d tptp.d Bool))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_d Xs)) tptp.one_one_nat) (@ (@ tptp.sorted_wrt_d P) Xs))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) tptp.one_one_nat) (@ (@ tptp.sorted_wrt_nat P) Xs))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs)) tptp.one_one_nat) (@ (@ tptp.sorted_wrt_int P) Xs))))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 Y)) (@ _let_1 Z))) (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat Y) Z))))))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.inf_in7913087082777306421at_nat X))) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 Y)) (@ _let_1 Z))) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat Y) Z))))))
% 3.70/4.04 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.sup_sup_assn (@ _let_1 Y)) (@ _let_1 Z))) (@ _let_1 (@ (@ tptp.sup_sup_assn Y) Z))))))
% 3.70/4.04 (assert (forall ((X tptp.filter_nat) (Y tptp.filter_nat) (Z tptp.filter_nat)) (let ((_let_1 (@ tptp.inf_inf_filter_nat X))) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.sup_sup_filter_nat (@ _let_1 Y)) (@ _let_1 Z))) (@ _let_1 (@ (@ tptp.sup_sup_filter_nat Y) Z))))))
% 3.70/4.04 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat (@ _let_1 Y)) (@ _let_1 Z))) (@ _let_1 (@ (@ tptp.sup_sup_set_nat Y) Z))))))
% 3.70/4.04 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat (@ _let_1 Y)) (@ _let_1 Z))) (@ _let_1 (@ (@ tptp.sup_sup_nat Y) Z))))))
% 3.70/4.04 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.inf_inf_int X))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int (@ _let_1 Y)) (@ _let_1 Z))) (@ _let_1 (@ (@ tptp.sup_sup_int Y) Z))))))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.sup_su6327502436637775413at_nat X))) (@ (@ tptp.ord_le3146513528884898305at_nat (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z))) (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat X))) (@ (@ tptp.ord_le1268244103169919719at_nat (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat Y) Z))) (@ (@ tptp.inf_in7913087082777306421at_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 3.70/4.04 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (@ (@ tptp.ord_less_eq_assn (@ _let_1 (@ (@ tptp.inf_inf_assn Y) Z))) (@ (@ tptp.inf_inf_assn (@ _let_1 Y)) (@ _let_1 Z))))))
% 3.70/4.04 (assert (forall ((X tptp.filter_nat) (Y tptp.filter_nat) (Z tptp.filter_nat)) (let ((_let_1 (@ tptp.sup_sup_filter_nat X))) (@ (@ tptp.ord_le2510731241096832064er_nat (@ _let_1 (@ (@ tptp.inf_inf_filter_nat Y) Z))) (@ (@ tptp.inf_inf_filter_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 3.70/4.04 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y) Z))) (@ (@ tptp.inf_inf_set_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 3.70/4.04 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z))) (@ (@ tptp.inf_inf_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 3.70/4.04 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.sup_sup_int X))) (@ (@ tptp.ord_less_eq_int (@ _let_1 (@ (@ tptp.inf_inf_int Y) Z))) (@ (@ tptp.inf_inf_int (@ _let_1 Y)) (@ _let_1 Z))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat))) (=> (@ _let_1 Xs) (@ _let_1 (@ (@ tptp.remove1_nat A2) Xs))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_int) (A2 tptp.int)) (let ((_let_1 (@ tptp.sorted_wrt_int tptp.ord_less_eq_int))) (=> (@ _let_1 Xs) (@ _let_1 (@ (@ tptp.remove1_int A2) Xs))))))
% 3.70/4.04 (assert (= tptp.insert9069300056098147895at_nat (lambda ((A3 tptp.produc3843707927480180839at_nat) (__flatten_var_0 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.insert9069300056098147895at_nat A3) tptp.bot_bo228742789529271731at_nat)) __flatten_var_0))))
% 3.70/4.04 (assert (= tptp.insert8211810215607154385at_nat (lambda ((A3 tptp.product_prod_nat_nat) (__flatten_var_0 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.insert8211810215607154385at_nat A3) tptp.bot_bo2099793752762293965at_nat)) __flatten_var_0))))
% 3.70/4.04 (assert (= tptp.insert_o2 (lambda ((A3 Bool) (__flatten_var_0 tptp.set_o)) (@ (@ tptp.sup_sup_set_o (@ (@ tptp.insert_o2 A3) tptp.bot_bot_set_o)) __flatten_var_0))))
% 3.70/4.04 (assert (= tptp.insert_nat2 (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.set_nat)) (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.insert_nat2 A3) tptp.bot_bot_set_nat)) __flatten_var_0))))
% 3.70/4.04 (assert (= tptp.insert_int2 (lambda ((A3 tptp.int) (__flatten_var_0 tptp.set_int)) (@ (@ tptp.sup_sup_set_int (@ (@ tptp.insert_int2 A3) tptp.bot_bot_set_int)) __flatten_var_0))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (X tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ (@ tptp.insert9069300056098147895at_nat X) tptp.bot_bo228742789529271731at_nat))) (let ((_let_2 (= B _let_1))) (let ((_let_3 (= A _let_1))) (= (= (@ (@ tptp.sup_su5525570899277871387at_nat A) B) _let_1) (or (and (= A tptp.bot_bo228742789529271731at_nat) _let_2) (and _let_3 (= B tptp.bot_bo228742789529271731at_nat)) (and _let_3 _let_2))))))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat))) (let ((_let_2 (= B _let_1))) (let ((_let_3 (= A _let_1))) (= (= (@ (@ tptp.sup_su6327502436637775413at_nat A) B) _let_1) (or (and (= A tptp.bot_bo2099793752762293965at_nat) _let_2) (and _let_3 (= B tptp.bot_bo2099793752762293965at_nat)) (and _let_3 _let_2))))))))
% 3.70/4.04 (assert (forall ((A tptp.set_o) (B tptp.set_o) (X Bool)) (let ((_let_1 (@ (@ tptp.insert_o2 X) tptp.bot_bot_set_o))) (let ((_let_2 (= B _let_1))) (let ((_let_3 (= A _let_1))) (= (= (@ (@ tptp.sup_sup_set_o A) B) _let_1) (or (and (= A tptp.bot_bot_set_o) _let_2) (and _let_3 (= B tptp.bot_bot_set_o)) (and _let_3 _let_2))))))))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat2 X) tptp.bot_bot_set_nat))) (let ((_let_2 (= B _let_1))) (let ((_let_3 (= A _let_1))) (= (= (@ (@ tptp.sup_sup_set_nat A) B) _let_1) (or (and (= A tptp.bot_bot_set_nat) _let_2) (and _let_3 (= B tptp.bot_bot_set_nat)) (and _let_3 _let_2))))))))
% 3.70/4.04 (assert (forall ((A tptp.set_int) (B tptp.set_int) (X tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int2 X) tptp.bot_bot_set_int))) (let ((_let_2 (= B _let_1))) (let ((_let_3 (= A _let_1))) (= (= (@ (@ tptp.sup_sup_set_int A) B) _let_1) (or (and (= A tptp.bot_bot_set_int) _let_2) (and _let_3 (= B tptp.bot_bot_set_int)) (and _let_3 _let_2))))))))
% 3.70/4.04 (assert (forall ((X tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ (@ tptp.insert9069300056098147895at_nat X) tptp.bot_bo228742789529271731at_nat))) (let ((_let_2 (= B _let_1))) (let ((_let_3 (= A _let_1))) (= (= _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A) B)) (or (and (= A tptp.bot_bo228742789529271731at_nat) _let_2) (and _let_3 (= B tptp.bot_bo228742789529271731at_nat)) (and _let_3 _let_2))))))))
% 3.70/4.04 (assert (forall ((X tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat))) (let ((_let_2 (= B _let_1))) (let ((_let_3 (= A _let_1))) (= (= _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat A) B)) (or (and (= A tptp.bot_bo2099793752762293965at_nat) _let_2) (and _let_3 (= B tptp.bot_bo2099793752762293965at_nat)) (and _let_3 _let_2))))))))
% 3.70/4.04 (assert (forall ((X Bool) (A tptp.set_o) (B tptp.set_o)) (let ((_let_1 (@ (@ tptp.insert_o2 X) tptp.bot_bot_set_o))) (let ((_let_2 (= B _let_1))) (let ((_let_3 (= A _let_1))) (= (= _let_1 (@ (@ tptp.sup_sup_set_o A) B)) (or (and (= A tptp.bot_bot_set_o) _let_2) (and _let_3 (= B tptp.bot_bot_set_o)) (and _let_3 _let_2))))))))
% 3.70/4.04 (assert (forall ((X tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ (@ tptp.insert_nat2 X) tptp.bot_bot_set_nat))) (let ((_let_2 (= B _let_1))) (let ((_let_3 (= A _let_1))) (= (= _let_1 (@ (@ tptp.sup_sup_set_nat A) B)) (or (and (= A tptp.bot_bot_set_nat) _let_2) (and _let_3 (= B tptp.bot_bot_set_nat)) (and _let_3 _let_2))))))))
% 3.70/4.04 (assert (forall ((X tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ (@ tptp.insert_int2 X) tptp.bot_bot_set_int))) (let ((_let_2 (= B _let_1))) (let ((_let_3 (= A _let_1))) (= (= _let_1 (@ (@ tptp.sup_sup_set_int A) B)) (or (and (= A tptp.bot_bot_set_int) _let_2) (and _let_3 (= B tptp.bot_bot_set_int)) (and _let_3 _let_2))))))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A) B) (= (@ (@ tptp.sup_su5525570899277871387at_nat A) (@ (@ tptp.minus_3314409938677909166at_nat B) A)) B))))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (= (@ (@ tptp.sup_sup_set_nat A) (@ (@ tptp.minus_minus_set_nat B) A)) B))))
% 3.70/4.04 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.minus_3314409938677909166at_nat A) B)) C2) (@ (@ tptp.ord_le1268244103169919719at_nat A) (@ (@ tptp.sup_su5525570899277871387at_nat B) C2)))))
% 3.70/4.04 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A) B)) C2) (@ (@ tptp.ord_less_eq_set_nat A) (@ (@ tptp.sup_sup_set_nat B) C2)))))
% 3.70/4.04 (assert (forall ((L tptp.list_Code_integer)) (= (@ (@ tptp.sorted710888440204495920nteger tptp.ord_le6747313008572928689nteger) L) (and (@ (@ tptp.sorted710888440204495920nteger tptp.ord_le3102999989581377725nteger) L) (@ tptp.distin1543349897113766820nteger L)))))
% 3.70/4.04 (assert (forall ((L tptp.list_num)) (= (@ (@ tptp.sorted_wrt_num tptp.ord_less_num) L) (and (@ (@ tptp.sorted_wrt_num tptp.ord_less_eq_num) L) (@ tptp.distinct_num L)))))
% 3.70/4.04 (assert (forall ((L tptp.list_nat)) (= (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) L) (and (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) L) (@ tptp.distinct_nat L)))))
% 3.70/4.04 (assert (forall ((L tptp.list_int)) (= (@ (@ tptp.sorted_wrt_int tptp.ord_less_int) L) (and (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) L) (@ tptp.distinct_int L)))))
% 3.70/4.04 (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))))
% 3.70/4.04 (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))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat))) (=> (@ _let_1 Xs) (=> (@ tptp.distinct_nat Xs) (=> (@ _let_1 Ys) (=> (@ tptp.distinct_nat Ys) (=> (= (@ tptp.set_nat2 Xs) (@ tptp.set_nat2 Ys)) (= Xs Ys)))))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.sorted_wrt_int tptp.ord_less_eq_int))) (=> (@ _let_1 Xs) (=> (@ tptp.distinct_int Xs) (=> (@ _let_1 Ys) (=> (@ tptp.distinct_int Ys) (=> (= (@ tptp.set_int2 Xs) (@ tptp.set_int2 Ys)) (= Xs Ys)))))))))
% 3.70/4.04 (assert (= tptp.sorted_wrt_c (lambda ((P2 (-> tptp.c tptp.c Bool)) (Xs3 tptp.list_c)) (forall ((I4 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_c Xs3))) (=> (@ (@ tptp.ord_less_nat I4) J2) (=> (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_c Xs3)) (@ (@ P2 (@ _let_1 I4)) (@ _let_1 J2)))))))))
% 3.70/4.04 (assert (= tptp.sorted_wrt_d (lambda ((P2 (-> tptp.d tptp.d Bool)) (Xs3 tptp.list_d)) (forall ((I4 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_d Xs3))) (=> (@ (@ tptp.ord_less_nat I4) J2) (=> (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_d Xs3)) (@ (@ P2 (@ _let_1 I4)) (@ _let_1 J2)))))))))
% 3.70/4.04 (assert (= tptp.sorted_wrt_nat (lambda ((P2 (-> tptp.nat tptp.nat Bool)) (Xs3 tptp.list_nat)) (forall ((I4 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs3))) (=> (@ (@ tptp.ord_less_nat I4) J2) (=> (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_nat Xs3)) (@ (@ P2 (@ _let_1 I4)) (@ _let_1 J2)))))))))
% 3.70/4.04 (assert (= tptp.sorted_wrt_int (lambda ((P2 (-> tptp.int tptp.int Bool)) (Xs3 tptp.list_int)) (forall ((I4 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs3))) (=> (@ (@ tptp.ord_less_nat I4) J2) (=> (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_int Xs3)) (@ (@ P2 (@ _let_1 I4)) (@ _let_1 J2)))))))))
% 3.70/4.04 (assert (forall ((P (-> tptp.c tptp.c Bool)) (Xs tptp.list_c) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_c Xs))) (=> (@ (@ tptp.sorted_wrt_c P) Xs) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_c Xs)) (@ (@ P (@ _let_1 I)) (@ _let_1 J))))))))
% 3.70/4.04 (assert (forall ((P (-> tptp.d tptp.d Bool)) (Xs tptp.list_d) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_d Xs))) (=> (@ (@ tptp.sorted_wrt_d P) Xs) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_d Xs)) (@ (@ P (@ _let_1 I)) (@ _let_1 J))))))))
% 3.70/4.04 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (Xs tptp.list_nat) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (=> (@ (@ tptp.sorted_wrt_nat P) Xs) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs)) (@ (@ P (@ _let_1 I)) (@ _let_1 J))))))))
% 3.70/4.04 (assert (forall ((P (-> tptp.int tptp.int Bool)) (Xs tptp.list_int) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs))) (=> (@ (@ tptp.sorted_wrt_int P) Xs) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_int Xs)) (@ (@ P (@ _let_1 I)) (@ _let_1 J))))))))
% 3.70/4.04 (assert (forall ((N tptp.nat) (Xs tptp.list_c)) (let ((_let_1 (@ tptp.butlast_c Xs))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_c _let_1)) (= (@ (@ tptp.nth_c _let_1) N) (@ (@ tptp.nth_c Xs) N))))))
% 3.70/4.04 (assert (forall ((N tptp.nat) (Xs tptp.list_d)) (let ((_let_1 (@ tptp.butlast_d Xs))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_d _let_1)) (= (@ (@ tptp.nth_d _let_1) N) (@ (@ tptp.nth_d Xs) N))))))
% 3.70/4.04 (assert (forall ((N tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ tptp.butlast_nat Xs))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat _let_1)) (= (@ (@ tptp.nth_nat _let_1) N) (@ (@ tptp.nth_nat Xs) N))))))
% 3.70/4.04 (assert (forall ((N tptp.nat) (Xs tptp.list_int)) (let ((_let_1 (@ tptp.butlast_int Xs))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int _let_1)) (= (@ (@ tptp.nth_int _let_1) N) (@ (@ tptp.nth_int Xs) N))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_nat)) (= (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) Xs) (forall ((I4 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (=> (@ (@ tptp.ord_less_eq_nat I4) J2) (=> (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I4)) (@ _let_1 J2)))))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_int)) (= (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) Xs) (forall ((I4 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs))) (=> (@ (@ tptp.ord_less_eq_nat I4) J2) (=> (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_int Xs)) (@ (@ tptp.ord_less_eq_int (@ _let_1 I4)) (@ _let_1 J2)))))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_nat) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (=> (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) Xs) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I)) (@ _let_1 J))))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_int) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs))) (=> (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) Xs) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_int Xs)) (@ (@ tptp.ord_less_eq_int (@ _let_1 I)) (@ _let_1 J))))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_nat)) (= (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) Xs) (forall ((I4 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (=> (@ (@ tptp.ord_less_nat I4) J2) (=> (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I4)) (@ _let_1 J2)))))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_int)) (= (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) Xs) (forall ((I4 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs))) (=> (@ (@ tptp.ord_less_nat I4) J2) (=> (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_int Xs)) (@ (@ tptp.ord_less_eq_int (@ _let_1 I4)) (@ _let_1 J2)))))))))
% 3.70/4.04 (assert (forall ((L tptp.list_nat)) (let ((_let_1 (@ tptp.merges1656613366846331073ps_nat L))) (and (@ tptp.distinct_nat _let_1) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) _let_1) (= (@ tptp.set_nat2 _let_1) (@ tptp.set_nat2 L))))))
% 3.70/4.04 (assert (forall ((L tptp.list_int)) (let ((_let_1 (@ tptp.merges1654122896337280797ps_int L))) (and (@ tptp.distinct_int _let_1) (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) _let_1) (= (@ tptp.set_int2 _let_1) (@ tptp.set_int2 L))))))
% 3.70/4.04 (assert (forall ((P (-> tptp.produc3658429121746597890et_nat Bool)) (Q (-> tptp.produc3658429121746597890et_nat Bool)) (H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (= (@ (@ (@ tptp.times_assn_raw P) Q) (@ (@ tptp.produc7507926704131184380et_nat H2) As2)) (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) (@ P (@ _let_1 As1)) (@ Q (@ _let_1 As22))))))))
% 3.70/4.04 (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 ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (= Xb (@ (@ tptp.produc7507926704131184380et_nat H) As)) (= Y (not (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) (@ X (@ _let_1 As1)) (@ Xa (@ _let_1 As22)))))))))))))
% 3.70/4.04 (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 ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (= Xb (@ (@ tptp.produc7507926704131184380et_nat H) As)) (not (exists ((As12 tptp.set_nat) (As23 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H))) (and (= As (@ (@ 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))))))))))))
% 3.70/4.04 (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 ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (= Xb (@ (@ tptp.produc7507926704131184380et_nat H) As)) (exists ((As13 tptp.set_nat) (As24 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H))) (and (= As (@ (@ 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)))))))))))
% 3.70/4.04 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool)) (M2 tptp.nat)) (=> (forall ((K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (@ P K))) (=> (forall ((K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (=> (forall ((I6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) I6) (@ P I6))) (@ P K)))) (@ P M2)))))
% 3.70/4.04 (assert (forall ((L12 tptp.list_nat) (L23 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.merge_nat L12) L23))) (let ((_let_2 (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat))) (=> (and (@ tptp.distinct_nat L12) (@ _let_2 L12)) (=> (and (@ tptp.distinct_nat L23) (@ _let_2 L23)) (and (@ tptp.distinct_nat _let_1) (@ _let_2 _let_1) (= (@ tptp.set_nat2 _let_1) (@ (@ tptp.sup_sup_set_nat (@ tptp.set_nat2 L12)) (@ tptp.set_nat2 L23))))))))))
% 3.70/4.04 (assert (forall ((L12 tptp.list_int) (L23 tptp.list_int)) (let ((_let_1 (@ (@ tptp.merge_int L12) L23))) (let ((_let_2 (@ tptp.sorted_wrt_int tptp.ord_less_eq_int))) (=> (and (@ tptp.distinct_int L12) (@ _let_2 L12)) (=> (and (@ tptp.distinct_int L23) (@ _let_2 L23)) (and (@ tptp.distinct_int _let_1) (@ _let_2 _let_1) (= (@ tptp.set_int2 _let_1) (@ (@ tptp.sup_sup_set_int (@ tptp.set_int2 L12)) (@ tptp.set_int2 L23))))))))))
% 3.70/4.04 (assert (forall ((From tptp.nat) (To tptp.nat) (Xs tptp.list_c) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat From) To) (=> (@ (@ tptp.ord_less_eq_nat To) (@ tptp.size_size_list_c Xs)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.minus_minus_nat To) From)) (= (@ (@ tptp.nth_c (@ (@ (@ tptp.slice_c From) To) Xs)) I) (@ (@ tptp.nth_c Xs) (@ (@ tptp.plus_plus_nat From) I))))))))
% 3.70/4.04 (assert (forall ((From tptp.nat) (To tptp.nat) (Xs tptp.list_d) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat From) To) (=> (@ (@ tptp.ord_less_eq_nat To) (@ tptp.size_size_list_d Xs)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.minus_minus_nat To) From)) (= (@ (@ tptp.nth_d (@ (@ (@ tptp.slice_d From) To) Xs)) I) (@ (@ tptp.nth_d Xs) (@ (@ tptp.plus_plus_nat From) I))))))))
% 3.70/4.04 (assert (forall ((From tptp.nat) (To tptp.nat) (Xs tptp.list_nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat From) To) (=> (@ (@ tptp.ord_less_eq_nat To) (@ tptp.size_size_list_nat Xs)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.minus_minus_nat To) From)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.slice_nat From) To) Xs)) I) (@ (@ tptp.nth_nat Xs) (@ (@ tptp.plus_plus_nat From) I))))))))
% 3.70/4.04 (assert (forall ((From tptp.nat) (To tptp.nat) (Xs tptp.list_int) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat From) To) (=> (@ (@ tptp.ord_less_eq_nat To) (@ tptp.size_size_list_int Xs)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.minus_minus_nat To) From)) (= (@ (@ tptp.nth_int (@ (@ (@ tptp.slice_int From) To) Xs)) I) (@ (@ tptp.nth_int Xs) (@ (@ tptp.plus_plus_nat From) I))))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_nat)) (= (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) (@ tptp.rev_nat Xs)) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (let ((_let_2 (@ tptp.suc I4))) (=> (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.ord_less_eq_nat (@ _let_1 _let_2)) (@ _let_1 I4)))))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_int)) (= (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) (@ tptp.rev_int Xs)) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs))) (let ((_let_2 (@ tptp.suc I4))) (=> (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_size_list_int Xs)) (@ (@ tptp.ord_less_eq_int (@ _let_1 _let_2)) (@ _let_1 I4)))))))))
% 3.70/4.04 (assert (forall ((B2 tptp.multis2468970476368604999at_nat) (A2 tptp.multis2468970476368604999at_nat) (C tptp.multis2468970476368604999at_nat)) (= (= (@ (@ tptp.plus_p7104986032573967614at_nat B2) A2) (@ (@ tptp.plus_p7104986032573967614at_nat C) A2)) (= B2 C))))
% 3.70/4.04 (assert (forall ((B2 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B2) A2) (@ (@ tptp.plus_plus_rat C) A2)) (= B2 C))))
% 3.70/4.04 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B2) A2) (@ (@ tptp.plus_plus_nat C) A2)) (= B2 C))))
% 3.70/4.04 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C tptp.int)) (= (= (@ (@ tptp.plus_plus_int B2) A2) (@ (@ tptp.plus_plus_int C) A2)) (= B2 C))))
% 3.70/4.04 (assert (forall ((A2 tptp.multis2468970476368604999at_nat) (B2 tptp.multis2468970476368604999at_nat) (C tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.plus_p7104986032573967614at_nat A2))) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A2))) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A2))) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A2))) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))))
% 3.70/4.04 (assert (forall ((P tptp.assn) (Q tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn (@ (@ tptp.sup_sup_assn P) Q)) H2) (or (@ (@ tptp.rep_assn P) H2) (@ (@ tptp.rep_assn Q) H2)))))
% 3.70/4.04 (assert (forall ((A2 Bool) (B2 Bool)) (= (@ (@ tptp.sup_sup_assn (@ tptp.pure_assn A2)) (@ tptp.pure_assn B2)) (@ tptp.pure_assn (or A2 B2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B2) C)) (@ (@ tptp.ord_less_eq_rat A2) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B2) C)) (@ (@ tptp.ord_less_eq_nat A2) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.ord_less_eq_int A2) B2))))
% 3.70/4.04 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_rat A2) B2)))))
% 3.70/4.04 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_nat A2) B2)))))
% 3.70/4.04 (assert (forall ((C tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_int A2) B2)))))
% 3.70/4.04 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_rat A2) B2)))))
% 3.70/4.04 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger C))) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_le6747313008572928689nteger A2) B2)))))
% 3.70/4.04 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_nat A2) B2)))))
% 3.70/4.04 (assert (forall ((C tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_int A2) B2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B2) C)) (@ (@ tptp.ord_less_rat A2) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) C)) (@ (@ tptp.plus_p5714425477246183910nteger B2) C)) (@ (@ tptp.ord_le6747313008572928689nteger A2) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B2) C)) (@ (@ tptp.ord_less_nat A2) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.ord_less_int A2) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A2) B2)) B2) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A2) B2)) B2) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A2) B2)) B2) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A2) B2)) B2) A2)))
% 3.70/4.04 (assert (forall ((C tptp.multis2468970476368604999at_nat) (A2 tptp.multis2468970476368604999at_nat) (B2 tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.plus_p7104986032573967614at_nat C))) (= (@ (@ tptp.minus_4286766774447292334at_nat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.minus_4286766774447292334at_nat A2) B2)))))
% 3.70/4.04 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.minus_minus_rat A2) B2)))))
% 3.70/4.04 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.minus_minus_nat A2) B2)))))
% 3.70/4.04 (assert (forall ((C tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.minus_minus_int (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.minus_minus_int A2) B2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.multis2468970476368604999at_nat) (B2 tptp.multis2468970476368604999at_nat)) (= (@ (@ tptp.minus_4286766774447292334at_nat (@ (@ tptp.plus_p7104986032573967614at_nat A2) B2)) A2) B2)))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A2) B2)) A2) B2)))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A2) B2)) A2) B2)))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A2) B2)) A2) B2)))
% 3.70/4.04 (assert (forall ((A2 tptp.multis2468970476368604999at_nat) (C tptp.multis2468970476368604999at_nat) (B2 tptp.multis2468970476368604999at_nat)) (= (@ (@ tptp.minus_4286766774447292334at_nat (@ (@ tptp.plus_p7104986032573967614at_nat A2) C)) (@ (@ tptp.plus_p7104986032573967614at_nat B2) C)) (@ (@ tptp.minus_4286766774447292334at_nat A2) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B2) C)) (@ (@ tptp.minus_minus_rat A2) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B2) C)) (@ (@ tptp.minus_minus_nat A2) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.minus_minus_int A2) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.multis2468970476368604999at_nat) (B2 tptp.multis2468970476368604999at_nat)) (= (@ (@ tptp.minus_4286766774447292334at_nat (@ (@ tptp.plus_p7104986032573967614at_nat A2) B2)) B2) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A2) B2)) B2) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A2) B2)) B2) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A2) B2)) B2) A2)))
% 3.70/4.04 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc N))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_nat (@ tptp.suc M2)) (@ tptp.suc N)))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M2)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M2) N))))
% 3.70/4.04 (assert (forall ((K3 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K3))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M2) N)))))
% 3.70/4.04 (assert (forall ((B2 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B2) A2) (= (@ (@ tptp.plus_plus_rat B2) (@ (@ tptp.minus_minus_rat A2) B2)) A2))))
% 3.70/4.04 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (= (@ (@ tptp.plus_plus_nat B2) (@ (@ tptp.minus_minus_nat A2) B2)) A2))))
% 3.70/4.04 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (= (@ (@ tptp.plus_plus_int B2) (@ (@ tptp.minus_minus_int A2) B2)) A2))))
% 3.70/4.04 (assert (forall ((B2 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B2) A2) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A2) B2)) B2) A2))))
% 3.70/4.04 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat A2) B2)) B2) A2))))
% 3.70/4.04 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A2) B2)) B2) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.suc A2))) (=> (@ (@ tptp.ord_less_nat A2) B2) (= (@ (@ tptp.ord_min_nat _let_1) B2) _let_1)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.suc A2))) (=> (@ (@ tptp.ord_less_nat A2) B2) (= (@ (@ tptp.ord_min_nat B2) _let_1) _let_1)))))
% 3.70/4.04 (assert (forall ((P tptp.assn) (Q tptp.assn) (H2 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) tptp.bot_bot_set_nat))) (= (@ (@ tptp.rep_assn (@ (@ tptp.sup_sup_assn P) Q)) _let_1) (or (@ (@ tptp.rep_assn P) _let_1) (@ (@ tptp.rep_assn Q) _let_1))))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M2) (= (@ tptp.suc (@ _let_1 M2)) (@ _let_1 (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat))))))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (not (forall ((Q5 tptp.nat)) (not (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) Q5)))))))))
% 3.70/4.04 (assert (forall ((I tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) M2)))))
% 3.70/4.04 (assert (forall ((I tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) I)))))
% 3.70/4.04 (assert (= tptp.ord_less_nat (lambda ((M tptp.nat) (N2 tptp.nat)) (exists ((K4 tptp.nat)) (= N2 (@ tptp.suc (@ (@ tptp.plus_plus_nat M) K4)))))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (exists ((K tptp.nat)) (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) K)))))))
% 3.70/4.04 (assert (forall ((B2 tptp.multis2468970476368604999at_nat) (A2 tptp.multis2468970476368604999at_nat) (C tptp.multis2468970476368604999at_nat)) (=> (= (@ (@ tptp.plus_p7104986032573967614at_nat B2) A2) (@ (@ tptp.plus_p7104986032573967614at_nat C) A2)) (= B2 C))))
% 3.70/4.04 (assert (forall ((B2 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat B2) A2) (@ (@ tptp.plus_plus_rat C) A2)) (= B2 C))))
% 3.70/4.04 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat B2) A2) (@ (@ tptp.plus_plus_nat C) A2)) (= B2 C))))
% 3.70/4.04 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C tptp.int)) (=> (= (@ (@ tptp.plus_plus_int B2) A2) (@ (@ tptp.plus_plus_int C) A2)) (= B2 C))))
% 3.70/4.04 (assert (forall ((A2 tptp.multis2468970476368604999at_nat) (B2 tptp.multis2468970476368604999at_nat) (C tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.plus_p7104986032573967614at_nat A2))) (=> (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A2))) (=> (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A2))) (=> (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A2))) (=> (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))))
% 3.70/4.04 (assert (forall ((B2 tptp.multis2468970476368604999at_nat) (A2 tptp.multis2468970476368604999at_nat) (C tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.plus_p7104986032573967614at_nat B2))) (let ((_let_2 (@ tptp.plus_p7104986032573967614at_nat A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 3.70/4.04 (assert (forall ((B2 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat B2))) (let ((_let_2 (@ tptp.plus_plus_rat A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 3.70/4.04 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat B2))) (let ((_let_2 (@ tptp.plus_plus_nat A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 3.70/4.04 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int B2))) (let ((_let_2 (@ tptp.plus_plus_int A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 3.70/4.04 (assert (= tptp.plus_p7104986032573967614at_nat (lambda ((A3 tptp.multis2468970476368604999at_nat) (B3 tptp.multis2468970476368604999at_nat)) (@ (@ tptp.plus_p7104986032573967614at_nat B3) A3))))
% 3.70/4.04 (assert (= tptp.plus_plus_rat (lambda ((A3 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.plus_plus_rat B3) A3))))
% 3.70/4.04 (assert (= tptp.plus_plus_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.plus_plus_nat B3) A3))))
% 3.70/4.04 (assert (= tptp.plus_plus_int (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ tptp.plus_plus_int B3) A3))))
% 3.70/4.04 (assert (forall ((B2 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B2) A2) (@ (@ tptp.plus_plus_rat C) A2)) (= B2 C))))
% 3.70/4.04 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C tptp.int)) (= (= (@ (@ tptp.plus_plus_int B2) A2) (@ (@ tptp.plus_plus_int C) A2)) (= B2 C))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A2))) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A2))) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))))
% 3.70/4.04 (assert (forall ((A2 tptp.multis2468970476368604999at_nat) (B2 tptp.multis2468970476368604999at_nat) (C tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.plus_p7104986032573967614at_nat A2))) (= (@ (@ tptp.plus_p7104986032573967614at_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_p7104986032573967614at_nat B2) C))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A2))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B2) C))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A2))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B2) C))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A2))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B2) C))))))
% 3.70/4.04 (assert (forall ((B tptp.multis2468970476368604999at_nat) (K3 tptp.multis2468970476368604999at_nat) (B2 tptp.multis2468970476368604999at_nat) (A2 tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.plus_p7104986032573967614at_nat A2))) (let ((_let_2 (@ tptp.plus_p7104986032573967614at_nat K3))) (=> (= B (@ _let_2 B2)) (= (@ _let_1 B) (@ _let_2 (@ _let_1 B2))))))))
% 3.70/4.04 (assert (forall ((B tptp.rat) (K3 tptp.rat) (B2 tptp.rat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A2))) (let ((_let_2 (@ tptp.plus_plus_rat K3))) (=> (= B (@ _let_2 B2)) (= (@ _let_1 B) (@ _let_2 (@ _let_1 B2))))))))
% 3.70/4.04 (assert (forall ((B tptp.nat) (K3 tptp.nat) (B2 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A2))) (let ((_let_2 (@ tptp.plus_plus_nat K3))) (=> (= B (@ _let_2 B2)) (= (@ _let_1 B) (@ _let_2 (@ _let_1 B2))))))))
% 3.70/4.04 (assert (forall ((B tptp.int) (K3 tptp.int) (B2 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A2))) (let ((_let_2 (@ tptp.plus_plus_int K3))) (=> (= B (@ _let_2 B2)) (= (@ _let_1 B) (@ _let_2 (@ _let_1 B2))))))))
% 3.70/4.04 (assert (forall ((A tptp.multis2468970476368604999at_nat) (K3 tptp.multis2468970476368604999at_nat) (A2 tptp.multis2468970476368604999at_nat) (B2 tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.plus_p7104986032573967614at_nat K3))) (=> (= A (@ _let_1 A2)) (= (@ (@ tptp.plus_p7104986032573967614at_nat A) B2) (@ _let_1 (@ (@ tptp.plus_p7104986032573967614at_nat A2) B2)))))))
% 3.70/4.04 (assert (forall ((A tptp.rat) (K3 tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat K3))) (=> (= A (@ _let_1 A2)) (= (@ (@ tptp.plus_plus_rat A) B2) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) B2)))))))
% 3.70/4.04 (assert (forall ((A tptp.nat) (K3 tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K3))) (=> (= A (@ _let_1 A2)) (= (@ (@ tptp.plus_plus_nat A) B2) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) B2)))))))
% 3.70/4.04 (assert (forall ((A tptp.int) (K3 tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K3))) (=> (= A (@ _let_1 A2)) (= (@ (@ tptp.plus_plus_int A) B2) (@ _let_1 (@ (@ tptp.plus_plus_int A2) B2)))))))
% 3.70/4.04 (assert (forall ((I tptp.rat) (J tptp.rat) (K3 tptp.rat) (L tptp.rat)) (=> (and (= I J) (= K3 L)) (= (@ (@ tptp.plus_plus_rat I) K3) (@ (@ tptp.plus_plus_rat J) L)))))
% 3.70/4.04 (assert (forall ((I tptp.nat) (J tptp.nat) (K3 tptp.nat) (L tptp.nat)) (=> (and (= I J) (= K3 L)) (= (@ (@ tptp.plus_plus_nat I) K3) (@ (@ tptp.plus_plus_nat J) L)))))
% 3.70/4.04 (assert (forall ((I tptp.int) (J tptp.int) (K3 tptp.int) (L tptp.int)) (=> (and (= I J) (= K3 L)) (= (@ (@ tptp.plus_plus_int I) K3) (@ (@ tptp.plus_plus_int J) L)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B2) C)) (@ (@ tptp.ord_less_eq_rat A2) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B2) C)) (@ (@ tptp.ord_less_eq_nat A2) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.ord_less_eq_int A2) B2))))
% 3.70/4.04 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_rat A2) B2)))))
% 3.70/4.04 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_nat A2) B2)))))
% 3.70/4.04 (assert (forall ((C tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_int A2) B2)))))
% 3.70/4.04 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (exists ((C5 tptp.nat)) (= B3 (@ (@ tptp.plus_plus_nat A3) C5))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B2) C)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B2) C)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B2) C)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (not (forall ((C4 tptp.nat)) (not (= B2 (@ (@ tptp.plus_plus_nat A2) C4))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_eq_rat C) D2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B2) D2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B2) D2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_eq_int C) D2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B2) D2))))))
% 3.70/4.04 (assert (forall ((I tptp.rat) (J tptp.rat) (K3 tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I) J) (@ (@ tptp.ord_less_eq_rat K3) L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K3)) (@ (@ tptp.plus_plus_rat J) L)))))
% 3.70/4.04 (assert (forall ((I tptp.nat) (J tptp.nat) (K3 tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat K3) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K3)) (@ (@ tptp.plus_plus_nat J) L)))))
% 3.70/4.04 (assert (forall ((I tptp.int) (J tptp.int) (K3 tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I) J) (@ (@ tptp.ord_less_eq_int K3) L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K3)) (@ (@ tptp.plus_plus_int J) L)))))
% 3.70/4.04 (assert (forall ((I tptp.rat) (J tptp.rat) (K3 tptp.rat) (L tptp.rat)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_rat K3) L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K3)) (@ (@ tptp.plus_plus_rat J) L)))))
% 3.70/4.04 (assert (forall ((I tptp.nat) (J tptp.nat) (K3 tptp.nat) (L tptp.nat)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_nat K3) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K3)) (@ (@ tptp.plus_plus_nat J) L)))))
% 3.70/4.04 (assert (forall ((I tptp.int) (J tptp.int) (K3 tptp.int) (L tptp.int)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_int K3) L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K3)) (@ (@ tptp.plus_plus_int J) L)))))
% 3.70/4.04 (assert (forall ((I tptp.rat) (J tptp.rat) (K3 tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I) J) (= K3 L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K3)) (@ (@ tptp.plus_plus_rat J) L)))))
% 3.70/4.04 (assert (forall ((I tptp.nat) (J tptp.nat) (K3 tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (= K3 L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K3)) (@ (@ tptp.plus_plus_nat J) L)))))
% 3.70/4.04 (assert (forall ((I tptp.int) (J tptp.int) (K3 tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I) J) (= K3 L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K3)) (@ (@ tptp.plus_plus_int J) L)))))
% 3.70/4.04 (assert (forall ((I tptp.rat) (J tptp.rat) (K3 tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I) J) (@ (@ tptp.ord_less_rat K3) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K3)) (@ (@ tptp.plus_plus_rat J) L)))))
% 3.70/4.04 (assert (forall ((I tptp.code_integer) (J tptp.code_integer) (K3 tptp.code_integer) (L tptp.code_integer)) (=> (and (@ (@ tptp.ord_le6747313008572928689nteger I) J) (@ (@ tptp.ord_le6747313008572928689nteger K3) L)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger I) K3)) (@ (@ tptp.plus_p5714425477246183910nteger J) L)))))
% 3.70/4.04 (assert (forall ((I tptp.nat) (J tptp.nat) (K3 tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_nat K3) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K3)) (@ (@ tptp.plus_plus_nat J) L)))))
% 3.70/4.04 (assert (forall ((I tptp.int) (J tptp.int) (K3 tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I) J) (@ (@ tptp.ord_less_int K3) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K3)) (@ (@ tptp.plus_plus_int J) L)))))
% 3.70/4.04 (assert (forall ((I tptp.rat) (J tptp.rat) (K3 tptp.rat) (L tptp.rat)) (=> (and (= I J) (@ (@ tptp.ord_less_rat K3) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K3)) (@ (@ tptp.plus_plus_rat J) L)))))
% 3.70/4.04 (assert (forall ((I tptp.code_integer) (J tptp.code_integer) (K3 tptp.code_integer) (L tptp.code_integer)) (=> (and (= I J) (@ (@ tptp.ord_le6747313008572928689nteger K3) L)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger I) K3)) (@ (@ tptp.plus_p5714425477246183910nteger J) L)))))
% 3.70/4.04 (assert (forall ((I tptp.nat) (J tptp.nat) (K3 tptp.nat) (L tptp.nat)) (=> (and (= I J) (@ (@ tptp.ord_less_nat K3) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K3)) (@ (@ tptp.plus_plus_nat J) L)))))
% 3.70/4.04 (assert (forall ((I tptp.int) (J tptp.int) (K3 tptp.int) (L tptp.int)) (=> (and (= I J) (@ (@ tptp.ord_less_int K3) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K3)) (@ (@ tptp.plus_plus_int J) L)))))
% 3.70/4.04 (assert (forall ((I tptp.rat) (J tptp.rat) (K3 tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I) J) (= K3 L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K3)) (@ (@ tptp.plus_plus_rat J) L)))))
% 3.70/4.04 (assert (forall ((I tptp.code_integer) (J tptp.code_integer) (K3 tptp.code_integer) (L tptp.code_integer)) (=> (and (@ (@ tptp.ord_le6747313008572928689nteger I) J) (= K3 L)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger I) K3)) (@ (@ tptp.plus_p5714425477246183910nteger J) L)))))
% 3.70/4.04 (assert (forall ((I tptp.nat) (J tptp.nat) (K3 tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (= K3 L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K3)) (@ (@ tptp.plus_plus_nat J) L)))))
% 3.70/4.04 (assert (forall ((I tptp.int) (J tptp.int) (K3 tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I) J) (= K3 L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K3)) (@ (@ tptp.plus_plus_int J) L)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (@ (@ tptp.ord_less_rat C) D2) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B2) D2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) D2) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) C)) (@ (@ tptp.plus_p5714425477246183910nteger B2) D2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_nat C) D2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B2) D2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ (@ tptp.ord_less_int C) D2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B2) D2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_rat A2) B2) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_nat A2) B2) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_int A2) B2) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B2) C)))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) C)) (@ (@ tptp.plus_p5714425477246183910nteger B2) C)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B2) C)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B2) C)))))
% 3.70/4.04 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_rat A2) B2)))))
% 3.70/4.04 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_le6747313008572928689nteger A2) B2)))))
% 3.70/4.04 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_nat A2) B2)))))
% 3.70/4.04 (assert (forall ((C tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_int A2) B2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B2) C)) (@ (@ tptp.ord_less_rat A2) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) C)) (@ (@ tptp.plus_p5714425477246183910nteger B2) C)) (@ (@ tptp.ord_le6747313008572928689nteger A2) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B2) C)) (@ (@ tptp.ord_less_nat A2) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.ord_less_int A2) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B2) C)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A2) B2)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B2) C)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A2) B2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B2) C)))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A2))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B2) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 B2)) (@ _let_1 C))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B2) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B2)) (@ _let_1 C))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B2)) (@ _let_1 C))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B2) C)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A2) B2)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B2) C)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A2) B2)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B2) C)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A2) B2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B2) C)))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A2))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B2) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 B2)) (@ _let_1 C))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B2) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B2)) (@ _let_1 C))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B2) C)) (@ (@ tptp.plus_plus_nat (@ _let_1 B2)) (@ _let_1 C))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B2)) (@ _let_1 C))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B2) C)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A2) B2)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B2) C)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A2) B2)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B2) C)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A2) B2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B2) C)))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (E tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A2) E)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B2) E)) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)) E)) C))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (E tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) E)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B2) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A2) B2)) E)) C))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (E tptp.nat) (B2 tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A2) E)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B2) E)) C)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A2) B2)) E)) C))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (E tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) E)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A2) B2)) E)) C))))
% 3.70/4.04 (assert (forall ((A tptp.rat) (K3 tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat K3))) (=> (= A (@ _let_1 A2)) (= (@ (@ tptp.minus_minus_rat A) B2) (@ _let_1 (@ (@ tptp.minus_minus_rat A2) B2)))))))
% 3.70/4.04 (assert (forall ((A tptp.int) (K3 tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K3))) (=> (= A (@ _let_1 A2)) (= (@ (@ tptp.minus_minus_int A) B2) (@ _let_1 (@ (@ tptp.minus_minus_int A2) B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.minus_minus_rat A2) B2) C) (= A2 (@ (@ tptp.plus_plus_rat C) B2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (= (= (@ (@ tptp.minus_minus_int A2) B2) C) (= A2 (@ (@ tptp.plus_plus_int C) B2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (= A2 (@ (@ tptp.minus_minus_rat C) B2)) (= (@ (@ tptp.plus_plus_rat A2) B2) C))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int)) (= (= A2 (@ (@ tptp.minus_minus_int C) B2)) (= (@ (@ tptp.plus_plus_int A2) B2) C))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B2) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B2)) C)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B2) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B2)) C)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.minus_minus_rat A2) (@ (@ tptp.minus_minus_rat B2) C)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A2) C)) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.minus_minus_int A2) (@ (@ tptp.minus_minus_int B2) C)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A2) C)) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A2) B2)) C) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A2) C)) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A2) B2)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A2) C)) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B2) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 C)) B2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.minus_minus_int (@ _let_1 C)) B2)))))
% 3.70/4.04 (assert (forall ((C tptp.multis2468970476368604999at_nat) (B2 tptp.multis2468970476368604999at_nat) (A2 tptp.multis2468970476368604999at_nat)) (=> (= (@ (@ tptp.plus_p7104986032573967614at_nat C) B2) A2) (= C (@ (@ tptp.minus_4286766774447292334at_nat A2) B2)))))
% 3.70/4.04 (assert (forall ((C tptp.rat) (B2 tptp.rat) (A2 tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat C) B2) A2) (= C (@ (@ tptp.minus_minus_rat A2) B2)))))
% 3.70/4.04 (assert (forall ((C tptp.nat) (B2 tptp.nat) (A2 tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat C) B2) A2) (= C (@ (@ tptp.minus_minus_nat A2) B2)))))
% 3.70/4.04 (assert (forall ((C tptp.int) (B2 tptp.int) (A2 tptp.int)) (=> (= (@ (@ tptp.plus_plus_int C) B2) A2) (= C (@ (@ tptp.minus_minus_int A2) B2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.multis2468970476368604999at_nat) (B2 tptp.multis2468970476368604999at_nat) (C tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.minus_4286766774447292334at_nat A2))) (= (@ (@ tptp.minus_4286766774447292334at_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_p7104986032573967614at_nat B2) C))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A2))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B2) C))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B2) C))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A2))) (= (@ (@ tptp.minus_minus_int (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B2) C))))))
% 3.70/4.04 (assert (forall ((A tptp.assn) (B tptp.assn) (C2 tptp.assn)) (= (@ (@ tptp.times_times_assn (@ (@ tptp.sup_sup_assn A) B)) C2) (@ (@ tptp.sup_sup_assn (@ (@ tptp.times_times_assn A) C2)) (@ (@ tptp.times_times_assn B) C2)))))
% 3.70/4.04 (assert (forall ((C2 tptp.assn) (A tptp.assn) (B tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn C2))) (= (@ _let_1 (@ (@ tptp.sup_sup_assn A) B)) (@ (@ tptp.sup_sup_assn (@ _let_1 A)) (@ _let_1 B))))))
% 3.70/4.04 (assert (forall ((I tptp.nat) (K3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K3) (=> (not (= K3 (@ tptp.suc I))) (not (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J3) (not (= K3 (@ tptp.suc J3))))))))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M2)) N) (@ (@ tptp.ord_less_nat M2) N))))
% 3.70/4.04 (assert (forall ((I tptp.nat) (K3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K3) (not (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J3) (not (= K3 (@ tptp.suc J3)))))))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc M2))) (=> (@ (@ tptp.ord_less_nat M2) N) (=> (not (= _let_1 N)) (@ (@ tptp.ord_less_nat _let_1) N))))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M2))) (=> (@ _let_1 (@ tptp.suc N)) (=> (not (@ _let_1 N)) (= M2 N))))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M2))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))))
% 3.70/4.04 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N)) (@ P I4))) (or (@ P N) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) N) (@ P I4)))))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M2))) (= (@ _let_1 (@ tptp.suc N)) (or (@ _let_1 N) (= M2 N))))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M2) N)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc M2)))))
% 3.70/4.04 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N)) (@ P I4))) (and (@ P N) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N) (@ P I4)))))))
% 3.70/4.04 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N)) M2) (exists ((M4 tptp.nat)) (and (= M2 (@ tptp.suc M4)) (@ (@ tptp.ord_less_nat N) M4))))))
% 3.70/4.04 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M2)) (=> (@ _let_1 (@ tptp.suc M2)) (= M2 N))))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M2)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M2) N))))
% 3.70/4.04 (assert (forall ((I tptp.nat) (J tptp.nat) (K3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) K3) (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K3)))))
% 3.70/4.04 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (forall ((I5 tptp.nat)) (@ (@ P I5) (@ tptp.suc I5))) (=> (forall ((I5 tptp.nat) (J3 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ P I5))) (=> (@ (@ tptp.ord_less_nat I5) J3) (=> (@ (@ tptp.ord_less_nat J3) K) (=> (@ _let_1 J3) (=> (@ (@ P J3) K) (@ _let_1 K))))))) (@ (@ P I) J))))))
% 3.70/4.04 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (forall ((I5 tptp.nat)) (=> (= J (@ tptp.suc I5)) (@ P I5))) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) J) (=> (@ P (@ tptp.suc I5)) (@ P I5)))) (@ P I))))))
% 3.70/4.04 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M2)) (= (@ _let_1 (@ tptp.suc M2)) (= N M2))))))
% 3.70/4.04 (assert (forall ((I tptp.nat) (J tptp.nat) (K3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) K3) (@ (@ tptp.ord_less_nat I) K3))))
% 3.70/4.04 (assert (forall ((I tptp.nat) (J tptp.nat) (K3 tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat K3) L) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K3)) (@ (@ tptp.plus_plus_nat J) L))))))
% 3.70/4.04 (assert (forall ((I tptp.nat) (J tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) I))))
% 3.70/4.04 (assert (forall ((J tptp.nat) (I tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J) I)) I))))
% 3.70/4.04 (assert (forall ((I tptp.nat) (J tptp.nat) (K3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K3)) (@ (@ tptp.plus_plus_nat J) K3)))))
% 3.70/4.04 (assert (forall ((I tptp.nat) (J tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M2))))))
% 3.70/4.04 (assert (forall ((I tptp.nat) (J tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M2) J))))))
% 3.70/4.04 (assert (forall ((K3 tptp.nat) (L tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat K3) L) (=> (= (@ (@ tptp.plus_plus_nat M2) L) (@ (@ tptp.plus_plus_nat K3) N)) (@ (@ tptp.ord_less_nat M2) N)))))
% 3.70/4.04 (assert (forall ((B tptp.assn) (A tptp.assn)) (@ (@ tptp.entails B) (@ (@ tptp.sup_sup_assn A) B))))
% 3.70/4.04 (assert (forall ((A tptp.assn) (B tptp.assn)) (@ (@ tptp.entails A) (@ (@ tptp.sup_sup_assn A) B))))
% 3.70/4.04 (assert (forall ((A tptp.assn) (C2 tptp.assn) (B tptp.assn)) (let ((_let_1 (@ tptp.entails A))) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.sup_sup_assn B) C2))))))
% 3.70/4.04 (assert (forall ((A tptp.assn) (B tptp.assn) (C2 tptp.assn)) (let ((_let_1 (@ tptp.entails A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_assn B) C2))))))
% 3.70/4.04 (assert (forall ((P tptp.assn) (Q tptp.assn) (R tptp.assn)) (=> (@ (@ tptp.entails (@ (@ tptp.sup_sup_assn P) Q)) R) (@ (@ tptp.entails Q) R))))
% 3.70/4.04 (assert (forall ((P tptp.assn) (Q tptp.assn) (R tptp.assn)) (=> (@ (@ tptp.entails (@ (@ tptp.sup_sup_assn P) Q)) R) (@ (@ tptp.entails P) R))))
% 3.70/4.04 (assert (forall ((A tptp.assn) (C2 tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.entails A) C2) (=> (@ (@ tptp.entails B) C2) (@ (@ tptp.entails (@ (@ tptp.sup_sup_assn A) B)) C2)))))
% 3.70/4.04 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat X))) (= (@ _let_1 (@ (@ tptp.ord_min_rat Y) Z)) (@ (@ tptp.ord_min_rat (@ _let_1 Y)) (@ _let_1 Z))))))
% 3.70/4.04 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X))) (= (@ _let_1 (@ (@ tptp.ord_min_int Y) Z)) (@ (@ tptp.ord_min_int (@ _let_1 Y)) (@ _let_1 Z))))))
% 3.70/4.04 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat X))) (= (@ _let_1 (@ (@ tptp.ord_min_nat Y) Z)) (@ (@ tptp.ord_min_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 3.70/4.04 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.ord_min_rat X) Y)) Z) (@ (@ tptp.ord_min_rat (@ (@ tptp.plus_plus_rat X) Z)) (@ (@ tptp.plus_plus_rat Y) Z)))))
% 3.70/4.04 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_min_int X) Y)) Z) (@ (@ tptp.ord_min_int (@ (@ tptp.plus_plus_int X) Z)) (@ (@ tptp.plus_plus_int Y) Z)))))
% 3.70/4.04 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_min_nat X) Y)) Z) (@ (@ tptp.ord_min_nat (@ (@ tptp.plus_plus_nat X) Z)) (@ (@ tptp.plus_plus_nat Y) Z)))))
% 3.70/4.04 (assert (forall ((A tptp.assn) (M5 tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.entailst A) M5) (=> (@ (@ tptp.entailst B) M5) (@ (@ tptp.entailst (@ (@ tptp.sup_sup_assn A) B)) M5)))))
% 3.70/4.04 (assert (forall ((A tptp.assn) (B tptp.assn) (C2 tptp.assn)) (=> (@ (@ tptp.entailst (@ (@ tptp.sup_sup_assn A) B)) C2) (@ (@ tptp.entailst A) C2))))
% 3.70/4.04 (assert (forall ((A tptp.assn) (B tptp.assn) (C2 tptp.assn)) (=> (@ (@ tptp.entailst (@ (@ tptp.sup_sup_assn A) B)) C2) (@ (@ tptp.entailst B) C2))))
% 3.70/4.04 (assert (forall ((A tptp.assn) (B tptp.assn) (C2 tptp.assn)) (let ((_let_1 (@ tptp.entailst A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_assn B) C2))))))
% 3.70/4.04 (assert (forall ((A tptp.assn) (C2 tptp.assn) (B tptp.assn)) (let ((_let_1 (@ tptp.entailst A))) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.sup_sup_assn B) C2))))))
% 3.70/4.04 (assert (forall ((A tptp.assn) (B tptp.assn)) (@ (@ tptp.entailst A) (@ (@ tptp.sup_sup_assn A) B))))
% 3.70/4.04 (assert (forall ((B tptp.assn) (A tptp.assn)) (@ (@ tptp.entailst B) (@ (@ tptp.sup_sup_assn A) B))))
% 3.70/4.04 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.sup_sup_assn X) tptp.bot_bot_assn) X)))
% 3.70/4.04 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.sup_sup_assn tptp.bot_bot_assn) X) X)))
% 3.70/4.04 (assert (forall ((I tptp.rat) (J tptp.rat) (K3 tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I) J) (@ (@ tptp.ord_less_rat K3) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K3)) (@ (@ tptp.plus_plus_rat J) L)))))
% 3.70/4.04 (assert (forall ((I tptp.code_integer) (J tptp.code_integer) (K3 tptp.code_integer) (L tptp.code_integer)) (=> (and (@ (@ tptp.ord_le3102999989581377725nteger I) J) (@ (@ tptp.ord_le6747313008572928689nteger K3) L)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger I) K3)) (@ (@ tptp.plus_p5714425477246183910nteger J) L)))))
% 3.70/4.04 (assert (forall ((I tptp.nat) (J tptp.nat) (K3 tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_nat K3) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K3)) (@ (@ tptp.plus_plus_nat J) L)))))
% 3.70/4.04 (assert (forall ((I tptp.int) (J tptp.int) (K3 tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I) J) (@ (@ tptp.ord_less_int K3) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K3)) (@ (@ tptp.plus_plus_int J) L)))))
% 3.70/4.04 (assert (forall ((I tptp.rat) (J tptp.rat) (K3 tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I) J) (@ (@ tptp.ord_less_eq_rat K3) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K3)) (@ (@ tptp.plus_plus_rat J) L)))))
% 3.70/4.04 (assert (forall ((I tptp.code_integer) (J tptp.code_integer) (K3 tptp.code_integer) (L tptp.code_integer)) (=> (and (@ (@ tptp.ord_le6747313008572928689nteger I) J) (@ (@ tptp.ord_le3102999989581377725nteger K3) L)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger I) K3)) (@ (@ tptp.plus_p5714425477246183910nteger J) L)))))
% 3.70/4.04 (assert (forall ((I tptp.nat) (J tptp.nat) (K3 tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_eq_nat K3) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K3)) (@ (@ tptp.plus_plus_nat J) L)))))
% 3.70/4.04 (assert (forall ((I tptp.int) (J tptp.int) (K3 tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I) J) (@ (@ tptp.ord_less_eq_int K3) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K3)) (@ (@ tptp.plus_plus_int J) L)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_rat C) D2) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B2) D2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) D2) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) C)) (@ (@ tptp.plus_p5714425477246183910nteger B2) D2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_nat C) D2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B2) D2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_int C) D2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B2) D2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (@ (@ tptp.ord_less_eq_rat C) D2) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B2) D2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) D2) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) C)) (@ (@ tptp.plus_p5714425477246183910nteger B2) D2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B2) D2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ (@ tptp.ord_less_eq_int C) D2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B2) D2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A2) B2)) C) (@ (@ tptp.ord_less_eq_rat A2) (@ (@ tptp.plus_plus_rat C) B2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A2) B2)) C) (@ (@ tptp.ord_less_eq_int A2) (@ (@ tptp.plus_plus_int C) B2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A2) (@ (@ tptp.minus_minus_rat C) B2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) B2)) C))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int A2) (@ (@ tptp.minus_minus_int C) B2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) B2)) C))))
% 3.70/4.04 (assert (forall ((I tptp.rat) (K3 tptp.rat) (N tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K3)) N) (@ (@ tptp.ord_less_eq_rat I) (@ (@ tptp.minus_minus_rat N) K3)))))
% 3.70/4.04 (assert (forall ((I tptp.nat) (K3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K3)) N) (@ (@ tptp.ord_less_eq_nat I) (@ (@ tptp.minus_minus_nat N) K3)))))
% 3.70/4.04 (assert (forall ((I tptp.int) (K3 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K3)) N) (@ (@ tptp.ord_less_eq_int I) (@ (@ tptp.minus_minus_int N) K3)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B2) A2)) A2) B2))))
% 3.70/4.04 (assert (forall ((I tptp.rat) (K3 tptp.rat) (N tptp.rat) (J tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_rat N) (@ (@ tptp.plus_plus_rat J) K3)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K3)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat N) K3)) J)))))))))
% 3.70/4.04 (assert (forall ((I tptp.nat) (K3 tptp.nat) (N tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat J) K3)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K3)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat N) K3)) J)))))))))
% 3.70/4.04 (assert (forall ((I tptp.int) (K3 tptp.int) (N tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int N) (@ (@ tptp.plus_plus_int J) K3)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K3)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int N) K3)) J)))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (@ (@ tptp.ord_less_eq_nat C) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B2) C)) A2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= (@ (@ tptp.ord_less_eq_nat C) (@ (@ tptp.minus_minus_nat B2) A2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat C) A2)) B2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat B2) A2)) (@ (@ tptp.minus_minus_nat (@ _let_1 B2)) A2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B2)) A2) (@ _let_1 (@ (@ tptp.minus_minus_nat B2) A2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B2) A2)) C) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B2) C)) A2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B2) C)) A2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B2) A2)) C)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= (@ (@ tptp.minus_minus_nat C) (@ (@ tptp.minus_minus_nat B2) A2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat C) A2)) B2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= (@ (@ tptp.plus_plus_nat A2) (@ (@ tptp.minus_minus_nat B2) A2)) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat A2) B2))) (=> _let_1 (=> _let_1 (= (= (@ (@ tptp.minus_minus_nat B2) A2) C) (= B2 (@ (@ tptp.plus_plus_nat C) A2))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat)) (@ (@ tptp.ord_less_rat A2) (@ (@ tptp.plus_plus_rat A2) tptp.one_one_rat))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer)) (@ (@ tptp.ord_le6747313008572928689nteger A2) (@ (@ tptp.plus_p5714425477246183910nteger A2) tptp.one_one_Code_integer))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat)) (@ (@ tptp.ord_less_nat A2) (@ (@ tptp.plus_plus_nat A2) tptp.one_one_nat))))
% 3.70/4.04 (assert (forall ((A2 tptp.int)) (@ (@ tptp.ord_less_int A2) (@ (@ tptp.plus_plus_int A2) tptp.one_one_int))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) tptp.one_one_rat)) (@ (@ tptp.plus_plus_rat B2) tptp.one_one_rat)))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) tptp.one_one_Code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger B2) tptp.one_one_Code_integer)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat B2) tptp.one_one_nat)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) tptp.one_one_int)) (@ (@ tptp.plus_plus_int B2) tptp.one_one_int)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A2) B2)) C) (@ (@ tptp.ord_less_rat A2) (@ (@ tptp.plus_plus_rat C) B2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.minus_8373710615458151222nteger A2) B2)) C) (@ (@ tptp.ord_le6747313008572928689nteger A2) (@ (@ tptp.plus_p5714425477246183910nteger C) B2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A2) B2)) C) (@ (@ tptp.ord_less_int A2) (@ (@ tptp.plus_plus_int C) B2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat A2) (@ (@ tptp.minus_minus_rat C) B2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) B2)) C))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A2) (@ (@ tptp.minus_8373710615458151222nteger C) B2)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)) C))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int A2) (@ (@ tptp.minus_minus_int C) B2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) B2)) C))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat A2) B2)) (= (@ (@ tptp.plus_plus_rat B2) (@ (@ tptp.minus_minus_rat A2) B2)) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (not (@ (@ tptp.ord_le6747313008572928689nteger A2) B2)) (= (@ (@ tptp.plus_p5714425477246183910nteger B2) (@ (@ tptp.minus_8373710615458151222nteger A2) B2)) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat A2) B2)) (= (@ (@ tptp.plus_plus_nat B2) (@ (@ tptp.minus_minus_nat A2) B2)) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (not (@ (@ tptp.ord_less_int A2) B2)) (= (@ (@ tptp.plus_plus_int B2) (@ (@ tptp.minus_minus_int A2) B2)) A2))))
% 3.70/4.04 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.times_3573771949741848930nteger X) X)) (@ (@ tptp.times_3573771949741848930nteger Y) Y)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger X) Y)) (@ (@ tptp.minus_8373710615458151222nteger X) Y)))))
% 3.70/4.04 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X) Y)) (@ (@ tptp.minus_minus_rat X) Y)))))
% 3.70/4.04 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X) Y)) (@ (@ tptp.minus_minus_int X) Y)))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (E tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer) (D2 tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A2) E)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B2) E)) D2)) (= C (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger B2) A2)) E)) D2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (E tptp.rat) (C tptp.rat) (B2 tptp.rat) (D2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) E)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B2) E)) D2)) (= C (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B2) A2)) E)) D2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (E tptp.int) (C tptp.int) (B2 tptp.int) (D2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) E)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) E)) D2)) (= C (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B2) A2)) E)) D2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (E tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer) (D2 tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A2) E)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B2) E)) D2)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger A2) B2)) E)) C) D2))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (E tptp.rat) (C tptp.rat) (B2 tptp.rat) (D2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) E)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B2) E)) D2)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A2) B2)) E)) C) D2))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (E tptp.int) (C tptp.int) (B2 tptp.int) (D2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) E)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) E)) D2)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A2) B2)) E)) C) D2))))
% 3.70/4.04 (assert (forall ((F4 (-> tptp.nat tptp.code_integer)) (N tptp.nat) (N6 tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 N5)) (@ F4 (@ tptp.suc N5)))) (=> (@ (@ tptp.ord_less_nat N) N6) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 N)) (@ F4 N6))))))
% 3.70/4.04 (assert (forall ((F4 (-> tptp.nat tptp.assn)) (N tptp.nat) (N6 tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_assn (@ F4 N5)) (@ F4 (@ tptp.suc N5)))) (=> (@ (@ tptp.ord_less_nat N) N6) (@ (@ tptp.ord_less_assn (@ F4 N)) (@ F4 N6))))))
% 3.70/4.04 (assert (forall ((F4 (-> tptp.nat tptp.num)) (N tptp.nat) (N6 tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_num (@ F4 N5)) (@ F4 (@ tptp.suc N5)))) (=> (@ (@ tptp.ord_less_nat N) N6) (@ (@ tptp.ord_less_num (@ F4 N)) (@ F4 N6))))))
% 3.70/4.04 (assert (forall ((F4 (-> tptp.nat tptp.nat)) (N tptp.nat) (N6 tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F4 N5)) (@ F4 (@ tptp.suc N5)))) (=> (@ (@ tptp.ord_less_nat N) N6) (@ (@ tptp.ord_less_nat (@ F4 N)) (@ F4 N6))))))
% 3.70/4.04 (assert (forall ((F4 (-> tptp.nat tptp.int)) (N tptp.nat) (N6 tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_int (@ F4 N5)) (@ F4 (@ tptp.suc N5)))) (=> (@ (@ tptp.ord_less_nat N) N6) (@ (@ tptp.ord_less_int (@ F4 N)) (@ F4 N6))))))
% 3.70/4.04 (assert (forall ((F4 (-> tptp.nat tptp.code_integer)) (N tptp.nat) (M2 tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 N5)) (@ F4 (@ tptp.suc N5)))) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 N)) (@ F4 M2)) (@ (@ tptp.ord_less_nat N) M2)))))
% 3.70/4.04 (assert (forall ((F4 (-> tptp.nat tptp.assn)) (N tptp.nat) (M2 tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_assn (@ F4 N5)) (@ F4 (@ tptp.suc N5)))) (= (@ (@ tptp.ord_less_assn (@ F4 N)) (@ F4 M2)) (@ (@ tptp.ord_less_nat N) M2)))))
% 3.70/4.04 (assert (forall ((F4 (-> tptp.nat tptp.num)) (N tptp.nat) (M2 tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_num (@ F4 N5)) (@ F4 (@ tptp.suc N5)))) (= (@ (@ tptp.ord_less_num (@ F4 N)) (@ F4 M2)) (@ (@ tptp.ord_less_nat N) M2)))))
% 3.70/4.04 (assert (forall ((F4 (-> tptp.nat tptp.nat)) (N tptp.nat) (M2 tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F4 N5)) (@ F4 (@ tptp.suc N5)))) (= (@ (@ tptp.ord_less_nat (@ F4 N)) (@ F4 M2)) (@ (@ tptp.ord_less_nat N) M2)))))
% 3.70/4.04 (assert (forall ((F4 (-> tptp.nat tptp.int)) (N tptp.nat) (M2 tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_int (@ F4 N5)) (@ F4 (@ tptp.suc N5)))) (= (@ (@ tptp.ord_less_int (@ F4 N)) (@ F4 M2)) (@ (@ tptp.ord_less_nat N) M2)))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N) (@ (@ tptp.ord_less_nat M2) N))))
% 3.70/4.04 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ P I) (=> (forall ((N5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N5) (=> (@ (@ tptp.ord_less_nat N5) J) (=> (@ P N5) (@ P (@ tptp.suc N5)))))) (@ P J))))))
% 3.70/4.04 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ P J) (=> (forall ((N5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N5) (=> (@ (@ tptp.ord_less_nat N5) J) (=> (@ P (@ tptp.suc N5)) (@ P N5))))) (@ P I))))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N) (@ (@ tptp.ord_less_nat M2) N))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc M2)) (= N M2)))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M2) (@ tptp.suc N)) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 3.70/4.04 (assert (= tptp.ord_less_nat (lambda ((N2 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) __flatten_var_0))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_nat M2) (@ tptp.suc N)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.suc A2))) (= (and (@ (@ tptp.ord_less_nat A2) B2) (@ (@ tptp.ord_less_eq_nat B2) _let_1)) (= B2 _let_1)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (and (@ (@ tptp.ord_less_eq_nat A2) B2) (@ (@ tptp.ord_less_nat B2) (@ tptp.suc A2))) (= B2 A2))))
% 3.70/4.04 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M2))) (=> (@ (@ tptp.ord_less_nat N) M2) (= (@ tptp.suc (@ _let_1 (@ tptp.suc N))) (@ _let_1 N))))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M2) N)) (@ tptp.suc M2))))
% 3.70/4.04 (assert (forall ((F4 (-> tptp.nat tptp.nat)) (M2 tptp.nat) (K3 tptp.nat)) (=> (forall ((M6 tptp.nat) (N5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M6) N5) (@ (@ tptp.ord_less_nat (@ F4 M6)) (@ F4 N5)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ F4 M2)) K3)) (@ F4 (@ (@ tptp.plus_plus_nat M2) K3))))))
% 3.70/4.04 (assert (forall ((K3 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K3)))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M2) N)))))
% 3.70/4.04 (assert (forall ((I tptp.nat) (J tptp.nat) (K3 tptp.nat)) (= (@ (@ tptp.ord_less_nat I) (@ (@ tptp.minus_minus_nat J) K3)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K3)) J))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M2) N)) (= (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.minus_minus_nat M2) N)) M2))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (A tptp.nat) (B2 tptp.nat) (N7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) A) (=> (@ (@ tptp.ord_less_nat B2) N7) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A2) N7)) B2)) (@ (@ tptp.times_times_nat A) N7))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (A7 tptp.nat) (B2 tptp.nat) (N7 tptp.nat) (B6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) A7) (=> (@ (@ tptp.ord_less_nat B2) N7) (=> (@ (@ tptp.ord_less_nat B6) N7) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A2) N7)) B2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A7) N7)) B6)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (A7 tptp.nat) (B2 tptp.nat) (B6 tptp.nat) (N7 tptp.nat)) (=> (= A2 A7) (=> (@ (@ tptp.ord_less_nat B2) B6) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A2) N7)) B2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A7) N7)) B6))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (A7 tptp.nat) (B2 tptp.nat) (B6 tptp.nat) (N7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) A7) (=> (@ (@ tptp.ord_less_eq_nat B2) B6) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A2) N7)) B2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A7) N7)) B6))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (E tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer) (D2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A2) E)) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B2) E)) D2)) (@ (@ tptp.ord_le3102999989581377725nteger C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger B2) A2)) E)) D2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (E tptp.rat) (C tptp.rat) (B2 tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B2) E)) D2)) (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B2) A2)) E)) D2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (E tptp.int) (C tptp.int) (B2 tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) E)) D2)) (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B2) A2)) E)) D2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (E tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer) (D2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A2) E)) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B2) E)) D2)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger A2) B2)) E)) C)) D2))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (E tptp.rat) (C tptp.rat) (B2 tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B2) E)) D2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A2) B2)) E)) C)) D2))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (E tptp.int) (C tptp.int) (B2 tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) E)) D2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A2) B2)) E)) C)) D2))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (E tptp.rat) (C tptp.rat) (B2 tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B2) E)) D2)) (@ (@ tptp.ord_less_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B2) A2)) E)) D2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (E tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer) (D2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A2) E)) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B2) E)) D2)) (@ (@ tptp.ord_le6747313008572928689nteger C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger B2) A2)) E)) D2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (E tptp.int) (C tptp.int) (B2 tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) E)) D2)) (@ (@ tptp.ord_less_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B2) A2)) E)) D2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (E tptp.rat) (C tptp.rat) (B2 tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B2) E)) D2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A2) B2)) E)) C)) D2))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (E tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer) (D2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A2) E)) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B2) E)) D2)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger A2) B2)) E)) C)) D2))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (E tptp.int) (C tptp.int) (B2 tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) E)) D2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A2) B2)) E)) C)) D2))))
% 3.70/4.04 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.times_3573771949741848930nteger X) X)) tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger X) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger X) tptp.one_one_Code_integer)))))
% 3.70/4.04 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) X)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X) tptp.one_one_rat)) (@ (@ tptp.minus_minus_rat X) tptp.one_one_rat)))))
% 3.70/4.04 (assert (forall ((X tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X) X)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) (@ (@ tptp.minus_minus_int X) tptp.one_one_int)))))
% 3.70/4.04 (assert (forall ((K3 tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J) K3)) I) (@ (@ tptp.ord_less_nat J) (@ (@ tptp.plus_plus_nat I) K3))))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) M2) (= (@ tptp.suc (@ _let_1 M2)) (@ _let_1 (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat))))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_nat)) (= (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) Xs) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.suc I4))) (let ((_let_2 (@ tptp.nth_nat Xs))) (=> (@ (@ tptp.ord_less_nat _let_1) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.ord_less_eq_nat (@ _let_2 I4)) (@ _let_2 _let_1)))))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_int)) (= (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) Xs) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.suc I4))) (let ((_let_2 (@ tptp.nth_int Xs))) (=> (@ (@ tptp.ord_less_nat _let_1) (@ tptp.size_size_list_int Xs)) (@ (@ tptp.ord_less_eq_int (@ _let_2 I4)) (@ _let_2 _let_1)))))))))
% 3.70/4.04 (assert (forall ((N tptp.nat) (Xs tptp.list_c)) (let ((_let_1 (@ tptp.size_size_list_c Xs))) (=> (@ (@ tptp.ord_less_nat N) _let_1) (= (@ (@ tptp.nth_c (@ tptp.rev_c Xs)) N) (@ (@ tptp.nth_c Xs) (@ (@ tptp.minus_minus_nat _let_1) (@ tptp.suc N))))))))
% 3.70/4.04 (assert (forall ((N tptp.nat) (Xs tptp.list_d)) (let ((_let_1 (@ tptp.size_size_list_d Xs))) (=> (@ (@ tptp.ord_less_nat N) _let_1) (= (@ (@ tptp.nth_d (@ tptp.rev_d Xs)) N) (@ (@ tptp.nth_d Xs) (@ (@ tptp.minus_minus_nat _let_1) (@ tptp.suc N))))))))
% 3.70/4.04 (assert (forall ((N tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Xs))) (=> (@ (@ tptp.ord_less_nat N) _let_1) (= (@ (@ tptp.nth_nat (@ tptp.rev_nat Xs)) N) (@ (@ tptp.nth_nat Xs) (@ (@ tptp.minus_minus_nat _let_1) (@ tptp.suc N))))))))
% 3.70/4.04 (assert (forall ((N tptp.nat) (Xs tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Xs))) (=> (@ (@ tptp.ord_less_nat N) _let_1) (= (@ (@ tptp.nth_int (@ tptp.rev_int Xs)) N) (@ (@ tptp.nth_int Xs) (@ (@ tptp.minus_minus_nat _let_1) (@ tptp.suc N))))))))
% 3.70/4.04 (assert (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I) J)) U)) M2)) N)))))
% 3.70/4.04 (assert (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N))))))
% 3.70/4.04 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((A3 tptp.code_integer) (__flatten_var_0 tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A3) tptp.one_one_Code_integer)) __flatten_var_0))))
% 3.70/4.04 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A3) tptp.one_one_nat)) __flatten_var_0))))
% 3.70/4.04 (assert (= tptp.ord_less_int (lambda ((A3 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A3) tptp.one_one_int)) __flatten_var_0))))
% 3.70/4.04 (assert (forall ((I tptp.nat) (J tptp.nat) (L tptp.list_Code_integer) (X tptp.code_integer)) (let ((_let_1 (@ tptp.nth_Code_integer L))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) I) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_s3445333598471063425nteger L)) (=> (@ (@ tptp.sorted710888440204495920nteger tptp.ord_le3102999989581377725nteger) L) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 I)) X) (=> (@ (@ tptp.ord_le6747313008572928689nteger X) (@ _let_1 J)) (not (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.nth_Code_integer L))) (=> (@ (@ tptp.ord_less_eq_nat I) K) (=> (@ (@ tptp.ord_less_nat K) J) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 K)) X) (not (@ (@ tptp.ord_le6747313008572928689nteger X) (@ _let_1 (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))))))))))))))))
% 3.70/4.04 (assert (forall ((I tptp.nat) (J tptp.nat) (L tptp.list_num) (X tptp.num)) (let ((_let_1 (@ tptp.nth_num L))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) I) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_num L)) (=> (@ (@ tptp.sorted_wrt_num tptp.ord_less_eq_num) L) (=> (@ (@ tptp.ord_less_eq_num (@ _let_1 I)) X) (=> (@ (@ tptp.ord_less_num X) (@ _let_1 J)) (not (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.nth_num L))) (=> (@ (@ tptp.ord_less_eq_nat I) K) (=> (@ (@ tptp.ord_less_nat K) J) (=> (@ (@ 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)))))))))))))))))))
% 3.70/4.04 (assert (forall ((I tptp.nat) (J tptp.nat) (L tptp.list_nat) (X tptp.nat)) (let ((_let_1 (@ tptp.nth_nat L))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) I) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat L)) (=> (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) L) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 I)) X) (=> (@ (@ tptp.ord_less_nat X) (@ _let_1 J)) (not (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.nth_nat L))) (=> (@ (@ tptp.ord_less_eq_nat I) K) (=> (@ (@ tptp.ord_less_nat K) J) (=> (@ (@ 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)))))))))))))))))))
% 3.70/4.04 (assert (forall ((I tptp.nat) (J tptp.nat) (L tptp.list_int) (X tptp.int)) (let ((_let_1 (@ tptp.nth_int L))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) I) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_int L)) (=> (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) L) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 I)) X) (=> (@ (@ tptp.ord_less_int X) (@ _let_1 J)) (not (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.nth_int L))) (=> (@ (@ tptp.ord_less_eq_nat I) K) (=> (@ (@ tptp.ord_less_nat K) J) (=> (@ (@ 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)))))))))))))))))))
% 3.70/4.04 (assert (forall ((W tptp.code_integer) (Y tptp.code_integer) (X tptp.code_integer) (Z tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger X))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger W))) (= (= (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X) (= Y Z)))))))
% 3.70/4.04 (assert (forall ((W tptp.rat) (Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X))) (let ((_let_2 (@ tptp.times_times_rat W))) (= (= (@ (@ tptp.plus_plus_rat (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_rat (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X) (= Y Z)))))))
% 3.70/4.04 (assert (forall ((W tptp.nat) (Y tptp.nat) (X tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat X))) (let ((_let_2 (@ tptp.times_times_nat W))) (= (= (@ (@ tptp.plus_plus_nat (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_nat (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X) (= Y Z)))))))
% 3.70/4.04 (assert (forall ((W tptp.int) (Y tptp.int) (X tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.times_times_int X))) (let ((_let_2 (@ tptp.times_times_int W))) (= (= (@ (@ tptp.plus_plus_int (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_int (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X) (= Y Z)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger B2))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger A2))) (= (and (not (= A2 B2)) (not (= C D2))) (not (= (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 C)) (@ _let_1 D2)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 D2)) (@ _let_1 C)))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat B2))) (let ((_let_2 (@ tptp.times_times_rat A2))) (= (and (not (= A2 B2)) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_rat (@ _let_2 C)) (@ _let_1 D2)) (@ (@ tptp.plus_plus_rat (@ _let_2 D2)) (@ _let_1 C)))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B2))) (let ((_let_2 (@ tptp.times_times_nat A2))) (= (and (not (= A2 B2)) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_nat (@ _let_2 C)) (@ _let_1 D2)) (@ (@ tptp.plus_plus_nat (@ _let_2 D2)) (@ _let_1 C)))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int B2))) (let ((_let_2 (@ tptp.times_times_int A2))) (= (and (not (= A2 B2)) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_int (@ _let_2 C)) (@ _let_1 D2)) (@ (@ tptp.plus_plus_int (@ _let_2 D2)) (@ _let_1 C)))))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_s1210847774152347623at_nat) (R tptp.set_Pr4329608150637261639at_nat) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.nth_se5679702624988424552at_nat Xs))) (=> (forall ((N5 tptp.nat)) (let ((_let_1 (@ tptp.nth_se5679702624988424552at_nat Xs))) (=> (@ (@ tptp.ord_less_nat N5) (@ (@ tptp.minus_minus_nat (@ tptp.size_s8736152011456118867at_nat Xs)) tptp.one_one_nat)) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ _let_1 (@ tptp.suc N5))) (@ _let_1 N5))) R)))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s8736152011456118867at_nat Xs)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ _let_1 N)) (@ _let_1 M2))) (@ tptp.transi2703068831062848130at_nat R))))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_c) (R tptp.set_Product_prod_c_c) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.nth_c Xs))) (=> (forall ((N5 tptp.nat)) (let ((_let_1 (@ tptp.nth_c Xs))) (=> (@ (@ tptp.ord_less_nat N5) (@ (@ tptp.minus_minus_nat (@ tptp.size_size_list_c Xs)) tptp.one_one_nat)) (@ (@ tptp.member5074992359041316560od_c_c (@ (@ tptp.product_Pair_c_c (@ _let_1 (@ tptp.suc N5))) (@ _let_1 N5))) R)))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_c Xs)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.member5074992359041316560od_c_c (@ (@ tptp.product_Pair_c_c (@ _let_1 N)) (@ _let_1 M2))) (@ tptp.transitive_trancl_c R))))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_d) (R tptp.set_Product_prod_d_d) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.nth_d Xs))) (=> (forall ((N5 tptp.nat)) (let ((_let_1 (@ tptp.nth_d Xs))) (=> (@ (@ tptp.ord_less_nat N5) (@ (@ tptp.minus_minus_nat (@ tptp.size_size_list_d Xs)) tptp.one_one_nat)) (@ (@ tptp.member2287536781371869328od_d_d (@ (@ tptp.product_Pair_d_d (@ _let_1 (@ tptp.suc N5))) (@ _let_1 N5))) R)))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_d Xs)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.member2287536781371869328od_d_d (@ (@ tptp.product_Pair_d_d (@ _let_1 N)) (@ _let_1 M2))) (@ tptp.transitive_trancl_d R))))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_int) (R tptp.set_Pr958786334691620121nt_int) (N tptp.nat) (M2 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))) R)))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int (@ _let_1 N)) (@ _let_1 M2))) (@ tptp.transi6261509568448316235cl_int R))))))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_nat) (R tptp.set_Pr1261947904930325089at_nat) (N tptp.nat) (M2 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))) R)))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat (@ _let_1 N)) (@ _let_1 M2))) (@ tptp.transi6264000038957366511cl_nat R))))))))
% 3.70/4.04 (assert (= tptp.neg_nu7757733837767384882nteger (lambda ((X2 tptp.code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger X2) X2)) tptp.one_one_Code_integer))))
% 3.70/4.04 (assert (= tptp.neg_nu3179335615603231917ec_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat X2) X2)) tptp.one_one_rat))))
% 3.70/4.04 (assert (= tptp.neg_nu3811975205180677377ec_int (lambda ((X2 tptp.int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int X2) X2)) tptp.one_one_int))))
% 3.70/4.04 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 3.70/4.04 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A2) tptp.zero_z3403309356797280102nteger) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.multis2468970476368604999at_nat)) (= (@ (@ tptp.plus_p7104986032573967614at_nat A2) tptp.zero_z1048942125864253310at_nat) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat A2) tptp.zero_zero_rat) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat A2) tptp.zero_zero_nat) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.plus_plus_int A2) tptp.zero_zero_int) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) A2)) (= A2 tptp.zero_z3403309356797280102nteger))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.plus_plus_rat A2) A2)) (= A2 tptp.zero_zero_rat))))
% 3.70/4.04 (assert (forall ((A2 tptp.int)) (= (= tptp.zero_zero_int (@ (@ tptp.plus_plus_int A2) A2)) (= A2 tptp.zero_zero_int))))
% 3.70/4.04 (assert (forall ((B2 tptp.code_integer) (A2 tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger B2) A2) A2) (= B2 tptp.zero_z3403309356797280102nteger))))
% 3.70/4.04 (assert (forall ((B2 tptp.multis2468970476368604999at_nat) (A2 tptp.multis2468970476368604999at_nat)) (= (= (@ (@ tptp.plus_p7104986032573967614at_nat B2) A2) A2) (= B2 tptp.zero_z1048942125864253310at_nat))))
% 3.70/4.04 (assert (forall ((B2 tptp.rat) (A2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B2) A2) A2) (= B2 tptp.zero_zero_rat))))
% 3.70/4.04 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B2) A2) A2) (= B2 tptp.zero_zero_nat))))
% 3.70/4.04 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int B2) A2) A2) (= B2 tptp.zero_zero_int))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger A2) B2) A2) (= B2 tptp.zero_z3403309356797280102nteger))))
% 3.70/4.04 (assert (forall ((A2 tptp.multis2468970476368604999at_nat) (B2 tptp.multis2468970476368604999at_nat)) (= (= (@ (@ tptp.plus_p7104986032573967614at_nat A2) B2) A2) (= B2 tptp.zero_z1048942125864253310at_nat))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A2) B2) A2) (= B2 tptp.zero_zero_rat))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat A2) B2) A2) (= B2 tptp.zero_zero_nat))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int A2) B2) A2) (= B2 tptp.zero_zero_int))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (= A2 (@ (@ tptp.plus_p5714425477246183910nteger B2) A2)) (= B2 tptp.zero_z3403309356797280102nteger))))
% 3.70/4.04 (assert (forall ((A2 tptp.multis2468970476368604999at_nat) (B2 tptp.multis2468970476368604999at_nat)) (= (= A2 (@ (@ tptp.plus_p7104986032573967614at_nat B2) A2)) (= B2 tptp.zero_z1048942125864253310at_nat))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (= A2 (@ (@ tptp.plus_plus_rat B2) A2)) (= B2 tptp.zero_zero_rat))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (= A2 (@ (@ tptp.plus_plus_nat B2) A2)) (= B2 tptp.zero_zero_nat))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (= A2 (@ (@ tptp.plus_plus_int B2) A2)) (= B2 tptp.zero_zero_int))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (= A2 (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)) (= B2 tptp.zero_z3403309356797280102nteger))))
% 3.70/4.04 (assert (forall ((A2 tptp.multis2468970476368604999at_nat) (B2 tptp.multis2468970476368604999at_nat)) (= (= A2 (@ (@ tptp.plus_p7104986032573967614at_nat A2) B2)) (= B2 tptp.zero_z1048942125864253310at_nat))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (= A2 (@ (@ tptp.plus_plus_rat A2) B2)) (= B2 tptp.zero_zero_rat))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (= A2 (@ (@ tptp.plus_plus_nat A2) B2)) (= B2 tptp.zero_zero_nat))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (= A2 (@ (@ tptp.plus_plus_int A2) B2)) (= B2 tptp.zero_zero_int))))
% 3.70/4.04 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))
% 3.70/4.04 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.plus_plus_nat X) Y)) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.zero_z3403309356797280102nteger) A2) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.multis2468970476368604999at_nat)) (= (@ (@ tptp.plus_p7104986032573967614at_nat tptp.zero_z1048942125864253310at_nat) A2) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A2) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A2) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A2) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger A2) C) (@ (@ tptp.times_3573771949741848930nteger B2) C)) (or (= C tptp.zero_z3403309356797280102nteger) (= A2 B2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (= (@ (@ tptp.times_times_rat A2) C) (@ (@ tptp.times_times_rat B2) C)) (or (= C tptp.zero_zero_rat) (= A2 B2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat A2) C) (@ (@ tptp.times_times_nat B2) C)) (or (= C tptp.zero_zero_nat) (= A2 B2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.times_times_int A2) C) (@ (@ tptp.times_times_int B2) C)) (or (= C tptp.zero_zero_int) (= A2 B2)))))
% 3.70/4.04 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (= (@ _let_1 A2) (@ _let_1 B2)) (or (= C tptp.zero_z3403309356797280102nteger) (= A2 B2))))))
% 3.70/4.04 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (= (@ _let_1 A2) (@ _let_1 B2)) (or (= C tptp.zero_zero_rat) (= A2 B2))))))
% 3.70/4.04 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (= (= (@ _let_1 A2) (@ _let_1 B2)) (or (= C tptp.zero_zero_nat) (= A2 B2))))))
% 3.70/4.04 (assert (forall ((C tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (= (@ _let_1 A2) (@ _let_1 B2)) (or (= C tptp.zero_zero_int) (= A2 B2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger A2) B2) tptp.zero_z3403309356797280102nteger) (or (= A2 tptp.zero_z3403309356797280102nteger) (= B2 tptp.zero_z3403309356797280102nteger)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (= (@ (@ tptp.times_times_rat A2) B2) tptp.zero_zero_rat) (or (= A2 tptp.zero_zero_rat) (= B2 tptp.zero_zero_rat)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat A2) B2) tptp.zero_zero_nat) (or (= A2 tptp.zero_zero_nat) (= B2 tptp.zero_zero_nat)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.times_times_int A2) B2) tptp.zero_zero_int) (or (= A2 tptp.zero_zero_int) (= B2 tptp.zero_zero_int)))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger A2) tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 3.70/4.04 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.times_times_rat A2) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 3.70/4.04 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.times_times_nat A2) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 3.70/4.04 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.times_times_int A2) tptp.zero_zero_int) tptp.zero_zero_int)))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger tptp.zero_z3403309356797280102nteger) A2) tptp.zero_z3403309356797280102nteger)))
% 3.70/4.04 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.zero_zero_rat) A2) tptp.zero_zero_rat)))
% 3.70/4.04 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) A2) tptp.zero_zero_nat)))
% 3.70/4.04 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) A2) tptp.zero_zero_int)))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A2) A2) tptp.zero_z3403309356797280102nteger)))
% 3.70/4.04 (assert (forall ((A2 tptp.multis2468970476368604999at_nat)) (= (@ (@ tptp.minus_4286766774447292334at_nat A2) A2) tptp.zero_z1048942125864253310at_nat)))
% 3.70/4.04 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A2) A2) tptp.zero_zero_rat)))
% 3.70/4.04 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat A2) A2) tptp.zero_zero_nat)))
% 3.70/4.04 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.minus_minus_int A2) A2) tptp.zero_zero_int)))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A2) tptp.zero_z3403309356797280102nteger) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.multis2468970476368604999at_nat)) (= (@ (@ tptp.minus_4286766774447292334at_nat A2) tptp.zero_z1048942125864253310at_nat) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A2) tptp.zero_zero_rat) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat A2) tptp.zero_zero_nat) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.minus_minus_int A2) tptp.zero_zero_int) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.multis2468970476368604999at_nat)) (= (@ (@ tptp.minus_4286766774447292334at_nat tptp.zero_z1048942125864253310at_nat) A2) tptp.zero_z1048942125864253310at_nat)))
% 3.70/4.04 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) A2) tptp.zero_zero_nat)))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A2) tptp.zero_z3403309356797280102nteger) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A2) tptp.zero_zero_rat) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.minus_minus_int A2) tptp.zero_zero_int) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A2) A2) tptp.zero_z3403309356797280102nteger)))
% 3.70/4.04 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A2) A2) tptp.zero_zero_rat)))
% 3.70/4.04 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.minus_minus_int A2) A2) tptp.zero_zero_int)))
% 3.70/4.04 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 3.70/4.04 (assert (forall ((N tptp.nat)) (= (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat)) (= (not (= A2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ tptp.insert9069300056098147895at_nat (@ (@ tptp.produc2922128104949294807at_nat A2) B2)) tptp.bot_bo228742789529271731at_nat))) (= (@ tptp.transi2703068831062848130at_nat _let_1) _let_1))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ (@ tptp.insert8211810215607154385at_nat (@ (@ tptp.product_Pair_nat_nat A2) B2)) tptp.bot_bo2099793752762293965at_nat))) (= (@ tptp.transi6264000038957366511cl_nat _let_1) _let_1))))
% 3.70/4.04 (assert (forall ((B2 tptp.code_integer) (A2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger B2) A2)) B2) (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger))))
% 3.70/4.04 (assert (forall ((B2 tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat B2) A2)) B2) (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat))))
% 3.70/4.04 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat B2) A2)) B2) (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat))))
% 3.70/4.04 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int B2) A2)) B2) (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)) B2) (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) B2)) B2) (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) B2)) B2) (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) B2)) B2) (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger A2) (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A2) (@ (@ tptp.plus_plus_rat A2) B2)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A2) (@ (@ tptp.plus_plus_nat A2) B2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int A2) (@ (@ tptp.plus_plus_int A2) B2)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger A2) (@ (@ tptp.plus_p5714425477246183910nteger B2) A2)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A2) (@ (@ tptp.plus_plus_rat B2) A2)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A2) (@ (@ tptp.plus_plus_nat B2) A2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int A2) (@ (@ tptp.plus_plus_int B2) A2)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) A2)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) A2)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat))))
% 3.70/4.04 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) A2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A2) A2)) (@ _let_1 A2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat A2) A2)) (@ _let_1 A2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A2) A2)) (@ _let_1 A2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.minus_8373710615458151222nteger A2) B2)) (@ (@ tptp.ord_le3102999989581377725nteger B2) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.minus_minus_rat A2) B2)) (@ (@ tptp.ord_less_eq_rat B2) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A2) B2)) (@ (@ tptp.ord_less_eq_int B2) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.minus_8373710615458151222nteger A2) B2)) (@ (@ tptp.ord_le3102999989581377725nteger B2) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.minus_minus_rat A2) B2)) (@ (@ tptp.ord_less_eq_rat B2) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A2) B2)) (@ (@ tptp.ord_less_eq_int B2) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat A2) A2)) (@ _let_1 A2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A2) A2)) (@ _let_1 A2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A2) A2)) (@ _let_1 A2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) A2)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) A2)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.zero_z3403309356797280102nteger))))
% 3.70/4.04 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) A2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat A2) (@ (@ tptp.plus_plus_rat B2) A2)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A2) (@ (@ tptp.plus_p5714425477246183910nteger B2) A2)) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_nat A2) (@ (@ tptp.plus_plus_nat B2) A2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int A2) (@ (@ tptp.plus_plus_int B2) A2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat A2) (@ (@ tptp.plus_plus_rat A2) B2)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A2) (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_nat A2) (@ (@ tptp.plus_plus_nat A2) B2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int A2) (@ (@ tptp.plus_plus_int A2) B2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) B2)) B2) (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)) B2) (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.zero_z3403309356797280102nteger))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) B2)) B2) (@ (@ tptp.ord_less_nat A2) tptp.zero_zero_nat))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) B2)) B2) (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int))))
% 3.70/4.04 (assert (forall ((B2 tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat B2) A2)) B2) (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat))))
% 3.70/4.04 (assert (forall ((B2 tptp.code_integer) (A2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger B2) A2)) B2) (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.zero_z3403309356797280102nteger))))
% 3.70/4.04 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat B2) A2)) B2) (@ (@ tptp.ord_less_nat A2) tptp.zero_zero_nat))))
% 3.70/4.04 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int B2) A2)) B2) (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.minus_minus_rat A2) B2)) (@ (@ tptp.ord_less_rat B2) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.minus_8373710615458151222nteger A2) B2)) (@ (@ tptp.ord_le6747313008572928689nteger B2) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A2) B2)) (@ (@ tptp.ord_less_int B2) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.minus_minus_rat A2) B2)) (@ (@ tptp.ord_less_rat B2) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.minus_8373710615458151222nteger A2) B2)) (@ (@ tptp.ord_le6747313008572928689nteger B2) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A2) B2)) (@ (@ tptp.ord_less_int B2) A2))))
% 3.70/4.04 (assert (forall ((C tptp.code_integer) (B2 tptp.code_integer)) (= (= C (@ (@ tptp.times_3573771949741848930nteger C) B2)) (or (= C tptp.zero_z3403309356797280102nteger) (= B2 tptp.one_one_Code_integer)))))
% 3.70/4.04 (assert (forall ((C tptp.rat) (B2 tptp.rat)) (= (= C (@ (@ tptp.times_times_rat C) B2)) (or (= C tptp.zero_zero_rat) (= B2 tptp.one_one_rat)))))
% 3.70/4.04 (assert (forall ((C tptp.int) (B2 tptp.int)) (= (= C (@ (@ tptp.times_times_int C) B2)) (or (= C tptp.zero_zero_int) (= B2 tptp.one_one_int)))))
% 3.70/4.04 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger C) A2) C) (or (= C tptp.zero_z3403309356797280102nteger) (= A2 tptp.one_one_Code_integer)))))
% 3.70/4.04 (assert (forall ((C tptp.rat) (A2 tptp.rat)) (= (= (@ (@ tptp.times_times_rat C) A2) C) (or (= C tptp.zero_zero_rat) (= A2 tptp.one_one_rat)))))
% 3.70/4.04 (assert (forall ((C tptp.int) (A2 tptp.int)) (= (= (@ (@ tptp.times_times_int C) A2) C) (or (= C tptp.zero_zero_int) (= A2 tptp.one_one_int)))))
% 3.70/4.04 (assert (forall ((C tptp.code_integer) (B2 tptp.code_integer)) (= (= C (@ (@ tptp.times_3573771949741848930nteger B2) C)) (or (= C tptp.zero_z3403309356797280102nteger) (= B2 tptp.one_one_Code_integer)))))
% 3.70/4.04 (assert (forall ((C tptp.rat) (B2 tptp.rat)) (= (= C (@ (@ tptp.times_times_rat B2) C)) (or (= C tptp.zero_zero_rat) (= B2 tptp.one_one_rat)))))
% 3.70/4.04 (assert (forall ((C tptp.int) (B2 tptp.int)) (= (= C (@ (@ tptp.times_times_int B2) C)) (or (= C tptp.zero_zero_int) (= B2 tptp.one_one_int)))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (C tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger A2) C) C) (or (= C tptp.zero_z3403309356797280102nteger) (= A2 tptp.one_one_Code_integer)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.times_times_rat A2) C) C) (or (= C tptp.zero_zero_rat) (= A2 tptp.one_one_rat)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (C tptp.int)) (= (= (@ (@ tptp.times_times_int A2) C) C) (or (= C tptp.zero_zero_int) (= A2 tptp.one_one_int)))))
% 3.70/4.04 (assert (forall ((A2 tptp.multis2468970476368604999at_nat) (B2 tptp.multis2468970476368604999at_nat)) (= (@ (@ tptp.minus_4286766774447292334at_nat A2) (@ (@ tptp.plus_p7104986032573967614at_nat A2) B2)) tptp.zero_z1048942125864253310at_nat)))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat A2) (@ (@ tptp.plus_plus_nat A2) B2)) tptp.zero_zero_nat)))
% 3.70/4.04 (assert (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))
% 3.70/4.04 (assert (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) tptp.one_one_rat) tptp.zero_zero_rat))
% 3.70/4.04 (assert (= (@ (@ tptp.minus_minus_int tptp.one_one_int) tptp.one_one_int) tptp.zero_zero_int))
% 3.70/4.04 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc tptp.zero_zero_nat)) (= N tptp.zero_zero_nat))))
% 3.70/4.04 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)) (or (@ _let_1 M2) (@ _let_1 N))))))
% 3.70/4.04 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) M2)) (@ (@ tptp.ord_less_nat M2) N))))
% 3.70/4.04 (assert (forall ((K3 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K3))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (@ (@ tptp.ord_less_nat M2) N))))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (K3 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat M2) K3)) (@ (@ tptp.times_times_nat N) K3)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (@ (@ tptp.ord_less_nat M2) N)))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.times_times_nat M2) N)) (and (@ _let_1 M2) (@ _let_1 N))))))
% 3.70/4.04 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) tptp.one_one_nat) (= N tptp.zero_zero_nat))))
% 3.70/4.04 (assert (forall ((Xs tptp.list_c)) (= (@ (@ (@ tptp.slice_c tptp.zero_zero_nat) (@ tptp.size_size_list_c Xs)) Xs) Xs)))
% 3.70/4.04 (assert (forall ((Xs tptp.list_d)) (= (@ (@ (@ tptp.slice_d tptp.zero_zero_nat) (@ tptp.size_size_list_d Xs)) Xs) Xs)))
% 3.70/4.04 (assert (forall ((Xs tptp.list_nat)) (= (@ (@ (@ tptp.slice_nat tptp.zero_zero_nat) (@ tptp.size_size_list_nat Xs)) Xs) Xs)))
% 3.70/4.04 (assert (forall ((Xs tptp.list_int)) (= (@ (@ (@ tptp.slice_int tptp.zero_zero_nat) (@ tptp.size_size_list_int Xs)) Xs) Xs)))
% 3.70/4.04 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) N))))
% 3.70/4.04 (assert (forall ((K3 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K3))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M2)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (K3 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M2) K3)) (@ (@ tptp.times_times_nat N) K3)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (@ (@ tptp.ord_less_eq_nat M2) N)))))
% 3.70/4.04 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) N))))
% 3.70/4.04 (assert (forall ((X tptp.assn) (Y tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 3.70/4.04 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (let ((_let_2 (@ tptp.sup_sup_assn Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 3.70/4.04 (assert (= tptp.sup_sup_assn (lambda ((X2 tptp.assn) (Y5 tptp.assn)) (@ (@ tptp.sup_sup_assn Y5) X2))))
% 3.70/4.04 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.sup_sup_assn X) X) X)))
% 3.70/4.04 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (= (@ (@ tptp.sup_sup_assn (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_sup_assn Y) Z))))))
% 3.70/4.04 (assert (forall ((X tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger X) (= X tptp.zero_z3403309356797280102nteger))))
% 3.70/4.04 (assert (forall ((X tptp.multis2468970476368604999at_nat)) (= (= tptp.zero_z1048942125864253310at_nat X) (= X tptp.zero_z1048942125864253310at_nat))))
% 3.70/4.04 (assert (forall ((X tptp.rat)) (= (= tptp.zero_zero_rat X) (= X tptp.zero_zero_rat))))
% 3.70/4.04 (assert (forall ((X tptp.nat)) (= (= tptp.zero_zero_nat X) (= X tptp.zero_zero_nat))))
% 3.70/4.04 (assert (forall ((X tptp.int)) (= (= tptp.zero_zero_int X) (= X tptp.zero_zero_int))))
% 3.70/4.04 (assert (forall ((U2 tptp.set_Pr4329608150637261639at_nat) (V tptp.set_Pr4329608150637261639at_nat) (X tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat X))) (=> (@ (@ tptp.ord_le1268244103169919719at_nat U2) V) (=> (@ _let_1 (@ tptp.transi2703068831062848130at_nat U2)) (@ _let_1 (@ tptp.transi2703068831062848130at_nat V)))))))
% 3.70/4.04 (assert (forall ((U2 tptp.set_Pr1261947904930325089at_nat) (V tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat U2) V) (=> (@ _let_1 (@ tptp.transi6264000038957366511cl_nat U2)) (@ _let_1 (@ tptp.transi6264000038957366511cl_nat V)))))))
% 3.70/4.04 (assert (forall ((R tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat R) (@ tptp.transi6264000038957366511cl_nat R))))
% 3.70/4.04 (assert (forall ((R tptp.set_Pr4329608150637261639at_nat) (X tptp.produc3843707927480180839at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat (@ tptp.transi2703068831062848130at_nat R)) (@ tptp.transi2703068831062848130at_nat (@ (@ tptp.insert9069300056098147895at_nat X) R)))))
% 3.70/4.04 (assert (forall ((R tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.transi6264000038957366511cl_nat R)) (@ tptp.transi6264000038957366511cl_nat (@ (@ tptp.insert8211810215607154385at_nat X) R)))))
% 3.70/4.04 (assert (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X)))
% 3.70/4.04 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (not (= N tptp.zero_zero_nat)))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (not (= N tptp.zero_zero_nat)))))
% 3.70/4.04 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 3.70/4.04 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 3.70/4.04 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 3.70/4.04 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 3.70/4.04 (assert (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 3.70/4.04 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.zero_z3403309356797280102nteger) A2) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.multis2468970476368604999at_nat)) (= (@ (@ tptp.plus_p7104986032573967614at_nat tptp.zero_z1048942125864253310at_nat) A2) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A2) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A2) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A2) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A2) tptp.zero_z3403309356797280102nteger) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.multis2468970476368604999at_nat)) (= (@ (@ tptp.plus_p7104986032573967614at_nat A2) tptp.zero_z1048942125864253310at_nat) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat A2) tptp.zero_zero_rat) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat A2) tptp.zero_zero_nat) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.plus_plus_int A2) tptp.zero_zero_int) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.zero_z3403309356797280102nteger) A2) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A2) A2)))
% 3.70/4.04 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A2) A2)))
% 3.70/4.04 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (= (= (@ (@ tptp.times_3573771949741848930nteger A2) C) (@ (@ tptp.times_3573771949741848930nteger B2) C)) (= A2 B2)))))
% 3.70/4.04 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ (@ tptp.times_times_rat A2) C) (@ (@ tptp.times_times_rat B2) C)) (= A2 B2)))))
% 3.70/4.04 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (= (= (@ (@ tptp.times_times_nat A2) C) (@ (@ tptp.times_times_nat B2) C)) (= A2 B2)))))
% 3.70/4.04 (assert (forall ((C tptp.int) (A2 tptp.int) (B2 tptp.int)) (=> (not (= C tptp.zero_zero_int)) (= (= (@ (@ tptp.times_times_int A2) C) (@ (@ tptp.times_times_int B2) C)) (= A2 B2)))))
% 3.70/4.04 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (= (= (@ _let_1 A2) (@ _let_1 B2)) (= A2 B2))))))
% 3.70/4.04 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ _let_1 A2) (@ _let_1 B2)) (= A2 B2))))))
% 3.70/4.04 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (not (= C tptp.zero_zero_nat)) (= (= (@ _let_1 A2) (@ _let_1 B2)) (= A2 B2))))))
% 3.70/4.04 (assert (forall ((C tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (= (@ _let_1 A2) (@ _let_1 B2)) (= A2 B2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (not (= A2 tptp.zero_z3403309356797280102nteger)) (=> (not (= B2 tptp.zero_z3403309356797280102nteger)) (not (= (@ (@ tptp.times_3573771949741848930nteger A2) B2) tptp.zero_z3403309356797280102nteger))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (not (= A2 tptp.zero_zero_rat)) (=> (not (= B2 tptp.zero_zero_rat)) (not (= (@ (@ tptp.times_times_rat A2) B2) tptp.zero_zero_rat))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (not (= A2 tptp.zero_zero_nat)) (=> (not (= B2 tptp.zero_zero_nat)) (not (= (@ (@ tptp.times_times_nat A2) B2) tptp.zero_zero_nat))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (not (= A2 tptp.zero_zero_int)) (=> (not (= B2 tptp.zero_zero_int)) (not (= (@ (@ tptp.times_times_int A2) B2) tptp.zero_zero_int))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (= (@ (@ tptp.times_3573771949741848930nteger A2) B2) tptp.zero_z3403309356797280102nteger) (or (= A2 tptp.zero_z3403309356797280102nteger) (= B2 tptp.zero_z3403309356797280102nteger)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (= (@ (@ tptp.times_times_rat A2) B2) tptp.zero_zero_rat) (or (= A2 tptp.zero_zero_rat) (= B2 tptp.zero_zero_rat)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (= (@ (@ tptp.times_times_nat A2) B2) tptp.zero_zero_nat) (or (= A2 tptp.zero_zero_nat) (= B2 tptp.zero_zero_nat)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (= (@ (@ tptp.times_times_int A2) B2) tptp.zero_zero_int) (or (= A2 tptp.zero_zero_int) (= B2 tptp.zero_zero_int)))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (not (= (@ (@ tptp.times_3573771949741848930nteger A2) B2) tptp.zero_z3403309356797280102nteger)) (and (not (= A2 tptp.zero_z3403309356797280102nteger)) (not (= B2 tptp.zero_z3403309356797280102nteger))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (not (= (@ (@ tptp.times_times_rat A2) B2) tptp.zero_zero_rat)) (and (not (= A2 tptp.zero_zero_rat)) (not (= B2 tptp.zero_zero_rat))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (not (= (@ (@ tptp.times_times_nat A2) B2) tptp.zero_zero_nat)) (and (not (= A2 tptp.zero_zero_nat)) (not (= B2 tptp.zero_zero_nat))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (not (= (@ (@ tptp.times_times_int A2) B2) tptp.zero_zero_int)) (and (not (= A2 tptp.zero_zero_int)) (not (= B2 tptp.zero_zero_int))))))
% 3.70/4.04 (assert (not (= tptp.zero_z3403309356797280102nteger tptp.one_one_Code_integer)))
% 3.70/4.04 (assert (not (= tptp.zero_zero_rat tptp.one_one_rat)))
% 3.70/4.04 (assert (not (= tptp.zero_zero_nat tptp.one_one_nat)))
% 3.70/4.04 (assert (not (= tptp.zero_zero_int tptp.one_one_int)))
% 3.70/4.04 (assert (= (lambda ((Y4 tptp.code_integer) (Z2 tptp.code_integer)) (= Y4 Z2)) (lambda ((A3 tptp.code_integer) (B3 tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A3) B3) tptp.zero_z3403309356797280102nteger))))
% 3.70/4.04 (assert (= (lambda ((Y4 tptp.rat) (Z2 tptp.rat)) (= Y4 Z2)) (lambda ((A3 tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A3) B3) tptp.zero_zero_rat))))
% 3.70/4.04 (assert (= (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2)) (lambda ((A3 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.minus_minus_int A3) B3) tptp.zero_zero_int))))
% 3.70/4.04 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N5) (=> (not (@ P N5)) (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N5) (not (@ P M3))))))) (@ P N)))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (not (= N tptp.zero_zero_nat)))))
% 3.70/4.04 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 3.70/4.04 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 3.70/4.04 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 3.70/4.04 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat)) (not (@ (@ tptp.ord_less_nat A2) tptp.zero_zero_nat))))
% 3.70/4.04 (assert (forall ((R2 tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger R2))) (=> (not (= R2 tptp.zero_z3403309356797280102nteger)) (=> (and (= A2 B2) (not (= C D2))) (not (= (@ (@ tptp.plus_p5714425477246183910nteger A2) (@ _let_1 C)) (@ (@ tptp.plus_p5714425477246183910nteger B2) (@ _let_1 D2)))))))))
% 3.70/4.04 (assert (forall ((R2 tptp.rat) (A2 tptp.rat) (B2 tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat R2))) (=> (not (= R2 tptp.zero_zero_rat)) (=> (and (= A2 B2) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_rat A2) (@ _let_1 C)) (@ (@ tptp.plus_plus_rat B2) (@ _let_1 D2)))))))))
% 3.70/4.04 (assert (forall ((R2 tptp.nat) (A2 tptp.nat) (B2 tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat R2))) (=> (not (= R2 tptp.zero_zero_nat)) (=> (and (= A2 B2) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_nat A2) (@ _let_1 C)) (@ (@ tptp.plus_plus_nat B2) (@ _let_1 D2)))))))))
% 3.70/4.04 (assert (forall ((R2 tptp.int) (A2 tptp.int) (B2 tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int R2))) (=> (not (= R2 tptp.zero_zero_int)) (=> (and (= A2 B2) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_int A2) (@ _let_1 C)) (@ (@ tptp.plus_plus_int B2) (@ _let_1 D2)))))))))
% 3.70/4.04 (assert (forall ((K3 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K3))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (= (= (@ _let_1 M2) (@ _let_1 N)) (= M2 N))))))
% 3.70/4.04 (assert (forall ((K3 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K3))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (= (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M2) N))))))
% 3.70/4.04 (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)))))))
% 3.70/4.04 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.zero_zero_rat) (= (= (@ (@ tptp.plus_plus_rat X) Y) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))))
% 3.70/4.04 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat Y) tptp.zero_zero_nat) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))))
% 3.70/4.04 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.zero_zero_int) (= (= (@ (@ tptp.plus_plus_int X) Y) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))))
% 3.70/4.04 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_p5714425477246183910nteger X) Y) tptp.zero_z3403309356797280102nteger) (and (= X tptp.zero_z3403309356797280102nteger) (= Y tptp.zero_z3403309356797280102nteger))))))))
% 3.70/4.04 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_rat X) Y) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))))))
% 3.70/4.04 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat))))))))
% 3.70/4.04 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_int X) Y) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le3102999989581377725nteger B2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)) tptp.zero_z3403309356797280102nteger)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) B2)) tptp.zero_zero_rat)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) B2)) tptp.zero_zero_nat)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) B2)) tptp.zero_zero_int)))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_int A2) B2)))))))
% 3.70/4.04 (assert (forall ((C tptp.code_integer) (B2 tptp.code_integer) (A2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger B2))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A2) C)))))))
% 3.70/4.04 (assert (forall ((C tptp.rat) (B2 tptp.rat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat B2))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) C)))))))
% 3.70/4.04 (assert (forall ((C tptp.nat) (B2 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) C)))))))
% 3.70/4.04 (assert (forall ((C tptp.int) (B2 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int B2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.plus_plus_int A2) C)))))))
% 3.70/4.04 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B2) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) C)) B2)))))
% 3.70/4.04 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) C)) B2)))))
% 3.70/4.04 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) C)) B2)))))
% 3.70/4.04 (assert (forall ((C tptp.int) (A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) C)) B2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger B2))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A2) C)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat B2))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) C)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) C)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int B2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A2) C)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) B2) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) C)) B2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat C) B2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) C)) B2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat C) B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) C)) B2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int C) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) C)) B2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B2) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) D2) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B2) D2)))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_eq_rat C) D2) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B2) D2)))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B2) D2)))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_eq_int C) D2) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B2) D2)))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B2) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) D2) (=> (@ _let_1 A2) (=> (@ _let_1 C) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B2) D2)))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_eq_rat C) D2) (=> (@ _let_1 A2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B2) D2)))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (=> (@ _let_1 A2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B2) D2)))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_eq_int C) D2) (=> (@ _let_1 A2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B2) D2)))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.times_3573771949741848930nteger A2) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A2) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A2) A2))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (or (and (@ _let_1 A2) (@ _let_1 B2)) (and (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B2) tptp.zero_z3403309356797280102nteger))) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A2) B2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (or (and (@ _let_1 A2) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat))) (@ _let_1 (@ (@ tptp.times_times_rat A2) B2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A2) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int))) (@ _let_1 (@ (@ tptp.times_times_int A2) B2))))))
% 3.70/4.04 (assert (forall ((B2 tptp.code_integer) (A2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le3102999989581377725nteger B2) A2) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A2)) (@ _let_1 B2)))))))
% 3.70/4.04 (assert (forall ((B2 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B2) A2) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2)))))))
% 3.70/4.04 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le3102999989581377725nteger B2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.times_3573771949741848930nteger A2) B2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A2) B2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A2) B2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B2) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A2)) (@ _let_1 B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)))))))
% 3.70/4.04 (assert (forall ((B2 tptp.code_integer) (A2 tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger B2) A2) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B2) C))))))
% 3.70/4.04 (assert (forall ((B2 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B2) A2) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B2) C))))))
% 3.70/4.04 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B2) C))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B2) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B2) C))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B2) C))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B2) C))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B2) C))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A2) B2)) tptp.zero_z3403309356797280102nteger) (or (and (@ _let_1 A2) (@ (@ tptp.ord_le3102999989581377725nteger B2) tptp.zero_z3403309356797280102nteger)) (and (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger) (@ _let_1 B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) B2)) tptp.zero_zero_rat) (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (@ _let_1 B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) B2)) tptp.zero_zero_int) (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (@ _let_1 B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (or (and (@ _let_1 A2) (@ (@ tptp.ord_le3102999989581377725nteger B2) tptp.zero_z3403309356797280102nteger)) (and (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger) (@ _let_1 B2))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A2) B2)) tptp.zero_z3403309356797280102nteger)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (@ _let_1 B2))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) B2)) tptp.zero_zero_rat)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_nat B2) tptp.zero_zero_nat)) (and (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat) (@ _let_1 B2))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) B2)) tptp.zero_zero_nat)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (@ _let_1 B2))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) B2)) tptp.zero_zero_int)))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A2) B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_rat A2) B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_nat A2) B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_int A2) B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ (@ tptp.ord_le3102999989581377725nteger B2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A2) B2)) tptp.zero_z3403309356797280102nteger)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) B2)) tptp.zero_zero_rat)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_eq_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) B2)) tptp.zero_zero_nat)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) B2)) tptp.zero_zero_int)))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B2) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A2) B2)) tptp.zero_z3403309356797280102nteger)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) B2)) tptp.zero_zero_rat)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) B2)) tptp.zero_zero_nat)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) B2)) tptp.zero_zero_int)))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ (@ tptp.ord_le3102999989581377725nteger B2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger B2) A2)) tptp.zero_z3403309356797280102nteger)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat B2) A2)) tptp.zero_zero_rat)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_eq_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat B2) A2)) tptp.zero_zero_nat)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int B2) A2)) tptp.zero_zero_int)))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A2) B2)) (or (and (@ _let_1 A2) (@ _let_1 B2)) (and (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B2) tptp.zero_z3403309356797280102nteger)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.times_times_rat A2) B2)) (or (and (@ _let_1 A2) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.times_times_int A2) B2)) (or (and (@ _let_1 A2) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B2) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A2)) (@ _let_1 B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)))))))
% 3.70/4.04 (assert (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer))
% 3.70/4.04 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 3.70/4.04 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 3.70/4.04 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 3.70/4.04 (assert (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer))
% 3.70/4.04 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 3.70/4.04 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 3.70/4.04 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 3.70/4.04 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 3.70/4.04 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 3.70/4.04 (assert (not (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 3.70/4.04 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.zero_zero_int)))
% 3.70/4.04 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((A3 tptp.code_integer) (B3 tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger A3) B3)) tptp.zero_z3403309356797280102nteger))))
% 3.70/4.04 (assert (= tptp.ord_less_eq_rat (lambda ((A3 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A3) B3)) tptp.zero_zero_rat))))
% 3.70/4.04 (assert (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A3) B3)) tptp.zero_zero_int))))
% 3.70/4.04 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat X) Y)) tptp.zero_zero_rat) (or (@ (@ tptp.ord_less_rat X) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat)))))
% 3.70/4.04 (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)))))
% 3.70/4.04 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X) Y)) tptp.zero_zero_int) (or (@ (@ tptp.ord_less_int X) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Y) tptp.zero_zero_int)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) B2)) tptp.zero_zero_rat)))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)) tptp.zero_z3403309356797280102nteger)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) B2)) tptp.zero_zero_nat)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) B2)) tptp.zero_zero_int)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_int A2) B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (not (forall ((C4 tptp.nat)) (=> (= B2 (@ (@ tptp.plus_plus_nat A2) C4)) (= C4 tptp.zero_zero_nat)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B2))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) C)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger B2))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A2) C)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) C)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A2) C)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A2) B2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.times_3573771949741848930nteger A2) B2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A2) B2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) A2)) tptp.zero_zero_rat))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) A2)) tptp.zero_z3403309356797280102nteger))))
% 3.70/4.04 (assert (forall ((A2 tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) A2)) tptp.zero_zero_int))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) B2)) tptp.zero_zero_rat) (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_rat B2) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (@ _let_1 B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) B2)) tptp.zero_z3403309356797280102nteger) (or (and (@ _let_1 A2) (@ (@ tptp.ord_le6747313008572928689nteger B2) tptp.zero_z3403309356797280102nteger)) (and (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.zero_z3403309356797280102nteger) (@ _let_1 B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) B2)) tptp.zero_zero_int) (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int) (@ _let_1 B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B2) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) B2)) tptp.zero_zero_rat)))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B2) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) B2)) tptp.zero_z3403309356797280102nteger)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) B2)) tptp.zero_zero_nat)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) B2)) tptp.zero_zero_int)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) B2)) tptp.zero_zero_rat)))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) B2)) tptp.zero_z3403309356797280102nteger)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) B2)) tptp.zero_zero_nat)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) B2)) tptp.zero_zero_int)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_rat A2) B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A2) B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_nat A2) B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_int A2) B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat B2) A2)) tptp.zero_zero_rat)))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger B2) A2)) tptp.zero_z3403309356797280102nteger)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat B2) A2)) tptp.zero_zero_nat)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int B2) A2)) tptp.zero_zero_int)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.times_times_rat A2) B2)) (or (and (@ _let_1 A2) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B2) tptp.zero_zero_rat)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A2) B2)) (or (and (@ _let_1 A2) (@ _let_1 B2)) (and (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B2) tptp.zero_z3403309356797280102nteger)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.times_times_int A2) B2)) (or (and (@ _let_1 A2) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.times_times_rat A2) B2)) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A2) B2)) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat A2) B2)) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.times_times_int A2) B2)) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 3.70/4.04 (assert (forall ((B2 tptp.rat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.times_times_rat B2) A2)) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 3.70/4.04 (assert (forall ((B2 tptp.code_integer) (A2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B2) A2)) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 3.70/4.04 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat B2) A2)) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 3.70/4.04 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.times_times_int B2) A2)) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 3.70/4.04 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_rat B2) A2))))))
% 3.70/4.04 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_le6747313008572928689nteger B2) A2))))))
% 3.70/4.04 (assert (forall ((C tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_int B2) A2))))))
% 3.70/4.04 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_rat A2) B2))))))
% 3.70/4.04 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_le6747313008572928689nteger A2) B2))))))
% 3.70/4.04 (assert (forall ((C tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (= (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_int A2) B2))))))
% 3.70/4.04 (assert (forall ((B2 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat B2) A2) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B2)))))))
% 3.70/4.04 (assert (forall ((B2 tptp.code_integer) (A2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) A2) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B2)))))))
% 3.70/4.04 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int B2) A2) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2)))))))
% 3.70/4.04 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B2)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A2) B2)) (and (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B2) A2)))))))
% 3.70/4.04 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B2)) (or (and (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A2) B2)) (and (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B2) A2)))))))
% 3.70/4.04 (assert (forall ((C tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A2) B2)) (and (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) A2)))))))
% 3.70/4.04 (assert (forall ((B2 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat B2) A2) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B2) C))))))
% 3.70/4.04 (assert (forall ((B2 tptp.code_integer) (A2 tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) A2) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B2) C))))))
% 3.70/4.04 (assert (forall ((B2 tptp.int) (A2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A2) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B2) C))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B2) C))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B2) C))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B2) C))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B2) C))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B2) C)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A2) B2)) (and (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B2) A2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B2) C)) (or (and (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A2) B2)) (and (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B2) A2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B2) C)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A2) B2)) (and (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) A2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2)))))))
% 3.70/4.04 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 3.70/4.04 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 3.70/4.04 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 3.70/4.04 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.zero_zero_int)))
% 3.70/4.04 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 3.70/4.04 (assert (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer))
% 3.70/4.04 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 3.70/4.04 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 3.70/4.04 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 3.70/4.04 (assert (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer))
% 3.70/4.04 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 3.70/4.04 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 3.70/4.04 (assert (= tptp.ord_less_rat (lambda ((A3 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A3) B3)) tptp.zero_zero_rat))))
% 3.70/4.04 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((A3 tptp.code_integer) (B3 tptp.code_integer)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.minus_8373710615458151222nteger A3) B3)) tptp.zero_z3403309356797280102nteger))))
% 3.70/4.04 (assert (= tptp.ord_less_int (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A3) B3)) tptp.zero_zero_int))))
% 3.70/4.04 (assert (forall ((K3 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K3))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 3.70/4.04 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N)) (@ P I4))) (or (@ P tptp.zero_zero_nat) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) N) (@ P (@ tptp.suc I4))))))))
% 3.70/4.04 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M tptp.nat)) (= N (@ tptp.suc M))))))
% 3.70/4.04 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N)) (@ P I4))) (and (@ P tptp.zero_zero_nat) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N) (@ P (@ tptp.suc I4))))))))
% 3.70/4.04 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M6 tptp.nat)) (= N (@ tptp.suc M6))))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M2) (@ tptp.suc N)) (or (= M2 tptp.zero_zero_nat) (exists ((J2 tptp.nat)) (and (= M2 (@ tptp.suc J2)) (@ (@ tptp.ord_less_nat J2) N)))))))
% 3.70/4.04 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N5 tptp.nat)) (=> (forall ((Nn tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Nn) N5) (@ P Nn))) (@ P (@ tptp.suc N5)))) (@ P N)))))
% 3.70/4.04 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N5 tptp.nat)) (=> (forall ((Nn tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Nn) N5) (@ P Nn))) (@ P (@ tptp.suc N5)))) (@ P N)))))
% 3.70/4.04 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P N) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat K) N) (forall ((I6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I6) K) (not (@ P I6)))) (@ P K)))))))
% 3.70/4.04 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (exists ((K tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.plus_plus_nat I) K) J))))))
% 3.70/4.04 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (= (@ tptp.suc N) M2) (= N (@ (@ tptp.minus_minus_nat M2) (@ tptp.suc tptp.zero_zero_nat))))))
% 3.70/4.04 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (=> (@ _let_1 M2) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M2) N)) M2))))))
% 3.70/4.04 (assert (forall ((I tptp.nat) (J tptp.nat) (K3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat I) K3)) (@ (@ tptp.times_times_nat J) K3))))))
% 3.70/4.04 (assert (forall ((I tptp.nat) (J tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K3))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (@ (@ tptp.ord_less_nat (@ _let_1 I)) (@ _let_1 J)))))))
% 3.70/4.04 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) X) (not (= X tptp.zero_zero_nat)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) B2)) tptp.zero_zero_rat)))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le3102999989581377725nteger B2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)) tptp.zero_z3403309356797280102nteger)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) B2)) tptp.zero_zero_nat)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) B2)) tptp.zero_zero_int)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_int A2) B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) B2)) tptp.zero_zero_rat)))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)) tptp.zero_z3403309356797280102nteger)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) B2)) tptp.zero_zero_nat)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) B2)) tptp.zero_zero_int)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B2) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B2) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B2) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2) (@ _let_1 (@ (@ tptp.plus_plus_int A2) B2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_eq_rat B2) C) (@ (@ tptp.ord_less_rat B2) (@ (@ tptp.plus_plus_rat A2) C))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ (@ tptp.ord_le3102999989581377725nteger B2) C) (@ (@ tptp.ord_le6747313008572928689nteger B2) (@ (@ tptp.plus_p5714425477246183910nteger A2) C))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (@ (@ tptp.ord_less_nat B2) (@ (@ tptp.plus_plus_nat A2) C))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_eq_int B2) C) (@ (@ tptp.ord_less_int B2) (@ (@ tptp.plus_plus_int A2) C))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B2))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) C)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger B2))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A2) C)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) C)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A2) C)))))))
% 3.70/4.04 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A2) B2)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B2) A2)))))))
% 3.70/4.04 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A2)) (@ _let_1 B2)) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger A2) B2)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B2) A2)))))))
% 3.70/4.04 (assert (forall ((C tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A2) B2)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B2) A2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B2) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A2) B2)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B2) A2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B2) C)) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger A2) B2)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B2) A2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B2) C)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A2) B2)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B2) A2))))))
% 3.70/4.04 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A2) B2))))))
% 3.70/4.04 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A2) B2))))))
% 3.70/4.04 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat A2) B2))))))
% 3.70/4.04 (assert (forall ((C tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A2) B2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (@ (@ tptp.ord_less_rat C) D2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B2) D2))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) D2) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B2) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B2) D2))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_nat C) D2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B2) D2))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ (@ tptp.ord_less_int C) D2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B2) D2))))))))
% 3.70/4.04 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B2)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A2) B2)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B2) A2)))))))
% 3.70/4.04 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B2)) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A2) B2)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B2) A2)))))))
% 3.70/4.04 (assert (forall ((C tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A2) B2)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) A2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B2) C)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A2) B2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B2) C)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A2) B2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B2) C)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat A2) B2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B2) C)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A2) B2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (@ (@ tptp.ord_less_rat C) D2) (=> (@ _let_1 A2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B2) D2)))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) D2) (=> (@ _let_1 A2) (=> (@ _let_1 C) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B2) D2)))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_nat C) D2) (=> (@ _let_1 A2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B2) D2)))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ (@ tptp.ord_less_int C) D2) (=> (@ _let_1 A2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B2) D2)))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B2) C)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A2) B2)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B2) A2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B2) C)) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A2) B2)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B2) A2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B2) C)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A2) B2)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) A2))))))
% 3.70/4.04 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_rat B2) A2))))))
% 3.70/4.04 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_le3102999989581377725nteger B2) A2))))))
% 3.70/4.04 (assert (forall ((C tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_int B2) A2))))))
% 3.70/4.04 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_rat A2) B2))))))
% 3.70/4.04 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_le3102999989581377725nteger A2) B2))))))
% 3.70/4.04 (assert (forall ((C tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_int A2) B2))))))
% 3.70/4.04 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A2) B2))))))
% 3.70/4.04 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A2)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger A2) B2))))))
% 3.70/4.04 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat A2) B2))))))
% 3.70/4.04 (assert (forall ((C tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A2) B2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B2) C)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A2) B2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B2) C)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger A2) B2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B2) C)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat A2) B2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B2) C)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A2) B2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_rat C) D2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B2) D2))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) D2) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B2) D2))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_nat C) D2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B2) D2))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_int C) D2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B2) D2))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (@ (@ tptp.ord_less_eq_rat C) D2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B2) D2))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) D2) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B2) D2))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B2) D2))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ (@ tptp.ord_less_eq_int C) D2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B2) D2))))))))
% 3.70/4.04 (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)))))
% 3.70/4.04 (assert (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y)))))
% 3.70/4.04 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)))))
% 3.70/4.04 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.one_one_Code_integer) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) A2)))))
% 3.70/4.04 (assert (forall ((C tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.one_one_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C)) A2)))))
% 3.70/4.04 (assert (forall ((C tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) tptp.one_one_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) C)) A2)))))
% 3.70/4.04 (assert (forall ((C tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.one_one_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) C)) A2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.one_one_Code_integer) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B2) (=> (@ (@ tptp.ord_le3102999989581377725nteger B2) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A2) B2)) tptp.one_one_Code_integer))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) tptp.one_one_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B2) (=> (@ (@ tptp.ord_less_eq_rat B2) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) B2)) tptp.one_one_rat))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.one_one_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B2) (=> (@ (@ tptp.ord_less_eq_nat B2) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) B2)) tptp.one_one_nat))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.one_one_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_eq_int B2) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) B2)) tptp.one_one_int))))))
% 3.70/4.04 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_le3102999989581377725nteger Y) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger X) Y)) X)))))))
% 3.70/4.04 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X) Y)) X)))))))
% 3.70/4.04 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X) Y)) X)))))))
% 3.70/4.04 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_le3102999989581377725nteger Y) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger Y) X)) X)))))))
% 3.70/4.04 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Y) X)) X)))))))
% 3.70/4.04 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int Y) X)) X)))))))
% 3.70/4.04 (assert (forall ((X tptp.rat) (Y tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y))) tptp.zero_zero_rat))))
% 3.70/4.04 (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))))
% 3.70/4.04 (assert (forall ((X tptp.int) (Y tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) tptp.zero_zero_int))))
% 3.70/4.04 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)))
% 3.70/4.04 (assert (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) tptp.one_one_Code_integer)))
% 3.70/4.04 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)))
% 3.70/4.04 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)))
% 3.70/4.04 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P N) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K tptp.nat)) (and (@ (@ tptp.ord_less_nat K) N) (forall ((I6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I6) K) (not (@ P I6)))) (@ P (@ tptp.suc K))))))))
% 3.70/4.04 (assert (forall ((X tptp.produc3843707927480180839at_nat) (Xs tptp.list_P5464809261938338413at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X) (@ tptp.set_Pr3765526544606949372at_nat Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s1588839187904960729at_nat Xs)))))
% 3.70/4.04 (assert (forall ((X tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s5460976970255530739at_nat Xs)))))
% 3.70/4.04 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xs tptp.list_P7985473006766602707_nat_o)) (=> (@ (@ tptp.member6576561426505652726_nat_o X) (@ tptp.set_Pr400311997697478754_nat_o Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s8908918004648414271_nat_o Xs)))))
% 3.70/4.04 (assert (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (=> (@ (@ tptp.member7957490590177025114n_assn X) (@ tptp.set_Pr1139785259514867910n_assn Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s6829681357464350627n_assn Xs)))))
% 3.70/4.04 (assert (forall ((X tptp.c) (Xs tptp.list_c)) (=> (@ (@ tptp.member_c X) (@ tptp.set_c2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_c Xs)))))
% 3.70/4.04 (assert (forall ((X tptp.d) (Xs tptp.list_d)) (=> (@ (@ tptp.member_d X) (@ tptp.set_d2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_d Xs)))))
% 3.70/4.04 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_nat Xs)))))
% 3.70/4.04 (assert (forall ((X tptp.int) (Xs tptp.list_int)) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_int Xs)))))
% 3.70/4.04 (assert (forall ((N tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I))) N))))
% 3.70/4.04 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M2) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat N) M2))))))
% 3.70/4.04 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M2) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat M2) N))))))
% 3.70/4.04 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 N) (=> (@ _let_1 M2) (@ _let_1 (@ (@ tptp.times_times_nat M2) N)))))))
% 3.70/4.04 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ P tptp.one_one_nat) (=> (forall ((N5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N5) (=> (@ P N5) (@ P (@ tptp.suc N5))))) (@ P N))))))
% 3.70/4.04 (assert (forall ((P (-> tptp.nat Bool)) (A2 tptp.nat) (B2 tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A2) B2)) (and (=> (@ (@ tptp.ord_less_nat A2) B2) (@ P tptp.zero_zero_nat)) (forall ((D5 tptp.nat)) (=> (= A2 (@ (@ tptp.plus_plus_nat B2) D5)) (@ P D5)))))))
% 3.70/4.04 (assert (forall ((P (-> tptp.nat Bool)) (A2 tptp.nat) (B2 tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A2) B2)) (not (or (and (@ (@ tptp.ord_less_nat A2) B2) (not (@ P tptp.zero_zero_nat))) (exists ((D5 tptp.nat)) (and (= A2 (@ (@ tptp.plus_plus_nat B2) D5)) (not (@ P D5)))))))))
% 3.70/4.04 (assert (forall ((C tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.times_times_rat C) B2)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) B2)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B2) tptp.one_one_rat))))))
% 3.70/4.04 (assert (forall ((C tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger C) (@ (@ tptp.times_3573771949741848930nteger C) B2)) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) B2)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B2) tptp.one_one_Code_integer))))))
% 3.70/4.04 (assert (forall ((C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.times_times_int C) B2)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) B2)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B2) tptp.one_one_int))))))
% 3.70/4.04 (assert (forall ((C tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat C) A2)) C) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A2) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A2))))))
% 3.70/4.04 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger C) A2)) C) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.one_one_Code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) A2))))))
% 3.70/4.04 (assert (forall ((C tptp.int) (A2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int C) A2)) C) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A2) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A2))))))
% 3.70/4.04 (assert (forall ((C tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.times_times_rat B2) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) B2)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B2) tptp.one_one_rat))))))
% 3.70/4.04 (assert (forall ((C tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger C) (@ (@ tptp.times_3573771949741848930nteger B2) C)) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) B2)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B2) tptp.one_one_Code_integer))))))
% 3.70/4.04 (assert (forall ((C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.times_times_int B2) C)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) B2)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B2) tptp.one_one_int))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C)) C) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A2) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) C) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.one_one_Code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) A2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) C)) C) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A2) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A2))))))
% 3.70/4.04 (assert (forall ((C tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat C) (@ (@ tptp.times_times_rat C) B2)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat tptp.one_one_rat) B2)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B2) tptp.one_one_rat))))))
% 3.70/4.04 (assert (forall ((C tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger C) (@ (@ tptp.times_3573771949741848930nteger C) B2)) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) B2)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B2) tptp.one_one_Code_integer))))))
% 3.70/4.04 (assert (forall ((C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int C) (@ (@ tptp.times_times_int C) B2)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int tptp.one_one_int) B2)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) tptp.one_one_int))))))
% 3.70/4.04 (assert (forall ((C tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat C) A2)) C) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A2) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) A2))))))
% 3.70/4.04 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger C) A2)) C) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.one_one_Code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A2))))))
% 3.70/4.04 (assert (forall ((C tptp.int) (A2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int C) A2)) C) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A2) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) A2))))))
% 3.70/4.04 (assert (forall ((C tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat C) (@ (@ tptp.times_times_rat B2) C)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat tptp.one_one_rat) B2)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B2) tptp.one_one_rat))))))
% 3.70/4.04 (assert (forall ((C tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger C) (@ (@ tptp.times_3573771949741848930nteger B2) C)) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) B2)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B2) tptp.one_one_Code_integer))))))
% 3.70/4.04 (assert (forall ((C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int C) (@ (@ tptp.times_times_int B2) C)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int tptp.one_one_int) B2)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) tptp.one_one_int))))))
% 3.70/4.04 (assert (forall ((A2 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) C) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A2) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) A2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) C) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.one_one_Code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C)) C) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A2) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) A2))))))
% 3.70/4.04 (assert (forall ((X tptp.code_integer) (A2 tptp.code_integer) (Y tptp.code_integer) (U tptp.code_integer) (V2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_le3102999989581377725nteger X) A2) (=> (@ (@ tptp.ord_le3102999989581377725nteger Y) A2) (=> (@ _let_1 U) (=> (@ _let_1 V2) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger U) V2) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger U) X)) (@ (@ tptp.times_3573771949741848930nteger V2) Y))) A2)))))))))
% 3.70/4.04 (assert (forall ((X tptp.rat) (A2 tptp.rat) (Y tptp.rat) (U tptp.rat) (V2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat X) A2) (=> (@ (@ tptp.ord_less_eq_rat Y) A2) (=> (@ _let_1 U) (=> (@ _let_1 V2) (=> (= (@ (@ tptp.plus_plus_rat U) V2) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat U) X)) (@ (@ tptp.times_times_rat V2) Y))) A2)))))))))
% 3.70/4.04 (assert (forall ((X tptp.int) (A2 tptp.int) (Y tptp.int) (U tptp.int) (V2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int X) A2) (=> (@ (@ tptp.ord_less_eq_int Y) A2) (=> (@ _let_1 U) (=> (@ _let_1 V2) (=> (= (@ (@ tptp.plus_plus_int U) V2) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X)) (@ (@ tptp.times_times_int V2) Y))) A2)))))))))
% 3.70/4.04 (assert (forall ((K3 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (=> (@ (@ tptp.ord_less_eq_nat K3) M2) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat K3) (@ tptp.suc tptp.zero_zero_nat))) M2)))))
% 3.70/4.04 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= N (@ tptp.suc (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 3.70/4.04 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M2)) N) (@ (@ tptp.minus_minus_nat M2) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 3.70/4.04 (assert (forall ((X tptp.rat) (A2 tptp.rat) (Y tptp.rat) (U tptp.rat) (V2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat X) A2) (=> (@ (@ tptp.ord_less_rat Y) A2) (=> (@ _let_1 U) (=> (@ _let_1 V2) (=> (= (@ (@ tptp.plus_plus_rat U) V2) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat U) X)) (@ (@ tptp.times_times_rat V2) Y))) A2)))))))))
% 3.70/4.04 (assert (forall ((X tptp.code_integer) (A2 tptp.code_integer) (Y tptp.code_integer) (U tptp.code_integer) (V2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X) A2) (=> (@ (@ tptp.ord_le6747313008572928689nteger Y) A2) (=> (@ _let_1 U) (=> (@ _let_1 V2) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger U) V2) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger U) X)) (@ (@ tptp.times_3573771949741848930nteger V2) Y))) A2)))))))))
% 3.70/4.04 (assert (forall ((X tptp.int) (A2 tptp.int) (Y tptp.int) (U tptp.int) (V2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int X) A2) (=> (@ (@ tptp.ord_less_int Y) A2) (=> (@ _let_1 U) (=> (@ _let_1 V2) (=> (= (@ (@ tptp.plus_plus_int U) V2) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X)) (@ (@ tptp.times_times_int V2) Y))) A2)))))))))
% 3.70/4.04 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (forall ((Z4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z4) (=> (@ (@ tptp.ord_less_rat Z4) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z4) X)) Y)))) (@ (@ tptp.ord_less_eq_rat X) Y))))
% 3.70/4.04 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y))) (or (not (= X tptp.zero_zero_rat)) (not (= Y tptp.zero_zero_rat))))))
% 3.70/4.04 (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))))))
% 3.70/4.04 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) (or (not (= X tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int))))))
% 3.70/4.04 (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)))))
% 3.70/4.04 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y))) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))
% 3.70/4.04 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))
% 3.70/4.04 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat Y) Z)) (@ (@ tptp.ord_less_eq_rat X) Y)))))
% 3.70/4.04 (assert (forall ((Z tptp.code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) Z) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger X) Z)) (@ (@ tptp.times_3573771949741848930nteger Y) Z)) (@ (@ tptp.ord_le3102999989581377725nteger X) Y)))))
% 3.70/4.04 (assert (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X) Z)) (@ (@ tptp.times_times_int Y) Z)) (@ (@ tptp.ord_less_eq_int X) Y)))))
% 3.70/4.04 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat Z))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_rat X) Y))))))
% 3.70/4.04 (assert (forall ((Z tptp.code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger Z))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) Z) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_le3102999989581377725nteger X) Y))))))
% 3.70/4.04 (assert (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.times_times_int Z))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_int X) Y))))))
% 3.70/4.04 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (forall ((E2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.plus_plus_rat Y) E2)))) (@ (@ tptp.ord_less_eq_rat X) Y))))
% 3.70/4.04 (assert (forall ((Q6 tptp.code_integer) (R2 tptp.code_integer)) (= (@ tptp.unique5706413561485394159nteger (@ (@ tptp.produc1086072967326762835nteger Q6) R2)) (= R2 tptp.zero_z3403309356797280102nteger))))
% 3.70/4.04 (assert (forall ((Q6 tptp.nat) (R2 tptp.nat)) (= (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.product_Pair_nat_nat Q6) R2)) (= R2 tptp.zero_zero_nat))))
% 3.70/4.04 (assert (forall ((Q6 tptp.int) (R2 tptp.int)) (= (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.product_Pair_int_int Q6) R2)) (= R2 tptp.zero_zero_int))))
% 3.70/4.04 (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)))))
% 3.70/4.04 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y)) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))
% 3.70/4.04 (assert (forall ((X tptp.int) (Y tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))
% 3.70/4.04 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat Y) Z)) (@ (@ tptp.ord_less_rat X) Y)))))
% 3.70/4.04 (assert (forall ((Z tptp.code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) Z) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger X) Z)) (@ (@ tptp.times_3573771949741848930nteger Y) Z)) (@ (@ tptp.ord_le6747313008572928689nteger X) Y)))))
% 3.70/4.04 (assert (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int X) Z)) (@ (@ tptp.times_times_int Y) Z)) (@ (@ tptp.ord_less_int X) Y)))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (R2 tptp.set_Pr4329608150637261639at_nat) (P (-> tptp.set_Pr1261947904930325089at_nat Bool))) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat A2) B2)) (@ tptp.transi2703068831062848130at_nat R2)) (=> (forall ((Y2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat Y2) B2)) R2) (@ P Y2))) (=> (forall ((Y2 tptp.set_Pr1261947904930325089at_nat) (Z4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat Y2) Z4)) R2) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat Z4) B2)) (@ tptp.transi2703068831062848130at_nat R2)) (=> (@ P Z4) (@ P Y2))))) (@ P A2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B2)) (@ tptp.transi6264000038957366511cl_nat R2)) (=> (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y2) B2)) R2) (@ P Y2))) (=> (forall ((Y2 tptp.nat) (Z4 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y2) Z4)) R2) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Z4) B2)) (@ tptp.transi6264000038957366511cl_nat R2)) (=> (@ P Z4) (@ P Y2))))) (@ P A2))))))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (R2 tptp.set_Pr4329608150637261639at_nat) (P (-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool))) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Y)) (@ tptp.transi2703068831062848130at_nat R2)) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat) (Y2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X3) Y2)) R2) (@ (@ P X3) Y2))) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat) (Y2 tptp.set_Pr1261947904930325089at_nat) (Z4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ P X3))) (let ((_let_2 (@ tptp.transi2703068831062848130at_nat R2))) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X3) Y2)) _let_2) (=> (@ _let_1 Y2) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat Y2) Z4)) _let_2) (=> (@ (@ P Y2) Z4) (@ _let_1 Z4)))))))) (@ (@ P X) Y))))))
% 3.70/4.04 (assert (forall ((X tptp.nat) (Y tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ tptp.transi6264000038957366511cl_nat R2)) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) Y2)) R2) (@ (@ P X3) Y2))) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat) (Z4 tptp.nat)) (let ((_let_1 (@ P X3))) (let ((_let_2 (@ tptp.transi6264000038957366511cl_nat R2))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) Y2)) _let_2) (=> (@ _let_1 Y2) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y2) Z4)) _let_2) (=> (@ (@ P Y2) Z4) (@ _let_1 Z4)))))))) (@ (@ P X) Y))))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (R2 tptp.set_Pr4329608150637261639at_nat) (C tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.transi2703068831062848130at_nat R2))) (let ((_let_2 (@ tptp.produc2922128104949294807at_nat A2))) (=> (@ (@ tptp.member8757157785044589968at_nat (@ _let_2 B2)) R2) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat B2) C)) _let_1) (@ (@ tptp.member8757157785044589968at_nat (@ _let_2 C)) _let_1)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.transi6264000038957366511cl_nat R2))) (let ((_let_2 (@ tptp.product_Pair_nat_nat A2))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ _let_2 B2)) R2) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B2) C)) _let_1) (@ (@ tptp.member8440522571783428010at_nat (@ _let_2 C)) _let_1)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (R2 tptp.set_Pr4329608150637261639at_nat) (C tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.transi2703068831062848130at_nat R2))) (let ((_let_2 (@ tptp.produc2922128104949294807at_nat A2))) (=> (@ (@ tptp.member8757157785044589968at_nat (@ _let_2 B2)) _let_1) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat B2) C)) R2) (@ (@ tptp.member8757157785044589968at_nat (@ _let_2 C)) _let_1)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.transi6264000038957366511cl_nat R2))) (let ((_let_2 (@ tptp.product_Pair_nat_nat A2))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ _let_2 B2)) _let_1) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B2) C)) R2) (@ (@ tptp.member8440522571783428010at_nat (@ _let_2 C)) _let_1)))))))
% 3.70/4.04 (assert (forall ((R2 tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat)) (not (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X3) X3)) (@ tptp.transi2703068831062848130at_nat R2)))) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Y)) R2) (not (= X Y))))))
% 3.70/4.04 (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))))))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat) (R2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Z)))) (=> (@ _let_1 (@ tptp.transi2703068831062848130at_nat R2)) (=> (not (@ _let_1 R2)) (not (forall ((Y2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Y2)) R2) (not (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat Y2) Z)) (@ tptp.transi2703068831062848130at_nat R2)))))))))))
% 3.70/4.04 (assert (forall ((X tptp.nat) (Z tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Z)))) (=> (@ _let_1 (@ tptp.transi6264000038957366511cl_nat R2)) (=> (not (@ _let_1 R2)) (not (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y2)) R2) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y2) Z)) (@ tptp.transi6264000038957366511cl_nat R2)))))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (R tptp.set_Pr4329608150637261639at_nat) (C tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.produc2922128104949294807at_nat A2))) (=> (@ (@ tptp.member8757157785044589968at_nat (@ _let_1 B2)) R) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat B2) C)) R) (@ (@ tptp.member8757157785044589968at_nat (@ _let_1 C)) (@ tptp.transi2703068831062848130at_nat R)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (R tptp.set_Pr1261947904930325089at_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.product_Pair_nat_nat A2))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 B2)) R) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B2) C)) R) (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 C)) (@ tptp.transi6264000038957366511cl_nat R)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (R2 tptp.set_Pr4329608150637261639at_nat) (P (-> tptp.set_Pr1261947904930325089at_nat Bool))) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat A2) B2)) (@ tptp.transi2703068831062848130at_nat R2)) (=> (forall ((Y2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat A2) Y2)) R2) (@ P Y2))) (=> (forall ((Y2 tptp.set_Pr1261947904930325089at_nat) (Z4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat A2) Y2)) (@ tptp.transi2703068831062848130at_nat R2)) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat Y2) Z4)) R2) (=> (@ P Y2) (@ P Z4))))) (@ P B2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B2)) (@ tptp.transi6264000038957366511cl_nat R2)) (=> (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) Y2)) R2) (@ P Y2))) (=> (forall ((Y2 tptp.nat) (Z4 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) Y2)) (@ tptp.transi6264000038957366511cl_nat R2)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y2) Z4)) R2) (=> (@ P Y2) (@ P Z4))))) (@ P B2))))))
% 3.70/4.04 (assert (forall ((Ax (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (Ay tptp.produc8923325533196201883nteger) (Bx (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (By tptp.produc8923325533196201883nteger) (R2 tptp.set_Pr1722956316086891245nteger) (P (-> (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger Bool))) (=> (@ (@ tptp.member2446009503569356342nteger (@ (@ tptp.produc7954516348491987909nteger (@ (@ tptp.produc8603105652947943368nteger Ax) Ay)) (@ (@ tptp.produc8603105652947943368nteger Bx) By))) (@ tptp.transi6228740973808232501nteger R2)) (=> (forall ((A4 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B4 tptp.produc8923325533196201883nteger)) (=> (@ (@ tptp.member2446009503569356342nteger (@ (@ tptp.produc7954516348491987909nteger (@ (@ tptp.produc8603105652947943368nteger Ax) Ay)) (@ (@ tptp.produc8603105652947943368nteger A4) B4))) R2) (@ (@ P A4) B4))) (=> (forall ((A4 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B4 tptp.produc8923325533196201883nteger) (Aa (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (Ba tptp.produc8923325533196201883nteger)) (let ((_let_1 (@ (@ tptp.produc8603105652947943368nteger A4) B4))) (=> (@ (@ tptp.member2446009503569356342nteger (@ (@ tptp.produc7954516348491987909nteger (@ (@ tptp.produc8603105652947943368nteger Ax) Ay)) _let_1)) (@ tptp.transi6228740973808232501nteger R2)) (=> (@ (@ tptp.member2446009503569356342nteger (@ (@ tptp.produc7954516348491987909nteger _let_1) (@ (@ tptp.produc8603105652947943368nteger Aa) Ba))) R2) (=> (@ (@ P A4) B4) (@ (@ P Aa) Ba)))))) (@ (@ P Bx) By))))))
% 3.70/4.04 (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) (P (-> (-> 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 ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.member4763271486408492550et_nat (@ (@ tptp.produc8599840265553166229et_nat (@ (@ tptp.produc5001842942810119800et_nat Ax) Ay)) (@ (@ tptp.produc5001842942810119800et_nat A4) B4))) R2) (@ (@ P A4) B4))) (=> (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.produc3658429121746597890et_nat) (Aa (-> tptp.produc3658429121746597890et_nat Bool)) (Ba tptp.produc3658429121746597890et_nat)) (let ((_let_1 (@ (@ tptp.produc5001842942810119800et_nat A4) B4))) (=> (@ (@ 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 Aa) Ba))) R2) (=> (@ (@ P A4) B4) (@ (@ P Aa) Ba)))))) (@ (@ P Bx) By))))))
% 3.70/4.04 (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) (P (-> (-> 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 ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.produc3925858234332021118et_nat)) (=> (@ (@ tptp.member6341495586645257982et_nat (@ (@ tptp.produc1940133919992309389et_nat (@ (@ tptp.produc2245416461498447860et_nat Ax) Ay)) (@ (@ tptp.produc2245416461498447860et_nat A4) B4))) R2) (@ (@ P A4) B4))) (=> (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.produc3925858234332021118et_nat) (Aa (-> tptp.produc3658429121746597890et_nat Bool)) (Ba tptp.produc3925858234332021118et_nat)) (let ((_let_1 (@ (@ tptp.produc2245416461498447860et_nat A4) B4))) (=> (@ (@ 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 Aa) Ba))) R2) (=> (@ (@ P A4) B4) (@ (@ P Aa) Ba)))))) (@ (@ P Bx) By))))))
% 3.70/4.04 (assert (forall ((Ax (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Ay tptp.product_prod_int_int) (Bx (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (By tptp.product_prod_int_int) (R2 tptp.set_Pr4708930517165415495nt_int) (P (-> (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.member6582457606847315088nt_int (@ (@ tptp.produc7601053194514725023nt_int (@ (@ tptp.produc5700946648718959541nt_int Ax) Ay)) (@ (@ tptp.produc5700946648718959541nt_int Bx) By))) (@ tptp.transi7434818091516421410nt_int R2)) (=> (forall ((A4 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B4 tptp.product_prod_int_int)) (=> (@ (@ tptp.member6582457606847315088nt_int (@ (@ tptp.produc7601053194514725023nt_int (@ (@ tptp.produc5700946648718959541nt_int Ax) Ay)) (@ (@ tptp.produc5700946648718959541nt_int A4) B4))) R2) (@ (@ P A4) B4))) (=> (forall ((A4 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B4 tptp.product_prod_int_int) (Aa (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Ba tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.produc5700946648718959541nt_int A4) B4))) (=> (@ (@ tptp.member6582457606847315088nt_int (@ (@ tptp.produc7601053194514725023nt_int (@ (@ tptp.produc5700946648718959541nt_int Ax) Ay)) _let_1)) (@ tptp.transi7434818091516421410nt_int R2)) (=> (@ (@ tptp.member6582457606847315088nt_int (@ (@ tptp.produc7601053194514725023nt_int _let_1) (@ (@ tptp.produc5700946648718959541nt_int Aa) Ba))) R2) (=> (@ (@ P A4) B4) (@ (@ P Aa) Ba)))))) (@ (@ P Bx) By))))))
% 3.70/4.04 (assert (forall ((Ax (-> tptp.int tptp.option6357759511663192854e_term)) (Ay tptp.product_prod_int_int) (Bx (-> tptp.int tptp.option6357759511663192854e_term)) (By tptp.product_prod_int_int) (R2 tptp.set_Pr8634505666381077339nt_int) (P (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.member4085533954029916580nt_int (@ (@ tptp.produc8406175334058502835nt_int (@ (@ tptp.produc4305682042979456191nt_int Ax) Ay)) (@ (@ tptp.produc4305682042979456191nt_int Bx) By))) (@ tptp.transi4533545184864474924nt_int R2)) (=> (forall ((A4 (-> tptp.int tptp.option6357759511663192854e_term)) (B4 tptp.product_prod_int_int)) (=> (@ (@ tptp.member4085533954029916580nt_int (@ (@ tptp.produc8406175334058502835nt_int (@ (@ tptp.produc4305682042979456191nt_int Ax) Ay)) (@ (@ tptp.produc4305682042979456191nt_int A4) B4))) R2) (@ (@ P A4) B4))) (=> (forall ((A4 (-> tptp.int tptp.option6357759511663192854e_term)) (B4 tptp.product_prod_int_int) (Aa (-> tptp.int tptp.option6357759511663192854e_term)) (Ba tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.produc4305682042979456191nt_int A4) B4))) (=> (@ (@ tptp.member4085533954029916580nt_int (@ (@ tptp.produc8406175334058502835nt_int (@ (@ tptp.produc4305682042979456191nt_int Ax) Ay)) _let_1)) (@ tptp.transi4533545184864474924nt_int R2)) (=> (@ (@ tptp.member4085533954029916580nt_int (@ (@ tptp.produc8406175334058502835nt_int _let_1) (@ (@ tptp.produc4305682042979456191nt_int Aa) Ba))) R2) (=> (@ (@ P A4) B4) (@ (@ P Aa) Ba)))))) (@ (@ P Bx) By))))))
% 3.70/4.04 (assert (forall ((A1 tptp.set_Pr1261947904930325089at_nat) (A22 tptp.set_Pr1261947904930325089at_nat) (R2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat A1) A22)))) (=> (@ _let_1 (@ tptp.transi2703068831062848130at_nat R2)) (=> (not (@ _let_1 R2)) (not (forall ((B4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat A1) B4)) (@ tptp.transi2703068831062848130at_nat R2)) (not (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat B4) A22)) R2))))))))))
% 3.70/4.04 (assert (forall ((A1 tptp.nat) (A22 tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A1) A22)))) (=> (@ _let_1 (@ tptp.transi6264000038957366511cl_nat R2)) (=> (not (@ _let_1 R2)) (not (forall ((B4 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A1) B4)) (@ tptp.transi6264000038957366511cl_nat R2)) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B4) A22)) R2))))))))))
% 3.70/4.04 (assert (forall ((A1 tptp.set_Pr1261947904930325089at_nat) (A22 tptp.set_Pr1261947904930325089at_nat) (R2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat A1) A22)) (@ tptp.transi2703068831062848130at_nat R2)) (or (exists ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (and (= A1 A3) (= A22 B3) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat A3) B3)) R2))) (exists ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C5 tptp.set_Pr1261947904930325089at_nat)) (and (= A1 A3) (= A22 C5) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat A3) B3)) (@ tptp.transi2703068831062848130at_nat R2)) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat B3) C5)) R2)))))))
% 3.70/4.04 (assert (forall ((A1 tptp.nat) (A22 tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A1) A22)) (@ tptp.transi6264000038957366511cl_nat R2)) (or (exists ((A3 tptp.nat) (B3 tptp.nat)) (and (= A1 A3) (= A22 B3) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A3) B3)) R2))) (exists ((A3 tptp.nat) (B3 tptp.nat) (C5 tptp.nat)) (and (= A1 A3) (= A22 C5) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A3) B3)) (@ tptp.transi6264000038957366511cl_nat R2)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B3) C5)) R2)))))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (R2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat A2) B2)))) (=> (@ _let_1 R2) (@ _let_1 (@ tptp.transi2703068831062848130at_nat R2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B2)))) (=> (@ _let_1 R2) (@ _let_1 (@ tptp.transi6264000038957366511cl_nat R2))))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (R2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat A2) B2)))) (=> (@ _let_1 (@ tptp.transi2703068831062848130at_nat R2)) (=> (not (@ _let_1 R2)) (not (forall ((C4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat A2) C4)) (@ tptp.transi2703068831062848130at_nat R2)) (not (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat C4) B2)) R2))))))))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B2)))) (=> (@ _let_1 (@ tptp.transi6264000038957366511cl_nat R2)) (=> (not (@ _let_1 R2)) (not (forall ((C4 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) C4)) (@ tptp.transi6264000038957366511cl_nat R2)) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat C4) B2)) R2))))))))))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (R2 tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.transi2703068831062848130at_nat R2))) (let ((_let_2 (@ tptp.produc2922128104949294807at_nat X))) (=> (@ (@ tptp.member8757157785044589968at_nat (@ _let_2 Y)) _let_1) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat Y) Z)) _let_1) (@ (@ tptp.member8757157785044589968at_nat (@ _let_2 Z)) _let_1)))))))
% 3.70/4.04 (assert (forall ((X tptp.nat) (Y tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (Z 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) Z)) _let_1) (@ (@ tptp.member8440522571783428010at_nat (@ _let_2 Z)) _let_1)))))))
% 3.70/4.04 (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)))))
% 3.70/4.04 (assert (@ tptp.biject3388518990857851981at_nat tptp.bot_bo228742789529271731at_nat))
% 3.70/4.04 (assert (@ tptp.bijective_nat_nat tptp.bot_bo2099793752762293965at_nat))
% 3.70/4.04 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.total_7212417256332265445at_nat (@ (@ tptp.insert9200635055090092081at_nat X) tptp.bot_bo3083307316010499117at_nat)) (@ (@ tptp.insert9069300056098147895at_nat (@ (@ tptp.produc2922128104949294807at_nat X) X)) tptp.bot_bo228742789529271731at_nat))))
% 3.70/4.04 (assert (forall ((X tptp.produc3843707927480180839at_nat)) (@ (@ tptp.total_1513685709984341995at_nat (@ (@ tptp.insert9069300056098147895at_nat X) tptp.bot_bo228742789529271731at_nat)) (@ (@ tptp.insert398606708087465655at_nat (@ (@ tptp.produc2335810615602371415at_nat X) X)) tptp.bot_bo7193250159860175667at_nat))))
% 3.70/4.04 (assert (forall ((X tptp.product_prod_nat_nat)) (@ (@ tptp.total_3592101749530773125at_nat (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat)) (@ (@ tptp.insert5050368324300391991at_nat (@ (@ tptp.produc6161850002892822231at_nat X) X)) tptp.bot_bo5327735625951526323at_nat))))
% 3.70/4.04 (assert (forall ((X Bool)) (@ (@ tptp.total_on_o (@ (@ tptp.insert_o2 X) tptp.bot_bot_set_o)) (@ (@ tptp.insert6201435330877294327od_o_o (@ (@ tptp.product_Pair_o_o X) X)) tptp.bot_bo7073875226086086771od_o_o))))
% 3.70/4.04 (assert (forall ((X tptp.nat)) (@ (@ tptp.total_on_nat (@ (@ tptp.insert_nat2 X) tptp.bot_bot_set_nat)) (@ (@ tptp.insert8211810215607154385at_nat (@ (@ tptp.product_Pair_nat_nat X) X)) tptp.bot_bo2099793752762293965at_nat))))
% 3.70/4.04 (assert (forall ((X tptp.int)) (@ (@ tptp.total_on_int (@ (@ tptp.insert_int2 X) tptp.bot_bot_set_int)) (@ (@ tptp.insert5033312907999012233nt_int (@ (@ tptp.product_Pair_int_int X) X)) tptp.bot_bo1796632182523588997nt_int))))
% 3.70/4.04 (assert (forall ((N tptp.nat) (X tptp.int) (Xs tptp.list_int)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.nth_int (@ (@ tptp.cons_int X) Xs)) N) (@ (@ tptp.nth_int Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 3.70/4.04 (assert (forall ((N tptp.nat) (X tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X) Xs)) N) (@ (@ tptp.nth_nat Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 3.70/4.04 (assert (forall ((N tptp.nat) (X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.nth_Pr1769885009046257848n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) N) (@ (@ tptp.nth_Pr1769885009046257848n_assn Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 3.70/4.04 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (R2 tptp.set_Pr4329608150637261639at_nat)) (= (@ tptp.field_3145993188331922222at_nat (@ (@ tptp.insert9069300056098147895at_nat (@ (@ tptp.produc2922128104949294807at_nat A2) B2)) R2)) (@ (@ tptp.sup_su3642409539654194069at_nat (@ (@ tptp.insert9200635055090092081at_nat A2) (@ (@ tptp.insert9200635055090092081at_nat B2) tptp.bot_bo3083307316010499117at_nat))) (@ tptp.field_3145993188331922222at_nat R2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.produc3843707927480180839at_nat) (B2 tptp.produc3843707927480180839at_nat) (R2 tptp.set_Pr5564308138774400199at_nat)) (= (@ tptp.field_2862844103579723188at_nat (@ (@ tptp.insert398606708087465655at_nat (@ (@ tptp.produc2335810615602371415at_nat A2) B2)) R2)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.insert9069300056098147895at_nat A2) (@ (@ tptp.insert9069300056098147895at_nat B2) tptp.bot_bo228742789529271731at_nat))) (@ tptp.field_2862844103579723188at_nat R2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.product_prod_nat_nat) (B2 tptp.product_prod_nat_nat) (R2 tptp.set_Pr8693737435421807431at_nat)) (= (@ tptp.field_4706345496283612622at_nat (@ (@ tptp.insert5050368324300391991at_nat (@ (@ tptp.produc6161850002892822231at_nat A2) B2)) R2)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.insert8211810215607154385at_nat A2) (@ (@ tptp.insert8211810215607154385at_nat B2) tptp.bot_bo2099793752762293965at_nat))) (@ tptp.field_4706345496283612622at_nat R2)))))
% 3.70/4.04 (assert (forall ((A2 Bool) (B2 Bool) (R2 tptp.set_Product_prod_o_o)) (= (@ tptp.field_o (@ (@ tptp.insert6201435330877294327od_o_o (@ (@ tptp.product_Pair_o_o A2) B2)) R2)) (@ (@ tptp.sup_sup_set_o (@ (@ tptp.insert_o2 A2) (@ (@ tptp.insert_o2 B2) tptp.bot_bot_set_o))) (@ tptp.field_o R2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.field_nat (@ (@ tptp.insert8211810215607154385at_nat (@ (@ tptp.product_Pair_nat_nat A2) B2)) R2)) (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.insert_nat2 A2) (@ (@ tptp.insert_nat2 B2) tptp.bot_bot_set_nat))) (@ tptp.field_nat R2)))))
% 3.70/4.04 (assert (forall ((A2 tptp.int) (B2 tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (= (@ tptp.field_int (@ (@ tptp.insert5033312907999012233nt_int (@ (@ tptp.product_Pair_int_int A2) B2)) R2)) (@ (@ tptp.sup_sup_set_int (@ (@ tptp.insert_int2 A2) (@ (@ tptp.insert_int2 B2) tptp.bot_bot_set_int))) (@ tptp.field_int R2)))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (Xs tptp.list_c) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) (@ tptp.size_size_list_c Xs)) (= (@ (@ tptp.nth_Pr2476257089995772766_nat_c (@ (@ tptp.enumerate_c N) Xs)) M2) (@ (@ tptp.product_Pair_nat_c (@ (@ tptp.plus_plus_nat N) M2)) (@ (@ tptp.nth_c Xs) M2))))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (Xs tptp.list_d) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) (@ tptp.size_size_list_d Xs)) (= (@ (@ tptp.nth_Pr2476257094299001567_nat_d (@ (@ tptp.enumerate_d N) Xs)) M2) (@ (@ tptp.product_Pair_nat_d (@ (@ tptp.plus_plus_nat N) M2)) (@ (@ tptp.nth_d Xs) M2))))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (Xs tptp.list_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_Pr7617993195940197384at_nat (@ (@ tptp.enumerate_nat N) Xs)) M2) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat N) M2)) (@ (@ tptp.nth_nat Xs) M2))))))
% 3.70/4.04 (assert (forall ((M2 tptp.nat) (Xs tptp.list_int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_Pr3440142176431000676at_int (@ (@ tptp.enumerate_int N) Xs)) M2) (@ (@ tptp.product_Pair_nat_int (@ (@ tptp.plus_plus_nat N) M2)) (@ (@ tptp.nth_int Xs) M2))))))
% 3.70/4.04 (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 ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As))) (=> (= Xb _let_1) (=> (@ (@ tptp.accp_P1862375125659990705et_nat tptp.times_assn_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) _let_1))) (exists ((As13 tptp.set_nat) (As24 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H))) (and (= As (@ (@ 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))))))))))))))
% 3.70/4.04 (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 ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As))) (=> (= Xb _let_1) (=> (@ (@ tptp.accp_P1862375125659990705et_nat tptp.times_assn_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) _let_1))) (not (exists ((As12 tptp.set_nat) (As23 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H))) (and (= As (@ (@ 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)))))))))))))))
% 3.70/4.04 (assert (forall ((X21 tptp.int) (X222 tptp.list_int) (Y21 tptp.int) (Y222 tptp.list_int)) (= (= (@ (@ tptp.cons_int X21) X222) (@ (@ tptp.cons_int Y21) Y222)) (and (= X21 Y21) (= X222 Y222)))))
% 3.70/4.04 (assert (forall ((X21 tptp.nat) (X222 tptp.list_nat) (Y21 tptp.nat) (Y222 tptp.list_nat)) (= (= (@ (@ tptp.cons_nat X21) X222) (@ (@ tptp.cons_nat Y21) Y222)) (and (= X21 Y21) (= X222 Y222)))))
% 3.70/4.04 (assert (forall ((X21 tptp.produc6575502325842934193n_assn) (X222 tptp.list_P8527749157015355191n_assn) (Y21 tptp.produc6575502325842934193n_assn) (Y222 tptp.list_P8527749157015355191n_assn)) (= (= (@ (@ tptp.cons_P2971678138204555879n_assn X21) X222) (@ (@ tptp.cons_P2971678138204555879n_assn Y21) Y222)) (and (= X21 Y21) (= X222 Y222)))))
% 3.70/4.04 (assert (forall ((R2 tptp.set_Product_prod_o_o) (S3 tptp.set_Product_prod_o_o)) (= (@ tptp.field_o (@ (@ tptp.sup_su5769328420594410459od_o_o R2) S3)) (@ (@ tptp.sup_sup_set_o (@ tptp.field_o R2)) (@ tptp.field_o S3)))))
% 3.70/4.04 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (S3 tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.field_nat (@ (@ tptp.sup_su6327502436637775413at_nat R2) S3)) (@ (@ tptp.sup_sup_set_nat (@ tptp.field_nat R2)) (@ tptp.field_nat S3)))))
% 3.70/4.04 (assert (forall ((R2 tptp.set_Pr5564308138774400199at_nat) (S3 tptp.set_Pr5564308138774400199at_nat)) (= (@ tptp.field_2862844103579723188at_nat (@ (@ tptp.sup_su6664651903789602459at_nat R2) S3)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ tptp.field_2862844103579723188at_nat R2)) (@ tptp.field_2862844103579723188at_nat S3)))))
% 3.70/4.04 (assert (forall ((R2 tptp.set_Pr4329608150637261639at_nat) (S3 tptp.set_Pr4329608150637261639at_nat)) (= (@ tptp.field_3145993188331922222at_nat (@ (@ tptp.sup_su5525570899277871387at_nat R2) S3)) (@ (@ tptp.sup_su3642409539654194069at_nat (@ tptp.field_3145993188331922222at_nat R2)) (@ tptp.field_3145993188331922222at_nat S3)))))
% 3.70/4.04 (assert (forall ((P (-> tptp.int Bool)) (X tptp.int) (Xs tptp.list_int)) (let ((_let_1 (@ tptp.list_ex_int P))) (= (@ _let_1 (@ (@ tptp.cons_int X) Xs)) (or (@ P X) (@ _let_1 Xs))))))
% 3.70/4.04 (assert (forall ((P (-> tptp.nat Bool)) (X tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ tptp.list_ex_nat P))) (= (@ _let_1 (@ (@ tptp.cons_nat X) Xs)) (or (@ P X) (@ _let_1 Xs))))))
% 3.70/4.04 (assert (forall ((P (-> tptp.produc6575502325842934193n_assn Bool)) (X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ tptp.list_e1087220904399170805n_assn P))) (= (@ _let_1 (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) (or (@ P X) (@ _let_1 Xs))))))
% 3.70/4.04 (assert (forall ((N tptp.nat) (Xs tptp.list_c)) (= (@ tptp.size_s385972143775086793_nat_c (@ (@ tptp.enumerate_c N) Xs)) (@ tptp.size_size_list_c Xs))))
% 3.70/4.04 (assert (forall ((N tptp.nat) (Xs tptp.list_d)) (= (@ tptp.size_s457006183821432778_nat_d (@ (@ tptp.enumerate_d N) Xs)) (@ tptp.size_size_list_d Xs))))
% 3.70/4.04 (assert (forall ((N tptp.nat) (Xs tptp.list_nat)) (= (@ tptp.size_s5460976970255530739at_nat (@ (@ tptp.enumerate_nat N) Xs)) (@ tptp.size_size_list_nat Xs))))
% 3.70/4.04 (assert (forall ((N tptp.nat) (Xs tptp.list_int)) (= (@ tptp.size_s2970893825323803983at_int (@ (@ tptp.enumerate_int N) Xs)) (@ tptp.size_size_list_int Xs))))
% 3.70/4.04 (assert (forall ((X21 tptp.product_prod_nat_nat) (X222 tptp.list_P6011104703257516679at_nat)) (= (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.cons_P6512896166579812791at_nat X21) X222)) (@ (@ tptp.insert8211810215607154385at_nat X21) (@ tptp.set_Pr5648618587558075414at_nat X222)))))
% 3.70/4.04 (assert (forall ((X21 tptp.produc3843707927480180839at_nat) (X222 tptp.list_P5464809261938338413at_nat)) (= (@ tptp.set_Pr3765526544606949372at_nat (@ (@ tptp.cons_P3940603068885512221at_nat X21) X222)) (@ (@ tptp.insert9069300056098147895at_nat X21) (@ tptp.set_Pr3765526544606949372at_nat X222)))))
% 3.70/4.04 (assert (forall ((X21 Bool) (X222 tptp.list_o)) (= (@ tptp.set_o2 (@ (@ tptp.cons_o X21) X222)) (@ (@ tptp.insert_o2 X21) (@ tptp.set_o2 X222)))))
% 3.70/4.04 (assert (forall ((X21 tptp.int) (X222 tptp.list_int)) (= (@ tptp.set_int2 (@ (@ tptp.cons_int X21) X222)) (@ (@ tptp.insert_int2 X21) (@ tptp.set_int2 X222)))))
% 3.70/4.04 (assert (forall ((X21 tptp.nat) (X222 tptp.list_nat)) (= (@ tptp.set_nat2 (@ (@ tptp.cons_nat X21) X222)) (@ (@ tptp.insert_nat2 X21) (@ tptp.set_nat2 X222)))))
% 3.70/4.04 (assert (forall ((X21 tptp.produc6575502325842934193n_assn) (X222 tptp.list_P8527749157015355191n_assn)) (= (@ tptp.set_Pr1139785259514867910n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X21) X222)) (@ (@ tptp.insert5290817439147925377n_assn X21) (@ tptp.set_Pr1139785259514867910n_assn X222)))))
% 3.70/4.04 (assert (forall ((X tptp.int) (Xs tptp.list_int)) (= (@ (@ tptp.nth_int (@ (@ tptp.cons_int X) Xs)) tptp.zero_zero_nat) X)))
% 3.70/4.04 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X) Xs)) tptp.zero_zero_nat) X)))
% 3.70/4.04 (assert (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (= (@ (@ tptp.nth_Pr1769885009046257848n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) tptp.zero_zero_nat) X)))
% 3.70/4.04 (assert (forall ((X tptp.int) (Xs tptp.list_int) (N tptp.nat)) (= (@ (@ tptp.nth_int (@ (@ tptp.cons_int X) Xs)) (@ tptp.suc N)) (@ (@ tptp.nth_int Xs) N))))
% 3.70/4.04 (assert (forall ((X tptp.nat) (Xs tptp.list_nat) (N tptp.nat)) (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X) Xs)) (@ tptp.suc N)) (@ (@ tptp.nth_nat Xs) N))))
% 3.70/4.05 (assert (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn) (N tptp.nat)) (= (@ (@ tptp.nth_Pr1769885009046257848n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) (@ tptp.suc N)) (@ (@ tptp.nth_Pr1769885009046257848n_assn Xs) N))))
% 3.70/4.05 (assert (forall ((X tptp.assn) (Xs tptp.list_assn) (Y tptp.assn) (Ys tptp.list_assn)) (= (@ (@ tptp.zip_assn_assn (@ (@ tptp.cons_assn X) Xs)) (@ (@ tptp.cons_assn Y) Ys)) (@ (@ tptp.cons_P2971678138204555879n_assn (@ (@ tptp.produc118845697133431529n_assn X) Y)) (@ (@ tptp.zip_assn_assn Xs) Ys)))))
% 3.70/4.05 (assert (forall ((X tptp.int) (Xs tptp.list_int) (Y tptp.int) (Ys tptp.list_int)) (= (@ (@ tptp.zip_int_int (@ (@ tptp.cons_int X) Xs)) (@ (@ tptp.cons_int Y) Ys)) (@ (@ tptp.cons_P3334398858971670639nt_int (@ (@ tptp.product_Pair_int_int X) Y)) (@ (@ tptp.zip_int_int Xs) Ys)))))
% 3.70/4.05 (assert (forall ((X tptp.int) (Xs tptp.list_int) (Y tptp.nat) (Ys tptp.list_nat)) (= (@ (@ tptp.zip_int_nat (@ (@ tptp.cons_int X) Xs)) (@ (@ tptp.cons_nat Y) Ys)) (@ (@ tptp.cons_P7512249878480867347nt_nat (@ (@ tptp.product_Pair_int_nat X) Y)) (@ (@ tptp.zip_int_nat Xs) Ys)))))
% 3.70/4.05 (assert (forall ((X tptp.nat) (Xs tptp.list_nat) (Y tptp.int) (Ys tptp.list_int)) (= (@ (@ tptp.zip_nat_int (@ (@ tptp.cons_nat X) Xs)) (@ (@ tptp.cons_int Y) Ys)) (@ (@ tptp.cons_P2335045147070616083at_int (@ (@ tptp.product_Pair_nat_int X) Y)) (@ (@ tptp.zip_nat_int Xs) Ys)))))
% 3.70/4.05 (assert (forall ((X tptp.nat) (Xs tptp.list_nat) (Y tptp.nat) (Ys tptp.list_nat)) (= (@ (@ tptp.zip_nat_nat (@ (@ tptp.cons_nat X) Xs)) (@ (@ tptp.cons_nat Y) Ys)) (@ (@ tptp.cons_P6512896166579812791at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ (@ tptp.zip_nat_nat Xs) Ys)))))
% 3.70/4.05 (assert (forall ((X tptp.int) (Xs tptp.list_int) (Y tptp.produc6575502325842934193n_assn) (Ys tptp.list_P8527749157015355191n_assn)) (= (@ (@ tptp.zip_in7098856637274830732n_assn (@ (@ tptp.cons_int X) Xs)) (@ (@ tptp.cons_P2971678138204555879n_assn Y) Ys)) (@ (@ tptp.cons_P8828502514829229636n_assn (@ (@ tptp.produc3313821056773121708n_assn X) Y)) (@ (@ tptp.zip_in7098856637274830732n_assn Xs) Ys)))))
% 3.70/4.05 (assert (forall ((X tptp.nat) (Xs tptp.list_nat) (Y tptp.produc6575502325842934193n_assn) (Ys tptp.list_P8527749157015355191n_assn)) (= (@ (@ tptp.zip_na5338819973521719528n_assn (@ (@ tptp.cons_nat X) Xs)) (@ (@ tptp.cons_P2971678138204555879n_assn Y) Ys)) (@ (@ tptp.cons_P7068465851076118432n_assn (@ (@ tptp.produc1553784393020010504n_assn X) Y)) (@ (@ tptp.zip_na5338819973521719528n_assn Xs) Ys)))))
% 3.70/4.05 (assert (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn) (Y tptp.int) (Ys tptp.list_int)) (= (@ (@ tptp.zip_Pr1015554993053626726sn_int (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) (@ (@ tptp.cons_int Y) Ys)) (@ (@ tptp.cons_P5155970366129889750sn_int (@ (@ tptp.produc6453891449406693510sn_int X) Y)) (@ (@ tptp.zip_Pr1015554993053626726sn_int Xs) Ys)))))
% 3.70/4.05 (assert (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn) (Y tptp.nat) (Ys tptp.list_nat)) (= (@ (@ tptp.zip_Pr1018045463562677002sn_nat (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) (@ (@ tptp.cons_nat Y) Ys)) (@ (@ tptp.cons_P110449348784310650sn_nat (@ (@ tptp.produc6456381919915743786sn_nat X) Y)) (@ (@ tptp.zip_Pr1018045463562677002sn_nat Xs) Ys)))))
% 3.70/4.05 (assert (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn) (Y tptp.produc6575502325842934193n_assn) (Ys tptp.list_P8527749157015355191n_assn)) (= (@ (@ tptp.zip_Pr8806919808394484215n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) (@ (@ tptp.cons_P2971678138204555879n_assn Y) Ys)) (@ (@ tptp.cons_P9150528168557782045n_assn (@ (@ tptp.produc6128706242671166167n_assn X) Y)) (@ (@ tptp.zip_Pr8806919808394484215n_assn Xs) Ys)))))
% 3.70/4.05 (assert (= (@ tptp.field_2862844103579723188at_nat tptp.bot_bo7193250159860175667at_nat) tptp.bot_bo228742789529271731at_nat))
% 3.70/4.05 (assert (= (@ tptp.field_4706345496283612622at_nat tptp.bot_bo5327735625951526323at_nat) tptp.bot_bo2099793752762293965at_nat))
% 3.70/4.05 (assert (= (@ tptp.field_o tptp.bot_bo7073875226086086771od_o_o) tptp.bot_bot_set_o))
% 3.70/4.05 (assert (= (@ tptp.field_int tptp.bot_bo1796632182523588997nt_int) tptp.bot_bot_set_int))
% 3.70/4.05 (assert (= (@ tptp.field_3145993188331922222at_nat tptp.bot_bo228742789529271731at_nat) tptp.bot_bo3083307316010499117at_nat))
% 3.70/4.05 (assert (= (@ tptp.field_nat tptp.bot_bo2099793752762293965at_nat) tptp.bot_bot_set_nat))
% 3.70/4.05 (assert (forall ((X tptp.produc3843707927480180839at_nat) (Xs tptp.list_P5464809261938338413at_nat)) (=> (not (@ (@ tptp.member8757157785044589968at_nat X) (@ tptp.set_Pr3765526544606949372at_nat Xs))) (= (@ (@ tptp.insert4149901806602606979at_nat X) Xs) (@ (@ tptp.cons_P3940603068885512221at_nat X) Xs)))))
% 3.70/4.05 (assert (forall ((X tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (=> (not (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs))) (= (@ (@ tptp.insert8944034826898310173at_nat X) Xs) (@ (@ tptp.cons_P6512896166579812791at_nat X) Xs)))))
% 3.70/4.05 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xs tptp.list_P7985473006766602707_nat_o)) (=> (not (@ (@ tptp.member6576561426505652726_nat_o X) (@ tptp.set_Pr400311997697478754_nat_o Xs))) (= (@ (@ tptp.insert8021100735160035049_nat_o X) Xs) (@ (@ tptp.cons_P6219271836124797827_nat_o X) Xs)))))
% 3.70/4.05 (assert (forall ((X tptp.int) (Xs tptp.list_int)) (=> (not (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs))) (= (@ (@ tptp.insert_int X) Xs) (@ (@ tptp.cons_int X) Xs)))))
% 3.70/4.05 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (=> (not (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs))) (= (@ (@ tptp.insert_nat X) Xs) (@ (@ tptp.cons_nat X) Xs)))))
% 3.70/4.05 (assert (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (=> (not (@ (@ tptp.member7957490590177025114n_assn X) (@ tptp.set_Pr1139785259514867910n_assn Xs))) (= (@ (@ tptp.insert3246601298802261197n_assn X) Xs) (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)))))
% 3.70/4.05 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Xs tptp.list_s1210847774152347623at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Ys tptp.list_s1210847774152347623at_nat) (R2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.listre8180072825634266816at_nat R2))) (= (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat (@ (@ tptp.cons_s6881495754146722583at_nat X) Xs)) (@ (@ tptp.cons_s6881495754146722583at_nat Y) Ys))) _let_1) (or (and (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Y)) R2) (= Xs Ys)) (and (= X Y) (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat Xs) Ys)) _let_1)))))))
% 3.70/4.05 (assert (forall ((X tptp.int) (Xs tptp.list_int) (Y tptp.int) (Ys tptp.list_int) (R2 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.listrel1_int R2))) (= (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int (@ (@ tptp.cons_int X) Xs)) (@ (@ tptp.cons_int Y) Ys))) _let_1) (or (and (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) R2) (= Xs Ys)) (and (= X Y) (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Xs) Ys)) _let_1)))))))
% 3.70/4.05 (assert (forall ((X tptp.nat) (Xs tptp.list_nat) (Y tptp.nat) (Ys tptp.list_nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.listrel1_nat R2))) (= (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat (@ (@ tptp.cons_nat X) Xs)) (@ (@ tptp.cons_nat Y) Ys))) _let_1) (or (and (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) R2) (= Xs Ys)) (and (= X Y) (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Xs) Ys)) _let_1)))))))
% 3.70/4.05 (assert (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn) (Y tptp.produc6575502325842934193n_assn) (Ys tptp.list_P8527749157015355191n_assn) (R2 tptp.set_Pr8116311503512020807n_assn)) (let ((_let_1 (@ tptp.listre4270255209692100112n_assn R2))) (= (@ (@ tptp.member3994142547374651152n_assn (@ (@ tptp.produc3014731801419794263n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) (@ (@ tptp.cons_P2971678138204555879n_assn Y) Ys))) _let_1) (or (and (@ (@ tptp.member4743710847862083984n_assn (@ (@ tptp.produc6128706242671166167n_assn X) Y)) R2) (= Xs Ys)) (and (= X Y) (@ (@ tptp.member3994142547374651152n_assn (@ (@ tptp.produc3014731801419794263n_assn Xs) Ys)) _let_1)))))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (X tptp.int) (Xs tptp.list_int)) (= (@ (@ tptp.enumerate_int N) (@ (@ tptp.cons_int X) Xs)) (@ (@ tptp.cons_P2335045147070616083at_int (@ (@ tptp.product_Pair_nat_int N) X)) (@ (@ tptp.enumerate_int (@ tptp.suc N)) Xs)))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (X tptp.nat) (Xs tptp.list_nat)) (= (@ (@ tptp.enumerate_nat N) (@ (@ tptp.cons_nat X) Xs)) (@ (@ tptp.cons_P6512896166579812791at_nat (@ (@ tptp.product_Pair_nat_nat N) X)) (@ (@ tptp.enumerate_nat (@ tptp.suc N)) Xs)))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (= (@ (@ tptp.enumer9200277086812776726n_assn N) (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) (@ (@ tptp.cons_P7068465851076118432n_assn (@ (@ tptp.produc1553784393020010504n_assn N) X)) (@ (@ tptp.enumer9200277086812776726n_assn (@ tptp.suc N)) Xs)))))
% 3.70/4.05 (assert (forall ((X tptp.int) (Xs tptp.list_int)) (not (= (@ (@ tptp.cons_int X) Xs) Xs))))
% 3.70/4.05 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (not (= (@ (@ tptp.cons_nat X) Xs) Xs))))
% 3.70/4.05 (assert (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (not (= (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs) Xs))))
% 3.70/4.05 (assert (forall ((N1 tptp.int) (R1 tptp.list_int) (N22 tptp.int) (R22 tptp.list_int)) (=> (= (@ (@ tptp.cons_int N1) R1) (@ (@ tptp.cons_int N22) R22)) (and (= N1 N22) (= R1 R22)))))
% 3.70/4.05 (assert (forall ((N1 tptp.nat) (R1 tptp.list_nat) (N22 tptp.nat) (R22 tptp.list_nat)) (=> (= (@ (@ tptp.cons_nat N1) R1) (@ (@ tptp.cons_nat N22) R22)) (and (= N1 N22) (= R1 R22)))))
% 3.70/4.05 (assert (forall ((N1 tptp.produc6575502325842934193n_assn) (R1 tptp.list_P8527749157015355191n_assn) (N22 tptp.produc6575502325842934193n_assn) (R22 tptp.list_P8527749157015355191n_assn)) (=> (= (@ (@ tptp.cons_P2971678138204555879n_assn N1) R1) (@ (@ tptp.cons_P2971678138204555879n_assn N22) R22)) (and (= N1 N22) (= R1 R22)))))
% 3.70/4.05 (assert (forall ((C2 tptp.multis2468970476368604999at_nat) (B tptp.multis2468970476368604999at_nat) (A tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.plus_p7104986032573967614at_nat A))) (=> (= (@ (@ tptp.minus_4286766774447292334at_nat C2) B) tptp.zero_z1048942125864253310at_nat) (= (@ (@ tptp.minus_4286766774447292334at_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.minus_4286766774447292334at_nat B) C2)))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int) (Xy tptp.product_prod_int_int) (Xys tptp.list_P5707943133018811711nt_int)) (=> (= (@ (@ tptp.zip_int_int Xs) Ys) (@ (@ tptp.cons_P3334398858971670639nt_int Xy) Xys)) (not (forall ((X3 tptp.int) (Xs5 tptp.list_int)) (=> (= Xs (@ (@ tptp.cons_int X3) Xs5)) (forall ((Y2 tptp.int) (Ys4 tptp.list_int)) (=> (= Ys (@ (@ tptp.cons_int Y2) Ys4)) (=> (= Xy (@ (@ tptp.product_Pair_int_int X3) Y2)) (not (= Xys (@ (@ tptp.zip_int_int Xs5) Ys4))))))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_nat) (Xy tptp.product_prod_int_nat) (Xys tptp.list_P8198026277950538467nt_nat)) (=> (= (@ (@ tptp.zip_int_nat Xs) Ys) (@ (@ tptp.cons_P7512249878480867347nt_nat Xy) Xys)) (not (forall ((X3 tptp.int) (Xs5 tptp.list_int)) (=> (= Xs (@ (@ tptp.cons_int X3) Xs5)) (forall ((Y2 tptp.nat) (Ys4 tptp.list_nat)) (=> (= Ys (@ (@ tptp.cons_nat Y2) Ys4)) (=> (= Xy (@ (@ tptp.product_Pair_int_nat X3) Y2)) (not (= Xys (@ (@ tptp.zip_int_nat Xs5) Ys4))))))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_int) (Xy tptp.product_prod_nat_int) (Xys tptp.list_P3521021558325789923at_int)) (=> (= (@ (@ tptp.zip_nat_int Xs) Ys) (@ (@ tptp.cons_P2335045147070616083at_int Xy) Xys)) (not (forall ((X3 tptp.nat) (Xs5 tptp.list_nat)) (=> (= Xs (@ (@ tptp.cons_nat X3) Xs5)) (forall ((Y2 tptp.int) (Ys4 tptp.list_int)) (=> (= Ys (@ (@ tptp.cons_int Y2) Ys4)) (=> (= Xy (@ (@ tptp.product_Pair_nat_int X3) Y2)) (not (= Xys (@ (@ tptp.zip_nat_int Xs5) Ys4))))))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (Xy tptp.product_prod_nat_nat) (Xys tptp.list_P6011104703257516679at_nat)) (=> (= (@ (@ tptp.zip_nat_nat Xs) Ys) (@ (@ tptp.cons_P6512896166579812791at_nat Xy) Xys)) (not (forall ((X3 tptp.nat) (Xs5 tptp.list_nat)) (=> (= Xs (@ (@ tptp.cons_nat X3) Xs5)) (forall ((Y2 tptp.nat) (Ys4 tptp.list_nat)) (=> (= Ys (@ (@ tptp.cons_nat Y2) Ys4)) (=> (= Xy (@ (@ tptp.product_Pair_nat_nat X3) Y2)) (not (= Xys (@ (@ tptp.zip_nat_nat Xs5) Ys4))))))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_assn) (Ys tptp.list_assn) (Xy tptp.produc6575502325842934193n_assn) (Xys tptp.list_P8527749157015355191n_assn)) (=> (= (@ (@ tptp.zip_assn_assn Xs) Ys) (@ (@ tptp.cons_P2971678138204555879n_assn Xy) Xys)) (not (forall ((X3 tptp.assn) (Xs5 tptp.list_assn)) (=> (= Xs (@ (@ tptp.cons_assn X3) Xs5)) (forall ((Y2 tptp.assn) (Ys4 tptp.list_assn)) (=> (= Ys (@ (@ tptp.cons_assn Y2) Ys4)) (=> (= Xy (@ (@ tptp.produc118845697133431529n_assn X3) Y2)) (not (= Xys (@ (@ tptp.zip_assn_assn Xs5) Ys4))))))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_P8527749157015355191n_assn) (Xy tptp.produc3167338625816234618n_assn) (Xys tptp.list_P1495281457390866698n_assn)) (=> (= (@ (@ tptp.zip_in7098856637274830732n_assn Xs) Ys) (@ (@ tptp.cons_P8828502514829229636n_assn Xy) Xys)) (not (forall ((X3 tptp.int) (Xs5 tptp.list_int)) (=> (= Xs (@ (@ tptp.cons_int X3) Xs5)) (forall ((Y2 tptp.produc6575502325842934193n_assn) (Ys4 tptp.list_P8527749157015355191n_assn)) (=> (= Ys (@ (@ tptp.cons_P2971678138204555879n_assn Y2) Ys4)) (=> (= Xy (@ (@ tptp.produc3313821056773121708n_assn X3) Y2)) (not (= Xys (@ (@ tptp.zip_in7098856637274830732n_assn Xs5) Ys4))))))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_P8527749157015355191n_assn) (Xy tptp.produc1407301962063123414n_assn) (Xys tptp.list_P7711101519850957926n_assn)) (=> (= (@ (@ tptp.zip_na5338819973521719528n_assn Xs) Ys) (@ (@ tptp.cons_P7068465851076118432n_assn Xy) Xys)) (not (forall ((X3 tptp.nat) (Xs5 tptp.list_nat)) (=> (= Xs (@ (@ tptp.cons_nat X3) Xs5)) (forall ((Y2 tptp.produc6575502325842934193n_assn) (Ys4 tptp.list_P8527749157015355191n_assn)) (=> (= Ys (@ (@ tptp.cons_P2971678138204555879n_assn Y2) Ys4)) (=> (= Xy (@ (@ tptp.produc1553784393020010504n_assn X3) Y2)) (not (= Xys (@ (@ tptp.zip_na5338819973521719528n_assn Xs5) Ys4))))))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_int) (Xy tptp.produc8718178513971670540sn_int) (Xys tptp.list_P421884338359569308sn_int)) (=> (= (@ (@ tptp.zip_Pr1015554993053626726sn_int Xs) Ys) (@ (@ tptp.cons_P5155970366129889750sn_int Xy) Xys)) (not (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs5 tptp.list_P8527749157015355191n_assn)) (=> (= Xs (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs5)) (forall ((Y2 tptp.int) (Ys4 tptp.list_int)) (=> (= Ys (@ (@ tptp.cons_int Y2) Ys4)) (=> (= Xy (@ (@ tptp.produc6453891449406693510sn_int X3) Y2)) (not (= Xys (@ (@ tptp.zip_Pr1015554993053626726sn_int Xs5) Ys4))))))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_nat) (Xy tptp.produc3672657496626091440sn_nat) (Xys tptp.list_P2911967483291296064sn_nat)) (=> (= (@ (@ tptp.zip_Pr1018045463562677002sn_nat Xs) Ys) (@ (@ tptp.cons_P110449348784310650sn_nat Xy) Xys)) (not (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs5 tptp.list_P8527749157015355191n_assn)) (=> (= Xs (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs5)) (forall ((Y2 tptp.nat) (Ys4 tptp.list_nat)) (=> (= Ys (@ (@ tptp.cons_nat Y2) Ys4)) (=> (= Xy (@ (@ tptp.produc6456381919915743786sn_nat X3) Y2)) (not (= Xys (@ (@ tptp.zip_Pr1018045463562677002sn_nat Xs5) Ys4))))))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_P8527749157015355191n_assn) (Xy tptp.produc9053633027152450663n_assn) (Xys tptp.list_P28140577958321773n_assn)) (=> (= (@ (@ tptp.zip_Pr8806919808394484215n_assn Xs) Ys) (@ (@ tptp.cons_P9150528168557782045n_assn Xy) Xys)) (not (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs5 tptp.list_P8527749157015355191n_assn)) (=> (= Xs (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs5)) (forall ((Y2 tptp.produc6575502325842934193n_assn) (Ys4 tptp.list_P8527749157015355191n_assn)) (=> (= Ys (@ (@ tptp.cons_P2971678138204555879n_assn Y2) Ys4)) (=> (= Xy (@ (@ tptp.produc6128706242671166167n_assn X3) Y2)) (not (= Xys (@ (@ tptp.zip_Pr8806919808394484215n_assn Xs5) Ys4))))))))))))
% 3.70/4.05 (assert (forall ((I tptp.produc3843707927480180839at_nat) (J tptp.produc3843707927480180839at_nat) (R tptp.set_Pr5564308138774400199at_nat)) (=> (@ (@ tptp.member6009668390874684176at_nat (@ (@ tptp.produc2335810615602371415at_nat I) J)) R) (@ (@ tptp.member8757157785044589968at_nat I) (@ tptp.field_2862844103579723188at_nat R)))))
% 3.70/4.05 (assert (forall ((I tptp.product_prod_nat_nat) (J tptp.product_prod_nat_nat) (R tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat I) J)) R) (@ (@ tptp.member8440522571783428010at_nat I) (@ tptp.field_4706345496283612622at_nat R)))))
% 3.70/4.05 (assert (forall ((I tptp.int) (J tptp.int) (R tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int I) J)) R) (@ (@ tptp.member_int I) (@ tptp.field_int R)))))
% 3.70/4.05 (assert (forall ((I (-> tptp.produc3658429121746597890et_nat Bool)) (J (-> tptp.produc3658429121746597890et_nat Bool)) (R tptp.set_Pr2161125870931222855_nat_o)) (=> (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o I) J)) R) (@ (@ tptp.member6576561426505652726_nat_o I) (@ tptp.field_81821745747897882_nat_o R)))))
% 3.70/4.05 (assert (forall ((I tptp.set_Pr1261947904930325089at_nat) (J tptp.set_Pr1261947904930325089at_nat) (R tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat I) J)) R) (@ (@ tptp.member2643936169264416010at_nat I) (@ tptp.field_3145993188331922222at_nat R)))))
% 3.70/4.05 (assert (forall ((I tptp.nat) (J tptp.nat) (R tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat I) J)) R) (@ (@ tptp.member_nat I) (@ tptp.field_nat R)))))
% 3.70/4.05 (assert (forall ((I Bool) (J Bool) (R tptp.set_Product_prod_o_o)) (=> (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o I) J)) R) (@ (@ tptp.member_o I) (@ tptp.field_o R)))))
% 3.70/4.05 (assert (forall ((I tptp.produc3843707927480180839at_nat) (J tptp.produc3843707927480180839at_nat) (R tptp.set_Pr5564308138774400199at_nat)) (=> (@ (@ tptp.member6009668390874684176at_nat (@ (@ tptp.produc2335810615602371415at_nat I) J)) R) (@ (@ tptp.member8757157785044589968at_nat J) (@ tptp.field_2862844103579723188at_nat R)))))
% 3.70/4.05 (assert (forall ((I tptp.product_prod_nat_nat) (J tptp.product_prod_nat_nat) (R tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat I) J)) R) (@ (@ tptp.member8440522571783428010at_nat J) (@ tptp.field_4706345496283612622at_nat R)))))
% 3.70/4.05 (assert (forall ((I tptp.int) (J tptp.int) (R tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int I) J)) R) (@ (@ tptp.member_int J) (@ tptp.field_int R)))))
% 3.70/4.05 (assert (forall ((I (-> tptp.produc3658429121746597890et_nat Bool)) (J (-> tptp.produc3658429121746597890et_nat Bool)) (R tptp.set_Pr2161125870931222855_nat_o)) (=> (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o I) J)) R) (@ (@ tptp.member6576561426505652726_nat_o J) (@ tptp.field_81821745747897882_nat_o R)))))
% 3.70/4.05 (assert (forall ((I tptp.set_Pr1261947904930325089at_nat) (J tptp.set_Pr1261947904930325089at_nat) (R tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat I) J)) R) (@ (@ tptp.member2643936169264416010at_nat J) (@ tptp.field_3145993188331922222at_nat R)))))
% 3.70/4.05 (assert (forall ((I tptp.nat) (J tptp.nat) (R tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat I) J)) R) (@ (@ tptp.member_nat J) (@ tptp.field_nat R)))))
% 3.70/4.05 (assert (forall ((I Bool) (J Bool) (R tptp.set_Product_prod_o_o)) (=> (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o I) J)) R) (@ (@ tptp.member_o J) (@ tptp.field_o R)))))
% 3.70/4.05 (assert (forall ((Y tptp.produc3843707927480180839at_nat) (X tptp.produc3843707927480180839at_nat) (Xs tptp.list_P5464809261938338413at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat Y))) (=> (@ _let_1 (@ tptp.set_Pr3765526544606949372at_nat (@ (@ tptp.cons_P3940603068885512221at_nat X) Xs))) (or (= Y X) (@ _let_1 (@ tptp.set_Pr3765526544606949372at_nat Xs)))))))
% 3.70/4.05 (assert (forall ((Y tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat Y))) (=> (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.cons_P6512896166579812791at_nat X) Xs))) (or (= Y X) (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat Xs)))))))
% 3.70/4.05 (assert (forall ((Y (-> tptp.produc3658429121746597890et_nat Bool)) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Xs tptp.list_P7985473006766602707_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o Y))) (=> (@ _let_1 (@ tptp.set_Pr400311997697478754_nat_o (@ (@ tptp.cons_P6219271836124797827_nat_o X) Xs))) (or (= Y X) (@ _let_1 (@ tptp.set_Pr400311997697478754_nat_o Xs)))))))
% 3.70/4.05 (assert (forall ((Y tptp.int) (X tptp.int) (Xs tptp.list_int)) (let ((_let_1 (@ tptp.member_int Y))) (=> (@ _let_1 (@ tptp.set_int2 (@ (@ tptp.cons_int X) Xs))) (or (= Y X) (@ _let_1 (@ tptp.set_int2 Xs)))))))
% 3.70/4.05 (assert (forall ((Y tptp.nat) (X tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ tptp.member_nat Y))) (=> (@ _let_1 (@ tptp.set_nat2 (@ (@ tptp.cons_nat X) Xs))) (or (= Y X) (@ _let_1 (@ tptp.set_nat2 Xs)))))))
% 3.70/4.05 (assert (forall ((Y tptp.produc6575502325842934193n_assn) (X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ tptp.member7957490590177025114n_assn Y))) (=> (@ _let_1 (@ tptp.set_Pr1139785259514867910n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs))) (or (= Y X) (@ _let_1 (@ tptp.set_Pr1139785259514867910n_assn Xs)))))))
% 3.70/4.05 (assert (forall ((E tptp.produc3843707927480180839at_nat) (A2 tptp.list_P5464809261938338413at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat E) (@ tptp.set_Pr3765526544606949372at_nat A2)) (=> (forall ((Z22 tptp.list_P5464809261938338413at_nat)) (not (= A2 (@ (@ tptp.cons_P3940603068885512221at_nat E) Z22)))) (not (forall ((Z1 tptp.produc3843707927480180839at_nat) (Z22 tptp.list_P5464809261938338413at_nat)) (=> (= A2 (@ (@ tptp.cons_P3940603068885512221at_nat Z1) Z22)) (not (@ (@ tptp.member8757157785044589968at_nat E) (@ tptp.set_Pr3765526544606949372at_nat Z22))))))))))
% 3.70/4.05 (assert (forall ((E tptp.product_prod_nat_nat) (A2 tptp.list_P6011104703257516679at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat E) (@ tptp.set_Pr5648618587558075414at_nat A2)) (=> (forall ((Z22 tptp.list_P6011104703257516679at_nat)) (not (= A2 (@ (@ tptp.cons_P6512896166579812791at_nat E) Z22)))) (not (forall ((Z1 tptp.product_prod_nat_nat) (Z22 tptp.list_P6011104703257516679at_nat)) (=> (= A2 (@ (@ tptp.cons_P6512896166579812791at_nat Z1) Z22)) (not (@ (@ tptp.member8440522571783428010at_nat E) (@ tptp.set_Pr5648618587558075414at_nat Z22))))))))))
% 3.70/4.05 (assert (forall ((E (-> tptp.produc3658429121746597890et_nat Bool)) (A2 tptp.list_P7985473006766602707_nat_o)) (=> (@ (@ tptp.member6576561426505652726_nat_o E) (@ tptp.set_Pr400311997697478754_nat_o A2)) (=> (forall ((Z22 tptp.list_P7985473006766602707_nat_o)) (not (= A2 (@ (@ tptp.cons_P6219271836124797827_nat_o E) Z22)))) (not (forall ((Z1 (-> tptp.produc3658429121746597890et_nat Bool)) (Z22 tptp.list_P7985473006766602707_nat_o)) (=> (= A2 (@ (@ tptp.cons_P6219271836124797827_nat_o Z1) Z22)) (not (@ (@ tptp.member6576561426505652726_nat_o E) (@ tptp.set_Pr400311997697478754_nat_o Z22))))))))))
% 3.70/4.05 (assert (forall ((E tptp.int) (A2 tptp.list_int)) (=> (@ (@ tptp.member_int E) (@ tptp.set_int2 A2)) (=> (forall ((Z22 tptp.list_int)) (not (= A2 (@ (@ tptp.cons_int E) Z22)))) (not (forall ((Z1 tptp.int) (Z22 tptp.list_int)) (=> (= A2 (@ (@ tptp.cons_int Z1) Z22)) (not (@ (@ tptp.member_int E) (@ tptp.set_int2 Z22))))))))))
% 3.70/4.05 (assert (forall ((E tptp.nat) (A2 tptp.list_nat)) (=> (@ (@ tptp.member_nat E) (@ tptp.set_nat2 A2)) (=> (forall ((Z22 tptp.list_nat)) (not (= A2 (@ (@ tptp.cons_nat E) Z22)))) (not (forall ((Z1 tptp.nat) (Z22 tptp.list_nat)) (=> (= A2 (@ (@ tptp.cons_nat Z1) Z22)) (not (@ (@ tptp.member_nat E) (@ tptp.set_nat2 Z22))))))))))
% 3.70/4.05 (assert (forall ((E tptp.produc6575502325842934193n_assn) (A2 tptp.list_P8527749157015355191n_assn)) (=> (@ (@ tptp.member7957490590177025114n_assn E) (@ tptp.set_Pr1139785259514867910n_assn A2)) (=> (forall ((Z22 tptp.list_P8527749157015355191n_assn)) (not (= A2 (@ (@ tptp.cons_P2971678138204555879n_assn E) Z22)))) (not (forall ((Z1 tptp.produc6575502325842934193n_assn) (Z22 tptp.list_P8527749157015355191n_assn)) (=> (= A2 (@ (@ tptp.cons_P2971678138204555879n_assn Z1) Z22)) (not (@ (@ tptp.member7957490590177025114n_assn E) (@ tptp.set_Pr1139785259514867910n_assn Z22))))))))))
% 3.70/4.05 (assert (forall ((X21 tptp.produc3843707927480180839at_nat) (X222 tptp.list_P5464809261938338413at_nat)) (@ (@ tptp.member8757157785044589968at_nat X21) (@ tptp.set_Pr3765526544606949372at_nat (@ (@ tptp.cons_P3940603068885512221at_nat X21) X222)))))
% 3.70/4.05 (assert (forall ((X21 tptp.product_prod_nat_nat) (X222 tptp.list_P6011104703257516679at_nat)) (@ (@ tptp.member8440522571783428010at_nat X21) (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.cons_P6512896166579812791at_nat X21) X222)))))
% 3.70/4.05 (assert (forall ((X21 (-> tptp.produc3658429121746597890et_nat Bool)) (X222 tptp.list_P7985473006766602707_nat_o)) (@ (@ tptp.member6576561426505652726_nat_o X21) (@ tptp.set_Pr400311997697478754_nat_o (@ (@ tptp.cons_P6219271836124797827_nat_o X21) X222)))))
% 3.70/4.05 (assert (forall ((X21 tptp.int) (X222 tptp.list_int)) (@ (@ tptp.member_int X21) (@ tptp.set_int2 (@ (@ tptp.cons_int X21) X222)))))
% 3.70/4.05 (assert (forall ((X21 tptp.nat) (X222 tptp.list_nat)) (@ (@ tptp.member_nat X21) (@ tptp.set_nat2 (@ (@ tptp.cons_nat X21) X222)))))
% 3.70/4.05 (assert (forall ((X21 tptp.produc6575502325842934193n_assn) (X222 tptp.list_P8527749157015355191n_assn)) (@ (@ tptp.member7957490590177025114n_assn X21) (@ tptp.set_Pr1139785259514867910n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X21) X222)))))
% 3.70/4.05 (assert (forall ((Y tptp.produc3843707927480180839at_nat) (X222 tptp.list_P5464809261938338413at_nat) (X21 tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat Y))) (=> (@ _let_1 (@ tptp.set_Pr3765526544606949372at_nat X222)) (@ _let_1 (@ tptp.set_Pr3765526544606949372at_nat (@ (@ tptp.cons_P3940603068885512221at_nat X21) X222)))))))
% 3.70/4.05 (assert (forall ((Y tptp.product_prod_nat_nat) (X222 tptp.list_P6011104703257516679at_nat) (X21 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat Y))) (=> (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat X222)) (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.cons_P6512896166579812791at_nat X21) X222)))))))
% 3.70/4.05 (assert (forall ((Y (-> tptp.produc3658429121746597890et_nat Bool)) (X222 tptp.list_P7985473006766602707_nat_o) (X21 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o Y))) (=> (@ _let_1 (@ tptp.set_Pr400311997697478754_nat_o X222)) (@ _let_1 (@ tptp.set_Pr400311997697478754_nat_o (@ (@ tptp.cons_P6219271836124797827_nat_o X21) X222)))))))
% 3.70/4.05 (assert (forall ((Y tptp.int) (X222 tptp.list_int) (X21 tptp.int)) (let ((_let_1 (@ tptp.member_int Y))) (=> (@ _let_1 (@ tptp.set_int2 X222)) (@ _let_1 (@ tptp.set_int2 (@ (@ tptp.cons_int X21) X222)))))))
% 3.70/4.05 (assert (forall ((Y tptp.nat) (X222 tptp.list_nat) (X21 tptp.nat)) (let ((_let_1 (@ tptp.member_nat Y))) (=> (@ _let_1 (@ tptp.set_nat2 X222)) (@ _let_1 (@ tptp.set_nat2 (@ (@ tptp.cons_nat X21) X222)))))))
% 3.70/4.05 (assert (forall ((Y tptp.produc6575502325842934193n_assn) (X222 tptp.list_P8527749157015355191n_assn) (X21 tptp.produc6575502325842934193n_assn)) (let ((_let_1 (@ tptp.member7957490590177025114n_assn Y))) (=> (@ _let_1 (@ tptp.set_Pr1139785259514867910n_assn X222)) (@ _let_1 (@ tptp.set_Pr1139785259514867910n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X21) X222)))))))
% 3.70/4.05 (assert (forall ((A2 tptp.int) (B2 tptp.int) (Xs tptp.list_int)) (let ((_let_1 (@ (@ tptp.cons_int B2) Xs))) (let ((_let_2 (@ tptp.cons_int A2))) (= (@ tptp.distinct_int (@ _let_2 _let_1)) (and (not (= A2 B2)) (@ tptp.distinct_int (@ _let_2 Xs)) (@ tptp.distinct_int _let_1)))))))
% 3.70/4.05 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat B2) Xs))) (let ((_let_2 (@ tptp.cons_nat A2))) (= (@ tptp.distinct_nat (@ _let_2 _let_1)) (and (not (= A2 B2)) (@ tptp.distinct_nat (@ _let_2 Xs)) (@ tptp.distinct_nat _let_1)))))))
% 3.70/4.05 (assert (forall ((A2 tptp.produc6575502325842934193n_assn) (B2 tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ (@ tptp.cons_P2971678138204555879n_assn B2) Xs))) (let ((_let_2 (@ tptp.cons_P2971678138204555879n_assn A2))) (= (@ tptp.distin4809818325527169450n_assn (@ _let_2 _let_1)) (and (not (= A2 B2)) (@ tptp.distin4809818325527169450n_assn (@ _let_2 Xs)) (@ tptp.distin4809818325527169450n_assn _let_1)))))))
% 3.70/4.05 (assert (forall ((X tptp.int) (Y tptp.int) (Xs tptp.list_int)) (let ((_let_1 (@ tptp.remove1_int X))) (let ((_let_2 (@ tptp.cons_int Y))) (let ((_let_3 (@ _let_1 (@ _let_2 Xs)))) (let ((_let_4 (= X Y))) (and (=> _let_4 (= _let_3 Xs)) (=> (not _let_4) (= _let_3 (@ _let_2 (@ _let_1 Xs)))))))))))
% 3.70/4.05 (assert (forall ((X tptp.nat) (Y tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ tptp.remove1_nat X))) (let ((_let_2 (@ tptp.cons_nat Y))) (let ((_let_3 (@ _let_1 (@ _let_2 Xs)))) (let ((_let_4 (= X Y))) (and (=> _let_4 (= _let_3 Xs)) (=> (not _let_4) (= _let_3 (@ _let_2 (@ _let_1 Xs)))))))))))
% 3.70/4.05 (assert (forall ((X tptp.produc6575502325842934193n_assn) (Y tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ tptp.remove1670527618125605709n_assn X))) (let ((_let_2 (@ tptp.cons_P2971678138204555879n_assn Y))) (let ((_let_3 (@ _let_1 (@ _let_2 Xs)))) (let ((_let_4 (= X Y))) (and (=> _let_4 (= _let_3 Xs)) (=> (not _let_4) (= _let_3 (@ _let_2 (@ _let_1 Xs)))))))))))
% 3.70/4.05 (assert (forall ((A tptp.set_se7855581050983116737at_nat) (R2 tptp.set_Pr4329608150637261639at_nat)) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat) (Y2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member2643936169264416010at_nat X3) A) (=> (@ (@ tptp.member2643936169264416010at_nat Y2) A) (=> (not (= X3 Y2)) (or (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X3) Y2)) R2) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat Y2) X3)) R2)))))) (@ (@ tptp.total_7212417256332265445at_nat A) R2))))
% 3.70/4.05 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (R2 tptp.set_Pr5564308138774400199at_nat)) (=> (forall ((X3 tptp.produc3843707927480180839at_nat) (Y2 tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X3) A) (=> (@ (@ tptp.member8757157785044589968at_nat Y2) A) (=> (not (= X3 Y2)) (or (@ (@ tptp.member6009668390874684176at_nat (@ (@ tptp.produc2335810615602371415at_nat X3) Y2)) R2) (@ (@ tptp.member6009668390874684176at_nat (@ (@ tptp.produc2335810615602371415at_nat Y2) X3)) R2)))))) (@ (@ tptp.total_1513685709984341995at_nat A) R2))))
% 3.70/4.05 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (R2 tptp.set_Pr8693737435421807431at_nat)) (=> (forall ((X3 tptp.product_prod_nat_nat) (Y2 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) A) (=> (@ (@ tptp.member8440522571783428010at_nat Y2) A) (=> (not (= X3 Y2)) (or (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X3) Y2)) R2) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat Y2) X3)) R2)))))) (@ (@ tptp.total_3592101749530773125at_nat A) R2))))
% 3.70/4.05 (assert (forall ((A tptp.set_nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A) (=> (@ (@ tptp.member_nat Y2) A) (=> (not (= X3 Y2)) (or (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) Y2)) R2) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y2) X3)) R2)))))) (@ (@ tptp.total_on_nat A) R2))))
% 3.70/4.05 (assert (forall ((A tptp.set_int) (R2 tptp.set_Pr958786334691620121nt_int)) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.member_int X3) A) (=> (@ (@ tptp.member_int Y2) A) (=> (not (= X3 Y2)) (or (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X3) Y2)) R2) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y2) X3)) R2)))))) (@ (@ tptp.total_on_int A) R2))))
% 3.70/4.05 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (R2 tptp.set_Pr2161125870931222855_nat_o)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X3) A) (=> (@ (@ tptp.member6576561426505652726_nat_o Y2) A) (=> (not (= X3 Y2)) (or (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o X3) Y2)) R2) (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o Y2) X3)) R2)))))) (@ (@ tptp.total_7429123086324524369_nat_o A) R2))))
% 3.70/4.05 (assert (= tptp.total_7212417256332265445at_nat (lambda ((A5 tptp.set_se7855581050983116737at_nat) (R4 tptp.set_Pr4329608150637261639at_nat)) (forall ((X2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member2643936169264416010at_nat X2) A5) (forall ((Y5 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member2643936169264416010at_nat Y5) A5) (=> (not (= X2 Y5)) (or (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X2) Y5)) R4) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat Y5) X2)) R4))))))))))
% 3.70/4.05 (assert (= tptp.total_on_nat (lambda ((A5 tptp.set_nat) (R4 tptp.set_Pr1261947904930325089at_nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A5) (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.member_nat Y5) A5) (=> (not (= X2 Y5)) (or (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X2) Y5)) R4) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y5) X2)) R4))))))))))
% 3.70/4.05 (assert (forall ((R2 tptp.set_Pr5564308138774400199at_nat)) (@ (@ tptp.total_1513685709984341995at_nat tptp.bot_bo228742789529271731at_nat) R2)))
% 3.70/4.05 (assert (forall ((R2 tptp.set_Pr8693737435421807431at_nat)) (@ (@ tptp.total_3592101749530773125at_nat tptp.bot_bo2099793752762293965at_nat) R2)))
% 3.70/4.05 (assert (forall ((R2 tptp.set_Product_prod_o_o)) (@ (@ tptp.total_on_o tptp.bot_bot_set_o) R2)))
% 3.70/4.05 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.total_on_nat tptp.bot_bot_set_nat) R2)))
% 3.70/4.05 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.total_on_int tptp.bot_bot_set_int) R2)))
% 3.70/4.05 (assert (forall ((X tptp.int) (Y tptp.int) (Xs tptp.list_int)) (let ((_let_1 (@ tptp.removeAll_int X))) (let ((_let_2 (@ _let_1 Xs))) (let ((_let_3 (@ tptp.cons_int Y))) (let ((_let_4 (@ _let_1 (@ _let_3 Xs)))) (let ((_let_5 (= X Y))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 3.70/4.05 (assert (forall ((X tptp.nat) (Y tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ tptp.removeAll_nat X))) (let ((_let_2 (@ _let_1 Xs))) (let ((_let_3 (@ tptp.cons_nat Y))) (let ((_let_4 (@ _let_1 (@ _let_3 Xs)))) (let ((_let_5 (= X Y))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 3.70/4.05 (assert (forall ((X tptp.produc6575502325842934193n_assn) (Y tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ tptp.remove1763081955827946941n_assn X))) (let ((_let_2 (@ _let_1 Xs))) (let ((_let_3 (@ tptp.cons_P2971678138204555879n_assn Y))) (let ((_let_4 (@ _let_1 (@ _let_3 Xs)))) (let ((_let_5 (= X Y))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 3.70/4.05 (assert (forall ((F4 (-> tptp.int tptp.int tptp.int)) (A2 tptp.int) (As2 tptp.list_int) (B2 tptp.int) (Bs tptp.list_int)) (let ((_let_1 (@ tptp.zipf_int_int_int F4))) (= (@ (@ _let_1 (@ (@ tptp.cons_int A2) As2)) (@ (@ tptp.cons_int B2) Bs)) (@ (@ tptp.cons_int (@ (@ F4 A2) B2)) (@ (@ _let_1 As2) Bs))))))
% 3.70/4.05 (assert (forall ((F4 (-> tptp.int tptp.int tptp.nat)) (A2 tptp.int) (As2 tptp.list_int) (B2 tptp.int) (Bs tptp.list_int)) (let ((_let_1 (@ tptp.zipf_int_int_nat F4))) (= (@ (@ _let_1 (@ (@ tptp.cons_int A2) As2)) (@ (@ tptp.cons_int B2) Bs)) (@ (@ tptp.cons_nat (@ (@ F4 A2) B2)) (@ (@ _let_1 As2) Bs))))))
% 3.70/4.05 (assert (forall ((F4 (-> tptp.int tptp.nat tptp.int)) (A2 tptp.int) (As2 tptp.list_int) (B2 tptp.nat) (Bs tptp.list_nat)) (let ((_let_1 (@ tptp.zipf_int_nat_int F4))) (= (@ (@ _let_1 (@ (@ tptp.cons_int A2) As2)) (@ (@ tptp.cons_nat B2) Bs)) (@ (@ tptp.cons_int (@ (@ F4 A2) B2)) (@ (@ _let_1 As2) Bs))))))
% 3.70/4.05 (assert (forall ((F4 (-> tptp.int tptp.nat tptp.nat)) (A2 tptp.int) (As2 tptp.list_int) (B2 tptp.nat) (Bs tptp.list_nat)) (let ((_let_1 (@ tptp.zipf_int_nat_nat F4))) (= (@ (@ _let_1 (@ (@ tptp.cons_int A2) As2)) (@ (@ tptp.cons_nat B2) Bs)) (@ (@ tptp.cons_nat (@ (@ F4 A2) B2)) (@ (@ _let_1 As2) Bs))))))
% 3.70/4.05 (assert (forall ((F4 (-> tptp.nat tptp.int tptp.int)) (A2 tptp.nat) (As2 tptp.list_nat) (B2 tptp.int) (Bs tptp.list_int)) (let ((_let_1 (@ tptp.zipf_nat_int_int F4))) (= (@ (@ _let_1 (@ (@ tptp.cons_nat A2) As2)) (@ (@ tptp.cons_int B2) Bs)) (@ (@ tptp.cons_int (@ (@ F4 A2) B2)) (@ (@ _let_1 As2) Bs))))))
% 3.70/4.05 (assert (forall ((F4 (-> tptp.nat tptp.int tptp.nat)) (A2 tptp.nat) (As2 tptp.list_nat) (B2 tptp.int) (Bs tptp.list_int)) (let ((_let_1 (@ tptp.zipf_nat_int_nat F4))) (= (@ (@ _let_1 (@ (@ tptp.cons_nat A2) As2)) (@ (@ tptp.cons_int B2) Bs)) (@ (@ tptp.cons_nat (@ (@ F4 A2) B2)) (@ (@ _let_1 As2) Bs))))))
% 3.70/4.05 (assert (forall ((F4 (-> tptp.nat tptp.nat tptp.int)) (A2 tptp.nat) (As2 tptp.list_nat) (B2 tptp.nat) (Bs tptp.list_nat)) (let ((_let_1 (@ tptp.zipf_nat_nat_int F4))) (= (@ (@ _let_1 (@ (@ tptp.cons_nat A2) As2)) (@ (@ tptp.cons_nat B2) Bs)) (@ (@ tptp.cons_int (@ (@ F4 A2) B2)) (@ (@ _let_1 As2) Bs))))))
% 3.70/4.05 (assert (forall ((F4 (-> tptp.nat tptp.nat tptp.nat)) (A2 tptp.nat) (As2 tptp.list_nat) (B2 tptp.nat) (Bs tptp.list_nat)) (let ((_let_1 (@ tptp.zipf_nat_nat_nat F4))) (= (@ (@ _let_1 (@ (@ tptp.cons_nat A2) As2)) (@ (@ tptp.cons_nat B2) Bs)) (@ (@ tptp.cons_nat (@ (@ F4 A2) B2)) (@ (@ _let_1 As2) Bs))))))
% 3.70/4.05 (assert (forall ((F4 (-> tptp.int tptp.int tptp.produc6575502325842934193n_assn)) (A2 tptp.int) (As2 tptp.list_int) (B2 tptp.int) (Bs tptp.list_int)) (let ((_let_1 (@ tptp.zipf_i7756021159461276697n_assn F4))) (= (@ (@ _let_1 (@ (@ tptp.cons_int A2) As2)) (@ (@ tptp.cons_int B2) Bs)) (@ (@ tptp.cons_P2971678138204555879n_assn (@ (@ F4 A2) B2)) (@ (@ _let_1 As2) Bs))))))
% 3.70/4.05 (assert (forall ((F4 (-> tptp.int tptp.nat tptp.produc6575502325842934193n_assn)) (A2 tptp.int) (As2 tptp.list_int) (B2 tptp.nat) (Bs tptp.list_nat)) (let ((_let_1 (@ tptp.zipf_i5995984495708165493n_assn F4))) (= (@ (@ _let_1 (@ (@ tptp.cons_int A2) As2)) (@ (@ tptp.cons_nat B2) Bs)) (@ (@ tptp.cons_P2971678138204555879n_assn (@ (@ F4 A2) B2)) (@ (@ _let_1 As2) Bs))))))
% 3.70/4.05 (assert (forall ((X tptp.int) (Xs tptp.list_int)) (not (@ tptp.null_int (@ (@ tptp.cons_int X) Xs)))))
% 3.70/4.05 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (not (@ tptp.null_nat (@ (@ tptp.cons_nat X) Xs)))))
% 3.70/4.05 (assert (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (not (@ tptp.null_P7596217980778516671n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (N tptp.nat)) (= (= (@ tptp.size_s6829681357464350627n_assn Xs) (@ tptp.suc N)) (exists ((Y5 tptp.produc6575502325842934193n_assn) (Ys3 tptp.list_P8527749157015355191n_assn)) (and (= Xs (@ (@ tptp.cons_P2971678138204555879n_assn Y5) Ys3)) (= (@ tptp.size_s6829681357464350627n_assn Ys3) N))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_c) (N tptp.nat)) (= (= (@ tptp.size_size_list_c Xs) (@ tptp.suc N)) (exists ((Y5 tptp.c) (Ys3 tptp.list_c)) (and (= Xs (@ (@ tptp.cons_c Y5) Ys3)) (= (@ tptp.size_size_list_c Ys3) N))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_d) (N tptp.nat)) (= (= (@ tptp.size_size_list_d Xs) (@ tptp.suc N)) (exists ((Y5 tptp.d) (Ys3 tptp.list_d)) (and (= Xs (@ (@ tptp.cons_d Y5) Ys3)) (= (@ tptp.size_size_list_d Ys3) N))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat) (N tptp.nat)) (= (= (@ tptp.size_size_list_nat Xs) (@ tptp.suc N)) (exists ((Y5 tptp.nat) (Ys3 tptp.list_nat)) (and (= Xs (@ (@ tptp.cons_nat Y5) Ys3)) (= (@ tptp.size_size_list_nat Ys3) N))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_int) (N tptp.nat)) (= (= (@ tptp.size_size_list_int Xs) (@ tptp.suc N)) (exists ((Y5 tptp.int) (Ys3 tptp.list_int)) (and (= Xs (@ (@ tptp.cons_int Y5) Ys3)) (= (@ tptp.size_size_list_int Ys3) N))))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (Xs tptp.list_P8527749157015355191n_assn)) (= (= (@ tptp.suc N) (@ tptp.size_s6829681357464350627n_assn Xs)) (exists ((Y5 tptp.produc6575502325842934193n_assn) (Ys3 tptp.list_P8527749157015355191n_assn)) (and (= Xs (@ (@ tptp.cons_P2971678138204555879n_assn Y5) Ys3)) (= (@ tptp.size_s6829681357464350627n_assn Ys3) N))))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (Xs tptp.list_c)) (= (= (@ tptp.suc N) (@ tptp.size_size_list_c Xs)) (exists ((Y5 tptp.c) (Ys3 tptp.list_c)) (and (= Xs (@ (@ tptp.cons_c Y5) Ys3)) (= (@ tptp.size_size_list_c Ys3) N))))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (Xs tptp.list_d)) (= (= (@ tptp.suc N) (@ tptp.size_size_list_d Xs)) (exists ((Y5 tptp.d) (Ys3 tptp.list_d)) (and (= Xs (@ (@ tptp.cons_d Y5) Ys3)) (= (@ tptp.size_size_list_d Ys3) N))))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (Xs tptp.list_nat)) (= (= (@ tptp.suc N) (@ tptp.size_size_list_nat Xs)) (exists ((Y5 tptp.nat) (Ys3 tptp.list_nat)) (and (= Xs (@ (@ tptp.cons_nat Y5) Ys3)) (= (@ tptp.size_size_list_nat Ys3) N))))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (Xs tptp.list_int)) (= (= (@ tptp.suc N) (@ tptp.size_size_list_int Xs)) (exists ((Y5 tptp.int) (Ys3 tptp.list_int)) (and (= Xs (@ (@ tptp.cons_int Y5) Ys3)) (= (@ tptp.size_size_list_int Ys3) N))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_int) (X tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) (@ tptp.set_int2 (@ (@ tptp.cons_int X) Xs)))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (X tptp.produc6575502325842934193n_assn)) (@ (@ tptp.ord_le171416862856029873n_assn (@ tptp.set_Pr1139785259514867910n_assn Xs)) (@ tptp.set_Pr1139785259514867910n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) (@ tptp.set_nat2 (@ (@ tptp.cons_nat X) Xs)))))
% 3.70/4.05 (assert (forall ((R2 tptp.set_Product_prod_o_o) (S3 tptp.set_Product_prod_o_o)) (=> (@ (@ tptp.ord_le192195778054999463od_o_o R2) S3) (@ (@ tptp.ord_less_eq_set_o (@ tptp.field_o R2)) (@ tptp.field_o S3)))))
% 3.70/4.05 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (S3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat R2) S3) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.field_nat R2)) (@ tptp.field_nat S3)))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_P8527749157015355191n_assn) (X tptp.produc6575502325842934193n_assn)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6829681357464350627n_assn Xs)) (@ tptp.size_s6829681357464350627n_assn Ys)) (not (= Xs (@ (@ tptp.cons_P2971678138204555879n_assn X) Ys))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_c) (X tptp.c)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_c Xs)) (@ tptp.size_size_list_c Ys)) (not (= Xs (@ (@ tptp.cons_c X) Ys))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_d) (Ys tptp.list_d) (X tptp.d)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_d Xs)) (@ tptp.size_size_list_d Ys)) (not (= Xs (@ (@ tptp.cons_d X) Ys))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) (@ tptp.size_size_list_nat Ys)) (not (= Xs (@ (@ tptp.cons_nat X) Ys))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs)) (@ tptp.size_size_list_int Ys)) (not (= Xs (@ (@ tptp.cons_int X) Ys))))))
% 3.70/4.05 (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)))))))
% 3.70/4.05 (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)))))))
% 3.70/4.05 (assert (forall ((X tptp.produc3843707927480180839at_nat) (Xs tptp.list_P5464809261938338413at_nat)) (= (@ tptp.distin5355857245021852384at_nat (@ (@ tptp.cons_P3940603068885512221at_nat X) Xs)) (and (not (@ (@ tptp.member8757157785044589968at_nat X) (@ tptp.set_Pr3765526544606949372at_nat Xs))) (@ tptp.distin5355857245021852384at_nat Xs)))))
% 3.70/4.05 (assert (forall ((X tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (= (@ tptp.distin6923225563576452346at_nat (@ (@ tptp.cons_P6512896166579812791at_nat X) Xs)) (and (not (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs))) (@ tptp.distin6923225563576452346at_nat Xs)))))
% 3.70/4.05 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xs tptp.list_P7985473006766602707_nat_o)) (= (@ tptp.distin299582740263731014_nat_o (@ (@ tptp.cons_P6219271836124797827_nat_o X) Xs)) (and (not (@ (@ tptp.member6576561426505652726_nat_o X) (@ tptp.set_Pr400311997697478754_nat_o Xs))) (@ tptp.distin299582740263731014_nat_o Xs)))))
% 3.70/4.05 (assert (forall ((X tptp.int) (Xs tptp.list_int)) (= (@ tptp.distinct_int (@ (@ tptp.cons_int X) Xs)) (and (not (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs))) (@ tptp.distinct_int Xs)))))
% 3.70/4.05 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (= (@ tptp.distinct_nat (@ (@ tptp.cons_nat X) Xs)) (and (not (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs))) (@ tptp.distinct_nat Xs)))))
% 3.70/4.05 (assert (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (= (@ tptp.distin4809818325527169450n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) (and (not (@ (@ tptp.member7957490590177025114n_assn X) (@ tptp.set_Pr1139785259514867910n_assn Xs))) (@ tptp.distin4809818325527169450n_assn Xs)))))
% 3.70/4.05 (assert (forall ((X tptp.int) (Xs tptp.list_int) (Y tptp.int)) (= (@ (@ (@ tptp.list_update_int (@ (@ tptp.cons_int X) Xs)) tptp.zero_zero_nat) Y) (@ (@ tptp.cons_int Y) Xs))))
% 3.70/4.05 (assert (forall ((X tptp.nat) (Xs tptp.list_nat) (Y tptp.nat)) (= (@ (@ (@ tptp.list_update_nat (@ (@ tptp.cons_nat X) Xs)) tptp.zero_zero_nat) Y) (@ (@ tptp.cons_nat Y) Xs))))
% 3.70/4.05 (assert (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn) (Y tptp.produc6575502325842934193n_assn)) (= (@ (@ (@ tptp.list_u4534839942911652127n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) tptp.zero_zero_nat) Y) (@ (@ tptp.cons_P2971678138204555879n_assn Y) Xs))))
% 3.70/4.05 (assert (forall ((X tptp.c) (Xs tptp.list_c) (Y tptp.c)) (= (@ (@ (@ tptp.list_update_c (@ (@ tptp.cons_c X) Xs)) tptp.zero_zero_nat) Y) (@ (@ tptp.cons_c Y) Xs))))
% 3.70/4.05 (assert (forall ((X tptp.d) (Xs tptp.list_d) (Y tptp.d)) (= (@ (@ (@ tptp.list_update_d (@ (@ tptp.cons_d X) Xs)) tptp.zero_zero_nat) Y) (@ (@ tptp.cons_d Y) Xs))))
% 3.70/4.05 (assert (forall ((X tptp.int) (Xs tptp.list_int) (I tptp.nat) (Y tptp.int)) (let ((_let_1 (@ tptp.cons_int X))) (= (@ (@ (@ tptp.list_update_int (@ _let_1 Xs)) (@ tptp.suc I)) Y) (@ _let_1 (@ (@ (@ tptp.list_update_int Xs) I) Y))))))
% 3.70/4.05 (assert (forall ((X tptp.nat) (Xs tptp.list_nat) (I tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.cons_nat X))) (= (@ (@ (@ tptp.list_update_nat (@ _let_1 Xs)) (@ tptp.suc I)) Y) (@ _let_1 (@ (@ (@ tptp.list_update_nat Xs) I) Y))))))
% 3.70/4.05 (assert (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn) (I tptp.nat) (Y tptp.produc6575502325842934193n_assn)) (let ((_let_1 (@ tptp.cons_P2971678138204555879n_assn X))) (= (@ (@ (@ tptp.list_u4534839942911652127n_assn (@ _let_1 Xs)) (@ tptp.suc I)) Y) (@ _let_1 (@ (@ (@ tptp.list_u4534839942911652127n_assn Xs) I) Y))))))
% 3.70/4.05 (assert (forall ((X tptp.c) (Xs tptp.list_c) (I tptp.nat) (Y tptp.c)) (let ((_let_1 (@ tptp.cons_c X))) (= (@ (@ (@ tptp.list_update_c (@ _let_1 Xs)) (@ tptp.suc I)) Y) (@ _let_1 (@ (@ (@ tptp.list_update_c Xs) I) Y))))))
% 3.70/4.05 (assert (forall ((X tptp.d) (Xs tptp.list_d) (I tptp.nat) (Y tptp.d)) (let ((_let_1 (@ tptp.cons_d X))) (= (@ (@ (@ tptp.list_update_d (@ _let_1 Xs)) (@ tptp.suc I)) Y) (@ _let_1 (@ (@ (@ tptp.list_update_d Xs) I) Y))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int) (R2 tptp.set_Pr958786334691620121nt_int) (X tptp.int)) (let ((_let_1 (@ tptp.listrel1_int R2))) (let ((_let_2 (@ tptp.cons_int X))) (=> (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Xs) Ys)) _let_1) (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int (@ _let_2 Xs)) (@ _let_2 Ys))) _let_1))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (R2 tptp.set_Pr1261947904930325089at_nat) (X tptp.nat)) (let ((_let_1 (@ tptp.listrel1_nat R2))) (let ((_let_2 (@ tptp.cons_nat X))) (=> (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Xs) Ys)) _let_1) (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat (@ _let_2 Xs)) (@ _let_2 Ys))) _let_1))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_P8527749157015355191n_assn) (R2 tptp.set_Pr8116311503512020807n_assn) (X tptp.produc6575502325842934193n_assn)) (let ((_let_1 (@ tptp.listre4270255209692100112n_assn R2))) (let ((_let_2 (@ tptp.cons_P2971678138204555879n_assn X))) (=> (@ (@ tptp.member3994142547374651152n_assn (@ (@ tptp.produc3014731801419794263n_assn Xs) Ys)) _let_1) (@ (@ tptp.member3994142547374651152n_assn (@ (@ tptp.produc3014731801419794263n_assn (@ _let_2 Xs)) (@ _let_2 Ys))) _let_1))))))
% 3.70/4.05 (assert (forall ((X1 tptp.code_integer) (X22 tptp.code_integer) (L12 tptp.list_Code_integer) (L23 tptp.list_Code_integer)) (let ((_let_1 (@ tptp.cons_Code_integer X1))) (let ((_let_2 (@ tptp.merge_Code_integer (@ _let_1 L12)))) (let ((_let_3 (@ tptp.cons_Code_integer X22))) (let ((_let_4 (@ _let_3 L23))) (let ((_let_5 (@ _let_2 _let_4))) (let ((_let_6 (= X1 X22))) (let ((_let_7 (@ tptp.merge_Code_integer L12))) (let ((_let_8 (@ (@ tptp.ord_le6747313008572928689nteger X1) X22))) (and (=> _let_8 (= _let_5 (@ _let_1 (@ _let_7 _let_4)))) (=> (not _let_8) (and (=> _let_6 (= _let_5 (@ _let_1 (@ _let_7 L23)))) (=> (not _let_6) (= _let_5 (@ _let_3 (@ _let_2 L23)))))))))))))))))
% 3.70/4.05 (assert (forall ((X1 tptp.num) (X22 tptp.num) (L12 tptp.list_num) (L23 tptp.list_num)) (let ((_let_1 (@ tptp.cons_num X1))) (let ((_let_2 (@ tptp.merge_num (@ _let_1 L12)))) (let ((_let_3 (@ tptp.cons_num X22))) (let ((_let_4 (@ _let_3 L23))) (let ((_let_5 (@ _let_2 _let_4))) (let ((_let_6 (= X1 X22))) (let ((_let_7 (@ tptp.merge_num L12))) (let ((_let_8 (@ (@ tptp.ord_less_num X1) X22))) (and (=> _let_8 (= _let_5 (@ _let_1 (@ _let_7 _let_4)))) (=> (not _let_8) (and (=> _let_6 (= _let_5 (@ _let_1 (@ _let_7 L23)))) (=> (not _let_6) (= _let_5 (@ _let_3 (@ _let_2 L23)))))))))))))))))
% 3.70/4.05 (assert (forall ((X1 tptp.nat) (X22 tptp.nat) (L12 tptp.list_nat) (L23 tptp.list_nat)) (let ((_let_1 (@ tptp.cons_nat X1))) (let ((_let_2 (@ tptp.merge_nat (@ _let_1 L12)))) (let ((_let_3 (@ tptp.cons_nat X22))) (let ((_let_4 (@ _let_3 L23))) (let ((_let_5 (@ _let_2 _let_4))) (let ((_let_6 (= X1 X22))) (let ((_let_7 (@ tptp.merge_nat L12))) (let ((_let_8 (@ (@ tptp.ord_less_nat X1) X22))) (and (=> _let_8 (= _let_5 (@ _let_1 (@ _let_7 _let_4)))) (=> (not _let_8) (and (=> _let_6 (= _let_5 (@ _let_1 (@ _let_7 L23)))) (=> (not _let_6) (= _let_5 (@ _let_3 (@ _let_2 L23)))))))))))))))))
% 3.70/4.05 (assert (forall ((X1 tptp.int) (X22 tptp.int) (L12 tptp.list_int) (L23 tptp.list_int)) (let ((_let_1 (@ tptp.cons_int X1))) (let ((_let_2 (@ tptp.merge_int (@ _let_1 L12)))) (let ((_let_3 (@ tptp.cons_int X22))) (let ((_let_4 (@ _let_3 L23))) (let ((_let_5 (@ _let_2 _let_4))) (let ((_let_6 (= X1 X22))) (let ((_let_7 (@ tptp.merge_int L12))) (let ((_let_8 (@ (@ tptp.ord_less_int X1) X22))) (and (=> _let_8 (= _let_5 (@ _let_1 (@ _let_7 _let_4)))) (=> (not _let_8) (and (=> _let_6 (= _let_5 (@ _let_1 (@ _let_7 L23)))) (=> (not _let_6) (= _let_5 (@ _let_3 (@ _let_2 L23)))))))))))))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.int tptp.int tptp.assn)) (A2 tptp.int) (As2 tptp.list_int) (C tptp.int) (Cs tptp.list_int)) (let ((_let_1 (@ tptp.vEBT_L74593716426352029nt_int P))) (= (@ (@ _let_1 (@ (@ tptp.cons_int A2) As2)) (@ (@ tptp.cons_int C) Cs)) (@ (@ tptp.times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.int tptp.nat tptp.assn)) (A2 tptp.int) (As2 tptp.list_int) (C tptp.nat) (Cs tptp.list_nat)) (let ((_let_1 (@ tptp.vEBT_L77084186935402305nt_nat P))) (= (@ (@ _let_1 (@ (@ tptp.cons_int A2) As2)) (@ (@ tptp.cons_nat C) Cs)) (@ (@ tptp.times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.int tptp.produc6575502325842934193n_assn tptp.assn)) (A2 tptp.int) (As2 tptp.list_int) (C tptp.produc6575502325842934193n_assn) (Cs tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ tptp.vEBT_L1620274777744359680n_assn P))) (= (@ (@ _let_1 (@ (@ tptp.cons_int A2) As2)) (@ (@ tptp.cons_P2971678138204555879n_assn C) Cs)) (@ (@ tptp.times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.nat tptp.int tptp.assn)) (A2 tptp.nat) (As2 tptp.list_nat) (C tptp.int) (Cs tptp.list_int)) (let ((_let_1 (@ tptp.vEBT_L8298612041380073281at_int P))) (= (@ (@ _let_1 (@ (@ tptp.cons_nat A2) As2)) (@ (@ tptp.cons_int C) Cs)) (@ (@ tptp.times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.nat tptp.nat tptp.assn)) (A2 tptp.nat) (As2 tptp.list_nat) (C tptp.nat) (Cs tptp.list_nat)) (let ((_let_1 (@ tptp.vEBT_L8301102511889123557at_nat P))) (= (@ (@ _let_1 (@ (@ tptp.cons_nat A2) As2)) (@ (@ tptp.cons_nat C) Cs)) (@ (@ tptp.times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.nat tptp.produc6575502325842934193n_assn tptp.assn)) (A2 tptp.nat) (As2 tptp.list_nat) (C tptp.produc6575502325842934193n_assn) (Cs tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ tptp.vEBT_L9083610150846024284n_assn P))) (= (@ (@ _let_1 (@ (@ tptp.cons_nat A2) As2)) (@ (@ tptp.cons_P2971678138204555879n_assn C) Cs)) (@ (@ tptp.times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.produc6575502325842934193n_assn tptp.int tptp.assn)) (A2 tptp.produc6575502325842934193n_assn) (As2 tptp.list_P8527749157015355191n_assn) (C tptp.int) (Cs tptp.list_int)) (let ((_let_1 (@ tptp.vEBT_L4760345170377931482sn_int P))) (= (@ (@ _let_1 (@ (@ tptp.cons_P2971678138204555879n_assn A2) As2)) (@ (@ tptp.cons_int C) Cs)) (@ (@ tptp.times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.produc6575502325842934193n_assn tptp.nat tptp.assn)) (A2 tptp.produc6575502325842934193n_assn) (As2 tptp.list_P8527749157015355191n_assn) (C tptp.nat) (Cs tptp.list_nat)) (let ((_let_1 (@ tptp.vEBT_L4762835640886981758sn_nat P))) (= (@ (@ _let_1 (@ (@ tptp.cons_P2971678138204555879n_assn A2) As2)) (@ (@ tptp.cons_nat C) Cs)) (@ (@ tptp.times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn tptp.assn)) (A2 tptp.produc6575502325842934193n_assn) (As2 tptp.list_P8527749157015355191n_assn) (C tptp.produc6575502325842934193n_assn) (Cs tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ tptp.vEBT_L3108143461992071043n_assn P))) (= (@ (@ _let_1 (@ (@ tptp.cons_P2971678138204555879n_assn A2) As2)) (@ (@ tptp.cons_P2971678138204555879n_assn C) Cs)) (@ (@ tptp.times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.int tptp.int tptp.assn)) (A2 tptp.int) (As2 tptp.list_int) (C tptp.int) (Cs tptp.list_int)) (let ((_let_1 (@ tptp.vEBT_L74593716426352029nt_int P))) (= (@ (@ _let_1 (@ (@ tptp.cons_int A2) As2)) (@ (@ tptp.cons_int C) Cs)) (@ (@ tptp.times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.int tptp.nat tptp.assn)) (A2 tptp.int) (As2 tptp.list_int) (C tptp.nat) (Cs tptp.list_nat)) (let ((_let_1 (@ tptp.vEBT_L77084186935402305nt_nat P))) (= (@ (@ _let_1 (@ (@ tptp.cons_int A2) As2)) (@ (@ tptp.cons_nat C) Cs)) (@ (@ tptp.times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.int tptp.produc6575502325842934193n_assn tptp.assn)) (A2 tptp.int) (As2 tptp.list_int) (C tptp.produc6575502325842934193n_assn) (Cs tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ tptp.vEBT_L1620274777744359680n_assn P))) (= (@ (@ _let_1 (@ (@ tptp.cons_int A2) As2)) (@ (@ tptp.cons_P2971678138204555879n_assn C) Cs)) (@ (@ tptp.times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.nat tptp.int tptp.assn)) (A2 tptp.nat) (As2 tptp.list_nat) (C tptp.int) (Cs tptp.list_int)) (let ((_let_1 (@ tptp.vEBT_L8298612041380073281at_int P))) (= (@ (@ _let_1 (@ (@ tptp.cons_nat A2) As2)) (@ (@ tptp.cons_int C) Cs)) (@ (@ tptp.times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.nat tptp.nat tptp.assn)) (A2 tptp.nat) (As2 tptp.list_nat) (C tptp.nat) (Cs tptp.list_nat)) (let ((_let_1 (@ tptp.vEBT_L8301102511889123557at_nat P))) (= (@ (@ _let_1 (@ (@ tptp.cons_nat A2) As2)) (@ (@ tptp.cons_nat C) Cs)) (@ (@ tptp.times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.nat tptp.produc6575502325842934193n_assn tptp.assn)) (A2 tptp.nat) (As2 tptp.list_nat) (C tptp.produc6575502325842934193n_assn) (Cs tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ tptp.vEBT_L9083610150846024284n_assn P))) (= (@ (@ _let_1 (@ (@ tptp.cons_nat A2) As2)) (@ (@ tptp.cons_P2971678138204555879n_assn C) Cs)) (@ (@ tptp.times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.produc6575502325842934193n_assn tptp.int tptp.assn)) (A2 tptp.produc6575502325842934193n_assn) (As2 tptp.list_P8527749157015355191n_assn) (C tptp.int) (Cs tptp.list_int)) (let ((_let_1 (@ tptp.vEBT_L4760345170377931482sn_int P))) (= (@ (@ _let_1 (@ (@ tptp.cons_P2971678138204555879n_assn A2) As2)) (@ (@ tptp.cons_int C) Cs)) (@ (@ tptp.times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.produc6575502325842934193n_assn tptp.nat tptp.assn)) (A2 tptp.produc6575502325842934193n_assn) (As2 tptp.list_P8527749157015355191n_assn) (C tptp.nat) (Cs tptp.list_nat)) (let ((_let_1 (@ tptp.vEBT_L4762835640886981758sn_nat P))) (= (@ (@ _let_1 (@ (@ tptp.cons_P2971678138204555879n_assn A2) As2)) (@ (@ tptp.cons_nat C) Cs)) (@ (@ tptp.times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn tptp.assn)) (A2 tptp.produc6575502325842934193n_assn) (As2 tptp.list_P8527749157015355191n_assn) (C tptp.produc6575502325842934193n_assn) (Cs tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ tptp.vEBT_L3108143461992071043n_assn P))) (= (@ (@ _let_1 (@ (@ tptp.cons_P2971678138204555879n_assn A2) As2)) (@ (@ tptp.cons_P2971678138204555879n_assn C) Cs)) (@ (@ tptp.times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))))
% 3.70/4.05 (assert (= tptp.insert4149901806602606979at_nat (lambda ((X2 tptp.produc3843707927480180839at_nat) (Xs3 tptp.list_P5464809261938338413at_nat)) (@ (@ (@ tptp.if_lis7508161100780771379at_nat (@ (@ tptp.member8757157785044589968at_nat X2) (@ tptp.set_Pr3765526544606949372at_nat Xs3))) Xs3) (@ (@ tptp.cons_P3940603068885512221at_nat X2) Xs3)))))
% 3.70/4.05 (assert (= tptp.insert8944034826898310173at_nat (lambda ((X2 tptp.product_prod_nat_nat) (Xs3 tptp.list_P6011104703257516679at_nat)) (@ (@ (@ tptp.if_lis9186351972506106189at_nat (@ (@ tptp.member8440522571783428010at_nat X2) (@ tptp.set_Pr5648618587558075414at_nat Xs3))) Xs3) (@ (@ tptp.cons_P6512896166579812791at_nat X2) Xs3)))))
% 3.70/4.05 (assert (= tptp.insert8021100735160035049_nat_o (lambda ((X2 (-> tptp.produc3658429121746597890et_nat Bool)) (Xs3 tptp.list_P7985473006766602707_nat_o)) (@ (@ (@ tptp.if_lis2904118647880296857_nat_o (@ (@ tptp.member6576561426505652726_nat_o X2) (@ tptp.set_Pr400311997697478754_nat_o Xs3))) Xs3) (@ (@ tptp.cons_P6219271836124797827_nat_o X2) Xs3)))))
% 3.70/4.05 (assert (= tptp.insert_int (lambda ((X2 tptp.int) (Xs3 tptp.list_int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.member_int X2) (@ tptp.set_int2 Xs3))) Xs3) (@ (@ tptp.cons_int X2) Xs3)))))
% 3.70/4.05 (assert (= tptp.insert_nat (lambda ((X2 tptp.nat) (Xs3 tptp.list_nat)) (@ (@ (@ tptp.if_list_nat (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Xs3))) Xs3) (@ (@ tptp.cons_nat X2) Xs3)))))
% 3.70/4.05 (assert (= tptp.insert3246601298802261197n_assn (lambda ((X2 tptp.produc6575502325842934193n_assn) (Xs3 tptp.list_P8527749157015355191n_assn)) (@ (@ (@ tptp.if_lis7173127979115136509n_assn (@ (@ tptp.member7957490590177025114n_assn X2) (@ tptp.set_Pr1139785259514867910n_assn Xs3))) Xs3) (@ (@ tptp.cons_P2971678138204555879n_assn X2) Xs3)))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (Xs tptp.list_P8527749157015355191n_assn)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.size_s6829681357464350627n_assn Xs)) (exists ((X2 tptp.produc6575502325842934193n_assn) (Ys3 tptp.list_P8527749157015355191n_assn)) (and (= Xs (@ (@ tptp.cons_P2971678138204555879n_assn X2) Ys3)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_s6829681357464350627n_assn Ys3)))))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (Xs tptp.list_c)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.size_size_list_c Xs)) (exists ((X2 tptp.c) (Ys3 tptp.list_c)) (and (= Xs (@ (@ tptp.cons_c X2) Ys3)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_c Ys3)))))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (Xs tptp.list_d)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.size_size_list_d Xs)) (exists ((X2 tptp.d) (Ys3 tptp.list_d)) (and (= Xs (@ (@ tptp.cons_d X2) Ys3)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_d Ys3)))))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (Xs tptp.list_nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.size_size_list_nat Xs)) (exists ((X2 tptp.nat) (Ys3 tptp.list_nat)) (and (= Xs (@ (@ tptp.cons_nat X2) Ys3)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_nat Ys3)))))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (Xs tptp.list_int)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.size_size_list_int Xs)) (exists ((X2 tptp.int) (Ys3 tptp.list_int)) (and (= Xs (@ (@ tptp.cons_int X2) Ys3)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_int Ys3)))))))
% 3.70/4.05 (assert (forall ((X tptp.nat) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat))) (= (@ _let_1 (@ (@ tptp.cons_nat X) Ys)) (and (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Ys)) (@ (@ tptp.ord_less_eq_nat X) X2))) (@ _let_1 Ys))))))
% 3.70/4.05 (assert (forall ((X tptp.int) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.sorted_wrt_int tptp.ord_less_eq_int))) (= (@ _let_1 (@ (@ tptp.cons_int X) Ys)) (and (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) (@ tptp.set_int2 Ys)) (@ (@ tptp.ord_less_eq_int X) X2))) (@ _let_1 Ys))))))
% 3.70/4.05 (assert (forall ((X tptp.code_integer) (Ys tptp.list_Code_integer)) (let ((_let_1 (@ tptp.sorted710888440204495920nteger tptp.ord_le6747313008572928689nteger))) (= (@ _let_1 (@ (@ tptp.cons_Code_integer X) Ys)) (and (forall ((X2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X2) (@ tptp.set_Code_integer2 Ys)) (@ (@ tptp.ord_le6747313008572928689nteger X) X2))) (@ _let_1 Ys))))))
% 3.70/4.05 (assert (forall ((X tptp.num) (Ys tptp.list_num)) (let ((_let_1 (@ tptp.sorted_wrt_num tptp.ord_less_num))) (= (@ _let_1 (@ (@ tptp.cons_num X) Ys)) (and (forall ((X2 tptp.num)) (=> (@ (@ tptp.member_num X2) (@ tptp.set_num2 Ys)) (@ (@ tptp.ord_less_num X) X2))) (@ _let_1 Ys))))))
% 3.70/4.05 (assert (forall ((X tptp.nat) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.sorted_wrt_nat tptp.ord_less_nat))) (= (@ _let_1 (@ (@ tptp.cons_nat X) Ys)) (and (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Ys)) (@ (@ tptp.ord_less_nat X) X2))) (@ _let_1 Ys))))))
% 3.70/4.05 (assert (forall ((X tptp.int) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.sorted_wrt_int tptp.ord_less_int))) (= (@ _let_1 (@ (@ tptp.cons_int X) Ys)) (and (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) (@ tptp.set_int2 Ys)) (@ (@ tptp.ord_less_int X) X2))) (@ _let_1 Ys))))))
% 3.70/4.05 (assert (= tptp.biject3388518990857851981at_nat (lambda ((R3 tptp.set_Pr4329608150637261639at_nat)) (and (forall ((X2 tptp.set_Pr1261947904930325089at_nat) (Y5 tptp.set_Pr1261947904930325089at_nat) (Z5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.produc2922128104949294807at_nat X2))) (=> (and (@ (@ tptp.member8757157785044589968at_nat (@ _let_1 Y5)) R3) (@ (@ tptp.member8757157785044589968at_nat (@ _let_1 Z5)) R3)) (= Y5 Z5)))) (forall ((X2 tptp.set_Pr1261947904930325089at_nat) (Y5 tptp.set_Pr1261947904930325089at_nat) (Z5 tptp.set_Pr1261947904930325089at_nat)) (=> (and (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X2) Z5)) R3) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat Y5) Z5)) R3)) (= X2 Y5)))))))
% 3.70/4.05 (assert (= tptp.bijective_nat_nat (lambda ((R3 tptp.set_Pr1261947904930325089at_nat)) (and (forall ((X2 tptp.nat) (Y5 tptp.nat) (Z5 tptp.nat)) (let ((_let_1 (@ tptp.product_Pair_nat_nat X2))) (=> (and (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 Y5)) R3) (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 Z5)) R3)) (= Y5 Z5)))) (forall ((X2 tptp.nat) (Y5 tptp.nat) (Z5 tptp.nat)) (=> (and (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X2) Z5)) R3) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y5) Z5)) R3)) (= X2 Y5)))))))
% 3.70/4.05 (assert (= tptp.biject9051520373387432658nteger (lambda ((R3 tptp.set_Pr1281608226676607948nteger)) (and (forall ((X2 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (Y5 tptp.produc8923325533196201883nteger) (Z5 tptp.produc8923325533196201883nteger)) (let ((_let_1 (@ tptp.produc8603105652947943368nteger X2))) (=> (and (@ (@ tptp.member4164122664394876845nteger (@ _let_1 Y5)) R3) (@ (@ tptp.member4164122664394876845nteger (@ _let_1 Z5)) R3)) (= Y5 Z5)))) (forall ((X2 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (Y5 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (Z5 tptp.produc8923325533196201883nteger)) (=> (and (@ (@ tptp.member4164122664394876845nteger (@ (@ tptp.produc8603105652947943368nteger X2) Z5)) R3) (@ (@ tptp.member4164122664394876845nteger (@ (@ tptp.produc8603105652947943368nteger Y5) Z5)) R3)) (= X2 Y5)))))))
% 3.70/4.05 (assert (= tptp.biject2615096655818420098et_nat (lambda ((R3 tptp.set_Pr3286484037609594932et_nat)) (and (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool)) (Y5 tptp.produc3658429121746597890et_nat) (Z5 tptp.produc3658429121746597890et_nat)) (let ((_let_1 (@ tptp.produc5001842942810119800et_nat X2))) (=> (and (@ (@ tptp.member1996754912294343701et_nat (@ _let_1 Y5)) R3) (@ (@ tptp.member1996754912294343701et_nat (@ _let_1 Z5)) R3)) (= Y5 Z5)))) (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool)) (Y5 (-> tptp.produc3658429121746597890et_nat Bool)) (Z5 tptp.produc3658429121746597890et_nat)) (=> (and (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat X2) Z5)) R3) (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat Y5) Z5)) R3)) (= X2 Y5)))))))
% 3.70/4.05 (assert (= tptp.biject1468766312547416318et_nat (lambda ((R3 tptp.set_Pr8536935166611901872et_nat)) (and (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool)) (Y5 tptp.produc3925858234332021118et_nat) (Z5 tptp.produc3925858234332021118et_nat)) (let ((_let_1 (@ tptp.produc2245416461498447860et_nat X2))) (=> (and (@ (@ tptp.member6124377750444531601et_nat (@ _let_1 Y5)) R3) (@ (@ tptp.member6124377750444531601et_nat (@ _let_1 Z5)) R3)) (= Y5 Z5)))) (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool)) (Y5 (-> tptp.produc3658429121746597890et_nat Bool)) (Z5 tptp.produc3925858234332021118et_nat)) (=> (and (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat X2) Z5)) R3) (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat Y5) Z5)) R3)) (= X2 Y5)))))))
% 3.70/4.05 (assert (= tptp.biject383251550997737151nt_int (lambda ((R3 tptp.set_Pr9222295170931077689nt_int)) (and (forall ((X2 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y5 tptp.product_prod_int_int) (Z5 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.produc5700946648718959541nt_int X2))) (=> (and (@ (@ tptp.member7618704894036264090nt_int (@ _let_1 Y5)) R3) (@ (@ tptp.member7618704894036264090nt_int (@ _let_1 Z5)) R3)) (= Y5 Z5)))) (forall ((X2 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y5 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Z5 tptp.product_prod_int_int)) (=> (and (@ (@ tptp.member7618704894036264090nt_int (@ (@ tptp.produc5700946648718959541nt_int X2) Z5)) R3) (@ (@ tptp.member7618704894036264090nt_int (@ (@ tptp.produc5700946648718959541nt_int Y5) Z5)) R3)) (= X2 Y5)))))))
% 3.70/4.05 (assert (= tptp.biject576505603616484041nt_int (lambda ((R3 tptp.set_Pr1872883991513573699nt_int)) (and (forall ((X2 (-> tptp.int tptp.option6357759511663192854e_term)) (Y5 tptp.product_prod_int_int) (Z5 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.produc4305682042979456191nt_int X2))) (=> (and (@ (@ tptp.member7034335876925520548nt_int (@ _let_1 Y5)) R3) (@ (@ tptp.member7034335876925520548nt_int (@ _let_1 Z5)) R3)) (= Y5 Z5)))) (forall ((X2 (-> tptp.int tptp.option6357759511663192854e_term)) (Y5 (-> tptp.int tptp.option6357759511663192854e_term)) (Z5 tptp.product_prod_int_int)) (=> (and (@ (@ tptp.member7034335876925520548nt_int (@ (@ tptp.produc4305682042979456191nt_int X2) Z5)) R3) (@ (@ tptp.member7034335876925520548nt_int (@ (@ tptp.produc4305682042979456191nt_int Y5) Z5)) R3)) (= X2 Y5)))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_s1210847774152347623at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Ys tptp.list_s1210847774152347623at_nat) (R2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat Xs) (@ (@ tptp.cons_s6881495754146722583at_nat Y) Ys))) (@ tptp.listre8180072825634266816at_nat R2)) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat)) (=> (= Xs (@ (@ tptp.cons_s6881495754146722583at_nat X3) Ys)) (not (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X3) Y)) R2)))) (not (forall ((Zs2 tptp.list_s1210847774152347623at_nat)) (=> (= Xs (@ (@ tptp.cons_s6881495754146722583at_nat Y) Zs2)) (not (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat Zs2) Ys)) (@ tptp.listre8180072825634266816at_nat R2))))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_int) (Y tptp.int) (Ys tptp.list_int) (R2 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Xs) (@ (@ tptp.cons_int Y) Ys))) (@ tptp.listrel1_int R2)) (=> (forall ((X3 tptp.int)) (=> (= Xs (@ (@ tptp.cons_int X3) Ys)) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X3) Y)) R2)))) (not (forall ((Zs2 tptp.list_int)) (=> (= Xs (@ (@ tptp.cons_int Y) Zs2)) (not (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Zs2) Ys)) (@ tptp.listrel1_int R2))))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat) (Y tptp.nat) (Ys tptp.list_nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Xs) (@ (@ tptp.cons_nat Y) Ys))) (@ tptp.listrel1_nat R2)) (=> (forall ((X3 tptp.nat)) (=> (= Xs (@ (@ tptp.cons_nat X3) Ys)) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) Y)) R2)))) (not (forall ((Zs2 tptp.list_nat)) (=> (= Xs (@ (@ tptp.cons_nat Y) Zs2)) (not (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Zs2) Ys)) (@ tptp.listrel1_nat R2))))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (Y tptp.produc6575502325842934193n_assn) (Ys tptp.list_P8527749157015355191n_assn) (R2 tptp.set_Pr8116311503512020807n_assn)) (=> (@ (@ tptp.member3994142547374651152n_assn (@ (@ tptp.produc3014731801419794263n_assn Xs) (@ (@ tptp.cons_P2971678138204555879n_assn Y) Ys))) (@ tptp.listre4270255209692100112n_assn R2)) (=> (forall ((X3 tptp.produc6575502325842934193n_assn)) (=> (= Xs (@ (@ tptp.cons_P2971678138204555879n_assn X3) Ys)) (not (@ (@ tptp.member4743710847862083984n_assn (@ (@ tptp.produc6128706242671166167n_assn X3) Y)) R2)))) (not (forall ((Zs2 tptp.list_P8527749157015355191n_assn)) (=> (= Xs (@ (@ tptp.cons_P2971678138204555879n_assn Y) Zs2)) (not (@ (@ tptp.member3994142547374651152n_assn (@ (@ tptp.produc3014731801419794263n_assn Zs2) Ys)) (@ tptp.listre4270255209692100112n_assn R2))))))))))
% 3.70/4.05 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Xs tptp.list_s1210847774152347623at_nat) (Ys tptp.list_s1210847774152347623at_nat) (R2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat (@ (@ tptp.cons_s6881495754146722583at_nat X) Xs)) Ys)) (@ tptp.listre8180072825634266816at_nat R2)) (=> (forall ((Y2 tptp.set_Pr1261947904930325089at_nat)) (=> (= Ys (@ (@ tptp.cons_s6881495754146722583at_nat Y2) Xs)) (not (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Y2)) R2)))) (not (forall ((Zs2 tptp.list_s1210847774152347623at_nat)) (=> (= Ys (@ (@ tptp.cons_s6881495754146722583at_nat X) Zs2)) (not (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat Xs) Zs2)) (@ tptp.listre8180072825634266816at_nat R2))))))))))
% 3.70/4.05 (assert (forall ((X tptp.int) (Xs tptp.list_int) (Ys tptp.list_int) (R2 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int (@ (@ tptp.cons_int X) Xs)) Ys)) (@ tptp.listrel1_int R2)) (=> (forall ((Y2 tptp.int)) (=> (= Ys (@ (@ tptp.cons_int Y2) Xs)) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y2)) R2)))) (not (forall ((Zs2 tptp.list_int)) (=> (= Ys (@ (@ tptp.cons_int X) Zs2)) (not (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Xs) Zs2)) (@ tptp.listrel1_int R2))))))))))
% 3.70/4.05 (assert (forall ((X tptp.nat) (Xs tptp.list_nat) (Ys tptp.list_nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat (@ (@ tptp.cons_nat X) Xs)) Ys)) (@ tptp.listrel1_nat R2)) (=> (forall ((Y2 tptp.nat)) (=> (= Ys (@ (@ tptp.cons_nat Y2) Xs)) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y2)) R2)))) (not (forall ((Zs2 tptp.list_nat)) (=> (= Ys (@ (@ tptp.cons_nat X) Zs2)) (not (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Xs) Zs2)) (@ tptp.listrel1_nat R2))))))))))
% 3.70/4.05 (assert (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_P8527749157015355191n_assn) (R2 tptp.set_Pr8116311503512020807n_assn)) (=> (@ (@ tptp.member3994142547374651152n_assn (@ (@ tptp.produc3014731801419794263n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) Ys)) (@ tptp.listre4270255209692100112n_assn R2)) (=> (forall ((Y2 tptp.produc6575502325842934193n_assn)) (=> (= Ys (@ (@ tptp.cons_P2971678138204555879n_assn Y2) Xs)) (not (@ (@ tptp.member4743710847862083984n_assn (@ (@ tptp.produc6128706242671166167n_assn X) Y2)) R2)))) (not (forall ((Zs2 tptp.list_P8527749157015355191n_assn)) (=> (= Ys (@ (@ tptp.cons_P2971678138204555879n_assn X) Zs2)) (not (@ (@ tptp.member3994142547374651152n_assn (@ (@ tptp.produc3014731801419794263n_assn Xs) Zs2)) (@ tptp.listre4270255209692100112n_assn R2))))))))))
% 3.70/4.05 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (R2 tptp.set_Pr4329608150637261639at_nat) (Xs tptp.list_s1210847774152347623at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Y)) R2) (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat (@ (@ tptp.cons_s6881495754146722583at_nat X) Xs)) (@ (@ tptp.cons_s6881495754146722583at_nat Y) Xs))) (@ tptp.listre8180072825634266816at_nat R2)))))
% 3.70/4.05 (assert (forall ((X tptp.int) (Y tptp.int) (R2 tptp.set_Pr958786334691620121nt_int) (Xs tptp.list_int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) R2) (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int (@ (@ tptp.cons_int X) Xs)) (@ (@ tptp.cons_int Y) Xs))) (@ tptp.listrel1_int R2)))))
% 3.70/4.05 (assert (forall ((X tptp.nat) (Y tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) R2) (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat (@ (@ tptp.cons_nat X) Xs)) (@ (@ tptp.cons_nat Y) Xs))) (@ tptp.listrel1_nat R2)))))
% 3.70/4.05 (assert (forall ((X tptp.produc6575502325842934193n_assn) (Y tptp.produc6575502325842934193n_assn) (R2 tptp.set_Pr8116311503512020807n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (=> (@ (@ tptp.member4743710847862083984n_assn (@ (@ tptp.produc6128706242671166167n_assn X) Y)) R2) (@ (@ tptp.member3994142547374651152n_assn (@ (@ tptp.produc3014731801419794263n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) (@ (@ tptp.cons_P2971678138204555879n_assn Y) Xs))) (@ tptp.listre4270255209692100112n_assn R2)))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_int) (Y tptp.int) (Ys tptp.list_int) (R2 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Xs) (@ (@ tptp.cons_int Y) Ys))) (@ tptp.listrel_int_int R2)) (not (forall ((X3 tptp.int) (Xs2 tptp.list_int)) (=> (= Xs (@ (@ tptp.cons_int X3) Xs2)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X3) Y)) R2) (not (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Xs2) Ys)) (@ tptp.listrel_int_int R2))))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat) (Y tptp.int) (Ys tptp.list_int) (R2 tptp.set_Pr7995236796853374141at_int)) (=> (@ (@ tptp.member4850886304473975718st_int (@ (@ tptp.produc7739558402351520821st_int Xs) (@ (@ tptp.cons_int Y) Ys))) (@ tptp.listrel_nat_int R2)) (not (forall ((X3 tptp.nat) (Xs2 tptp.list_nat)) (=> (= Xs (@ (@ tptp.cons_nat X3) Xs2)) (=> (@ (@ tptp.member4262671552274231302at_int (@ (@ tptp.product_Pair_nat_int X3) Y)) R2) (not (@ (@ tptp.member4850886304473975718st_int (@ (@ tptp.produc7739558402351520821st_int Xs2) Ys)) (@ tptp.listrel_nat_int R2))))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_int) (Y tptp.nat) (Ys tptp.list_nat) (R2 tptp.set_Pr3448869479623346877nt_nat)) (=> (@ (@ tptp.member9189046780804443046st_nat (@ (@ tptp.produc4542114716404682293st_nat Xs) (@ (@ tptp.cons_nat Y) Ys))) (@ tptp.listrel_int_nat R2)) (not (forall ((X3 tptp.int) (Xs2 tptp.list_int)) (=> (= Xs (@ (@ tptp.cons_int X3) Xs2)) (=> (@ (@ tptp.member216504246829706758nt_nat (@ (@ tptp.product_Pair_int_nat X3) Y)) R2) (not (@ (@ tptp.member9189046780804443046st_nat (@ (@ tptp.produc4542114716404682293st_nat Xs2) Ys)) (@ tptp.listrel_int_nat R2))))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat) (Y tptp.nat) (Ys tptp.list_nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Xs) (@ (@ tptp.cons_nat Y) Ys))) (@ tptp.listrel_nat_nat R2)) (not (forall ((X3 tptp.nat) (Xs2 tptp.list_nat)) (=> (= Xs (@ (@ tptp.cons_nat X3) Xs2)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) Y)) R2) (not (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Xs2) Ys)) (@ tptp.listrel_nat_nat R2))))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (Y tptp.int) (Ys tptp.list_int) (R2 tptp.set_Pr2181989527757714242sn_int)) (=> (@ (@ tptp.member5295696281703116473st_int (@ (@ tptp.produc1996262876970182428st_int Xs) (@ (@ tptp.cons_int Y) Ys))) (@ tptp.listre8029020076619294380sn_int R2)) (not (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn)) (=> (= Xs (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)) (=> (@ (@ tptp.member5792320502188913699sn_int (@ (@ tptp.produc6453891449406693510sn_int X3) Y)) R2) (not (@ (@ tptp.member5295696281703116473st_int (@ (@ tptp.produc1996262876970182428st_int Xs2) Ys)) (@ tptp.listre8029020076619294380sn_int R2))))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (Y tptp.nat) (Ys tptp.list_nat) (R2 tptp.set_Pr4672072672689440998sn_nat)) (=> (@ (@ tptp.member7785779426634843229st_nat (@ (@ tptp.produc6174113896479379136st_nat Xs) (@ (@ tptp.cons_nat Y) Ys))) (@ tptp.listre8031510547128344656sn_nat R2)) (not (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn)) (=> (= Xs (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)) (=> (@ (@ tptp.member746799484843334599sn_nat (@ (@ tptp.produc6456381919915743786sn_nat X3) Y)) R2) (not (@ (@ tptp.member7785779426634843229st_nat (@ (@ tptp.produc6174113896479379136st_nat Xs2) Ys)) (@ tptp.listre8031510547128344656sn_nat R2))))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_int) (Y tptp.produc6575502325842934193n_assn) (Ys tptp.list_P8527749157015355191n_assn) (R2 tptp.set_Pr3255386646789011632n_assn)) (=> (@ (@ tptp.member490958779117458567n_assn (@ (@ tptp.produc4510294837168919970n_assn Xs) (@ (@ tptp.cons_P2971678138204555879n_assn Y) Ys))) (@ tptp.listre4888949683985722578n_assn R2)) (not (forall ((X3 tptp.int) (Xs2 tptp.list_int)) (=> (= Xs (@ (@ tptp.cons_int X3) Xs2)) (=> (@ (@ tptp.member241480614033477777n_assn (@ (@ tptp.produc3313821056773121708n_assn X3) Y)) R2) (not (@ (@ tptp.member490958779117458567n_assn (@ (@ tptp.produc4510294837168919970n_assn Xs2) Ys)) (@ tptp.listre4888949683985722578n_assn R2))))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat) (Y tptp.produc6575502325842934193n_assn) (Ys tptp.list_P8527749157015355191n_assn) (R2 tptp.set_Pr247834672394327052n_assn)) (=> (@ (@ tptp.member3687432546746012131n_assn (@ (@ tptp.produc7706768604797473534n_assn Xs) (@ (@ tptp.cons_P2971678138204555879n_assn Y) Ys))) (@ tptp.listre3128913020232611374n_assn R2)) (not (forall ((X3 tptp.nat) (Xs2 tptp.list_nat)) (=> (= Xs (@ (@ tptp.cons_nat X3) Xs2)) (=> (@ (@ tptp.member7704815987135142381n_assn (@ (@ tptp.produc1553784393020010504n_assn X3) Y)) R2) (not (@ (@ tptp.member3687432546746012131n_assn (@ (@ tptp.produc7706768604797473534n_assn Xs2) Ys)) (@ tptp.listre3128913020232611374n_assn R2))))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (Y tptp.produc6575502325842934193n_assn) (Ys tptp.list_P8527749157015355191n_assn) (R2 tptp.set_Pr8116311503512020807n_assn)) (=> (@ (@ tptp.member3994142547374651152n_assn (@ (@ tptp.produc3014731801419794263n_assn Xs) (@ (@ tptp.cons_P2971678138204555879n_assn Y) Ys))) (@ tptp.listre5253995379918703921n_assn R2)) (not (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn)) (=> (= Xs (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)) (=> (@ (@ tptp.member4743710847862083984n_assn (@ (@ tptp.produc6128706242671166167n_assn X3) Y)) R2) (not (@ (@ tptp.member3994142547374651152n_assn (@ (@ tptp.produc3014731801419794263n_assn Xs2) Ys)) (@ tptp.listre5253995379918703921n_assn R2))))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_s1210847774152347623at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Ys tptp.list_s1210847774152347623at_nat) (R2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat Xs) (@ (@ tptp.cons_s6881495754146722583at_nat Y) Ys))) (@ tptp.listre2047417242196832561at_nat R2)) (not (forall ((X3 tptp.set_Pr1261947904930325089at_nat) (Xs2 tptp.list_s1210847774152347623at_nat)) (=> (= Xs (@ (@ tptp.cons_s6881495754146722583at_nat X3) Xs2)) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X3) Y)) R2) (not (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat Xs2) Ys)) (@ tptp.listre2047417242196832561at_nat R2))))))))))
% 3.70/4.05 (assert (forall ((Y tptp.int) (Ys tptp.list_int) (Xs tptp.list_int) (R2 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int (@ (@ tptp.cons_int Y) Ys)) Xs)) (@ tptp.listrel_int_int R2)) (not (forall ((Y2 tptp.int) (Ys5 tptp.list_int)) (=> (= Xs (@ (@ tptp.cons_int Y2) Ys5)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y) Y2)) R2) (not (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Ys) Ys5)) (@ tptp.listrel_int_int R2))))))))))
% 3.70/4.05 (assert (forall ((Y tptp.int) (Ys tptp.list_int) (Xs tptp.list_nat) (R2 tptp.set_Pr3448869479623346877nt_nat)) (=> (@ (@ tptp.member9189046780804443046st_nat (@ (@ tptp.produc4542114716404682293st_nat (@ (@ tptp.cons_int Y) Ys)) Xs)) (@ tptp.listrel_int_nat R2)) (not (forall ((Y2 tptp.nat) (Ys5 tptp.list_nat)) (=> (= Xs (@ (@ tptp.cons_nat Y2) Ys5)) (=> (@ (@ tptp.member216504246829706758nt_nat (@ (@ tptp.product_Pair_int_nat Y) Y2)) R2) (not (@ (@ tptp.member9189046780804443046st_nat (@ (@ tptp.produc4542114716404682293st_nat Ys) Ys5)) (@ tptp.listrel_int_nat R2))))))))))
% 3.70/4.05 (assert (forall ((Y tptp.nat) (Ys tptp.list_nat) (Xs tptp.list_int) (R2 tptp.set_Pr7995236796853374141at_int)) (=> (@ (@ tptp.member4850886304473975718st_int (@ (@ tptp.produc7739558402351520821st_int (@ (@ tptp.cons_nat Y) Ys)) Xs)) (@ tptp.listrel_nat_int R2)) (not (forall ((Y2 tptp.int) (Ys5 tptp.list_int)) (=> (= Xs (@ (@ tptp.cons_int Y2) Ys5)) (=> (@ (@ tptp.member4262671552274231302at_int (@ (@ tptp.product_Pair_nat_int Y) Y2)) R2) (not (@ (@ tptp.member4850886304473975718st_int (@ (@ tptp.produc7739558402351520821st_int Ys) Ys5)) (@ tptp.listrel_nat_int R2))))))))))
% 3.70/4.05 (assert (forall ((Y tptp.nat) (Ys tptp.list_nat) (Xs tptp.list_nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat (@ (@ tptp.cons_nat Y) Ys)) Xs)) (@ tptp.listrel_nat_nat R2)) (not (forall ((Y2 tptp.nat) (Ys5 tptp.list_nat)) (=> (= Xs (@ (@ tptp.cons_nat Y2) Ys5)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y) Y2)) R2) (not (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Ys) Ys5)) (@ tptp.listrel_nat_nat R2))))))))))
% 3.70/4.05 (assert (forall ((Y tptp.int) (Ys tptp.list_int) (Xs tptp.list_P8527749157015355191n_assn) (R2 tptp.set_Pr3255386646789011632n_assn)) (=> (@ (@ tptp.member490958779117458567n_assn (@ (@ tptp.produc4510294837168919970n_assn (@ (@ tptp.cons_int Y) Ys)) Xs)) (@ tptp.listre4888949683985722578n_assn R2)) (not (forall ((Y2 tptp.produc6575502325842934193n_assn) (Ys5 tptp.list_P8527749157015355191n_assn)) (=> (= Xs (@ (@ tptp.cons_P2971678138204555879n_assn Y2) Ys5)) (=> (@ (@ tptp.member241480614033477777n_assn (@ (@ tptp.produc3313821056773121708n_assn Y) Y2)) R2) (not (@ (@ tptp.member490958779117458567n_assn (@ (@ tptp.produc4510294837168919970n_assn Ys) Ys5)) (@ tptp.listre4888949683985722578n_assn R2))))))))))
% 3.70/4.05 (assert (forall ((Y tptp.nat) (Ys tptp.list_nat) (Xs tptp.list_P8527749157015355191n_assn) (R2 tptp.set_Pr247834672394327052n_assn)) (=> (@ (@ tptp.member3687432546746012131n_assn (@ (@ tptp.produc7706768604797473534n_assn (@ (@ tptp.cons_nat Y) Ys)) Xs)) (@ tptp.listre3128913020232611374n_assn R2)) (not (forall ((Y2 tptp.produc6575502325842934193n_assn) (Ys5 tptp.list_P8527749157015355191n_assn)) (=> (= Xs (@ (@ tptp.cons_P2971678138204555879n_assn Y2) Ys5)) (=> (@ (@ tptp.member7704815987135142381n_assn (@ (@ tptp.produc1553784393020010504n_assn Y) Y2)) R2) (not (@ (@ tptp.member3687432546746012131n_assn (@ (@ tptp.produc7706768604797473534n_assn Ys) Ys5)) (@ tptp.listre3128913020232611374n_assn R2))))))))))
% 3.70/4.05 (assert (forall ((Y tptp.produc6575502325842934193n_assn) (Ys tptp.list_P8527749157015355191n_assn) (Xs tptp.list_int) (R2 tptp.set_Pr2181989527757714242sn_int)) (=> (@ (@ tptp.member5295696281703116473st_int (@ (@ tptp.produc1996262876970182428st_int (@ (@ tptp.cons_P2971678138204555879n_assn Y) Ys)) Xs)) (@ tptp.listre8029020076619294380sn_int R2)) (not (forall ((Y2 tptp.int) (Ys5 tptp.list_int)) (=> (= Xs (@ (@ tptp.cons_int Y2) Ys5)) (=> (@ (@ tptp.member5792320502188913699sn_int (@ (@ tptp.produc6453891449406693510sn_int Y) Y2)) R2) (not (@ (@ tptp.member5295696281703116473st_int (@ (@ tptp.produc1996262876970182428st_int Ys) Ys5)) (@ tptp.listre8029020076619294380sn_int R2))))))))))
% 3.70/4.05 (assert (forall ((Y tptp.produc6575502325842934193n_assn) (Ys tptp.list_P8527749157015355191n_assn) (Xs tptp.list_nat) (R2 tptp.set_Pr4672072672689440998sn_nat)) (=> (@ (@ tptp.member7785779426634843229st_nat (@ (@ tptp.produc6174113896479379136st_nat (@ (@ tptp.cons_P2971678138204555879n_assn Y) Ys)) Xs)) (@ tptp.listre8031510547128344656sn_nat R2)) (not (forall ((Y2 tptp.nat) (Ys5 tptp.list_nat)) (=> (= Xs (@ (@ tptp.cons_nat Y2) Ys5)) (=> (@ (@ tptp.member746799484843334599sn_nat (@ (@ tptp.produc6456381919915743786sn_nat Y) Y2)) R2) (not (@ (@ tptp.member7785779426634843229st_nat (@ (@ tptp.produc6174113896479379136st_nat Ys) Ys5)) (@ tptp.listre8031510547128344656sn_nat R2))))))))))
% 3.70/4.05 (assert (forall ((Y tptp.produc6575502325842934193n_assn) (Ys tptp.list_P8527749157015355191n_assn) (Xs tptp.list_P8527749157015355191n_assn) (R2 tptp.set_Pr8116311503512020807n_assn)) (=> (@ (@ tptp.member3994142547374651152n_assn (@ (@ tptp.produc3014731801419794263n_assn (@ (@ tptp.cons_P2971678138204555879n_assn Y) Ys)) Xs)) (@ tptp.listre5253995379918703921n_assn R2)) (not (forall ((Y2 tptp.produc6575502325842934193n_assn) (Ys5 tptp.list_P8527749157015355191n_assn)) (=> (= Xs (@ (@ tptp.cons_P2971678138204555879n_assn Y2) Ys5)) (=> (@ (@ tptp.member4743710847862083984n_assn (@ (@ tptp.produc6128706242671166167n_assn Y) Y2)) R2) (not (@ (@ tptp.member3994142547374651152n_assn (@ (@ tptp.produc3014731801419794263n_assn Ys) Ys5)) (@ tptp.listre5253995379918703921n_assn R2))))))))))
% 3.70/4.05 (assert (forall ((Y tptp.set_Pr1261947904930325089at_nat) (Ys tptp.list_s1210847774152347623at_nat) (Xs tptp.list_s1210847774152347623at_nat) (R2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat (@ (@ tptp.cons_s6881495754146722583at_nat Y) Ys)) Xs)) (@ tptp.listre2047417242196832561at_nat R2)) (not (forall ((Y2 tptp.set_Pr1261947904930325089at_nat) (Ys5 tptp.list_s1210847774152347623at_nat)) (=> (= Xs (@ (@ tptp.cons_s6881495754146722583at_nat Y2) Ys5)) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat Y) Y2)) R2) (not (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat Ys) Ys5)) (@ tptp.listre2047417242196832561at_nat R2))))))))))
% 3.70/4.05 (assert (forall ((X tptp.int) (Y tptp.int) (R2 tptp.set_Pr958786334691620121nt_int) (Xs tptp.list_int) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.listrel_int_int R2))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) R2) (=> (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Xs) Ys)) _let_1) (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int (@ (@ tptp.cons_int X) Xs)) (@ (@ tptp.cons_int Y) Ys))) _let_1))))))
% 3.70/4.05 (assert (forall ((X tptp.int) (Y tptp.nat) (R2 tptp.set_Pr3448869479623346877nt_nat) (Xs tptp.list_int) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.listrel_int_nat R2))) (=> (@ (@ tptp.member216504246829706758nt_nat (@ (@ tptp.product_Pair_int_nat X) Y)) R2) (=> (@ (@ tptp.member9189046780804443046st_nat (@ (@ tptp.produc4542114716404682293st_nat Xs) Ys)) _let_1) (@ (@ tptp.member9189046780804443046st_nat (@ (@ tptp.produc4542114716404682293st_nat (@ (@ tptp.cons_int X) Xs)) (@ (@ tptp.cons_nat Y) Ys))) _let_1))))))
% 3.70/4.05 (assert (forall ((X tptp.nat) (Y tptp.int) (R2 tptp.set_Pr7995236796853374141at_int) (Xs tptp.list_nat) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.listrel_nat_int R2))) (=> (@ (@ tptp.member4262671552274231302at_int (@ (@ tptp.product_Pair_nat_int X) Y)) R2) (=> (@ (@ tptp.member4850886304473975718st_int (@ (@ tptp.produc7739558402351520821st_int Xs) Ys)) _let_1) (@ (@ tptp.member4850886304473975718st_int (@ (@ tptp.produc7739558402351520821st_int (@ (@ tptp.cons_nat X) Xs)) (@ (@ tptp.cons_int Y) Ys))) _let_1))))))
% 3.70/4.05 (assert (forall ((X tptp.nat) (Y tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (Xs tptp.list_nat) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.listrel_nat_nat R2))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) R2) (=> (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Xs) Ys)) _let_1) (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat (@ (@ tptp.cons_nat X) Xs)) (@ (@ tptp.cons_nat Y) Ys))) _let_1))))))
% 3.70/4.05 (assert (forall ((X tptp.int) (Y tptp.produc6575502325842934193n_assn) (R2 tptp.set_Pr3255386646789011632n_assn) (Xs tptp.list_int) (Ys tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ tptp.listre4888949683985722578n_assn R2))) (=> (@ (@ tptp.member241480614033477777n_assn (@ (@ tptp.produc3313821056773121708n_assn X) Y)) R2) (=> (@ (@ tptp.member490958779117458567n_assn (@ (@ tptp.produc4510294837168919970n_assn Xs) Ys)) _let_1) (@ (@ tptp.member490958779117458567n_assn (@ (@ tptp.produc4510294837168919970n_assn (@ (@ tptp.cons_int X) Xs)) (@ (@ tptp.cons_P2971678138204555879n_assn Y) Ys))) _let_1))))))
% 3.70/4.05 (assert (forall ((X tptp.nat) (Y tptp.produc6575502325842934193n_assn) (R2 tptp.set_Pr247834672394327052n_assn) (Xs tptp.list_nat) (Ys tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ tptp.listre3128913020232611374n_assn R2))) (=> (@ (@ tptp.member7704815987135142381n_assn (@ (@ tptp.produc1553784393020010504n_assn X) Y)) R2) (=> (@ (@ tptp.member3687432546746012131n_assn (@ (@ tptp.produc7706768604797473534n_assn Xs) Ys)) _let_1) (@ (@ tptp.member3687432546746012131n_assn (@ (@ tptp.produc7706768604797473534n_assn (@ (@ tptp.cons_nat X) Xs)) (@ (@ tptp.cons_P2971678138204555879n_assn Y) Ys))) _let_1))))))
% 3.70/4.05 (assert (forall ((X tptp.produc6575502325842934193n_assn) (Y tptp.int) (R2 tptp.set_Pr2181989527757714242sn_int) (Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.listre8029020076619294380sn_int R2))) (=> (@ (@ tptp.member5792320502188913699sn_int (@ (@ tptp.produc6453891449406693510sn_int X) Y)) R2) (=> (@ (@ tptp.member5295696281703116473st_int (@ (@ tptp.produc1996262876970182428st_int Xs) Ys)) _let_1) (@ (@ tptp.member5295696281703116473st_int (@ (@ tptp.produc1996262876970182428st_int (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) (@ (@ tptp.cons_int Y) Ys))) _let_1))))))
% 3.70/4.05 (assert (forall ((X tptp.produc6575502325842934193n_assn) (Y tptp.nat) (R2 tptp.set_Pr4672072672689440998sn_nat) (Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.listre8031510547128344656sn_nat R2))) (=> (@ (@ tptp.member746799484843334599sn_nat (@ (@ tptp.produc6456381919915743786sn_nat X) Y)) R2) (=> (@ (@ tptp.member7785779426634843229st_nat (@ (@ tptp.produc6174113896479379136st_nat Xs) Ys)) _let_1) (@ (@ tptp.member7785779426634843229st_nat (@ (@ tptp.produc6174113896479379136st_nat (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) (@ (@ tptp.cons_nat Y) Ys))) _let_1))))))
% 3.70/4.05 (assert (forall ((X tptp.produc6575502325842934193n_assn) (Y tptp.produc6575502325842934193n_assn) (R2 tptp.set_Pr8116311503512020807n_assn) (Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ tptp.listre5253995379918703921n_assn R2))) (=> (@ (@ tptp.member4743710847862083984n_assn (@ (@ tptp.produc6128706242671166167n_assn X) Y)) R2) (=> (@ (@ tptp.member3994142547374651152n_assn (@ (@ tptp.produc3014731801419794263n_assn Xs) Ys)) _let_1) (@ (@ tptp.member3994142547374651152n_assn (@ (@ tptp.produc3014731801419794263n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) (@ (@ tptp.cons_P2971678138204555879n_assn Y) Ys))) _let_1))))))
% 3.70/4.05 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (R2 tptp.set_Pr4329608150637261639at_nat) (Xs tptp.list_s1210847774152347623at_nat) (Ys tptp.list_s1210847774152347623at_nat)) (let ((_let_1 (@ tptp.listre2047417242196832561at_nat R2))) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Y)) R2) (=> (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat Xs) Ys)) _let_1) (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat (@ (@ tptp.cons_s6881495754146722583at_nat X) Xs)) (@ (@ tptp.cons_s6881495754146722583at_nat Y) Ys))) _let_1))))))
% 3.70/4.05 (assert (forall ((X21 tptp.produc6575502325842934193n_assn) (X222 tptp.list_P8527749157015355191n_assn)) (= (@ tptp.size_s6829681357464350627n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X21) X222)) (@ (@ tptp.plus_plus_nat (@ tptp.size_s6829681357464350627n_assn X222)) (@ tptp.suc tptp.zero_zero_nat)))))
% 3.70/4.05 (assert (forall ((X21 tptp.c) (X222 tptp.list_c)) (= (@ tptp.size_size_list_c (@ (@ tptp.cons_c X21) X222)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_list_c X222)) (@ tptp.suc tptp.zero_zero_nat)))))
% 3.70/4.05 (assert (forall ((X21 tptp.d) (X222 tptp.list_d)) (= (@ tptp.size_size_list_d (@ (@ tptp.cons_d X21) X222)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_list_d X222)) (@ tptp.suc tptp.zero_zero_nat)))))
% 3.70/4.05 (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)))))
% 3.70/4.05 (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)))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (X tptp.int) (Xs tptp.list_int)) (let ((_let_1 (@ (@ tptp.nth_int (@ (@ tptp.cons_int X) Xs)) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_int Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (X tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X) Xs)) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_nat Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ (@ tptp.nth_Pr1769885009046257848n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_Pr1769885009046257848n_assn Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))))
% 3.70/4.05 (assert (forall ((X tptp.produc3843707927480180839at_nat) (Xs tptp.list_P5464809261938338413at_nat) (N tptp.nat)) (=> (not (@ (@ tptp.member8757157785044589968at_nat X) (@ tptp.set_Pr3765526544606949372at_nat Xs))) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_s1588839187904960729at_nat Xs)) (= (= (@ (@ tptp.nth_Pr1239524528086697198at_nat (@ (@ tptp.cons_P3940603068885512221at_nat X) Xs)) N) X) (= N tptp.zero_zero_nat))))))
% 3.70/4.05 (assert (forall ((X tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat) (N tptp.nat)) (=> (not (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs))) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_s5460976970255530739at_nat Xs)) (= (= (@ (@ tptp.nth_Pr7617993195940197384at_nat (@ (@ tptp.cons_P6512896166579812791at_nat X) Xs)) N) X) (= N tptp.zero_zero_nat))))))
% 3.70/4.05 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xs tptp.list_P7985473006766602707_nat_o) (N tptp.nat)) (=> (not (@ (@ tptp.member6576561426505652726_nat_o X) (@ tptp.set_Pr400311997697478754_nat_o Xs))) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_s8908918004648414271_nat_o Xs)) (= (= (@ (@ tptp.nth_Pr6840583978799713108_nat_o (@ (@ tptp.cons_P6219271836124797827_nat_o X) Xs)) N) X) (= N tptp.zero_zero_nat))))))
% 3.70/4.05 (assert (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn) (N tptp.nat)) (=> (not (@ (@ tptp.member7957490590177025114n_assn X) (@ tptp.set_Pr1139785259514867910n_assn Xs))) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_s6829681357464350627n_assn Xs)) (= (= (@ (@ tptp.nth_Pr1769885009046257848n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) N) X) (= N tptp.zero_zero_nat))))))
% 3.70/4.05 (assert (forall ((X tptp.c) (Xs tptp.list_c) (N tptp.nat)) (=> (not (@ (@ tptp.member_c X) (@ tptp.set_c2 Xs))) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_c Xs)) (= (= (@ (@ tptp.nth_c (@ (@ tptp.cons_c X) Xs)) N) X) (= N tptp.zero_zero_nat))))))
% 3.70/4.05 (assert (forall ((X tptp.d) (Xs tptp.list_d) (N tptp.nat)) (=> (not (@ (@ tptp.member_d X) (@ tptp.set_d2 Xs))) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_d Xs)) (= (= (@ (@ tptp.nth_d (@ (@ tptp.cons_d X) Xs)) N) X) (= N tptp.zero_zero_nat))))))
% 3.70/4.05 (assert (forall ((X tptp.nat) (Xs tptp.list_nat) (N tptp.nat)) (=> (not (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs))) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_nat Xs)) (= (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X) Xs)) N) X) (= N tptp.zero_zero_nat))))))
% 3.70/4.05 (assert (forall ((X tptp.int) (Xs tptp.list_int) (N tptp.nat)) (=> (not (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs))) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_int Xs)) (= (= (@ (@ tptp.nth_int (@ (@ tptp.cons_int X) Xs)) N) X) (= N tptp.zero_zero_nat))))))
% 3.70/4.05 (assert (forall ((X tptp.int) (Y tptp.int) (Xs tptp.list_int) (N tptp.nat)) (=> (not (= X Y)) (= (= (@ (@ tptp.nth_int (@ (@ tptp.cons_int X) Xs)) N) Y) (and (= (@ (@ tptp.nth_int Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) Y) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))))
% 3.70/4.05 (assert (forall ((X tptp.nat) (Y tptp.nat) (Xs tptp.list_nat) (N tptp.nat)) (=> (not (= X Y)) (= (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X) Xs)) N) Y) (and (= (@ (@ tptp.nth_nat Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) Y) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))))
% 3.70/4.05 (assert (forall ((X tptp.produc6575502325842934193n_assn) (Y tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn) (N tptp.nat)) (=> (not (= X Y)) (= (= (@ (@ tptp.nth_Pr1769885009046257848n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) N) Y) (and (= (@ (@ tptp.nth_Pr1769885009046257848n_assn Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) Y) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))))
% 3.70/4.05 (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)))))))))))
% 3.70/4.05 (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)))))))))))
% 3.70/4.05 (assert (forall ((Begin tptp.nat) (End tptp.nat) (X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ (@ tptp.minus_minus_nat End) tptp.one_one_nat))) (let ((_let_2 (@ tptp.cons_P2971678138204555879n_assn X))) (let ((_let_3 (@ tptp.slice_7964966981652229398n_assn 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_7964966981652229398n_assn (@ (@ tptp.minus_minus_nat Begin) tptp.one_one_nat)) _let_1) Xs)))))))))))
% 3.70/4.05 (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 ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As))) (=> (= Xb _let_1) (=> (= Y (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) (@ 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)))))))))))))
% 3.70/4.05 (assert (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (= (@ tptp.size_s6829681357464350627n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) (@ tptp.suc (@ tptp.size_s6829681357464350627n_assn Xs)))))
% 3.70/4.05 (assert (forall ((X tptp.c) (Xs tptp.list_c)) (= (@ tptp.size_size_list_c (@ (@ tptp.cons_c X) Xs)) (@ tptp.suc (@ tptp.size_size_list_c Xs)))))
% 3.70/4.05 (assert (forall ((X tptp.d) (Xs tptp.list_d)) (= (@ tptp.size_size_list_d (@ (@ tptp.cons_d X) Xs)) (@ tptp.suc (@ tptp.size_size_list_d Xs)))))
% 3.70/4.05 (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)))))
% 3.70/4.05 (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)))))
% 3.70/4.05 (assert (forall ((M2 tptp.set_Pr1261947904930325089at_nat) (Ms tptp.list_s1210847774152347623at_nat) (N tptp.set_Pr1261947904930325089at_nat) (Ns tptp.list_s1210847774152347623at_nat) (R2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.lenlex1357538814655152620at_nat R2))) (let ((_let_2 (@ tptp.size_s8736152011456118867at_nat Ns))) (let ((_let_3 (@ tptp.size_s8736152011456118867at_nat Ms))) (= (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat (@ (@ tptp.cons_s6881495754146722583at_nat M2) Ms)) (@ (@ tptp.cons_s6881495754146722583at_nat N) Ns))) _let_1) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat M2) N)) R2)) (and (= M2 N) (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat Ms) Ns)) _let_1)))))))))
% 3.70/4.05 (assert (forall ((M2 tptp.produc6575502325842934193n_assn) (Ms tptp.list_P8527749157015355191n_assn) (N tptp.produc6575502325842934193n_assn) (Ns tptp.list_P8527749157015355191n_assn) (R2 tptp.set_Pr8116311503512020807n_assn)) (let ((_let_1 (@ tptp.lenlex6671093235567761724n_assn R2))) (let ((_let_2 (@ tptp.size_s6829681357464350627n_assn Ns))) (let ((_let_3 (@ tptp.size_s6829681357464350627n_assn Ms))) (= (@ (@ tptp.member3994142547374651152n_assn (@ (@ tptp.produc3014731801419794263n_assn (@ (@ tptp.cons_P2971678138204555879n_assn M2) Ms)) (@ (@ tptp.cons_P2971678138204555879n_assn N) Ns))) _let_1) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ (@ tptp.member4743710847862083984n_assn (@ (@ tptp.produc6128706242671166167n_assn M2) N)) R2)) (and (= M2 N) (@ (@ tptp.member3994142547374651152n_assn (@ (@ tptp.produc3014731801419794263n_assn Ms) Ns)) _let_1)))))))))
% 3.70/4.05 (assert (forall ((M2 tptp.c) (Ms tptp.list_c) (N tptp.c) (Ns tptp.list_c) (R2 tptp.set_Product_prod_c_c)) (let ((_let_1 (@ tptp.lenlex_c R2))) (let ((_let_2 (@ tptp.size_size_list_c Ns))) (let ((_let_3 (@ tptp.size_size_list_c Ms))) (= (@ (@ tptp.member7012247553653173456list_c (@ (@ tptp.produc5515445818230282391list_c (@ (@ tptp.cons_c M2) Ms)) (@ (@ tptp.cons_c N) Ns))) _let_1) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ (@ tptp.member5074992359041316560od_c_c (@ (@ tptp.product_Pair_c_c M2) N)) R2)) (and (= M2 N) (@ (@ tptp.member7012247553653173456list_c (@ (@ tptp.produc5515445818230282391list_c Ms) Ns)) _let_1)))))))))
% 3.70/4.05 (assert (forall ((M2 tptp.d) (Ms tptp.list_d) (N tptp.d) (Ns tptp.list_d) (R2 tptp.set_Product_prod_d_d)) (let ((_let_1 (@ tptp.lenlex_d R2))) (let ((_let_2 (@ tptp.size_size_list_d Ns))) (let ((_let_3 (@ tptp.size_size_list_d Ms))) (= (@ (@ tptp.member1810801192463332112list_d (@ (@ tptp.produc242965421297323863list_d (@ (@ tptp.cons_d M2) Ms)) (@ (@ tptp.cons_d N) Ns))) _let_1) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ (@ tptp.member2287536781371869328od_d_d (@ (@ tptp.product_Pair_d_d M2) N)) R2)) (and (= M2 N) (@ (@ tptp.member1810801192463332112list_d (@ (@ tptp.produc242965421297323863list_d Ms) Ns)) _let_1)))))))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (Ms tptp.list_nat) (N tptp.nat) (Ns tptp.list_nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.lenlex_nat R2))) (let ((_let_2 (@ tptp.size_size_list_nat Ns))) (let ((_let_3 (@ tptp.size_size_list_nat Ms))) (= (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat (@ (@ tptp.cons_nat M2) Ms)) (@ (@ tptp.cons_nat N) Ns))) _let_1) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat M2) N)) R2)) (and (= M2 N) (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Ms) Ns)) _let_1)))))))))
% 3.70/4.05 (assert (forall ((M2 tptp.int) (Ms tptp.list_int) (N tptp.int) (Ns tptp.list_int) (R2 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.lenlex_int R2))) (let ((_let_2 (@ tptp.size_size_list_int Ns))) (let ((_let_3 (@ tptp.size_size_list_int Ms))) (= (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int (@ (@ tptp.cons_int M2) Ms)) (@ (@ tptp.cons_int N) Ns))) _let_1) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int M2) N)) R2)) (and (= M2 N) (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Ms) Ns)) _let_1)))))))))
% 3.70/4.05 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Xs tptp.list_s1210847774152347623at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Ys tptp.list_s1210847774152347623at_nat) (R2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.lex_se2245640040323279819at_nat R2))) (= (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat (@ (@ tptp.cons_s6881495754146722583at_nat X) Xs)) (@ (@ tptp.cons_s6881495754146722583at_nat Y) Ys))) _let_1) (or (and (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Y)) R2) (= (@ tptp.size_s8736152011456118867at_nat Xs) (@ tptp.size_s8736152011456118867at_nat Ys))) (and (= X Y) (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat Xs) Ys)) _let_1)))))))
% 3.70/4.05 (assert (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn) (Y tptp.produc6575502325842934193n_assn) (Ys tptp.list_P8527749157015355191n_assn) (R2 tptp.set_Pr8116311503512020807n_assn)) (let ((_let_1 (@ tptp.lex_Pr7559194461235888923n_assn R2))) (= (@ (@ tptp.member3994142547374651152n_assn (@ (@ tptp.produc3014731801419794263n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) (@ (@ tptp.cons_P2971678138204555879n_assn Y) Ys))) _let_1) (or (and (@ (@ tptp.member4743710847862083984n_assn (@ (@ tptp.produc6128706242671166167n_assn X) Y)) R2) (= (@ tptp.size_s6829681357464350627n_assn Xs) (@ tptp.size_s6829681357464350627n_assn Ys))) (and (= X Y) (@ (@ tptp.member3994142547374651152n_assn (@ (@ tptp.produc3014731801419794263n_assn Xs) Ys)) _let_1)))))))
% 3.70/4.05 (assert (forall ((X tptp.c) (Xs tptp.list_c) (Y tptp.c) (Ys tptp.list_c) (R2 tptp.set_Product_prod_c_c)) (let ((_let_1 (@ tptp.lex_c R2))) (= (@ (@ tptp.member7012247553653173456list_c (@ (@ tptp.produc5515445818230282391list_c (@ (@ tptp.cons_c X) Xs)) (@ (@ tptp.cons_c Y) Ys))) _let_1) (or (and (@ (@ tptp.member5074992359041316560od_c_c (@ (@ tptp.product_Pair_c_c X) Y)) R2) (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_c Ys))) (and (= X Y) (@ (@ tptp.member7012247553653173456list_c (@ (@ tptp.produc5515445818230282391list_c Xs) Ys)) _let_1)))))))
% 3.70/4.05 (assert (forall ((X tptp.d) (Xs tptp.list_d) (Y tptp.d) (Ys tptp.list_d) (R2 tptp.set_Product_prod_d_d)) (let ((_let_1 (@ tptp.lex_d R2))) (= (@ (@ tptp.member1810801192463332112list_d (@ (@ tptp.produc242965421297323863list_d (@ (@ tptp.cons_d X) Xs)) (@ (@ tptp.cons_d Y) Ys))) _let_1) (or (and (@ (@ tptp.member2287536781371869328od_d_d (@ (@ tptp.product_Pair_d_d X) Y)) R2) (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_d Ys))) (and (= X Y) (@ (@ tptp.member1810801192463332112list_d (@ (@ tptp.produc242965421297323863list_d Xs) Ys)) _let_1)))))))
% 3.70/4.05 (assert (forall ((X tptp.nat) (Xs tptp.list_nat) (Y tptp.nat) (Ys tptp.list_nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.lex_nat R2))) (= (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat (@ (@ tptp.cons_nat X) Xs)) (@ (@ tptp.cons_nat Y) Ys))) _let_1) (or (and (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) R2) (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys))) (and (= X Y) (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Xs) Ys)) _let_1)))))))
% 3.70/4.05 (assert (forall ((X tptp.int) (Xs tptp.list_int) (Y tptp.int) (Ys tptp.list_int) (R2 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.lex_int R2))) (= (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int (@ (@ tptp.cons_int X) Xs)) (@ (@ tptp.cons_int Y) Ys))) _let_1) (or (and (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) R2) (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys))) (and (= X Y) (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Xs) Ys)) _let_1)))))))
% 3.70/4.05 (assert (forall ((X (-> tptp.int tptp.int tptp.assn)) (Xa tptp.list_int) (Xb tptp.list_int) (Y tptp.assn)) (let ((_let_1 (not (= Y tptp.bot_bot_assn)))) (let ((_let_2 (= Xa tptp.nil_int))) (let ((_let_3 (= Xb tptp.nil_int))) (=> (= (@ (@ (@ tptp.vEBT_L74593716426352029nt_int X) Xa) Xb) Y) (=> (=> _let_2 (=> _let_3 (not (= Y tptp.one_one_assn)))) (=> (forall ((A4 tptp.int) (As tptp.list_int)) (=> (= Xa (@ (@ tptp.cons_int A4) As)) (forall ((C4 tptp.int) (Cs2 tptp.list_int)) (=> (= Xb (@ (@ tptp.cons_int C4) Cs2)) (not (= Y (@ (@ tptp.times_times_assn (@ (@ X A4) C4)) (@ (@ (@ tptp.vEBT_L74593716426352029nt_int X) As) Cs2)))))))) (=> (=> (exists ((V3 tptp.int) (Va tptp.list_int)) (= Xa (@ (@ tptp.cons_int V3) Va))) (=> _let_3 _let_1)) (not (=> _let_2 (=> (exists ((V3 tptp.int) (Va tptp.list_int)) (= Xb (@ (@ tptp.cons_int V3) Va))) _let_1))))))))))))
% 3.70/4.05 (assert (forall ((X (-> tptp.int tptp.nat tptp.assn)) (Xa tptp.list_int) (Xb tptp.list_nat) (Y tptp.assn)) (let ((_let_1 (not (= Y tptp.bot_bot_assn)))) (let ((_let_2 (= Xa tptp.nil_int))) (let ((_let_3 (= Xb tptp.nil_nat))) (=> (= (@ (@ (@ tptp.vEBT_L77084186935402305nt_nat X) Xa) Xb) Y) (=> (=> _let_2 (=> _let_3 (not (= Y tptp.one_one_assn)))) (=> (forall ((A4 tptp.int) (As tptp.list_int)) (=> (= Xa (@ (@ tptp.cons_int A4) As)) (forall ((C4 tptp.nat) (Cs2 tptp.list_nat)) (=> (= Xb (@ (@ tptp.cons_nat C4) Cs2)) (not (= Y (@ (@ tptp.times_times_assn (@ (@ X A4) C4)) (@ (@ (@ tptp.vEBT_L77084186935402305nt_nat X) As) Cs2)))))))) (=> (=> (exists ((V3 tptp.int) (Va tptp.list_int)) (= Xa (@ (@ tptp.cons_int V3) Va))) (=> _let_3 _let_1)) (not (=> _let_2 (=> (exists ((V3 tptp.nat) (Va tptp.list_nat)) (= Xb (@ (@ tptp.cons_nat V3) Va))) _let_1))))))))))))
% 3.70/4.05 (assert (forall ((X (-> tptp.int tptp.produc6575502325842934193n_assn tptp.assn)) (Xa tptp.list_int) (Xb tptp.list_P8527749157015355191n_assn) (Y tptp.assn)) (let ((_let_1 (not (= Y tptp.bot_bot_assn)))) (let ((_let_2 (= Xa tptp.nil_int))) (let ((_let_3 (= Xb tptp.nil_Pr5671120429643327159n_assn))) (=> (= (@ (@ (@ tptp.vEBT_L1620274777744359680n_assn X) Xa) Xb) Y) (=> (=> _let_2 (=> _let_3 (not (= Y tptp.one_one_assn)))) (=> (forall ((A4 tptp.int) (As tptp.list_int)) (=> (= Xa (@ (@ tptp.cons_int A4) As)) (forall ((C4 tptp.produc6575502325842934193n_assn) (Cs2 tptp.list_P8527749157015355191n_assn)) (=> (= Xb (@ (@ tptp.cons_P2971678138204555879n_assn C4) Cs2)) (not (= Y (@ (@ tptp.times_times_assn (@ (@ X A4) C4)) (@ (@ (@ tptp.vEBT_L1620274777744359680n_assn X) As) Cs2)))))))) (=> (=> (exists ((V3 tptp.int) (Va tptp.list_int)) (= Xa (@ (@ tptp.cons_int V3) Va))) (=> _let_3 _let_1)) (not (=> _let_2 (=> (exists ((V3 tptp.produc6575502325842934193n_assn) (Va tptp.list_P8527749157015355191n_assn)) (= Xb (@ (@ tptp.cons_P2971678138204555879n_assn V3) Va))) _let_1))))))))))))
% 3.70/4.05 (assert (forall ((X (-> tptp.nat tptp.int tptp.assn)) (Xa tptp.list_nat) (Xb tptp.list_int) (Y tptp.assn)) (let ((_let_1 (not (= Y tptp.bot_bot_assn)))) (let ((_let_2 (= Xa tptp.nil_nat))) (let ((_let_3 (= Xb tptp.nil_int))) (=> (= (@ (@ (@ tptp.vEBT_L8298612041380073281at_int X) Xa) Xb) Y) (=> (=> _let_2 (=> _let_3 (not (= Y tptp.one_one_assn)))) (=> (forall ((A4 tptp.nat) (As tptp.list_nat)) (=> (= Xa (@ (@ tptp.cons_nat A4) As)) (forall ((C4 tptp.int) (Cs2 tptp.list_int)) (=> (= Xb (@ (@ tptp.cons_int C4) Cs2)) (not (= Y (@ (@ tptp.times_times_assn (@ (@ X A4) C4)) (@ (@ (@ tptp.vEBT_L8298612041380073281at_int X) As) Cs2)))))))) (=> (=> (exists ((V3 tptp.nat) (Va tptp.list_nat)) (= Xa (@ (@ tptp.cons_nat V3) Va))) (=> _let_3 _let_1)) (not (=> _let_2 (=> (exists ((V3 tptp.int) (Va tptp.list_int)) (= Xb (@ (@ tptp.cons_int V3) Va))) _let_1))))))))))))
% 3.70/4.05 (assert (forall ((X (-> tptp.nat tptp.nat tptp.assn)) (Xa tptp.list_nat) (Xb tptp.list_nat) (Y tptp.assn)) (let ((_let_1 (not (= Y tptp.bot_bot_assn)))) (let ((_let_2 (= Xa tptp.nil_nat))) (let ((_let_3 (= Xb tptp.nil_nat))) (=> (= (@ (@ (@ tptp.vEBT_L8301102511889123557at_nat X) Xa) Xb) Y) (=> (=> _let_2 (=> _let_3 (not (= Y tptp.one_one_assn)))) (=> (forall ((A4 tptp.nat) (As tptp.list_nat)) (=> (= Xa (@ (@ tptp.cons_nat A4) As)) (forall ((C4 tptp.nat) (Cs2 tptp.list_nat)) (=> (= Xb (@ (@ tptp.cons_nat C4) Cs2)) (not (= Y (@ (@ tptp.times_times_assn (@ (@ X A4) C4)) (@ (@ (@ tptp.vEBT_L8301102511889123557at_nat X) As) Cs2)))))))) (=> (=> (exists ((V3 tptp.nat) (Va tptp.list_nat)) (= Xa (@ (@ tptp.cons_nat V3) Va))) (=> _let_3 _let_1)) (not (=> _let_2 (=> (exists ((V3 tptp.nat) (Va tptp.list_nat)) (= Xb (@ (@ tptp.cons_nat V3) Va))) _let_1))))))))))))
% 3.70/4.05 (assert (forall ((X (-> tptp.nat tptp.produc6575502325842934193n_assn tptp.assn)) (Xa tptp.list_nat) (Xb tptp.list_P8527749157015355191n_assn) (Y tptp.assn)) (let ((_let_1 (not (= Y tptp.bot_bot_assn)))) (let ((_let_2 (= Xa tptp.nil_nat))) (let ((_let_3 (= Xb tptp.nil_Pr5671120429643327159n_assn))) (=> (= (@ (@ (@ tptp.vEBT_L9083610150846024284n_assn X) Xa) Xb) Y) (=> (=> _let_2 (=> _let_3 (not (= Y tptp.one_one_assn)))) (=> (forall ((A4 tptp.nat) (As tptp.list_nat)) (=> (= Xa (@ (@ tptp.cons_nat A4) As)) (forall ((C4 tptp.produc6575502325842934193n_assn) (Cs2 tptp.list_P8527749157015355191n_assn)) (=> (= Xb (@ (@ tptp.cons_P2971678138204555879n_assn C4) Cs2)) (not (= Y (@ (@ tptp.times_times_assn (@ (@ X A4) C4)) (@ (@ (@ tptp.vEBT_L9083610150846024284n_assn X) As) Cs2)))))))) (=> (=> (exists ((V3 tptp.nat) (Va tptp.list_nat)) (= Xa (@ (@ tptp.cons_nat V3) Va))) (=> _let_3 _let_1)) (not (=> _let_2 (=> (exists ((V3 tptp.produc6575502325842934193n_assn) (Va tptp.list_P8527749157015355191n_assn)) (= Xb (@ (@ tptp.cons_P2971678138204555879n_assn V3) Va))) _let_1))))))))))))
% 3.70/4.05 (assert (forall ((X (-> tptp.produc6575502325842934193n_assn tptp.int tptp.assn)) (Xa tptp.list_P8527749157015355191n_assn) (Xb tptp.list_int) (Y tptp.assn)) (let ((_let_1 (not (= Y tptp.bot_bot_assn)))) (let ((_let_2 (= Xa tptp.nil_Pr5671120429643327159n_assn))) (let ((_let_3 (= Xb tptp.nil_int))) (=> (= (@ (@ (@ tptp.vEBT_L4760345170377931482sn_int X) Xa) Xb) Y) (=> (=> _let_2 (=> _let_3 (not (= Y tptp.one_one_assn)))) (=> (forall ((A4 tptp.produc6575502325842934193n_assn) (As tptp.list_P8527749157015355191n_assn)) (=> (= Xa (@ (@ tptp.cons_P2971678138204555879n_assn A4) As)) (forall ((C4 tptp.int) (Cs2 tptp.list_int)) (=> (= Xb (@ (@ tptp.cons_int C4) Cs2)) (not (= Y (@ (@ tptp.times_times_assn (@ (@ X A4) C4)) (@ (@ (@ tptp.vEBT_L4760345170377931482sn_int X) As) Cs2)))))))) (=> (=> (exists ((V3 tptp.produc6575502325842934193n_assn) (Va tptp.list_P8527749157015355191n_assn)) (= Xa (@ (@ tptp.cons_P2971678138204555879n_assn V3) Va))) (=> _let_3 _let_1)) (not (=> _let_2 (=> (exists ((V3 tptp.int) (Va tptp.list_int)) (= Xb (@ (@ tptp.cons_int V3) Va))) _let_1))))))))))))
% 3.70/4.05 (assert (forall ((X (-> tptp.produc6575502325842934193n_assn tptp.nat tptp.assn)) (Xa tptp.list_P8527749157015355191n_assn) (Xb tptp.list_nat) (Y tptp.assn)) (let ((_let_1 (not (= Y tptp.bot_bot_assn)))) (let ((_let_2 (= Xa tptp.nil_Pr5671120429643327159n_assn))) (let ((_let_3 (= Xb tptp.nil_nat))) (=> (= (@ (@ (@ tptp.vEBT_L4762835640886981758sn_nat X) Xa) Xb) Y) (=> (=> _let_2 (=> _let_3 (not (= Y tptp.one_one_assn)))) (=> (forall ((A4 tptp.produc6575502325842934193n_assn) (As tptp.list_P8527749157015355191n_assn)) (=> (= Xa (@ (@ tptp.cons_P2971678138204555879n_assn A4) As)) (forall ((C4 tptp.nat) (Cs2 tptp.list_nat)) (=> (= Xb (@ (@ tptp.cons_nat C4) Cs2)) (not (= Y (@ (@ tptp.times_times_assn (@ (@ X A4) C4)) (@ (@ (@ tptp.vEBT_L4762835640886981758sn_nat X) As) Cs2)))))))) (=> (=> (exists ((V3 tptp.produc6575502325842934193n_assn) (Va tptp.list_P8527749157015355191n_assn)) (= Xa (@ (@ tptp.cons_P2971678138204555879n_assn V3) Va))) (=> _let_3 _let_1)) (not (=> _let_2 (=> (exists ((V3 tptp.nat) (Va tptp.list_nat)) (= Xb (@ (@ tptp.cons_nat V3) Va))) _let_1))))))))))))
% 3.70/4.05 (assert (forall ((X (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn tptp.assn)) (Xa tptp.list_P8527749157015355191n_assn) (Xb tptp.list_P8527749157015355191n_assn) (Y tptp.assn)) (let ((_let_1 (not (= Y tptp.bot_bot_assn)))) (let ((_let_2 (= Xa tptp.nil_Pr5671120429643327159n_assn))) (let ((_let_3 (= Xb tptp.nil_Pr5671120429643327159n_assn))) (=> (= (@ (@ (@ tptp.vEBT_L3108143461992071043n_assn X) Xa) Xb) Y) (=> (=> _let_2 (=> _let_3 (not (= Y tptp.one_one_assn)))) (=> (forall ((A4 tptp.produc6575502325842934193n_assn) (As tptp.list_P8527749157015355191n_assn)) (=> (= Xa (@ (@ tptp.cons_P2971678138204555879n_assn A4) As)) (forall ((C4 tptp.produc6575502325842934193n_assn) (Cs2 tptp.list_P8527749157015355191n_assn)) (=> (= Xb (@ (@ tptp.cons_P2971678138204555879n_assn C4) Cs2)) (not (= Y (@ (@ tptp.times_times_assn (@ (@ X A4) C4)) (@ (@ (@ tptp.vEBT_L3108143461992071043n_assn X) As) Cs2)))))))) (=> (=> (exists ((V3 tptp.produc6575502325842934193n_assn) (Va tptp.list_P8527749157015355191n_assn)) (= Xa (@ (@ tptp.cons_P2971678138204555879n_assn V3) Va))) (=> _let_3 _let_1)) (not (=> _let_2 (=> (exists ((V3 tptp.produc6575502325842934193n_assn) (Va tptp.list_P8527749157015355191n_assn)) (= Xb (@ (@ tptp.cons_P2971678138204555879n_assn V3) Va))) _let_1))))))))))))
% 3.70/4.05 (assert (forall ((X tptp.int) (Y tptp.int) (Xs tptp.list_int)) (let ((_let_1 (@ (@ tptp.count_list_int Xs) Y))) (let ((_let_2 (@ (@ tptp.count_list_int (@ (@ tptp.cons_int X) Xs)) Y))) (let ((_let_3 (= X Y))) (and (=> _let_3 (= _let_2 (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))))
% 3.70/4.05 (assert (forall ((X tptp.nat) (Y tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ (@ tptp.count_list_nat Xs) Y))) (let ((_let_2 (@ (@ tptp.count_list_nat (@ (@ tptp.cons_nat X) Xs)) Y))) (let ((_let_3 (= X Y))) (and (=> _let_3 (= _let_2 (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))))
% 3.70/4.05 (assert (forall ((X tptp.produc6575502325842934193n_assn) (Y tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ (@ tptp.count_2530312006313534765n_assn Xs) Y))) (let ((_let_2 (@ (@ tptp.count_2530312006313534765n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) Y))) (let ((_let_3 (= X Y))) (and (=> _let_3 (= _let_2 (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))))
% 3.70/4.05 (assert (forall ((X tptp.produc3843707927480180839at_nat) (Xs tptp.list_P5464809261938338413at_nat)) (=> (not (@ (@ tptp.member8757157785044589968at_nat X) (@ tptp.set_Pr3765526544606949372at_nat Xs))) (= (@ (@ tptp.count_1483299019173949923at_nat Xs) X) tptp.zero_zero_nat))))
% 3.70/4.05 (assert (forall ((X tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (=> (not (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs))) (= (@ (@ tptp.count_4203492906077236349at_nat Xs) X) tptp.zero_zero_nat))))
% 3.70/4.05 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xs tptp.list_P7985473006766602707_nat_o)) (=> (not (@ (@ tptp.member6576561426505652726_nat_o X) (@ tptp.set_Pr400311997697478754_nat_o Xs))) (= (@ (@ tptp.count_5695430372156137289_nat_o Xs) X) tptp.zero_zero_nat))))
% 3.70/4.05 (assert (forall ((X tptp.int) (Xs tptp.list_int)) (=> (not (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs))) (= (@ (@ tptp.count_list_int Xs) X) tptp.zero_zero_nat))))
% 3.70/4.05 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (=> (not (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs))) (= (@ (@ tptp.count_list_nat Xs) X) tptp.zero_zero_nat))))
% 3.70/4.05 (assert (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (=> (not (@ (@ tptp.member7957490590177025114n_assn X) (@ tptp.set_Pr1139785259514867910n_assn Xs))) (= (@ (@ tptp.count_2530312006313534765n_assn Xs) X) tptp.zero_zero_nat))))
% 3.70/4.05 (assert (forall ((B2 tptp.rat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B2))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B2) (=> (@ (@ tptp.ord_less_rat B2) tptp.one_one_rat) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M2)))))))
% 3.70/4.05 (assert (forall ((B2 tptp.code_integer) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger B2))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) tptp.one_one_Code_integer) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M2)))))))
% 3.70/4.05 (assert (forall ((B2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (=> (@ (@ tptp.ord_less_nat B2) tptp.one_one_nat) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M2)))))))
% 3.70/4.05 (assert (forall ((B2 tptp.int) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_int B2) tptp.one_one_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M2)))))))
% 3.70/4.05 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (F4 (-> tptp.set_Pr1261947904930325089at_nat tptp.nat)) (Fs tptp.list_s9130966667114977576at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Y)))) (let ((_let_2 (@ F4 Y))) (let ((_let_3 (@ F4 X))) (= (@ _let_1 (@ tptp.measur2694323259624372065at_nat (@ (@ tptp.cons_s2538900923071588440at_nat F4) Fs))) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ _let_1 (@ tptp.measur2694323259624372065at_nat Fs))))))))))
% 3.70/4.05 (assert (forall ((X tptp.nat) (Y tptp.nat) (F4 (-> tptp.nat tptp.nat)) (Fs tptp.list_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)))) (let ((_let_2 (@ F4 Y))) (let ((_let_3 (@ F4 X))) (= (@ _let_1 (@ tptp.measures_nat (@ (@ tptp.cons_nat_nat F4) Fs))) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ _let_1 (@ tptp.measures_nat Fs))))))))))
% 3.70/4.05 (assert (forall ((X tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat X) N)) (or (@ _let_1 X) (= N tptp.zero_zero_nat))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (= (= (@ (@ tptp.zip_int_int Xs) Ys) tptp.nil_Pr2300489316682597567nt_int) (or (= Xs tptp.nil_int) (= Ys tptp.nil_int)))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_nat)) (= (= (@ (@ tptp.zip_int_nat Xs) Ys) tptp.nil_Pr6478340336191794275nt_nat) (or (= Xs tptp.nil_int) (= Ys tptp.nil_nat)))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_P8527749157015355191n_assn)) (= (= (@ (@ tptp.zip_in7098856637274830732n_assn Xs) Ys) tptp.nil_Pr2440414457004260852n_assn) (or (= Xs tptp.nil_int) (= Ys tptp.nil_Pr5671120429643327159n_assn)))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_int)) (= (= (@ (@ tptp.zip_nat_int Xs) Ys) tptp.nil_Pr1301135604781543011at_int) (or (= Xs tptp.nil_nat) (= Ys tptp.nil_int)))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (= (= (@ (@ tptp.zip_nat_nat Xs) Ys) tptp.nil_Pr5478986624290739719at_nat) (or (= Xs tptp.nil_nat) (= Ys tptp.nil_nat)))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_P8527749157015355191n_assn)) (= (= (@ (@ tptp.zip_na5338819973521719528n_assn Xs) Ys) tptp.nil_Pr680377793251149648n_assn) (or (= Xs tptp.nil_nat) (= Ys tptp.nil_Pr5671120429643327159n_assn)))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_int)) (= (= (@ (@ tptp.zip_Pr1015554993053626726sn_int Xs) Ys) tptp.nil_Pr7991254345159696774sn_int) (or (= Xs tptp.nil_Pr5671120429643327159n_assn) (= Ys tptp.nil_int)))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_nat)) (= (= (@ (@ tptp.zip_Pr1018045463562677002sn_nat Xs) Ys) tptp.nil_Pr2945733327814117674sn_nat) (or (= Xs tptp.nil_Pr5671120429643327159n_assn) (= Ys tptp.nil_nat)))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_P8527749157015355191n_assn)) (= (= (@ (@ tptp.zip_Pr8806919808394484215n_assn Xs) Ys) tptp.nil_Pr4327835960982145133n_assn) (or (= Xs tptp.nil_Pr5671120429643327159n_assn) (= Ys tptp.nil_Pr5671120429643327159n_assn)))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_assn) (Ys tptp.list_assn)) (= (= (@ (@ tptp.zip_assn_assn Xs) Ys) tptp.nil_Pr5671120429643327159n_assn) (or (= Xs tptp.nil_assn) (= Ys tptp.nil_assn)))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (= (= tptp.nil_Pr2300489316682597567nt_int (@ (@ tptp.zip_int_int Xs) Ys)) (or (= Xs tptp.nil_int) (= Ys tptp.nil_int)))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_nat)) (= (= tptp.nil_Pr6478340336191794275nt_nat (@ (@ tptp.zip_int_nat Xs) Ys)) (or (= Xs tptp.nil_int) (= Ys tptp.nil_nat)))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_P8527749157015355191n_assn)) (= (= tptp.nil_Pr2440414457004260852n_assn (@ (@ tptp.zip_in7098856637274830732n_assn Xs) Ys)) (or (= Xs tptp.nil_int) (= Ys tptp.nil_Pr5671120429643327159n_assn)))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_int)) (= (= tptp.nil_Pr1301135604781543011at_int (@ (@ tptp.zip_nat_int Xs) Ys)) (or (= Xs tptp.nil_nat) (= Ys tptp.nil_int)))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (= (= tptp.nil_Pr5478986624290739719at_nat (@ (@ tptp.zip_nat_nat Xs) Ys)) (or (= Xs tptp.nil_nat) (= Ys tptp.nil_nat)))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_P8527749157015355191n_assn)) (= (= tptp.nil_Pr680377793251149648n_assn (@ (@ tptp.zip_na5338819973521719528n_assn Xs) Ys)) (or (= Xs tptp.nil_nat) (= Ys tptp.nil_Pr5671120429643327159n_assn)))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_int)) (= (= tptp.nil_Pr7991254345159696774sn_int (@ (@ tptp.zip_Pr1015554993053626726sn_int Xs) Ys)) (or (= Xs tptp.nil_Pr5671120429643327159n_assn) (= Ys tptp.nil_int)))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_nat)) (= (= tptp.nil_Pr2945733327814117674sn_nat (@ (@ tptp.zip_Pr1018045463562677002sn_nat Xs) Ys)) (or (= Xs tptp.nil_Pr5671120429643327159n_assn) (= Ys tptp.nil_nat)))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_P8527749157015355191n_assn)) (= (= tptp.nil_Pr4327835960982145133n_assn (@ (@ tptp.zip_Pr8806919808394484215n_assn Xs) Ys)) (or (= Xs tptp.nil_Pr5671120429643327159n_assn) (= Ys tptp.nil_Pr5671120429643327159n_assn)))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_assn) (Ys tptp.list_assn)) (= (= tptp.nil_Pr5671120429643327159n_assn (@ (@ tptp.zip_assn_assn Xs) Ys)) (or (= Xs tptp.nil_assn) (= Ys tptp.nil_assn)))))
% 3.70/4.05 (assert (forall ((Ys tptp.list_assn)) (= (@ (@ tptp.zip_assn_assn tptp.nil_assn) Ys) tptp.nil_Pr5671120429643327159n_assn)))
% 3.70/4.05 (assert (forall ((Xs tptp.list_int)) (= (= tptp.nil_int (@ tptp.rev_int Xs)) (= Xs tptp.nil_int))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat)) (= (= tptp.nil_nat (@ tptp.rev_nat Xs)) (= Xs tptp.nil_nat))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn)) (= (= tptp.nil_Pr5671120429643327159n_assn (@ tptp.rev_Pr4855572775806611735n_assn Xs)) (= Xs tptp.nil_Pr5671120429643327159n_assn))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_int)) (= (= (@ tptp.rev_int Xs) tptp.nil_int) (= Xs tptp.nil_int))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat)) (= (= (@ tptp.rev_nat Xs) tptp.nil_nat) (= Xs tptp.nil_nat))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn)) (= (= (@ tptp.rev_Pr4855572775806611735n_assn Xs) tptp.nil_Pr5671120429643327159n_assn) (= Xs tptp.nil_Pr5671120429643327159n_assn))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_int) (K3 tptp.nat) (X tptp.int)) (= (= (@ (@ (@ tptp.list_update_int Xs) K3) X) tptp.nil_int) (= Xs tptp.nil_int))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat) (K3 tptp.nat) (X tptp.nat)) (= (= (@ (@ (@ tptp.list_update_nat Xs) K3) X) tptp.nil_nat) (= Xs tptp.nil_nat))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (K3 tptp.nat) (X tptp.produc6575502325842934193n_assn)) (= (= (@ (@ (@ tptp.list_u4534839942911652127n_assn Xs) K3) X) tptp.nil_Pr5671120429643327159n_assn) (= Xs tptp.nil_Pr5671120429643327159n_assn))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_c) (K3 tptp.nat) (X tptp.c)) (= (= (@ (@ (@ tptp.list_update_c Xs) K3) X) tptp.nil_c) (= Xs tptp.nil_c))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_d) (K3 tptp.nat) (X tptp.d)) (= (= (@ (@ (@ tptp.list_update_d Xs) K3) X) tptp.nil_d) (= Xs tptp.nil_d))))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.enumerate_int N) tptp.nil_int) tptp.nil_Pr1301135604781543011at_int)))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.enumerate_nat N) tptp.nil_nat) tptp.nil_Pr5478986624290739719at_nat)))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.enumer9200277086812776726n_assn N) tptp.nil_Pr5671120429643327159n_assn) tptp.nil_Pr680377793251149648n_assn)))
% 3.70/4.05 (assert (forall ((Xs tptp.list_int)) (= (= (@ tptp.rotate1_int Xs) tptp.nil_int) (= Xs tptp.nil_int))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat)) (= (= (@ tptp.rotate1_nat Xs) tptp.nil_nat) (= Xs tptp.nil_nat))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn)) (= (= (@ tptp.rotate328796349445179396n_assn Xs) tptp.nil_Pr5671120429643327159n_assn) (= Xs tptp.nil_Pr5671120429643327159n_assn))))
% 3.70/4.05 (assert (forall ((P (-> tptp.int Bool))) (not (@ (@ tptp.list_ex_int P) tptp.nil_int))))
% 3.70/4.05 (assert (forall ((P (-> tptp.nat Bool))) (not (@ (@ tptp.list_ex_nat P) tptp.nil_nat))))
% 3.70/4.05 (assert (forall ((P (-> tptp.produc6575502325842934193n_assn Bool))) (not (@ (@ tptp.list_e1087220904399170805n_assn P) tptp.nil_Pr5671120429643327159n_assn))))
% 3.70/4.05 (assert (forall ((Begin tptp.nat) (End tptp.nat)) (= (@ (@ (@ tptp.slice_int Begin) End) tptp.nil_int) tptp.nil_int)))
% 3.70/4.05 (assert (forall ((Begin tptp.nat) (End tptp.nat)) (= (@ (@ (@ tptp.slice_nat Begin) End) tptp.nil_nat) tptp.nil_nat)))
% 3.70/4.05 (assert (forall ((Begin tptp.nat) (End tptp.nat)) (= (@ (@ (@ tptp.slice_7964966981652229398n_assn Begin) End) tptp.nil_Pr5671120429643327159n_assn) tptp.nil_Pr5671120429643327159n_assn)))
% 3.70/4.05 (assert (forall ((I tptp.nat) (Xs tptp.list_int)) (= (@ (@ (@ tptp.slice_int I) I) Xs) tptp.nil_int)))
% 3.70/4.05 (assert (forall ((I tptp.nat) (Xs tptp.list_nat)) (= (@ (@ (@ tptp.slice_nat I) I) Xs) tptp.nil_nat)))
% 3.70/4.05 (assert (forall ((I tptp.nat) (Xs tptp.list_P8527749157015355191n_assn)) (= (@ (@ (@ tptp.slice_7964966981652229398n_assn I) I) Xs) tptp.nil_Pr5671120429643327159n_assn)))
% 3.70/4.05 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (not (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Y)) (@ tptp.measur2694323259624372065at_nat tptp.nil_se7398569966080822440at_nat)))))
% 3.70/4.05 (assert (forall ((X tptp.nat) (Y tptp.nat)) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ tptp.measures_nat tptp.nil_nat_nat)))))
% 3.70/4.05 (assert (forall ((A2 tptp.rat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A2))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A2) (= (= (@ _let_1 M2) (@ _let_1 N)) (= M2 N))))))
% 3.70/4.05 (assert (forall ((A2 tptp.code_integer) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A2))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A2) (= (= (@ _let_1 M2) (@ _let_1 N)) (= M2 N))))))
% 3.70/4.05 (assert (forall ((A2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A2) (= (= (@ _let_1 M2) (@ _let_1 N)) (= M2 N))))))
% 3.70/4.05 (assert (forall ((A2 tptp.int) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A2))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A2) (= (= (@ _let_1 M2) (@ _let_1 N)) (= M2 N))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn)) (= (= (@ tptp.set_Pr1139785259514867910n_assn Xs) tptp.bot_bo1176836662018730877n_assn) (= Xs tptp.nil_Pr5671120429643327159n_assn))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_P5464809261938338413at_nat)) (= (= (@ tptp.set_Pr3765526544606949372at_nat Xs) tptp.bot_bo228742789529271731at_nat) (= Xs tptp.nil_Pr8341282898164651117at_nat))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_P6011104703257516679at_nat)) (= (= (@ tptp.set_Pr5648618587558075414at_nat Xs) tptp.bot_bo2099793752762293965at_nat) (= Xs tptp.nil_Pr5478986624290739719at_nat))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_o)) (= (= (@ tptp.set_o2 Xs) tptp.bot_bot_set_o) (= Xs tptp.nil_o))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat)) (= (= (@ tptp.set_nat2 Xs) tptp.bot_bot_set_nat) (= Xs tptp.nil_nat))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_int)) (= (= (@ tptp.set_int2 Xs) tptp.bot_bot_set_int) (= Xs tptp.nil_int))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn)) (= (= tptp.bot_bo1176836662018730877n_assn (@ tptp.set_Pr1139785259514867910n_assn Xs)) (= Xs tptp.nil_Pr5671120429643327159n_assn))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_P5464809261938338413at_nat)) (= (= tptp.bot_bo228742789529271731at_nat (@ tptp.set_Pr3765526544606949372at_nat Xs)) (= Xs tptp.nil_Pr8341282898164651117at_nat))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_P6011104703257516679at_nat)) (= (= tptp.bot_bo2099793752762293965at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs)) (= Xs tptp.nil_Pr5478986624290739719at_nat))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_o)) (= (= tptp.bot_bot_set_o (@ tptp.set_o2 Xs)) (= Xs tptp.nil_o))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat)) (= (= tptp.bot_bot_set_nat (@ tptp.set_nat2 Xs)) (= Xs tptp.nil_nat))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_int)) (= (= tptp.bot_bot_set_int (@ tptp.set_int2 Xs)) (= Xs tptp.nil_int))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn)) (= (= (@ tptp.size_s6829681357464350627n_assn Xs) tptp.zero_zero_nat) (= Xs tptp.nil_Pr5671120429643327159n_assn))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_c)) (= (= (@ tptp.size_size_list_c Xs) tptp.zero_zero_nat) (= Xs tptp.nil_c))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_d)) (= (= (@ tptp.size_size_list_d Xs) tptp.zero_zero_nat) (= Xs tptp.nil_d))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat)) (= (= (@ tptp.size_size_list_nat Xs) tptp.zero_zero_nat) (= Xs tptp.nil_nat))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_int)) (= (= (@ tptp.size_size_list_int Xs) tptp.zero_zero_nat) (= Xs tptp.nil_int))))
% 3.70/4.05 (assert (forall ((X tptp.int) (Xs tptp.list_int)) (let ((_let_1 (@ (@ tptp.cons_int X) tptp.nil_int))) (= (= _let_1 (@ tptp.rev_int Xs)) (= _let_1 Xs)))))
% 3.70/4.05 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat X) tptp.nil_nat))) (= (= _let_1 (@ tptp.rev_nat Xs)) (= _let_1 Xs)))))
% 3.70/4.05 (assert (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ (@ tptp.cons_P2971678138204555879n_assn X) tptp.nil_Pr5671120429643327159n_assn))) (= (= _let_1 (@ tptp.rev_Pr4855572775806611735n_assn Xs)) (= _let_1 Xs)))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_int) (X tptp.int)) (let ((_let_1 (@ (@ tptp.cons_int X) tptp.nil_int))) (= (= (@ tptp.rev_int Xs) _let_1) (= Xs _let_1)))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.cons_nat X) tptp.nil_nat))) (= (= (@ tptp.rev_nat Xs) _let_1) (= Xs _let_1)))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (X tptp.produc6575502325842934193n_assn)) (let ((_let_1 (@ (@ tptp.cons_P2971678138204555879n_assn X) tptp.nil_Pr5671120429643327159n_assn))) (= (= (@ tptp.rev_Pr4855572775806611735n_assn Xs) _let_1) (= Xs _let_1)))))
% 3.70/4.05 (assert (forall ((Ns tptp.list_int) (R2 tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int tptp.nil_int) Ns)) (@ tptp.lenlex_int R2)) (not (= Ns tptp.nil_int)))))
% 3.70/4.05 (assert (forall ((Ns tptp.list_nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat tptp.nil_nat) Ns)) (@ tptp.lenlex_nat R2)) (not (= Ns tptp.nil_nat)))))
% 3.70/4.05 (assert (forall ((Ns tptp.list_P8527749157015355191n_assn) (R2 tptp.set_Pr8116311503512020807n_assn)) (= (@ (@ tptp.member3994142547374651152n_assn (@ (@ tptp.produc3014731801419794263n_assn tptp.nil_Pr5671120429643327159n_assn) Ns)) (@ tptp.lenlex6671093235567761724n_assn R2)) (not (= Ns tptp.nil_Pr5671120429643327159n_assn)))))
% 3.70/4.05 (assert (forall ((X tptp.int)) (= (@ (@ tptp.insert_int X) tptp.nil_int) (@ (@ tptp.cons_int X) tptp.nil_int))))
% 3.70/4.05 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.insert_nat X) tptp.nil_nat) (@ (@ tptp.cons_nat X) tptp.nil_nat))))
% 3.70/4.05 (assert (forall ((X tptp.produc6575502325842934193n_assn)) (= (@ (@ tptp.insert3246601298802261197n_assn X) tptp.nil_Pr5671120429643327159n_assn) (@ (@ tptp.cons_P2971678138204555879n_assn X) tptp.nil_Pr5671120429643327159n_assn))))
% 3.70/4.05 (assert (forall ((P (-> tptp.int tptp.int tptp.assn)) (L3 tptp.list_int)) (= (@ (@ (@ tptp.vEBT_L74593716426352029nt_int P) tptp.nil_int) L3) (@ tptp.pure_assn (= L3 tptp.nil_int)))))
% 3.70/4.05 (assert (forall ((P (-> tptp.int tptp.nat tptp.assn)) (L3 tptp.list_nat)) (= (@ (@ (@ tptp.vEBT_L77084186935402305nt_nat P) tptp.nil_int) L3) (@ tptp.pure_assn (= L3 tptp.nil_nat)))))
% 3.70/4.05 (assert (forall ((P (-> tptp.int tptp.produc6575502325842934193n_assn tptp.assn)) (L3 tptp.list_P8527749157015355191n_assn)) (= (@ (@ (@ tptp.vEBT_L1620274777744359680n_assn P) tptp.nil_int) L3) (@ tptp.pure_assn (= L3 tptp.nil_Pr5671120429643327159n_assn)))))
% 3.70/4.05 (assert (forall ((P (-> tptp.nat tptp.int tptp.assn)) (L3 tptp.list_int)) (= (@ (@ (@ tptp.vEBT_L8298612041380073281at_int P) tptp.nil_nat) L3) (@ tptp.pure_assn (= L3 tptp.nil_int)))))
% 3.70/4.05 (assert (forall ((P (-> tptp.nat tptp.nat tptp.assn)) (L3 tptp.list_nat)) (= (@ (@ (@ tptp.vEBT_L8301102511889123557at_nat P) tptp.nil_nat) L3) (@ tptp.pure_assn (= L3 tptp.nil_nat)))))
% 3.70/4.05 (assert (forall ((P (-> tptp.nat tptp.produc6575502325842934193n_assn tptp.assn)) (L3 tptp.list_P8527749157015355191n_assn)) (= (@ (@ (@ tptp.vEBT_L9083610150846024284n_assn P) tptp.nil_nat) L3) (@ tptp.pure_assn (= L3 tptp.nil_Pr5671120429643327159n_assn)))))
% 3.70/4.05 (assert (forall ((P (-> tptp.produc6575502325842934193n_assn tptp.int tptp.assn)) (L3 tptp.list_int)) (= (@ (@ (@ tptp.vEBT_L4760345170377931482sn_int P) tptp.nil_Pr5671120429643327159n_assn) L3) (@ tptp.pure_assn (= L3 tptp.nil_int)))))
% 3.70/4.05 (assert (forall ((P (-> tptp.produc6575502325842934193n_assn tptp.nat tptp.assn)) (L3 tptp.list_nat)) (= (@ (@ (@ tptp.vEBT_L4762835640886981758sn_nat P) tptp.nil_Pr5671120429643327159n_assn) L3) (@ tptp.pure_assn (= L3 tptp.nil_nat)))))
% 3.70/4.05 (assert (forall ((P (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn tptp.assn)) (L3 tptp.list_P8527749157015355191n_assn)) (= (@ (@ (@ tptp.vEBT_L3108143461992071043n_assn P) tptp.nil_Pr5671120429643327159n_assn) L3) (@ tptp.pure_assn (= L3 tptp.nil_Pr5671120429643327159n_assn)))))
% 3.70/4.05 (assert (forall ((P (-> tptp.int tptp.int tptp.assn)) (L tptp.list_int)) (= (@ (@ (@ tptp.vEBT_L74593716426352029nt_int P) L) tptp.nil_int) (@ tptp.pure_assn (= L tptp.nil_int)))))
% 3.70/4.05 (assert (forall ((P (-> tptp.nat tptp.int tptp.assn)) (L tptp.list_nat)) (= (@ (@ (@ tptp.vEBT_L8298612041380073281at_int P) L) tptp.nil_int) (@ tptp.pure_assn (= L tptp.nil_nat)))))
% 3.70/4.05 (assert (forall ((P (-> tptp.produc6575502325842934193n_assn tptp.int tptp.assn)) (L tptp.list_P8527749157015355191n_assn)) (= (@ (@ (@ tptp.vEBT_L4760345170377931482sn_int P) L) tptp.nil_int) (@ tptp.pure_assn (= L tptp.nil_Pr5671120429643327159n_assn)))))
% 3.70/4.05 (assert (forall ((P (-> tptp.int tptp.nat tptp.assn)) (L tptp.list_int)) (= (@ (@ (@ tptp.vEBT_L77084186935402305nt_nat P) L) tptp.nil_nat) (@ tptp.pure_assn (= L tptp.nil_int)))))
% 3.70/4.05 (assert (forall ((P (-> tptp.nat tptp.nat tptp.assn)) (L tptp.list_nat)) (= (@ (@ (@ tptp.vEBT_L8301102511889123557at_nat P) L) tptp.nil_nat) (@ tptp.pure_assn (= L tptp.nil_nat)))))
% 3.70/4.05 (assert (forall ((P (-> tptp.produc6575502325842934193n_assn tptp.nat tptp.assn)) (L tptp.list_P8527749157015355191n_assn)) (= (@ (@ (@ tptp.vEBT_L4762835640886981758sn_nat P) L) tptp.nil_nat) (@ tptp.pure_assn (= L tptp.nil_Pr5671120429643327159n_assn)))))
% 3.70/4.05 (assert (forall ((P (-> tptp.int tptp.produc6575502325842934193n_assn tptp.assn)) (L tptp.list_int)) (= (@ (@ (@ tptp.vEBT_L1620274777744359680n_assn P) L) tptp.nil_Pr5671120429643327159n_assn) (@ tptp.pure_assn (= L tptp.nil_int)))))
% 3.70/4.05 (assert (forall ((P (-> tptp.nat tptp.produc6575502325842934193n_assn tptp.assn)) (L tptp.list_nat)) (= (@ (@ (@ tptp.vEBT_L9083610150846024284n_assn P) L) tptp.nil_Pr5671120429643327159n_assn) (@ tptp.pure_assn (= L tptp.nil_nat)))))
% 3.70/4.05 (assert (forall ((P (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn tptp.assn)) (L tptp.list_P8527749157015355191n_assn)) (= (@ (@ (@ tptp.vEBT_L3108143461992071043n_assn P) L) tptp.nil_Pr5671120429643327159n_assn) (@ tptp.pure_assn (= L tptp.nil_Pr5671120429643327159n_assn)))))
% 3.70/4.05 (assert (forall ((B2 tptp.rat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B2))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) B2) (= (@ (@ tptp.ord_less_rat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 3.70/4.05 (assert (forall ((B2 tptp.code_integer) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger B2))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) B2) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 3.70/4.05 (assert (forall ((B2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B2) (= (@ (@ tptp.ord_less_nat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 3.70/4.05 (assert (forall ((B2 tptp.int) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B2))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B2) (= (@ (@ tptp.ord_less_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 3.70/4.05 (assert (forall ((A2 tptp.code_integer) (N tptp.nat)) (= (= (@ (@ tptp.power_8256067586552552935nteger A2) N) tptp.zero_z3403309356797280102nteger) (and (= A2 tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 3.70/4.05 (assert (forall ((A2 tptp.rat) (N tptp.nat)) (= (= (@ (@ tptp.power_power_rat A2) N) tptp.zero_zero_rat) (and (= A2 tptp.zero_zero_rat) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 3.70/4.05 (assert (forall ((A2 tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.power_power_nat A2) N) tptp.zero_zero_nat) (and (= A2 tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 3.70/4.05 (assert (forall ((A2 tptp.int) (N tptp.nat)) (= (= (@ (@ tptp.power_power_int A2) N) tptp.zero_zero_int) (and (= A2 tptp.zero_zero_int) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s6829681357464350627n_assn Xs)) (not (= Xs tptp.nil_Pr5671120429643327159n_assn)))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_c)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_c Xs)) (not (= Xs tptp.nil_c)))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_d)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_d Xs)) (not (= Xs tptp.nil_d)))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_nat Xs)) (not (= Xs tptp.nil_nat)))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_int)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_int Xs)) (not (= Xs tptp.nil_int)))))
% 3.70/4.05 (assert (forall ((B2 tptp.rat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B2))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B2) (=> (@ (@ tptp.ord_less_rat B2) tptp.one_one_rat) (= (@ (@ tptp.ord_less_rat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M2)))))))
% 3.70/4.05 (assert (forall ((B2 tptp.code_integer) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger B2))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) tptp.one_one_Code_integer) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M2)))))))
% 3.70/4.05 (assert (forall ((B2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (=> (@ (@ tptp.ord_less_nat B2) tptp.one_one_nat) (= (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M2)))))))
% 3.70/4.05 (assert (forall ((B2 tptp.int) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_int B2) tptp.one_one_int) (= (@ (@ tptp.ord_less_int (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M2)))))))
% 3.70/4.05 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A2) N)) (@ (@ tptp.power_8256067586552552935nteger B2) N)) (@ (@ tptp.ord_le3102999989581377725nteger A2) B2))))))))
% 3.70/4.05 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A2) N)) (@ (@ tptp.power_power_rat B2) N)) (@ (@ tptp.ord_less_eq_rat A2) B2))))))))
% 3.70/4.05 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A2) N)) (@ (@ tptp.power_power_nat B2) N)) (@ (@ tptp.ord_less_eq_nat A2) B2))))))))
% 3.70/4.05 (assert (forall ((A2 tptp.int) (B2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A2) N)) (@ (@ tptp.power_power_int B2) N)) (@ (@ tptp.ord_less_eq_int A2) B2))))))))
% 3.70/4.05 (assert (forall ((B2 tptp.rat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B2))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) B2) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 3.70/4.05 (assert (forall ((B2 tptp.code_integer) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger B2))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) B2) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 3.70/4.05 (assert (forall ((B2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B2) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 3.70/4.05 (assert (forall ((B2 tptp.int) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B2))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B2) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 3.70/4.05 (assert (forall ((L tptp.list_P8527749157015355191n_assn)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.size_s6829681357464350627n_assn L)) (not (= L tptp.nil_Pr5671120429643327159n_assn)))))
% 3.70/4.05 (assert (forall ((L tptp.list_c)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.size_size_list_c L)) (not (= L tptp.nil_c)))))
% 3.70/4.05 (assert (forall ((L tptp.list_d)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.size_size_list_d L)) (not (= L tptp.nil_d)))))
% 3.70/4.05 (assert (forall ((L tptp.list_nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.size_size_list_nat L)) (not (= L tptp.nil_nat)))))
% 3.70/4.05 (assert (forall ((L tptp.list_int)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.size_size_list_int L)) (not (= L tptp.nil_int)))))
% 3.70/4.05 (assert (forall ((X tptp.list_list_int)) (=> (not (= X tptp.nil_list_int)) (=> (forall ((Xss tptp.list_list_int)) (not (= X (@ (@ tptp.cons_list_int tptp.nil_int) Xss)))) (not (forall ((X3 tptp.int) (Xs2 tptp.list_int) (Xss tptp.list_list_int)) (not (= X (@ (@ tptp.cons_list_int (@ (@ tptp.cons_int X3) Xs2)) Xss)))))))))
% 3.70/4.05 (assert (forall ((X tptp.list_list_nat)) (=> (not (= X tptp.nil_list_nat)) (=> (forall ((Xss tptp.list_list_nat)) (not (= X (@ (@ tptp.cons_list_nat tptp.nil_nat) Xss)))) (not (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Xss tptp.list_list_nat)) (not (= X (@ (@ tptp.cons_list_nat (@ (@ tptp.cons_nat X3) Xs2)) Xss)))))))))
% 3.70/4.05 (assert (forall ((X tptp.list_l6351802567095793725n_assn)) (=> (not (= X tptp.nil_li5476096274760905021n_assn)) (=> (forall ((Xss tptp.list_l6351802567095793725n_assn)) (not (= X (@ (@ tptp.cons_l2423627976422276333n_assn tptp.nil_Pr5671120429643327159n_assn) Xss)))) (not (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn) (Xss tptp.list_l6351802567095793725n_assn)) (not (= X (@ (@ tptp.cons_l2423627976422276333n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)) Xss)))))))))
% 3.70/4.05 (assert (forall ((Ns tptp.list_int) (R2 tptp.set_Pr958786334691620121nt_int)) (not (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Ns) tptp.nil_int)) (@ tptp.lenlex_int R2)))))
% 3.70/4.05 (assert (forall ((Ns tptp.list_nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (not (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Ns) tptp.nil_nat)) (@ tptp.lenlex_nat R2)))))
% 3.70/4.05 (assert (forall ((Ns tptp.list_P8527749157015355191n_assn) (R2 tptp.set_Pr8116311503512020807n_assn)) (not (@ (@ tptp.member3994142547374651152n_assn (@ (@ tptp.produc3014731801419794263n_assn Ns) tptp.nil_Pr5671120429643327159n_assn)) (@ tptp.lenlex6671093235567761724n_assn R2)))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_int) (R2 tptp.set_Pr958786334691620121nt_int)) (not (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Xs) tptp.nil_int)) (@ tptp.lex_int R2)))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (not (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Xs) tptp.nil_nat)) (@ tptp.lex_nat R2)))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (R2 tptp.set_Pr8116311503512020807n_assn)) (not (@ (@ tptp.member3994142547374651152n_assn (@ (@ tptp.produc3014731801419794263n_assn Xs) tptp.nil_Pr5671120429643327159n_assn)) (@ tptp.lex_Pr7559194461235888923n_assn R2)))))
% 3.70/4.05 (assert (forall ((Ys tptp.list_int) (R2 tptp.set_Pr958786334691620121nt_int)) (not (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int tptp.nil_int) Ys)) (@ tptp.lex_int R2)))))
% 3.70/4.05 (assert (forall ((Ys tptp.list_nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (not (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat tptp.nil_nat) Ys)) (@ tptp.lex_nat R2)))))
% 3.70/4.05 (assert (forall ((Ys tptp.list_P8527749157015355191n_assn) (R2 tptp.set_Pr8116311503512020807n_assn)) (not (@ (@ tptp.member3994142547374651152n_assn (@ (@ tptp.produc3014731801419794263n_assn tptp.nil_Pr5671120429643327159n_assn) Ys)) (@ tptp.lex_Pr7559194461235888923n_assn R2)))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_assn)) (= (@ (@ tptp.zip_assn_assn Xs) tptp.nil_assn) tptp.nil_Pr5671120429643327159n_assn)))
% 3.70/4.05 (assert (forall ((A tptp.multis2468970476368604999at_nat) (B tptp.multis2468970476368604999at_nat) (M5 tptp.multis2468970476368604999at_nat) (N7 tptp.multis2468970476368604999at_nat)) (=> (= (@ (@ tptp.plus_p7104986032573967614at_nat A) B) (@ (@ tptp.plus_p7104986032573967614at_nat M5) N7)) (not (forall ((Am tptp.multis2468970476368604999at_nat) (An tptp.multis2468970476368604999at_nat)) (=> (= A (@ (@ tptp.plus_p7104986032573967614at_nat Am) An)) (forall ((Bm tptp.multis2468970476368604999at_nat) (Bn tptp.multis2468970476368604999at_nat)) (=> (= B (@ (@ tptp.plus_p7104986032573967614at_nat Bm) Bn)) (=> (= M5 (@ (@ tptp.plus_p7104986032573967614at_nat Am) Bm)) (not (= N7 (@ (@ tptp.plus_p7104986032573967614at_nat An) Bn))))))))))))
% 3.70/4.05 (assert (forall ((Y tptp.int)) (= (@ (@ tptp.count_list_int tptp.nil_int) Y) tptp.zero_zero_nat)))
% 3.70/4.05 (assert (forall ((Y tptp.nat)) (= (@ (@ tptp.count_list_nat tptp.nil_nat) Y) tptp.zero_zero_nat)))
% 3.70/4.05 (assert (forall ((Y tptp.produc6575502325842934193n_assn)) (= (@ (@ tptp.count_2530312006313534765n_assn tptp.nil_Pr5671120429643327159n_assn) Y) tptp.zero_zero_nat)))
% 3.70/4.05 (assert (forall ((Uu tptp.list_assn)) (= (@ (@ tptp.product_assn_assn tptp.nil_assn) Uu) tptp.nil_Pr5671120429643327159n_assn)))
% 3.70/4.05 (assert (forall ((A2 tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger A2) N))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) A2) (@ (@ tptp.times_3573771949741848930nteger A2) _let_1)))))
% 3.70/4.05 (assert (forall ((A2 tptp.assn) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_assn A2) N))) (= (@ (@ tptp.times_times_assn _let_1) A2) (@ (@ tptp.times_times_assn A2) _let_1)))))
% 3.70/4.05 (assert (forall ((A2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A2) N))) (= (@ (@ tptp.times_times_rat _let_1) A2) (@ (@ tptp.times_times_rat A2) _let_1)))))
% 3.70/4.05 (assert (forall ((A2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A2) N))) (= (@ (@ tptp.times_times_nat _let_1) A2) (@ (@ tptp.times_times_nat A2) _let_1)))))
% 3.70/4.05 (assert (forall ((A2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A2) N))) (= (@ (@ tptp.times_times_int _let_1) A2) (@ (@ tptp.times_times_int A2) _let_1)))))
% 3.70/4.05 (assert (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.times_3573771949741848930nteger A2) B2)) N) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger A2) N)) (@ (@ tptp.power_8256067586552552935nteger B2) N)))))
% 3.70/4.05 (assert (forall ((A2 tptp.assn) (B2 tptp.assn) (N tptp.nat)) (= (@ (@ tptp.power_power_assn (@ (@ tptp.times_times_assn A2) B2)) N) (@ (@ tptp.times_times_assn (@ (@ tptp.power_power_assn A2) N)) (@ (@ tptp.power_power_assn B2) N)))))
% 3.70/4.05 (assert (forall ((A2 tptp.rat) (B2 tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ (@ tptp.times_times_rat A2) B2)) N) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat A2) N)) (@ (@ tptp.power_power_rat B2) N)))))
% 3.70/4.05 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.times_times_nat A2) B2)) N) (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat A2) N)) (@ (@ tptp.power_power_nat B2) N)))))
% 3.70/4.05 (assert (forall ((A2 tptp.int) (B2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.times_times_int A2) B2)) N) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int A2) N)) (@ (@ tptp.power_power_int B2) N)))))
% 3.70/4.05 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger X) N))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger Y))) (=> (= (@ (@ tptp.times_3573771949741848930nteger X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) Y) (@ _let_2 _let_1)))))))
% 3.70/4.05 (assert (forall ((X tptp.assn) (Y tptp.assn) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_assn X) N))) (let ((_let_2 (@ tptp.times_times_assn Y))) (=> (= (@ (@ tptp.times_times_assn X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_times_assn _let_1) Y) (@ _let_2 _let_1)))))))
% 3.70/4.05 (assert (forall ((X tptp.rat) (Y tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat X) N))) (let ((_let_2 (@ tptp.times_times_rat Y))) (=> (= (@ (@ tptp.times_times_rat X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_times_rat _let_1) Y) (@ _let_2 _let_1)))))))
% 3.70/4.05 (assert (forall ((X tptp.nat) (Y tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat X) N))) (let ((_let_2 (@ tptp.times_times_nat Y))) (=> (= (@ (@ tptp.times_times_nat X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_times_nat _let_1) Y) (@ _let_2 _let_1)))))))
% 3.70/4.05 (assert (forall ((X tptp.int) (Y tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int X) N))) (let ((_let_2 (@ tptp.times_times_int Y))) (=> (= (@ (@ tptp.times_times_int X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_times_int _let_1) Y) (@ _let_2 _let_1)))))))
% 3.70/4.05 (assert (forall ((X tptp.produc5834231552977413017st_int)) (=> (forall ((P5 (-> tptp.int tptp.int Bool))) (not (= X (@ (@ tptp.produc8618682346314911123st_int P5) tptp.nil_int)))) (=> (forall ((P5 (-> tptp.int tptp.int Bool)) (X3 tptp.int)) (not (= X (@ (@ tptp.produc8618682346314911123st_int P5) (@ (@ tptp.cons_int X3) tptp.nil_int))))) (not (forall ((P5 (-> tptp.int tptp.int Bool)) (X3 tptp.int) (Y2 tptp.int) (Xs2 tptp.list_int)) (not (= X (@ (@ tptp.produc8618682346314911123st_int P5) (@ (@ tptp.cons_int X3) (@ (@ tptp.cons_int Y2) Xs2)))))))))))
% 3.70/4.05 (assert (forall ((X tptp.produc254973753779126261st_nat)) (=> (forall ((P5 (-> tptp.nat tptp.nat Bool))) (not (= X (@ (@ tptp.produc4727192421694094319st_nat P5) tptp.nil_nat)))) (=> (forall ((P5 (-> tptp.nat tptp.nat Bool)) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc4727192421694094319st_nat P5) (@ (@ tptp.cons_nat X3) tptp.nil_nat))))) (not (forall ((P5 (-> tptp.nat tptp.nat Bool)) (X3 tptp.nat) (Y2 tptp.nat) (Xs2 tptp.list_nat)) (not (= X (@ (@ tptp.produc4727192421694094319st_nat P5) (@ (@ tptp.cons_nat X3) (@ (@ tptp.cons_nat Y2) Xs2)))))))))))
% 3.70/4.05 (assert (forall ((X tptp.produc4530688714081574576n_assn)) (=> (forall ((P5 (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn Bool))) (not (= X (@ (@ tptp.produc6115016301897879072n_assn P5) tptp.nil_Pr5671120429643327159n_assn)))) (=> (forall ((P5 (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn Bool)) (X3 tptp.produc6575502325842934193n_assn)) (not (= X (@ (@ tptp.produc6115016301897879072n_assn P5) (@ (@ tptp.cons_P2971678138204555879n_assn X3) tptp.nil_Pr5671120429643327159n_assn))))) (not (forall ((P5 (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn Bool)) (X3 tptp.produc6575502325842934193n_assn) (Y2 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn)) (not (= X (@ (@ tptp.produc6115016301897879072n_assn P5) (@ (@ tptp.cons_P2971678138204555879n_assn X3) (@ (@ tptp.cons_P2971678138204555879n_assn Y2) Xs2)))))))))))
% 3.70/4.05 (assert (forall ((X tptp.produc5834231552977413017st_int)) (=> (forall ((P5 (-> tptp.int tptp.int Bool))) (not (= X (@ (@ tptp.produc8618682346314911123st_int P5) tptp.nil_int)))) (not (forall ((P5 (-> tptp.int tptp.int Bool)) (X3 tptp.int) (Ys5 tptp.list_int)) (not (= X (@ (@ tptp.produc8618682346314911123st_int P5) (@ (@ tptp.cons_int X3) Ys5)))))))))
% 3.70/4.05 (assert (forall ((X tptp.produc254973753779126261st_nat)) (=> (forall ((P5 (-> tptp.nat tptp.nat Bool))) (not (= X (@ (@ tptp.produc4727192421694094319st_nat P5) tptp.nil_nat)))) (not (forall ((P5 (-> tptp.nat tptp.nat Bool)) (X3 tptp.nat) (Ys5 tptp.list_nat)) (not (= X (@ (@ tptp.produc4727192421694094319st_nat P5) (@ (@ tptp.cons_nat X3) Ys5)))))))))
% 3.70/4.05 (assert (forall ((X tptp.produc4530688714081574576n_assn)) (=> (forall ((P5 (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn Bool))) (not (= X (@ (@ tptp.produc6115016301897879072n_assn P5) tptp.nil_Pr5671120429643327159n_assn)))) (not (forall ((P5 (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn Bool)) (X3 tptp.produc6575502325842934193n_assn) (Ys5 tptp.list_P8527749157015355191n_assn)) (not (= X (@ (@ tptp.produc6115016301897879072n_assn P5) (@ (@ tptp.cons_P2971678138204555879n_assn X3) Ys5)))))))))
% 3.70/4.05 (assert (forall ((L tptp.list_int)) (=> (not (= L tptp.nil_int)) (not (forall ((X3 tptp.int) (Xs2 tptp.list_int)) (not (= L (@ (@ tptp.cons_int X3) Xs2))))))))
% 3.70/4.05 (assert (forall ((L tptp.list_nat)) (=> (not (= L tptp.nil_nat)) (not (forall ((X3 tptp.nat) (Xs2 tptp.list_nat)) (not (= L (@ (@ tptp.cons_nat X3) Xs2))))))))
% 3.70/4.05 (assert (forall ((L tptp.list_P8527749157015355191n_assn)) (=> (not (= L tptp.nil_Pr5671120429643327159n_assn)) (not (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn)) (not (= L (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2))))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.list_int tptp.list_int Bool)) (W1 tptp.list_int) (W2 tptp.list_int)) (=> (@ (@ P tptp.nil_int) tptp.nil_int) (=> (forall ((E2 tptp.int) (W12 tptp.list_int) (W22 tptp.list_int)) (=> (@ (@ P W12) W22) (@ (@ P (@ (@ tptp.cons_int E2) W12)) W22))) (=> (forall ((E2 tptp.int) (W13 tptp.list_int) (W23 tptp.list_int)) (let ((_let_1 (@ P W13))) (=> (@ _let_1 W23) (@ _let_1 (@ (@ tptp.cons_int E2) W23))))) (@ (@ P W1) W2))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.list_int tptp.list_nat Bool)) (W1 tptp.list_int) (W2 tptp.list_nat)) (=> (@ (@ P tptp.nil_int) tptp.nil_nat) (=> (forall ((E2 tptp.int) (W12 tptp.list_int) (W22 tptp.list_nat)) (=> (@ (@ P W12) W22) (@ (@ P (@ (@ tptp.cons_int E2) W12)) W22))) (=> (forall ((E2 tptp.nat) (W13 tptp.list_int) (W23 tptp.list_nat)) (let ((_let_1 (@ P W13))) (=> (@ _let_1 W23) (@ _let_1 (@ (@ tptp.cons_nat E2) W23))))) (@ (@ P W1) W2))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.list_int tptp.list_P8527749157015355191n_assn Bool)) (W1 tptp.list_int) (W2 tptp.list_P8527749157015355191n_assn)) (=> (@ (@ P tptp.nil_int) tptp.nil_Pr5671120429643327159n_assn) (=> (forall ((E2 tptp.int) (W12 tptp.list_int) (W22 tptp.list_P8527749157015355191n_assn)) (=> (@ (@ P W12) W22) (@ (@ P (@ (@ tptp.cons_int E2) W12)) W22))) (=> (forall ((E2 tptp.produc6575502325842934193n_assn) (W13 tptp.list_int) (W23 tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ P W13))) (=> (@ _let_1 W23) (@ _let_1 (@ (@ tptp.cons_P2971678138204555879n_assn E2) W23))))) (@ (@ P W1) W2))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.list_nat tptp.list_int Bool)) (W1 tptp.list_nat) (W2 tptp.list_int)) (=> (@ (@ P tptp.nil_nat) tptp.nil_int) (=> (forall ((E2 tptp.nat) (W12 tptp.list_nat) (W22 tptp.list_int)) (=> (@ (@ P W12) W22) (@ (@ P (@ (@ tptp.cons_nat E2) W12)) W22))) (=> (forall ((E2 tptp.int) (W13 tptp.list_nat) (W23 tptp.list_int)) (let ((_let_1 (@ P W13))) (=> (@ _let_1 W23) (@ _let_1 (@ (@ tptp.cons_int E2) W23))))) (@ (@ P W1) W2))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.list_nat tptp.list_nat Bool)) (W1 tptp.list_nat) (W2 tptp.list_nat)) (=> (@ (@ P tptp.nil_nat) tptp.nil_nat) (=> (forall ((E2 tptp.nat) (W12 tptp.list_nat) (W22 tptp.list_nat)) (=> (@ (@ P W12) W22) (@ (@ P (@ (@ tptp.cons_nat E2) W12)) W22))) (=> (forall ((E2 tptp.nat) (W13 tptp.list_nat) (W23 tptp.list_nat)) (let ((_let_1 (@ P W13))) (=> (@ _let_1 W23) (@ _let_1 (@ (@ tptp.cons_nat E2) W23))))) (@ (@ P W1) W2))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.list_nat tptp.list_P8527749157015355191n_assn Bool)) (W1 tptp.list_nat) (W2 tptp.list_P8527749157015355191n_assn)) (=> (@ (@ P tptp.nil_nat) tptp.nil_Pr5671120429643327159n_assn) (=> (forall ((E2 tptp.nat) (W12 tptp.list_nat) (W22 tptp.list_P8527749157015355191n_assn)) (=> (@ (@ P W12) W22) (@ (@ P (@ (@ tptp.cons_nat E2) W12)) W22))) (=> (forall ((E2 tptp.produc6575502325842934193n_assn) (W13 tptp.list_nat) (W23 tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ P W13))) (=> (@ _let_1 W23) (@ _let_1 (@ (@ tptp.cons_P2971678138204555879n_assn E2) W23))))) (@ (@ P W1) W2))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.list_P8527749157015355191n_assn tptp.list_int Bool)) (W1 tptp.list_P8527749157015355191n_assn) (W2 tptp.list_int)) (=> (@ (@ P tptp.nil_Pr5671120429643327159n_assn) tptp.nil_int) (=> (forall ((E2 tptp.produc6575502325842934193n_assn) (W12 tptp.list_P8527749157015355191n_assn) (W22 tptp.list_int)) (=> (@ (@ P W12) W22) (@ (@ P (@ (@ tptp.cons_P2971678138204555879n_assn E2) W12)) W22))) (=> (forall ((E2 tptp.int) (W13 tptp.list_P8527749157015355191n_assn) (W23 tptp.list_int)) (let ((_let_1 (@ P W13))) (=> (@ _let_1 W23) (@ _let_1 (@ (@ tptp.cons_int E2) W23))))) (@ (@ P W1) W2))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.list_P8527749157015355191n_assn tptp.list_nat Bool)) (W1 tptp.list_P8527749157015355191n_assn) (W2 tptp.list_nat)) (=> (@ (@ P tptp.nil_Pr5671120429643327159n_assn) tptp.nil_nat) (=> (forall ((E2 tptp.produc6575502325842934193n_assn) (W12 tptp.list_P8527749157015355191n_assn) (W22 tptp.list_nat)) (=> (@ (@ P W12) W22) (@ (@ P (@ (@ tptp.cons_P2971678138204555879n_assn E2) W12)) W22))) (=> (forall ((E2 tptp.nat) (W13 tptp.list_P8527749157015355191n_assn) (W23 tptp.list_nat)) (let ((_let_1 (@ P W13))) (=> (@ _let_1 W23) (@ _let_1 (@ (@ tptp.cons_nat E2) W23))))) (@ (@ P W1) W2))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.list_P8527749157015355191n_assn tptp.list_P8527749157015355191n_assn Bool)) (W1 tptp.list_P8527749157015355191n_assn) (W2 tptp.list_P8527749157015355191n_assn)) (=> (@ (@ P tptp.nil_Pr5671120429643327159n_assn) tptp.nil_Pr5671120429643327159n_assn) (=> (forall ((E2 tptp.produc6575502325842934193n_assn) (W12 tptp.list_P8527749157015355191n_assn) (W22 tptp.list_P8527749157015355191n_assn)) (=> (@ (@ P W12) W22) (@ (@ P (@ (@ tptp.cons_P2971678138204555879n_assn E2) W12)) W22))) (=> (forall ((E2 tptp.produc6575502325842934193n_assn) (W13 tptp.list_P8527749157015355191n_assn) (W23 tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ P W13))) (=> (@ _let_1 W23) (@ _let_1 (@ (@ tptp.cons_P2971678138204555879n_assn E2) W23))))) (@ (@ P W1) W2))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.list_int Bool)) (Xs tptp.list_int)) (=> (@ P tptp.nil_int) (=> (forall ((X3 tptp.int)) (@ P (@ (@ tptp.cons_int X3) tptp.nil_int))) (=> (forall ((X12 tptp.int) (X23 tptp.int) (Xs2 tptp.list_int)) (=> (@ P Xs2) (@ P (@ (@ tptp.cons_int X12) (@ (@ tptp.cons_int X23) Xs2))))) (@ P Xs))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.list_nat Bool)) (Xs tptp.list_nat)) (=> (@ P tptp.nil_nat) (=> (forall ((X3 tptp.nat)) (@ P (@ (@ tptp.cons_nat X3) tptp.nil_nat))) (=> (forall ((X12 tptp.nat) (X23 tptp.nat) (Xs2 tptp.list_nat)) (=> (@ P Xs2) (@ P (@ (@ tptp.cons_nat X12) (@ (@ tptp.cons_nat X23) Xs2))))) (@ P Xs))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.list_P8527749157015355191n_assn Bool)) (Xs tptp.list_P8527749157015355191n_assn)) (=> (@ P tptp.nil_Pr5671120429643327159n_assn) (=> (forall ((X3 tptp.produc6575502325842934193n_assn)) (@ P (@ (@ tptp.cons_P2971678138204555879n_assn X3) tptp.nil_Pr5671120429643327159n_assn))) (=> (forall ((X12 tptp.produc6575502325842934193n_assn) (X23 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn)) (=> (@ P Xs2) (@ P (@ (@ tptp.cons_P2971678138204555879n_assn X12) (@ (@ tptp.cons_P2971678138204555879n_assn X23) Xs2))))) (@ P Xs))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.list_int tptp.list_int Bool)) (R (-> tptp.int tptp.int Bool)) (Xs tptp.list_int) (Ys tptp.list_int)) (=> (forall ((Xs2 tptp.list_int)) (@ (@ P Xs2) tptp.nil_int)) (=> (forall ((X_1 tptp.list_int)) (@ (@ P tptp.nil_int) X_1)) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int) (Y2 tptp.int) (Ys5 tptp.list_int)) (let ((_let_1 (@ (@ tptp.cons_int Y2) Ys5))) (=> (@ (@ R X3) Y2) (=> (@ (@ P Xs2) _let_1) (@ (@ P (@ (@ tptp.cons_int X3) Xs2)) _let_1))))) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int) (Y2 tptp.int) (Ys5 tptp.list_int)) (let ((_let_1 (@ P (@ (@ tptp.cons_int X3) Xs2)))) (=> (not (@ (@ R X3) Y2)) (=> (@ _let_1 Ys5) (@ _let_1 (@ (@ tptp.cons_int Y2) Ys5)))))) (@ (@ P Xs) Ys)))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.list_nat tptp.list_int Bool)) (R (-> tptp.nat tptp.int Bool)) (Xs tptp.list_nat) (Ys tptp.list_int)) (=> (forall ((Xs2 tptp.list_nat)) (@ (@ P Xs2) tptp.nil_int)) (=> (forall ((X_1 tptp.list_int)) (@ (@ P tptp.nil_nat) X_1)) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.int) (Ys5 tptp.list_int)) (let ((_let_1 (@ (@ tptp.cons_int Y2) Ys5))) (=> (@ (@ R X3) Y2) (=> (@ (@ P Xs2) _let_1) (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) _let_1))))) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.int) (Ys5 tptp.list_int)) (let ((_let_1 (@ P (@ (@ tptp.cons_nat X3) Xs2)))) (=> (not (@ (@ R X3) Y2)) (=> (@ _let_1 Ys5) (@ _let_1 (@ (@ tptp.cons_int Y2) Ys5)))))) (@ (@ P Xs) Ys)))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.list_P8527749157015355191n_assn tptp.list_int Bool)) (R (-> tptp.produc6575502325842934193n_assn tptp.int Bool)) (Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_int)) (=> (forall ((Xs2 tptp.list_P8527749157015355191n_assn)) (@ (@ P Xs2) tptp.nil_int)) (=> (forall ((X_1 tptp.list_int)) (@ (@ P tptp.nil_Pr5671120429643327159n_assn) X_1)) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn) (Y2 tptp.int) (Ys5 tptp.list_int)) (let ((_let_1 (@ (@ tptp.cons_int Y2) Ys5))) (=> (@ (@ R X3) Y2) (=> (@ (@ P Xs2) _let_1) (@ (@ P (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)) _let_1))))) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn) (Y2 tptp.int) (Ys5 tptp.list_int)) (let ((_let_1 (@ P (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)))) (=> (not (@ (@ R X3) Y2)) (=> (@ _let_1 Ys5) (@ _let_1 (@ (@ tptp.cons_int Y2) Ys5)))))) (@ (@ P Xs) Ys)))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.list_int tptp.list_nat Bool)) (R (-> tptp.int tptp.nat Bool)) (Xs tptp.list_int) (Ys tptp.list_nat)) (=> (forall ((Xs2 tptp.list_int)) (@ (@ P Xs2) tptp.nil_nat)) (=> (forall ((X_1 tptp.list_nat)) (@ (@ P tptp.nil_int) X_1)) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int) (Y2 tptp.nat) (Ys5 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat Y2) Ys5))) (=> (@ (@ R X3) Y2) (=> (@ (@ P Xs2) _let_1) (@ (@ P (@ (@ tptp.cons_int X3) Xs2)) _let_1))))) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int) (Y2 tptp.nat) (Ys5 tptp.list_nat)) (let ((_let_1 (@ P (@ (@ tptp.cons_int X3) Xs2)))) (=> (not (@ (@ R X3) Y2)) (=> (@ _let_1 Ys5) (@ _let_1 (@ (@ tptp.cons_nat Y2) Ys5)))))) (@ (@ P Xs) Ys)))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.list_nat tptp.list_nat Bool)) (R (-> tptp.nat tptp.nat Bool)) (Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (forall ((Xs2 tptp.list_nat)) (@ (@ P Xs2) tptp.nil_nat)) (=> (forall ((X_1 tptp.list_nat)) (@ (@ P tptp.nil_nat) X_1)) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.nat) (Ys5 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat Y2) Ys5))) (=> (@ (@ R X3) Y2) (=> (@ (@ P Xs2) _let_1) (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) _let_1))))) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.nat) (Ys5 tptp.list_nat)) (let ((_let_1 (@ P (@ (@ tptp.cons_nat X3) Xs2)))) (=> (not (@ (@ R X3) Y2)) (=> (@ _let_1 Ys5) (@ _let_1 (@ (@ tptp.cons_nat Y2) Ys5)))))) (@ (@ P Xs) Ys)))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.list_P8527749157015355191n_assn tptp.list_nat Bool)) (R (-> tptp.produc6575502325842934193n_assn tptp.nat Bool)) (Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_nat)) (=> (forall ((Xs2 tptp.list_P8527749157015355191n_assn)) (@ (@ P Xs2) tptp.nil_nat)) (=> (forall ((X_1 tptp.list_nat)) (@ (@ P tptp.nil_Pr5671120429643327159n_assn) X_1)) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn) (Y2 tptp.nat) (Ys5 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat Y2) Ys5))) (=> (@ (@ R X3) Y2) (=> (@ (@ P Xs2) _let_1) (@ (@ P (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)) _let_1))))) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn) (Y2 tptp.nat) (Ys5 tptp.list_nat)) (let ((_let_1 (@ P (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)))) (=> (not (@ (@ R X3) Y2)) (=> (@ _let_1 Ys5) (@ _let_1 (@ (@ tptp.cons_nat Y2) Ys5)))))) (@ (@ P Xs) Ys)))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.list_int tptp.list_P8527749157015355191n_assn Bool)) (R (-> tptp.int tptp.produc6575502325842934193n_assn Bool)) (Xs tptp.list_int) (Ys tptp.list_P8527749157015355191n_assn)) (=> (forall ((Xs2 tptp.list_int)) (@ (@ P Xs2) tptp.nil_Pr5671120429643327159n_assn)) (=> (forall ((X_1 tptp.list_P8527749157015355191n_assn)) (@ (@ P tptp.nil_int) X_1)) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int) (Y2 tptp.produc6575502325842934193n_assn) (Ys5 tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ (@ tptp.cons_P2971678138204555879n_assn Y2) Ys5))) (=> (@ (@ R X3) Y2) (=> (@ (@ P Xs2) _let_1) (@ (@ P (@ (@ tptp.cons_int X3) Xs2)) _let_1))))) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int) (Y2 tptp.produc6575502325842934193n_assn) (Ys5 tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ P (@ (@ tptp.cons_int X3) Xs2)))) (=> (not (@ (@ R X3) Y2)) (=> (@ _let_1 Ys5) (@ _let_1 (@ (@ tptp.cons_P2971678138204555879n_assn Y2) Ys5)))))) (@ (@ P Xs) Ys)))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.list_nat tptp.list_P8527749157015355191n_assn Bool)) (R (-> tptp.nat tptp.produc6575502325842934193n_assn Bool)) (Xs tptp.list_nat) (Ys tptp.list_P8527749157015355191n_assn)) (=> (forall ((Xs2 tptp.list_nat)) (@ (@ P Xs2) tptp.nil_Pr5671120429643327159n_assn)) (=> (forall ((X_1 tptp.list_P8527749157015355191n_assn)) (@ (@ P tptp.nil_nat) X_1)) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.produc6575502325842934193n_assn) (Ys5 tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ (@ tptp.cons_P2971678138204555879n_assn Y2) Ys5))) (=> (@ (@ R X3) Y2) (=> (@ (@ P Xs2) _let_1) (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) _let_1))))) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.produc6575502325842934193n_assn) (Ys5 tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ P (@ (@ tptp.cons_nat X3) Xs2)))) (=> (not (@ (@ R X3) Y2)) (=> (@ _let_1 Ys5) (@ _let_1 (@ (@ tptp.cons_P2971678138204555879n_assn Y2) Ys5)))))) (@ (@ P Xs) Ys)))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.list_P8527749157015355191n_assn tptp.list_P8527749157015355191n_assn Bool)) (R (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn Bool)) (Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_P8527749157015355191n_assn)) (=> (forall ((Xs2 tptp.list_P8527749157015355191n_assn)) (@ (@ P Xs2) tptp.nil_Pr5671120429643327159n_assn)) (=> (forall ((X_1 tptp.list_P8527749157015355191n_assn)) (@ (@ P tptp.nil_Pr5671120429643327159n_assn) X_1)) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn) (Y2 tptp.produc6575502325842934193n_assn) (Ys5 tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ (@ tptp.cons_P2971678138204555879n_assn Y2) Ys5))) (=> (@ (@ R X3) Y2) (=> (@ (@ P Xs2) _let_1) (@ (@ P (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)) _let_1))))) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn) (Y2 tptp.produc6575502325842934193n_assn) (Ys5 tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ P (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)))) (=> (not (@ (@ R X3) Y2)) (=> (@ _let_1 Ys5) (@ _let_1 (@ (@ tptp.cons_P2971678138204555879n_assn Y2) Ys5)))))) (@ (@ P Xs) Ys)))))))
% 3.70/4.05 (assert (forall ((X21 tptp.int) (X222 tptp.list_int)) (not (= tptp.nil_int (@ (@ tptp.cons_int X21) X222)))))
% 3.70/4.05 (assert (forall ((X21 tptp.nat) (X222 tptp.list_nat)) (not (= tptp.nil_nat (@ (@ tptp.cons_nat X21) X222)))))
% 3.70/4.05 (assert (forall ((X21 tptp.produc6575502325842934193n_assn) (X222 tptp.list_P8527749157015355191n_assn)) (not (= tptp.nil_Pr5671120429643327159n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X21) X222)))))
% 3.70/4.05 (assert (forall ((List tptp.list_int) (X21 tptp.int) (X222 tptp.list_int)) (=> (= List (@ (@ tptp.cons_int X21) X222)) (not (= List tptp.nil_int)))))
% 3.70/4.05 (assert (forall ((List tptp.list_nat) (X21 tptp.nat) (X222 tptp.list_nat)) (=> (= List (@ (@ tptp.cons_nat X21) X222)) (not (= List tptp.nil_nat)))))
% 3.70/4.05 (assert (forall ((List tptp.list_P8527749157015355191n_assn) (X21 tptp.produc6575502325842934193n_assn) (X222 tptp.list_P8527749157015355191n_assn)) (=> (= List (@ (@ tptp.cons_P2971678138204555879n_assn X21) X222)) (not (= List tptp.nil_Pr5671120429643327159n_assn)))))
% 3.70/4.05 (assert (forall ((Y tptp.list_int)) (=> (not (= Y tptp.nil_int)) (not (forall ((X212 tptp.int) (X223 tptp.list_int)) (not (= Y (@ (@ tptp.cons_int X212) X223))))))))
% 3.70/4.05 (assert (forall ((Y tptp.list_nat)) (=> (not (= Y tptp.nil_nat)) (not (forall ((X212 tptp.nat) (X223 tptp.list_nat)) (not (= Y (@ (@ tptp.cons_nat X212) X223))))))))
% 3.70/4.05 (assert (forall ((Y tptp.list_P8527749157015355191n_assn)) (=> (not (= Y tptp.nil_Pr5671120429643327159n_assn)) (not (forall ((X212 tptp.produc6575502325842934193n_assn) (X223 tptp.list_P8527749157015355191n_assn)) (not (= Y (@ (@ tptp.cons_P2971678138204555879n_assn X212) X223))))))))
% 3.70/4.05 (assert (forall ((X tptp.list_int)) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int)) (not (= X (@ (@ tptp.cons_int X3) Xs2)))) (= X tptp.nil_int))))
% 3.70/4.05 (assert (forall ((X tptp.list_nat)) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat)) (not (= X (@ (@ tptp.cons_nat X3) Xs2)))) (= X tptp.nil_nat))))
% 3.70/4.05 (assert (forall ((X tptp.list_int)) (=> (not (= X tptp.nil_int)) (=> (forall ((X3 tptp.int)) (not (= X (@ (@ tptp.cons_int X3) tptp.nil_int)))) (not (forall ((X3 tptp.int) (Y2 tptp.int) (Xs2 tptp.list_int)) (not (= X (@ (@ tptp.cons_int X3) (@ (@ tptp.cons_int Y2) Xs2))))))))))
% 3.70/4.05 (assert (forall ((X tptp.list_nat)) (=> (not (= X tptp.nil_nat)) (=> (forall ((X3 tptp.nat)) (not (= X (@ (@ tptp.cons_nat X3) tptp.nil_nat)))) (not (forall ((X3 tptp.nat) (Y2 tptp.nat) (Xs2 tptp.list_nat)) (not (= X (@ (@ tptp.cons_nat X3) (@ (@ tptp.cons_nat Y2) Xs2))))))))))
% 3.70/4.05 (assert (forall ((X tptp.list_P8527749157015355191n_assn)) (=> (not (= X tptp.nil_Pr5671120429643327159n_assn)) (=> (forall ((X3 tptp.produc6575502325842934193n_assn)) (not (= X (@ (@ tptp.cons_P2971678138204555879n_assn X3) tptp.nil_Pr5671120429643327159n_assn)))) (not (forall ((X3 tptp.produc6575502325842934193n_assn) (Y2 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn)) (not (= X (@ (@ tptp.cons_P2971678138204555879n_assn X3) (@ (@ tptp.cons_P2971678138204555879n_assn Y2) Xs2))))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_int)) (= (not (= Xs tptp.nil_int)) (exists ((Y5 tptp.int) (Ys3 tptp.list_int)) (= Xs (@ (@ tptp.cons_int Y5) Ys3))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat)) (= (not (= Xs tptp.nil_nat)) (exists ((Y5 tptp.nat) (Ys3 tptp.list_nat)) (= Xs (@ (@ tptp.cons_nat Y5) Ys3))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn)) (= (not (= Xs tptp.nil_Pr5671120429643327159n_assn)) (exists ((Y5 tptp.produc6575502325842934193n_assn) (Ys3 tptp.list_P8527749157015355191n_assn)) (= Xs (@ (@ tptp.cons_P2971678138204555879n_assn Y5) Ys3))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.list_int tptp.list_int Bool)) (Xs tptp.list_int) (Ys tptp.list_int)) (=> (@ (@ P tptp.nil_int) tptp.nil_int) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int)) (@ (@ P (@ (@ tptp.cons_int X3) Xs2)) tptp.nil_int)) (=> (forall ((Y2 tptp.int) (Ys5 tptp.list_int)) (@ (@ P tptp.nil_int) (@ (@ tptp.cons_int Y2) Ys5))) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int) (Y2 tptp.int) (Ys5 tptp.list_int)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ tptp.cons_int X3) Xs2)) (@ (@ tptp.cons_int Y2) Ys5)))) (@ (@ P Xs) Ys)))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.list_int tptp.list_nat Bool)) (Xs tptp.list_int) (Ys tptp.list_nat)) (=> (@ (@ P tptp.nil_int) tptp.nil_nat) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int)) (@ (@ P (@ (@ tptp.cons_int X3) Xs2)) tptp.nil_nat)) (=> (forall ((Y2 tptp.nat) (Ys5 tptp.list_nat)) (@ (@ P tptp.nil_int) (@ (@ tptp.cons_nat Y2) Ys5))) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int) (Y2 tptp.nat) (Ys5 tptp.list_nat)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ tptp.cons_int X3) Xs2)) (@ (@ tptp.cons_nat Y2) Ys5)))) (@ (@ P Xs) Ys)))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.list_int tptp.list_P8527749157015355191n_assn Bool)) (Xs tptp.list_int) (Ys tptp.list_P8527749157015355191n_assn)) (=> (@ (@ P tptp.nil_int) tptp.nil_Pr5671120429643327159n_assn) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int)) (@ (@ P (@ (@ tptp.cons_int X3) Xs2)) tptp.nil_Pr5671120429643327159n_assn)) (=> (forall ((Y2 tptp.produc6575502325842934193n_assn) (Ys5 tptp.list_P8527749157015355191n_assn)) (@ (@ P tptp.nil_int) (@ (@ tptp.cons_P2971678138204555879n_assn Y2) Ys5))) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int) (Y2 tptp.produc6575502325842934193n_assn) (Ys5 tptp.list_P8527749157015355191n_assn)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ tptp.cons_int X3) Xs2)) (@ (@ tptp.cons_P2971678138204555879n_assn Y2) Ys5)))) (@ (@ P Xs) Ys)))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.list_nat tptp.list_int Bool)) (Xs tptp.list_nat) (Ys tptp.list_int)) (=> (@ (@ P tptp.nil_nat) tptp.nil_int) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat)) (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) tptp.nil_int)) (=> (forall ((Y2 tptp.int) (Ys5 tptp.list_int)) (@ (@ P tptp.nil_nat) (@ (@ tptp.cons_int Y2) Ys5))) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.int) (Ys5 tptp.list_int)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) (@ (@ tptp.cons_int Y2) Ys5)))) (@ (@ P Xs) Ys)))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.list_nat tptp.list_nat Bool)) (Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (@ (@ P tptp.nil_nat) tptp.nil_nat) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat)) (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) tptp.nil_nat)) (=> (forall ((Y2 tptp.nat) (Ys5 tptp.list_nat)) (@ (@ P tptp.nil_nat) (@ (@ tptp.cons_nat Y2) Ys5))) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.nat) (Ys5 tptp.list_nat)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) (@ (@ tptp.cons_nat Y2) Ys5)))) (@ (@ P Xs) Ys)))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.list_nat tptp.list_P8527749157015355191n_assn Bool)) (Xs tptp.list_nat) (Ys tptp.list_P8527749157015355191n_assn)) (=> (@ (@ P tptp.nil_nat) tptp.nil_Pr5671120429643327159n_assn) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat)) (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) tptp.nil_Pr5671120429643327159n_assn)) (=> (forall ((Y2 tptp.produc6575502325842934193n_assn) (Ys5 tptp.list_P8527749157015355191n_assn)) (@ (@ P tptp.nil_nat) (@ (@ tptp.cons_P2971678138204555879n_assn Y2) Ys5))) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.produc6575502325842934193n_assn) (Ys5 tptp.list_P8527749157015355191n_assn)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) (@ (@ tptp.cons_P2971678138204555879n_assn Y2) Ys5)))) (@ (@ P Xs) Ys)))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.list_P8527749157015355191n_assn tptp.list_int Bool)) (Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_int)) (=> (@ (@ P tptp.nil_Pr5671120429643327159n_assn) tptp.nil_int) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn)) (@ (@ P (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)) tptp.nil_int)) (=> (forall ((Y2 tptp.int) (Ys5 tptp.list_int)) (@ (@ P tptp.nil_Pr5671120429643327159n_assn) (@ (@ tptp.cons_int Y2) Ys5))) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn) (Y2 tptp.int) (Ys5 tptp.list_int)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)) (@ (@ tptp.cons_int Y2) Ys5)))) (@ (@ P Xs) Ys)))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.list_P8527749157015355191n_assn tptp.list_nat Bool)) (Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_nat)) (=> (@ (@ P tptp.nil_Pr5671120429643327159n_assn) tptp.nil_nat) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn)) (@ (@ P (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)) tptp.nil_nat)) (=> (forall ((Y2 tptp.nat) (Ys5 tptp.list_nat)) (@ (@ P tptp.nil_Pr5671120429643327159n_assn) (@ (@ tptp.cons_nat Y2) Ys5))) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn) (Y2 tptp.nat) (Ys5 tptp.list_nat)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)) (@ (@ tptp.cons_nat Y2) Ys5)))) (@ (@ P Xs) Ys)))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.list_P8527749157015355191n_assn tptp.list_P8527749157015355191n_assn Bool)) (Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_P8527749157015355191n_assn)) (=> (@ (@ P tptp.nil_Pr5671120429643327159n_assn) tptp.nil_Pr5671120429643327159n_assn) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn)) (@ (@ P (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)) tptp.nil_Pr5671120429643327159n_assn)) (=> (forall ((Y2 tptp.produc6575502325842934193n_assn) (Ys5 tptp.list_P8527749157015355191n_assn)) (@ (@ P tptp.nil_Pr5671120429643327159n_assn) (@ (@ tptp.cons_P2971678138204555879n_assn Y2) Ys5))) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn) (Y2 tptp.produc6575502325842934193n_assn) (Ys5 tptp.list_P8527749157015355191n_assn)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)) (@ (@ tptp.cons_P2971678138204555879n_assn Y2) Ys5)))) (@ (@ P Xs) Ys)))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_int) (P (-> tptp.list_int Bool))) (=> (not (= Xs tptp.nil_int)) (=> (forall ((X3 tptp.int)) (@ P (@ (@ tptp.cons_int X3) tptp.nil_int))) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int)) (=> (not (= Xs2 tptp.nil_int)) (=> (@ P Xs2) (@ P (@ (@ tptp.cons_int X3) Xs2))))) (@ P Xs))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat) (P (-> tptp.list_nat Bool))) (=> (not (= Xs tptp.nil_nat)) (=> (forall ((X3 tptp.nat)) (@ P (@ (@ tptp.cons_nat X3) tptp.nil_nat))) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat)) (=> (not (= Xs2 tptp.nil_nat)) (=> (@ P Xs2) (@ P (@ (@ tptp.cons_nat X3) Xs2))))) (@ P Xs))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (P (-> tptp.list_P8527749157015355191n_assn Bool))) (=> (not (= Xs tptp.nil_Pr5671120429643327159n_assn)) (=> (forall ((X3 tptp.produc6575502325842934193n_assn)) (@ P (@ (@ tptp.cons_P2971678138204555879n_assn X3) tptp.nil_Pr5671120429643327159n_assn))) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn)) (=> (not (= Xs2 tptp.nil_Pr5671120429643327159n_assn)) (=> (@ P Xs2) (@ P (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2))))) (@ P Xs))))))
% 3.70/4.05 (assert (@ tptp.distinct_int tptp.nil_int))
% 3.70/4.05 (assert (@ tptp.distinct_nat tptp.nil_nat))
% 3.70/4.05 (assert (@ tptp.distin4809818325527169450n_assn tptp.nil_Pr5671120429643327159n_assn))
% 3.70/4.05 (assert (forall ((P (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn Bool))) (@ (@ tptp.sorted3986126766855596574n_assn P) tptp.nil_Pr5671120429643327159n_assn)))
% 3.70/4.05 (assert (forall ((P (-> tptp.nat tptp.nat Bool))) (@ (@ tptp.sorted_wrt_nat P) tptp.nil_nat)))
% 3.70/4.05 (assert (forall ((P (-> tptp.int tptp.int Bool))) (@ (@ tptp.sorted_wrt_int P) tptp.nil_int)))
% 3.70/4.05 (assert (= (@ tptp.rev_int tptp.nil_int) tptp.nil_int))
% 3.70/4.05 (assert (= (@ tptp.rev_nat tptp.nil_nat) tptp.nil_nat))
% 3.70/4.05 (assert (= (@ tptp.rev_Pr4855572775806611735n_assn tptp.nil_Pr5671120429643327159n_assn) tptp.nil_Pr5671120429643327159n_assn))
% 3.70/4.05 (assert (forall ((I tptp.nat) (V2 tptp.int)) (= (@ (@ (@ tptp.list_update_int tptp.nil_int) I) V2) tptp.nil_int)))
% 3.70/4.05 (assert (forall ((I tptp.nat) (V2 tptp.nat)) (= (@ (@ (@ tptp.list_update_nat tptp.nil_nat) I) V2) tptp.nil_nat)))
% 3.70/4.05 (assert (forall ((I tptp.nat) (V2 tptp.produc6575502325842934193n_assn)) (= (@ (@ (@ tptp.list_u4534839942911652127n_assn tptp.nil_Pr5671120429643327159n_assn) I) V2) tptp.nil_Pr5671120429643327159n_assn)))
% 3.70/4.05 (assert (forall ((I tptp.nat) (V2 tptp.c)) (= (@ (@ (@ tptp.list_update_c tptp.nil_c) I) V2) tptp.nil_c)))
% 3.70/4.05 (assert (forall ((I tptp.nat) (V2 tptp.d)) (= (@ (@ (@ tptp.list_update_d tptp.nil_d) I) V2) tptp.nil_d)))
% 3.70/4.05 (assert (forall ((I tptp.nat) (Y tptp.int)) (= (@ (@ (@ tptp.list_update_int tptp.nil_int) I) Y) tptp.nil_int)))
% 3.70/4.05 (assert (forall ((I tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.list_update_nat tptp.nil_nat) I) Y) tptp.nil_nat)))
% 3.70/4.05 (assert (forall ((I tptp.nat) (Y tptp.produc6575502325842934193n_assn)) (= (@ (@ (@ tptp.list_u4534839942911652127n_assn tptp.nil_Pr5671120429643327159n_assn) I) Y) tptp.nil_Pr5671120429643327159n_assn)))
% 3.70/4.05 (assert (forall ((I tptp.nat) (Y tptp.c)) (= (@ (@ (@ tptp.list_update_c tptp.nil_c) I) Y) tptp.nil_c)))
% 3.70/4.05 (assert (forall ((I tptp.nat) (Y tptp.d)) (= (@ (@ (@ tptp.list_update_d tptp.nil_d) I) Y) tptp.nil_d)))
% 3.70/4.05 (assert (= (@ tptp.butlast_int tptp.nil_int) tptp.nil_int))
% 3.70/4.05 (assert (= (@ tptp.butlast_nat tptp.nil_nat) tptp.nil_nat))
% 3.70/4.05 (assert (= (@ tptp.butlas3012047794866324995n_assn tptp.nil_Pr5671120429643327159n_assn) tptp.nil_Pr5671120429643327159n_assn))
% 3.70/4.05 (assert (forall ((X tptp.int)) (= (@ (@ tptp.remove1_int X) tptp.nil_int) tptp.nil_int)))
% 3.70/4.05 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.remove1_nat X) tptp.nil_nat) tptp.nil_nat)))
% 3.70/4.05 (assert (forall ((X tptp.produc6575502325842934193n_assn)) (= (@ (@ tptp.remove1670527618125605709n_assn X) tptp.nil_Pr5671120429643327159n_assn) tptp.nil_Pr5671120429643327159n_assn)))
% 3.70/4.05 (assert (forall ((X tptp.int)) (= (@ (@ tptp.removeAll_int X) tptp.nil_int) tptp.nil_int)))
% 3.70/4.05 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.removeAll_nat X) tptp.nil_nat) tptp.nil_nat)))
% 3.70/4.05 (assert (forall ((X tptp.produc6575502325842934193n_assn)) (= (@ (@ tptp.remove1763081955827946941n_assn X) tptp.nil_Pr5671120429643327159n_assn) tptp.nil_Pr5671120429643327159n_assn)))
% 3.70/4.05 (assert (forall ((L23 tptp.list_int)) (= (@ (@ tptp.merge_int tptp.nil_int) L23) L23)))
% 3.70/4.05 (assert (forall ((L23 tptp.list_nat)) (= (@ (@ tptp.merge_nat tptp.nil_nat) L23) L23)))
% 3.70/4.05 (assert (= (@ tptp.rotate1_int tptp.nil_int) tptp.nil_int))
% 3.70/4.05 (assert (= (@ tptp.rotate1_nat tptp.nil_nat) tptp.nil_nat))
% 3.70/4.05 (assert (= (@ tptp.rotate328796349445179396n_assn tptp.nil_Pr5671120429643327159n_assn) tptp.nil_Pr5671120429643327159n_assn))
% 3.70/4.05 (assert (forall ((F4 (-> tptp.int tptp.int tptp.int))) (= (@ (@ (@ tptp.zipf_int_int_int F4) tptp.nil_int) tptp.nil_int) tptp.nil_int)))
% 3.70/4.05 (assert (forall ((F4 (-> tptp.int tptp.int tptp.nat))) (= (@ (@ (@ tptp.zipf_int_int_nat F4) tptp.nil_int) tptp.nil_int) tptp.nil_nat)))
% 3.70/4.05 (assert (forall ((F4 (-> tptp.int tptp.nat tptp.int))) (= (@ (@ (@ tptp.zipf_int_nat_int F4) tptp.nil_int) tptp.nil_nat) tptp.nil_int)))
% 3.70/4.05 (assert (forall ((F4 (-> tptp.int tptp.nat tptp.nat))) (= (@ (@ (@ tptp.zipf_int_nat_nat F4) tptp.nil_int) tptp.nil_nat) tptp.nil_nat)))
% 3.70/4.05 (assert (forall ((F4 (-> tptp.nat tptp.int tptp.int))) (= (@ (@ (@ tptp.zipf_nat_int_int F4) tptp.nil_nat) tptp.nil_int) tptp.nil_int)))
% 3.70/4.05 (assert (forall ((F4 (-> tptp.nat tptp.int tptp.nat))) (= (@ (@ (@ tptp.zipf_nat_int_nat F4) tptp.nil_nat) tptp.nil_int) tptp.nil_nat)))
% 3.70/4.05 (assert (forall ((F4 (-> tptp.nat tptp.nat tptp.int))) (= (@ (@ (@ tptp.zipf_nat_nat_int F4) tptp.nil_nat) tptp.nil_nat) tptp.nil_int)))
% 3.70/4.05 (assert (forall ((F4 (-> tptp.nat tptp.nat tptp.nat))) (= (@ (@ (@ tptp.zipf_nat_nat_nat F4) tptp.nil_nat) tptp.nil_nat) tptp.nil_nat)))
% 3.70/4.05 (assert (forall ((F4 (-> tptp.int tptp.int tptp.produc6575502325842934193n_assn))) (= (@ (@ (@ tptp.zipf_i7756021159461276697n_assn F4) tptp.nil_int) tptp.nil_int) tptp.nil_Pr5671120429643327159n_assn)))
% 3.70/4.05 (assert (forall ((F4 (-> tptp.int tptp.nat tptp.produc6575502325842934193n_assn))) (= (@ (@ (@ tptp.zipf_i5995984495708165493n_assn F4) tptp.nil_int) tptp.nil_nat) tptp.nil_Pr5671120429643327159n_assn)))
% 3.70/4.05 (assert (@ tptp.null_int tptp.nil_int))
% 3.70/4.05 (assert (@ tptp.null_nat tptp.nil_nat))
% 3.70/4.05 (assert (@ tptp.null_P7596217980778516671n_assn tptp.nil_Pr5671120429643327159n_assn))
% 3.70/4.05 (assert (forall ((Xs tptp.list_int)) (= (= Xs tptp.nil_int) (@ tptp.null_int Xs))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat)) (= (= Xs tptp.nil_nat) (@ tptp.null_nat Xs))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn)) (= (= Xs tptp.nil_Pr5671120429643327159n_assn) (@ tptp.null_P7596217980778516671n_assn Xs))))
% 3.70/4.05 (assert (forall ((A2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.power_power_rat A2) N))))))
% 3.70/4.05 (assert (forall ((A2 tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A2) N))))))
% 3.70/4.05 (assert (forall ((A2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.power_power_nat A2) N))))))
% 3.70/4.05 (assert (forall ((A2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.power_power_int A2) N))))))
% 3.70/4.05 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (N tptp.nat)) (=> (= (@ (@ tptp.times_3573771949741848930nteger X) Y) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger X) N)) (@ (@ tptp.power_8256067586552552935nteger Y) N)) tptp.one_one_Code_integer))))
% 3.70/4.05 (assert (forall ((X tptp.assn) (Y tptp.assn) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_assn X) Y) tptp.one_one_assn) (= (@ (@ tptp.times_times_assn (@ (@ tptp.power_power_assn X) N)) (@ (@ tptp.power_power_assn Y) N)) tptp.one_one_assn))))
% 3.70/4.05 (assert (forall ((X tptp.rat) (Y tptp.rat) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_rat X) Y) tptp.one_one_rat) (= (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X) N)) (@ (@ tptp.power_power_rat Y) N)) tptp.one_one_rat))))
% 3.70/4.05 (assert (forall ((X tptp.nat) (Y tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_nat X) Y) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat X) N)) (@ (@ tptp.power_power_nat Y) N)) tptp.one_one_nat))))
% 3.70/4.05 (assert (forall ((X tptp.int) (Y tptp.int) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_int X) Y) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X) N)) (@ (@ tptp.power_power_int Y) N)) tptp.one_one_int))))
% 3.70/4.05 (assert (forall ((A2 tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_3573771949741848930nteger A2) (@ _let_1 N))))))
% 3.70/4.05 (assert (forall ((A2 tptp.assn) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_assn A2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_assn A2) (@ _let_1 N))))))
% 3.70/4.05 (assert (forall ((A2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_rat A2) (@ _let_1 N))))))
% 3.70/4.05 (assert (forall ((A2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat A2) (@ _let_1 N))))))
% 3.70/4.05 (assert (forall ((A2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int A2) (@ _let_1 N))))))
% 3.70/4.05 (assert (forall ((A2 tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 N)) A2)))))
% 3.70/4.05 (assert (forall ((A2 tptp.assn) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_assn A2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_assn (@ _let_1 N)) A2)))))
% 3.70/4.05 (assert (forall ((A2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_rat (@ _let_1 N)) A2)))))
% 3.70/4.05 (assert (forall ((A2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat (@ _let_1 N)) A2)))))
% 3.70/4.05 (assert (forall ((A2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int (@ _let_1 N)) A2)))))
% 3.70/4.05 (assert (forall ((A2 tptp.code_integer) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 M2)) (@ _let_1 N))))))
% 3.70/4.05 (assert (forall ((A2 tptp.assn) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_assn A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.times_times_assn (@ _let_1 M2)) (@ _let_1 N))))))
% 3.70/4.05 (assert (forall ((A2 tptp.rat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.times_times_rat (@ _let_1 M2)) (@ _let_1 N))))))
% 3.70/4.05 (assert (forall ((A2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.times_times_nat (@ _let_1 M2)) (@ _let_1 N))))))
% 3.70/4.05 (assert (forall ((A2 tptp.int) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.times_times_int (@ _let_1 M2)) (@ _let_1 N))))))
% 3.70/4.05 (assert (forall ((I tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) I) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M2) N))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_c) (P (-> tptp.list_c tptp.list_c Bool))) (=> (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_c Ys)) (=> (@ (@ P tptp.nil_c) tptp.nil_c) (=> (forall ((X3 tptp.c) (Xs2 tptp.list_c) (Y2 tptp.c) (Ys5 tptp.list_c)) (=> (= (@ tptp.size_size_list_c Xs2) (@ tptp.size_size_list_c Ys5)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ tptp.cons_c X3) Xs2)) (@ (@ tptp.cons_c Y2) Ys5))))) (@ (@ P Xs) Ys))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_d) (P (-> tptp.list_c tptp.list_d Bool))) (=> (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_d Ys)) (=> (@ (@ P tptp.nil_c) tptp.nil_d) (=> (forall ((X3 tptp.c) (Xs2 tptp.list_c) (Y2 tptp.d) (Ys5 tptp.list_d)) (=> (= (@ tptp.size_size_list_c Xs2) (@ tptp.size_size_list_d Ys5)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ tptp.cons_c X3) Xs2)) (@ (@ tptp.cons_d Y2) Ys5))))) (@ (@ P Xs) Ys))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_nat) (P (-> tptp.list_c tptp.list_nat Bool))) (=> (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_nat Ys)) (=> (@ (@ P tptp.nil_c) tptp.nil_nat) (=> (forall ((X3 tptp.c) (Xs2 tptp.list_c) (Y2 tptp.nat) (Ys5 tptp.list_nat)) (=> (= (@ tptp.size_size_list_c Xs2) (@ tptp.size_size_list_nat Ys5)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ tptp.cons_c X3) Xs2)) (@ (@ tptp.cons_nat Y2) Ys5))))) (@ (@ P Xs) Ys))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_int) (P (-> tptp.list_c tptp.list_int Bool))) (=> (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_int Ys)) (=> (@ (@ P tptp.nil_c) tptp.nil_int) (=> (forall ((X3 tptp.c) (Xs2 tptp.list_c) (Y2 tptp.int) (Ys5 tptp.list_int)) (=> (= (@ tptp.size_size_list_c Xs2) (@ tptp.size_size_list_int Ys5)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ tptp.cons_c X3) Xs2)) (@ (@ tptp.cons_int Y2) Ys5))))) (@ (@ P Xs) Ys))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_d) (Ys tptp.list_c) (P (-> tptp.list_d tptp.list_c Bool))) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_c Ys)) (=> (@ (@ P tptp.nil_d) tptp.nil_c) (=> (forall ((X3 tptp.d) (Xs2 tptp.list_d) (Y2 tptp.c) (Ys5 tptp.list_c)) (=> (= (@ tptp.size_size_list_d Xs2) (@ tptp.size_size_list_c Ys5)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ tptp.cons_d X3) Xs2)) (@ (@ tptp.cons_c Y2) Ys5))))) (@ (@ P Xs) Ys))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_d) (Ys tptp.list_d) (P (-> tptp.list_d tptp.list_d Bool))) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_d Ys)) (=> (@ (@ P tptp.nil_d) tptp.nil_d) (=> (forall ((X3 tptp.d) (Xs2 tptp.list_d) (Y2 tptp.d) (Ys5 tptp.list_d)) (=> (= (@ tptp.size_size_list_d Xs2) (@ tptp.size_size_list_d Ys5)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ tptp.cons_d X3) Xs2)) (@ (@ tptp.cons_d Y2) Ys5))))) (@ (@ P Xs) Ys))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_d) (Ys tptp.list_nat) (P (-> tptp.list_d tptp.list_nat Bool))) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_nat Ys)) (=> (@ (@ P tptp.nil_d) tptp.nil_nat) (=> (forall ((X3 tptp.d) (Xs2 tptp.list_d) (Y2 tptp.nat) (Ys5 tptp.list_nat)) (=> (= (@ tptp.size_size_list_d Xs2) (@ tptp.size_size_list_nat Ys5)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ tptp.cons_d X3) Xs2)) (@ (@ tptp.cons_nat Y2) Ys5))))) (@ (@ P Xs) Ys))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_d) (Ys tptp.list_int) (P (-> tptp.list_d tptp.list_int Bool))) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_int Ys)) (=> (@ (@ P tptp.nil_d) tptp.nil_int) (=> (forall ((X3 tptp.d) (Xs2 tptp.list_d) (Y2 tptp.int) (Ys5 tptp.list_int)) (=> (= (@ tptp.size_size_list_d Xs2) (@ tptp.size_size_list_int Ys5)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ tptp.cons_d X3) Xs2)) (@ (@ tptp.cons_int Y2) Ys5))))) (@ (@ P Xs) Ys))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_c) (P (-> tptp.list_nat tptp.list_c Bool))) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_c Ys)) (=> (@ (@ P tptp.nil_nat) tptp.nil_c) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.c) (Ys5 tptp.list_c)) (=> (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_size_list_c Ys5)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) (@ (@ tptp.cons_c Y2) Ys5))))) (@ (@ P Xs) Ys))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_d) (P (-> tptp.list_nat tptp.list_d Bool))) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_d Ys)) (=> (@ (@ P tptp.nil_nat) tptp.nil_d) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.d) (Ys5 tptp.list_d)) (=> (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_size_list_d Ys5)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) (@ (@ tptp.cons_d Y2) Ys5))))) (@ (@ P Xs) Ys))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_c) (Zs tptp.list_c) (P (-> tptp.list_c tptp.list_c tptp.list_c Bool))) (let ((_let_1 (@ tptp.size_size_list_c Ys))) (=> (= (@ tptp.size_size_list_c Xs) _let_1) (=> (= _let_1 (@ tptp.size_size_list_c Zs)) (=> (@ (@ (@ P tptp.nil_c) tptp.nil_c) tptp.nil_c) (=> (forall ((X3 tptp.c) (Xs2 tptp.list_c) (Y2 tptp.c) (Ys5 tptp.list_c) (Z4 tptp.c) (Zs2 tptp.list_c)) (let ((_let_1 (@ tptp.size_size_list_c Ys5))) (=> (= (@ tptp.size_size_list_c Xs2) _let_1) (=> (= _let_1 (@ tptp.size_size_list_c Zs2)) (=> (@ (@ (@ P Xs2) Ys5) Zs2) (@ (@ (@ P (@ (@ tptp.cons_c X3) Xs2)) (@ (@ tptp.cons_c Y2) Ys5)) (@ (@ tptp.cons_c Z4) Zs2))))))) (@ (@ (@ P Xs) Ys) Zs))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_c) (Zs tptp.list_d) (P (-> tptp.list_c tptp.list_c tptp.list_d Bool))) (let ((_let_1 (@ tptp.size_size_list_c Ys))) (=> (= (@ tptp.size_size_list_c Xs) _let_1) (=> (= _let_1 (@ tptp.size_size_list_d Zs)) (=> (@ (@ (@ P tptp.nil_c) tptp.nil_c) tptp.nil_d) (=> (forall ((X3 tptp.c) (Xs2 tptp.list_c) (Y2 tptp.c) (Ys5 tptp.list_c) (Z4 tptp.d) (Zs2 tptp.list_d)) (let ((_let_1 (@ tptp.size_size_list_c Ys5))) (=> (= (@ tptp.size_size_list_c Xs2) _let_1) (=> (= _let_1 (@ tptp.size_size_list_d Zs2)) (=> (@ (@ (@ P Xs2) Ys5) Zs2) (@ (@ (@ P (@ (@ tptp.cons_c X3) Xs2)) (@ (@ tptp.cons_c Y2) Ys5)) (@ (@ tptp.cons_d Z4) Zs2))))))) (@ (@ (@ P Xs) Ys) Zs))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_c) (Zs tptp.list_nat) (P (-> tptp.list_c tptp.list_c tptp.list_nat Bool))) (let ((_let_1 (@ tptp.size_size_list_c Ys))) (=> (= (@ tptp.size_size_list_c Xs) _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Zs)) (=> (@ (@ (@ P tptp.nil_c) tptp.nil_c) tptp.nil_nat) (=> (forall ((X3 tptp.c) (Xs2 tptp.list_c) (Y2 tptp.c) (Ys5 tptp.list_c) (Z4 tptp.nat) (Zs2 tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_c Ys5))) (=> (= (@ tptp.size_size_list_c Xs2) _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Zs2)) (=> (@ (@ (@ P Xs2) Ys5) Zs2) (@ (@ (@ P (@ (@ tptp.cons_c X3) Xs2)) (@ (@ tptp.cons_c Y2) Ys5)) (@ (@ tptp.cons_nat Z4) Zs2))))))) (@ (@ (@ P Xs) Ys) Zs))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_c) (Zs tptp.list_int) (P (-> tptp.list_c tptp.list_c tptp.list_int Bool))) (let ((_let_1 (@ tptp.size_size_list_c Ys))) (=> (= (@ tptp.size_size_list_c Xs) _let_1) (=> (= _let_1 (@ tptp.size_size_list_int Zs)) (=> (@ (@ (@ P tptp.nil_c) tptp.nil_c) tptp.nil_int) (=> (forall ((X3 tptp.c) (Xs2 tptp.list_c) (Y2 tptp.c) (Ys5 tptp.list_c) (Z4 tptp.int) (Zs2 tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_c Ys5))) (=> (= (@ tptp.size_size_list_c Xs2) _let_1) (=> (= _let_1 (@ tptp.size_size_list_int Zs2)) (=> (@ (@ (@ P Xs2) Ys5) Zs2) (@ (@ (@ P (@ (@ tptp.cons_c X3) Xs2)) (@ (@ tptp.cons_c Y2) Ys5)) (@ (@ tptp.cons_int Z4) Zs2))))))) (@ (@ (@ P Xs) Ys) Zs))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_d) (Zs tptp.list_c) (P (-> tptp.list_c tptp.list_d tptp.list_c Bool))) (let ((_let_1 (@ tptp.size_size_list_d Ys))) (=> (= (@ tptp.size_size_list_c Xs) _let_1) (=> (= _let_1 (@ tptp.size_size_list_c Zs)) (=> (@ (@ (@ P tptp.nil_c) tptp.nil_d) tptp.nil_c) (=> (forall ((X3 tptp.c) (Xs2 tptp.list_c) (Y2 tptp.d) (Ys5 tptp.list_d) (Z4 tptp.c) (Zs2 tptp.list_c)) (let ((_let_1 (@ tptp.size_size_list_d Ys5))) (=> (= (@ tptp.size_size_list_c Xs2) _let_1) (=> (= _let_1 (@ tptp.size_size_list_c Zs2)) (=> (@ (@ (@ P Xs2) Ys5) Zs2) (@ (@ (@ P (@ (@ tptp.cons_c X3) Xs2)) (@ (@ tptp.cons_d Y2) Ys5)) (@ (@ tptp.cons_c Z4) Zs2))))))) (@ (@ (@ P Xs) Ys) Zs))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_d) (Zs tptp.list_d) (P (-> tptp.list_c tptp.list_d tptp.list_d Bool))) (let ((_let_1 (@ tptp.size_size_list_d Ys))) (=> (= (@ tptp.size_size_list_c Xs) _let_1) (=> (= _let_1 (@ tptp.size_size_list_d Zs)) (=> (@ (@ (@ P tptp.nil_c) tptp.nil_d) tptp.nil_d) (=> (forall ((X3 tptp.c) (Xs2 tptp.list_c) (Y2 tptp.d) (Ys5 tptp.list_d) (Z4 tptp.d) (Zs2 tptp.list_d)) (let ((_let_1 (@ tptp.size_size_list_d Ys5))) (=> (= (@ tptp.size_size_list_c Xs2) _let_1) (=> (= _let_1 (@ tptp.size_size_list_d Zs2)) (=> (@ (@ (@ P Xs2) Ys5) Zs2) (@ (@ (@ P (@ (@ tptp.cons_c X3) Xs2)) (@ (@ tptp.cons_d Y2) Ys5)) (@ (@ tptp.cons_d Z4) Zs2))))))) (@ (@ (@ P Xs) Ys) Zs))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_d) (Zs tptp.list_nat) (P (-> tptp.list_c tptp.list_d tptp.list_nat Bool))) (let ((_let_1 (@ tptp.size_size_list_d Ys))) (=> (= (@ tptp.size_size_list_c Xs) _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Zs)) (=> (@ (@ (@ P tptp.nil_c) tptp.nil_d) tptp.nil_nat) (=> (forall ((X3 tptp.c) (Xs2 tptp.list_c) (Y2 tptp.d) (Ys5 tptp.list_d) (Z4 tptp.nat) (Zs2 tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_d Ys5))) (=> (= (@ tptp.size_size_list_c Xs2) _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Zs2)) (=> (@ (@ (@ P Xs2) Ys5) Zs2) (@ (@ (@ P (@ (@ tptp.cons_c X3) Xs2)) (@ (@ tptp.cons_d Y2) Ys5)) (@ (@ tptp.cons_nat Z4) Zs2))))))) (@ (@ (@ P Xs) Ys) Zs))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_d) (Zs tptp.list_int) (P (-> tptp.list_c tptp.list_d tptp.list_int Bool))) (let ((_let_1 (@ tptp.size_size_list_d Ys))) (=> (= (@ tptp.size_size_list_c Xs) _let_1) (=> (= _let_1 (@ tptp.size_size_list_int Zs)) (=> (@ (@ (@ P tptp.nil_c) tptp.nil_d) tptp.nil_int) (=> (forall ((X3 tptp.c) (Xs2 tptp.list_c) (Y2 tptp.d) (Ys5 tptp.list_d) (Z4 tptp.int) (Zs2 tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_d Ys5))) (=> (= (@ tptp.size_size_list_c Xs2) _let_1) (=> (= _let_1 (@ tptp.size_size_list_int Zs2)) (=> (@ (@ (@ P Xs2) Ys5) Zs2) (@ (@ (@ P (@ (@ tptp.cons_c X3) Xs2)) (@ (@ tptp.cons_d Y2) Ys5)) (@ (@ tptp.cons_int Z4) Zs2))))))) (@ (@ (@ P Xs) Ys) Zs))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_nat) (Zs tptp.list_c) (P (-> tptp.list_c tptp.list_nat tptp.list_c Bool))) (let ((_let_1 (@ tptp.size_size_list_nat Ys))) (=> (= (@ tptp.size_size_list_c Xs) _let_1) (=> (= _let_1 (@ tptp.size_size_list_c Zs)) (=> (@ (@ (@ P tptp.nil_c) tptp.nil_nat) tptp.nil_c) (=> (forall ((X3 tptp.c) (Xs2 tptp.list_c) (Y2 tptp.nat) (Ys5 tptp.list_nat) (Z4 tptp.c) (Zs2 tptp.list_c)) (let ((_let_1 (@ tptp.size_size_list_nat Ys5))) (=> (= (@ tptp.size_size_list_c Xs2) _let_1) (=> (= _let_1 (@ tptp.size_size_list_c Zs2)) (=> (@ (@ (@ P Xs2) Ys5) Zs2) (@ (@ (@ P (@ (@ tptp.cons_c X3) Xs2)) (@ (@ tptp.cons_nat Y2) Ys5)) (@ (@ tptp.cons_c Z4) Zs2))))))) (@ (@ (@ P Xs) Ys) Zs))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_c) (Ys tptp.list_nat) (Zs tptp.list_d) (P (-> tptp.list_c tptp.list_nat tptp.list_d Bool))) (let ((_let_1 (@ tptp.size_size_list_nat Ys))) (=> (= (@ tptp.size_size_list_c Xs) _let_1) (=> (= _let_1 (@ tptp.size_size_list_d Zs)) (=> (@ (@ (@ P tptp.nil_c) tptp.nil_nat) tptp.nil_d) (=> (forall ((X3 tptp.c) (Xs2 tptp.list_c) (Y2 tptp.nat) (Ys5 tptp.list_nat) (Z4 tptp.d) (Zs2 tptp.list_d)) (let ((_let_1 (@ tptp.size_size_list_nat Ys5))) (=> (= (@ tptp.size_size_list_c Xs2) _let_1) (=> (= _let_1 (@ tptp.size_size_list_d Zs2)) (=> (@ (@ (@ P Xs2) Ys5) Zs2) (@ (@ (@ P (@ (@ tptp.cons_c X3) Xs2)) (@ (@ tptp.cons_nat Y2) Ys5)) (@ (@ tptp.cons_d Z4) Zs2))))))) (@ (@ (@ P Xs) Ys) Zs))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (Zs tptp.list_int) (Ws tptp.list_c) (P (-> tptp.list_nat tptp.list_nat tptp.list_int tptp.list_c Bool))) (let ((_let_1 (@ tptp.size_size_list_int Zs))) (let ((_let_2 (@ tptp.size_size_list_nat Ys))) (=> (= (@ tptp.size_size_list_nat Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_c Ws)) (=> (@ (@ (@ (@ P tptp.nil_nat) tptp.nil_nat) tptp.nil_int) tptp.nil_c) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.nat) (Ys5 tptp.list_nat) (Z4 tptp.int) (Zs2 tptp.list_int) (W3 tptp.c) (Ws2 tptp.list_c)) (let ((_let_1 (@ tptp.size_size_list_int Zs2))) (let ((_let_2 (@ tptp.size_size_list_nat Ys5))) (=> (= (@ tptp.size_size_list_nat Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_c Ws2)) (=> (@ (@ (@ (@ P Xs2) Ys5) Zs2) Ws2) (@ (@ (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) (@ (@ tptp.cons_nat Y2) Ys5)) (@ (@ tptp.cons_int Z4) Zs2)) (@ (@ tptp.cons_c W3) Ws2))))))))) (@ (@ (@ (@ P Xs) Ys) Zs) Ws))))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (Zs tptp.list_int) (Ws tptp.list_d) (P (-> tptp.list_nat tptp.list_nat tptp.list_int tptp.list_d Bool))) (let ((_let_1 (@ tptp.size_size_list_int Zs))) (let ((_let_2 (@ tptp.size_size_list_nat Ys))) (=> (= (@ tptp.size_size_list_nat Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_d Ws)) (=> (@ (@ (@ (@ P tptp.nil_nat) tptp.nil_nat) tptp.nil_int) tptp.nil_d) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.nat) (Ys5 tptp.list_nat) (Z4 tptp.int) (Zs2 tptp.list_int) (W3 tptp.d) (Ws2 tptp.list_d)) (let ((_let_1 (@ tptp.size_size_list_int Zs2))) (let ((_let_2 (@ tptp.size_size_list_nat Ys5))) (=> (= (@ tptp.size_size_list_nat Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_d Ws2)) (=> (@ (@ (@ (@ P Xs2) Ys5) Zs2) Ws2) (@ (@ (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) (@ (@ tptp.cons_nat Y2) Ys5)) (@ (@ tptp.cons_int Z4) Zs2)) (@ (@ tptp.cons_d W3) Ws2))))))))) (@ (@ (@ (@ P Xs) Ys) Zs) Ws))))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (Zs tptp.list_int) (Ws tptp.list_nat) (P (-> tptp.list_nat tptp.list_nat tptp.list_int tptp.list_nat Bool))) (let ((_let_1 (@ tptp.size_size_list_int Zs))) (let ((_let_2 (@ tptp.size_size_list_nat Ys))) (=> (= (@ tptp.size_size_list_nat Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Ws)) (=> (@ (@ (@ (@ P tptp.nil_nat) tptp.nil_nat) tptp.nil_int) tptp.nil_nat) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.nat) (Ys5 tptp.list_nat) (Z4 tptp.int) (Zs2 tptp.list_int) (W3 tptp.nat) (Ws2 tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_int Zs2))) (let ((_let_2 (@ tptp.size_size_list_nat Ys5))) (=> (= (@ tptp.size_size_list_nat Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Ws2)) (=> (@ (@ (@ (@ P Xs2) Ys5) Zs2) Ws2) (@ (@ (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) (@ (@ tptp.cons_nat Y2) Ys5)) (@ (@ tptp.cons_int Z4) Zs2)) (@ (@ tptp.cons_nat W3) Ws2))))))))) (@ (@ (@ (@ P Xs) Ys) Zs) Ws))))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (Zs tptp.list_int) (Ws tptp.list_int) (P (-> tptp.list_nat tptp.list_nat tptp.list_int tptp.list_int Bool))) (let ((_let_1 (@ tptp.size_size_list_int Zs))) (let ((_let_2 (@ tptp.size_size_list_nat Ys))) (=> (= (@ tptp.size_size_list_nat Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_int Ws)) (=> (@ (@ (@ (@ P tptp.nil_nat) tptp.nil_nat) tptp.nil_int) tptp.nil_int) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.nat) (Ys5 tptp.list_nat) (Z4 tptp.int) (Zs2 tptp.list_int) (W3 tptp.int) (Ws2 tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Zs2))) (let ((_let_2 (@ tptp.size_size_list_nat Ys5))) (=> (= (@ tptp.size_size_list_nat Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_int Ws2)) (=> (@ (@ (@ (@ P Xs2) Ys5) Zs2) Ws2) (@ (@ (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) (@ (@ tptp.cons_nat Y2) Ys5)) (@ (@ tptp.cons_int Z4) Zs2)) (@ (@ tptp.cons_int W3) Ws2))))))))) (@ (@ (@ (@ P Xs) Ys) Zs) Ws))))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_int) (Zs tptp.list_c) (Ws tptp.list_c) (P (-> tptp.list_nat tptp.list_int tptp.list_c tptp.list_c Bool))) (let ((_let_1 (@ tptp.size_size_list_c Zs))) (let ((_let_2 (@ tptp.size_size_list_int Ys))) (=> (= (@ tptp.size_size_list_nat Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_c Ws)) (=> (@ (@ (@ (@ P tptp.nil_nat) tptp.nil_int) tptp.nil_c) tptp.nil_c) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.int) (Ys5 tptp.list_int) (Z4 tptp.c) (Zs2 tptp.list_c) (W3 tptp.c) (Ws2 tptp.list_c)) (let ((_let_1 (@ tptp.size_size_list_c Zs2))) (let ((_let_2 (@ tptp.size_size_list_int Ys5))) (=> (= (@ tptp.size_size_list_nat Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_c Ws2)) (=> (@ (@ (@ (@ P Xs2) Ys5) Zs2) Ws2) (@ (@ (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) (@ (@ tptp.cons_int Y2) Ys5)) (@ (@ tptp.cons_c Z4) Zs2)) (@ (@ tptp.cons_c W3) Ws2))))))))) (@ (@ (@ (@ P Xs) Ys) Zs) Ws))))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_int) (Zs tptp.list_c) (Ws tptp.list_d) (P (-> tptp.list_nat tptp.list_int tptp.list_c tptp.list_d Bool))) (let ((_let_1 (@ tptp.size_size_list_c Zs))) (let ((_let_2 (@ tptp.size_size_list_int Ys))) (=> (= (@ tptp.size_size_list_nat Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_d Ws)) (=> (@ (@ (@ (@ P tptp.nil_nat) tptp.nil_int) tptp.nil_c) tptp.nil_d) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.int) (Ys5 tptp.list_int) (Z4 tptp.c) (Zs2 tptp.list_c) (W3 tptp.d) (Ws2 tptp.list_d)) (let ((_let_1 (@ tptp.size_size_list_c Zs2))) (let ((_let_2 (@ tptp.size_size_list_int Ys5))) (=> (= (@ tptp.size_size_list_nat Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_d Ws2)) (=> (@ (@ (@ (@ P Xs2) Ys5) Zs2) Ws2) (@ (@ (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) (@ (@ tptp.cons_int Y2) Ys5)) (@ (@ tptp.cons_c Z4) Zs2)) (@ (@ tptp.cons_d W3) Ws2))))))))) (@ (@ (@ (@ P Xs) Ys) Zs) Ws))))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_int) (Zs tptp.list_c) (Ws tptp.list_nat) (P (-> tptp.list_nat tptp.list_int tptp.list_c tptp.list_nat Bool))) (let ((_let_1 (@ tptp.size_size_list_c Zs))) (let ((_let_2 (@ tptp.size_size_list_int Ys))) (=> (= (@ tptp.size_size_list_nat Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Ws)) (=> (@ (@ (@ (@ P tptp.nil_nat) tptp.nil_int) tptp.nil_c) tptp.nil_nat) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.int) (Ys5 tptp.list_int) (Z4 tptp.c) (Zs2 tptp.list_c) (W3 tptp.nat) (Ws2 tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_c Zs2))) (let ((_let_2 (@ tptp.size_size_list_int Ys5))) (=> (= (@ tptp.size_size_list_nat Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Ws2)) (=> (@ (@ (@ (@ P Xs2) Ys5) Zs2) Ws2) (@ (@ (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) (@ (@ tptp.cons_int Y2) Ys5)) (@ (@ tptp.cons_c Z4) Zs2)) (@ (@ tptp.cons_nat W3) Ws2))))))))) (@ (@ (@ (@ P Xs) Ys) Zs) Ws))))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_int) (Zs tptp.list_c) (Ws tptp.list_int) (P (-> tptp.list_nat tptp.list_int tptp.list_c tptp.list_int Bool))) (let ((_let_1 (@ tptp.size_size_list_c Zs))) (let ((_let_2 (@ tptp.size_size_list_int Ys))) (=> (= (@ tptp.size_size_list_nat Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_int Ws)) (=> (@ (@ (@ (@ P tptp.nil_nat) tptp.nil_int) tptp.nil_c) tptp.nil_int) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.int) (Ys5 tptp.list_int) (Z4 tptp.c) (Zs2 tptp.list_c) (W3 tptp.int) (Ws2 tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_c Zs2))) (let ((_let_2 (@ tptp.size_size_list_int Ys5))) (=> (= (@ tptp.size_size_list_nat Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_int Ws2)) (=> (@ (@ (@ (@ P Xs2) Ys5) Zs2) Ws2) (@ (@ (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) (@ (@ tptp.cons_int Y2) Ys5)) (@ (@ tptp.cons_c Z4) Zs2)) (@ (@ tptp.cons_int W3) Ws2))))))))) (@ (@ (@ (@ P Xs) Ys) Zs) Ws))))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_int) (Zs tptp.list_d) (Ws tptp.list_c) (P (-> tptp.list_nat tptp.list_int tptp.list_d tptp.list_c Bool))) (let ((_let_1 (@ tptp.size_size_list_d Zs))) (let ((_let_2 (@ tptp.size_size_list_int Ys))) (=> (= (@ tptp.size_size_list_nat Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_c Ws)) (=> (@ (@ (@ (@ P tptp.nil_nat) tptp.nil_int) tptp.nil_d) tptp.nil_c) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.int) (Ys5 tptp.list_int) (Z4 tptp.d) (Zs2 tptp.list_d) (W3 tptp.c) (Ws2 tptp.list_c)) (let ((_let_1 (@ tptp.size_size_list_d Zs2))) (let ((_let_2 (@ tptp.size_size_list_int Ys5))) (=> (= (@ tptp.size_size_list_nat Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_c Ws2)) (=> (@ (@ (@ (@ P Xs2) Ys5) Zs2) Ws2) (@ (@ (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) (@ (@ tptp.cons_int Y2) Ys5)) (@ (@ tptp.cons_d Z4) Zs2)) (@ (@ tptp.cons_c W3) Ws2))))))))) (@ (@ (@ (@ P Xs) Ys) Zs) Ws))))))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_int) (Zs tptp.list_d) (Ws tptp.list_d) (P (-> tptp.list_nat tptp.list_int tptp.list_d tptp.list_d Bool))) (let ((_let_1 (@ tptp.size_size_list_d Zs))) (let ((_let_2 (@ tptp.size_size_list_int Ys))) (=> (= (@ tptp.size_size_list_nat Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_d Ws)) (=> (@ (@ (@ (@ P tptp.nil_nat) tptp.nil_int) tptp.nil_d) tptp.nil_d) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.int) (Ys5 tptp.list_int) (Z4 tptp.d) (Zs2 tptp.list_d) (W3 tptp.d) (Ws2 tptp.list_d)) (let ((_let_1 (@ tptp.size_size_list_d Zs2))) (let ((_let_2 (@ tptp.size_size_list_int Ys5))) (=> (= (@ tptp.size_size_list_nat Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_d Ws2)) (=> (@ (@ (@ (@ P Xs2) Ys5) Zs2) Ws2) (@ (@ (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) (@ (@ tptp.cons_int Y2) Ys5)) (@ (@ tptp.cons_d Z4) Zs2)) (@ (@ tptp.cons_d W3) Ws2))))))))) (@ (@ (@ (@ P Xs) Ys) Zs) Ws))))))))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (K3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.ord_less_nat K3) (@ (@ tptp.power_power_nat N) K3)))))
% 3.70/4.05 (assert (forall ((K3 tptp.nat)) (let ((_let_1 (@ tptp.suc K3))) (= (@ tptp.set_or1210151606488870762an_nat _let_1) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_or1210151606488870762an_nat K3)) (@ (@ tptp.insert_nat2 _let_1) tptp.bot_bot_set_nat))))))
% 3.70/4.05 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B3)))))
% 3.70/4.05 (assert (forall ((P (-> tptp.int Bool)) (X tptp.nat) (Y tptp.nat)) (= (@ P (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat X) Y))) (and (=> (@ (@ tptp.ord_less_eq_nat Y) X) (@ P (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int X)) (@ tptp.semiri1314217659103216013at_int Y)))) (=> (@ (@ tptp.ord_less_nat X) Y) (@ P tptp.zero_zero_int))))))
% 3.70/4.05 (assert (forall ((X tptp.int) (X6 tptp.int) (P Bool) (P3 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ _let_1 X6))) (=> (= X X6) (=> (=> _let_2 (= P P3)) (= (=> (@ _let_1 X) P) (=> _let_2 P3))))))))
% 3.70/4.05 (assert (forall ((X tptp.int) (X6 tptp.int) (P Bool) (P3 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ _let_1 X6))) (=> (= X X6) (=> (=> _let_2 (= P P3)) (= (and (@ _let_1 X) P) (and _let_2 P3))))))))
% 3.70/4.05 (assert (forall ((D2 tptp.int) (P (-> tptp.int Bool)) (K3 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X3 tptp.int)) (=> (@ P X3) (@ P (@ (@ tptp.plus_plus_int X3) D2)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K3) (forall ((X7 tptp.int)) (=> (@ P X7) (@ P (@ (@ tptp.plus_plus_int X7) (@ (@ tptp.times_times_int K3) D2))))))))))
% 3.70/4.05 (assert (forall ((D2 tptp.int) (P (-> tptp.int Bool)) (K3 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X3 tptp.int)) (=> (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) D2)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K3) (forall ((X7 tptp.int)) (=> (@ P X7) (@ P (@ (@ tptp.minus_minus_int X7) (@ (@ tptp.times_times_int K3) D2))))))))))
% 3.70/4.05 (assert (forall ((D2 tptp.int) (P1 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P1 X3) (@ P1 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D2))))) (=> (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z3) (= (@ P X3) (@ P1 X3))))) (=> (exists ((X_12 tptp.int)) (@ P1 X_12)) (exists ((X_1 tptp.int)) (@ P X_1))))))))
% 3.70/4.05 (assert (forall ((D2 tptp.int) (P3 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P3 X3) (@ P3 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D2))))) (=> (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((X_12 tptp.int)) (@ P3 X_12)) (exists ((X_1 tptp.int)) (@ P X_1))))))))
% 3.70/4.05 (assert (forall ((K3 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K3) (not (forall ((N5 tptp.nat)) (=> (= K3 (@ tptp.semiri1314217659103216013at_int N5)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N5))))))))
% 3.70/4.05 (assert (forall ((K3 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K3) (exists ((N5 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N5) (= K3 (@ tptp.semiri1314217659103216013at_int N5)))))))
% 3.70/4.05 (assert (forall ((I tptp.int) (J tptp.int) (K3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int K3)))) (=> (@ (@ tptp.ord_less_int I) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (@ (@ tptp.ord_less_int (@ _let_1 I)) (@ _let_1 J)))))))
% 3.70/4.05 (assert (forall ((K3 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 K3) L) (@ (@ tptp.product_Pair_int_int Q6) R2)) (and (= K3 (@ (@ 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)))))))))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (F4 (-> tptp.nat tptp.int)) (K3 tptp.int)) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) N) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F4 (@ (@ tptp.plus_plus_nat I5) tptp.one_one_nat))) (@ F4 I5)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F4 tptp.zero_zero_nat)) K3) (=> (@ (@ tptp.ord_less_eq_int K3) (@ F4 N)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I5) N) (= (@ F4 I5) K3))))))))
% 3.70/4.05 (assert (forall ((A2 tptp.int) (B2 tptp.int) (Q6 tptp.int) (R2 tptp.int) (Q7 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ (@ tptp.eucl_rel_int A2) B2))) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q6) R2)) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q7) R5)) (= R2 R5))))))
% 3.70/4.05 (assert (forall ((A2 tptp.int) (B2 tptp.int) (Q6 tptp.int) (R2 tptp.int) (Q7 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ (@ tptp.eucl_rel_int A2) B2))) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q6) R2)) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q7) R5)) (= Q6 Q7))))))
% 3.70/4.05 (assert (forall ((K3 tptp.int)) (@ (@ (@ tptp.eucl_rel_int K3) tptp.zero_zero_int) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K3))))
% 3.70/4.05 (assert (forall ((L tptp.int) (K3 tptp.int) (Q6 tptp.int)) (=> (not (= L tptp.zero_zero_int)) (=> (= K3 (@ (@ tptp.times_times_int Q6) L)) (@ (@ (@ tptp.eucl_rel_int K3) L) (@ (@ tptp.product_Pair_int_int Q6) tptp.zero_zero_int))))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (N tptp.nat) (F4 (-> tptp.nat tptp.int)) (K3 tptp.int)) (=> (forall ((I5 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat M2) I5) (@ (@ tptp.ord_less_nat I5) N)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F4 (@ tptp.suc I5))) (@ F4 I5)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (=> (@ (@ tptp.ord_less_eq_int (@ F4 M2)) K3) (=> (@ (@ tptp.ord_less_eq_int K3) (@ F4 N)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M2) I5) (@ (@ tptp.ord_less_eq_nat I5) N) (= (@ F4 I5) K3)))))))))
% 3.70/4.05 (assert (forall ((D2 tptp.int) (Z tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (@ (@ tptp.ord_less_int Z) (@ (@ tptp.plus_plus_int X) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) Z))) tptp.one_one_int)) D2))))))
% 3.70/4.05 (assert (forall ((D2 tptp.int) (X tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int X))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (@ (@ tptp.ord_less_int (@ _let_1 (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ _let_1 Z))) tptp.one_one_int)) D2))) Z)))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (F4 (-> tptp.nat tptp.int)) (K3 tptp.int)) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) N) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F4 (@ tptp.suc I5))) (@ F4 I5)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F4 tptp.zero_zero_nat)) K3) (=> (@ (@ tptp.ord_less_eq_int K3) (@ F4 N)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I5) N) (= (@ F4 I5) K3))))))))
% 3.70/4.05 (assert (= tptp.upto_aux (lambda ((I4 tptp.int) (J2 tptp.int) (Js tptp.list_int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_int J2) I4)) Js) (@ (@ (@ tptp.upto_aux I4) (@ (@ tptp.minus_minus_int J2) tptp.one_one_int)) (@ (@ tptp.cons_int J2) Js))))))
% 3.70/4.05 (assert (= tptp.eucl_rel_int (lambda ((A12 tptp.int) (A23 tptp.int) (A32 tptp.product_prod_int_int)) (or (exists ((K4 tptp.int)) (and (= A12 K4) (= A23 tptp.zero_zero_int) (= A32 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K4)))) (exists ((L4 tptp.int) (K4 tptp.int) (Q8 tptp.int)) (and (= A12 K4) (= A23 L4) (= A32 (@ (@ tptp.product_Pair_int_int Q8) tptp.zero_zero_int)) (not (= L4 tptp.zero_zero_int)) (= K4 (@ (@ tptp.times_times_int Q8) L4)))) (exists ((R4 tptp.int) (L4 tptp.int) (K4 tptp.int) (Q8 tptp.int)) (and (= A12 K4) (= A23 L4) (= A32 (@ (@ tptp.product_Pair_int_int Q8) R4)) (= (@ tptp.sgn_sgn_int R4) (@ tptp.sgn_sgn_int L4)) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R4)) (@ tptp.abs_abs_int L4)) (= K4 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q8) L4)) R4))))))))
% 3.70/4.05 (assert (forall ((A1 tptp.int) (A22 tptp.int) (A33 tptp.product_prod_int_int)) (=> (@ (@ (@ tptp.eucl_rel_int A1) A22) A33) (=> (=> (= A22 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 (= A22 tptp.zero_zero_int)) (not (= A1 (@ (@ tptp.times_times_int Q5) A22)))))) (not (forall ((R6 tptp.int) (Q5 tptp.int)) (=> (= A33 (@ (@ tptp.product_Pair_int_int Q5) R6)) (=> (= (@ tptp.sgn_sgn_int R6) (@ tptp.sgn_sgn_int A22)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R6)) (@ tptp.abs_abs_int A22)) (not (= A1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q5) A22)) R6)))))))))))))
% 3.70/4.05 (assert (forall ((R2 tptp.int) (L tptp.int) (K3 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)) (=> (= K3 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q6) L)) R2)) (@ (@ (@ tptp.eucl_rel_int K3) L) (@ (@ tptp.product_Pair_int_int Q6) R2)))))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (K3 tptp.int)) (let ((_let_1 (@ tptp.power_power_int K3))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K3) (= (@ (@ tptp.divide_divide_int (@ _let_1 M2)) K3) (@ _let_1 (@ (@ tptp.minus_minus_nat M2) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 3.70/4.05 (assert (= (@ (@ tptp.times_times_assn tptp.top_top_assn) tptp.top_top_assn) tptp.top_top_assn))
% 3.70/4.05 (assert (not (= tptp.top_top_assn tptp.one_one_assn)))
% 3.70/4.05 (assert (forall ((A tptp.assn)) (@ (@ tptp.entailst A) tptp.top_top_assn)))
% 3.70/4.05 (assert (not (= tptp.top_top_assn tptp.bot_bot_assn)))
% 3.70/4.05 (assert (forall ((A tptp.assn) (B tptp.assn)) (let ((_let_1 (@ tptp.entailst A))) (= (@ _let_1 (@ (@ tptp.times_times_assn B) tptp.top_top_assn)) (@ _let_1 B)))))
% 3.70/4.05 (assert (forall ((A tptp.assn) (B tptp.assn)) (= (@ (@ tptp.entailst (@ (@ tptp.times_times_assn A) tptp.top_top_assn)) B) (@ (@ tptp.entailst A) B))))
% 3.70/4.05 (assert (forall ((P tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn tptp.top_top_assn))) (let ((_let_2 (@ _let_1 P))) (= (@ _let_1 _let_2) _let_2)))))
% 3.70/4.05 (assert (forall ((P tptp.assn)) (@ (@ tptp.entails P) tptp.top_top_assn)))
% 3.70/4.05 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.sup_sup_assn X) tptp.top_top_assn) tptp.top_top_assn)))
% 3.70/4.05 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.sup_sup_assn tptp.top_top_assn) X) tptp.top_top_assn)))
% 3.70/4.05 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn X) tptp.top_top_assn) X)))
% 3.70/4.05 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn tptp.top_top_assn) X) X)))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M2)) (@ tptp.semiri1408675320244567234ct_nat N))))))
% 3.70/4.05 (assert (forall ((P tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P) H2) (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn P) tptp.top_top_assn)) H2))))
% 3.70/4.05 (assert (forall ((P tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn P) tptp.top_top_assn)) H2) (not (forall ((H5 tptp.produc3658429121746597890et_nat)) (not (@ (@ tptp.rep_assn P) H5)))))))
% 3.70/4.05 (assert (forall ((A tptp.assn) (A6 tptp.assn) (B tptp.assn) (B9 tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn A6))) (=> (@ (@ tptp.entails A) (@ _let_1 tptp.top_top_assn)) (=> (@ (@ tptp.entails B) (@ (@ tptp.times_times_assn B9) tptp.top_top_assn)) (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn A) B)) tptp.top_top_assn)) (@ (@ tptp.times_times_assn (@ _let_1 B9)) tptp.top_top_assn)))))))
% 3.70/4.05 (assert (forall ((A tptp.assn)) (@ (@ tptp.entails A) (@ (@ tptp.times_times_assn A) tptp.top_top_assn))))
% 3.70/4.05 (assert (forall ((P tptp.assn) (Q tptp.assn) (R tptp.assn)) (let ((_let_1 (@ (@ tptp.times_times_assn Q) tptp.top_top_assn))) (=> (@ (@ tptp.entails P) _let_1) (@ (@ tptp.entails (@ (@ tptp.times_times_assn P) R)) _let_1)))))
% 3.70/4.05 (assert (forall ((P tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 Q) (@ _let_1 (@ (@ tptp.times_times_assn Q) tptp.top_top_assn))))))
% 3.70/4.05 (assert (forall ((K3 tptp.int) (L tptp.int) (Q6 tptp.int) (R2 tptp.int)) (=> (@ (@ (@ tptp.eucl_rel_int K3) L) (@ (@ tptp.product_Pair_int_int Q6) R2)) (= (@ (@ tptp.divide_divide_int K3) L) Q6))))
% 3.70/4.05 (assert (forall ((H2 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.rep_assn tptp.top_top_assn) (@ (@ tptp.produc7507926704131184380et_nat H2) tptp.bot_bot_set_nat))))
% 3.70/4.05 (assert (= tptp.entailst (lambda ((P2 tptp.assn) (Q2 tptp.assn)) (@ (@ tptp.entails (@ (@ tptp.times_times_assn P2) tptp.top_top_assn)) (@ (@ tptp.times_times_assn Q2) tptp.top_top_assn)))))
% 3.70/4.05 (assert (= tptp.entailst (lambda ((A5 tptp.assn) (B7 tptp.assn)) (@ (@ tptp.entails A5) (@ (@ tptp.times_times_assn B7) tptp.top_top_assn)))))
% 3.70/4.05 (assert (forall ((P tptp.assn) (Q tptp.assn)) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn P) tptp.top_top_assn)) (@ (@ tptp.times_times_assn Q) tptp.top_top_assn)) (@ (@ tptp.entailst P) Q))))
% 3.70/4.05 (assert (forall ((A tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.entails A) (@ (@ tptp.times_times_assn B) tptp.top_top_assn)) (@ (@ tptp.entailst A) B))))
% 3.70/4.05 (assert (forall ((A tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.entailst A) B) (@ (@ tptp.entails A) (@ (@ tptp.times_times_assn B) tptp.top_top_assn)))))
% 3.70/4.05 (assert (forall ((P tptp.assn) (Q tptp.assn)) (=> (@ (@ (@ tptp.fI_QUERY P) Q) tptp.top_top_assn) (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn Q) tptp.top_top_assn)))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (= (@ (@ tptp.divide_divide_nat M2) N) tptp.zero_zero_nat))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat M2) N)) N) M2))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N) M2)) N) M2))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.divide_divide_nat M2) N) tptp.zero_zero_nat) (or (@ (@ tptp.ord_less_nat M2) N) (= N tptp.zero_zero_nat)))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (I tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.times_times_nat I) N)) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M2) N)) I))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.divide_divide_nat M2) N)) (and (@ (@ tptp.ord_less_eq_nat N) M2) (@ _let_1 N))))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (N tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat K3))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M2)))))))
% 3.70/4.05 (assert (forall ((Q6 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q6) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M2) Q6)) N) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.times_times_nat N) Q6))))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (= (= (@ (@ tptp.divide_divide_nat M2) N) M2) (= N tptp.one_one_nat)))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M2) N)) M2)))))
% 3.70/4.05 (assert (= tptp.divide_divide_nat (lambda ((M tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (or (@ (@ tptp.ord_less_nat M) N2) (= N2 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M) N2)) N2))))))
% 3.70/4.05 (assert (forall ((Q6 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q6) (= (@ (@ tptp.ord_less_eq_nat M2) (@ (@ tptp.divide_divide_nat N) Q6)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M2) Q6)) N)))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (Q6 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q6)) M2) (=> (@ (@ tptp.ord_less_nat M2) (@ _let_1 (@ tptp.suc Q6))) (= (@ (@ tptp.divide_divide_nat M2) N) Q6))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.nat Bool)) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (= N tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.divide_divide_nat M2) N)) (and (=> _let_1 (@ P tptp.zero_zero_nat)) (=> (not _let_1) (forall ((I4 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J2) N) (=> (= M2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) I4)) J2)) (@ P I4))))))))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M2) N)) N))))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat N) (@ (@ tptp.divide_divide_nat M2) N)))))))
% 3.70/4.05 (assert (forall ((K3 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K3))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (= (@ (@ tptp.divide_divide_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.divide_divide_nat M2) N))))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ (@ tptp.divide_divide_nat M2) N) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M2) N)) N)))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.nat Bool)) (M2 tptp.nat) (N tptp.nat)) (= (@ P (@ (@ tptp.divide_divide_nat M2) N)) (or (and (= N tptp.zero_zero_nat) (@ P tptp.zero_zero_nat)) (exists ((Q8 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q8)) M2) (@ (@ tptp.ord_less_nat M2) (@ _let_1 (@ tptp.suc Q8))) (@ P Q8))))))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (@ (@ tptp.ord_less_nat M2) N)) (= (@ (@ tptp.divide_divide_nat M2) N) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M2) N)) N)))))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (= (@ (@ tptp.modulo_modulo_nat M2) N) M2))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat M2) N)) N))))
% 3.70/4.05 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ (@ tptp.modulo_modulo_nat A) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.modulo_modulo_nat B) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat A) N)) (@ (@ tptp.divide_divide_nat B) N))))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat) (P6 tptp.nat) (M2 tptp.nat)) (=> (@ P N) (=> (@ (@ tptp.ord_less_nat N) P6) (=> (@ (@ tptp.ord_less_nat M2) P6) (=> (forall ((N5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N5) P6) (=> (@ P N5) (@ P (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N5)) P6))))) (@ P M2)))))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M2) N)) (= (@ (@ tptp.modulo_modulo_nat M2) N) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M2) N)) N)))))
% 3.70/4.05 (assert (= tptp.modulo_modulo_nat (lambda ((M tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat M) N2)) M) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M) N2)) N2)))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M2) N)) N))))
% 3.70/4.05 (assert (forall ((P (-> tptp.nat Bool)) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (= N tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.modulo_modulo_nat M2) N)) (and (=> _let_1 (@ P M2)) (=> (not _let_1) (forall ((I4 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J2) N) (=> (= M2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) I4)) J2)) (@ P J2))))))))))
% 3.70/4.05 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) N)) (@ (@ (@ tptp.if_nat (= (@ (@ tptp.modulo_modulo_nat B) N) tptp.zero_zero_nat)) tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.divide_divide_nat B) N))))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M2) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat M2) N))) M2) tptp.one_one_nat))))
% 3.70/4.05 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M2 tptp.nat) (N tptp.nat)) (=> (forall ((M6 tptp.nat)) (@ (@ P M6) tptp.zero_zero_nat)) (=> (forall ((M6 tptp.nat) (N5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N5) (=> (@ (@ P N5) (@ (@ tptp.modulo_modulo_nat M6) N5)) (@ (@ P M6) N5)))) (@ (@ P M2) N)))))
% 3.70/4.05 (assert (forall ((K3 tptp.int) (L tptp.int) (Q6 tptp.int) (R2 tptp.int)) (=> (@ (@ (@ tptp.eucl_rel_int K3) L) (@ (@ tptp.product_Pair_int_int Q6) R2)) (= (@ (@ tptp.modulo_modulo_int K3) L) R2))))
% 3.70/4.05 (assert (forall ((K3 tptp.int) (L tptp.int)) (@ (@ (@ tptp.eucl_rel_int K3) L) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int K3) L)) (@ (@ tptp.modulo_modulo_int K3) L)))))
% 3.70/4.05 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.bezw X) tptp.zero_zero_nat) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))))
% 3.70/4.05 (assert (= tptp.minus_minus_assn (lambda ((A3 tptp.assn) (B3 tptp.assn)) (@ (@ tptp.inf_inf_assn A3) (@ tptp.uminus_uminus_assn B3)))))
% 3.70/4.05 (assert (forall ((M2 tptp.int)) (=> (forall ((N5 tptp.nat)) (not (= M2 (@ tptp.semiri1314217659103216013at_int N5)))) (not (forall ((N5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N5) (not (= M2 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N5))))))))))
% 3.70/4.05 (assert (forall ((K3 tptp.int)) (=> (not (= K3 tptp.zero_zero_int)) (=> (forall ((N5 tptp.nat)) (=> (= K3 (@ tptp.semiri1314217659103216013at_int N5)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N5)))) (not (forall ((N5 tptp.nat)) (=> (= K3 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N5))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N5)))))))))
% 3.70/4.05 (assert (forall ((K3 tptp.int)) (=> (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int) (not (forall ((N5 tptp.nat)) (=> (= K3 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N5))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N5))))))))
% 3.70/4.05 (assert (forall ((A2 tptp.int) (B2 tptp.int) (Q6 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.if_int (= R2 tptp.zero_zero_int)))) (let ((_let_2 (@ tptp.uminus_uminus_int Q6))) (=> (@ (@ (@ tptp.eucl_rel_int A2) B2) (@ (@ tptp.product_Pair_int_int Q6) R2)) (=> (not (= B2 tptp.zero_zero_int)) (@ (@ (@ tptp.eucl_rel_int (@ tptp.uminus_uminus_int A2)) B2) (@ (@ tptp.product_Pair_int_int (@ (@ _let_1 _let_2) (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int))) (@ (@ _let_1 tptp.zero_zero_int) (@ (@ tptp.minus_minus_int B2) R2))))))))))
% 3.70/4.05 (assert (forall ((M5 tptp.list_P8527749157015355191n_assn) (P tptp.assn)) (@ (@ (@ (@ tptp.fI_RESULT M5) P) tptp.one_one_assn) tptp.top_top_assn)))
% 3.70/4.05 (assert (forall ((M5 tptp.list_P8527749157015355191n_assn) (F tptp.assn)) (@ (@ (@ (@ tptp.fI_RESULT M5) F) tptp.one_one_assn) F)))
% 3.70/4.05 (assert (forall ((M5 tptp.list_P8527749157015355191n_assn)) (@ (@ (@ (@ tptp.fI_RESULT M5) tptp.one_one_assn) tptp.one_one_assn) tptp.one_one_assn)))
% 3.70/4.05 (assert (= (@ tptp.complete_Sup_Sup_nat tptp.bot_bot_set_nat) tptp.zero_zero_nat))
% 3.70/4.05 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))) (let ((_let_2 (@ tptp.numeral_numeral_int M2))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 3.70/4.05 (assert (forall ((J tptp.int) (I tptp.int)) (=> (@ (@ tptp.ord_less_int J) I) (= (@ (@ tptp.upto I) J) tptp.nil_int))))
% 3.70/4.05 (assert (forall ((I tptp.int) (J tptp.int)) (= (= tptp.nil_int (@ (@ tptp.upto I) J)) (@ (@ tptp.ord_less_int J) I))))
% 3.70/4.05 (assert (forall ((I tptp.int) (J tptp.int)) (= (= (@ (@ tptp.upto I) J) tptp.nil_int) (@ (@ tptp.ord_less_int J) I))))
% 3.70/4.05 (assert (forall ((I tptp.int)) (= (@ (@ tptp.upto I) I) (@ (@ tptp.cons_int I) tptp.nil_int))))
% 3.70/4.05 (assert (forall ((I tptp.int) (K3 tptp.nat) (J tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int I) (@ tptp.semiri1314217659103216013at_int K3)))) (=> (@ (@ tptp.ord_less_eq_int _let_1) J) (= (@ (@ tptp.nth_int (@ (@ tptp.upto I) J)) K3) _let_1)))))
% 3.70/4.05 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M2))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 3.70/4.05 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2)))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 3.70/4.05 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2)))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 3.70/4.05 (assert (forall ((I tptp.int) (J tptp.int)) (@ tptp.distinct_int (@ (@ tptp.upto I) J))))
% 3.70/4.05 (assert (forall ((M2 tptp.int) (N tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) (@ (@ tptp.upto M2) N))))
% 3.70/4.05 (assert (forall ((I tptp.int) (J tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_int) (@ (@ tptp.upto I) J))))
% 3.70/4.05 (assert (= tptp.upto_aux (lambda ((I4 tptp.int) (J2 tptp.int) (__flatten_var_0 tptp.list_int)) (@ (@ tptp.append_int (@ (@ tptp.upto I4) J2)) __flatten_var_0))))
% 3.70/4.05 (assert (= tptp.upto (lambda ((I4 tptp.int) (J2 tptp.int)) (@ (@ (@ tptp.upto_aux I4) J2) tptp.nil_int))))
% 3.70/4.05 (assert (forall ((I tptp.int) (J tptp.int) (K3 tptp.int)) (let ((_let_1 (@ tptp.upto I))) (=> (@ (@ tptp.ord_less_eq_int I) J) (=> (@ (@ tptp.ord_less_eq_int J) K3) (= (@ _let_1 K3) (@ (@ tptp.append_int (@ _let_1 J)) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int J) tptp.one_one_int)) K3))))))))
% 3.70/4.05 (assert (forall ((I tptp.int) (J tptp.int) (K3 tptp.int)) (let ((_let_1 (@ tptp.upto I))) (=> (@ (@ tptp.ord_less_eq_int I) J) (=> (@ (@ tptp.ord_less_eq_int J) K3) (= (@ _let_1 K3) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.upto J) K3))))))))
% 3.70/4.05 (assert (forall ((I tptp.int) (J tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I) J) (= (@ (@ tptp.upto I) J) (@ (@ tptp.cons_int I) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I) tptp.one_one_int)) J))))))
% 3.70/4.05 (assert (= tptp.upto (lambda ((I4 tptp.int) (J2 tptp.int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_eq_int I4) J2)) (@ (@ tptp.cons_int I4) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) J2))) tptp.nil_int))))
% 3.70/4.05 (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)))))))
% 3.70/4.05 (assert (forall ((I tptp.int) (J tptp.int)) (let ((_let_1 (@ tptp.upto I))) (=> (@ (@ tptp.ord_less_eq_int I) J) (= (@ _let_1 J) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.cons_int J) tptp.nil_int)))))))
% 3.70/4.05 (assert (forall ((I tptp.int) (J tptp.int) (K3 tptp.int)) (let ((_let_1 (@ tptp.upto I))) (=> (@ (@ tptp.ord_less_eq_int I) J) (=> (@ (@ tptp.ord_less_eq_int J) K3) (= (@ _let_1 K3) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.cons_int J) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int J) tptp.one_one_int)) K3)))))))))
% 3.70/4.05 (assert (forall ((X tptp.num) (N tptp.nat) (A2 tptp.int)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)) (@ tptp.nat2 A2)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) A2))))
% 3.70/4.05 (assert (forall ((A2 tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 A2)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)) (@ (@ tptp.ord_less_int A2) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 3.70/4.05 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z)) (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_int W) Z)))))
% 3.70/4.05 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 3.70/4.05 (assert (forall ((I tptp.int) (J tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.upto I) J)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int J) I)) tptp.one_one_int)))))
% 3.70/4.05 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z))))
% 3.70/4.05 (assert (forall ((Z tptp.int) (W tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int W) Z)))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (Z tptp.int)) (= (@ (@ tptp.ord_less_nat M2) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M2)) Z))))
% 3.70/4.05 (assert (forall ((W tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int W) Z)))))
% 3.70/4.05 (assert (forall ((W tptp.int) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) M2) (@ (@ tptp.ord_less_int W) (@ tptp.semiri1314217659103216013at_int M2))))))
% 3.70/4.05 (assert (forall ((B2 tptp.int) (A2 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 B2) tptp.zero_zero_int) (=> (@ (@ (@ tptp.eucl_rel_int (@ (@ tptp.plus_plus_int A2) tptp.one_one_int)) B2) (@ _let_2 R2)) (@ (@ (@ tptp.eucl_rel_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 A2))) (@ _let_1 B2)) (@ _let_2 (@ (@ tptp.minus_minus_int (@ _let_1 R2)) tptp.one_one_int)))))))))
% 3.70/4.05 (assert (forall ((B2 tptp.int) (A2 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) B2) (=> (@ (@ (@ tptp.eucl_rel_int A2) B2) (@ _let_3 R2)) (@ (@ (@ tptp.eucl_rel_int (@ _let_2 (@ _let_1 A2))) (@ _let_1 B2)) (@ _let_3 (@ _let_2 (@ _let_1 R2)))))))))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat M2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (= _let_1 tptp.one_one_nat)))))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (or (= N tptp.zero_zero_nat) (= N (@ tptp.suc tptp.zero_zero_nat))))))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (or (= N tptp.zero_zero_nat) (= N (@ tptp.suc tptp.zero_zero_nat))))))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 3.70/4.05 (assert (forall ((B2 tptp.nat) (K3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B2) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) K3) (exists ((N5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N5)) K3) (@ (@ tptp.ord_less_nat K3) (@ _let_1 (@ (@ tptp.plus_plus_nat N5) tptp.one_one_nat))))))))))
% 3.70/4.05 (assert (forall ((B2 tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ _let_1 B2) (=> (@ _let_1 K3) (exists ((N5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (and (@ (@ tptp.ord_less_nat (@ _let_1 N5)) K3) (@ (@ tptp.ord_less_eq_nat K3) (@ _let_1 (@ (@ tptp.plus_plus_nat N5) tptp.one_one_nat)))))))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N5 tptp.nat)) (=> (@ P N5) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N5) (@ P (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N5))))) (=> (forall ((N5 tptp.nat)) (=> (@ P N5) (@ P (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N5))))) (@ P N))))))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 3.70/4.05 (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))))
% 3.70/4.05 (assert (= tptp.dvd_dvd_int (lambda ((D5 tptp.int) (T2 tptp.int)) (@ (@ tptp.dvd_dvd_int D5) (@ tptp.uminus_uminus_int T2)))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_nat M2) N) (not (@ (@ tptp.dvd_dvd_nat N) M2))))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (=> (@ (@ tptp.dvd_dvd_nat M2) N) (@ _let_1 M2))))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M2))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2)) (or (@ (@ tptp.ord_less_nat N) M2) (@ _let_1 N))))))
% 3.70/4.05 (assert (forall ((K3 tptp.int) (M2 tptp.int) (T tptp.int)) (let ((_let_1 (@ tptp.times_times_int K3))) (=> (not (= K3 tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int M2) T) (@ (@ tptp.dvd_dvd_int (@ _let_1 M2)) (@ _let_1 T)))))))
% 3.70/4.05 (assert (forall ((K3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat K3) N) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat K3) N)))))
% 3.70/4.05 (assert (forall ((K3 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K3))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.dvd_dvd_nat M2) N))))))
% 3.70/4.05 (assert (forall ((K3 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K3))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (@ (@ tptp.dvd_dvd_nat M2) N))))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.modulo_modulo_nat M2) N)) (not (@ (@ tptp.dvd_dvd_nat N) M2)))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat N) M2)) M2) (= N tptp.one_one_nat)))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat M2) N)) M2) (= N tptp.one_one_nat)))))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)))) (= (@ _let_2 N) (@ _let_2 (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1)))))))))
% 3.70/4.05 (assert (forall ((R2 tptp.nat) (N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat R2) N) (=> (@ (@ tptp.ord_less_eq_nat R2) M2) (=> (@ (@ tptp.dvd_dvd_nat N) (@ (@ tptp.minus_minus_nat M2) R2)) (= (@ (@ tptp.modulo_modulo_nat M2) N) R2))))))
% 3.70/4.05 (assert (forall ((I tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) I) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) M2) M2))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M2)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N) M2) M2) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M2)) M2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) M2))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (K3 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int _let_1) K3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int N) K3)) (@ (@ tptp.minus_minus_int K3) _let_1)))))))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.suc tptp.zero_zero_nat))) (=> (= (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))) _let_3) (@ (@ tptp.dvd_dvd_nat _let_2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) _let_3)) _let_2))))))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)) (or (@ (@ tptp.ord_less_nat M2) N) (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)))))))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 3.70/4.05 (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)))))))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (=> (= (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (not (@ (@ tptp.dvd_dvd_nat _let_2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) _let_2))))))))
% 3.70/4.05 (assert (forall ((X tptp.product_prod_num_num)) (=> (not (= X (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one))) (=> (forall ((N5 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit0 N5))))) (=> (forall ((N5 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit1 N5))))) (=> (forall ((M6 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M6)) tptp.one)))) (=> (forall ((M6 tptp.num) (N5 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M6)) (@ tptp.bit0 N5))))) (=> (forall ((M6 tptp.num) (N5 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M6)) (@ tptp.bit1 N5))))) (=> (forall ((M6 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M6)) tptp.one)))) (=> (forall ((M6 tptp.num) (N5 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M6)) (@ tptp.bit0 N5))))) (not (forall ((M6 tptp.num) (N5 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M6)) (@ tptp.bit1 N5))))))))))))))))
% 3.70/4.05 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (let ((_let_2 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))
% 3.70/4.05 (assert (= tptp.unique5052692396658037445od_int (lambda ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))
% 3.70/4.05 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bitM M2)) (@ tptp.bit0 tptp.one)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M2)) tptp.one_one_int)) tptp.one_one_int))))
% 3.70/4.05 (assert (forall ((K3 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat K3)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat (@ tptp.pred_numeral K3)) N))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (K3 tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K3)) (@ (@ tptp.ord_less_nat N) (@ tptp.pred_numeral K3)))))
% 3.70/4.05 (assert (= tptp.divmod_nat (lambda ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.modulo_modulo_nat M) N2)))))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.bit_se2002935070580805687sk_nat N)) (@ _let_1 N)))))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.ord_less_nat N) (@ tptp.bit_se2002935070580805687sk_nat N)))))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat (@ tptp.bit_se2002935070580805687sk_nat N)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 3.70/4.05 (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_int2 tptp.zero_zero_int) (@ (@ tptp.insert_int2 (@ 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)))))))))))))
% 3.70/4.05 (assert (forall ((K3 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 K3)) (not (@ _let_2 L)))))) (let ((_let_4 (@ (@ tptp.bit_se725231765392027082nd_int K3) L))) (let ((_let_5 (@ (@ tptp.insert_int2 tptp.zero_zero_int) (@ (@ tptp.insert_int2 (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_6 (and (@ (@ tptp.member_int K3) _let_5) (@ (@ tptp.member_int L) _let_5)))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int K3) 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 K3) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1))))))))))))))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (M2 tptp.nat) (K3 tptp.int)) (=> (@ (@ tptp.ord_less_nat N) M2) (=> (@ (@ tptp.bit_se1146084159140164899it_int K3) N) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int M2) K3))))))
% 3.70/4.05 (assert (forall ((K3 tptp.int)) (not (forall ((N5 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K3))) (=> (forall ((M3 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K3))) (=> (@ (@ tptp.ord_less_eq_nat N5) M3) (= (@ _let_1 M3) (@ _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)))))))))))
% 3.70/4.05 (assert (forall ((A0 tptp.int) (A1 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int A0) A1)) (=> (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.insert_int2 tptp.zero_zero_int) (@ (@ tptp.insert_int2 (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int K) L2)) (=> (=> (not (and (@ (@ tptp.member_int K) _let_2) (@ (@ tptp.member_int L2) _let_2))) (@ (@ P (@ (@ tptp.divide_divide_int K) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))) (@ (@ P K) L2)))))) (@ (@ P A0) A1)))))
% 3.70/4.05 (assert (forall ((I tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.upto I) J))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int I) J))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I) J)) (and (=> _let_2 (= _let_1 (@ (@ tptp.cons_int I) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I) tptp.one_one_int)) J)))) (=> (not _let_2) (= _let_1 tptp.nil_int))))))))
% 3.70/4.05 (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)))))))))
% 3.70/4.05 (assert (forall ((A0 tptp.int) (A1 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int A0) A1)) (=> (forall ((I5 tptp.int) (J3 tptp.int)) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I5) J3)) (=> (=> (@ (@ tptp.ord_less_eq_int I5) J3) (@ (@ P (@ (@ tptp.plus_plus_int I5) tptp.one_one_int)) J3)) (@ (@ P I5) J3)))) (@ (@ P A0) A1)))))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.num_of_nat (@ tptp.suc N)))) (let ((_let_2 (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (and (=> _let_2 (= _let_1 (@ tptp.inc (@ tptp.num_of_nat N)))) (=> (not _let_2) (= _let_1 tptp.one)))))))
% 3.70/4.05 (assert (= tptp.binomial (lambda ((N2 tptp.nat) (K4 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) K4))) (let ((_let_2 (@ tptp.ord_less_nat N2))) (@ (@ (@ tptp.if_nat (@ _let_2 K4)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_2 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K4))) (@ (@ tptp.binomial N2) _let_1)) (@ (@ tptp.divide_divide_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) N2) tptp.one_one_nat)) (@ tptp.semiri1408675320244567234ct_nat K4)))))))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.nat_set_decode Z))) (=> (not (@ (@ tptp.member_nat N) _let_1)) (= (@ tptp.nat_set_decode (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) Z)) (@ (@ tptp.insert_nat2 N) _let_1))))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (K3 tptp.nat)) (= (= (@ (@ tptp.binomial N) K3) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat N) K3))))
% 3.70/4.05 (assert (= (@ tptp.nat_set_decode tptp.zero_zero_nat) tptp.bot_bot_set_nat))
% 3.70/4.05 (assert (forall ((N tptp.nat) (K3 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.binomial N) K3)) (@ (@ tptp.ord_less_eq_nat K3) N))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (K3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K3) (= (@ (@ tptp.binomial N) K3) tptp.zero_zero_nat))))
% 3.70/4.05 (assert (forall ((K3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.binomial N) K3)))))
% 3.70/4.05 (assert (forall ((X tptp.product_prod_nat_nat)) (not (forall ((K tptp.nat) (M6 tptp.nat)) (not (= X (@ (@ tptp.product_Pair_nat_nat K) M6)))))))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.numeral_numeral_nat (@ tptp.num_of_nat N)) N))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_2 N) (=> (@ _let_2 K3) (= (@ (@ tptp.binomial N) K3) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))) (@ _let_1 K3)))))))))
% 3.70/4.05 (assert (forall ((K3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (= (@ (@ tptp.times_times_nat K3) (@ (@ tptp.binomial N) K3)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat)))))))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat N) N)) (@ tptp.bit0 (@ tptp.num_of_nat N))))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (= (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.plus_plus_num (@ tptp.num_of_nat M2)) (@ tptp.num_of_nat N))))))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) (let ((_let_2 (@ tptp.suc K3))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.binomial N) _let_2) (@ (@ tptp.plus_plus_nat (@ _let_1 _let_2)) (@ _let_1 K3))))))))
% 3.70/4.05 (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))))))))))
% 3.70/4.05 (assert (= tptp.nat_prod_decode_aux (lambda ((K4 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc K4))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat M) K4)) (@ (@ tptp.product_Pair_nat_nat M) (@ (@ tptp.minus_minus_nat K4) M))) (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat M) _let_1)))))))
% 3.70/4.05 (assert (forall ((D tptp.int) (P (-> tptp.int Bool)) (P3 (-> tptp.int Bool)) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X3) (= (@ P X3) (@ P3 X3))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ P X3) (@ P (@ (@ tptp.plus_plus_int X3) D))))) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P3 X3) (@ P3 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D))))) (= (exists ((X8 tptp.int)) (@ P X8)) (or (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (@ P3 X2))) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (exists ((Y5 tptp.int)) (and (@ (@ tptp.member_int Y5) A) (@ P (@ (@ tptp.minus_minus_int Y5) X2))))))))))))))
% 3.70/4.05 (assert (= tptp.set_or1266510415728281911st_int (lambda ((I4 tptp.int) (J2 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I4) J2)))))
% 3.70/4.05 (assert (forall ((D tptp.int) (B tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) D))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ Q X3) (@ Q (@ (@ tptp.minus_minus_int X3) D))))) (forall ((X7 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X7) D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B) (not (= X7 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (and (@ P X7) (@ Q X7)) (and (@ P _let_1) (@ Q _let_1))))))))))
% 3.70/4.05 (assert (forall ((D tptp.int) (B tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) D))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ Q X3) (@ Q (@ (@ tptp.minus_minus_int X3) D))))) (forall ((X7 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X7) D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B) (not (= X7 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (or (@ P X7) (@ Q X7)) (or (@ P _let_1) (@ Q _let_1))))))))))
% 3.70/4.05 (assert (forall ((D tptp.int) (A tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ P X3) (@ P (@ (@ tptp.plus_plus_int X3) D))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ Q X3) (@ Q (@ (@ tptp.plus_plus_int X3) D))))) (forall ((X7 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int X7) D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A) (not (= X7 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (and (@ P X7) (@ Q X7)) (and (@ P _let_1) (@ Q _let_1))))))))))
% 3.70/4.05 (assert (forall ((D tptp.int) (A tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ P X3) (@ P (@ (@ tptp.plus_plus_int X3) D))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ Q X3) (@ Q (@ (@ tptp.plus_plus_int X3) D))))) (forall ((X7 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int X7) D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A) (not (= X7 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (or (@ P X7) (@ Q X7)) (or (@ P _let_1) (@ Q _let_1))))))))))
% 3.70/4.05 (assert (forall ((D2 tptp.int) (D tptp.int) (A tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D) (forall ((X7 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X7))) (let ((_let_2 (@ tptp.dvd_dvd_int D2))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A) (not (= X7 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (not (@ _let_2 (@ _let_1 T))) (not (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 D)) T)))))))))))
% 3.70/4.05 (assert (forall ((D2 tptp.int) (D tptp.int) (A tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D) (forall ((X7 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X7))) (let ((_let_2 (@ tptp.dvd_dvd_int D2))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A) (not (= X7 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ _let_2 (@ _let_1 T)) (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 D)) T))))))))))
% 3.70/4.05 (assert (forall ((D2 tptp.int) (D tptp.int) (B tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D) (forall ((X7 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D2))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B) (not (= X7 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (not (@ _let_1 (@ (@ tptp.plus_plus_int X7) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X7) D)) T))))))))))
% 3.70/4.05 (assert (forall ((D2 tptp.int) (D tptp.int) (B tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D) (forall ((X7 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D2))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B) (not (= X7 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ _let_1 (@ (@ tptp.plus_plus_int X7) T)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X7) D)) T)))))))))
% 3.70/4.05 (assert (forall ((D2 tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D2))))) (= (exists ((X8 tptp.int)) (@ P X8)) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D2)) (@ P X2))))))))
% 3.70/4.05 (assert (forall ((D tptp.int) (A tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (forall ((X7 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A) (not (= X7 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ _let_1 X7) (@ _let_1 (@ (@ tptp.plus_plus_int X7) D)))))))))
% 3.70/4.05 (assert (forall ((D tptp.int) (T tptp.int) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (@ (@ tptp.member_int T) A) (forall ((X7 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A) (not (= X7 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_int X7) T) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X7) D)) T))))))))
% 3.70/4.05 (assert (forall ((D tptp.int) (T tptp.int) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (@ (@ tptp.member_int T) A) (forall ((X7 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A) (not (= X7 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (not (= X7 T)) (not (= (@ (@ tptp.plus_plus_int X7) D) T)))))))))
% 3.70/4.05 (assert (forall ((D tptp.int) (T tptp.int) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T) tptp.one_one_int)) A) (forall ((X7 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A) (not (= X7 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (= X7 T) (= (@ (@ tptp.plus_plus_int X7) D) T))))))))
% 3.70/4.05 (assert (forall ((D tptp.int) (T tptp.int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (@ (@ tptp.member_int T) B) (forall ((X7 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B) (not (= X7 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ _let_1 X7) (@ _let_1 (@ (@ tptp.minus_minus_int X7) D))))))))))
% 3.70/4.05 (assert (forall ((D tptp.int) (B tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (forall ((X7 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B) (not (= X7 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_int X7) T) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int X7) D)) T)))))))
% 3.70/4.05 (assert (forall ((D tptp.int) (T tptp.int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (@ (@ tptp.member_int T) B) (forall ((X7 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B) (not (= X7 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (not (= X7 T)) (not (= (@ (@ tptp.minus_minus_int X7) D) T)))))))))
% 3.70/4.05 (assert (forall ((D tptp.int) (T tptp.int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T) tptp.one_one_int)) B) (forall ((X7 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B) (not (= X7 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (= X7 T) (= (@ (@ tptp.minus_minus_int X7) D) T))))))))
% 3.70/4.05 (assert (= tptp.set_or1266510415728281911st_int (lambda ((I4 tptp.int) (J2 tptp.int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_int J2) I4)) tptp.bot_bot_set_int) (@ (@ tptp.insert_int2 I4) (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) J2))))))
% 3.70/4.05 (assert (forall ((D tptp.int) (B tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (forall ((X7 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B) (not (= X7 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X7) T) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int X7) D)) T)))))))
% 3.70/4.05 (assert (forall ((D tptp.int) (T tptp.int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T) tptp.one_one_int)) B) (forall ((X7 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B) (not (= X7 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ _let_1 X7) (@ _let_1 (@ (@ tptp.minus_minus_int X7) D))))))))))
% 3.70/4.05 (assert (forall ((D tptp.int) (T tptp.int) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T) tptp.one_one_int)) A) (forall ((X7 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A) (not (= X7 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X7) T) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int X7) D)) T))))))))
% 3.70/4.05 (assert (forall ((D tptp.int) (A tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (forall ((X7 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A) (not (= X7 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ _let_1 X7) (@ _let_1 (@ (@ tptp.plus_plus_int X7) D)))))))))
% 3.70/4.05 (assert (forall ((D tptp.int) (P (-> tptp.int Bool)) (P3 (-> tptp.int Bool)) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z3) (= (@ P X3) (@ P3 X3))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) D))))) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P3 X3) (@ P3 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D))))) (= (exists ((X8 tptp.int)) (@ P X8)) (or (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (@ P3 X2))) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (exists ((Y5 tptp.int)) (and (@ (@ tptp.member_int Y5) B) (@ P (@ (@ tptp.plus_plus_int Y5) X2))))))))))))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat M2) N)) (@ tptp.transi6264000038957366511cl_nat tptp.pred_nat)) (@ (@ tptp.ord_less_nat M2) N))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ P M))) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P X2))))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ P M))) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P X2))))))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.suc N))) (= (@ _let_1 _let_2) (@ (@ tptp.insert_nat2 _let_2) (@ _let_1 N)))))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.insert_nat2 M2) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N)) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_nat2 _let_2) (@ _let_1 N))))))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.set_or1269000886237332187st_nat M2) N) (@ (@ tptp.insert_nat2 M2) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N))))))
% 3.70/4.05 (assert (= tptp.set_or5832277885323065728an_int (lambda ((I4 tptp.int) (J2 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) (@ (@ tptp.minus_minus_int J2) tptp.one_one_int))))))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.insert_nat2 tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))
% 3.70/4.05 (assert (= (@ tptp.set_ord_atMost_nat tptp.zero_zero_nat) (@ (@ tptp.insert_nat2 tptp.zero_zero_nat) tptp.bot_bot_set_nat)))
% 3.70/4.05 (assert (forall ((K3 tptp.nat)) (let ((_let_1 (@ tptp.suc K3))) (= (@ tptp.set_ord_atMost_nat _let_1) (@ (@ tptp.insert_nat2 _let_1) (@ tptp.set_ord_atMost_nat K3))))))
% 3.70/4.05 (assert (forall ((K3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat K3))) (= (@ tptp.set_ord_atMost_nat _let_1) (@ (@ tptp.insert_nat2 _let_1) (@ tptp.set_ord_atMost_nat (@ tptp.pred_numeral K3)))))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.minus_minus_nat J) (@ tptp.suc I))) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I) J))) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) N))))))
% 3.70/4.05 (assert (forall ((K3 tptp.nat)) (let ((_let_1 (@ tptp.suc K3))) (= (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.append_nat (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_atMost_nat K3))) (@ (@ tptp.cons_nat _let_1) tptp.nil_nat))))))
% 3.70/4.05 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.suc I))) (=> (@ (@ tptp.ord_less_nat _let_1) J) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I) J)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat _let_1) J))))))))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.insert_nat2 tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ _let_1 N)))))))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (= (@ tptp.set_ord_atMost_nat (@ tptp.suc N)) (@ (@ tptp.insert_nat2 tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_atMost_nat N))))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.minus_minus_nat J) I)) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I) J))) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) N))))))
% 3.70/4.05 (assert (= tptp.finite_finite_nat (lambda ((N8 tptp.set_nat)) (exists ((M tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) N8) (@ (@ tptp.ord_less_nat X2) M)))))))
% 3.70/4.05 (assert (forall ((N7 tptp.set_nat) (N tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) N7) (@ (@ tptp.ord_less_nat X3) N))) (@ tptp.finite_finite_nat N7))))
% 3.70/4.05 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.suc I))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) J) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I) J)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat _let_1) J))))))))
% 3.70/4.05 (assert (forall ((M5 tptp.set_nat)) (=> (@ tptp.finite_finite_nat M5) (= (@ tptp.gcd_Gcd_nat M5) (@ tptp.gcd_Gcd_nat (@ (@ tptp.minus_minus_set_nat M5) (@ (@ tptp.insert_nat2 tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))))
% 3.70/4.05 (assert (forall ((A tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (@ (@ tptp.member_nat N) A)) (= (@ tptp.nat_set_encode (@ (@ tptp.insert_nat2 N) A)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.nat_set_encode A)))))))
% 3.70/4.05 (assert (= (@ tptp.nat_set_encode tptp.bot_bot_set_nat) tptp.zero_zero_nat))
% 3.70/4.05 (assert (= tptp.set_or6656581121297822940st_int (lambda ((I4 tptp.int) (J2 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) J2)))))
% 3.70/4.05 (assert (forall ((K3 tptp.nat) (S tptp.set_nat)) (=> (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K3) M6) (exists ((N9 tptp.nat)) (and (@ (@ tptp.ord_less_nat M6) N9) (@ (@ tptp.member_nat N9) S))))) (not (@ tptp.finite_finite_nat S)))))
% 3.70/4.05 (assert (forall ((S tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S)) (forall ((M tptp.nat)) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.member_nat N2) S)))))))
% 3.70/4.05 (assert (forall ((K3 tptp.nat)) (= (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_lessThan_nat (@ tptp.suc K3))) (@ (@ tptp.append_nat (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_lessThan_nat K3))) (@ (@ tptp.cons_nat K3) tptp.nil_nat)))))
% 3.70/4.05 (assert (= (@ tptp.set_ord_lessThan_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))
% 3.70/4.05 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M2) (@ tptp.suc M2)) (@ (@ tptp.insert_nat2 M2) tptp.bot_bot_set_nat))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M tptp.nat)) (and (@ (@ tptp.ord_less_nat M) N) (@ P M))) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P X2))))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ P M))) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P X2))))))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat N) tptp.bot_bot_set_nat) (= N tptp.zero_zero_nat))))
% 3.70/4.05 (assert (forall ((K3 tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K3)) (@ (@ tptp.insert_nat2 K3) (@ tptp.set_ord_lessThan_nat K3)))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M2) tptp.zero_zero_nat) tptp.bot_bot_set_nat)))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.insert_nat2 tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.insert_nat2 N) (@ _let_1 N))))))
% 3.70/4.05 (assert (forall ((K3 tptp.num)) (let ((_let_1 (@ tptp.pred_numeral K3))) (= (@ tptp.set_ord_lessThan_nat (@ tptp.numeral_numeral_nat K3)) (@ (@ tptp.insert_nat2 _let_1) (@ tptp.set_ord_lessThan_nat _let_1))))))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc N)) (@ (@ tptp.insert_nat2 tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_lessThan_nat N))))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M2))) (let ((_let_2 (@ _let_1 (@ tptp.suc N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat M2) N))) (and (=> _let_3 (= _let_2 (@ (@ tptp.insert_nat2 N) (@ _let_1 N)))) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_nat))))))))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.insert_nat2 tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ _let_1 N)))))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (K3 tptp.num)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M2))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat K3)))) (let ((_let_3 (@ tptp.pred_numeral K3))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat M2) _let_3))) (and (=> _let_4 (= _let_2 (@ (@ tptp.insert_nat2 _let_3) (@ _let_1 _let_3)))) (=> (not _let_4) (= _let_2 tptp.bot_bot_set_nat)))))))))
% 3.70/4.05 (assert (= tptp.set_or4662586982721622107an_int (lambda ((I4 tptp.int) (J2 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I4) (@ (@ tptp.minus_minus_int J2) tptp.one_one_int))))))
% 3.70/4.05 (assert (forall ((K3 tptp.nat)) (= (@ tptp.set_ord_atLeast_nat (@ tptp.suc K3)) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_atLeast_nat K3)) (@ (@ tptp.insert_nat2 K3) tptp.bot_bot_set_nat)))))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.ord_less_nat I4) N)))) N)))
% 3.70/4.05 (assert (forall ((K3 tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat N2) K3))))))
% 3.70/4.05 (assert (forall ((M5 tptp.set_nat) (I tptp.nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M5)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K4 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K4)) M5) (@ (@ tptp.ord_less_nat K4) I))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K4 tptp.nat)) (and (@ (@ tptp.member_nat K4) M5) (@ (@ tptp.ord_less_nat K4) (@ tptp.suc I))))))))))
% 3.70/4.05 (assert (forall ((M5 tptp.set_nat) (I tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M5) (= (@ tptp.suc (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K4 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K4)) M5) (@ (@ tptp.ord_less_nat K4) I)))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K4 tptp.nat)) (and (@ (@ tptp.member_nat K4) M5) (@ (@ tptp.ord_less_nat K4) (@ tptp.suc I))))))))))
% 3.70/4.05 (assert (forall ((M5 tptp.set_nat) (I tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M5) (not (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K4 tptp.nat)) (and (@ (@ tptp.member_nat K4) M5) (@ (@ tptp.ord_less_nat K4) (@ tptp.suc I)))))) tptp.zero_zero_nat)))))
% 3.70/4.05 (assert (forall ((P (-> tptp.nat Bool)) (I tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((K4 tptp.nat)) (and (@ P K4) (@ (@ tptp.ord_less_nat K4) I)))))))
% 3.70/4.05 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B3)))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((D5 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D5) M2)))))))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.image_nat_nat (lambda ((M tptp.nat)) (@ (@ tptp.modulo_modulo_nat M) N))) tptp.top_top_set_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)))))
% 3.70/4.05 (assert (forall ((C tptp.nat) (Y tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat X) Y))) (let ((_let_2 (@ (@ tptp.ord_less_nat X) Y))) (let ((_let_3 (@ (@ tptp.ord_less_nat C) Y))) (and (=> _let_3 (= (@ (@ tptp.image_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat I4) C))) _let_1) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.minus_minus_nat X) C)) (@ (@ tptp.minus_minus_nat Y) C)))) (=> (not _let_3) (and (=> _let_2 (= (@ (@ tptp.image_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat I4) C))) _let_1) (@ (@ tptp.insert_nat2 tptp.zero_zero_nat) tptp.bot_bot_set_nat))) (=> (not _let_2) (= (@ (@ tptp.image_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat I4) C))) _let_1) tptp.bot_bot_set_nat))))))))))
% 3.70/4.05 (assert (= tptp.complete_Sup_Sup_nat (lambda ((X8 tptp.set_nat)) (@ (@ (@ tptp.if_nat (= X8 tptp.bot_bot_set_nat)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat X8)))))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 N)) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ tptp.collect_nat (lambda ((Q8 tptp.nat)) (@ (@ tptp.ord_less_nat Q8) N))))))))
% 3.70/4.05 (assert (= tptp.divmod_nat (lambda ((M tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (or (= N2 tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat M) N2))) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) M)) (@ (@ 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 M) N2)) N2))))))
% 3.70/4.05 (assert (= tptp.unique5026877609467782581ep_nat (lambda ((L4 tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q8 tptp.nat) (R4 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 L4))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat _let_2) R4)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R4) _let_2))) (@ (@ tptp.product_Pair_nat_nat _let_1) R4)))))) __flatten_var_0))))
% 3.70/4.05 (assert (= tptp.unique5024387138958732305ep_int (lambda ((L4 tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q8 tptp.int) (R4 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 L4))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_eq_int _let_2) R4)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R4) _let_2))) (@ (@ tptp.product_Pair_int_int _let_1) R4)))))) __flatten_var_0))))
% 3.70/4.05 (assert (@ tptp.wf_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_nat))))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (@ tptp.bNF_We3818239936649020644el_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_nat X2) N) (@ (@ tptp.ord_less_nat Y5) N) (@ (@ tptp.ord_less_eq_nat X2) Y5))))))))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (= (@ tptp.field_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_nat X2) N) (@ (@ tptp.ord_less_nat Y5) N) (@ (@ tptp.ord_less_eq_nat X2) Y5)))))) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_nat X2) N))))))
% 3.70/4.05 (assert (= tptp.bNF_Ca8459412986667044542atLess (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_nat))))
% 3.70/4.05 (assert (forall ((I tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.upto I) J))) (= (@ (@ tptp.linord1735203802627413978nt_int (lambda ((X2 tptp.int)) X2)) _let_1) _let_1))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.upt M2) N))) (= (@ tptp.remdups_nat _let_1) _let_1))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.upt M2) N))) (= (@ (@ tptp.linord738340561235409698at_nat (lambda ((X2 tptp.nat)) X2)) _let_1) _let_1))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.tl_nat (@ (@ tptp.upt M2) N)) (@ (@ tptp.upt (@ tptp.suc M2)) N))))
% 3.70/4.05 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (= (@ tptp.hd_nat (@ (@ tptp.upt I) J)) I))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (I tptp.nat) (J tptp.nat)) (= (@ (@ tptp.drop_nat M2) (@ (@ tptp.upt I) J)) (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat I) M2)) J))))
% 3.70/4.05 (assert (forall ((I tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I) M2))) (let ((_let_2 (@ tptp.upt I))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) N) (= (@ (@ tptp.take_nat M2) (@ _let_2 N)) (@ _let_2 _let_1)))))))
% 3.70/4.05 (assert (forall ((J tptp.nat)) (= (= (@ (@ tptp.upt tptp.zero_zero_nat) J) tptp.nil_nat) (= J tptp.zero_zero_nat))))
% 3.70/4.05 (assert (forall ((J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.upt I) J) tptp.nil_nat))))
% 3.70/4.05 (assert (forall ((I tptp.nat) (J tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ tptp.upt I))) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat J) K3)) (= (@ (@ tptp.append_nat (@ _let_1 J)) (@ (@ tptp.upt J) K3)) (@ _let_1 K3))))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or4665077453230672383an_nat M2) N)) (@ (@ tptp.upt M2) N))))
% 3.70/4.05 (assert (forall ((I tptp.nat) (J tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.upt I) J)) (@ (@ tptp.minus_minus_nat J) I))))
% 3.70/4.05 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (= (@ tptp.last_nat (@ (@ tptp.upt I) J)) (@ (@ tptp.minus_minus_nat J) tptp.one_one_nat)))))
% 3.70/4.05 (assert (forall ((I tptp.nat) (J tptp.nat)) (= (= (@ (@ tptp.upt I) J) tptp.nil_nat) (or (= J tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat J) I)))))
% 3.70/4.05 (assert (forall ((I tptp.nat) (K3 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I) K3))) (=> (@ (@ tptp.ord_less_nat _let_1) J) (= (@ (@ tptp.nth_nat (@ (@ tptp.upt I) J)) K3) _let_1)))))
% 3.70/4.05 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (let ((_let_2 (@ tptp.numeral_numeral_nat M2))) (let ((_let_3 (@ (@ tptp.upt _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_nat _let_2) (@ (@ tptp.upt (@ tptp.suc _let_2)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_nat)))))))))
% 3.70/4.05 (assert (= tptp.set_or4665077453230672383an_nat (lambda ((I4 tptp.nat) (J2 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt I4) J2)))))
% 3.70/4.05 (assert (forall ((I tptp.nat) (J tptp.nat)) (@ tptp.distinct_nat (@ (@ tptp.upt I) J))))
% 3.70/4.05 (assert (forall ((Ofs tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat I4) Ofs))) (@ (@ tptp.upt A2) B2)) (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat A2) Ofs)) (@ (@ tptp.plus_plus_nat B2) Ofs)))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.map_nat_nat tptp.suc) (@ (@ tptp.upt M2) N)) (@ (@ tptp.upt (@ tptp.suc M2)) (@ tptp.suc N)))))
% 3.70/4.05 (assert (= tptp.set_or1269000886237332187st_nat (lambda ((N2 tptp.nat) (M tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt N2) (@ tptp.suc M))))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.upt M2))) (= (@ tptp.butlast_nat (@ _let_1 N)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 3.70/4.05 (assert (= tptp.set_ord_lessThan_nat (lambda ((N2 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) N2)))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Ns tptp.list_nat) (Q6 tptp.nat)) (let ((_let_1 (@ (@ tptp.cons_nat N) Ns))) (= (= (@ (@ tptp.cons_nat M2) _let_1) (@ (@ tptp.upt M2) Q6)) (= _let_1 (@ (@ tptp.upt (@ tptp.suc M2)) Q6))))))
% 3.70/4.05 (assert (forall ((I tptp.nat)) (= (@ (@ tptp.upt I) tptp.zero_zero_nat) tptp.nil_nat)))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) (@ (@ tptp.upt M2) N))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat I4) N))) (@ (@ tptp.upt tptp.zero_zero_nat) M2)) (@ (@ tptp.upt N) (@ (@ tptp.plus_plus_nat M2) N)))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) (@ (@ tptp.upt M2) N))))
% 3.70/4.05 (assert (= tptp.set_or6659071591806873216st_nat (lambda ((N2 tptp.nat) (M tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N2)) (@ tptp.suc M))))))
% 3.70/4.05 (assert (forall ((I tptp.nat) (J tptp.nat) (Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (= (@ (@ tptp.upt I) J) (@ (@ tptp.append_nat Xs) Ys)) (exists ((K4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I) K4) (@ (@ tptp.ord_less_eq_nat K4) J) (= (@ (@ tptp.upt I) K4) Xs) (= (@ (@ tptp.upt K4) J) Ys)))))))
% 3.70/4.05 (assert (= tptp.set_or5834768355832116004an_nat (lambda ((N2 tptp.nat) (M tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N2)) M)))))
% 3.70/4.05 (assert (= tptp.set_ord_atMost_nat (lambda ((N2 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) (@ tptp.suc N2))))))
% 3.70/4.05 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (= (@ (@ tptp.upt I) J) (@ (@ tptp.cons_nat I) (@ (@ tptp.upt (@ tptp.suc I)) J))))))
% 3.70/4.05 (assert (forall ((U tptp.nat) (U3 tptp.nat) (P (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.upt tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.filter_nat2 P))) (=> (@ (@ tptp.ord_less_eq_nat U) U3) (=> (forall ((I5 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat U) I5) (@ (@ tptp.ord_less_nat I5) U3)) (not (@ P I5)))) (= (@ _let_2 (@ _let_1 U)) (@ _let_2 (@ _let_1 U3)))))))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))) (@ (@ tptp.upt (@ tptp.suc M2)) (@ tptp.suc N))) (@ (@ tptp.upt M2) N))))
% 3.70/4.05 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.upt tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat I) J) (= (@ (@ tptp.append_nat (@ _let_1 I)) (@ (@ tptp.upt I) J)) (@ _let_1 J))))))
% 3.70/4.05 (assert (forall ((I tptp.nat) (J tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J) K3))) (let ((_let_2 (@ tptp.upt I))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ _let_2 _let_1) (@ (@ tptp.append_nat (@ _let_2 J)) (@ (@ tptp.upt J) _let_1))))))))
% 3.70/4.05 (assert (forall ((I tptp.nat) (J tptp.nat) (X tptp.nat) (Xs tptp.list_nat)) (= (= (@ (@ tptp.upt I) J) (@ (@ tptp.cons_nat X) Xs)) (and (@ (@ tptp.ord_less_nat I) J) (= I X) (= (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat I) tptp.one_one_nat)) J) Xs)))))
% 3.70/4.05 (assert (= tptp.upt (lambda ((I4 tptp.nat) (J2 tptp.nat)) (@ (@ (@ tptp.if_list_nat (@ (@ tptp.ord_less_nat I4) J2)) (@ (@ tptp.cons_nat I4) (@ (@ tptp.upt (@ tptp.suc I4)) J2))) tptp.nil_nat))))
% 3.70/4.05 (assert (forall ((L tptp.nat) (H2 tptp.nat) (Is1 tptp.list_nat) (I tptp.nat) (Is2 tptp.list_nat)) (let ((_let_1 (@ tptp.upt L))) (= (= (@ _let_1 H2) (@ (@ tptp.append_nat Is1) (@ (@ tptp.cons_nat I) Is2))) (and (= Is1 (@ _let_1 I)) (= Is2 (@ (@ tptp.upt (@ tptp.suc I)) H2)) (@ (@ tptp.ord_less_eq_nat L) I) (@ (@ tptp.ord_less_nat I) H2))))))
% 3.70/4.05 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.upt I))) (let ((_let_2 (@ _let_1 (@ tptp.suc J)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat I) J))) (and (=> _let_3 (= _let_2 (@ (@ tptp.append_nat (@ _let_1 J)) (@ (@ tptp.cons_nat J) tptp.nil_nat)))) (=> (not _let_3) (= _let_2 tptp.nil_nat))))))))
% 3.70/4.05 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.upt I))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ _let_1 (@ tptp.suc J)) (@ (@ tptp.append_nat (@ _let_1 J)) (@ (@ tptp.cons_nat J) tptp.nil_nat)))))))
% 3.70/4.05 (assert (= tptp.unique4921790084139445826nteger (lambda ((L4 tptp.num) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q8 tptp.code_integer) (R4 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q8))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger L4))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le3102999989581377725nteger _let_2) R4)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R4) _let_2))) (@ (@ tptp.produc1086072967326762835nteger _let_1) R4)))))) __flatten_var_0))))
% 3.70/4.05 (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))))
% 3.70/4.05 (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))))
% 3.70/4.05 (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))))
% 3.70/4.05 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (= (@ (@ tptp.image_4470545334726330049nteger (lambda ((X2 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger X2) L))) (@ (@ tptp.set_or8404916559141939852nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.minus_8373710615458151222nteger U) L))) (@ (@ tptp.set_or8404916559141939852nteger L) U))))
% 3.70/4.05 (assert (= tptp.unique3479559517661332726nteger (lambda ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 3.70/4.05 (assert (forall ((S tptp.set_nat)) (=> (@ tptp.finite_finite_nat S) (exists ((R6 (-> tptp.nat tptp.nat))) (and (@ (@ tptp.strict1292158309912662752at_nat R6) (@ tptp.set_ord_lessThan_nat (@ tptp.finite_card_nat S))) (forall ((N9 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N9) (@ tptp.finite_card_nat S)) (@ (@ tptp.member_nat (@ R6 N9)) S))))))))
% 3.70/4.05 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.set_or8404916559141939852nteger L) U))))
% 3.70/4.05 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.set_or189985376899183464nteger L) U))))
% 3.70/4.05 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.set_or4266950643985792945nteger L) U))))
% 3.70/4.05 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.set_or2715278749043346189nteger L) U))))
% 3.70/4.05 (assert (forall ((U tptp.code_integer)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.set_or8404916559141939852nteger tptp.zero_z3403309356797280102nteger) U))))
% 3.70/4.05 (assert (= tptp.code_bit_cut_integer (lambda ((K4 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ tptp.divide6298287555418463151nteger K4) _let_1)) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) K4)))))))
% 3.70/4.05 (assert (= tptp.code_divmod_integer (lambda ((K4 tptp.code_integer) (L4 tptp.code_integer)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger K4) L4)) (@ (@ tptp.modulo364778990260209775nteger K4) L4)))))
% 3.70/4.05 (assert (= tptp.code_bit_cut_integer (lambda ((K4 tptp.code_integer)) (@ (@ (@ tptp.if_Pro5737122678794959658eger_o (= K4 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc6677183202524767010eger_o tptp.zero_z3403309356797280102nteger) false)) (@ (@ tptp.produc9125791028180074456eger_o (lambda ((R4 tptp.code_integer) (S6 tptp.code_integer)) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) K4)) R4) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger R4)) S6))) (= S6 tptp.one_one_Code_integer)))) (@ (@ tptp.code_divmod_abs K4) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 3.70/4.05 (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)))))))
% 3.70/4.05 (assert (forall ((J tptp.code_integer)) (= (@ (@ tptp.code_divmod_abs tptp.zero_z3403309356797280102nteger) J) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))))
% 3.70/4.05 (assert (forall ((J tptp.code_integer)) (= (@ (@ tptp.code_divmod_abs J) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer J)))))
% 3.70/4.05 (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)))))))
% 3.70/4.05 (assert (= tptp.code_divmod_abs (lambda ((K4 tptp.code_integer) (L4 tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer L4))) (let ((_let_2 (@ tptp.abs_abs_Code_integer K4))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 3.70/4.05 (assert (= tptp.code_divmod_integer (lambda ((K4 tptp.code_integer) (L4 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.code_divmod_abs K4) L4))) (let ((_let_2 (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_3 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= K4 tptp.zero_z3403309356797280102nteger)) (@ _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ _let_3 L4)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ _let_3 K4)) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R4 tptp.code_integer) (S6 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R4))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S6 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger L4) S6)))))) _let_1))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= L4 tptp.zero_z3403309356797280102nteger)) (@ _let_2 K4)) (@ (@ tptp.produc6499014454317279255nteger tptp.uminus1351360451143612070nteger) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le6747313008572928689nteger K4) tptp.zero_z3403309356797280102nteger)) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R4 tptp.code_integer) (S6 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R4))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S6 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger L4)) S6)))))) _let_1))))))))))))
% 3.70/4.05 (assert (forall ((M5 tptp.set_nat)) (=> (@ tptp.finite_finite_nat M5) (=> (not (= M5 tptp.bot_bot_set_nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M5)) (= (@ tptp.gcd_Gcd_nat M5) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_nat_set_nat (lambda ((M tptp.nat)) (@ tptp.collect_nat (lambda ((D5 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D5) M))))) M5)))))))))
% 3.70/4.05 (assert (= (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_nat_set_nat tptp.set_or1210151606488870762an_nat) tptp.top_top_set_nat)) tptp.bot_bot_set_nat))
% 3.70/4.05 (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 ((X2 tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y5))) (let ((_let_2 (@ tptp.times_times_nat X2))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U4)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U4))))))) __flatten_var_0))) Xa) X)))))
% 3.70/4.05 (assert (forall ((K5 tptp.set_nat)) (=> (not (= K5 tptp.bot_bot_set_nat)) (@ (@ tptp.member_nat (@ tptp.complete_Inf_Inf_nat K5)) K5))))
% 3.70/4.05 (assert (forall ((Z tptp.int)) (not (forall ((X3 tptp.nat) (Y2 tptp.nat)) (not (= Z (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat X3) Y2))))))))
% 3.70/4.05 (assert (= tptp.zero_zero_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))))
% 3.70/4.05 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N2 tptp.nat)) (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat N2) tptp.zero_zero_nat)))))
% 3.70/4.05 (assert (forall ((X tptp.product_prod_nat_nat)) (= (@ tptp.uminus_uminus_int (@ tptp.abs_Integ X)) (@ tptp.abs_Integ (@ (@ tptp.produc2626176000494625587at_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y5) X2))) X)))))
% 3.70/4.05 (assert (= tptp.one_one_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))))
% 3.70/4.05 (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 ((X2 tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat U4) Y5)))) __flatten_var_0))) Xa) X))))
% 3.70/4.05 (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 ((X2 tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) U4)) (@ (@ tptp.plus_plus_nat Y5) V4)))) __flatten_var_0))) Xa) X)))))
% 3.70/4.05 (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 ((X2 tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat Y5) U4)))) __flatten_var_0))) Xa) X)))))
% 3.70/4.05 (assert (= tptp.code_divmod_integer (lambda ((K4 tptp.code_integer) (L4 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.code_divmod_abs K4) L4))) (let ((_let_2 (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= K4 tptp.zero_z3403309356797280102nteger)) (@ _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= L4 tptp.zero_z3403309356797280102nteger)) (@ _let_2 K4)) (@ (@ (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_C8797469213163452608nteger tptp.produc6499014454317279255nteger) tptp.times_3573771949741848930nteger)) tptp.sgn_sgn_Code_integer) L4) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= (@ tptp.sgn_sgn_Code_integer K4) (@ tptp.sgn_sgn_Code_integer L4))) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R4 tptp.code_integer) (S6 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R4))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S6 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer L4)) S6)))))) _let_1))))))))))
% 3.70/4.05 (assert (= tptp.ord_less_int (lambda ((X2 tptp.int) (Xa4 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y5 tptp.nat) (Z5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat Y5) V4)) (@ (@ tptp.plus_plus_nat U4) Z5)))) __flatten_var_0))) (@ tptp.rep_Integ X2)) (@ tptp.rep_Integ Xa4)))))
% 3.70/4.05 (assert (forall ((X tptp.assn) (Y tptp.assn) (A2 tptp.assn) (B2 tptp.assn)) (=> (@ (@ tptp.syntax7398250324933576852n_assn (@ (@ tptp.times_times_assn X) Y)) A2) (= (@ (@ tptp.times_times_assn A2) B2) (@ (@ tptp.times_times_assn B2) A2)))))
% 3.70/4.05 (assert (= tptp.uminus_uminus_int (@ (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ) (@ tptp.produc2626176000494625587at_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y5) X2))))))
% 3.70/4.05 (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 ((X2 tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y5))) (let ((_let_2 (@ tptp.times_times_nat X2))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U4)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U4))))))) __flatten_var_0))))))
% 3.70/4.05 (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 ((X2 tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat Y5) U4)))) __flatten_var_0))))))
% 3.70/4.05 (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 ((X2 tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) U4)) (@ (@ tptp.plus_plus_nat Y5) V4)))) __flatten_var_0))))))
% 3.70/4.05 (assert (@ (@ (@ (@ tptp.semila1623282765462674594er_nat tptp.ord_max_nat) tptp.zero_zero_nat) (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y5) X2))) (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.ord_less_nat Y5) X2))))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ tptp.order_mono_nat_nat (@ tptp.times_times_nat N)))))
% 3.70/4.05 (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 ((X2 tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat U4) Y5)))) __flatten_var_0))))))
% 3.70/4.05 (assert (forall ((X tptp.nat) (Xa tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.bezw Xa) (@ (@ tptp.modulo_modulo_nat X) Xa)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (let ((_let_3 (= Xa tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X) Xa) Y) (and (=> _let_3 (= Y (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_3) (= Y (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Xa))))))))))))))
% 3.70/4.05 (assert (= tptp.bezw (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y5) (@ (@ tptp.modulo_modulo_nat X2) Y5)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= Y5 tptp.zero_zero_nat)) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X2) Y5)))))))))))
% 3.70/4.05 (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)))))))))))
% 3.70/4.05 (assert (forall ((X tptp.nat) (Xa tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.bezw_rel) (@ (@ tptp.product_Pair_nat_nat X) Xa)))) (let ((_let_2 (@ (@ tptp.bezw Xa) (@ (@ tptp.modulo_modulo_nat X) Xa)))) (let ((_let_3 (@ tptp.product_snd_int_int _let_2))) (let ((_let_4 (= Xa tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X) Xa) Y) (=> _let_1 (not (=> (and (=> _let_4 (= Y (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_4) (= Y (@ (@ tptp.product_Pair_int_int _let_3) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_2)) (@ (@ tptp.times_times_int _let_3) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Xa)))))))) (not _let_1)))))))))))
% 3.70/4.05 (assert (forall ((B2 Bool) (H2 tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn (@ tptp.pure_assn B2)) H2) (and (= (@ tptp.produc8586169260539613262et_nat H2) tptp.bot_bot_set_nat) B2))))
% 3.70/4.05 (assert (forall ((H2 tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn tptp.one_one_assn) H2) (= (@ tptp.produc8586169260539613262et_nat H2) tptp.bot_bot_set_nat))))
% 3.70/4.05 (assert (forall ((M2 tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ tptp.foldr_assn_assn tptp.times_times_assn))) (=> (forall ((X3 tptp.produc6575502325842934193n_assn)) (=> (@ (@ tptp.member7957490590177025114n_assn X3) (@ tptp.set_Pr1139785259514867910n_assn M2)) (@ (@ tptp.produc7274209992780475162assn_o tptp.entails) X3))) (@ (@ tptp.entails (@ (@ _let_1 (@ (@ tptp.map_Pr8991440229025900053n_assn tptp.produc9167289414957590229n_assn) M2)) tptp.one_one_assn)) (@ (@ _let_1 (@ (@ tptp.map_Pr8991440229025900053n_assn tptp.produc2051961928117032727n_assn) M2)) tptp.one_one_assn))))))
% 3.70/4.05 (assert (forall ((P tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn P) tptp.top_top_assn)) H2) (not (forall ((H5 tptp.produc3658429121746597890et_nat)) (=> (= (@ tptp.produc1824681642469235216et_nat H5) (@ tptp.produc1824681642469235216et_nat H2)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.produc8586169260539613262et_nat H5)) (@ tptp.produc8586169260539613262et_nat H2)) (not (@ (@ tptp.rep_assn P) H5)))))))))
% 3.70/4.05 (assert (= tptp.fI_RESULT (lambda ((M7 tptp.list_P8527749157015355191n_assn) (UP tptp.assn) (UQ tptp.assn) (F3 tptp.assn)) (let ((_let_1 (@ tptp.foldr_assn_assn tptp.times_times_assn))) (=> (forall ((X2 tptp.produc6575502325842934193n_assn)) (=> (@ (@ tptp.member7957490590177025114n_assn X2) (@ tptp.set_Pr1139785259514867910n_assn M7)) (@ (@ tptp.produc7274209992780475162assn_o tptp.entails) X2))) (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ _let_1 (@ (@ tptp.map_Pr8991440229025900053n_assn tptp.produc9167289414957590229n_assn) M7)) tptp.one_one_assn)) UP)) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ _let_1 (@ (@ tptp.map_Pr8991440229025900053n_assn tptp.produc2051961928117032727n_assn) M7)) tptp.one_one_assn)) UQ)) F3)))))))
% 3.70/4.05 (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))))))))))
% 3.70/4.05 (assert (= tptp.fi (lambda ((M tptp.list_P8527749157015355191n_assn) (P7 tptp.assn) (Q8 tptp.assn) (Up tptp.assn) (Uq tptp.assn) (F6 tptp.assn)) (let ((_let_1 (@ tptp.foldr_assn_assn tptp.times_times_assn))) (=> (forall ((X2 tptp.produc6575502325842934193n_assn)) (=> (@ (@ tptp.member7957490590177025114n_assn X2) (@ tptp.set_Pr1139785259514867910n_assn M)) (@ (@ tptp.produc7274209992780475162assn_o tptp.entails) X2))) (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ _let_1 (@ (@ tptp.map_Pr8991440229025900053n_assn tptp.produc9167289414957590229n_assn) M)) tptp.one_one_assn)) P7)) Up)) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ _let_1 (@ (@ tptp.map_Pr8991440229025900053n_assn tptp.produc2051961928117032727n_assn) M)) tptp.one_one_assn)) Q8)) Uq)) F6)))))))
% 3.70/4.05 (assert (forall ((M2 tptp.list_P8527749157015355191n_assn) (Ps2 tptp.assn) (Qs tptp.assn) (Q6 tptp.assn) (P6 tptp.assn) (Up2 tptp.assn) (Uq2 tptp.assn) (F4 tptp.assn)) (let ((_let_1 (@ (@ tptp.times_times_assn Qs) Q6))) (let ((_let_2 (@ tptp.fi M2))) (=> (@ (@ (@ (@ (@ _let_2 Ps2) _let_1) (@ (@ tptp.times_times_assn P6) Up2)) Uq2) F4) (@ (@ (@ (@ (@ _let_2 (@ (@ tptp.times_times_assn Ps2) P6)) _let_1) Up2) Uq2) F4))))))
% 3.70/4.05 (assert (forall ((M2 tptp.list_P8527749157015355191n_assn) (P6 tptp.assn) (Up2 tptp.assn) (Q6 tptp.assn) (Uq2 tptp.assn) (F4 tptp.assn)) (=> (@ (@ (@ (@ tptp.fI_RESULT M2) (@ (@ tptp.times_times_assn P6) Up2)) (@ (@ tptp.times_times_assn Q6) Uq2)) F4) (@ (@ (@ (@ (@ (@ tptp.fi M2) P6) Q6) Up2) Uq2) F4))))
% 3.70/4.05 (assert (forall ((P tptp.assn) (Q tptp.assn) (F tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn tptp.sln))) (=> (@ (@ (@ (@ (@ (@ tptp.fi tptp.nil_Pr5671120429643327159n_assn) (@ _let_1 P)) (@ _let_1 Q)) tptp.sln) tptp.sln) F) (@ (@ (@ tptp.fI_QUERY P) Q) F)))))
% 3.70/4.05 (assert (forall ((P tptp.assn)) (= (@ (@ tptp.times_times_assn P) tptp.sln) P)))
% 3.70/4.05 (assert (forall ((P tptp.assn)) (= (@ (@ tptp.times_times_assn tptp.sln) P) P)))
% 3.70/4.05 (assert (= tptp.sln tptp.one_one_assn))
% 3.70/4.05 (assert (forall ((M2 tptp.list_P8527749157015355191n_assn) (Up2 tptp.assn) (Qs tptp.assn) (Q6 tptp.assn) (Uq2 tptp.assn) (F4 tptp.assn)) (let ((_let_1 (@ tptp.fi M2))) (=> (@ (@ (@ (@ (@ _let_1 (@ (@ tptp.times_times_assn tptp.sln) Up2)) Qs) tptp.sln) (@ (@ tptp.times_times_assn Q6) Uq2)) F4) (@ (@ (@ (@ (@ _let_1 tptp.sln) (@ (@ tptp.times_times_assn Qs) Q6)) Up2) Uq2) F4)))))
% 3.70/4.05 (assert (forall ((P6 tptp.assn) (Q6 tptp.assn) (M2 tptp.list_P8527749157015355191n_assn) (Ps2 tptp.assn) (Up2 tptp.assn) (Qs tptp.assn) (Uq2 tptp.assn) (F4 tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn Qs))) (let ((_let_2 (@ tptp.times_times_assn Ps2))) (=> (@ (@ tptp.entails P6) Q6) (=> (@ (@ (@ (@ (@ (@ tptp.fi (@ (@ tptp.cons_P2971678138204555879n_assn (@ (@ tptp.produc118845697133431529n_assn P6) Q6)) M2)) (@ _let_2 Up2)) (@ _let_1 Uq2)) tptp.sln) tptp.sln) F4) (@ (@ (@ (@ (@ (@ tptp.fi M2) (@ _let_2 P6)) (@ _let_1 Q6)) Up2) Uq2) F4)))))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat M2) N)) (@ tptp.transi2905341329935302413cl_nat tptp.pred_nat)) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.vimage_nat_nat tptp.suc))) (= (@ _let_1 (@ (@ tptp.insert_nat2 (@ tptp.suc N)) A)) (@ (@ tptp.insert_nat2 N) (@ _let_1 A))))))
% 3.70/4.05 (assert (forall ((A tptp.set_nat)) (let ((_let_1 (@ tptp.vimage_nat_nat tptp.suc))) (= (@ _let_1 (@ (@ tptp.insert_nat2 tptp.zero_zero_nat) A)) (@ _let_1 A)))))
% 3.70/4.05 (assert (forall ((S tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat S) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.finite_card_nat S)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.infini8530281810654367211te_nat S) N))))))
% 3.70/4.05 (assert (@ (@ (@ (@ tptp.bNF_re578469030762574527_nat_o (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2))) (@ (@ tptp.bNF_re4705727531993890431at_o_o (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2))) (lambda ((Y4 Bool) (Z2 Bool)) (= Y4 Z2)))) tptp.ord_less_nat) tptp.ord_less_nat))
% 3.70/4.05 (assert (@ (@ (@ (@ tptp.bNF_re7408651293131936558nt_int tptp.pcr_int) (@ (@ tptp.bNF_re7400052026677387805at_int tptp.pcr_int) tptp.pcr_int)) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y5))) (let ((_let_2 (@ tptp.times_times_nat X2))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U4)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U4))))))) __flatten_var_0)))) tptp.times_times_int))
% 3.70/4.05 (assert (@ (@ tptp.pcr_int (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat)) tptp.zero_zero_int))
% 3.70/4.05 (assert (@ (@ (@ (@ tptp.bNF_re6830278522597306478at_int (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2))) tptp.pcr_int) (lambda ((N2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat N2) tptp.zero_zero_nat))) tptp.semiri1314217659103216013at_int))
% 3.70/4.05 (assert (@ (@ (@ (@ tptp.bNF_re7400052026677387805at_int tptp.pcr_int) tptp.pcr_int) (@ tptp.produc2626176000494625587at_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y5) X2)))) tptp.uminus_uminus_int))
% 3.70/4.05 (assert (@ (@ tptp.pcr_int (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat)) tptp.one_one_int))
% 3.70/4.05 (assert (@ (@ (@ (@ tptp.bNF_re717283939379294677_int_o tptp.pcr_int) (@ (@ tptp.bNF_re6644619430987730960nt_o_o tptp.pcr_int) (lambda ((Y4 Bool) (Z2 Bool)) (= Y4 Z2)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat U4) Y5)))) __flatten_var_0)))) tptp.ord_less_int))
% 3.70/4.05 (assert (@ (@ (@ (@ tptp.bNF_re7408651293131936558nt_int tptp.pcr_int) (@ (@ tptp.bNF_re7400052026677387805at_int tptp.pcr_int) tptp.pcr_int)) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) U4)) (@ (@ tptp.plus_plus_nat Y5) V4)))) __flatten_var_0)))) tptp.plus_plus_int))
% 3.70/4.05 (assert (@ (@ (@ (@ tptp.bNF_re7408651293131936558nt_int tptp.pcr_int) (@ (@ tptp.bNF_re7400052026677387805at_int tptp.pcr_int) tptp.pcr_int)) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat Y5) U4)))) __flatten_var_0)))) tptp.minus_minus_int))
% 3.70/4.05 (assert (@ (@ (@ (@ tptp.bNF_re3099431351363272937at_nat tptp.intrel) (@ (@ tptp.bNF_re2241393799969408733at_nat tptp.intrel) tptp.intrel)) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y5))) (let ((_let_2 (@ tptp.times_times_nat X2))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U4)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U4))))))) __flatten_var_0)))) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y5))) (let ((_let_2 (@ tptp.times_times_nat X2))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U4)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U4))))))) __flatten_var_0)))))
% 3.70/4.05 (assert (forall ((X tptp.nat) (Y tptp.nat) (U tptp.nat) (V2 tptp.nat)) (= (@ (@ tptp.intrel (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ (@ tptp.product_Pair_nat_nat U) V2)) (= (@ (@ tptp.plus_plus_nat X) V2) (@ (@ tptp.plus_plus_nat U) Y)))))
% 3.70/4.05 (assert (@ (@ (@ tptp.filterlim_nat_nat tptp.suc) tptp.at_top_nat) tptp.at_top_nat))
% 3.70/4.05 (assert (let ((_let_1 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))) (@ (@ tptp.intrel _let_1) _let_1)))
% 3.70/4.05 (assert (@ (@ (@ tptp.filter3212408913953519116et_nat tptp.set_ord_atMost_nat) (@ tptp.finite3254316476582989077op_nat tptp.top_top_set_nat)) tptp.at_top_nat))
% 3.70/4.05 (assert (@ (@ (@ tptp.filter3212408913953519116et_nat tptp.set_ord_lessThan_nat) (@ tptp.finite3254316476582989077op_nat tptp.top_top_set_nat)) tptp.at_top_nat))
% 3.70/4.05 (assert (@ (@ (@ (@ tptp.bNF_re2241393799969408733at_nat tptp.intrel) tptp.intrel) (@ tptp.produc2626176000494625587at_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y5) X2)))) (@ tptp.produc2626176000494625587at_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y5) X2)))))
% 3.70/4.05 (assert (let ((_let_1 (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.intrel _let_1) _let_1)))
% 3.70/4.05 (assert (@ (@ (@ (@ tptp.bNF_re4202695980764964119_nat_o tptp.intrel) (@ (@ tptp.bNF_re3666534408544137501at_o_o tptp.intrel) (lambda ((Y4 Bool) (Z2 Bool)) (= Y4 Z2)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat U4) Y5)))) __flatten_var_0)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat U4) Y5)))) __flatten_var_0)))))
% 3.70/4.05 (assert (@ (@ (@ (@ tptp.bNF_re3099431351363272937at_nat tptp.intrel) (@ (@ tptp.bNF_re2241393799969408733at_nat tptp.intrel) tptp.intrel)) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat Y5) U4)))) __flatten_var_0)))) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat Y5) U4)))) __flatten_var_0)))))
% 3.70/4.05 (assert (@ (@ (@ (@ tptp.bNF_re3099431351363272937at_nat tptp.intrel) (@ (@ tptp.bNF_re2241393799969408733at_nat tptp.intrel) tptp.intrel)) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) U4)) (@ (@ tptp.plus_plus_nat Y5) V4)))) __flatten_var_0)))) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) U4)) (@ (@ tptp.plus_plus_nat Y5) V4)))) __flatten_var_0)))))
% 3.70/4.05 (assert (not (= tptp.at_top_nat tptp.bot_bot_filter_nat)))
% 3.70/4.05 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat (lambda ((I4 tptp.nat)) (@ P (@ tptp.suc I4)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 3.70/4.05 (assert (forall ((P (-> tptp.nat Bool)) (K3 tptp.nat)) (= (@ (@ tptp.eventually_nat (lambda ((N2 tptp.nat)) (@ P (@ (@ tptp.plus_plus_nat N2) K3)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 3.70/4.05 (assert (not (@ (@ tptp.eventually_nat (lambda ((N2 tptp.nat)) false)) tptp.at_top_nat)))
% 3.70/4.05 (assert (forall ((C tptp.nat) (P (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) X3) (@ P X3))) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 3.70/4.05 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (exists ((N8 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N2) (@ P N2)))))))
% 3.70/4.05 (assert (forall ((F tptp.filter_nat)) (= (@ (@ tptp.ord_le2510731241096832064er_nat F) tptp.at_top_nat) (forall ((N8 tptp.nat)) (@ (@ tptp.eventually_nat (@ tptp.ord_less_eq_nat N8)) F)))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (K3 tptp.int) (L tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ (@ tptp.bit_concat_bit M2) K3) L)) N) (or (and (@ (@ tptp.ord_less_nat N) M2) (@ (@ tptp.bit_se1146084159140164899it_int K3) N)) (and (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.bit_se1146084159140164899it_int L) (@ (@ tptp.minus_minus_nat N) M2)))))))
% 3.70/4.05 (assert (@ (@ (@ tptp.ordering_top_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y5) X2))) (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.ord_less_nat Y5) X2))) tptp.zero_zero_nat))
% 3.70/4.05 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (S3 tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_nat S3) T) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A2) S3)) (@ (@ tptp.product_Pair_nat_nat B2) T))) tptp.fun_pair_less)))))
% 3.70/4.05 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.product_Pair_nat_nat X))) (= (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ _let_1 Y)) (@ _let_1 Z))) tptp.fun_pair_less) (@ (@ tptp.ord_less_nat Y) Z)))))
% 3.70/4.05 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (S3 tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A2) S3)) (@ (@ tptp.product_Pair_nat_nat B2) T))) tptp.fun_pair_less))))
% 3.70/4.05 (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)))))))
% 3.70/4.05 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (S3 tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat S3) T) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A2) S3)) (@ (@ tptp.product_Pair_nat_nat B2) T))) tptp.fun_pair_leq)))))
% 3.70/4.05 (assert (forall ((X4 tptp.set_Pr1261947904930325089at_nat)) (=> (not (= X4 tptp.bot_bo2099793752762293965at_nat)) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X4) tptp.bot_bo2099793752762293965at_nat)) tptp.fun_min_strict))))
% 3.70/4.05 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (S3 tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A2) S3)) (@ (@ tptp.product_Pair_nat_nat B2) T))) tptp.fun_pair_leq))))
% 3.70/4.05 (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))))))
% 3.70/4.05 (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)))))))
% 3.70/4.05 (assert (forall ((X4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat X4) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat tptp.bot_bo2099793752762293965at_nat) X4)) tptp.fun_max_weak))))
% 3.70/4.05 (assert (forall ((X4 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X4) tptp.bot_bo2099793752762293965at_nat)) tptp.fun_min_weak)))
% 3.70/4.05 (assert (@ tptp.fun_re2478310338295953701at_nat (@ (@ tptp.produc9060074326276436823at_nat tptp.fun_min_strict) tptp.fun_min_weak)))
% 3.70/4.05 (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))))
% 3.70/4.05 (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))))
% 3.70/4.05 (assert (forall ((Y tptp.product_prod_nat_nat) (Y6 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (X4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat Y) Y6) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X) Y)) tptp.fun_pair_less) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X4) Y6)) tptp.fun_max_strict) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ (@ tptp.insert8211810215607154385at_nat X) X4)) Y6)) tptp.fun_max_strict))))))
% 3.70/4.05 (assert (@ tptp.fun_re2478310338295953701at_nat (@ (@ tptp.produc9060074326276436823at_nat tptp.fun_max_strict) tptp.fun_max_weak)))
% 3.70/4.05 (assert (forall ((Y6 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat Y6) (=> (not (= Y6 tptp.bot_bo2099793752762293965at_nat)) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat tptp.bot_bo2099793752762293965at_nat) Y6)) tptp.fun_max_strict)))))
% 3.70/4.05 (assert (forall ((A tptp.multis2468970476368604999at_nat) (B tptp.multis2468970476368604999at_nat) (Z6 tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.plus_p7104986032573967614at_nat Z6))) (=> (or (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ tptp.set_ms8126754132646256062at_nat A)) (@ tptp.set_ms8126754132646256062at_nat B))) tptp.fun_max_strict) (and (= A tptp.zero_z1048942125864253310at_nat) (= B tptp.zero_z1048942125864253310at_nat))) (@ (@ tptp.member6689249552917799696at_nat (@ (@ tptp.produc4348348721325984599at_nat (@ _let_1 A)) (@ _let_1 B))) tptp.ms_weak)))))
% 3.70/4.05 (assert (forall ((A tptp.multis2468970476368604999at_nat) (B tptp.multis2468970476368604999at_nat) (Z6 tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.plus_p7104986032573967614at_nat Z6))) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ tptp.set_ms8126754132646256062at_nat A)) (@ tptp.set_ms8126754132646256062at_nat B))) tptp.fun_max_strict) (@ (@ tptp.member6689249552917799696at_nat (@ (@ tptp.produc4348348721325984599at_nat (@ _let_1 A)) (@ _let_1 B))) tptp.ms_strict)))))
% 3.70/4.05 (assert (@ tptp.fun_re7357418987779152907at_nat (@ (@ tptp.produc5245064249948416855at_nat tptp.ms_strict) tptp.ms_weak)))
% 3.70/4.05 (assert (forall ((Z6 tptp.multis2468970476368604999at_nat) (Z7 tptp.multis2468970476368604999at_nat) (A tptp.multis2468970476368604999at_nat) (B tptp.multis2468970476368604999at_nat)) (=> (@ (@ tptp.pw_leq Z6) Z7) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ tptp.set_ms8126754132646256062at_nat A)) (@ tptp.set_ms8126754132646256062at_nat B))) tptp.fun_max_strict) (@ (@ tptp.member6689249552917799696at_nat (@ (@ tptp.produc4348348721325984599at_nat (@ (@ tptp.plus_p7104986032573967614at_nat Z6) A)) (@ (@ tptp.plus_p7104986032573967614at_nat Z7) B))) tptp.ms_weak)))))
% 3.70/4.05 (assert (forall ((Z6 tptp.multis2468970476368604999at_nat) (Z7 tptp.multis2468970476368604999at_nat) (A tptp.multis2468970476368604999at_nat) (B tptp.multis2468970476368604999at_nat)) (=> (@ (@ tptp.pw_leq Z6) Z7) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ tptp.set_ms8126754132646256062at_nat A)) (@ tptp.set_ms8126754132646256062at_nat B))) tptp.fun_max_strict) (@ (@ tptp.member6689249552917799696at_nat (@ (@ tptp.produc4348348721325984599at_nat (@ (@ tptp.plus_p7104986032573967614at_nat Z6) A)) (@ (@ tptp.plus_p7104986032573967614at_nat Z7) B))) tptp.ms_strict)))))
% 3.70/4.05 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X) Y)) tptp.fun_pair_leq) (@ (@ tptp.pw_leq (@ (@ tptp.add_ms2612439473150266591at_nat X) tptp.zero_z1048942125864253310at_nat)) (@ (@ tptp.add_ms2612439473150266591at_nat Y) tptp.zero_z1048942125864253310at_nat)))))
% 3.70/4.05 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat) (X4 tptp.multis2468970476368604999at_nat) (Y6 tptp.multis2468970476368604999at_nat)) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X) Y)) tptp.fun_pair_leq) (=> (@ (@ tptp.pw_leq X4) Y6) (@ (@ tptp.pw_leq (@ (@ tptp.plus_p7104986032573967614at_nat (@ (@ tptp.add_ms2612439473150266591at_nat X) tptp.zero_z1048942125864253310at_nat)) X4)) (@ (@ tptp.plus_p7104986032573967614at_nat (@ (@ tptp.add_ms2612439473150266591at_nat Y) tptp.zero_z1048942125864253310at_nat)) Y6))))))
% 3.70/4.05 (assert (= tptp.pw_leq (lambda ((A12 tptp.multis2468970476368604999at_nat) (A23 tptp.multis2468970476368604999at_nat)) (or (and (= A12 tptp.zero_z1048942125864253310at_nat) (= A23 tptp.zero_z1048942125864253310at_nat)) (exists ((X2 tptp.product_prod_nat_nat) (Y5 tptp.product_prod_nat_nat) (X8 tptp.multis2468970476368604999at_nat) (Y7 tptp.multis2468970476368604999at_nat)) (and (= A12 (@ (@ tptp.plus_p7104986032573967614at_nat (@ (@ tptp.add_ms2612439473150266591at_nat X2) tptp.zero_z1048942125864253310at_nat)) X8)) (= A23 (@ (@ tptp.plus_p7104986032573967614at_nat (@ (@ tptp.add_ms2612439473150266591at_nat Y5) tptp.zero_z1048942125864253310at_nat)) Y7)) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X2) Y5)) tptp.fun_pair_leq) (@ (@ tptp.pw_leq X8) Y7)))))))
% 3.70/4.05 (assert (forall ((A1 tptp.multis2468970476368604999at_nat) (A22 tptp.multis2468970476368604999at_nat)) (=> (@ (@ tptp.pw_leq A1) A22) (=> (=> (= A1 tptp.zero_z1048942125864253310at_nat) (not (= A22 tptp.zero_z1048942125864253310at_nat))) (not (forall ((X3 tptp.product_prod_nat_nat) (Y2 tptp.product_prod_nat_nat) (X9 tptp.multis2468970476368604999at_nat)) (=> (= A1 (@ (@ tptp.plus_p7104986032573967614at_nat (@ (@ tptp.add_ms2612439473150266591at_nat X3) tptp.zero_z1048942125864253310at_nat)) X9)) (forall ((Y8 tptp.multis2468970476368604999at_nat)) (=> (= A22 (@ (@ tptp.plus_p7104986032573967614at_nat (@ (@ tptp.add_ms2612439473150266591at_nat Y2) tptp.zero_z1048942125864253310at_nat)) Y8)) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X3) Y2)) tptp.fun_pair_leq) (not (@ (@ tptp.pw_leq X9) Y8))))))))))))
% 3.70/4.05 (assert (forall ((Z6 tptp.multis2468970476368604999at_nat) (Z7 tptp.multis2468970476368604999at_nat)) (=> (@ (@ tptp.pw_leq Z6) Z7) (@ (@ tptp.member6689249552917799696at_nat (@ (@ tptp.produc4348348721325984599at_nat (@ (@ tptp.plus_p7104986032573967614at_nat Z6) tptp.zero_z1048942125864253310at_nat)) (@ (@ tptp.plus_p7104986032573967614at_nat Z7) tptp.zero_z1048942125864253310at_nat))) tptp.ms_weak))))
% 3.70/4.05 (assert (forall ((X4 tptp.multis2468970476368604999at_nat) (Y6 tptp.multis2468970476368604999at_nat)) (=> (@ (@ tptp.pw_leq X4) Y6) (exists ((A9 tptp.multis2468970476368604999at_nat) (B5 tptp.multis2468970476368604999at_nat) (Z8 tptp.multis2468970476368604999at_nat)) (and (= X4 (@ (@ tptp.plus_p7104986032573967614at_nat A9) Z8)) (= Y6 (@ (@ tptp.plus_p7104986032573967614at_nat B5) Z8)) (or (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ tptp.set_ms8126754132646256062at_nat A9)) (@ tptp.set_ms8126754132646256062at_nat B5))) tptp.fun_max_strict) (and (= B5 tptp.zero_z1048942125864253310at_nat) (= A9 tptp.zero_z1048942125864253310at_nat))))))))
% 3.70/4.05 (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))))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (@ (@ tptp.order_2888998067076097458on_nat (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_nat X2) N)))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_nat X2) N) (@ (@ tptp.ord_less_nat Y5) N) (@ (@ tptp.ord_less_eq_nat X2) Y5))))))))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (@ (@ tptp.order_2888998067076097458on_nat (@ tptp.field_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_nat X2) N) (@ (@ tptp.ord_less_nat Y5) N) (@ (@ tptp.ord_less_eq_nat X2) Y5))))))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_nat X2) N) (@ (@ tptp.ord_less_nat Y5) N) (@ (@ tptp.ord_less_eq_nat X2) Y5))))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool))) (= (@ (@ tptp.eventu1038000079068216329at_nat P) (@ (@ tptp.prod_filter_nat_nat tptp.at_top_nat) tptp.at_top_nat)) (exists ((N8 tptp.nat)) (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) M) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N2) (@ P (@ (@ tptp.product_Pair_nat_nat N2) M))))))))))
% 3.70/4.05 (assert (= tptp.top_top_set_o (@ (@ tptp.insert_o2 false) (@ (@ tptp.insert_o2 true) tptp.bot_bot_set_o))))
% 3.70/4.05 (assert (and (not (@ (@ tptp.member444158400953824016od_o_o (@ (@ tptp.produc763777882069021527od_o_o tptp.bNF_Cardinal_ctwo) tptp.bNF_Cardinal_czero_o)) tptp.bNF_We2654380646378065620so_o_o)) (@ (@ tptp.bNF_Ca8331644756375544342r_on_o (@ tptp.field_o tptp.bNF_Cardinal_ctwo)) tptp.bNF_Cardinal_ctwo)))
% 3.70/4.05 (assert (@ (@ tptp.member4095101504841534314at_nat (@ (@ tptp.produc8517790099723286449at_nat tptp.bNF_Cardinal_ctwo) tptp.bNF_Ca8665028551170535155natLeq)) tptp.bNF_We8182288985678559134_o_nat))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.order_underS_nat tptp.bNF_Ca8665028551170535155natLeq) N) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_nat X2) N))))))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bNF_Ca8665028551170535155natLeq) (@ (@ tptp.produc457027306803732586at_nat (@ (@ tptp.order_underS_nat tptp.bNF_Ca8665028551170535155natLeq) N)) (lambda ((Uu2 tptp.nat)) (@ (@ tptp.order_underS_nat tptp.bNF_Ca8665028551170535155natLeq) N)))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_nat X2) N) (@ (@ tptp.ord_less_nat Y5) N) (@ (@ tptp.ord_less_eq_nat X2) Y5))))))))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bNF_Ca8665028551170535155natLeq) (@ (@ tptp.produc457027306803732586at_nat (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_nat X2) N)))) (lambda ((Uu2 tptp.nat)) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_nat X2) N)))))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_nat X2) N) (@ (@ tptp.ord_less_nat Y5) N) (@ (@ tptp.ord_less_eq_nat X2) Y5))))))))
% 3.70/4.05 (assert (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ tptp.bNF_Ca3793111618940312692of_nat tptp.top_top_set_nat)) tptp.bNF_Ca8665028551170535155natLeq)) tptp.bNF_We5258908940166488438at_nat))
% 3.70/4.05 (assert (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ tptp.bNF_Ca3793111618940312692of_nat (@ tptp.field_nat tptp.bNF_Ca8665028551170535155natLeq))) tptp.bNF_Ca8665028551170535155natLeq)) tptp.bNF_We5258908940166488438at_nat))
% 3.70/4.05 (assert (@ (@ (@ (@ tptp.bNF_re7627151682743391978at_rat tptp.pcr_rat) (@ (@ tptp.bNF_re8279943556446156061nt_rat tptp.pcr_rat) tptp.pcr_rat)) (lambda ((X2 tptp.product_prod_int_int) (Y5 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Y5))) (let ((_let_2 (@ tptp.product_snd_int_int X2))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) _let_1)) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y5)) _let_2))) (@ (@ tptp.times_times_int _let_2) _let_1)))))) tptp.plus_plus_rat))
% 3.70/4.05 (assert (@ (@ tptp.pcr_rat (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int)) tptp.one_one_rat))
% 3.70/4.05 (assert (@ (@ tptp.pcr_rat (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) tptp.zero_zero_rat))
% 3.70/4.05 (assert (@ (@ (@ (@ tptp.bNF_re7627151682743391978at_rat tptp.pcr_rat) (@ (@ tptp.bNF_re8279943556446156061nt_rat tptp.pcr_rat) tptp.pcr_rat)) (lambda ((X2 tptp.product_prod_int_int) (Y5 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) (@ tptp.product_fst_int_int Y5))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int X2)) (@ tptp.product_snd_int_int Y5))))) tptp.times_times_rat))
% 3.70/4.05 (assert (@ (@ (@ (@ tptp.bNF_re8279943556446156061nt_rat tptp.pcr_rat) tptp.pcr_rat) (lambda ((X2 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int (@ tptp.product_fst_int_int X2))) (@ tptp.product_snd_int_int X2)))) tptp.uminus_uminus_rat))
% 3.70/4.05 (assert (forall ((Q6 tptp.int) (P6 tptp.int)) (=> (@ (@ tptp.ord_less_int Q6) tptp.zero_zero_int) (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P6) Q6)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int P6)) (@ tptp.uminus_uminus_int Q6)))))))
% 3.70/4.05 (assert (@ (@ (@ (@ tptp.bNF_re8279943556446156061nt_rat tptp.pcr_rat) tptp.pcr_rat) (lambda ((X2 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_fst_int_int X2))) (@ (@ (@ 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 X2)) _let_1))))) tptp.inverse_inverse_rat))
% 3.70/4.05 (assert (forall ((P6 tptp.int)) (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P6) tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))))
% 3.70/4.05 (assert (forall ((R2 tptp.product_prod_int_int) (P6 tptp.int) (Q6 tptp.int)) (=> (= (@ tptp.normalize R2) (@ (@ tptp.product_Pair_int_int P6) Q6)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q6))))
% 3.70/4.05 (assert (forall ((Q6 tptp.int) (S3 tptp.int) (P6 tptp.int) (R2 tptp.int)) (=> (not (= Q6 tptp.zero_zero_int)) (=> (not (= S3 tptp.zero_zero_int)) (=> (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P6) Q6)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int R2) S3))) (= (@ (@ tptp.times_times_int P6) S3) (@ (@ tptp.times_times_int R2) Q6)))))))
% 3.70/4.05 (assert (forall ((P6 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.inverse_inverse_rat P6)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= A3 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A3)) B3)) (@ tptp.abs_abs_int A3))))) (@ tptp.quotient_of P6)))))
% 3.70/4.05 (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)))))))))))))
% 3.70/4.05 (assert (forall ((K3 tptp.num)) (= (@ tptp.quotient_of (@ tptp.numeral_numeral_rat K3)) (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int K3)) tptp.one_one_int))))
% 3.70/4.05 (assert (= (@ tptp.quotient_of tptp.one_one_rat) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int)))
% 3.70/4.05 (assert (= (@ tptp.quotient_of tptp.zero_zero_rat) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)))
% 3.70/4.05 (assert (forall ((K3 tptp.num)) (= (@ tptp.quotient_of (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat K3))) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K3))) tptp.one_one_int))))
% 3.70/4.05 (assert (= (@ tptp.quotient_of (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int)))
% 3.70/4.05 (assert (forall ((Xs tptp.list_int)) (= (@ tptp.gcd_Gcd_int (@ tptp.set_int2 Xs)) (@ (@ (@ tptp.fold_int_int tptp.gcd_gcd_int) Xs) tptp.zero_zero_int))))
% 3.70/4.05 (assert (forall ((R2 tptp.rat) (N tptp.int) (D2 tptp.int)) (=> (= (@ tptp.quotient_of R2) (@ (@ tptp.product_Pair_int_int N) D2)) (= R2 (@ (@ tptp.divide_divide_rat (@ tptp.ring_1_of_int_rat N)) (@ tptp.ring_1_of_int_rat D2))))))
% 3.70/4.05 (assert (forall ((R2 tptp.rat) (P6 tptp.int) (Q6 tptp.int)) (=> (= (@ tptp.quotient_of R2) (@ (@ tptp.product_Pair_int_int P6) Q6)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q6))))
% 3.70/4.05 (assert (forall ((P6 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.abs_abs_rat P6)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.product_Pair_int_int (@ tptp.abs_abs_int A3)) __flatten_var_0))) (@ tptp.quotient_of P6)))))
% 3.70/4.05 (assert (forall ((P6 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.sgn_sgn_rat P6)) (@ (@ tptp.product_Pair_int_int (@ tptp.sgn_sgn_int (@ tptp.product_fst_int_int (@ tptp.quotient_of P6)))) tptp.one_one_int))))
% 3.70/4.05 (assert (forall ((P6 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.uminus_uminus_rat P6)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int A3)) __flatten_var_0))) (@ tptp.quotient_of P6)))))
% 3.70/4.05 (assert (forall ((P6 tptp.rat) (Q6 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.divide_divide_rat P6) Q6)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (C5 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B3 tptp.int) (D5 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int A3) D5)) (@ (@ tptp.times_times_int C5) B3))))) (@ tptp.quotient_of Q6)))) (@ tptp.quotient_of P6)))))
% 3.70/4.05 (assert (forall ((P6 tptp.rat) (Q6 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.minus_minus_rat P6) Q6)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (C5 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B3 tptp.int) (D5 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A3) D5)) (@ (@ tptp.times_times_int B3) C5))) (@ (@ tptp.times_times_int C5) D5))))) (@ tptp.quotient_of Q6)))) (@ tptp.quotient_of P6)))))
% 3.70/4.05 (assert (forall ((P6 tptp.rat) (Q6 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.times_times_rat P6) Q6)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (C5 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B3 tptp.int) (D5 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int A3) B3)) (@ (@ tptp.times_times_int C5) D5))))) (@ tptp.quotient_of Q6)))) (@ tptp.quotient_of P6)))))
% 3.70/4.05 (assert (forall ((P6 tptp.rat) (Q6 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.plus_plus_rat P6) Q6)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (C5 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B3 tptp.int) (D5 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A3) D5)) (@ (@ tptp.times_times_int B3) C5))) (@ (@ tptp.times_times_int C5) D5))))) (@ tptp.quotient_of Q6)))) (@ tptp.quotient_of P6)))))
% 3.70/4.05 (assert (forall ((A2 tptp.int)) (= (@ tptp.quotient_of (@ tptp.of_int A2)) (@ (@ tptp.product_Pair_int_int A2) tptp.one_one_int))))
% 3.70/4.05 (assert (forall ((K3 tptp.num)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int tptp.one_one_int) (@ tptp.numeral_numeral_int K3))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat K3)))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.gcd_gcd_nat M2) N)) (or (not (= M2 tptp.zero_zero_nat)) (not (= N tptp.zero_zero_nat))))))
% 3.70/4.05 (assert (forall ((A tptp.set_nat)) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (@ (@ tptp.member_nat A4) A) (=> (@ (@ tptp.member_nat B4) A) (@ (@ tptp.member_nat (@ (@ tptp.gcd_gcd_nat A4) B4)) A)))) (=> (not (= A tptp.bot_bot_set_nat)) (@ (@ tptp.member_nat (@ tptp.gcd_Gcd_nat A)) A)))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat)) (= (@ tptp.gcd_Gcd_nat (@ tptp.set_nat2 Xs)) (@ (@ (@ tptp.fold_nat_nat tptp.gcd_gcd_nat) Xs) tptp.zero_zero_nat))))
% 3.70/4.05 (assert (forall ((K3 tptp.num) (L tptp.num)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int K3)) (@ tptp.numeral_numeral_int L))) (@ (@ tptp.divide_divide_rat (@ tptp.numeral_numeral_rat K3)) (@ tptp.numeral_numeral_rat L)))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.gcd_gcd_nat M2) N) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((D5 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D5))) (and (@ _let_1 M2) (@ _let_1 N))))))))))
% 3.70/4.05 (assert (forall ((K3 tptp.num)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int K3)) tptp.one_one_int)) (@ tptp.numeral_numeral_rat K3))))
% 3.70/4.05 (assert (forall ((A2 tptp.int)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int A2) tptp.zero_zero_int)) tptp.zero_zero_rat)))
% 3.70/4.05 (assert (forall ((A2 tptp.int)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) A2)) tptp.zero_zero_rat)))
% 3.70/4.05 (assert (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int)) tptp.one_one_rat))
% 3.70/4.05 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.product_Pair_int_int A2))) (= (@ tptp.frct (@ _let_1 (@ tptp.uminus_uminus_int B2))) (@ tptp.uminus_uminus_rat (@ tptp.frct (@ _let_1 B2)))))))
% 3.70/4.05 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int A2)) B2)) (@ tptp.uminus_uminus_rat (@ tptp.frct (@ (@ tptp.product_Pair_int_int A2) B2))))))
% 3.70/4.05 (assert (forall ((X tptp.nat) (Xa tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.gcd_nat_rel) (@ (@ tptp.product_Pair_nat_nat X) Xa)))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= (@ (@ tptp.gcd_gcd_nat X) Xa) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y X)) (=> (not _let_2) (= Y (@ (@ tptp.gcd_gcd_nat Xa) (@ (@ tptp.modulo_modulo_nat X) Xa))))) (not _let_1)))))))))
% 3.70/4.05 (assert (@ (@ (@ (@ tptp.bNF_re5228765855967844073nt_int tptp.ratrel) (@ (@ tptp.bNF_re7145576690424134365nt_int tptp.ratrel) tptp.ratrel)) (lambda ((X2 tptp.product_prod_int_int) (Y5 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Y5))) (let ((_let_2 (@ tptp.product_snd_int_int X2))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) _let_1)) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y5)) _let_2))) (@ (@ tptp.times_times_int _let_2) _let_1)))))) (lambda ((X2 tptp.product_prod_int_int) (Y5 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Y5))) (let ((_let_2 (@ tptp.product_snd_int_int X2))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) _let_1)) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y5)) _let_2))) (@ (@ tptp.times_times_int _let_2) _let_1)))))))
% 3.70/4.05 (assert (let ((_let_1 (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int))) (@ (@ tptp.ratrel _let_1) _let_1)))
% 3.70/4.05 (assert (let ((_let_1 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))) (@ (@ tptp.ratrel _let_1) _let_1)))
% 3.70/4.05 (assert (@ (@ (@ (@ tptp.bNF_re157797125943740599nt_int (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2))) (@ (@ tptp.bNF_re6250860962936578807nt_int (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2))) tptp.ratrel)) (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= B3 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int A3) B3)))) (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= B3 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int A3) B3)))))
% 3.70/4.05 (assert (@ (@ (@ (@ tptp.bNF_re5228765855967844073nt_int tptp.ratrel) (@ (@ tptp.bNF_re7145576690424134365nt_int tptp.ratrel) tptp.ratrel)) (lambda ((X2 tptp.product_prod_int_int) (Y5 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) (@ tptp.product_fst_int_int Y5))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int X2)) (@ tptp.product_snd_int_int Y5))))) (lambda ((X2 tptp.product_prod_int_int) (Y5 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) (@ tptp.product_fst_int_int Y5))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int X2)) (@ tptp.product_snd_int_int Y5))))))
% 3.70/4.05 (assert (@ (@ (@ (@ tptp.bNF_re7145576690424134365nt_int tptp.ratrel) tptp.ratrel) (lambda ((X2 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int (@ tptp.product_fst_int_int X2))) (@ tptp.product_snd_int_int X2)))) (lambda ((X2 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int (@ tptp.product_fst_int_int X2))) (@ tptp.product_snd_int_int X2)))))
% 3.70/4.05 (assert (@ (@ (@ (@ tptp.bNF_re7145576690424134365nt_int tptp.ratrel) tptp.ratrel) (lambda ((X2 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_fst_int_int X2))) (@ (@ (@ 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 X2)) _let_1))))) (lambda ((X2 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_fst_int_int X2))) (@ (@ (@ 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 X2)) _let_1))))))
% 3.70/4.05 (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))))))))))
% 3.70/4.05 (assert (forall ((X tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_fst_int_int X))) (=> (@ (@ tptp.ratrel X) X) (= (@ tptp.inverse_inverse_rat (@ tptp.abs_Rat X)) (@ tptp.abs_Rat (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= _let_1 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ tptp.product_snd_int_int X)) _let_1))))))))
% 3.70/4.05 (assert (= tptp.one_one_rat (@ tptp.abs_Rat (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int))))
% 3.70/4.05 (assert (= tptp.zero_zero_rat (@ tptp.abs_Rat (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))))
% 3.70/4.05 (assert (forall ((X tptp.product_prod_int_int)) (=> (@ (@ tptp.ratrel X) X) (= (@ tptp.uminus_uminus_rat (@ tptp.abs_Rat X)) (@ tptp.abs_Rat (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int (@ tptp.product_fst_int_int X))) (@ tptp.product_snd_int_int X)))))))
% 3.70/4.05 (assert (forall ((Xa tptp.product_prod_int_int) (X tptp.product_prod_int_int)) (=> (@ (@ tptp.ratrel Xa) Xa) (=> (@ (@ tptp.ratrel X) X) (= (@ (@ tptp.times_times_rat (@ tptp.abs_Rat Xa)) (@ tptp.abs_Rat X)) (@ tptp.abs_Rat (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Xa)) (@ tptp.product_fst_int_int X))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int Xa)) (@ tptp.product_snd_int_int X)))))))))
% 3.70/4.05 (assert (= tptp.inverse_inverse_rat (@ (@ (@ tptp.map_fu5673905371560938248nt_rat tptp.rep_Rat) tptp.abs_Rat) (lambda ((X2 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_fst_int_int X2))) (@ (@ (@ 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 X2)) _let_1)))))))
% 3.70/4.05 (assert (= tptp.uminus_uminus_rat (@ (@ (@ tptp.map_fu5673905371560938248nt_rat tptp.rep_Rat) tptp.abs_Rat) (lambda ((X2 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int (@ tptp.product_fst_int_int X2))) (@ tptp.product_snd_int_int X2))))))
% 3.70/4.05 (assert (= tptp.plus_plus_rat (@ (@ (@ tptp.map_fu4333342158222067775at_rat tptp.rep_Rat) (@ (@ tptp.map_fu5673905371560938248nt_rat tptp.rep_Rat) tptp.abs_Rat)) (lambda ((X2 tptp.product_prod_int_int) (Y5 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Y5))) (let ((_let_2 (@ tptp.product_snd_int_int X2))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) _let_1)) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y5)) _let_2))) (@ (@ tptp.times_times_int _let_2) _let_1))))))))
% 3.70/4.05 (assert (= tptp.times_times_rat (@ (@ (@ tptp.map_fu4333342158222067775at_rat tptp.rep_Rat) (@ (@ tptp.map_fu5673905371560938248nt_rat tptp.rep_Rat) tptp.abs_Rat)) (lambda ((X2 tptp.product_prod_int_int) (Y5 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) (@ tptp.product_fst_int_int Y5))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int X2)) (@ tptp.product_snd_int_int Y5)))))))
% 3.70/4.05 (assert (forall ((X tptp.assn)) (= (@ tptp.abs_assn (@ tptp.rep_assn X)) X)))
% 3.70/4.05 (assert (forall ((P (-> tptp.produc3658429121746597890et_nat Bool)) (Pr tptp.assn)) (=> (forall ((H tptp.produc3658429121746597890et_nat)) (= (@ P H) (@ (@ tptp.rep_assn Pr) H))) (= Pr (@ tptp.abs_assn P)))))
% 3.70/4.05 (assert (forall ((P (-> tptp.produc3658429121746597890et_nat Bool)) (Pr tptp.assn)) (=> (forall ((H tptp.produc3658429121746597890et_nat)) (= (@ P H) (@ (@ tptp.rep_assn Pr) H))) (= (@ tptp.abs_assn P) Pr))))
% 3.70/4.05 (assert (= tptp.pure_assn (lambda ((B3 Bool)) (@ tptp.abs_assn (@ tptp.pure_a825153325127701367it_nat B3)))))
% 3.70/4.05 (assert (= tptp.bot_bot_assn (@ tptp.abs_assn (lambda ((Uu2 tptp.produc3658429121746597890et_nat)) false))))
% 3.70/4.05 (assert (= tptp.one_one_assn (@ tptp.abs_assn tptp.one_assn_raw)))
% 3.70/4.05 (assert (= tptp.sup_sup_assn (lambda ((P2 tptp.assn) (Q2 tptp.assn)) (@ tptp.abs_assn (lambda ((H3 tptp.produc3658429121746597890et_nat)) (or (@ (@ tptp.rep_assn P2) H3) (@ (@ tptp.rep_assn Q2) H3)))))))
% 3.70/4.05 (assert (= tptp.inf_inf_assn (lambda ((P2 tptp.assn) (Q2 tptp.assn)) (@ tptp.abs_assn (lambda ((H3 tptp.produc3658429121746597890et_nat)) (and (@ (@ tptp.rep_assn P2) H3) (@ (@ tptp.rep_assn Q2) H3)))))))
% 3.70/4.05 (assert (= tptp.times_times_assn (lambda ((P2 tptp.assn) (Q2 tptp.assn)) (@ tptp.abs_assn (@ (@ tptp.times_assn_raw (@ tptp.rep_assn P2)) (@ tptp.rep_assn Q2))))))
% 3.70/4.05 (assert (= tptp.wand_assn (lambda ((P2 tptp.assn) (Q2 tptp.assn)) (@ tptp.abs_assn (@ (@ tptp.wand_raw (@ tptp.rep_assn P2)) (@ tptp.rep_assn Q2))))))
% 3.70/4.05 (assert (= tptp.uminus_uminus_assn (lambda ((P2 tptp.assn)) (@ tptp.abs_assn (lambda ((H3 tptp.produc3658429121746597890et_nat)) (and (@ tptp.in_range H3) (not (@ (@ tptp.rep_assn P2) H3))))))))
% 3.70/4.05 (assert (forall ((H2 tptp.heap_e7401611519738050253t_unit)) (@ tptp.in_range (@ (@ tptp.produc7507926704131184380et_nat H2) tptp.bot_bot_set_nat))))
% 3.70/4.05 (assert (forall ((H2 tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn tptp.top_top_assn) H2) (@ tptp.in_range H2))))
% 3.70/4.05 (assert (forall ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat) (As3 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H2))) (= (@ tptp.in_range (@ _let_1 (@ (@ tptp.sup_sup_set_nat As2) As3))) (and (@ tptp.in_range (@ _let_1 As2)) (@ tptp.in_range (@ _let_1 As3)))))))
% 3.70/4.05 (assert (forall ((P tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn (@ tptp.uminus_uminus_assn P)) H2) (and (@ tptp.in_range H2) (not (@ (@ tptp.rep_assn P) H2))))))
% 3.70/4.05 (assert (forall ((As2 tptp.set_nat) (As3 tptp.set_nat) (H2 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H2))) (=> (@ (@ tptp.ord_less_eq_set_nat As2) As3) (=> (@ tptp.in_range (@ _let_1 As3)) (@ tptp.in_range (@ _let_1 As2)))))))
% 3.70/4.05 (assert (forall ((P tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P) H2) (@ tptp.in_range H2))))
% 3.70/4.05 (assert (= tptp.top_top_assn (@ tptp.abs_assn tptp.in_range)))
% 3.70/4.05 (assert (forall ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat) (Q tptp.assn) (R tptp.assn)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) As2))) (=> (@ tptp.in_range _let_1) (=> (forall ((H5 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H5))) (=> (= (@ (@ tptp.inf_inf_set_nat As2) As4) tptp.bot_bot_set_nat) (=> (@ (@ (@ tptp.relH As2) H2) H5) (=> (@ tptp.in_range (@ _let_1 As2)) (=> (@ (@ tptp.rep_assn Q) (@ _let_1 As4)) (@ (@ tptp.rep_assn R) (@ _let_1 (@ (@ tptp.sup_sup_set_nat As2) As4))))))))) (@ (@ tptp.rep_assn (@ (@ tptp.wand_assn Q) R)) _let_1))))))
% 3.70/4.05 (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 ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As))) (=> (= Xb _let_1) (and (@ tptp.in_range _let_1) (forall ((H5 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H5))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As) As4) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As) H) H5) (@ tptp.in_range (@ _let_1 As)) (@ X (@ _let_1 As4))) (@ Xa (@ _let_1 (@ (@ tptp.sup_sup_set_nat As) As4))))))))))))))
% 3.70/4.05 (assert (forall ((As2 tptp.set_nat) (As3 tptp.set_nat) (H2 tptp.heap_e7401611519738050253t_unit) (H4 tptp.heap_e7401611519738050253t_unit)) (= (@ (@ (@ tptp.relH (@ (@ tptp.sup_sup_set_nat As2) As3)) H2) H4) (and (@ (@ (@ tptp.relH As2) H2) H4) (@ (@ (@ tptp.relH As3) H2) H4)))))
% 3.70/4.05 (assert (forall ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (=> (@ tptp.in_range (@ (@ tptp.produc7507926704131184380et_nat H2) As2)) (@ (@ (@ tptp.relH As2) H2) H2))))
% 3.70/4.05 (assert (forall ((As2 tptp.set_nat) (H2 tptp.heap_e7401611519738050253t_unit) (H4 tptp.heap_e7401611519738050253t_unit)) (=> (@ (@ (@ tptp.relH As2) H2) H4) (@ tptp.in_range (@ (@ tptp.produc7507926704131184380et_nat H2) As2)))))
% 3.70/4.05 (assert (forall ((As2 tptp.set_nat) (H2 tptp.heap_e7401611519738050253t_unit) (H4 tptp.heap_e7401611519738050253t_unit)) (=> (@ (@ (@ tptp.relH As2) H2) H4) (@ tptp.in_range (@ (@ tptp.produc7507926704131184380et_nat H4) As2)))))
% 3.70/4.05 (assert (forall ((As2 tptp.set_nat) (H2 tptp.heap_e7401611519738050253t_unit) (H4 tptp.heap_e7401611519738050253t_unit) (P tptp.assn)) (let ((_let_1 (@ tptp.rep_assn P))) (=> (@ (@ (@ tptp.relH As2) H2) H4) (= (@ _let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) As2)) (@ _let_1 (@ (@ tptp.produc7507926704131184380et_nat H4) As2)))))))
% 3.70/4.05 (assert (forall ((As2 tptp.set_nat) (H12 tptp.heap_e7401611519738050253t_unit) (H23 tptp.heap_e7401611519738050253t_unit) (H32 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ tptp.relH As2))) (let ((_let_2 (@ _let_1 H12))) (=> (@ _let_2 H23) (=> (@ (@ _let_1 H23) H32) (@ _let_2 H32)))))))
% 3.70/4.05 (assert (forall ((As2 tptp.set_nat) (H2 tptp.heap_e7401611519738050253t_unit) (H4 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ tptp.relH As2))) (=> (@ (@ _let_1 H2) H4) (@ (@ _let_1 H4) H2)))))
% 3.70/4.05 (assert (forall ((Bs tptp.set_nat) (H2 tptp.heap_e7401611519738050253t_unit) (H4 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (=> (@ (@ (@ tptp.relH Bs) H2) H4) (=> (@ (@ tptp.ord_less_eq_set_nat As2) Bs) (@ (@ (@ tptp.relH As2) H2) H4)))))
% 3.70/4.05 (assert (forall ((P (-> tptp.produc3658429121746597890et_nat Bool)) (Q (-> tptp.produc3658429121746597890et_nat Bool)) (H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) As2))) (= (@ (@ (@ tptp.wand_raw P) Q) _let_1) (and (@ tptp.in_range _let_1) (forall ((H6 tptp.heap_e7401611519738050253t_unit) (As5 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H6))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As2) As5) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As2) H2) H6) (@ tptp.in_range (@ _let_1 As2)) (@ P (@ _let_1 As5))) (@ Q (@ _let_1 (@ (@ tptp.sup_sup_set_nat As2) As5)))))))))))
% 3.70/4.05 (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 ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As))) (=> (= Xb _let_1) (= Y (not (and (@ tptp.in_range _let_1) (forall ((H6 tptp.heap_e7401611519738050253t_unit) (As5 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H6))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As) As5) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As) H) H6) (@ tptp.in_range (@ _let_1 As)) (@ X (@ _let_1 As5))) (@ Xa (@ _let_1 (@ (@ tptp.sup_sup_set_nat As) As5))))))))))))))))
% 3.70/4.05 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat)) (=> (@ (@ (@ tptp.wand_raw X) Xa) Xb) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As))) (=> (= Xb _let_1) (not (and (@ tptp.in_range _let_1) (forall ((H7 tptp.heap_e7401611519738050253t_unit) (As6 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H7))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As) As6) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As) H) H7) (@ tptp.in_range (@ _let_1 As)) (@ X (@ _let_1 As6))) (@ Xa (@ _let_1 (@ (@ tptp.sup_sup_set_nat As) As6)))))))))))))))
% 3.70/4.05 (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 ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As))) (=> (= Xb _let_1) (=> (@ (@ tptp.accp_P1862375125659990705et_nat tptp.wand_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) _let_1))) (and (@ tptp.in_range _let_1) (forall ((H5 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H5))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As) As4) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As) H) H5) (@ tptp.in_range (@ _let_1 As)) (@ X (@ _let_1 As4))) (@ Xa (@ _let_1 (@ (@ tptp.sup_sup_set_nat As) As4))))))))))))))))
% 3.70/4.05 (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 ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As))) (=> (= 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 ((H7 tptp.heap_e7401611519738050253t_unit) (As6 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H7))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As) As6) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As) H) H7) (@ tptp.in_range (@ _let_1 As)) (@ X (@ _let_1 As6))) (@ Xa (@ _let_1 (@ (@ tptp.sup_sup_set_nat As) As6)))))))))))))))))
% 3.70/4.05 (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 ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As))) (=> (= Xb _let_1) (=> (= Y (and (@ tptp.in_range _let_1) (forall ((H6 tptp.heap_e7401611519738050253t_unit) (As5 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H6))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As) As5) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As) H) H6) (@ tptp.in_range (@ _let_1 As)) (@ X (@ _let_1 As5))) (@ Xa (@ _let_1 (@ (@ tptp.sup_sup_set_nat As) As5)))))))) (not (@ (@ tptp.accp_P1862375125659990705et_nat tptp.wand_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) _let_1)))))))))))))
% 3.70/4.05 (assert (forall ((Q6 tptp.int) (P6 tptp.int)) (let ((_let_1 (@ (@ tptp.product_Pair_int_int P6) Q6))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q6) (=> (@ (@ tptp.algebr932160517623751201me_int P6) Q6) (= (@ tptp.normalize _let_1) _let_1))))))
% 3.70/4.05 (assert (forall ((R2 tptp.product_prod_int_int) (P6 tptp.int) (Q6 tptp.int)) (=> (= (@ tptp.normalize R2) (@ (@ tptp.product_Pair_int_int P6) Q6)) (@ (@ tptp.algebr932160517623751201me_int P6) Q6))))
% 3.70/4.05 (assert (forall ((R2 tptp.rat) (P6 tptp.int) (Q6 tptp.int)) (=> (= (@ tptp.quotient_of R2) (@ (@ tptp.product_Pair_int_int P6) Q6)) (@ (@ tptp.algebr932160517623751201me_int P6) Q6))))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.algebr934650988132801477me_nat N) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.algebr934650988132801477me_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) N))))
% 3.70/4.05 (assert (@ (@ (@ (@ tptp.bNF_re3461391660133120880nt_rat (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2))) (@ (@ tptp.bNF_re2214769303045360666nt_rat (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2))) tptp.pcr_rat)) (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= B3 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int A3) B3)))) tptp.fract))
% 3.70/4.05 (assert (forall ((A2 tptp.int) (B2 tptp.int) (P6 tptp.int) (Q6 tptp.int)) (let ((_let_1 (@ (@ tptp.fract A2) B2))) (=> (= (@ tptp.quotient_of _let_1) (@ (@ tptp.product_Pair_int_int P6) Q6)) (= (@ (@ tptp.fract P6) Q6) _let_1)))))
% 3.70/4.05 (assert (forall ((A2 tptp.int) (B2 tptp.int) (P6 tptp.int) (Q6 tptp.int)) (=> (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int A2) B2)) (@ (@ tptp.product_Pair_int_int P6) Q6)) (= (@ (@ tptp.fract P6) Q6) (@ (@ tptp.fract A2) B2)))))
% 3.70/4.05 (assert (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ tptp.quotient_of (@ (@ tptp.fract A2) B2)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int A2) B2)))))
% 3.70/4.05 (assert (= tptp.fract (lambda ((Xa4 tptp.int) (X2 tptp.int)) (@ tptp.abs_Rat (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= X2 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int Xa4) X2))))))
% 3.70/4.05 (assert (forall ((X tptp.produc8763457246119570046nteger)) (not (forall ((F5 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (D3 tptp.code_integer) (I5 tptp.code_integer)) (not (= X (@ (@ tptp.produc6137756002093451184nteger F5) (@ (@ tptp.produc1086072967326762835nteger D3) I5))))))))
% 3.70/4.05 (assert (forall ((X tptp.produc7773217078559923341nt_int)) (not (forall ((F5 (-> tptp.int tptp.option6357759511663192854e_term)) (D3 tptp.int) (I5 tptp.int)) (not (= X (@ (@ tptp.produc4305682042979456191nt_int F5) (@ (@ tptp.product_Pair_int_int D3) I5))))))))
% 3.70/4.05 (assert (forall ((X tptp.produc2285326912895808259nt_int)) (not (forall ((F5 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (D3 tptp.int) (I5 tptp.int)) (not (= X (@ (@ tptp.produc5700946648718959541nt_int F5) (@ (@ tptp.product_Pair_int_int D3) I5))))))))
% 3.70/4.05 (assert (forall ((X tptp.produc1908205239877642774nteger)) (not (forall ((F5 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (D3 tptp.code_integer) (I5 tptp.code_integer)) (not (= X (@ (@ tptp.produc8603105652947943368nteger F5) (@ (@ tptp.produc1086072967326762835nteger D3) I5))))))))
% 3.70/4.05 (assert (forall ((X tptp.list_nat) (Y tptp.nat)) (=> (= (@ tptp.nat_list_encode X) Y) (=> (=> (= X tptp.nil_nat) (not (= Y tptp.zero_zero_nat))) (not (forall ((X3 tptp.nat) (Xs2 tptp.list_nat)) (=> (= X (@ (@ tptp.cons_nat X3) Xs2)) (not (= Y (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X3) (@ tptp.nat_list_encode Xs2)))))))))))))
% 3.70/4.05 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (= (@ tptp.nat_list_encode (@ (@ tptp.cons_nat X) Xs)) (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X) (@ tptp.nat_list_encode Xs)))))))
% 3.70/4.05 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat A2) (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat A2) B2)))))
% 3.70/4.05 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat B2) (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat A2) B2)))))
% 3.70/4.05 (assert (forall ((X tptp.list_nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.accp_list_nat tptp.nat_list_encode_rel))) (=> (= (@ tptp.nat_list_encode X) Y) (=> (@ _let_1 X) (=> (=> (= X tptp.nil_nat) (=> (= Y tptp.zero_zero_nat) (not (@ _let_1 tptp.nil_nat)))) (not (forall ((X3 tptp.nat) (Xs2 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat X3) Xs2))) (=> (= X _let_1) (=> (= Y (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X3) (@ tptp.nat_list_encode Xs2))))) (not (@ (@ tptp.accp_list_nat tptp.nat_list_encode_rel) _let_1)))))))))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.frequently_nat P) tptp.cofinite_nat) (forall ((M tptp.nat)) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M) N2) (@ P N2)))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (@ P tptp.zero_zero_nat) (=> (forall ((I5 tptp.nat)) (=> (@ P I5) (exists ((J4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) J4) (@ P J4) (@ Q J4))))) (@ (@ tptp.frequently_nat Q) tptp.cofinite_nat)))))
% 3.70/4.05 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat P) tptp.cofinite_nat) (exists ((M tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ P N2)))))))
% 3.70/4.05 (assert (= tptp.cofinite_nat tptp.at_top_nat))
% 3.70/4.05 (assert (forall ((P (-> tptp.int Bool)) (I tptp.int) (J tptp.int)) (= (@ (@ tptp.list_ex_int P) (@ (@ tptp.upto I) J)) (not (@ (@ (@ tptp.all_interval_int (@ (@ tptp.comp_o_o_int (lambda ((_lvar_0 Bool)) (not _lvar_0))) P)) I) J)))))
% 3.70/4.05 (assert (= tptp.all_interval_int (lambda ((P2 (-> tptp.int Bool)) (I4 tptp.int) (J2 tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int I4) J2)) (@ P2 X2))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.int Bool)) (I tptp.int) (J tptp.int)) (= (@ (@ tptp.list_all_int P) (@ (@ tptp.upto I) J)) (@ (@ (@ tptp.all_interval_int P) I) J))))
% 3.70/4.05 (assert (forall ((P Bool)) (@ tptp.is_pure_assn (@ tptp.pure_assn P))))
% 3.70/4.05 (assert (forall ((A2 tptp.assn) (B2 tptp.assn)) (=> (@ tptp.is_pure_assn A2) (=> (@ tptp.is_pure_assn B2) (@ tptp.is_pure_assn (@ (@ tptp.times_times_assn A2) B2))))))
% 3.70/4.05 (assert (= (@ tptp.gcd_Lcm_nat tptp.bot_bot_set_nat) tptp.one_one_nat))
% 3.70/4.05 (assert (@ tptp.is_pure_assn tptp.one_one_assn))
% 3.70/4.05 (assert (= tptp.is_pure_assn (lambda ((A3 tptp.assn)) (exists ((P2 Bool)) (= A3 (@ tptp.pure_assn P2))))))
% 3.70/4.05 (assert (forall ((A2 tptp.assn)) (=> (@ tptp.is_pure_assn A2) (not (forall ((P5 Bool)) (not (= A2 (@ tptp.pure_assn P5))))))))
% 3.70/4.05 (assert (@ tptp.is_pure_assn tptp.bot_bot_assn))
% 3.70/4.05 (assert (forall ((M5 tptp.set_nat)) (=> (@ tptp.finite_finite_nat M5) (=> (not (= M5 tptp.bot_bot_set_nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M5)) (=> (forall ((M6 tptp.nat) (N5 tptp.nat)) (=> (@ (@ tptp.member_nat M6) M5) (=> (@ (@ tptp.member_nat N5) M5) (@ (@ tptp.member_nat (@ (@ tptp.gcd_lcm_nat M6) N5)) M5)))) (= (@ tptp.gcd_Lcm_nat M5) (@ tptp.lattic8265883725875713057ax_nat M5))))))))
% 3.70/4.05 (assert (forall ((N tptp.nat) (M5 tptp.set_nat)) (= (@ tptp.gcd_Lcm_nat (@ (@ tptp.insert_nat2 N) M5)) (@ (@ tptp.gcd_lcm_nat N) (@ tptp.gcd_Lcm_nat M5)))))
% 3.70/4.05 (assert (forall ((M5 tptp.set_nat)) (=> (@ tptp.finite_finite_nat M5) (=> (not (= M5 tptp.bot_bot_set_nat)) (=> (forall ((M6 tptp.nat) (N5 tptp.nat)) (=> (@ (@ tptp.member_nat M6) M5) (=> (@ (@ tptp.member_nat N5) M5) (@ (@ tptp.member_nat (@ (@ tptp.gcd_lcm_nat M6) N5)) M5)))) (@ (@ tptp.member_nat (@ tptp.gcd_Lcm_nat M5)) M5))))))
% 3.70/4.05 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.gcd_lcm_nat M2) N)))))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_nat)) (= (@ tptp.gcd_Lcm_nat (@ tptp.set_nat2 Xs)) (@ (@ (@ tptp.fold_nat_nat tptp.gcd_lcm_nat) Xs) tptp.one_one_nat))))
% 3.70/4.05 (assert (forall ((Xs tptp.list_int)) (= (@ tptp.gcd_Lcm_int (@ tptp.set_int2 Xs)) (@ (@ (@ tptp.fold_int_int tptp.gcd_lcm_int) Xs) tptp.one_one_int))))
% 3.70/4.05 (assert (forall ((P (-> tptp.produc3658429121746597890et_nat Bool))) (=> (forall ((As tptp.set_nat) (H tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As))) (=> (@ P _let_1) (@ tptp.in_range _let_1)))) (=> (forall ((As tptp.set_nat) (H tptp.heap_e7401611519738050253t_unit) (H5 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H5) As))) (=> (@ P (@ (@ tptp.produc7507926704131184380et_nat H) As)) (=> (@ (@ (@ tptp.relH As) H) H5) (=> (@ tptp.in_range _let_1) (@ P _let_1)))))) (@ tptp.proper P)))))
% 3.70/4.05 (assert (forall ((P (-> tptp.produc3658429121746597890et_nat Bool)) (H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat) (H4 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H4) As2))) (=> (@ tptp.proper P) (=> (@ P (@ (@ tptp.produc7507926704131184380et_nat H2) As2)) (=> (@ (@ (@ tptp.relH As2) H2) H4) (=> (@ tptp.in_range _let_1) (@ P _let_1))))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.produc3658429121746597890et_nat Bool)) (Q (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.proper P) (=> (@ tptp.proper Q) (@ tptp.proper (lambda ((H3 tptp.produc3658429121746597890et_nat)) (and (@ P H3) (@ Q H3))))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.produc3658429121746597890et_nat Bool)) (Q (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.proper P) (=> (@ tptp.proper Q) (@ tptp.proper (lambda ((H3 tptp.produc3658429121746597890et_nat)) (or (@ P H3) (@ Q H3))))))))
% 3.70/4.05 (assert (@ tptp.proper (lambda ((Uu2 tptp.produc3658429121746597890et_nat)) false)))
% 3.70/4.05 (assert (@ tptp.proper tptp.in_range))
% 3.70/4.05 (assert (@ tptp.proper tptp.one_assn_raw))
% 3.70/4.05 (assert (forall ((P (-> tptp.produc3658429121746597890et_nat Bool)) (Q (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.proper P) (=> (@ tptp.proper Q) (@ tptp.proper (@ (@ tptp.times_assn_raw P) Q))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.produc3658429121746597890et_nat Bool)) (Q (-> tptp.produc3658429121746597890et_nat Bool))) (@ tptp.proper (@ (@ tptp.wand_raw P) Q))))
% 3.70/4.05 (assert (forall ((P (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.proper P) (@ tptp.proper (lambda ((H3 tptp.produc3658429121746597890et_nat)) (and (@ tptp.in_range H3) (not (@ P H3))))))))
% 3.70/4.05 (assert (forall ((B2 Bool)) (@ tptp.proper (@ tptp.pure_a825153325127701367it_nat B2))))
% 3.70/4.05 (assert (forall ((Y (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o Y) (@ tptp.collec939566748876313656_nat_o tptp.proper)) (= (@ tptp.rep_assn (@ tptp.abs_assn Y)) Y))))
% 3.70/4.05 (assert (forall ((X tptp.assn)) (not (forall ((Y2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (= X (@ tptp.abs_assn Y2)) (not (@ (@ tptp.member6576561426505652726_nat_o Y2) (@ tptp.collec939566748876313656_nat_o tptp.proper))))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.assn Bool)) (X tptp.assn)) (=> (forall ((Y2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o Y2) (@ tptp.collec939566748876313656_nat_o tptp.proper)) (@ P (@ tptp.abs_assn Y2)))) (@ P X))))
% 3.70/4.05 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Y (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.collec939566748876313656_nat_o tptp.proper))) (=> (@ (@ tptp.member6576561426505652726_nat_o X) _let_1) (=> (@ (@ tptp.member6576561426505652726_nat_o Y) _let_1) (= (= (@ tptp.abs_assn X) (@ tptp.abs_assn Y)) (= X Y)))))))
% 3.70/4.05 (assert (forall ((Y (-> tptp.produc3658429121746597890et_nat Bool)) (P (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o Y) (@ tptp.collec939566748876313656_nat_o tptp.proper)) (=> (forall ((X3 tptp.assn)) (@ P (@ tptp.rep_assn X3))) (@ P Y)))))
% 3.70/4.05 (assert (forall ((Y (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o Y) (@ tptp.collec939566748876313656_nat_o tptp.proper)) (not (forall ((X3 tptp.assn)) (not (= Y (@ tptp.rep_assn X3))))))))
% 3.70/4.05 (assert (forall ((X tptp.assn)) (@ (@ tptp.member6576561426505652726_nat_o (@ tptp.rep_assn X)) (@ tptp.collec939566748876313656_nat_o tptp.proper))))
% 3.70/4.05 (assert (forall ((P (-> tptp.produc3658429121746597890et_nat Bool)) (H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) As2))) (=> (@ tptp.proper P) (=> (@ P _let_1) (@ tptp.in_range _let_1))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.produc3658429121746597890et_nat Bool)) (As2 tptp.set_nat) (H2 tptp.heap_e7401611519738050253t_unit) (H4 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H4) As2))) (=> (@ tptp.proper P) (=> (@ (@ (@ tptp.relH As2) H2) H4) (=> (@ tptp.in_range _let_1) (= (@ P (@ (@ tptp.produc7507926704131184380et_nat H2) As2)) (@ P _let_1))))))))
% 3.70/4.05 (assert (= tptp.proper (lambda ((P2 (-> tptp.produc3658429121746597890et_nat Bool))) (forall ((H3 tptp.heap_e7401611519738050253t_unit) (H6 tptp.heap_e7401611519738050253t_unit) (As7 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H6) As7))) (let ((_let_2 (@ (@ tptp.produc7507926704131184380et_nat H3) As7))) (let ((_let_3 (@ P2 _let_2))) (and (=> _let_3 (@ tptp.in_range _let_2)) (=> (and _let_3 (@ (@ (@ tptp.relH As7) H3) H6) (@ tptp.in_range _let_1)) (@ P2 _let_1))))))))))
% 3.70/4.05 (assert (forall ((P (-> tptp.nat Bool)) (I tptp.nat) (J tptp.nat)) (= (@ (@ tptp.list_ex_nat P) (@ (@ tptp.upt I) J)) (not (@ (@ (@ tptp.all_interval_nat (@ (@ tptp.comp_o_o_nat (lambda ((_lvar_0 Bool)) (not _lvar_0))) P)) I) J)))))
% 3.70/4.05 (assert (forall ((P (-> tptp.nat Bool)) (I tptp.nat) (J tptp.nat)) (= (@ (@ tptp.list_all_nat P) (@ (@ tptp.upt I) J)) (@ (@ (@ tptp.all_interval_nat P) I) J))))
% 3.70/4.05 (assert (= tptp.all_interval_nat (lambda ((P2 (-> tptp.nat Bool)) (I4 tptp.nat) (J2 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or4665077453230672383an_nat I4) J2)) (@ P2 X2))))))
% 3.70/4.05 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.nat_of_num (@ tptp.num_of_nat N)) N))))
% 3.70/4.05 (assert (forall ((X tptp.num)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.nat_of_num X))))
% 3.70/4.05 (assert (= tptp.ord_less_num (lambda ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_nat (@ tptp.nat_of_num M)) (@ tptp.nat_of_num N2)))))
% 3.70/4.05 (assert (forall ((N tptp.code_natural)) (let ((_let_1 (@ tptp.code_nat_of_natural N))) (=> (not (= N tptp.zero_z2226904508553997617atural)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat _let_1) (@ tptp.suc tptp.zero_zero_nat))) _let_1)))))
% 3.70/4.05 (assert (= tptp.ord_le5570908160329646204atural (lambda ((X2 tptp.code_natural) (Xa4 tptp.code_natural)) (@ (@ tptp.ord_less_nat (@ tptp.code_nat_of_natural X2)) (@ tptp.code_nat_of_natural Xa4)))))
% 3.70/4.05 (assert (forall ((V2 tptp.code_natural) (W 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 W) _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 W) _let_4)) (@ tptp.numera5444537566228673987atural (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 _let_2)))))))))))))) (let ((_let_9 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 _let_3)))))))))))))))) (let ((_let_10 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 _let_7))))))))) (let ((_let_11 (@ (@ (@ tptp.minus_shift (@ tptp.numera5444537566228673987atural (@ tptp.bit1 _let_10))) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.modulo8411746178871703098atural V2) _let_9)) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 _let_6))))))))))))) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural V2) _let_9)) (@ tptp.numera5444537566228673987atural (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 _let_5))))))))))))))))) (= (@ tptp.next (@ (@ tptp.produc3574140220909816553atural V2) W)) (@ (@ 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))))))))))))))))
% 3.70/4.05 (assert (forall ((X tptp.produc989692990947075319atural)) (not (forall ((F5 (-> tptp.produc4972180933644002618e_term tptp.option6357759511663192854e_term)) (D3 tptp.code_natural) (I5 tptp.code_natural)) (not (= X (@ (@ tptp.produc3831813291587773865atural F5) (@ (@ tptp.produc3574140220909816553atural D3) I5))))))))
% 3.70/4.05 (assert (forall ((X tptp.produc8731074985263844745atural)) (not (forall ((F5 (-> tptp.code_natural tptp.option6357759511663192854e_term)) (D3 tptp.code_natural) (I5 tptp.code_natural)) (not (= X (@ (@ tptp.produc2252593628808123835atural F5) (@ (@ tptp.produc3574140220909816553atural D3) I5))))))))
% 3.70/4.05 (assert (forall ((X tptp.produc7822875418678951345atural)) (not (forall ((B4 tptp.code_natural) (I5 tptp.code_natural)) (not (= X (@ (@ tptp.produc3574140220909816553atural B4) I5)))))))
% 3.70/4.05 (assert (= tptp.split_seed (lambda ((S6 tptp.produc7822875418678951345atural)) (@ (@ tptp.produc8282080750456430313atural (lambda ((V4 tptp.code_natural) (W4 tptp.code_natural)) (@ (@ tptp.produc8282080750456430313atural (lambda ((V5 tptp.code_natural) (W5 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)))))))))) V4)) W5)) (@ (@ tptp.produc3574140220909816553atural V5) (@ (@ tptp.inc_shift (@ tptp.numera5444537566228673987atural (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 _let_1)))))))))) W4)))))) (@ tptp.produc6591912806276919810atural (@ tptp.next S6))))) S6))))
% 3.70/4.05 (assert (forall ((X tptp.product_prod_int_int)) (not (forall ((D3 tptp.int) (I5 tptp.int)) (not (= X (@ (@ tptp.product_Pair_int_int D3) I5)))))))
% 3.70/4.05 (assert (= tptp.range (lambda ((K4 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)))))))))))))))))))))))))))))))) K4)) (lambda ((L4 tptp.code_natural) (__flatten_var_0 tptp.produc7822875418678951345atural)) (@ (@ (@ tptp.produc5538323210962509403atural tptp.next) (lambda ((V4 tptp.code_natural) (__flatten_var_0 tptp.produc7822875418678951345atural)) (@ (@ tptp.produc6639722614265839536atural (@ (@ tptp.plus_p4538020629002901425atural V4) (@ (@ tptp.times_2397367101498566445atural L4) (@ 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 ((V4 tptp.code_natural) (__flatten_var_0 tptp.produc7822875418678951345atural)) (@ (@ tptp.produc6639722614265839536atural (@ (@ tptp.modulo8411746178871703098atural V4) K4)) __flatten_var_0))) __flatten_var_0))))
% 3.70/4.05 (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))))
% 3.70/4.05 (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))))))))))
% 3.70/4.05 (assert (forall ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (= (@ tptp.in_range (@ (@ tptp.produc7507926704131184380et_nat H2) As2)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) As2) (@ (@ tptp.ord_less_nat X2) (@ tptp.lim_Product_unit H2)))))))
% 3.70/4.05 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (=> (not (@ tptp.in_range X)) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (= X (@ (@ tptp.produc7507926704131184380et_nat H) As)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) As) (@ (@ tptp.ord_less_nat X3) (@ tptp.lim_Product_unit H))))))))))
% 3.70/4.05 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (=> (@ tptp.in_range X) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (= X (@ (@ tptp.produc7507926704131184380et_nat H) As)) (not (forall ((X7 tptp.nat)) (=> (@ (@ tptp.member_nat X7) As) (@ (@ tptp.ord_less_nat X7) (@ tptp.lim_Product_unit H)))))))))))
% 3.70/4.05 (assert (forall ((X tptp.produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ tptp.in_range X) Y) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (= X (@ (@ tptp.produc7507926704131184380et_nat H) As)) (= Y (not (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) As) (@ (@ tptp.ord_less_nat X2) (@ tptp.lim_Product_unit H))))))))))))
% 3.70/4.05 (assert (= tptp.hoare_new_addrs (lambda ((H3 tptp.heap_e7401611519738050253t_unit) (As7 tptp.set_nat) (H6 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.sup_sup_set_nat As7) (@ tptp.collect_nat (lambda ((A3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat (@ tptp.lim_Product_unit H3)) A3) (@ (@ tptp.ord_less_nat A3) (@ tptp.lim_Product_unit H6)))))))))
% 3.70/4.05 (assert (forall ((P Bool) (H2 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ (@ tptp.heap_T875086893843062177t_unit (@ tptp.refine_Imp_assert P)) H2))) (and (=> P (= _let_1 (@ tptp.some_P1914260805536162275it_nat (@ (@ tptp.produc7133225469290080770it_nat tptp.product_Unity) (@ (@ tptp.produc584006145561248582it_nat H2) tptp.zero_zero_nat))))) (=> (not P) (= _let_1 tptp.none_P9117596204409417319it_nat))))))
% 3.70/4.05 (assert (forall ((P tptp.assn) (Phi Bool)) (=> (forall ((H tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P) H) Phi)) (@ (@ (@ tptp.hoare_8945653483474564448t_unit P) (@ tptp.refine_Imp_assert Phi)) (lambda ((Uu2 tptp.product_unit)) P)))))
% 3.70/4.05 (assert (= tptp.heap_Time_wait (lambda ((N2 tptp.nat)) (@ tptp.heap_T6183433275982383450t_unit (lambda ((H3 tptp.heap_e7401611519738050253t_unit)) (@ tptp.some_P1914260805536162275it_nat (@ (@ tptp.produc7133225469290080770it_nat tptp.product_Unity) (@ (@ tptp.produc584006145561248582it_nat H3) N2))))))))
% 3.70/4.05 (assert (= tptp.ord_less_nat (@ tptp.transi2163837189807498211lp_nat (lambda ((M tptp.nat) (N2 tptp.nat)) (= N2 (@ tptp.suc M))))))
% 3.70/4.05 (assert (@ (@ (@ tptp.type_d3909072315231072503_nat_o tptp.rep_assn) tptp.abs_assn) (@ tptp.collec939566748876313656_nat_o tptp.proper)))
% 3.70/4.05 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int false) X) Y) Y)))
% 3.70/4.05 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int true) X) Y) X)))
% 3.70/4.05 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat false) X) Y) Y)))
% 3.70/4.05 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat true) X) Y) X)))
% 3.70/4.05 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (@ (@ (@ tptp.if_assn false) X) Y) Y)))
% 3.70/4.05 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (@ (@ (@ tptp.if_assn true) X) Y) X)))
% 3.70/4.05 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer false) X) Y) Y)))
% 3.70/4.05 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer true) X) Y) X)))
% 3.70/4.05 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ (@ tptp.if_set_int false) X) Y) Y)))
% 3.70/4.05 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ (@ tptp.if_set_int true) X) Y) X)))
% 3.70/4.05 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ (@ tptp.if_set_nat false) X) Y) Y)))
% 3.70/4.05 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ (@ tptp.if_set_nat true) X) Y) X)))
% 3.70/4.05 (assert (forall ((X tptp.list_int) (Y tptp.list_int)) (= (@ (@ (@ tptp.if_list_int false) X) Y) Y)))
% 3.70/4.05 (assert (forall ((X tptp.list_int) (Y tptp.list_int)) (= (@ (@ (@ tptp.if_list_int true) X) Y) X)))
% 3.70/4.05 (assert (forall ((X tptp.list_nat) (Y tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat false) X) Y) Y)))
% 3.70/4.05 (assert (forall ((X tptp.list_nat) (Y tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat true) X) Y) X)))
% 3.70/4.05 (assert (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (= (@ (@ (@ tptp.if_filter_nat false) X) Y) Y)))
% 3.70/4.05 (assert (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (= (@ (@ (@ tptp.if_filter_nat true) X) Y) X)))
% 3.70/4.05 (assert (forall ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int false) X) Y) Y)))
% 3.70/4.05 (assert (forall ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int true) X) Y) X)))
% 3.70/4.05 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat false) X) Y) Y)))
% 3.70/4.05 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat true) X) Y) X)))
% 3.70/4.05 (assert (forall ((X tptp.produc6271795597528267376eger_o) (Y tptp.produc6271795597528267376eger_o)) (= (@ (@ (@ tptp.if_Pro5737122678794959658eger_o false) X) Y) Y)))
% 3.70/4.05 (assert (forall ((X tptp.produc6271795597528267376eger_o) (Y tptp.produc6271795597528267376eger_o)) (= (@ (@ (@ tptp.if_Pro5737122678794959658eger_o true) X) Y) X)))
% 11.78/12.12 (assert (forall ((X tptp.list_P6011104703257516679at_nat) (Y tptp.list_P6011104703257516679at_nat)) (= (@ (@ (@ tptp.if_lis9186351972506106189at_nat false) X) Y) Y)))
% 11.78/12.12 (assert (forall ((X tptp.list_P6011104703257516679at_nat) (Y tptp.list_P6011104703257516679at_nat)) (= (@ (@ (@ tptp.if_lis9186351972506106189at_nat true) X) Y) X)))
% 11.78/12.12 (assert (forall ((X tptp.produc8923325533196201883nteger) (Y tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger false) X) Y) Y)))
% 11.78/12.12 (assert (forall ((X tptp.produc8923325533196201883nteger) (Y tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger true) X) Y) X)))
% 11.78/12.12 (assert (forall ((X tptp.list_P8527749157015355191n_assn) (Y tptp.list_P8527749157015355191n_assn)) (= (@ (@ (@ tptp.if_lis7173127979115136509n_assn false) X) Y) Y)))
% 11.78/12.12 (assert (forall ((X tptp.list_P8527749157015355191n_assn) (Y tptp.list_P8527749157015355191n_assn)) (= (@ (@ (@ tptp.if_lis7173127979115136509n_assn true) X) Y) X)))
% 11.78/12.13 (assert (forall ((X tptp.list_P7985473006766602707_nat_o) (Y tptp.list_P7985473006766602707_nat_o)) (= (@ (@ (@ tptp.if_lis2904118647880296857_nat_o false) X) Y) Y)))
% 11.78/12.13 (assert (forall ((X tptp.list_P7985473006766602707_nat_o) (Y tptp.list_P7985473006766602707_nat_o)) (= (@ (@ (@ tptp.if_lis2904118647880296857_nat_o true) X) Y) X)))
% 11.78/12.13 (assert (forall ((P Bool)) (or (= P true) (= P false))))
% 11.78/12.13 (assert (forall ((X tptp.list_P5464809261938338413at_nat) (Y tptp.list_P5464809261938338413at_nat)) (= (@ (@ (@ tptp.if_lis7508161100780771379at_nat false) X) Y) Y)))
% 11.78/12.13 (assert (forall ((X tptp.list_P5464809261938338413at_nat) (Y tptp.list_P5464809261938338413at_nat)) (= (@ (@ (@ tptp.if_lis7508161100780771379at_nat true) X) Y) X)))
% 11.78/12.13 (assert (not (@ (@ tptp.entails tptp.p) tptp.q)))
% 11.78/12.13 (set-info :filename cvc5---1.0.5_8296)
% 11.78/12.13 (check-sat-assuming ( true ))
% 11.78/12.13 ------- get file name : TPTP file name is ITP219^3
% 11.78/12.13 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_8296.smt2...
% 11.78/12.13 --- Run --ho-elim --full-saturate-quant at 10...
% 11.78/12.13 % SZS status Theorem for ITP219^3
% 11.78/12.13 % SZS output start Proof for ITP219^3
% 11.78/12.13 (
% 11.78/12.13 (let ((_let_1 (@ tptp.entails tptp.p))) (let ((_let_2 (not (@ _let_1 tptp.q)))) (let ((_let_3 (= tptp.heap_Time_wait (lambda ((N2 tptp.nat)) (@ tptp.heap_T6183433275982383450t_unit (lambda ((H3 tptp.heap_e7401611519738050253t_unit)) (@ tptp.some_P1914260805536162275it_nat (@ (@ tptp.produc7133225469290080770it_nat tptp.product_Unity) (@ (@ tptp.produc584006145561248582it_nat H3) N2))))))))) (let ((_let_4 (= tptp.hoare_new_addrs (lambda ((H3 tptp.heap_e7401611519738050253t_unit) (As7 tptp.set_nat) (H6 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.sup_sup_set_nat As7) (@ tptp.collect_nat (lambda ((A3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat (@ tptp.lim_Product_unit H3)) A3) (@ (@ tptp.ord_less_nat A3) (@ tptp.lim_Product_unit H6)))))))))) (let ((_let_5 (= tptp.range (lambda ((K4 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)))))))))))))))))))))))))))))))) K4)) (lambda ((L4 tptp.code_natural) (__flatten_var_0 tptp.produc7822875418678951345atural)) (@ (@ (@ tptp.produc5538323210962509403atural tptp.next) (lambda ((V4 tptp.code_natural) (__flatten_var_0 tptp.produc7822875418678951345atural)) (@ (@ tptp.produc6639722614265839536atural (@ (@ tptp.plus_p4538020629002901425atural V4) (@ (@ tptp.times_2397367101498566445atural L4) (@ 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 ((V4 tptp.code_natural) (__flatten_var_0 tptp.produc7822875418678951345atural)) (@ (@ tptp.produc6639722614265839536atural (@ (@ tptp.modulo8411746178871703098atural V4) K4)) __flatten_var_0))) __flatten_var_0))))) (let ((_let_6 (= tptp.split_seed (lambda ((S6 tptp.produc7822875418678951345atural)) (@ (@ tptp.produc8282080750456430313atural (lambda ((V4 tptp.code_natural) (W4 tptp.code_natural)) (@ (@ tptp.produc8282080750456430313atural (lambda ((V5 tptp.code_natural) (W5 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)))))))))) V4)) W5)) (@ (@ tptp.produc3574140220909816553atural V5) (@ (@ tptp.inc_shift (@ tptp.numera5444537566228673987atural (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 _let_1)))))))))) W4)))))) (@ tptp.produc6591912806276919810atural (@ tptp.next S6))))) S6))))) (let ((_let_7 (= tptp.ord_le5570908160329646204atural (lambda ((X2 tptp.code_natural) (Xa4 tptp.code_natural)) (@ (@ tptp.ord_less_nat (@ tptp.code_nat_of_natural X2)) (@ tptp.code_nat_of_natural Xa4)))))) (let ((_let_8 (= tptp.all_interval_nat (lambda ((P2 (-> tptp.nat Bool)) (I4 tptp.nat) (J2 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or4665077453230672383an_nat I4) J2)) (@ P2 X2))))))) (let ((_let_9 (= tptp.proper (lambda ((P2 (-> tptp.produc3658429121746597890et_nat Bool))) (forall ((H3 tptp.heap_e7401611519738050253t_unit) (H6 tptp.heap_e7401611519738050253t_unit) (As7 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H6) As7))) (let ((_let_2 (@ (@ tptp.produc7507926704131184380et_nat H3) As7))) (let ((_let_3 (@ P2 _let_2))) (and (=> _let_3 (@ tptp.in_range _let_2)) (=> (and _let_3 (@ (@ (@ tptp.relH As7) H3) H6) (@ tptp.in_range _let_1)) (@ P2 _let_1))))))))))) (let ((_let_10 (= tptp.is_pure_assn (lambda ((A3 tptp.assn)) (exists ((P2 Bool)) (= A3 (@ tptp.pure_assn P2))))))) (let ((_let_11 (@ tptp.gcd_Lcm_nat tptp.bot_bot_set_nat))) (let ((_let_12 (= _let_11 tptp.one_one_nat))) (let ((_let_13 (= tptp.all_interval_int (lambda ((P2 (-> tptp.int Bool)) (I4 tptp.int) (J2 tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int I4) J2)) (@ P2 X2))))))) (let ((_let_14 (= tptp.cofinite_nat tptp.at_top_nat))) (let ((_let_15 (= tptp.fract (lambda ((Xa4 tptp.int) (X2 tptp.int)) (@ tptp.abs_Rat (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= X2 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int Xa4) X2))))))) (let ((_let_16 (= tptp.top_top_assn (@ tptp.abs_assn tptp.in_range)))) (let ((_let_17 (= tptp.uminus_uminus_assn (lambda ((P2 tptp.assn)) (@ tptp.abs_assn (lambda ((H3 tptp.produc3658429121746597890et_nat)) (and (@ tptp.in_range H3) (not (@ (@ tptp.rep_assn P2) H3))))))))) (let ((_let_18 (= tptp.wand_assn (lambda ((P2 tptp.assn) (Q2 tptp.assn)) (@ tptp.abs_assn (@ (@ tptp.wand_raw (@ tptp.rep_assn P2)) (@ tptp.rep_assn Q2))))))) (let ((_let_19 (= tptp.times_times_assn (lambda ((P2 tptp.assn) (Q2 tptp.assn)) (@ tptp.abs_assn (@ (@ tptp.times_assn_raw (@ tptp.rep_assn P2)) (@ tptp.rep_assn Q2))))))) (let ((_let_20 (= tptp.inf_inf_assn (lambda ((P2 tptp.assn) (Q2 tptp.assn)) (@ tptp.abs_assn (lambda ((H3 tptp.produc3658429121746597890et_nat)) (and (@ (@ tptp.rep_assn P2) H3) (@ (@ tptp.rep_assn Q2) H3)))))))) (let ((_let_21 (= tptp.sup_sup_assn (lambda ((P2 tptp.assn) (Q2 tptp.assn)) (@ tptp.abs_assn (lambda ((H3 tptp.produc3658429121746597890et_nat)) (or (@ (@ tptp.rep_assn P2) H3) (@ (@ tptp.rep_assn Q2) H3)))))))) (let ((_let_22 (= tptp.pure_assn (lambda ((B3 Bool)) (@ tptp.abs_assn (@ tptp.pure_a825153325127701367it_nat B3)))))) (let ((_let_23 (@ (@ tptp.map_fu5673905371560938248nt_rat tptp.rep_Rat) tptp.abs_Rat))) (let ((_let_24 (@ (@ tptp.map_fu4333342158222067775at_rat tptp.rep_Rat) _let_23))) (let ((_let_25 (= tptp.times_times_rat (@ _let_24 (lambda ((X2 tptp.product_prod_int_int) (Y5 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) (@ tptp.product_fst_int_int Y5))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int X2)) (@ tptp.product_snd_int_int Y5)))))))) (let ((_let_26 (= tptp.plus_plus_rat (@ _let_24 (lambda ((X2 tptp.product_prod_int_int) (Y5 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Y5))) (let ((_let_2 (@ tptp.product_snd_int_int X2))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) _let_1)) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y5)) _let_2))) (@ (@ tptp.times_times_int _let_2) _let_1))))))))) (let ((_let_27 (= tptp.uminus_uminus_rat (@ _let_23 (lambda ((X2 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int (@ tptp.product_fst_int_int X2))) (@ tptp.product_snd_int_int X2))))))) (let ((_let_28 (= tptp.inverse_inverse_rat (@ _let_23 (lambda ((X2 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_fst_int_int X2))) (@ (@ (@ 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 X2)) _let_1)))))))) (let ((_let_29 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))) (let ((_let_30 (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int))) (let ((_let_31 (@ (@ tptp.bNF_re7145576690424134365nt_int tptp.ratrel) tptp.ratrel))) (let ((_let_32 (@ (@ tptp.bNF_re5228765855967844073nt_int tptp.ratrel) _let_31))) (let ((_let_33 (@ tptp.frct _let_30))) (let ((_let_34 (= _let_33 tptp.one_one_rat))) (let ((_let_35 (= 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_36 (@ (@ tptp.bNF_re8279943556446156061nt_rat tptp.pcr_rat) tptp.pcr_rat))) (let ((_let_37 (@ (@ tptp.bNF_re7627151682743391978at_rat tptp.pcr_rat) _let_36))) (let ((_let_38 (= tptp.top_top_set_o (@ (@ tptp.insert_o2 false) (@ (@ tptp.insert_o2 true) tptp.bot_bot_set_o))))) (let ((_let_39 (@ (@ tptp.insert9069300056098147895at_nat (@ (@ tptp.produc2922128104949294807at_nat tptp.bot_bo2099793752762293965at_nat) tptp.bot_bo2099793752762293965at_nat)) tptp.bot_bo228742789529271731at_nat))) (let ((_let_40 (= tptp.fun_min_weak (@ (@ tptp.sup_su5525570899277871387at_nat (@ tptp.min_ex6901939911449802026at_nat tptp.fun_pair_leq)) _let_39)))) (let ((_let_41 (= tptp.fun_max_weak (@ (@ tptp.sup_su5525570899277871387at_nat (@ tptp.max_ex8135407076693332796at_nat tptp.fun_pair_leq)) _let_39)))) (let ((_let_42 (@ (@ tptp.bNF_re2241393799969408733at_nat tptp.intrel) tptp.intrel))) (let ((_let_43 (@ (@ tptp.bNF_re3099431351363272937at_nat tptp.intrel) _let_42))) (let ((_let_44 (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))) (let ((_let_45 (@ tptp.finite3254316476582989077op_nat tptp.top_top_set_nat))) (let ((_let_46 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))) (let ((_let_47 (@ (@ tptp.bNF_re7400052026677387805at_int tptp.pcr_int) tptp.pcr_int))) (let ((_let_48 (@ (@ tptp.bNF_re7408651293131936558nt_int tptp.pcr_int) _let_47))) (let ((_let_49 (= tptp.sln tptp.one_one_assn))) (let ((_let_50 (= tptp.fi (lambda ((M tptp.list_P8527749157015355191n_assn) (P7 tptp.assn) (Q8 tptp.assn) (Up tptp.assn) (Uq tptp.assn) (F6 tptp.assn)) (let ((_let_1 (@ tptp.foldr_assn_assn tptp.times_times_assn))) (=> (forall ((X2 tptp.produc6575502325842934193n_assn)) (=> (@ (@ tptp.member7957490590177025114n_assn X2) (@ tptp.set_Pr1139785259514867910n_assn M)) (@ (@ tptp.produc7274209992780475162assn_o tptp.entails) X2))) (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ _let_1 (@ (@ tptp.map_Pr8991440229025900053n_assn tptp.produc9167289414957590229n_assn) M)) tptp.one_one_assn)) P7)) Up)) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ _let_1 (@ (@ tptp.map_Pr8991440229025900053n_assn tptp.produc2051961928117032727n_assn) M)) tptp.one_one_assn)) Q8)) Uq)) F6)))))))) (let ((_let_51 (= tptp.fI_RESULT (lambda ((M7 tptp.list_P8527749157015355191n_assn) (UP tptp.assn) (UQ tptp.assn) (F3 tptp.assn)) (let ((_let_1 (@ tptp.foldr_assn_assn tptp.times_times_assn))) (=> (forall ((X2 tptp.produc6575502325842934193n_assn)) (=> (@ (@ tptp.member7957490590177025114n_assn X2) (@ tptp.set_Pr1139785259514867910n_assn M7)) (@ (@ tptp.produc7274209992780475162assn_o tptp.entails) X2))) (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ _let_1 (@ (@ tptp.map_Pr8991440229025900053n_assn tptp.produc9167289414957590229n_assn) M7)) tptp.one_one_assn)) UP)) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ _let_1 (@ (@ tptp.map_Pr8991440229025900053n_assn tptp.produc2051961928117032727n_assn) M7)) tptp.one_one_assn)) UQ)) F3)))))))) (let ((_let_52 (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ))) (let ((_let_53 (@ (@ tptp.map_fu4960017516451851995nt_int tptp.rep_Integ) _let_52))) (let ((_let_54 (= tptp.plus_plus_int (@ _let_53 (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) U4)) (@ (@ tptp.plus_plus_nat Y5) V4)))) __flatten_var_0))))))) (let ((_let_55 (= tptp.minus_minus_int (@ _let_53 (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat Y5) U4)))) __flatten_var_0))))))) (let ((_let_56 (= tptp.times_times_int (@ _let_53 (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y5))) (let ((_let_2 (@ tptp.times_times_nat X2))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U4)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U4))))))) __flatten_var_0))))))) (let ((_let_57 (= tptp.uminus_uminus_int (@ _let_52 (@ tptp.produc2626176000494625587at_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y5) X2))))))) (let ((_let_58 (= tptp.one_one_int (@ tptp.abs_Integ _let_44)))) (let ((_let_59 (= tptp.semiri1314217659103216013at_int (lambda ((N2 tptp.nat)) (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat N2) tptp.zero_zero_nat)))))) (let ((_let_60 (= tptp.code_divmod_abs (lambda ((K4 tptp.code_integer) (L4 tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer L4))) (let ((_let_2 (@ tptp.abs_abs_Code_integer K4))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))) (let ((_let_61 (= tptp.code_divmod_integer (lambda ((K4 tptp.code_integer) (L4 tptp.code_integer)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger K4) L4)) (@ (@ tptp.modulo364778990260209775nteger K4) L4)))))) (let ((_let_62 (= tptp.code_bit_cut_integer (lambda ((K4 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ tptp.divide6298287555418463151nteger K4) _let_1)) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) K4)))))))) (let ((_let_63 (= tptp.unique3479559517661332726nteger (lambda ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))) (let ((_let_64 (= tptp.unique4921790084139445826nteger (lambda ((L4 tptp.num) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q8 tptp.code_integer) (R4 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q8))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger L4))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le3102999989581377725nteger _let_2) R4)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R4) _let_2))) (@ (@ tptp.produc1086072967326762835nteger _let_1) R4)))))) __flatten_var_0))))) (let ((_let_65 (= tptp.set_ord_atMost_nat (lambda ((N2 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) (@ tptp.suc N2))))))) (let ((_let_66 (= tptp.set_or5834768355832116004an_nat (lambda ((N2 tptp.nat) (M tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N2)) M)))))) (let ((_let_67 (= tptp.set_or6659071591806873216st_nat (lambda ((N2 tptp.nat) (M tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N2)) (@ tptp.suc M))))))) (let ((_let_68 (= tptp.set_ord_lessThan_nat (lambda ((N2 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) N2)))))) (let ((_let_69 (= tptp.set_or1269000886237332187st_nat (lambda ((N2 tptp.nat) (M tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt N2) (@ tptp.suc M))))))) (let ((_let_70 (= tptp.set_or4665077453230672383an_nat (lambda ((I4 tptp.nat) (J2 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt I4) J2)))))) (let ((_let_71 (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_nat)))) (let ((_let_72 (= tptp.bNF_Ca8459412986667044542atLess _let_71))) (let ((_let_73 (= tptp.unique5024387138958732305ep_int (lambda ((L4 tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q8 tptp.int) (R4 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 L4))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_eq_int _let_2) R4)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R4) _let_2))) (@ (@ tptp.product_Pair_int_int _let_1) R4)))))) __flatten_var_0))))) (let ((_let_74 (= tptp.unique5026877609467782581ep_nat (lambda ((L4 tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q8 tptp.nat) (R4 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 L4))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat _let_2) R4)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R4) _let_2))) (@ (@ tptp.product_Pair_nat_nat _let_1) R4)))))) __flatten_var_0))))) (let ((_let_75 (= tptp.set_or4662586982721622107an_int (lambda ((I4 tptp.int) (J2 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I4) (@ (@ tptp.minus_minus_int J2) tptp.one_one_int))))))) (let ((_let_76 (= tptp.set_or6656581121297822940st_int (lambda ((I4 tptp.int) (J2 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) J2)))))) (let ((_let_77 (= tptp.finite_finite_nat (lambda ((N8 tptp.set_nat)) (exists ((M tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) N8) (@ (@ tptp.ord_less_nat X2) M)))))))) (let ((_let_78 (= tptp.set_or5832277885323065728an_int (lambda ((I4 tptp.int) (J2 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) (@ (@ tptp.minus_minus_int J2) tptp.one_one_int))))))) (let ((_let_79 (= tptp.set_or1266510415728281911st_int (lambda ((I4 tptp.int) (J2 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I4) J2)))))) (let ((_let_80 (= tptp.divmod_nat (lambda ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.modulo_modulo_nat M) N2)))))) (let ((_let_81 (= tptp.unique5052692396658037445od_int (lambda ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))) (let ((_let_82 (= tptp.unique5055182867167087721od_nat (lambda ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (let ((_let_2 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))) (let ((_let_83 (= tptp.upto_aux (lambda ((I4 tptp.int) (J2 tptp.int) (__flatten_var_0 tptp.list_int)) (@ (@ tptp.append_int (@ (@ tptp.upto I4) J2)) __flatten_var_0))))) (let ((_let_84 (@ tptp.complete_Sup_Sup_nat tptp.bot_bot_set_nat))) (let ((_let_85 (= _let_84 tptp.zero_zero_nat))) (let ((_let_86 (= tptp.minus_minus_assn (lambda ((A3 tptp.assn) (B3 tptp.assn)) (@ (@ tptp.inf_inf_assn A3) (@ tptp.uminus_uminus_assn B3)))))) (let ((_let_87 (= tptp.entailst (lambda ((P2 tptp.assn) (Q2 tptp.assn)) (@ (@ tptp.entails (@ (@ tptp.times_times_assn P2) tptp.top_top_assn)) (@ (@ tptp.times_times_assn Q2) tptp.top_top_assn)))))) (let ((_let_88 (= tptp.eucl_rel_int (lambda ((A12 tptp.int) (A23 tptp.int) (A32 tptp.product_prod_int_int)) (or (exists ((K4 tptp.int)) (and (= A12 K4) (= A23 tptp.zero_zero_int) (= A32 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K4)))) (exists ((L4 tptp.int) (K4 tptp.int) (Q8 tptp.int)) (and (= A12 K4) (= A23 L4) (= A32 (@ (@ tptp.product_Pair_int_int Q8) tptp.zero_zero_int)) (not (= L4 tptp.zero_zero_int)) (= K4 (@ (@ tptp.times_times_int Q8) L4)))) (exists ((R4 tptp.int) (L4 tptp.int) (K4 tptp.int) (Q8 tptp.int)) (and (= A12 K4) (= A23 L4) (= A32 (@ (@ tptp.product_Pair_int_int Q8) R4)) (= (@ tptp.sgn_sgn_int R4) (@ tptp.sgn_sgn_int L4)) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R4)) (@ tptp.abs_abs_int L4)) (= K4 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q8) L4)) R4))))))))) (let ((_let_89 (= tptp.biject576505603616484041nt_int (lambda ((R3 tptp.set_Pr1872883991513573699nt_int)) (and (forall ((X2 (-> tptp.int tptp.option6357759511663192854e_term)) (Y5 tptp.product_prod_int_int) (Z5 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.produc4305682042979456191nt_int X2))) (=> (and (@ (@ tptp.member7034335876925520548nt_int (@ _let_1 Y5)) R3) (@ (@ tptp.member7034335876925520548nt_int (@ _let_1 Z5)) R3)) (= Y5 Z5)))) (forall ((X2 (-> tptp.int tptp.option6357759511663192854e_term)) (Y5 (-> tptp.int tptp.option6357759511663192854e_term)) (Z5 tptp.product_prod_int_int)) (=> (and (@ (@ tptp.member7034335876925520548nt_int (@ (@ tptp.produc4305682042979456191nt_int X2) Z5)) R3) (@ (@ tptp.member7034335876925520548nt_int (@ (@ tptp.produc4305682042979456191nt_int Y5) Z5)) R3)) (= X2 Y5)))))))) (let ((_let_90 (= tptp.biject383251550997737151nt_int (lambda ((R3 tptp.set_Pr9222295170931077689nt_int)) (and (forall ((X2 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y5 tptp.product_prod_int_int) (Z5 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.produc5700946648718959541nt_int X2))) (=> (and (@ (@ tptp.member7618704894036264090nt_int (@ _let_1 Y5)) R3) (@ (@ tptp.member7618704894036264090nt_int (@ _let_1 Z5)) R3)) (= Y5 Z5)))) (forall ((X2 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y5 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Z5 tptp.product_prod_int_int)) (=> (and (@ (@ tptp.member7618704894036264090nt_int (@ (@ tptp.produc5700946648718959541nt_int X2) Z5)) R3) (@ (@ tptp.member7618704894036264090nt_int (@ (@ tptp.produc5700946648718959541nt_int Y5) Z5)) R3)) (= X2 Y5)))))))) (let ((_let_91 (= tptp.biject1468766312547416318et_nat (lambda ((R3 tptp.set_Pr8536935166611901872et_nat)) (and (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool)) (Y5 tptp.produc3925858234332021118et_nat) (Z5 tptp.produc3925858234332021118et_nat)) (let ((_let_1 (@ tptp.produc2245416461498447860et_nat X2))) (=> (and (@ (@ tptp.member6124377750444531601et_nat (@ _let_1 Y5)) R3) (@ (@ tptp.member6124377750444531601et_nat (@ _let_1 Z5)) R3)) (= Y5 Z5)))) (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool)) (Y5 (-> tptp.produc3658429121746597890et_nat Bool)) (Z5 tptp.produc3925858234332021118et_nat)) (=> (and (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat X2) Z5)) R3) (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat Y5) Z5)) R3)) (= X2 Y5)))))))) (let ((_let_92 (= tptp.biject2615096655818420098et_nat (lambda ((R3 tptp.set_Pr3286484037609594932et_nat)) (and (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool)) (Y5 tptp.produc3658429121746597890et_nat) (Z5 tptp.produc3658429121746597890et_nat)) (let ((_let_1 (@ tptp.produc5001842942810119800et_nat X2))) (=> (and (@ (@ tptp.member1996754912294343701et_nat (@ _let_1 Y5)) R3) (@ (@ tptp.member1996754912294343701et_nat (@ _let_1 Z5)) R3)) (= Y5 Z5)))) (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool)) (Y5 (-> tptp.produc3658429121746597890et_nat Bool)) (Z5 tptp.produc3658429121746597890et_nat)) (=> (and (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat X2) Z5)) R3) (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat Y5) Z5)) R3)) (= X2 Y5)))))))) (let ((_let_93 (= tptp.biject9051520373387432658nteger (lambda ((R3 tptp.set_Pr1281608226676607948nteger)) (and (forall ((X2 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (Y5 tptp.produc8923325533196201883nteger) (Z5 tptp.produc8923325533196201883nteger)) (let ((_let_1 (@ tptp.produc8603105652947943368nteger X2))) (=> (and (@ (@ tptp.member4164122664394876845nteger (@ _let_1 Y5)) R3) (@ (@ tptp.member4164122664394876845nteger (@ _let_1 Z5)) R3)) (= Y5 Z5)))) (forall ((X2 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (Y5 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (Z5 tptp.produc8923325533196201883nteger)) (=> (and (@ (@ tptp.member4164122664394876845nteger (@ (@ tptp.produc8603105652947943368nteger X2) Z5)) R3) (@ (@ tptp.member4164122664394876845nteger (@ (@ tptp.produc8603105652947943368nteger Y5) Z5)) R3)) (= X2 Y5)))))))) (let ((_let_94 (= tptp.bijective_nat_nat (lambda ((R3 tptp.set_Pr1261947904930325089at_nat)) (and (forall ((X2 tptp.nat) (Y5 tptp.nat) (Z5 tptp.nat)) (let ((_let_1 (@ tptp.product_Pair_nat_nat X2))) (=> (and (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 Y5)) R3) (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 Z5)) R3)) (= Y5 Z5)))) (forall ((X2 tptp.nat) (Y5 tptp.nat) (Z5 tptp.nat)) (=> (and (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X2) Z5)) R3) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y5) Z5)) R3)) (= X2 Y5)))))))) (let ((_let_95 (= tptp.biject3388518990857851981at_nat (lambda ((R3 tptp.set_Pr4329608150637261639at_nat)) (and (forall ((X2 tptp.set_Pr1261947904930325089at_nat) (Y5 tptp.set_Pr1261947904930325089at_nat) (Z5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.produc2922128104949294807at_nat X2))) (=> (and (@ (@ tptp.member8757157785044589968at_nat (@ _let_1 Y5)) R3) (@ (@ tptp.member8757157785044589968at_nat (@ _let_1 Z5)) R3)) (= Y5 Z5)))) (forall ((X2 tptp.set_Pr1261947904930325089at_nat) (Y5 tptp.set_Pr1261947904930325089at_nat) (Z5 tptp.set_Pr1261947904930325089at_nat)) (=> (and (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X2) Z5)) R3) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat Y5) Z5)) R3)) (= X2 Y5)))))))) (let ((_let_96 (= tptp.insert3246601298802261197n_assn (lambda ((X2 tptp.produc6575502325842934193n_assn) (Xs3 tptp.list_P8527749157015355191n_assn)) (@ (@ (@ tptp.if_lis7173127979115136509n_assn (@ (@ tptp.member7957490590177025114n_assn X2) (@ tptp.set_Pr1139785259514867910n_assn Xs3))) Xs3) (@ (@ tptp.cons_P2971678138204555879n_assn X2) Xs3)))))) (let ((_let_97 (= tptp.insert_nat (lambda ((X2 tptp.nat) (Xs3 tptp.list_nat)) (@ (@ (@ tptp.if_list_nat (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Xs3))) Xs3) (@ (@ tptp.cons_nat X2) Xs3)))))) (let ((_let_98 (= tptp.insert_int (lambda ((X2 tptp.int) (Xs3 tptp.list_int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.member_int X2) (@ tptp.set_int2 Xs3))) Xs3) (@ (@ tptp.cons_int X2) Xs3)))))) (let ((_let_99 (= tptp.insert8021100735160035049_nat_o (lambda ((X2 (-> tptp.produc3658429121746597890et_nat Bool)) (Xs3 tptp.list_P7985473006766602707_nat_o)) (@ (@ (@ tptp.if_lis2904118647880296857_nat_o (@ (@ tptp.member6576561426505652726_nat_o X2) (@ tptp.set_Pr400311997697478754_nat_o Xs3))) Xs3) (@ (@ tptp.cons_P6219271836124797827_nat_o X2) Xs3)))))) (let ((_let_100 (= tptp.insert8944034826898310173at_nat (lambda ((X2 tptp.product_prod_nat_nat) (Xs3 tptp.list_P6011104703257516679at_nat)) (@ (@ (@ tptp.if_lis9186351972506106189at_nat (@ (@ tptp.member8440522571783428010at_nat X2) (@ tptp.set_Pr5648618587558075414at_nat Xs3))) Xs3) (@ (@ tptp.cons_P6512896166579812791at_nat X2) Xs3)))))) (let ((_let_101 (= tptp.insert4149901806602606979at_nat (lambda ((X2 tptp.produc3843707927480180839at_nat) (Xs3 tptp.list_P5464809261938338413at_nat)) (@ (@ (@ tptp.if_lis7508161100780771379at_nat (@ (@ tptp.member8757157785044589968at_nat X2) (@ tptp.set_Pr3765526544606949372at_nat Xs3))) Xs3) (@ (@ tptp.cons_P3940603068885512221at_nat X2) Xs3)))))) (let ((_let_102 (= tptp.total_on_nat (lambda ((A5 tptp.set_nat) (R4 tptp.set_Pr1261947904930325089at_nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A5) (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.member_nat Y5) A5) (=> (not (= X2 Y5)) (or (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X2) Y5)) R4) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y5) X2)) R4))))))))))) (let ((_let_103 (= tptp.total_7212417256332265445at_nat (lambda ((A5 tptp.set_se7855581050983116737at_nat) (R4 tptp.set_Pr4329608150637261639at_nat)) (forall ((X2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member2643936169264416010at_nat X2) A5) (forall ((Y5 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member2643936169264416010at_nat Y5) A5) (=> (not (= X2 Y5)) (or (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X2) Y5)) R4) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat Y5) X2)) R4))))))))))) (let ((_let_104 (@ tptp.field_3145993188331922222at_nat tptp.bot_bo228742789529271731at_nat))) (let ((_let_105 (= _let_104 tptp.bot_bo3083307316010499117at_nat))) (let ((_let_106 (@ tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_107 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (let ((_let_108 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_109 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_110 (@ _let_106 tptp.one_one_int))) (let ((_let_111 (@ _let_107 tptp.one_one_nat))) (let ((_let_112 (@ _let_108 tptp.one_one_Code_integer))) (let ((_let_113 (@ _let_109 tptp.one_one_rat))) (let ((_let_114 (@ tptp.ord_less_int tptp.one_one_int))) (let ((_let_115 (@ tptp.ord_less_nat tptp.one_one_nat))) (let ((_let_116 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (let ((_let_117 (@ tptp.ord_less_rat tptp.one_one_rat))) (let ((_let_118 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))) (let ((_let_119 (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))) (let ((_let_120 (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))) (let ((_let_121 (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer))) (let ((_let_122 (= (@ (@ tptp.minus_minus_int tptp.one_one_int) tptp.one_one_int) tptp.zero_zero_int))) (let ((_let_123 (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) tptp.one_one_rat) tptp.zero_zero_rat))) (let ((_let_124 (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))) (let ((_let_125 (= tptp.neg_nu3811975205180677377ec_int (lambda ((X2 tptp.int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int X2) X2)) tptp.one_one_int))))) (let ((_let_126 (= tptp.neg_nu3179335615603231917ec_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat X2) X2)) tptp.one_one_rat))))) (let ((_let_127 (= tptp.neg_nu7757733837767384882nteger (lambda ((X2 tptp.code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger X2) X2)) tptp.one_one_Code_integer))))) (let ((_let_128 (= tptp.sorted_wrt_int (lambda ((P2 (-> tptp.int tptp.int Bool)) (Xs3 tptp.list_int)) (forall ((I4 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs3))) (=> (@ (@ tptp.ord_less_nat I4) J2) (=> (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_int Xs3)) (@ (@ P2 (@ _let_1 I4)) (@ _let_1 J2)))))))))) (let ((_let_129 (= tptp.sorted_wrt_nat (lambda ((P2 (-> tptp.nat tptp.nat Bool)) (Xs3 tptp.list_nat)) (forall ((I4 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs3))) (=> (@ (@ tptp.ord_less_nat I4) J2) (=> (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_nat Xs3)) (@ (@ P2 (@ _let_1 I4)) (@ _let_1 J2)))))))))) (let ((_let_130 (= tptp.sorted_wrt_d (lambda ((P2 (-> tptp.d tptp.d Bool)) (Xs3 tptp.list_d)) (forall ((I4 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_d Xs3))) (=> (@ (@ tptp.ord_less_nat I4) J2) (=> (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_d Xs3)) (@ (@ P2 (@ _let_1 I4)) (@ _let_1 J2)))))))))) (let ((_let_131 (= tptp.sorted_wrt_c (lambda ((P2 (-> tptp.c tptp.c Bool)) (Xs3 tptp.list_c)) (forall ((I4 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_c Xs3))) (=> (@ (@ tptp.ord_less_nat I4) J2) (=> (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_c Xs3)) (@ (@ P2 (@ _let_1 I4)) (@ _let_1 J2)))))))))) (let ((_let_132 (= tptp.ord_le2604355607129572851at_nat (lambda ((B3 tptp.set_Pr4329608150637261639at_nat) (A3 tptp.set_Pr4329608150637261639at_nat)) (and (= A3 (@ (@ tptp.sup_su5525570899277871387at_nat A3) B3)) (not (= A3 B3))))))) (let ((_let_133 (= tptp.ord_min_int (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A3) B3)) A3) B3))))) (let ((_let_134 (= tptp.ord_min_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A3) B3)) A3) B3))))) (let ((_let_135 (= tptp.ord_min_set_nat (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (@ (@ (@ tptp.if_set_nat (@ (@ tptp.ord_less_eq_set_nat A3) B3)) A3) B3))))) (let ((_let_136 (= tptp.ord_min_filter_nat (lambda ((A3 tptp.filter_nat) (B3 tptp.filter_nat)) (@ (@ (@ tptp.if_filter_nat (@ (@ tptp.ord_le2510731241096832064er_nat A3) B3)) A3) B3))))) (let ((_let_137 (= tptp.ord_min_assn (lambda ((A3 tptp.assn) (B3 tptp.assn)) (@ (@ (@ tptp.if_assn (@ (@ tptp.ord_less_eq_assn A3) B3)) A3) B3))))) (let ((_let_138 (= tptp.ord_less_filter_nat (lambda ((X2 tptp.filter_nat) (Y5 tptp.filter_nat)) (and (@ (@ tptp.ord_le2510731241096832064er_nat X2) Y5) (not (= X2 Y5))))))) (let ((_let_139 (= tptp.ord_less_num (lambda ((X2 tptp.num) (Y5 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X2) Y5) (not (= X2 Y5))))))) (let ((_let_140 (= tptp.ord_le6747313008572928689nteger (lambda ((X2 tptp.code_integer) (Y5 tptp.code_integer)) (and (@ (@ tptp.ord_le3102999989581377725nteger X2) Y5) (not (= X2 Y5))))))) (let ((_let_141 (= tptp.ord_less_int (lambda ((A3 tptp.int) (B3 tptp.int)) (and (= A3 (@ (@ tptp.inf_inf_int A3) B3)) (not (= A3 B3))))))) (let ((_let_142 (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (and (= A3 (@ (@ tptp.inf_inf_nat A3) B3)) (not (= A3 B3))))))) (let ((_let_143 (= tptp.ord_less_assn (lambda ((A3 tptp.assn) (B3 tptp.assn)) (and (= A3 (@ (@ tptp.inf_inf_assn A3) B3)) (not (= A3 B3))))))) (let ((_let_144 (= tptp.ord_le7866589430770878221at_nat (lambda ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (and (= A3 (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)) (not (= A3 B3))))))) (let ((_let_145 (= tptp.ord_less_set_nat (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (and (= A3 (@ (@ tptp.inf_inf_set_nat A3) B3)) (not (= A3 B3))))))) (let ((_let_146 (= tptp.ord_less_eq_int (lambda ((X2 tptp.int) (Y5 tptp.int)) (= (@ (@ tptp.inf_inf_int X2) Y5) X2))))) (let ((_let_147 (= tptp.ord_less_eq_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (= (@ (@ tptp.inf_inf_nat X2) Y5) X2))))) (let ((_let_148 (= tptp.ord_le2510731241096832064er_nat (lambda ((X2 tptp.filter_nat) (Y5 tptp.filter_nat)) (= (@ (@ tptp.inf_inf_filter_nat X2) Y5) X2))))) (let ((_let_149 (= tptp.ord_less_eq_assn (lambda ((X2 tptp.assn) (Y5 tptp.assn)) (= (@ (@ tptp.inf_inf_assn X2) Y5) X2))))) (let ((_let_150 (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B7 tptp.set_nat)) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X2))) (=> (@ _let_1 A5) (@ _let_1 B7)))))))) (let ((_let_151 (= tptp.ord_le2965882846123202637_nat_o (lambda ((A5 tptp.set_Pr4532377907799695533_nat_o) (B7 tptp.set_Pr4532377907799695533_nat_o)) (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o X2))) (=> (@ _let_1 A5) (@ _let_1 B7)))))))) (let ((_let_152 (= tptp.ord_less_eq_set_int (lambda ((A5 tptp.set_int) (B7 tptp.set_int)) (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.member_int X2))) (=> (@ _let_1 A5) (@ _let_1 B7)))))))) (let ((_let_153 (= tptp.ord_le3146513528884898305at_nat (lambda ((A5 tptp.set_Pr1261947904930325089at_nat) (B7 tptp.set_Pr1261947904930325089at_nat)) (forall ((X2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X2))) (=> (@ _let_1 A5) (@ _let_1 B7)))))))) (let ((_let_154 (= tptp.ord_le1268244103169919719at_nat (lambda ((A5 tptp.set_Pr4329608150637261639at_nat) (B7 tptp.set_Pr4329608150637261639at_nat)) (forall ((X2 tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat X2))) (=> (@ _let_1 A5) (@ _let_1 B7)))))))) (let ((_let_155 (= tptp.pairwise_nat (lambda ((R3 (-> tptp.nat tptp.nat Bool)) (S2 tptp.set_nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) S2) (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.member_nat Y5) (@ (@ tptp.minus_minus_set_nat S2) (@ (@ tptp.insert_nat2 X2) tptp.bot_bot_set_nat))) (@ (@ R3 X2) Y5))))))))) (let ((_let_156 (= tptp.pairwise_int (lambda ((R3 (-> tptp.int tptp.int Bool)) (S2 tptp.set_int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) S2) (forall ((Y5 tptp.int)) (=> (@ (@ tptp.member_int Y5) (@ (@ tptp.minus_minus_set_int S2) (@ (@ tptp.insert_int2 X2) tptp.bot_bot_set_int))) (@ (@ R3 X2) Y5))))))))) (let ((_let_157 (= tptp.pairwise_o (lambda ((R3 (-> Bool Bool Bool)) (S2 tptp.set_o)) (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) S2) (forall ((Y5 Bool)) (=> (@ (@ tptp.member_o Y5) (@ (@ tptp.minus_minus_set_o S2) (@ (@ tptp.insert_o2 X2) tptp.bot_bot_set_o))) (@ (@ R3 X2) Y5))))))))) (let ((_let_158 (= tptp.pairwi6357175311820755948at_nat (lambda ((R3 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (S2 tptp.set_Pr1261947904930325089at_nat)) (forall ((X2 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X2) S2) (forall ((Y5 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat Y5) (@ (@ tptp.minus_1356011639430497352at_nat S2) (@ (@ tptp.insert8211810215607154385at_nat X2) tptp.bot_bo2099793752762293965at_nat))) (@ (@ R3 X2) Y5))))))))) (let ((_let_159 (= tptp.pairwi3222497012029234898at_nat (lambda ((R3 (-> tptp.produc3843707927480180839at_nat tptp.produc3843707927480180839at_nat Bool)) (S2 tptp.set_Pr4329608150637261639at_nat)) (forall ((X2 tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X2) S2) (forall ((Y5 tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat Y5) (@ (@ tptp.minus_3314409938677909166at_nat S2) (@ (@ tptp.insert9069300056098147895at_nat X2) tptp.bot_bo228742789529271731at_nat))) (@ (@ R3 X2) Y5))))))))) (let ((_let_160 (= (@ tptp.pure_assn true) tptp.one_one_assn))) (let ((_let_161 (= tptp.distinct_int (lambda ((Xs3 tptp.list_int)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs3)) (forall ((J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs3))) (=> (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_int Xs3)) (=> (not (= I4 J2)) (not (= (@ _let_1 I4) (@ _let_1 J2))))))))))))) (let ((_let_162 (= tptp.distinct_nat (lambda ((Xs3 tptp.list_nat)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs3)) (forall ((J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs3))) (=> (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_nat Xs3)) (=> (not (= I4 J2)) (not (= (@ _let_1 I4) (@ _let_1 J2))))))))))))) (let ((_let_163 (= tptp.distinct_d (lambda ((Xs3 tptp.list_d)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_d Xs3)) (forall ((J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_d Xs3))) (=> (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_d Xs3)) (=> (not (= I4 J2)) (not (= (@ _let_1 I4) (@ _let_1 J2))))))))))))) (let ((_let_164 (= tptp.distinct_c (lambda ((Xs3 tptp.list_c)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_c Xs3)) (forall ((J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_c Xs3))) (=> (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_c Xs3)) (=> (not (= I4 J2)) (not (= (@ _let_1 I4) (@ _let_1 J2))))))))))))) (let ((_let_165 (= (@ tptp.pure_assn false) tptp.bot_bot_assn))) (let ((_let_166 (= tptp.list_ex_int (lambda ((P2 (-> tptp.int Bool)) (Xs3 tptp.list_int)) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_int Xs3)) (@ P2 (@ (@ tptp.nth_int Xs3) N2)))))))) (let ((_let_167 (= tptp.list_ex_nat (lambda ((P2 (-> tptp.nat Bool)) (Xs3 tptp.list_nat)) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs3)) (@ P2 (@ (@ tptp.nth_nat Xs3) N2)))))))) (let ((_let_168 (= tptp.list_ex_d (lambda ((P2 (-> tptp.d Bool)) (Xs3 tptp.list_d)) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_d Xs3)) (@ P2 (@ (@ tptp.nth_d Xs3) N2)))))))) (let ((_let_169 (= tptp.list_ex_c (lambda ((P2 (-> tptp.c Bool)) (Xs3 tptp.list_c)) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_c Xs3)) (@ P2 (@ (@ tptp.nth_c Xs3) N2)))))))) (let ((_let_170 (= tptp.is_empty_int (lambda ((A5 tptp.set_int)) (= A5 tptp.bot_bot_set_int))))) (let ((_let_171 (= tptp.is_empty_nat (lambda ((A5 tptp.set_nat)) (= A5 tptp.bot_bot_set_nat))))) (let ((_let_172 (= tptp.is_empty_o (lambda ((A5 tptp.set_o)) (= A5 tptp.bot_bot_set_o))))) (let ((_let_173 (= tptp.is_emp1662574758705540307at_nat (lambda ((A5 tptp.set_Pr1261947904930325089at_nat)) (= A5 tptp.bot_bo2099793752762293965at_nat))))) (let ((_let_174 (= tptp.is_emp7572232645145209145at_nat (lambda ((A5 tptp.set_Pr4329608150637261639at_nat)) (= A5 tptp.bot_bo228742789529271731at_nat))))) (let ((_let_175 (= tptp.remove_nat (lambda ((X2 tptp.nat) (A5 tptp.set_nat)) (@ (@ tptp.minus_minus_set_nat A5) (@ (@ tptp.insert_nat2 X2) tptp.bot_bot_set_nat)))))) (let ((_let_176 (= tptp.remove_int (lambda ((X2 tptp.int) (A5 tptp.set_int)) (@ (@ tptp.minus_minus_set_int A5) (@ (@ tptp.insert_int2 X2) tptp.bot_bot_set_int)))))) (let ((_let_177 (= tptp.remove_o (lambda ((X2 Bool) (A5 tptp.set_o)) (@ (@ tptp.minus_minus_set_o A5) (@ (@ tptp.insert_o2 X2) tptp.bot_bot_set_o)))))) (let ((_let_178 (= tptp.remove6466555014256735590at_nat (lambda ((X2 tptp.product_prod_nat_nat) (A5 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.minus_1356011639430497352at_nat A5) (@ (@ tptp.insert8211810215607154385at_nat X2) tptp.bot_bo2099793752762293965at_nat)))))) (let ((_let_179 (= tptp.remove5300788332298244428at_nat (lambda ((X2 tptp.produc3843707927480180839at_nat) (A5 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.minus_3314409938677909166at_nat A5) (@ (@ tptp.insert9069300056098147895at_nat X2) tptp.bot_bo228742789529271731at_nat)))))) (let ((_let_180 (= tptp.is_singleton_int (lambda ((A5 tptp.set_int)) (= A5 (@ (@ tptp.insert_int2 (@ tptp.the_elem_int A5)) tptp.bot_bot_set_int)))))) (let ((_let_181 (= tptp.is_singleton_nat (lambda ((A5 tptp.set_nat)) (= A5 (@ (@ tptp.insert_nat2 (@ tptp.the_elem_nat A5)) tptp.bot_bot_set_nat)))))) (let ((_let_182 (= tptp.is_singleton_o (lambda ((A5 tptp.set_o)) (= A5 (@ (@ tptp.insert_o2 (@ tptp.the_elem_o A5)) tptp.bot_bot_set_o)))))) (let ((_let_183 (= tptp.is_sin2850979758926227957at_nat (lambda ((A5 tptp.set_Pr1261947904930325089at_nat)) (= A5 (@ (@ tptp.insert8211810215607154385at_nat (@ tptp.the_el2281957884133575798at_nat A5)) tptp.bot_bo2099793752762293965at_nat)))))) (let ((_let_184 (= tptp.is_sin2937591304547752795at_nat (lambda ((A5 tptp.set_Pr4329608150637261639at_nat)) (= A5 (@ (@ tptp.insert9069300056098147895at_nat (@ tptp.the_el221668144340439132at_nat A5)) tptp.bot_bo228742789529271731at_nat)))))) (let ((_let_185 (= tptp.bot_bot_set_int (@ tptp.collect_int tptp.bot_bot_int_o)))) (let ((_let_186 (= tptp.bot_bot_set_nat (@ tptp.collect_nat tptp.bot_bot_nat_o)))) (let ((_let_187 (= tptp.bot_bot_set_o (@ tptp.collect_o tptp.bot_bot_o_o)))) (let ((_let_188 (= tptp.bot_bo2099793752762293965at_nat (@ tptp.collec3392354462482085612at_nat tptp.bot_bo482883023278783056_nat_o)))) (let ((_let_189 (= tptp.bot_bo228742789529271731at_nat (@ tptp.collec6321179662152712658at_nat tptp.bot_bo6829958733157050602_nat_o)))) (let ((_let_190 (= tptp.bot_bo7824918357723582233_nat_o (@ tptp.collec939566748876313656_nat_o tptp.bot_bo7963750851167320836at_o_o)))) (let ((_let_191 (= tptp.fI_QUERY (lambda ((P2 tptp.assn) (Q2 tptp.assn) (F3 tptp.assn)) (@ (@ tptp.entails P2) (@ (@ tptp.times_times_assn Q2) F3)))))) (let ((_let_192 (@ tptp.size_size_list_c tptp.xs))) (let ((_let_193 (= tptp.entails (lambda ((P2 tptp.assn) (Q2 tptp.assn)) (forall ((H3 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P2) H3) (@ (@ tptp.rep_assn Q2) H3))))))) (let ((_let_194 (forall ((P tptp.assn)) (@ (@ tptp.entails tptp.bot_bot_assn) P)))) (let ((_let_195 (@ _let_1 tptp.bot_bot_assn))) (let ((_let_196 (ho_1208 (ho_1207 k_1209 tptp.q) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4752))) (let ((_let_197 (ho_1208 (ho_1207 k_1209 (ho_1334 k_1333 (ho_1843 k_1842 BOOLEAN_TERM_VARIABLE_555099))) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4752))) (let ((_let_198 (not _let_197))) (let ((_let_199 (or _let_198 _let_196))) (let ((_let_200 (ho_1207 k_1209 tptp.p))) (let ((_let_201 (ho_1208 _let_200 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4752))) (let ((_let_202 (not _let_201))) (let ((_let_203 (or _let_202 _let_196))) (let ((_let_204 (forall ((H3 tptp.produc3658429121746597890et_nat)) (or (not (ho_1208 (ho_1207 k_1209 tptp.p) H3)) (ho_1208 (ho_1207 k_1209 tptp.q) H3))))) (let ((_let_205 (not _let_203))) (let ((_let_206 (not _let_204))) (let ((_let_207 (EQ_RESOLVE (ASSUME :args (_let_193)) (MACRO_SR_EQ_INTRO :args (_let_193 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_208 (EQ_RESOLVE (ASSUME :args (_let_191)) (MACRO_SR_EQ_INTRO _let_207 :args (_let_191 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_209 (ASSUME :args (_let_190)))) (let ((_let_210 (ASSUME :args (_let_189)))) (let ((_let_211 (ASSUME :args (_let_188)))) (let ((_let_212 (ASSUME :args (_let_187)))) (let ((_let_213 (ASSUME :args (_let_186)))) (let ((_let_214 (ASSUME :args (_let_185)))) (let ((_let_215 (EQ_RESOLVE (ASSUME :args (_let_184)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args (_let_184 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_216 (EQ_RESOLVE (ASSUME :args (_let_183)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args (_let_183 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_217 (EQ_RESOLVE (ASSUME :args (_let_182)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args (_let_182 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_218 (EQ_RESOLVE (ASSUME :args (_let_181)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args (_let_181 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_219 (EQ_RESOLVE (ASSUME :args (_let_180)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args (_let_180 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_220 (EQ_RESOLVE (ASSUME :args (_let_179)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args (_let_179 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_221 (EQ_RESOLVE (ASSUME :args (_let_178)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args (_let_178 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_222 (EQ_RESOLVE (ASSUME :args (_let_177)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args (_let_177 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_223 (EQ_RESOLVE (ASSUME :args (_let_176)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args (_let_176 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_224 (EQ_RESOLVE (ASSUME :args (_let_175)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args (_let_175 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_225 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_174)) (MACRO_SR_EQ_INTRO :args (_let_174 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args ((= tptp.is_emp7572232645145209145at_nat (lambda ((A5 tptp.set_Pr4329608150637261639at_nat)) (= tptp.bot_bo228742789529271731at_nat A5))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_226 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_173)) (MACRO_SR_EQ_INTRO :args (_let_173 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args ((= tptp.is_emp1662574758705540307at_nat (lambda ((A5 tptp.set_Pr1261947904930325089at_nat)) (= tptp.bot_bo2099793752762293965at_nat A5))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_227 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_172)) (MACRO_SR_EQ_INTRO :args (_let_172 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args ((= tptp.is_empty_o (lambda ((A5 tptp.set_o)) (= tptp.bot_bot_set_o A5))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_228 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_171)) (MACRO_SR_EQ_INTRO :args (_let_171 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args ((= tptp.is_empty_nat (lambda ((A5 tptp.set_nat)) (= tptp.bot_bot_set_nat A5))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_229 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_170)) (MACRO_SR_EQ_INTRO :args (_let_170 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args ((= tptp.is_empty_int (lambda ((A5 tptp.set_int)) (= tptp.bot_bot_set_int A5))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_230 (EQ_RESOLVE (ASSUME :args (_let_169)) (MACRO_SR_EQ_INTRO :args (_let_169 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_231 (EQ_RESOLVE (ASSUME :args (_let_168)) (MACRO_SR_EQ_INTRO :args (_let_168 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_232 (EQ_RESOLVE (ASSUME :args (_let_167)) (MACRO_SR_EQ_INTRO :args (_let_167 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_233 (EQ_RESOLVE (ASSUME :args (_let_166)) (MACRO_SR_EQ_INTRO :args (_let_166 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_234 (SYMM (ASSUME :args (_let_165))))) (let ((_let_235 (EQ_RESOLVE (ASSUME :args (_let_164)) (MACRO_SR_EQ_INTRO :args (_let_164 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_236 (EQ_RESOLVE (ASSUME :args (_let_163)) (MACRO_SR_EQ_INTRO :args (_let_163 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_237 (EQ_RESOLVE (ASSUME :args (_let_162)) (MACRO_SR_EQ_INTRO :args (_let_162 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_238 (EQ_RESOLVE (ASSUME :args (_let_161)) (MACRO_SR_EQ_INTRO :args (_let_161 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_239 (SYMM (ASSUME :args (_let_160))))) (let ((_let_240 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_159)) (MACRO_SR_EQ_INTRO :args (_let_159 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args ((= tptp.pairwi3222497012029234898at_nat (lambda ((R3 (-> tptp.produc3843707927480180839at_nat tptp.produc3843707927480180839at_nat Bool)) (S2 tptp.set_Pr4329608150637261639at_nat)) (forall ((X2 tptp.produc3843707927480180839at_nat) (BOUND_VARIABLE_103372 tptp.produc3843707927480180839at_nat)) (or (not (@ (@ tptp.member8757157785044589968at_nat X2) S2)) (not (@ (@ tptp.member8757157785044589968at_nat BOUND_VARIABLE_103372) (@ (@ tptp.minus_3314409938677909166at_nat S2) (@ (@ tptp.insert9069300056098147895at_nat X2) tptp.bot_bo228742789529271731at_nat)))) (@ (@ R3 X2) BOUND_VARIABLE_103372))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_241 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_158)) (MACRO_SR_EQ_INTRO :args (_let_158 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args ((= tptp.pairwi6357175311820755948at_nat (lambda ((R3 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (S2 tptp.set_Pr1261947904930325089at_nat)) (forall ((X2 tptp.product_prod_nat_nat) (BOUND_VARIABLE_103397 tptp.product_prod_nat_nat)) (or (not (@ (@ tptp.member8440522571783428010at_nat X2) S2)) (not (@ (@ tptp.member8440522571783428010at_nat BOUND_VARIABLE_103397) (@ (@ tptp.minus_1356011639430497352at_nat S2) (@ (@ tptp.insert8211810215607154385at_nat X2) tptp.bot_bo2099793752762293965at_nat)))) (@ (@ R3 X2) BOUND_VARIABLE_103397))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_242 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_157)) (MACRO_SR_EQ_INTRO :args (_let_157 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args ((= tptp.pairwise_o (lambda ((R3 (-> Bool Bool Bool)) (S2 tptp.set_o)) (forall ((X2 Bool) (BOUND_VARIABLE_103422 Bool)) (or (not (@ (@ tptp.member_o X2) S2)) (not (@ (@ tptp.member_o BOUND_VARIABLE_103422) (@ (@ tptp.minus_minus_set_o S2) (@ (@ tptp.insert_o2 X2) tptp.bot_bot_set_o)))) (@ (@ R3 X2) BOUND_VARIABLE_103422))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_243 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_156)) (MACRO_SR_EQ_INTRO :args (_let_156 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args ((= tptp.pairwise_int (lambda ((R3 (-> tptp.int tptp.int Bool)) (S2 tptp.set_int)) (forall ((X2 tptp.int) (BOUND_VARIABLE_103447 tptp.int)) (or (not (@ (@ tptp.member_int X2) S2)) (not (@ (@ tptp.member_int BOUND_VARIABLE_103447) (@ (@ tptp.minus_minus_set_int S2) (@ (@ tptp.insert_int2 X2) tptp.bot_bot_set_int)))) (@ (@ R3 X2) BOUND_VARIABLE_103447))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_244 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_155)) (MACRO_SR_EQ_INTRO :args (_let_155 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args ((= tptp.pairwise_nat (lambda ((R3 (-> tptp.nat tptp.nat Bool)) (S2 tptp.set_nat)) (forall ((X2 tptp.nat) (BOUND_VARIABLE_103472 tptp.nat)) (or (not (@ (@ tptp.member_nat X2) S2)) (not (@ (@ tptp.member_nat BOUND_VARIABLE_103472) (@ (@ tptp.minus_minus_set_nat S2) (@ (@ tptp.insert_nat2 X2) tptp.bot_bot_set_nat)))) (@ (@ R3 X2) BOUND_VARIABLE_103472))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_245 (EQ_RESOLVE (ASSUME :args (_let_154)) (MACRO_SR_EQ_INTRO :args (_let_154 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_246 (EQ_RESOLVE (ASSUME :args (_let_153)) (MACRO_SR_EQ_INTRO :args (_let_153 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_247 (EQ_RESOLVE (ASSUME :args (_let_152)) (MACRO_SR_EQ_INTRO :args (_let_152 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_248 (EQ_RESOLVE (ASSUME :args (_let_151)) (MACRO_SR_EQ_INTRO :args (_let_151 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_249 (EQ_RESOLVE (ASSUME :args (_let_150)) (MACRO_SR_EQ_INTRO :args (_let_150 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_250 (EQ_RESOLVE (ASSUME :args (_let_149)) (MACRO_SR_EQ_INTRO :args (_let_149 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_251 (EQ_RESOLVE (ASSUME :args (_let_148)) (MACRO_SR_EQ_INTRO :args (_let_148 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_252 (EQ_RESOLVE (ASSUME :args (_let_147)) (MACRO_SR_EQ_INTRO :args (_let_147 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_253 (EQ_RESOLVE (ASSUME :args (_let_146)) (MACRO_SR_EQ_INTRO :args (_let_146 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_254 (ASSUME :args (_let_145)))) (let ((_let_255 (ASSUME :args (_let_144)))) (let ((_let_256 (ASSUME :args (_let_143)))) (let ((_let_257 (ASSUME :args (_let_142)))) (let ((_let_258 (ASSUME :args (_let_141)))) (let ((_let_259 (ASSUME :args (_let_140)))) (let ((_let_260 (ASSUME :args (_let_139)))) (let ((_let_261 (EQ_RESOLVE (ASSUME :args (_let_138)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args (_let_138 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_262 (EQ_RESOLVE (ASSUME :args (_let_137)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args (_let_137 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_263 (EQ_RESOLVE (ASSUME :args (_let_136)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args (_let_136 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_264 (EQ_RESOLVE (ASSUME :args (_let_135)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args (_let_135 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_265 (EQ_RESOLVE (ASSUME :args (_let_134)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args (_let_134 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_266 (EQ_RESOLVE (ASSUME :args (_let_133)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args (_let_133 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_267 (EQ_RESOLVE (ASSUME :args (_let_132)) (MACRO_SR_EQ_INTRO :args (_let_132 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_268 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_131)) (MACRO_SR_EQ_INTRO :args (_let_131 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args ((= tptp.sorted_wrt_c (lambda ((P2 (-> tptp.c tptp.c Bool)) (Xs3 tptp.list_c)) (forall ((I4 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_c Xs3))) (or (not (@ (@ tptp.ord_less_nat I4) J2)) (not (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_c Xs3))) (@ (@ P2 (@ _let_1 I4)) (@ _let_1 J2))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_269 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_130)) (MACRO_SR_EQ_INTRO :args (_let_130 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args ((= tptp.sorted_wrt_d (lambda ((P2 (-> tptp.d tptp.d Bool)) (Xs3 tptp.list_d)) (forall ((I4 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_d Xs3))) (or (not (@ (@ tptp.ord_less_nat I4) J2)) (not (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_d Xs3))) (@ (@ P2 (@ _let_1 I4)) (@ _let_1 J2))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_270 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_129)) (MACRO_SR_EQ_INTRO :args (_let_129 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args ((= tptp.sorted_wrt_nat (lambda ((P2 (-> tptp.nat tptp.nat Bool)) (Xs3 tptp.list_nat)) (forall ((I4 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs3))) (or (not (@ (@ tptp.ord_less_nat I4) J2)) (not (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_nat Xs3))) (@ (@ P2 (@ _let_1 I4)) (@ _let_1 J2))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_271 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_128)) (MACRO_SR_EQ_INTRO :args (_let_128 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args ((= tptp.sorted_wrt_int (lambda ((P2 (-> tptp.int tptp.int Bool)) (Xs3 tptp.list_int)) (forall ((I4 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs3))) (or (not (@ (@ tptp.ord_less_nat I4) J2)) (not (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_int Xs3))) (@ (@ P2 (@ _let_1 I4)) (@ _let_1 J2))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_272 (ASSUME :args (_let_127)))) (let ((_let_273 (ASSUME :args (_let_126)))) (let ((_let_274 (ASSUME :args (_let_125)))) (let ((_let_275 (SYMM (ASSUME :args (_let_124))))) (let ((_let_276 (SYMM (ASSUME :args (_let_123))))) (let ((_let_277 (SYMM (ASSUME :args (_let_122))))) (let ((_let_278 (EQ_RESOLVE (SYMM (ASSUME :args (_let_105))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args ((= tptp.bot_bo3083307316010499117at_nat _let_104) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_279 (EQ_RESOLVE (ASSUME :args (_let_103)) (MACRO_SR_EQ_INTRO :args (_let_103 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_280 (EQ_RESOLVE (ASSUME :args (_let_102)) (MACRO_SR_EQ_INTRO :args (_let_102 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_281 (ASSUME :args (_let_101)))) (let ((_let_282 (ASSUME :args (_let_100)))) (let ((_let_283 (ASSUME :args (_let_99)))) (let ((_let_284 (ASSUME :args (_let_98)))) (let ((_let_285 (ASSUME :args (_let_97)))) (let ((_let_286 (ASSUME :args (_let_96)))) (let ((_let_287 (EQ_RESOLVE (ASSUME :args (_let_95)) (MACRO_SR_EQ_INTRO :args (_let_95 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_288 (EQ_RESOLVE (ASSUME :args (_let_94)) (MACRO_SR_EQ_INTRO :args (_let_94 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_289 (EQ_RESOLVE (ASSUME :args (_let_93)) (MACRO_SR_EQ_INTRO :args (_let_93 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_290 (EQ_RESOLVE (ASSUME :args (_let_92)) (MACRO_SR_EQ_INTRO :args (_let_92 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_291 (EQ_RESOLVE (ASSUME :args (_let_91)) (MACRO_SR_EQ_INTRO :args (_let_91 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_292 (EQ_RESOLVE (ASSUME :args (_let_90)) (MACRO_SR_EQ_INTRO :args (_let_90 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_293 (EQ_RESOLVE (ASSUME :args (_let_89)) (MACRO_SR_EQ_INTRO :args (_let_89 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_294 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_88)) (MACRO_SR_EQ_INTRO :args (_let_88 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args ((= tptp.eucl_rel_int (lambda ((A12 tptp.int) (A23 tptp.int) (A32 tptp.product_prod_int_int)) (let ((_let_1 (= tptp.zero_zero_int A23))) (or (not (or (not _let_1) (not (= A32 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) A12))))) (not (or _let_1 (forall ((Q8 tptp.int)) (or (not (= A32 (@ (@ tptp.product_Pair_int_int Q8) tptp.zero_zero_int))) (not (= A12 (@ (@ tptp.times_times_int Q8) A23))))))) (not (forall ((R4 tptp.int) (Q8 tptp.int)) (or (not (= A32 (@ (@ tptp.product_Pair_int_int Q8) R4))) (not (= (@ tptp.sgn_sgn_int R4) (@ tptp.sgn_sgn_int A23))) (not (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R4)) (@ tptp.abs_abs_int A23))) (not (= A12 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q8) A23)) R4)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_295 (EQ_RESOLVE (ASSUME :args (_let_87)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args (_let_87 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_296 (ASSUME :args (_let_86)))) (let ((_let_297 (EQ_RESOLVE (SYMM (ASSUME :args (_let_85))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args ((= tptp.zero_zero_nat _let_84) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_298 (ASSUME :args (_let_83)))) (let ((_let_299 (ASSUME :args (_let_82)))) (let ((_let_300 (ASSUME :args (_let_81)))) (let ((_let_301 (ASSUME :args (_let_80)))) (let ((_let_302 (ASSUME :args (_let_79)))) (let ((_let_303 (ASSUME :args (_let_78)))) (let ((_let_304 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_77)) (MACRO_SR_EQ_INTRO :args (_let_77 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args ((= tptp.finite_finite_nat (lambda ((N8 tptp.set_nat)) (not (forall ((M tptp.nat)) (not (forall ((X2 tptp.nat)) (or (not (@ (@ tptp.member_nat X2) N8)) (@ (@ tptp.ord_less_nat X2) M)))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_305 (ASSUME :args (_let_76)))) (let ((_let_306 (ASSUME :args (_let_75)))) (let ((_let_307 (EQ_RESOLVE (ASSUME :args (_let_74)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args (_let_74 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_308 (EQ_RESOLVE (ASSUME :args (_let_73)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args (_let_73 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_309 (EQ_RESOLVE (ASSUME :args (_let_72)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args (_let_72 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_310 (ASSUME :args (_let_70)))) (let ((_let_311 (ASSUME :args (_let_69)))) (let ((_let_312 (EQ_RESOLVE (ASSUME :args (_let_68)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args (_let_68 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_313 (ASSUME :args (_let_67)))) (let ((_let_314 (ASSUME :args (_let_66)))) (let ((_let_315 (EQ_RESOLVE (ASSUME :args (_let_65)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args (_let_65 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_316 (ASSUME :args (_let_64)))) (let ((_let_317 (ASSUME :args (_let_63)))) (let ((_let_318 (ASSUME :args (_let_62)))) (let ((_let_319 (ASSUME :args (_let_61)))) (let ((_let_320 (ASSUME :args (_let_60)))) (let ((_let_321 (EQ_RESOLVE (ASSUME :args (_let_59)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args (_let_59 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_322 (EQ_RESOLVE (ASSUME :args (_let_58)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args (_let_58 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_323 (ASSUME :args (_let_57)))) (let ((_let_324 (ASSUME :args (_let_56)))) (let ((_let_325 (ASSUME :args (_let_55)))) (let ((_let_326 (ASSUME :args (_let_54)))) (let ((_let_327 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_51)) (MACRO_SR_EQ_INTRO :args (_let_51 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args ((= tptp.fI_RESULT (lambda ((M7 tptp.list_P8527749157015355191n_assn) (UP tptp.assn) (UQ tptp.assn) (F3 tptp.assn)) (let ((_let_1 (@ tptp.foldr_assn_assn tptp.times_times_assn))) (=> (forall ((X2 tptp.produc6575502325842934193n_assn)) (or (not (@ (@ tptp.member7957490590177025114n_assn X2) (@ tptp.set_Pr1139785259514867910n_assn M7))) (@ (@ tptp.produc7274209992780475162assn_o tptp.entails) X2))) (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ _let_1 (@ (@ tptp.map_Pr8991440229025900053n_assn tptp.produc9167289414957590229n_assn) M7)) tptp.one_one_assn)) UP)) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ _let_1 (@ (@ tptp.map_Pr8991440229025900053n_assn tptp.produc2051961928117032727n_assn) M7)) tptp.one_one_assn)) UQ)) F3)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_328 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_50)) (MACRO_SR_EQ_INTRO :args (_let_50 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args ((= tptp.fi (lambda ((M tptp.list_P8527749157015355191n_assn) (P7 tptp.assn) (Q8 tptp.assn) (Up tptp.assn) (Uq tptp.assn) (F6 tptp.assn)) (let ((_let_1 (@ tptp.foldr_assn_assn tptp.times_times_assn))) (=> (forall ((X2 tptp.produc6575502325842934193n_assn)) (or (not (@ (@ tptp.member7957490590177025114n_assn X2) (@ tptp.set_Pr1139785259514867910n_assn M))) (@ (@ tptp.produc7274209992780475162assn_o tptp.entails) X2))) (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ _let_1 (@ (@ tptp.map_Pr8991440229025900053n_assn tptp.produc9167289414957590229n_assn) M)) tptp.one_one_assn)) P7)) Up)) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ _let_1 (@ (@ tptp.map_Pr8991440229025900053n_assn tptp.produc2051961928117032727n_assn) M)) tptp.one_one_assn)) Q8)) Uq)) F6)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_329 (EQ_RESOLVE (ASSUME :args (_let_49)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args (_let_49 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_330 (EQ_RESOLVE (ASSUME :args (_let_41)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args (_let_41 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_331 (EQ_RESOLVE (ASSUME :args (_let_40)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args (_let_40 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_332 (EQ_RESOLVE (ASSUME :args (_let_38)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args (_let_38 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_333 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_35)) (MACRO_SR_EQ_INTRO :args (_let_35 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args ((= 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 (= tptp.zero_zero_int _let_1)) (@ (@ 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)))))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_334 (EQ_RESOLVE (SYMM (ASSUME :args (_let_34))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args ((= tptp.one_one_rat _let_33) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_335 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args ((= tptp.inverse_inverse_rat (@ _let_23 (lambda ((X2 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_fst_int_int X2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= tptp.zero_zero_int _let_1)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ tptp.product_snd_int_int X2)) _let_1)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_336 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_337 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_338 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_339 (ASSUME :args (_let_22)))) (let ((_let_340 (ASSUME :args (_let_21)))) (let ((_let_341 (ASSUME :args (_let_20)))) (let ((_let_342 (ASSUME :args (_let_19)))) (let ((_let_343 (ASSUME :args (_let_18)))) (let ((_let_344 (ASSUME :args (_let_17)))) (let ((_let_345 (ASSUME :args (_let_16)))) (let ((_let_346 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args ((= tptp.fract (lambda ((Xa4 tptp.int) (X2 tptp.int)) (@ tptp.abs_Rat (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= tptp.zero_zero_int X2)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int Xa4) X2))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_347 (SYMM (ASSUME :args (_let_14))))) (let ((_let_348 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args ((= tptp.all_interval_int (lambda ((P2 (-> tptp.int Bool)) (I4 tptp.int) (J2 tptp.int)) (forall ((X2 tptp.int)) (or (not (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int I4) J2))) (@ P2 X2))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_349 (EQ_RESOLVE (SYMM (ASSUME :args (_let_12))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args ((= tptp.one_one_nat _let_11) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_350 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args ((= tptp.is_pure_assn (lambda ((A3 tptp.assn)) (not (forall ((P2 Bool)) (not (= A3 (@ tptp.pure_assn P2))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_351 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_352 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args ((= tptp.all_interval_nat (lambda ((P2 (-> tptp.nat Bool)) (I4 tptp.nat) (J2 tptp.nat)) (forall ((X2 tptp.nat)) (or (not (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or4665077453230672383an_nat I4) J2))) (@ P2 X2))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_353 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_354 (ASSUME :args (_let_6)))) (let ((_let_355 (ASSUME :args (_let_5)))) (let ((_let_356 (AND_INTRO (ASSUME :args (_let_3)) (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207) :args (_let_4 SB_DEFAULT SBA_FIXPOINT))) _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207))) (let ((_let_357 (EQ_RESOLVE (ASSUME :args (_let_2)) (TRANS (MACRO_SR_EQ_INTRO _let_356 :args (_let_2 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((H3 tptp.produc3658429121746597890et_nat)) (or (not (@ (@ tptp.rep_assn tptp.p) H3)) (@ (@ tptp.rep_assn tptp.q) H3)))) _let_206))))))) (let ((_let_358 (or))) (let ((_let_359 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_357) :args (_let_206))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_206) _let_204))) (REFL :args (_let_205)) :args _let_358)) _let_357 :args (_let_205 true _let_204)))) (let ((_let_360 (forall ((P tptp.assn) (H3 tptp.produc3658429121746597890et_nat)) (or (not (ho_1208 (ho_1207 k_1209 (ho_1334 k_1333 (ho_1843 k_1842 false))) H3)) (ho_1208 (ho_1207 k_1209 P) H3))))) (let ((_let_361 (EQ_RESOLVE (ASSUME :args (_let_194)) (TRANS (MACRO_SR_EQ_INTRO _let_356 :args (_let_194 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((P tptp.assn) (H3 tptp.produc3658429121746597890et_nat)) (or (not (@ (@ tptp.rep_assn (@ tptp.abs_assn (@ tptp.pure_a825153325127701367it_nat false))) H3)) (@ (@ tptp.rep_assn P) H3))) _let_360))))))) (let ((_let_362 (=>))) (let ((_let_363 (CONG (CONG (REFL :args (k_1209)) (CONG (REFL :args (k_1333)) (CONG (REFL :args (k_1842)) (MACRO_SR_PRED_INTRO :args ((= false BOOLEAN_TERM_VARIABLE_555099))) :args (APPLY_UF ho_1843)) :args (APPLY_UF ho_1334)) :args (APPLY_UF ho_1207)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4752)) :args (APPLY_UF ho_1208)))) (let ((_let_364 (_let_360))) (let ((_let_365 (or _let_202 _let_197))) (let ((_let_366 (forall ((H3 tptp.produc3658429121746597890et_nat)) (or (not (ho_1208 (ho_1207 k_1209 tptp.p) H3)) (ho_1208 (ho_1207 k_1209 (ho_1334 k_1333 (ho_1843 k_1842 false))) H3))))) (let ((_let_367 (EQ_RESOLVE (ASSUME :args (_let_195)) (TRANS (MACRO_SR_EQ_INTRO _let_356 :args (_let_195 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((H3 tptp.produc3658429121746597890et_nat)) (or (not (@ (@ tptp.rep_assn tptp.p) H3)) (@ (@ tptp.rep_assn (@ tptp.abs_assn (@ tptp.pure_a825153325127701367it_nat false))) H3))) _let_366))))))) (let ((_let_368 (_let_366))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_199)) :args ((or _let_196 _let_198 (not _let_199)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_365)) :args ((or _let_202 _let_197 (not _let_365)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_203 0)) (CONG (REFL :args (_let_203)) (MACRO_SR_PRED_INTRO :args ((= (not _let_202) _let_201))) :args _let_358)) :args ((or _let_201 _let_203))) _let_359 :args (_let_201 true _let_203)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE _let_367 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4752 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (ho_1208 _let_200 H3) false))))) :args _let_368) (CONG (REFL :args _let_368) (CONG (REFL :args (_let_202)) _let_363 :args _let_358) :args _let_362))) _let_367 :args (_let_365 false _let_366)) :args (_let_197 false _let_201 false _let_365)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE _let_361 :args (tptp.q SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4752 QUANTIFIERS_INST_E_MATCHING ((not (= (ho_1208 (ho_1207 k_1209 P) H3) true))))) :args _let_364) (CONG (REFL :args _let_364) (CONG (CONG _let_363 :args (not)) (REFL :args (_let_196)) :args _let_358) :args _let_362))) _let_361 :args (_let_199 false _let_360)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_203 1)) _let_359 :args ((not _let_196) true _let_203)) :args (false false _let_197 false _let_199 true _let_196)) :args ((forall ((P tptp.assn) (Q tptp.assn)) (=> (forall ((H tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P) H) (@ (@ tptp.rep_assn Q) H))) (@ (@ tptp.entails P) Q))) _let_195 (@ (@ tptp.member_nat tptp.i2) tptp.i) (forall ((A tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.entails A) B) (=> (@ (@ tptp.entails B) A) (= A B)))) (forall ((P tptp.assn)) (@ (@ tptp.entails P) P)) (forall ((P tptp.assn) (Q tptp.assn) (R tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 Q) (=> (@ (@ tptp.entails Q) R) (@ _let_1 R))))) (forall ((P tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ (@ tptp.entails P) Q))) (=> _let_1 _let_1))) _let_194 (forall ((P tptp.assn) (H2 tptp.produc3658429121746597890et_nat) (Q tptp.assn)) (=> (@ (@ tptp.rep_assn P) H2) (=> (@ (@ tptp.entails P) Q) (@ (@ tptp.rep_assn Q) H2)))) (forall ((P tptp.assn) (Q tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.entails P) Q) (=> (@ (@ tptp.rep_assn P) H2) (@ (@ tptp.rep_assn Q) H2)))) _let_193 (forall ((P tptp.assn)) (= (@ (@ tptp.entails P) tptp.bot_bot_assn) (forall ((H3 tptp.produc3658429121746597890et_nat)) (not (@ (@ tptp.rep_assn P) H3))))) (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L824818263033719201sn_c_d tptp.i) tptp.a) (@ (@ (@ tptp.list_update_c tptp.xs) tptp.i2) tptp.x)) (@ (@ (@ tptp.list_update_d tptp.xsi) tptp.i2) tptp.xi))) tptp.f)) tptp.q) (forall ((P tptp.assn) (Q tptp.assn)) (=> (@ (@ tptp.entails P) Q) (@ (@ tptp.entailst P) Q))) (forall ((X tptp.assn) (Y tptp.assn)) (= (= (@ tptp.rep_assn X) (@ tptp.rep_assn Y)) (= X Y))) (forall ((A tptp.assn)) (@ (@ tptp.entailst A) A)) (forall ((P tptp.assn)) (= (@ (@ tptp.times_times_assn tptp.bot_bot_assn) P) tptp.bot_bot_assn)) (forall ((P tptp.assn)) (= (@ (@ tptp.times_times_assn P) tptp.bot_bot_assn) tptp.bot_bot_assn)) (forall ((A2 tptp.assn) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn A2))) (= (@ (@ tptp.times_times_assn (@ _let_1 B2)) C) (@ (@ tptp.times_times_assn (@ _let_1 C)) B2)))) (forall ((A2 tptp.assn) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn A2))) (let ((_let_2 (@ tptp.times_times_assn B2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (= tptp.times_times_assn (lambda ((A3 tptp.assn) (B3 tptp.assn)) (@ (@ tptp.times_times_assn B3) A3))) (forall ((H2 tptp.produc3658429121746597890et_nat)) (not (@ (@ tptp.rep_assn tptp.bot_bot_assn) H2))) (forall ((A tptp.assn) (B tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn A) B)) H2) (exists ((H1 tptp.produc3658429121746597890et_nat) (H22 tptp.produc3658429121746597890et_nat)) (and (@ (@ tptp.rep_assn A) H1) (@ (@ tptp.rep_assn B) H22))))) (forall ((A2 tptp.assn) (B2 tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn A2) B2)) H2) (not (=> (exists ((X_1 tptp.produc3658429121746597890et_nat)) (@ (@ tptp.rep_assn A2) X_1)) (forall ((H_2 tptp.produc3658429121746597890et_nat)) (not (@ (@ tptp.rep_assn B2) H_2))))))) (forall ((A tptp.assn) (B tptp.assn) (C2 tptp.assn)) (let ((_let_1 (@ tptp.entailst A))) (=> (@ _let_1 B) (=> (@ (@ tptp.entailst B) C2) (@ _let_1 C2))))) (forall ((A2 tptp.assn) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn A2))) (= (@ (@ tptp.times_times_assn (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_assn B2) C))))) (forall ((F tptp.assn) (F2 tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.entailst F) F2) (@ (@ tptp.entailst (@ (@ tptp.times_times_assn F) A)) F2))) (forall ((F tptp.assn) (F2 tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.entailst F) F2) (@ (@ tptp.entailst (@ (@ tptp.times_times_assn F) A)) (@ (@ tptp.times_times_assn F2) A)))) (forall ((P tptp.assn) (Q tptp.assn) (A tptp.assn) (F tptp.assn) (B tptp.assn)) (let ((_let_1 (@ tptp.entailst A))) (=> (@ (@ tptp.entailst P) Q) (=> (@ _let_1 (@ (@ tptp.times_times_assn P) F)) (=> (@ (@ tptp.entailst (@ (@ tptp.times_times_assn Q) F)) B) (@ _let_1 B)))))) (forall ((A tptp.assn) (B tptp.assn) (C2 tptp.assn) (D tptp.assn)) (=> (@ (@ tptp.entailst A) B) (=> (@ (@ tptp.entailst C2) D) (@ (@ tptp.entailst (@ (@ tptp.times_times_assn A) C2)) (@ (@ tptp.times_times_assn B) D))))) (= tptp.times_times_assn (lambda ((P2 tptp.assn) (Q2 tptp.assn)) (@ (@ tptp.times_times_assn Q2) P2))) (forall ((P tptp.assn) (Q tptp.assn) (R tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn P))) (= (@ (@ tptp.times_times_assn (@ _let_1 Q)) R) (@ _let_1 (@ (@ tptp.times_times_assn Q) R))))) (forall ((Ps tptp.assn) (H2 tptp.produc3658429121746597890et_nat) (P tptp.assn) (R tptp.assn) (F tptp.assn)) (=> (@ (@ tptp.rep_assn Ps) H2) (=> (@ (@ tptp.entails P) R) (=> (@ (@ tptp.entails Ps) (@ (@ tptp.times_times_assn P) F)) (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn R) F)) H2))))) (forall ((P tptp.assn) (R tptp.assn) (Ps tptp.assn) (F tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails Ps))) (=> (@ (@ tptp.entails P) R) (=> (@ _let_1 (@ (@ tptp.times_times_assn P) F)) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn R) F)) Q) (@ _let_1 Q)))))) (forall ((P tptp.assn) (P3 tptp.assn) (Q tptp.assn) (Q3 tptp.assn)) (=> (@ (@ tptp.entails P) P3) (=> (@ (@ tptp.entails Q) Q3) (@ (@ tptp.entails (@ (@ tptp.times_times_assn P) Q)) (@ (@ tptp.times_times_assn P3) Q3))))) (forall ((A tptp.assn) (B tptp.assn) (C2 tptp.assn)) (let ((_let_1 (@ tptp.entails A))) (=> (@ _let_1 (@ (@ tptp.times_times_assn B) C2)) (@ _let_1 (@ (@ tptp.times_times_assn C2) B))))) (forall ((A tptp.assn) (B tptp.assn) (C2 tptp.assn)) (=> (@ (@ tptp.entails A) B) (@ (@ tptp.entails (@ (@ tptp.times_times_assn A) C2)) (@ (@ tptp.times_times_assn B) C2)))) (forall ((A tptp.assn) (B tptp.assn) (C2 tptp.assn)) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn A) B)) C2) (@ (@ tptp.entails (@ (@ tptp.times_times_assn B) A)) C2))) (@ _let_1 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.a tptp.x) tptp.xi)) (@ (@ (@ (@ tptp.vEBT_L824818263033719201sn_c_d (@ (@ tptp.minus_minus_set_nat tptp.i) (@ (@ tptp.insert_nat2 tptp.i2) tptp.bot_bot_set_nat))) tptp.a) tptp.xs) tptp.xsi))) tptp.f)) (forall ((Xs tptp.list_c) (I tptp.nat) (X tptp.c) (Y tptp.c)) (let ((_let_1 (@ (@ tptp.list_update_c Xs) I))) (= (@ (@ (@ tptp.list_update_c (@ _let_1 X)) I) Y) (@ _let_1 Y)))) (forall ((Xs tptp.list_d) (I tptp.nat) (X tptp.d) (Y tptp.d)) (let ((_let_1 (@ (@ tptp.list_update_d Xs) I))) (= (@ (@ (@ tptp.list_update_d (@ _let_1 X)) I) Y) (@ _let_1 Y)))) (not (= _let_192 (@ tptp.size_size_list_d tptp.xsi))) (@ (@ tptp.ord_less_nat tptp.i2) _let_192) (forall ((P tptp.assn) (Q tptp.assn) (F tptp.assn)) (=> (@ (@ (@ tptp.fI_QUERY P) Q) F) (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn Q) F)))) (forall ((A2 tptp.produc3843707927480180839at_nat) (P (-> tptp.produc3843707927480180839at_nat Bool))) (= (@ (@ tptp.member8757157785044589968at_nat A2) (@ tptp.collec6321179662152712658at_nat P)) (@ P A2))) (forall ((A2 tptp.int) (P (-> tptp.int Bool))) (= (@ (@ tptp.member_int A2) (@ tptp.collect_int P)) (@ P A2))) (forall ((A2 tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A2) (@ tptp.collect_nat P)) (@ P A2))) (forall ((A2 tptp.product_prod_nat_nat) (P (-> tptp.product_prod_nat_nat Bool))) (= (@ (@ tptp.member8440522571783428010at_nat A2) (@ tptp.collec3392354462482085612at_nat P)) (@ P A2))) (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (P (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (= (@ (@ tptp.member6576561426505652726_nat_o A2) (@ tptp.collec939566748876313656_nat_o P)) (@ P A2))) (forall ((A tptp.set_Pr4329608150637261639at_nat)) (= (@ tptp.collec6321179662152712658at_nat (lambda ((X2 tptp.produc3843707927480180839at_nat)) (@ (@ tptp.member8757157785044589968at_nat X2) A))) A)) (forall ((A tptp.set_int)) (= (@ tptp.collect_int (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) A))) A)) (forall ((A tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) A))) A)) (forall ((A tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.collec3392354462482085612at_nat (lambda ((X2 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X2) A))) A)) (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (= (@ tptp.collec939566748876313656_nat_o (lambda ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (@ (@ tptp.member6576561426505652726_nat_o X2) A))) A)) (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_nat P) (@ tptp.collect_nat Q)))) (forall ((P (-> tptp.product_prod_nat_nat Bool)) (Q (-> tptp.product_prod_nat_nat Bool))) (=> (forall ((X3 tptp.product_prod_nat_nat)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collec3392354462482085612at_nat P) (@ tptp.collec3392354462482085612at_nat Q)))) (forall ((P (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool)) (Q (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (= (@ P X3) (@ Q X3))) (= (@ tptp.collec939566748876313656_nat_o P) (@ tptp.collec939566748876313656_nat_o Q)))) _let_191 (forall ((Q tptp.assn) (R tptp.assn) (F tptp.assn) (S tptp.assn) (P tptp.assn) (X4 tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ tptp.wand_assn Q) R)) F)) S) (=> (@ _let_1 (@ (@ tptp.times_times_assn F) X4)) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn Q) X4)) R) (@ _let_1 S)))))) (forall ((Q tptp.assn) (P tptp.assn) (R tptp.assn)) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn Q) P)) R) (@ (@ tptp.entails P) (@ (@ tptp.wand_assn Q) R)))) (forall ((P tptp.assn) (Q tptp.assn)) (@ (@ tptp.entails (@ (@ tptp.times_times_assn P) (@ (@ tptp.wand_assn P) Q))) Q)) (forall ((Xs tptp.list_c) (I tptp.nat) (X tptp.c)) (= (@ tptp.size_size_list_c (@ (@ (@ tptp.list_update_c Xs) I) X)) (@ tptp.size_size_list_c Xs))) (forall ((Xs tptp.list_d) (I tptp.nat) (X tptp.d)) (= (@ tptp.size_size_list_d (@ (@ (@ tptp.list_update_d Xs) I) X)) (@ tptp.size_size_list_d Xs))) (forall ((Xs tptp.list_nat) (I tptp.nat) (X tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ (@ tptp.list_update_nat Xs) I) X)) (@ tptp.size_size_list_nat Xs))) (forall ((Xs tptp.list_int) (I tptp.nat) (X tptp.int)) (= (@ tptp.size_size_list_int (@ (@ (@ tptp.list_update_int Xs) I) X)) (@ tptp.size_size_list_int Xs))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X) Y) (not (@ (@ tptp.ord_le6747313008572928689nteger Y) X)))) (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_assn X) Y) (not (@ (@ tptp.ord_less_assn Y) X)))) (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (@ (@ tptp.ord_less_num Y) X)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (@ (@ tptp.ord_less_int Y) X)))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X) Y) (not (= Y X)))) (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_assn X) Y) (not (= Y X)))) (forall ((X tptp.num) (Y tptp.num)) (=> (@ 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(@ (@ tptp.ord_less_nat X) Y) (= X Y) (@ (@ tptp.ord_less_nat Y) X))) (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_int X) Y) (= X Y) (@ (@ tptp.ord_less_int Y) X))) (forall ((X tptp.code_integer) (Y tptp.code_integer) (P Bool)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X) Y) (=> (@ (@ tptp.ord_le6747313008572928689nteger Y) X) P))) (forall ((X tptp.assn) (Y tptp.assn) (P Bool)) (=> (@ (@ tptp.ord_less_assn X) Y) (=> (@ (@ tptp.ord_less_assn Y) X) P))) (forall ((X tptp.num) (Y tptp.num) (P Bool)) (=> (@ (@ tptp.ord_less_num X) Y) (=> (@ (@ tptp.ord_less_num Y) X) P))) (forall ((X tptp.nat) (Y tptp.nat) (P Bool)) (=> (@ (@ tptp.ord_less_nat X) Y) (=> (@ (@ tptp.ord_less_nat Y) X) P))) (forall ((X tptp.int) (Y tptp.int) (P Bool)) (=> (@ (@ tptp.ord_less_int X) Y) (=> (@ (@ tptp.ord_less_int Y) X) P))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X) Y) (not (@ (@ tptp.ord_le6747313008572928689nteger Y) X)))) (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_assn X) Y) (not (@ (@ tptp.ord_less_assn Y) X)))) (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (@ (@ tptp.ord_less_num Y) X)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (@ (@ tptp.ord_less_int Y) X)))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (F4 (-> tptp.code_integer tptp.code_integer)) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 B2)) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 A2)) C))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (F4 (-> tptp.code_integer tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (@ (@ tptp.ord_less_assn (@ F4 B2)) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_less_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_assn (@ F4 A2)) C))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (F4 (-> tptp.code_integer tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (@ (@ tptp.ord_less_num (@ F4 B2)) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_num (@ F4 A2)) C))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (F4 (-> tptp.code_integer tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (@ (@ tptp.ord_less_nat (@ F4 B2)) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_less_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_nat (@ F4 A2)) C))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (F4 (-> tptp.code_integer tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (@ (@ tptp.ord_less_int (@ F4 B2)) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_less_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_int (@ F4 A2)) C))))) (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.code_integer)) (C tptp.code_integer)) (=> (@ (@ tptp.ord_less_assn A2) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 B2)) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 A2)) C))))) (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_assn A2) B2) (=> (@ (@ tptp.ord_less_assn (@ F4 B2)) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_assn (@ F4 A2)) C))))) (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_assn A2) B2) (=> (@ (@ tptp.ord_less_num (@ F4 B2)) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_num (@ F4 A2)) C))))) (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_assn A2) B2) (=> (@ (@ tptp.ord_less_nat (@ F4 B2)) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_nat (@ F4 A2)) C))))) (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_assn A2) B2) (=> (@ (@ tptp.ord_less_int (@ F4 B2)) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_int (@ F4 A2)) C))))) (forall ((A2 tptp.code_integer) (F4 (-> tptp.code_integer tptp.code_integer)) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((A2 tptp.code_integer) (F4 (-> tptp.assn tptp.code_integer)) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_assn B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((A2 tptp.code_integer) (F4 (-> tptp.num tptp.code_integer)) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_num B2) C) (=> (forall ((X3 tptp.num) (Y2 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((A2 tptp.code_integer) (F4 (-> tptp.nat tptp.code_integer)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_nat B2) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((A2 tptp.code_integer) (F4 (-> tptp.int tptp.code_integer)) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_int B2) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((A2 tptp.assn) (F4 (-> tptp.code_integer tptp.assn)) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_less_assn A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_less_assn (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((A2 tptp.assn) (F4 (-> tptp.assn tptp.assn)) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_assn B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_assn (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((A2 tptp.assn) (F4 (-> tptp.num tptp.assn)) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_assn A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_num B2) C) (=> (forall ((X3 tptp.num) (Y2 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y2) (@ (@ tptp.ord_less_assn (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((A2 tptp.assn) (F4 (-> tptp.nat tptp.assn)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_assn A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_nat B2) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_less_assn (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((A2 tptp.assn) (F4 (-> tptp.int tptp.assn)) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_assn A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_int B2) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y2) (@ (@ tptp.ord_less_assn (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((X tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger X) X))) (forall ((X tptp.assn)) (not (@ (@ tptp.ord_less_assn X) X))) (forall ((X tptp.num)) (not (@ (@ tptp.ord_less_num X) X))) (forall ((X tptp.nat)) (not (@ (@ tptp.ord_less_nat X) X))) (forall ((X tptp.int)) (not (@ (@ tptp.ord_less_int X) X))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (F4 (-> tptp.code_integer tptp.code_integer)) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 A2)) C))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (F4 (-> tptp.code_integer tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_less_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_assn (@ F4 A2)) C))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (F4 (-> tptp.code_integer tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_num (@ F4 A2)) C))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (F4 (-> tptp.code_integer tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_less_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_nat (@ F4 A2)) C))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (F4 (-> tptp.code_integer tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_less_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_int (@ F4 A2)) C))))) (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.code_integer)) (C tptp.code_integer)) (=> (@ (@ tptp.ord_less_assn A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 A2)) C))))) (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_assn A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_assn (@ F4 A2)) C))))) (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_assn A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_num (@ F4 A2)) C))))) (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_assn A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_nat (@ F4 A2)) C))))) (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_assn A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_int (@ F4 A2)) C))))) (forall ((A2 tptp.code_integer) (F4 (-> tptp.code_integer tptp.code_integer)) (B2 tptp.code_integer) (C tptp.code_integer)) (=> (= A2 (@ F4 B2)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger A2) (@ F4 C)))))) (forall ((A2 tptp.assn) (F4 (-> tptp.code_integer tptp.assn)) (B2 tptp.code_integer) (C tptp.code_integer)) (=> (= A2 (@ F4 B2)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_less_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_assn A2) (@ F4 C)))))) (forall ((A2 tptp.num) (F4 (-> tptp.code_integer tptp.num)) (B2 tptp.code_integer) (C tptp.code_integer)) (=> (= A2 (@ F4 B2)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_num A2) (@ F4 C)))))) (forall ((A2 tptp.nat) (F4 (-> tptp.code_integer tptp.nat)) (B2 tptp.code_integer) (C tptp.code_integer)) (=> (= A2 (@ F4 B2)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_less_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_nat A2) (@ F4 C)))))) (forall ((A2 tptp.int) (F4 (-> tptp.code_integer tptp.int)) (B2 tptp.code_integer) (C tptp.code_integer)) (=> (= A2 (@ F4 B2)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_less_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_int A2) (@ F4 C)))))) (forall ((A2 tptp.code_integer) (F4 (-> tptp.assn tptp.code_integer)) (B2 tptp.assn) (C tptp.assn)) (=> (= A2 (@ F4 B2)) (=> (@ (@ tptp.ord_less_assn B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger A2) (@ F4 C)))))) (forall ((A2 tptp.assn) (F4 (-> tptp.assn tptp.assn)) (B2 tptp.assn) (C tptp.assn)) (=> (= A2 (@ F4 B2)) (=> (@ (@ tptp.ord_less_assn B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_assn A2) (@ F4 C)))))) (forall ((A2 tptp.num) (F4 (-> tptp.assn tptp.num)) (B2 tptp.assn) (C tptp.assn)) (=> (= A2 (@ F4 B2)) (=> (@ (@ tptp.ord_less_assn B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ 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tptp.ord_less_assn X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_assn Y) Z) (@ _let_1 Z))))) (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_num Y) Z) (@ _let_1 Z))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_nat Y) Z) (@ _let_1 Z))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ _let_1 Z))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (not (@ (@ tptp.ord_le6747313008572928689nteger B2) A2)))) (forall ((A2 tptp.assn) (B2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn A2) B2) (not (@ (@ tptp.ord_less_assn B2) A2)))) (forall ((A2 tptp.num) (B2 tptp.num)) (=> (@ (@ tptp.ord_less_num A2) B2) (not (@ (@ tptp.ord_less_num B2) A2)))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (not (@ (@ tptp.ord_less_nat B2) A2)))) (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (not (@ (@ tptp.ord_less_int B2) A2)))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (not (= X Y)) (or (@ (@ tptp.ord_le6747313008572928689nteger X) Y) (@ (@ tptp.ord_le6747313008572928689nteger Y) X)))) (forall ((X tptp.num) (Y tptp.num)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_num X) Y) (@ (@ tptp.ord_less_num Y) X)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_nat Y) X)))) (forall ((X tptp.int) (Y tptp.int)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_int X) Y) (@ (@ tptp.ord_less_int Y) X)))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X) Y) (not (@ (@ tptp.ord_le6747313008572928689nteger Y) X)))) (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_assn X) Y) (not (@ (@ tptp.ord_less_assn Y) X)))) (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (@ (@ tptp.ord_less_num Y) X)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (@ (@ tptp.ord_less_int Y) X)))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_le6747313008572928689nteger X) Y)) (@ (@ tptp.ord_le6747313008572928689nteger Y) X)))) (forall ((X tptp.num) (Y tptp.num)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (@ (@ tptp.ord_less_num Y) X)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))) (forall ((X tptp.int) (Y tptp.int)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_int Y) X)))) (forall ((Xs tptp.list_c) (Ys tptp.list_c)) (=> (not (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_c Ys))) (not (= Xs Ys)))) (forall ((Xs tptp.list_d) (Ys tptp.list_d)) (=> (not (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_d Ys))) (not (= Xs Ys)))) (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys))) (not (= Xs Ys)))) (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys))) (not (= Xs Ys)))) (forall ((N tptp.nat)) (exists ((Xs2 tptp.list_c)) (= (@ tptp.size_size_list_c Xs2) N))) (forall ((N tptp.nat)) (exists ((Xs2 tptp.list_d)) (= (@ tptp.size_size_list_d Xs2) N))) (forall ((N tptp.nat)) (exists ((Xs2 tptp.list_nat)) (= (@ tptp.size_size_list_nat Xs2) N))) (forall ((N tptp.nat)) (exists ((Xs2 tptp.list_int)) (= (@ tptp.size_size_list_int Xs2) N))) (forall ((P (-> tptp.list_c Bool)) (Xs tptp.list_c)) (=> (forall ((Xs2 tptp.list_c)) (=> (forall ((Ys2 tptp.list_c)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_c Ys2)) (@ tptp.size_size_list_c Xs2)) (@ P Ys2))) (@ P Xs2))) (@ P Xs))) (forall ((P (-> tptp.list_d Bool)) (Xs tptp.list_d)) (=> (forall ((Xs2 tptp.list_d)) (=> (forall ((Ys2 tptp.list_d)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_d Ys2)) (@ tptp.size_size_list_d Xs2)) (@ P Ys2))) (@ P Xs2))) (@ P Xs))) (forall ((P (-> tptp.list_nat Bool)) (Xs tptp.list_nat)) (=> (forall ((Xs2 tptp.list_nat)) (=> (forall ((Ys2 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat Ys2)) (@ tptp.size_size_list_nat Xs2)) (@ P Ys2))) (@ P Xs2))) (@ P Xs))) (forall ((P (-> tptp.list_int Bool)) (Xs tptp.list_int)) (=> (forall ((Xs2 tptp.list_int)) (=> (forall ((Ys2 tptp.list_int)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_int Ys2)) (@ tptp.size_size_list_int Xs2)) (@ P Ys2))) (@ P Xs2))) (@ P Xs))) (forall ((B2 tptp.code_integer) (A2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) A2) (not (= A2 B2)))) (forall ((B2 tptp.assn) (A2 tptp.assn)) (=> (@ (@ 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tptp.ord_le6747313008572928689nteger B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))) (forall ((B2 tptp.assn) (A2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn C))) (=> (@ (@ tptp.ord_less_assn B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))) (forall ((B2 tptp.num) (A2 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ (@ tptp.ord_less_num B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))) (forall ((B2 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_nat B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))) (forall ((B2 tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ (@ tptp.ord_less_int B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (not (@ (@ tptp.ord_le6747313008572928689nteger X) Y)) (or (@ (@ tptp.ord_le6747313008572928689nteger Y) X) (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_num X) Y)) (or (@ (@ tptp.ord_less_num Y) X) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (or (@ (@ tptp.ord_less_nat Y) X) (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_int X) Y)) (or (@ (@ tptp.ord_less_int Y) X) (= X Y)))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) C) (@ _let_1 C))))) (forall ((A2 tptp.assn) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_assn B2) C) (@ _let_1 C))))) (forall ((A2 tptp.num) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_num B2) C) (@ _let_1 C))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat B2) C) (@ _let_1 C))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_int B2) C) (@ _let_1 C))))) (forall ((P (-> tptp.code_integer tptp.code_integer Bool)) (A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (forall ((A4 tptp.code_integer) (B4 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A4) B4) (@ (@ P A4) B4))) (=> (forall ((A4 tptp.code_integer)) (@ (@ P A4) A4)) (=> (forall ((A4 tptp.code_integer) (B4 tptp.code_integer)) (=> (@ (@ P B4) A4) (@ (@ P A4) B4))) (@ (@ P A2) B2))))) (forall ((P (-> tptp.num tptp.num Bool)) (A2 tptp.num) (B2 tptp.num)) (=> (forall ((A4 tptp.num) (B4 tptp.num)) (=> (@ (@ tptp.ord_less_num A4) B4) (@ (@ P A4) B4))) (=> (forall ((A4 tptp.num)) (@ (@ P A4) A4)) (=> (forall ((A4 tptp.num) (B4 tptp.num)) (=> (@ (@ P B4) A4) (@ (@ P A4) B4))) (@ (@ P A2) B2))))) (forall ((P (-> tptp.nat tptp.nat Bool)) (A2 tptp.nat) (B2 tptp.nat)) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (@ (@ 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(not (= I I2)) (= (@ (@ (@ tptp.list_update_c (@ (@ _let_1 I) X)) I2) X6) (@ (@ (@ tptp.list_update_c (@ (@ _let_1 I2) X6)) I) X))))) (forall ((I tptp.nat) (I2 tptp.nat) (Xs tptp.list_d) (X tptp.d) (X6 tptp.d)) (let ((_let_1 (@ tptp.list_update_d Xs))) (=> (not (= I I2)) (= (@ (@ (@ tptp.list_update_d (@ (@ _let_1 I) X)) I2) X6) (@ (@ (@ tptp.list_update_d (@ (@ _let_1 I2) X6)) I) X))))) (forall ((A2 tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.insert9069300056098147895at_nat A2))) (= (@ _let_1 (@ (@ tptp.minus_3314409938677909166at_nat A) (@ _let_1 tptp.bot_bo228742789529271731at_nat))) (@ _let_1 A)))) (forall ((A2 tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A2))) (= (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A) (@ _let_1 tptp.bot_bo2099793752762293965at_nat))) (@ _let_1 A)))) (forall ((A2 Bool) (A tptp.set_o)) (let ((_let_1 (@ 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tptp.minus_minus_set_o A) tptp.bot_bot_set_o) A)) (forall ((A tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int A) tptp.bot_bot_set_int) A)) (forall ((A tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat A) tptp.bot_bot_set_nat) A)) (forall ((A tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.minus_3314409938677909166at_nat tptp.bot_bo228742789529271731at_nat) A) tptp.bot_bo228742789529271731at_nat)) (forall ((A tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.minus_1356011639430497352at_nat tptp.bot_bo2099793752762293965at_nat) A) tptp.bot_bo2099793752762293965at_nat)) (forall ((A tptp.set_o)) (= (@ (@ tptp.minus_minus_set_o tptp.bot_bot_set_o) A) tptp.bot_bot_set_o)) (forall ((A tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int tptp.bot_bot_set_int) A) tptp.bot_bot_set_int)) (forall ((A tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat tptp.bot_bot_set_nat) A) tptp.bot_bot_set_nat)) (forall ((A tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.minus_3314409938677909166at_nat A) A) tptp.bot_bo228742789529271731at_nat)) (forall ((A tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.minus_1356011639430497352at_nat A) A) tptp.bot_bo2099793752762293965at_nat)) (forall ((A tptp.set_o)) (= (@ (@ tptp.minus_minus_set_o A) A) tptp.bot_bot_set_o)) (forall ((A tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int A) A) tptp.bot_bot_set_int)) (forall ((A tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat A) A) tptp.bot_bot_set_nat)) (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool))) (@ (@ tptp.member6576561426505652726_nat_o A2) (@ (@ tptp.insert5175938949040314269_nat_o A2) tptp.bot_bo7824918357723582233_nat_o))) (forall ((A2 tptp.produc3843707927480180839at_nat)) (@ (@ tptp.member8757157785044589968at_nat A2) (@ (@ tptp.insert9069300056098147895at_nat A2) tptp.bot_bo228742789529271731at_nat))) (forall ((A2 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat A2) (@ (@ tptp.insert8211810215607154385at_nat A2) tptp.bot_bo2099793752762293965at_nat))) (forall ((A2 Bool)) (@ (@ tptp.member_o A2) (@ (@ tptp.insert_o2 A2) tptp.bot_bot_set_o))) (forall ((A2 tptp.nat)) (@ (@ tptp.member_nat A2) (@ (@ tptp.insert_nat2 A2) tptp.bot_bot_set_nat))) (forall ((A2 tptp.int)) (@ (@ tptp.member_int A2) (@ (@ tptp.insert_int2 A2) tptp.bot_bot_set_int))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (A2 tptp.produc3843707927480180839at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.insert9069300056098147895at_nat A2))) (let ((_let_2 (@ tptp.minus_3314409938677909166at_nat A))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_3314409938677909166at_nat (@ _let_2 B)) (@ _let_1 tptp.bot_bo228742789529271731at_nat)))))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (A2 tptp.product_prod_nat_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A2))) (let ((_let_2 (@ tptp.minus_1356011639430497352at_nat A))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_2 B)) (@ _let_1 tptp.bot_bo2099793752762293965at_nat)))))) (forall ((A tptp.set_o) (A2 Bool) (B tptp.set_o)) (let ((_let_1 (@ tptp.insert_o2 A2))) (let ((_let_2 (@ tptp.minus_minus_set_o A))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_minus_set_o (@ _let_2 B)) (@ _let_1 tptp.bot_bot_set_o)))))) (forall ((A tptp.set_int) (A2 tptp.int) (B tptp.set_int)) (let ((_let_1 (@ tptp.insert_int2 A2))) (let ((_let_2 (@ tptp.minus_minus_set_int A))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_minus_set_int (@ _let_2 B)) (@ _let_1 tptp.bot_bot_set_int)))))) (forall ((A tptp.set_nat) (A2 tptp.nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat2 A2))) (let ((_let_2 (@ tptp.minus_minus_set_nat A))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_minus_set_nat (@ _let_2 B)) (@ _let_1 tptp.bot_bot_set_nat)))))) (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.insert5175938949040314269_nat_o A2))) (=> (@ (@ tptp.member6576561426505652726_nat_o A2) A) (= (@ _let_1 (@ (@ tptp.minus_1801376950450012436_nat_o A) (@ _let_1 tptp.bot_bo7824918357723582233_nat_o))) A)))) (forall ((A2 tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.insert9069300056098147895at_nat A2))) (=> (@ (@ tptp.member8757157785044589968at_nat A2) A) (= (@ _let_1 (@ (@ tptp.minus_3314409938677909166at_nat A) (@ _let_1 tptp.bot_bo228742789529271731at_nat))) A)))) (forall ((A2 tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A2))) (=> (@ (@ tptp.member8440522571783428010at_nat A2) A) (= (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A) (@ _let_1 tptp.bot_bo2099793752762293965at_nat))) A)))) (forall ((A2 Bool) (A tptp.set_o)) (let ((_let_1 (@ tptp.insert_o2 A2))) (=> (@ (@ tptp.member_o A2) A) (= (@ _let_1 (@ (@ tptp.minus_minus_set_o A) (@ _let_1 tptp.bot_bot_set_o))) A)))) (forall ((A2 tptp.int) (A tptp.set_int)) (let ((_let_1 (@ tptp.insert_int2 A2))) (=> (@ (@ tptp.member_int A2) A) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A) (@ _let_1 tptp.bot_bot_set_int))) A)))) (forall ((A2 tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat2 A2))) (=> (@ (@ tptp.member_nat A2) A) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) (@ _let_1 tptp.bot_bot_set_nat))) A)))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (A2 tptp.produc3843707927480180839at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.insert9069300056098147895at_nat A2))) (let ((_let_2 (@ tptp.minus_3314409938677909166at_nat A))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_3314409938677909166at_nat (@ _let_2 (@ _let_1 tptp.bot_bo228742789529271731at_nat))) B))))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (A2 tptp.product_prod_nat_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A2))) (let ((_let_2 (@ tptp.minus_1356011639430497352at_nat A))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_2 (@ _let_1 tptp.bot_bo2099793752762293965at_nat))) B))))) (forall ((A tptp.set_o) (A2 Bool) (B tptp.set_o)) (let ((_let_1 (@ tptp.insert_o2 A2))) (let ((_let_2 (@ tptp.minus_minus_set_o A))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_minus_set_o (@ _let_2 (@ _let_1 tptp.bot_bot_set_o))) B))))) (forall ((A tptp.set_int) (A2 tptp.int) (B tptp.set_int)) (let ((_let_1 (@ tptp.insert_int2 A2))) (let ((_let_2 (@ tptp.minus_minus_set_int A))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_minus_set_int (@ _let_2 (@ _let_1 tptp.bot_bot_set_int))) B))))) (forall ((A tptp.set_nat) (A2 tptp.nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat2 A2))) (let ((_let_2 (@ tptp.minus_minus_set_nat A))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_minus_set_nat (@ _let_2 (@ _let_1 tptp.bot_bot_set_nat))) B))))) (forall ((X tptp.produc3843707927480180839at_nat) (Y tptp.produc3843707927480180839at_nat) (A 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 A)) _let_1) (@ _let_2 (@ (@ tptp.minus_3314409938677909166at_nat A) _let_1))))))) (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat) (A 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 A)) _let_1) (@ _let_2 (@ (@ tptp.minus_1356011639430497352at_nat A) _let_1))))))) (forall ((X Bool) (Y Bool) (A tptp.set_o)) (let ((_let_1 (@ (@ tptp.insert_o2 Y) tptp.bot_bot_set_o))) (let ((_let_2 (@ tptp.insert_o2 X))) (=> (not (= X Y)) (= (@ (@ tptp.minus_minus_set_o (@ _let_2 A)) _let_1) (@ _let_2 (@ (@ tptp.minus_minus_set_o A) _let_1))))))) (forall ((X tptp.int) (Y tptp.int) (A tptp.set_int)) (let ((_let_1 (@ (@ tptp.insert_int2 Y) tptp.bot_bot_set_int))) (let ((_let_2 (@ tptp.insert_int2 X))) (=> (not (= X Y)) (= (@ (@ tptp.minus_minus_set_int (@ _let_2 A)) _let_1) (@ _let_2 (@ (@ tptp.minus_minus_set_int A) _let_1))))))) (forall ((X tptp.nat) (Y tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ (@ tptp.insert_nat2 Y) tptp.bot_bot_set_nat))) (let ((_let_2 (@ tptp.insert_nat2 X))) (=> (not (= X Y)) (= (@ (@ tptp.minus_minus_set_nat (@ _let_2 A)) _let_1) (@ _let_2 (@ (@ tptp.minus_minus_set_nat A) _let_1))))))) (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.insert5175938949040314269_nat_o X))) (=> (not (@ (@ tptp.member6576561426505652726_nat_o X) A)) (= (@ (@ tptp.minus_1801376950450012436_nat_o (@ _let_1 A)) (@ _let_1 tptp.bot_bo7824918357723582233_nat_o)) A)))) (forall ((X tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.insert9069300056098147895at_nat X))) (=> (not (@ (@ tptp.member8757157785044589968at_nat X) A)) (= (@ (@ tptp.minus_3314409938677909166at_nat (@ _let_1 A)) (@ _let_1 tptp.bot_bo228742789529271731at_nat)) A)))) (forall ((X tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat X))) (=> (not (@ (@ tptp.member8440522571783428010at_nat X) A)) (= (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_1 A)) (@ _let_1 tptp.bot_bo2099793752762293965at_nat)) A)))) (forall ((X Bool) (A tptp.set_o)) (let ((_let_1 (@ tptp.insert_o2 X))) (=> (not (@ (@ tptp.member_o X) A)) (= (@ (@ tptp.minus_minus_set_o (@ _let_1 A)) (@ _let_1 tptp.bot_bot_set_o)) A)))) (forall ((X tptp.int) (A tptp.set_int)) (let ((_let_1 (@ tptp.insert_int2 X))) (=> (not (@ (@ tptp.member_int X) A)) (= (@ (@ tptp.minus_minus_set_int (@ _let_1 A)) (@ _let_1 tptp.bot_bot_set_int)) A)))) (forall ((X tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat2 X))) (=> (not (@ (@ tptp.member_nat X) A)) (= (@ (@ tptp.minus_minus_set_nat (@ _let_1 A)) (@ _let_1 tptp.bot_bot_set_nat)) A)))) (forall ((P (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (= (= tptp.bot_bo7824918357723582233_nat_o (@ tptp.collec939566748876313656_nat_o P)) (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (not (@ P X2))))) (forall ((P (-> tptp.produc3843707927480180839at_nat Bool))) (= (= tptp.bot_bo228742789529271731at_nat (@ tptp.collec6321179662152712658at_nat P)) (forall ((X2 tptp.produc3843707927480180839at_nat)) (not (@ P X2))))) (forall ((P (-> tptp.product_prod_nat_nat Bool))) (= (= tptp.bot_bo2099793752762293965at_nat (@ tptp.collec3392354462482085612at_nat P)) (forall ((X2 tptp.product_prod_nat_nat)) (not (@ P X2))))) (forall ((P (-> Bool Bool))) (= (= tptp.bot_bot_set_o (@ tptp.collect_o P)) (forall ((X2 Bool)) (not (@ P X2))))) (forall ((P (-> tptp.nat Bool))) (= (= tptp.bot_bot_set_nat (@ tptp.collect_nat P)) (forall ((X2 tptp.nat)) (not (@ P X2))))) (forall ((P (-> tptp.int Bool))) (= (= tptp.bot_bot_set_int (@ tptp.collect_int P)) (forall ((X2 tptp.int)) (not (@ P X2))))) (forall ((P (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (= (= (@ tptp.collec939566748876313656_nat_o P) tptp.bot_bo7824918357723582233_nat_o) (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (not (@ P X2))))) (forall ((P (-> tptp.produc3843707927480180839at_nat Bool))) (= (= (@ tptp.collec6321179662152712658at_nat P) tptp.bot_bo228742789529271731at_nat) (forall ((X2 tptp.produc3843707927480180839at_nat)) (not (@ P X2))))) (forall ((P (-> tptp.product_prod_nat_nat Bool))) (= (= (@ tptp.collec3392354462482085612at_nat P) tptp.bot_bo2099793752762293965at_nat) (forall ((X2 tptp.product_prod_nat_nat)) (not (@ P X2))))) (forall ((P (-> Bool Bool))) (= (= (@ tptp.collect_o P) tptp.bot_bot_set_o) (forall ((X2 Bool)) (not (@ P X2))))) (forall ((P (-> tptp.nat Bool))) (= (= (@ tptp.collect_nat P) tptp.bot_bot_set_nat) (forall ((X2 tptp.nat)) (not (@ P X2))))) (forall ((P (-> tptp.int Bool))) (= (= (@ tptp.collect_int P) tptp.bot_bot_set_int) (forall ((X2 tptp.int)) (not (@ P X2))))) (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (= (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (not (@ (@ tptp.member6576561426505652726_nat_o X2) A))) (= A tptp.bot_bo7824918357723582233_nat_o))) (forall ((A tptp.set_Pr4329608150637261639at_nat)) (= (forall ((X2 tptp.produc3843707927480180839at_nat)) (not (@ (@ tptp.member8757157785044589968at_nat X2) A))) (= A tptp.bot_bo228742789529271731at_nat))) (forall ((A tptp.set_Pr1261947904930325089at_nat)) (= (forall ((X2 tptp.product_prod_nat_nat)) (not (@ (@ tptp.member8440522571783428010at_nat X2) A))) (= A tptp.bot_bo2099793752762293965at_nat))) (forall ((A tptp.set_o)) (= (forall ((X2 Bool)) (not (@ (@ tptp.member_o X2) A))) (= A tptp.bot_bot_set_o))) (forall ((A tptp.set_nat)) (= (forall ((X2 tptp.nat)) (not (@ (@ tptp.member_nat X2) A))) (= A tptp.bot_bot_set_nat))) (forall ((A tptp.set_int)) (= (forall ((X2 tptp.int)) (not (@ (@ tptp.member_int X2) A))) (= A tptp.bot_bot_set_int))) (forall ((C (-> tptp.produc3658429121746597890et_nat Bool))) (not (@ (@ tptp.member6576561426505652726_nat_o C) tptp.bot_bo7824918357723582233_nat_o))) (forall ((C tptp.produc3843707927480180839at_nat)) (not (@ (@ tptp.member8757157785044589968at_nat C) tptp.bot_bo228742789529271731at_nat))) (forall ((C tptp.product_prod_nat_nat)) (not (@ (@ tptp.member8440522571783428010at_nat C) tptp.bot_bo2099793752762293965at_nat))) (forall ((C Bool)) (not (@ (@ tptp.member_o C) tptp.bot_bot_set_o))) (forall ((C tptp.nat)) (not (@ (@ tptp.member_nat C) tptp.bot_bot_set_nat))) (forall ((C tptp.int)) (not (@ (@ tptp.member_int C) tptp.bot_bot_set_int))) (forall ((A2 Bool) (B tptp.set_o) (B2 Bool)) (let ((_let_1 (@ tptp.member_o A2))) (=> (=> (not (@ _let_1 B)) (= A2 B2)) (@ _let_1 (@ (@ tptp.insert_o2 B2) B))))) (forall ((A2 tptp.produc3843707927480180839at_nat) (B tptp.set_Pr4329608150637261639at_nat) (B2 tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat A2))) (=> (=> (not (@ _let_1 B)) (= A2 B2)) (@ _let_1 (@ (@ tptp.insert9069300056098147895at_nat B2) B))))) (forall ((A2 tptp.product_prod_nat_nat) (B tptp.set_Pr1261947904930325089at_nat) (B2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat A2))) (=> (=> (not (@ _let_1 B)) (= A2 B2)) (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat B2) B))))) (forall ((A2 tptp.nat) (B tptp.set_nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat A2))) (=> (=> (not (@ _let_1 B)) (= A2 B2)) (@ _let_1 (@ (@ tptp.insert_nat2 B2) B))))) (forall ((A2 tptp.int) (B tptp.set_int) (B2 tptp.int)) (let ((_let_1 (@ tptp.member_int A2))) (=> (=> (not (@ _let_1 B)) (= A2 B2)) (@ 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_let_2)))) (forall ((X tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat X))) (let ((_let_2 (@ _let_1 A))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.insert9069300056098147895at_nat X))) (let ((_let_2 (@ _let_1 A))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X Bool) (A tptp.set_o)) (let ((_let_1 (@ tptp.insert_o2 X))) (let ((_let_2 (@ _let_1 A))) (= (@ _let_1 _let_2) _let_2)))) (forall ((C tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.minus_3314409938677909166at_nat A) B)))))) (forall ((C tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A) B)))))) (forall ((C tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A) B)))))) (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.minus_1801376950450012436_nat_o A) B)))))) (forall ((C tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B)))))) (forall ((C tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (= (@ _let_1 (@ (@ tptp.minus_3314409938677909166at_nat A) B)) (and (@ _let_1 A) (not (@ _let_1 B)))))) (forall ((C tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (= (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A) B)) (and (@ _let_1 A) (not (@ _let_1 B)))))) (forall ((C tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A) B)) (and (@ _let_1 A) (not (@ _let_1 B)))))) (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (= (@ _let_1 (@ (@ tptp.minus_1801376950450012436_nat_o A) B)) (and (@ _let_1 A) (not (@ _let_1 B)))))) (forall ((C tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ 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(@ (@ tptp.member8757157785044589968at_nat B4) (@ (@ tptp.minus_3314409938677909166at_nat B) A))))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat A) B) (exists ((B4 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat B4) (@ (@ tptp.minus_1356011639430497352at_nat B) A))))) (forall ((A tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A) B) (exists ((B4 tptp.int)) (@ (@ tptp.member_int B4) (@ (@ tptp.minus_minus_set_int B) A))))) (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.ord_le2453136405763929_nat_o A) B) (exists ((B4 (-> tptp.produc3658429121746597890et_nat Bool))) (@ (@ tptp.member6576561426505652726_nat_o B4) (@ (@ tptp.minus_1801376950450012436_nat_o B) A))))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A) B) (exists ((B4 tptp.nat)) (@ (@ tptp.member_nat B4) (@ (@ 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(=> (@ (@ tptp.member6576561426505652726_nat_o A2) A) (exists ((B5 tptp.set_Pr4532377907799695533_nat_o)) (and (= A (@ (@ tptp.insert5175938949040314269_nat_o A2) B5)) (not (@ (@ tptp.member6576561426505652726_nat_o A2) B5)))))) (forall ((C tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_3314409938677909166at_nat A) B)) (not (=> (@ _let_1 A) (@ _let_1 B)))))) (forall ((C tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A) B)) (not (=> (@ _let_1 A) (@ _let_1 B)))))) (forall ((C tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A) B)) (not (=> (@ _let_1 A) (@ _let_1 B)))))) (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ _let_1 (@ (@ tptp.minus_1801376950450012436_nat_o A) B)) (not (=> (@ _let_1 A) (@ _let_1 B)))))) (forall ((C tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B)) (not (=> (@ _let_1 A) (@ _let_1 B)))))) (forall ((C tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_3314409938677909166at_nat A) B)) (@ _let_1 A)))) (forall ((C tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A) B)) (@ _let_1 A)))) (forall ((C tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A) B)) (@ _let_1 A)))) (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ _let_1 (@ (@ tptp.minus_1801376950450012436_nat_o A) B)) (@ _let_1 A)))) (forall ((C tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B)) (@ _let_1 A)))) (forall ((C tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_3314409938677909166at_nat A) B)) (not (@ _let_1 B))))) (forall ((C tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A) B)) (not (@ _let_1 B))))) (forall ((C tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A) B)) (not (@ _let_1 B))))) (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ _let_1 (@ (@ tptp.minus_1801376950450012436_nat_o A) B)) (not (@ _let_1 B))))) (forall ((C tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B)) (not (@ _let_1 B))))) (forall ((A2 tptp.produc3843707927480180839at_nat) (B2 tptp.produc3843707927480180839at_nat)) (=> (= (@ (@ tptp.insert9069300056098147895at_nat A2) tptp.bot_bo228742789529271731at_nat) (@ (@ tptp.insert9069300056098147895at_nat B2) tptp.bot_bo228742789529271731at_nat)) (= A2 B2))) (forall ((A2 tptp.product_prod_nat_nat) (B2 tptp.product_prod_nat_nat)) (=> (= (@ (@ tptp.insert8211810215607154385at_nat A2) tptp.bot_bo2099793752762293965at_nat) (@ (@ tptp.insert8211810215607154385at_nat B2) tptp.bot_bo2099793752762293965at_nat)) (= A2 B2))) (forall ((A2 Bool) (B2 Bool)) (=> (= (@ (@ tptp.insert_o2 A2) tptp.bot_bot_set_o) (@ (@ tptp.insert_o2 B2) tptp.bot_bot_set_o)) (= A2 B2))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (= (@ (@ tptp.insert_nat2 A2) tptp.bot_bot_set_nat) (@ (@ tptp.insert_nat2 B2) tptp.bot_bot_set_nat)) (= A2 B2))) (forall ((A2 tptp.int) (B2 tptp.int)) (=> (= (@ (@ tptp.insert_int2 A2) tptp.bot_bot_set_int) (@ (@ tptp.insert_int2 B2) tptp.bot_bot_set_int)) (= A2 B2))) (forall ((A2 tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (not (= (@ (@ tptp.insert9069300056098147895at_nat A2) A) tptp.bot_bo228742789529271731at_nat))) (forall ((A2 tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat)) (not (= (@ (@ tptp.insert8211810215607154385at_nat A2) A) tptp.bot_bo2099793752762293965at_nat))) (forall ((A2 Bool) (A tptp.set_o)) (not (= (@ (@ tptp.insert_o2 A2) A) tptp.bot_bot_set_o))) (forall ((A2 tptp.nat) (A tptp.set_nat)) (not (= (@ (@ tptp.insert_nat2 A2) A) tptp.bot_bot_set_nat))) (forall ((A2 tptp.int) (A tptp.set_int)) (not (= (@ (@ tptp.insert_int2 A2) A) tptp.bot_bot_set_int))) (forall ((A2 tptp.produc3843707927480180839at_nat) (B2 tptp.produc3843707927480180839at_nat) (C tptp.produc3843707927480180839at_nat) (D2 tptp.produc3843707927480180839at_nat)) (= (= (@ (@ tptp.insert9069300056098147895at_nat A2) (@ (@ tptp.insert9069300056098147895at_nat B2) tptp.bot_bo228742789529271731at_nat)) (@ (@ tptp.insert9069300056098147895at_nat C) (@ (@ tptp.insert9069300056098147895at_nat D2) tptp.bot_bo228742789529271731at_nat))) (or (and (= A2 C) (= B2 D2)) (and (= A2 D2) (= B2 C))))) (forall ((A2 tptp.product_prod_nat_nat) (B2 tptp.product_prod_nat_nat) (C tptp.product_prod_nat_nat) (D2 tptp.product_prod_nat_nat)) (= (= (@ (@ tptp.insert8211810215607154385at_nat A2) (@ (@ tptp.insert8211810215607154385at_nat B2) tptp.bot_bo2099793752762293965at_nat)) (@ (@ tptp.insert8211810215607154385at_nat C) (@ (@ tptp.insert8211810215607154385at_nat D2) tptp.bot_bo2099793752762293965at_nat))) (or (and (= A2 C) (= B2 D2)) (and (= A2 D2) (= B2 C))))) (forall ((A2 Bool) (B2 Bool) (C Bool) (D2 Bool)) (= (= (@ (@ tptp.insert_o2 A2) (@ (@ tptp.insert_o2 B2) tptp.bot_bot_set_o)) (@ (@ tptp.insert_o2 C) (@ (@ tptp.insert_o2 D2) tptp.bot_bot_set_o))) (or (and (= A2 C) (= B2 D2)) (and (= A2 D2) (= B2 C))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat) (D2 tptp.nat)) (= (= (@ (@ tptp.insert_nat2 A2) (@ (@ tptp.insert_nat2 B2) tptp.bot_bot_set_nat)) (@ (@ tptp.insert_nat2 C) (@ (@ tptp.insert_nat2 D2) tptp.bot_bot_set_nat))) (or (and (= A2 C) (= B2 D2)) (and (= A2 D2) (= B2 C))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int) (D2 tptp.int)) (= (= (@ (@ tptp.insert_int2 A2) (@ (@ tptp.insert_int2 B2) tptp.bot_bot_set_int)) (@ (@ tptp.insert_int2 C) (@ (@ tptp.insert_int2 D2) tptp.bot_bot_set_int))) (or (and (= A2 C) (= B2 D2)) (and (= A2 D2) (= B2 C))))) (forall ((B2 (-> tptp.produc3658429121746597890et_nat Bool)) (A2 (-> tptp.produc3658429121746597890et_nat Bool))) (= (@ (@ tptp.member6576561426505652726_nat_o B2) (@ (@ tptp.insert5175938949040314269_nat_o A2) tptp.bot_bo7824918357723582233_nat_o)) (= B2 A2))) (forall ((B2 tptp.produc3843707927480180839at_nat) (A2 tptp.produc3843707927480180839at_nat)) (= (@ (@ tptp.member8757157785044589968at_nat B2) (@ (@ tptp.insert9069300056098147895at_nat A2) tptp.bot_bo228742789529271731at_nat)) (= B2 A2))) (forall ((B2 tptp.product_prod_nat_nat) (A2 tptp.product_prod_nat_nat)) (= (@ (@ tptp.member8440522571783428010at_nat B2) (@ (@ tptp.insert8211810215607154385at_nat A2) tptp.bot_bo2099793752762293965at_nat)) (= B2 A2))) (forall ((B2 Bool) (A2 Bool)) (= (@ (@ tptp.member_o B2) (@ (@ tptp.insert_o2 A2) tptp.bot_bot_set_o)) (= B2 A2))) (forall ((B2 tptp.nat) (A2 tptp.nat)) (= (@ (@ tptp.member_nat B2) (@ (@ tptp.insert_nat2 A2) tptp.bot_bot_set_nat)) (= B2 A2))) (forall ((B2 tptp.int) (A2 tptp.int)) (= (@ (@ tptp.member_int B2) (@ (@ tptp.insert_int2 A2) tptp.bot_bot_set_int)) (= B2 A2))) (forall ((B2 (-> tptp.produc3658429121746597890et_nat Bool)) (A2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o B2) (@ (@ tptp.insert5175938949040314269_nat_o A2) tptp.bot_bo7824918357723582233_nat_o)) (= B2 A2))) (forall ((B2 tptp.produc3843707927480180839at_nat) (A2 tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat B2) (@ (@ tptp.insert9069300056098147895at_nat A2) tptp.bot_bo228742789529271731at_nat)) (= B2 A2))) (forall ((B2 tptp.product_prod_nat_nat) (A2 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat B2) (@ (@ tptp.insert8211810215607154385at_nat A2) tptp.bot_bo2099793752762293965at_nat)) (= B2 A2))) (forall ((B2 Bool) (A2 Bool)) (=> (@ (@ tptp.member_o B2) (@ (@ tptp.insert_o2 A2) tptp.bot_bot_set_o)) (= B2 A2))) (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.member_nat B2) (@ (@ tptp.insert_nat2 A2) tptp.bot_bot_set_nat)) (= B2 A2))) (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.insert_int2 A2) tptp.bot_bot_set_int)) (= B2 A2))) (forall ((X Bool) (B tptp.set_o) (A tptp.set_o)) (let ((_let_1 (@ (@ tptp.minus_minus_set_o A) B))) (let ((_let_2 (@ tptp.insert_o2 X))) (let ((_let_3 (@ (@ tptp.minus_minus_set_o (@ _let_2 A)) B))) (let ((_let_4 (@ (@ tptp.member_o X) B))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))) (forall ((X tptp.produc3843707927480180839at_nat) (B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ (@ tptp.minus_3314409938677909166at_nat A) B))) (let ((_let_2 (@ tptp.insert9069300056098147895at_nat X))) (let ((_let_3 (@ (@ tptp.minus_3314409938677909166at_nat (@ _let_2 A)) B))) (let ((_let_4 (@ (@ tptp.member8757157785044589968at_nat X) B))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))) (forall ((X tptp.product_prod_nat_nat) (B tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ tptp.minus_1356011639430497352at_nat A) B))) (let ((_let_2 (@ tptp.insert8211810215607154385at_nat X))) (let ((_let_3 (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_2 A)) B))) (let ((_let_4 (@ (@ tptp.member8440522571783428010at_nat X) B))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))) (forall ((X tptp.int) (B tptp.set_int) (A tptp.set_int)) (let ((_let_1 (@ (@ tptp.minus_minus_set_int A) B))) (let ((_let_2 (@ tptp.insert_int2 X))) (let ((_let_3 (@ (@ tptp.minus_minus_set_int (@ _let_2 A)) B))) (let ((_let_4 (@ (@ tptp.member_int X) B))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))) (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.set_Pr4532377907799695533_nat_o) (A tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ (@ tptp.minus_1801376950450012436_nat_o A) B))) (let ((_let_2 (@ tptp.insert5175938949040314269_nat_o X))) (let ((_let_3 (@ (@ tptp.minus_1801376950450012436_nat_o (@ _let_2 A)) B))) (let ((_let_4 (@ (@ tptp.member6576561426505652726_nat_o X) B))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))) (forall ((X tptp.nat) (B tptp.set_nat) (A tptp.set_nat)) (let ((_let_1 (@ (@ tptp.minus_minus_set_nat A) B))) (let ((_let_2 (@ tptp.insert_nat2 X))) (let ((_let_3 (@ (@ tptp.minus_minus_set_nat (@ _let_2 A)) B))) (let ((_let_4 (@ (@ tptp.member_nat X) B))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))) (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (X4 tptp.set_Pr4532377907799695533_nat_o)) (=> (not (@ (@ tptp.member6576561426505652726_nat_o X) X4)) (= (@ (@ tptp.minus_1801376950450012436_nat_o X4) (@ (@ tptp.insert5175938949040314269_nat_o X) tptp.bot_bo7824918357723582233_nat_o)) X4))) (forall ((X tptp.produc3843707927480180839at_nat) (X4 tptp.set_Pr4329608150637261639at_nat)) (=> (not (@ (@ tptp.member8757157785044589968at_nat X) X4)) (= (@ (@ tptp.minus_3314409938677909166at_nat X4) (@ (@ tptp.insert9069300056098147895at_nat X) tptp.bot_bo228742789529271731at_nat)) X4))) (forall ((X tptp.product_prod_nat_nat) (X4 tptp.set_Pr1261947904930325089at_nat)) (=> (not (@ (@ tptp.member8440522571783428010at_nat X) X4)) (= (@ (@ tptp.minus_1356011639430497352at_nat X4) (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat)) X4))) (forall ((X Bool) (X4 tptp.set_o)) (=> (not (@ (@ tptp.member_o X) X4)) (= (@ (@ tptp.minus_minus_set_o X4) (@ (@ tptp.insert_o2 X) tptp.bot_bot_set_o)) X4))) (forall ((X tptp.int) (X4 tptp.set_int)) (=> (not (@ (@ tptp.member_int X) X4)) (= (@ (@ tptp.minus_minus_set_int X4) (@ (@ tptp.insert_int2 X) tptp.bot_bot_set_int)) X4))) (forall ((X tptp.nat) (X4 tptp.set_nat)) (=> (not (@ (@ tptp.member_nat X) X4)) (= (@ (@ tptp.minus_minus_set_nat X4) (@ (@ tptp.insert_nat2 X) tptp.bot_bot_set_nat)) X4))) (forall ((P tptp.assn) (A (-> tptp.c tptp.nat tptp.assn)) (Xs tptp.list_c) (I tptp.nat) (Xsi tptp.list_nat) (I3 tptp.set_nat) (F tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_c Xs) I)) (@ (@ tptp.nth_nat Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L6585172037124793648_c_nat (@ (@ tptp.minus_minus_set_nat I3) (@ (@ tptp.insert_nat2 I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_c Xs)) (=> (@ (@ tptp.member_nat I) I3) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L6585172037124793648_c_nat I3) A) Xs) Xsi)) F)) Q) (@ _let_1 Q))))))) (forall ((P tptp.assn) (A (-> tptp.c tptp.int tptp.assn)) (Xs tptp.list_c) (I tptp.nat) (Xsi tptp.list_int) (I3 tptp.set_nat) (F tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_c Xs) I)) (@ (@ tptp.nth_int Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L6582681566615743372_c_int (@ (@ tptp.minus_minus_set_nat I3) (@ (@ tptp.insert_nat2 I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_c Xs)) (=> (@ (@ tptp.member_nat I) I3) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L6582681566615743372_c_int I3) A) Xs) Xsi)) F)) Q) (@ _let_1 Q))))))) (forall ((P tptp.assn) (A (-> tptp.d tptp.nat tptp.assn)) (Xs tptp.list_d) (I tptp.nat) (Xsi tptp.list_nat) (I3 tptp.set_nat) (F tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_d Xs) I)) (@ (@ tptp.nth_nat Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7820616366081188145_d_nat (@ (@ tptp.minus_minus_set_nat I3) (@ (@ tptp.insert_nat2 I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_d Xs)) (=> (@ (@ tptp.member_nat I) I3) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L7820616366081188145_d_nat I3) A) Xs) Xsi)) F)) Q) (@ _let_1 Q))))))) (forall ((P tptp.assn) (A (-> tptp.d tptp.int tptp.assn)) (Xs tptp.list_d) (I tptp.nat) (Xsi tptp.list_int) (I3 tptp.set_nat) (F tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_d Xs) I)) (@ (@ tptp.nth_int Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7818125895572137869_d_int (@ (@ tptp.minus_minus_set_nat I3) (@ (@ tptp.insert_nat2 I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_d Xs)) (=> (@ (@ tptp.member_nat I) I3) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L7818125895572137869_d_int I3) A) Xs) Xsi)) F)) Q) (@ _let_1 Q))))))) (forall ((P tptp.assn) (A (-> tptp.nat tptp.nat tptp.assn)) (Xs tptp.list_nat) (I tptp.nat) (Xsi tptp.list_nat) (I3 tptp.set_nat) (F tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_nat Xs) I)) (@ (@ tptp.nth_nat Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7892069108621897922at_nat (@ (@ tptp.minus_minus_set_nat I3) (@ (@ tptp.insert_nat2 I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs)) (=> (@ (@ tptp.member_nat I) I3) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L7892069108621897922at_nat I3) A) Xs) Xsi)) F)) Q) (@ _let_1 Q))))))) (forall ((P tptp.assn) (A (-> tptp.nat tptp.int tptp.assn)) (Xs tptp.list_nat) (I tptp.nat) (Xsi tptp.list_int) (I3 tptp.set_nat) (F tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_nat Xs) I)) (@ (@ tptp.nth_int Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7889578638112847646at_int (@ (@ tptp.minus_minus_set_nat I3) (@ (@ tptp.insert_nat2 I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs)) (=> (@ (@ tptp.member_nat I) I3) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L7889578638112847646at_int I3) A) Xs) Xsi)) F)) Q) (@ _let_1 Q))))))) (forall ((P tptp.assn) (A (-> tptp.int tptp.nat tptp.assn)) (Xs tptp.list_int) (I tptp.nat) (Xsi tptp.list_nat) (I3 tptp.set_nat) (F tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_int Xs) I)) (@ (@ tptp.nth_nat Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L8891422820522952478nt_nat (@ (@ tptp.minus_minus_set_nat I3) (@ (@ tptp.insert_nat2 I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs)) (=> (@ (@ tptp.member_nat I) I3) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L8891422820522952478nt_nat I3) A) Xs) Xsi)) F)) Q) (@ _let_1 Q))))))) (forall ((P tptp.assn) (A (-> tptp.int tptp.int tptp.assn)) (Xs tptp.list_int) (I tptp.nat) (Xsi tptp.list_int) (I3 tptp.set_nat) (F tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_int Xs) I)) (@ (@ tptp.nth_int Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L8888932350013902202nt_int (@ (@ tptp.minus_minus_set_nat I3) (@ (@ tptp.insert_nat2 I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs)) (=> (@ (@ tptp.member_nat I) I3) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L8888932350013902202nt_int I3) A) Xs) Xsi)) F)) Q) (@ _let_1 Q))))))) (forall ((P tptp.assn) (A (-> tptp.c tptp.d tptp.assn)) (Xs tptp.list_c) (I tptp.nat) (Xsi tptp.list_d) (I3 tptp.set_nat) (F tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_c Xs) I)) (@ (@ tptp.nth_d Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L824818263033719201sn_c_d (@ (@ tptp.minus_minus_set_nat I3) (@ (@ tptp.insert_nat2 I) tptp.bot_bot_set_nat))) A) Xs) Xsi))) F)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_c Xs)) (=> (@ (@ tptp.member_nat I) I3) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L824818263033719201sn_c_d I3) A) Xs) Xsi)) F)) Q) (@ _let_1 Q))))))) (forall ((X tptp.produc3843707927480180839at_nat)) (= (@ tptp.the_el221668144340439132at_nat (@ (@ tptp.insert9069300056098147895at_nat X) tptp.bot_bo228742789529271731at_nat)) X)) (forall ((X tptp.product_prod_nat_nat)) (= (@ tptp.the_el2281957884133575798at_nat (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat)) X)) (forall ((X Bool)) (= (@ tptp.the_elem_o (@ (@ tptp.insert_o2 X) tptp.bot_bot_set_o)) X)) (forall ((X tptp.nat)) (= (@ tptp.the_elem_nat (@ (@ tptp.insert_nat2 X) tptp.bot_bot_set_nat)) X)) (forall ((X tptp.int)) (= (@ tptp.the_elem_int (@ (@ tptp.insert_int2 X) tptp.bot_bot_set_int)) X)) (forall ((I tptp.nat) (I3 tptp.set_nat) (Xs tptp.list_c) (A (-> tptp.c tptp.nat tptp.assn)) (Xsi tptp.list_nat)) (=> (@ (@ tptp.member_nat I) I3) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_c Xs)) (= (@ (@ (@ (@ tptp.vEBT_L6585172037124793648_c_nat I3) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_c Xs) I)) (@ (@ tptp.nth_nat Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L6585172037124793648_c_nat (@ (@ tptp.minus_minus_set_nat I3) (@ (@ tptp.insert_nat2 I) tptp.bot_bot_set_nat))) A) Xs) Xsi)))))) (forall ((I tptp.nat) (I3 tptp.set_nat) (Xs tptp.list_c) (A (-> tptp.c tptp.int tptp.assn)) (Xsi tptp.list_int)) (=> (@ (@ tptp.member_nat I) I3) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_c Xs)) (= (@ (@ (@ (@ tptp.vEBT_L6582681566615743372_c_int I3) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_c Xs) I)) (@ (@ tptp.nth_int Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L6582681566615743372_c_int (@ (@ tptp.minus_minus_set_nat I3) (@ (@ tptp.insert_nat2 I) tptp.bot_bot_set_nat))) A) Xs) Xsi)))))) (forall ((I tptp.nat) (I3 tptp.set_nat) (Xs tptp.list_d) (A (-> tptp.d tptp.nat tptp.assn)) (Xsi tptp.list_nat)) (=> (@ (@ tptp.member_nat I) I3) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_d Xs)) (= (@ (@ (@ (@ tptp.vEBT_L7820616366081188145_d_nat I3) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_d Xs) I)) (@ (@ tptp.nth_nat Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7820616366081188145_d_nat (@ (@ tptp.minus_minus_set_nat I3) (@ (@ tptp.insert_nat2 I) tptp.bot_bot_set_nat))) A) Xs) Xsi)))))) (forall ((I tptp.nat) (I3 tptp.set_nat) (Xs tptp.list_d) (A (-> tptp.d tptp.int tptp.assn)) (Xsi tptp.list_int)) (=> (@ (@ tptp.member_nat I) I3) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_d Xs)) (= (@ (@ (@ (@ tptp.vEBT_L7818125895572137869_d_int I3) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_d Xs) I)) (@ (@ tptp.nth_int Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7818125895572137869_d_int (@ (@ tptp.minus_minus_set_nat I3) (@ (@ tptp.insert_nat2 I) tptp.bot_bot_set_nat))) A) Xs) Xsi)))))) (forall ((I tptp.nat) (I3 tptp.set_nat) (Xs tptp.list_nat) (A (-> tptp.nat tptp.nat tptp.assn)) (Xsi tptp.list_nat)) (=> (@ (@ tptp.member_nat I) I3) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs)) (= (@ (@ (@ (@ tptp.vEBT_L7892069108621897922at_nat I3) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_nat Xs) I)) (@ (@ tptp.nth_nat Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7892069108621897922at_nat (@ (@ tptp.minus_minus_set_nat I3) (@ (@ tptp.insert_nat2 I) tptp.bot_bot_set_nat))) A) Xs) Xsi)))))) (forall ((I tptp.nat) (I3 tptp.set_nat) (Xs tptp.list_nat) (A (-> tptp.nat tptp.int tptp.assn)) (Xsi tptp.list_int)) (=> (@ (@ tptp.member_nat I) I3) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs)) (= (@ (@ (@ (@ tptp.vEBT_L7889578638112847646at_int I3) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_nat Xs) I)) (@ (@ tptp.nth_int Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7889578638112847646at_int (@ (@ tptp.minus_minus_set_nat I3) (@ (@ tptp.insert_nat2 I) tptp.bot_bot_set_nat))) A) Xs) Xsi)))))) (forall ((I tptp.nat) (I3 tptp.set_nat) (Xs tptp.list_int) (A (-> tptp.int tptp.nat tptp.assn)) (Xsi tptp.list_nat)) (=> (@ (@ tptp.member_nat I) I3) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs)) (= (@ (@ (@ (@ tptp.vEBT_L8891422820522952478nt_nat I3) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_int Xs) I)) (@ (@ tptp.nth_nat Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L8891422820522952478nt_nat (@ (@ tptp.minus_minus_set_nat I3) (@ (@ tptp.insert_nat2 I) tptp.bot_bot_set_nat))) A) Xs) Xsi)))))) (forall ((I tptp.nat) (I3 tptp.set_nat) (Xs tptp.list_int) (A (-> tptp.int tptp.int tptp.assn)) (Xsi tptp.list_int)) (=> (@ (@ tptp.member_nat I) I3) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs)) (= (@ (@ (@ (@ tptp.vEBT_L8888932350013902202nt_int I3) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_int Xs) I)) (@ (@ tptp.nth_int Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L8888932350013902202nt_int (@ (@ tptp.minus_minus_set_nat I3) (@ (@ tptp.insert_nat2 I) tptp.bot_bot_set_nat))) A) Xs) Xsi)))))) (forall ((I tptp.nat) (I3 tptp.set_nat) (Xs tptp.list_c) (A (-> tptp.c tptp.d tptp.assn)) (Xsi tptp.list_d)) (=> (@ (@ tptp.member_nat I) I3) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_c Xs)) (= (@ (@ (@ (@ tptp.vEBT_L824818263033719201sn_c_d I3) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_c Xs) I)) (@ (@ tptp.nth_d Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L824818263033719201sn_c_d (@ (@ tptp.minus_minus_set_nat I3) (@ (@ tptp.insert_nat2 I) tptp.bot_bot_set_nat))) A) Xs) Xsi)))))) (forall ((X tptp.produc3843707927480180839at_nat)) (@ tptp.is_sin2937591304547752795at_nat (@ (@ tptp.insert9069300056098147895at_nat X) tptp.bot_bo228742789529271731at_nat))) (forall ((X tptp.product_prod_nat_nat)) (@ tptp.is_sin2850979758926227957at_nat (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat))) (forall ((X Bool)) (@ tptp.is_singleton_o (@ (@ tptp.insert_o2 X) tptp.bot_bot_set_o))) (forall ((X tptp.nat)) (@ tptp.is_singleton_nat (@ (@ tptp.insert_nat2 X) tptp.bot_bot_set_nat))) (forall ((X tptp.int)) (@ tptp.is_singleton_int (@ (@ tptp.insert_int2 X) tptp.bot_bot_set_int))) (forall ((P (-> tptp.code_integer Bool)) (D tptp.code_integer) (Q (-> tptp.code_integer Bool))) (=> (forall ((X3 tptp.code_integer) (K tptp.code_integer)) (= (@ P X3) (@ P (@ (@ tptp.minus_8373710615458151222nteger X3) (@ (@ tptp.times_3573771949741848930nteger K) D))))) (=> (forall ((X3 tptp.code_integer) (K tptp.code_integer)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_8373710615458151222nteger X3) (@ (@ tptp.times_3573771949741848930nteger K) D))))) (forall ((X7 tptp.code_integer) (K2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.minus_8373710615458151222nteger X7) (@ (@ tptp.times_3573771949741848930nteger K2) D)))) (= (or (@ P X7) (@ Q X7)) (or (@ P _let_1) (@ Q _let_1)))))))) (forall ((P (-> tptp.rat Bool)) (D tptp.rat) (Q (-> tptp.rat Bool))) (=> (forall ((X3 tptp.rat) (K tptp.rat)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K) D))))) (=> (forall ((X3 tptp.rat) (K tptp.rat)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K) D))))) (forall ((X7 tptp.rat) (K2 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X7) (@ (@ tptp.times_times_rat K2) D)))) (= (or (@ P X7) (@ Q X7)) (or (@ P _let_1) (@ Q _let_1)))))))) (forall ((P (-> tptp.int Bool)) (D tptp.int) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D))))) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D))))) (forall ((X7 tptp.int) (K2 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X7) (@ (@ tptp.times_times_int K2) D)))) (= (or (@ P X7) (@ Q X7)) (or (@ P _let_1) (@ Q _let_1)))))))) (forall ((P (-> tptp.code_integer Bool)) (D tptp.code_integer) (Q (-> tptp.code_integer Bool))) (=> (forall ((X3 tptp.code_integer) (K tptp.code_integer)) (= (@ P X3) (@ P (@ (@ tptp.minus_8373710615458151222nteger X3) (@ (@ tptp.times_3573771949741848930nteger K) D))))) (=> (forall ((X3 tptp.code_integer) (K tptp.code_integer)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_8373710615458151222nteger X3) (@ (@ tptp.times_3573771949741848930nteger K) D))))) (forall ((X7 tptp.code_integer) (K2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.minus_8373710615458151222nteger X7) (@ (@ tptp.times_3573771949741848930nteger K2) D)))) (= (and (@ P X7) (@ Q X7)) (and (@ P _let_1) (@ Q _let_1)))))))) (forall ((P (-> tptp.rat Bool)) (D tptp.rat) (Q (-> tptp.rat Bool))) (=> (forall ((X3 tptp.rat) (K tptp.rat)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K) D))))) (=> (forall ((X3 tptp.rat) (K tptp.rat)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K) D))))) (forall ((X7 tptp.rat) (K2 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X7) (@ (@ tptp.times_times_rat K2) D)))) (= (and (@ P X7) (@ Q X7)) (and (@ P _let_1) (@ Q _let_1)))))))) (forall ((P (-> tptp.int Bool)) (D tptp.int) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D))))) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D))))) (forall ((X7 tptp.int) (K2 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X7) (@ (@ tptp.times_times_int K2) D)))) (= (and (@ P X7) (@ Q X7)) (and (@ P _let_1) (@ Q _let_1)))))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger A2) B2)) C) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B2) C)))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A2) B2)) C) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B2) C)))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A2) B2)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B2) C)))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A2))) (= (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger B2) C)) (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 B2)) (@ _let_1 C))))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B2) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B2)) (@ _let_1 C))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B2) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B2)) (@ _let_1 C))))) (forall ((B2 tptp.code_integer) (C tptp.code_integer) (A2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger B2) C)) A2) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.times_3573771949741848930nteger B2) A2)) (@ (@ tptp.times_3573771949741848930nteger C) A2)))) (forall ((B2 tptp.rat) (C tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B2) C)) A2) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat B2) A2)) (@ (@ tptp.times_times_rat C) A2)))) (forall ((B2 tptp.nat) (C tptp.nat) (A2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat B2) C)) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat B2) A2)) (@ (@ tptp.times_times_nat C) A2)))) (forall ((B2 tptp.int) (C tptp.int) (A2 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B2) C)) A2) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int B2) A2)) (@ (@ tptp.times_times_int C) A2)))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A2))) (= (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger B2) C)) (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 B2)) (@ _let_1 C))))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B2) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B2)) (@ _let_1 C))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat B2) C)) (@ (@ tptp.minus_minus_nat (@ _let_1 B2)) (@ _let_1 C))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B2) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B2)) (@ _let_1 C))))) (forall ((A2 tptp.rat) (B2 tptp.rat) (D2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (@ (@ tptp.ord_less_rat D2) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A2) C)) (@ (@ tptp.minus_minus_rat B2) D2))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (D2 tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger D2) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.minus_8373710615458151222nteger A2) C)) (@ (@ tptp.minus_8373710615458151222nteger B2) D2))))) (forall ((A2 tptp.int) (B2 tptp.int) (D2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ (@ tptp.ord_less_int D2) C) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A2) C)) (@ (@ tptp.minus_minus_int B2) D2))))) (forall ((I tptp.nat) (J tptp.nat) (Xs tptp.list_nat) (X tptp.nat)) (=> (not (= I J)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs) I) X)) J) (@ (@ tptp.nth_nat Xs) J)))) (forall ((I tptp.nat) (J tptp.nat) (Xs tptp.list_int) (X tptp.int)) (=> (not (= I J)) (= (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs) I) X)) J) (@ (@ tptp.nth_int Xs) J)))) (forall ((I tptp.nat) (J tptp.nat) (Xs tptp.list_c) (X tptp.c)) (=> (not (= I J)) (= (@ (@ tptp.nth_c (@ (@ (@ tptp.list_update_c Xs) I) X)) J) (@ (@ tptp.nth_c Xs) J)))) (forall ((I tptp.nat) (J tptp.nat) (Xs tptp.list_d) (X tptp.d)) (=> (not (= I J)) (= (@ (@ tptp.nth_d (@ (@ (@ tptp.list_update_d Xs) I) X)) J) (@ (@ tptp.nth_d Xs) J)))) (forall ((Xs tptp.list_nat) (I tptp.nat)) (= (@ (@ (@ tptp.list_update_nat Xs) I) (@ (@ tptp.nth_nat Xs) I)) Xs)) (forall ((Xs tptp.list_int) (I tptp.nat)) (= (@ (@ (@ tptp.list_update_int Xs) I) (@ (@ tptp.nth_int Xs) I)) Xs)) (forall ((Xs tptp.list_c) (I tptp.nat)) (= (@ (@ (@ tptp.list_update_c Xs) I) (@ (@ tptp.nth_c Xs) I)) Xs)) (forall ((Xs tptp.list_d) (I tptp.nat)) (= (@ (@ (@ tptp.list_update_d Xs) I) (@ (@ tptp.nth_d Xs) I)) Xs)) (forall ((I tptp.nat) (Xs tptp.list_c) (X tptp.c)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_c Xs)) (= (@ (@ tptp.nth_c (@ (@ (@ tptp.list_update_c Xs) I) X)) I) X))) (forall ((I tptp.nat) (Xs tptp.list_d) (X tptp.d)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_d Xs)) (= (@ (@ tptp.nth_d (@ (@ (@ tptp.list_update_d Xs) I) X)) I) X))) (forall ((I tptp.nat) (Xs tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs) I) X)) I) X))) (forall ((I tptp.nat) (Xs tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs) I) X)) I) X))) (forall ((I tptp.nat) (L tptp.list_c) (J tptp.nat) (X tptp.c)) (=> (not (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_c L))) (= (@ (@ tptp.nth_c (@ (@ (@ tptp.list_update_c L) J) X)) I) (@ (@ tptp.nth_c L) I)))) (forall ((I tptp.nat) (L tptp.list_d) (J tptp.nat) (X tptp.d)) (=> (not (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_d L))) (= (@ (@ tptp.nth_d (@ (@ (@ tptp.list_update_d L) J) X)) I) (@ (@ tptp.nth_d L) I)))) (forall ((I tptp.nat) (L tptp.list_nat) (J tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat L))) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat L) J) X)) I) (@ (@ tptp.nth_nat L) I)))) (forall ((I tptp.nat) (L tptp.list_int) (J tptp.nat) (X tptp.int)) (=> (not (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int L))) (= (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int L) J) X)) I) (@ (@ tptp.nth_int L) I)))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (C tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (=> (@ (@ tptp.ord_le2604355607129572851at_nat A) B) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ (@ tptp.ord_le7866589430770878221at_nat A) B) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ (@ tptp.ord_less_set_nat A) B) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ (@ tptp.ord_less_set_int A) B) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o) (C (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ (@ tptp.ord_le2453136405763929_nat_o A) B) (=> (@ _let_1 A) (@ _let_1 B))))) (= (lambda ((Y4 tptp.list_c) (Z2 tptp.list_c)) (= Y4 Z2)) (lambda ((Xs3 tptp.list_c) (Ys3 tptp.list_c)) (and (= (@ tptp.size_size_list_c Xs3) (@ tptp.size_size_list_c Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_c Xs3)) (= (@ (@ tptp.nth_c Xs3) I4) (@ (@ tptp.nth_c Ys3) I4))))))) (= (lambda ((Y4 tptp.list_d) (Z2 tptp.list_d)) (= Y4 Z2)) (lambda ((Xs3 tptp.list_d) (Ys3 tptp.list_d)) (and (= (@ tptp.size_size_list_d Xs3) (@ tptp.size_size_list_d Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_d Xs3)) (= (@ (@ tptp.nth_d Xs3) I4) (@ (@ tptp.nth_d Ys3) I4))))))) (= (lambda ((Y4 tptp.list_nat) (Z2 tptp.list_nat)) (= Y4 Z2)) (lambda ((Xs3 tptp.list_nat) (Ys3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs3) (@ tptp.size_size_list_nat Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs3)) (= (@ (@ tptp.nth_nat Xs3) I4) (@ (@ tptp.nth_nat Ys3) I4))))))) (= (lambda ((Y4 tptp.list_int) (Z2 tptp.list_int)) (= Y4 Z2)) (lambda ((Xs3 tptp.list_int) (Ys3 tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs3) (@ tptp.size_size_list_int Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs3)) (= (@ (@ tptp.nth_int Xs3) I4) (@ (@ tptp.nth_int Ys3) I4))))))) (forall ((K3 tptp.nat) (P (-> tptp.nat tptp.c Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K3) (exists ((X8 tptp.c)) (@ (@ P I4) X8)))) (exists ((Xs3 tptp.list_c)) (and (= (@ tptp.size_size_list_c Xs3) K3) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K3) (@ (@ P I4) (@ (@ tptp.nth_c Xs3) I4)))))))) (forall ((K3 tptp.nat) (P (-> tptp.nat tptp.d Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K3) (exists ((X8 tptp.d)) (@ (@ P I4) X8)))) (exists ((Xs3 tptp.list_d)) (and (= (@ tptp.size_size_list_d Xs3) K3) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K3) (@ (@ P I4) (@ (@ tptp.nth_d Xs3) I4)))))))) (forall ((K3 tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K3) (exists ((X8 tptp.nat)) (@ (@ P I4) X8)))) (exists ((Xs3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs3) K3) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K3) (@ (@ P I4) (@ (@ tptp.nth_nat Xs3) I4)))))))) (forall ((K3 tptp.nat) (P (-> tptp.nat tptp.int Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K3) (exists ((X8 tptp.int)) (@ (@ P I4) X8)))) (exists ((Xs3 tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs3) K3) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K3) (@ (@ P I4) (@ (@ tptp.nth_int Xs3) I4)))))))) (forall ((Xs tptp.list_c) (Ys tptp.list_c)) (=> (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_c Ys)) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_c Xs)) (= (@ (@ tptp.nth_c Xs) I5) (@ (@ tptp.nth_c Ys) I5)))) (= Xs Ys)))) (forall ((Xs tptp.list_d) (Ys tptp.list_d)) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_d Ys)) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_d Xs)) (= (@ (@ tptp.nth_d Xs) I5) (@ (@ tptp.nth_d Ys) I5)))) (= Xs Ys)))) (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys)) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I5) (@ (@ tptp.nth_nat Ys) I5)))) (= Xs Ys)))) (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (=> (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys)) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int Xs) I5) (@ (@ tptp.nth_int Ys) I5)))) (= Xs Ys)))) (forall ((N tptp.nat) (P (-> tptp.c tptp.nat Bool))) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) N) (exists ((Li2 tptp.c)) (@ (@ P Li2) I5)))) (not (forall ((L2 tptp.list_c)) (=> (= (@ tptp.size_size_list_c L2) N) (not (forall ((I6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I6) N) (@ (@ P (@ (@ tptp.nth_c L2) I6)) I6))))))))) (forall ((N tptp.nat) (P (-> tptp.d tptp.nat Bool))) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) N) (exists ((Li2 tptp.d)) (@ (@ P Li2) I5)))) (not (forall ((L2 tptp.list_d)) (=> (= (@ tptp.size_size_list_d L2) N) (not (forall ((I6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I6) N) (@ (@ P (@ (@ tptp.nth_d L2) I6)) I6))))))))) (forall ((N tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) N) (exists ((Li2 tptp.nat)) (@ (@ P Li2) I5)))) (not (forall ((L2 tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat L2) N) (not (forall ((I6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I6) N) (@ (@ P (@ (@ tptp.nth_nat L2) I6)) I6))))))))) (forall ((N tptp.nat) (P (-> tptp.int tptp.nat Bool))) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) N) (exists ((Li2 tptp.int)) (@ (@ P Li2) I5)))) (not (forall ((L2 tptp.list_int)) (=> (= (@ tptp.size_size_list_int L2) N) (not (forall ((I6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I6) N) (@ (@ P (@ (@ tptp.nth_int L2) I6)) I6))))))))) _let_184 _let_183 _let_182 _let_181 _let_180 (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (=> (not (= A tptp.bot_bo7824918357723582233_nat_o)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X3) A) (=> (@ (@ tptp.member6576561426505652726_nat_o Y2) A) (= X3 Y2)))) (@ tptp.is_sin5180296473474724033_nat_o A)))) (forall ((A tptp.set_Pr4329608150637261639at_nat)) (=> (not (= A tptp.bot_bo228742789529271731at_nat)) (=> (forall ((X3 tptp.produc3843707927480180839at_nat) (Y2 tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X3) A) (=> (@ (@ tptp.member8757157785044589968at_nat Y2) A) (= X3 Y2)))) (@ tptp.is_sin2937591304547752795at_nat A)))) (forall ((A tptp.set_Pr1261947904930325089at_nat)) (=> (not (= A tptp.bot_bo2099793752762293965at_nat)) (=> (forall ((X3 tptp.product_prod_nat_nat) (Y2 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) A) (=> (@ (@ tptp.member8440522571783428010at_nat Y2) A) (= X3 Y2)))) (@ tptp.is_sin2850979758926227957at_nat A)))) (forall ((A tptp.set_o)) (=> (not (= A tptp.bot_bot_set_o)) (=> (forall ((X3 Bool) (Y2 Bool)) (=> (@ (@ tptp.member_o X3) A) (=> (@ (@ tptp.member_o Y2) A) (= X3 Y2)))) (@ tptp.is_singleton_o A)))) (forall ((A tptp.set_nat)) (=> (not (= A tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat) (Y2 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tptp.code_integer)) (forall ((X7 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X7) Z4) (= (or (@ P X7) (@ Q X7)) (or (@ P3 X7) (@ Q3 X7))))))))) (forall ((P (-> tptp.num Bool)) (P3 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q3 (-> tptp.num Bool))) (=> (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z3) (= (@ Q X3) (@ Q3 X3))))) (exists ((Z4 tptp.num)) (forall ((X7 tptp.num)) (=> (@ (@ tptp.ord_less_num X7) Z4) (= (or (@ P X7) (@ Q X7)) (or (@ P3 X7) (@ Q3 X7))))))))) (forall ((P (-> tptp.nat Bool)) (P3 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q3 (-> tptp.nat Bool))) (=> (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z3) (= (@ Q X3) (@ Q3 X3))))) (exists ((Z4 tptp.nat)) (forall ((X7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X7) Z4) (= (or (@ P X7) (@ Q X7)) (or (@ P3 X7) (@ Q3 X7))))))))) (forall ((P (-> tptp.int Bool)) (P3 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q3 (-> tptp.int Bool))) (=> (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z3) (= (@ Q X3) (@ Q3 X3))))) (exists ((Z4 tptp.int)) (forall ((X7 tptp.int)) (=> (@ (@ tptp.ord_less_int X7) Z4) (= (or (@ P X7) (@ Q X7)) (or (@ P3 X7) (@ Q3 X7))))))))) (forall ((T tptp.code_integer)) (exists ((Z4 tptp.code_integer)) (forall ((X7 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X7) Z4) (not (= X7 T)))))) (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X7 tptp.num)) (=> (@ (@ tptp.ord_less_num X7) Z4) (not (= X7 T)))))) (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X7) Z4) (not (= X7 T)))))) (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X7 tptp.int)) (=> (@ (@ tptp.ord_less_int X7) Z4) (not (= X7 T)))))) (forall ((T tptp.code_integer)) (exists ((Z4 tptp.code_integer)) (forall ((X7 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X7) Z4) (not (= X7 T)))))) (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X7 tptp.num)) (=> (@ (@ tptp.ord_less_num X7) Z4) (not (= X7 T)))))) (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X7) Z4) (not (= X7 T)))))) (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X7 tptp.int)) (=> (@ (@ tptp.ord_less_int X7) Z4) (not (= X7 T)))))) (forall ((T tptp.code_integer)) (exists ((Z4 tptp.code_integer)) (forall ((X7 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger X7))) (=> (@ _let_1 Z4) (@ _let_1 T)))))) (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X7 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X7))) (=> (@ _let_1 Z4) (@ _let_1 T)))))) (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X7 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X7))) (=> (@ _let_1 Z4) (@ _let_1 T)))))) (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X7 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X7))) (=> (@ _let_1 Z4) (@ _let_1 T)))))) (forall ((T tptp.code_integer)) (exists ((Z4 tptp.code_integer)) (forall ((X7 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X7) Z4) (not (@ (@ tptp.ord_le6747313008572928689nteger T) X7)))))) (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X7 tptp.num)) (=> (@ (@ tptp.ord_less_num X7) Z4) (not (@ (@ tptp.ord_less_num T) X7)))))) (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X7) Z4) (not (@ (@ tptp.ord_less_nat T) X7)))))) (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X7 tptp.int)) (=> (@ (@ tptp.ord_less_int X7) Z4) (not (@ (@ tptp.ord_less_int T) X7)))))) (forall ((B2 tptp.code_integer) (A2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger B2))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((B2 tptp.assn) (A2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn B2))) (let ((_let_2 (@ tptp.times_times_assn A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((B2 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat B2))) (let ((_let_2 (@ tptp.times_times_rat A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((B2 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B2))) (let ((_let_2 (@ tptp.times_times_nat A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((B2 tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int B2))) (let ((_let_2 (@ tptp.times_times_int A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (= tptp.times_3573771949741848930nteger (lambda ((A3 tptp.code_integer) (B3 tptp.code_integer)) (@ (@ tptp.times_3573771949741848930nteger B3) A3))) (= tptp.times_times_assn (lambda ((A3 tptp.assn) (B3 tptp.assn)) (@ (@ tptp.times_times_assn B3) A3))) (= tptp.times_times_rat (lambda ((A3 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.times_times_rat B3) A3))) (= tptp.times_times_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.times_times_nat B3) A3))) (= tptp.times_times_int (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ tptp.times_times_int B3) A3))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A2))) (= (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B2) C))))) (forall ((A2 tptp.assn) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn A2))) (= (@ (@ tptp.times_times_assn (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_assn B2) C))))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A2))) (= (@ (@ tptp.times_times_rat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_rat B2) C))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A2))) (= (@ (@ tptp.times_times_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_nat B2) C))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A2))) (= (@ (@ tptp.times_times_int (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_int B2) C))))) (forall ((I3 tptp.set_nat) (I7 tptp.set_nat) (Xs tptp.list_c) (Xs4 tptp.list_c) (Xsi tptp.list_c) (Xsi2 tptp.list_c) (A (-> tptp.c tptp.c tptp.assn)) (A6 (-> tptp.c tptp.c tptp.assn))) (=> (= I3 I7) (=> (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_c Xs4)) (=> (= (@ tptp.size_size_list_c Xsi) (@ tptp.size_size_list_c Xsi2)) (=> (forall ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_c Xsi2) I5))) (let ((_let_2 (@ (@ tptp.nth_c Xs4) I5))) (let ((_let_3 (@ (@ tptp.nth_c Xsi) I5))) (let ((_let_4 (@ (@ tptp.nth_c Xs) I5))) (let ((_let_5 (@ tptp.size_size_list_c Xs))) (=> (@ (@ tptp.member_nat I5) I3) (=> (@ (@ tptp.ord_less_nat I5) _let_5) (=> (= _let_5 (@ tptp.size_size_list_c Xsi)) (and (= _let_4 _let_2) (= _let_3 _let_1) (= (@ (@ A _let_4) _let_3) (@ (@ A6 _let_2) _let_1)))))))))))) (= (@ (@ (@ (@ tptp.vEBT_L824818263033719200sn_c_c I3) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L824818263033719200sn_c_c I7) A6) Xs4) Xsi2))))))) (forall ((I3 tptp.set_nat) (I7 tptp.set_nat) (Xs tptp.list_c) (Xs4 tptp.list_c) (Xsi tptp.list_nat) (Xsi2 tptp.list_nat) (A (-> tptp.c tptp.nat tptp.assn)) (A6 (-> tptp.c tptp.nat tptp.assn))) (=> (= I3 I7) (=> (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_c Xs4)) (=> (= (@ tptp.size_size_list_nat Xsi) (@ tptp.size_size_list_nat Xsi2)) (=> (forall ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat Xsi2) I5))) (let ((_let_2 (@ (@ tptp.nth_c Xs4) I5))) (let ((_let_3 (@ (@ tptp.nth_nat Xsi) I5))) (let ((_let_4 (@ (@ tptp.nth_c Xs) I5))) (let ((_let_5 (@ tptp.size_size_list_c Xs))) (=> (@ (@ tptp.member_nat I5) I3) (=> (@ (@ tptp.ord_less_nat I5) _let_5) (=> (= _let_5 (@ tptp.size_size_list_nat Xsi)) (and (= _let_4 _let_2) (= _let_3 _let_1) (= (@ (@ A _let_4) _let_3) (@ (@ A6 _let_2) _let_1)))))))))))) (= (@ (@ (@ (@ tptp.vEBT_L6585172037124793648_c_nat I3) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L6585172037124793648_c_nat I7) A6) Xs4) Xsi2))))))) (forall ((I3 tptp.set_nat) (I7 tptp.set_nat) (Xs tptp.list_c) (Xs4 tptp.list_c) (Xsi tptp.list_int) (Xsi2 tptp.list_int) (A (-> tptp.c tptp.int tptp.assn)) (A6 (-> tptp.c tptp.int tptp.assn))) (=> (= I3 I7) (=> (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_c Xs4)) (=> (= (@ tptp.size_size_list_int Xsi) (@ tptp.size_size_list_int Xsi2)) (=> (forall ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_int Xsi2) I5))) (let ((_let_2 (@ (@ tptp.nth_c Xs4) I5))) (let ((_let_3 (@ (@ tptp.nth_int Xsi) I5))) (let ((_let_4 (@ (@ tptp.nth_c Xs) I5))) (let ((_let_5 (@ tptp.size_size_list_c Xs))) (=> (@ (@ tptp.member_nat I5) I3) (=> (@ (@ tptp.ord_less_nat I5) _let_5) (=> (= _let_5 (@ tptp.size_size_list_int Xsi)) (and (= _let_4 _let_2) (= _let_3 _let_1) (= (@ (@ A _let_4) _let_3) (@ (@ A6 _let_2) _let_1)))))))))))) (= (@ (@ (@ (@ tptp.vEBT_L6582681566615743372_c_int I3) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L6582681566615743372_c_int I7) A6) Xs4) Xsi2))))))) (forall ((I3 tptp.set_nat) (I7 tptp.set_nat) (Xs tptp.list_d) (Xs4 tptp.list_d) (Xsi tptp.list_c) (Xsi2 tptp.list_c) (A (-> tptp.d tptp.c tptp.assn)) (A6 (-> tptp.d tptp.c tptp.assn))) (=> (= I3 I7) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_d Xs4)) (=> (= (@ tptp.size_size_list_c Xsi) (@ tptp.size_size_list_c Xsi2)) (=> (forall ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_c Xsi2) I5))) (let ((_let_2 (@ (@ tptp.nth_d Xs4) I5))) (let ((_let_3 (@ (@ tptp.nth_c Xsi) I5))) (let ((_let_4 (@ (@ tptp.nth_d Xs) I5))) (let ((_let_5 (@ tptp.size_size_list_d Xs))) (=> (@ (@ tptp.member_nat I5) I3) (=> (@ (@ tptp.ord_less_nat I5) _let_5) (=> (= _let_5 (@ tptp.size_size_list_c Xsi)) (and (= _let_4 _let_2) (= _let_3 _let_1) (= (@ (@ A _let_4) _let_3) (@ (@ A6 _let_2) _let_1)))))))))))) (= (@ (@ (@ (@ tptp.vEBT_L7260734717915818975sn_d_c I3) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L7260734717915818975sn_d_c I7) A6) Xs4) Xsi2))))))) (forall ((I3 tptp.set_nat) (I7 tptp.set_nat) (Xs tptp.list_d) (Xs4 tptp.list_d) (Xsi tptp.list_d) (Xsi2 tptp.list_d) (A (-> tptp.d tptp.d tptp.assn)) (A6 (-> tptp.d tptp.d tptp.assn))) (=> (= I3 I7) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_d Xs4)) (=> (= (@ tptp.size_size_list_d Xsi) (@ tptp.size_size_list_d Xsi2)) (=> (forall ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_d Xsi2) I5))) (let ((_let_2 (@ (@ tptp.nth_d Xs4) I5))) (let ((_let_3 (@ (@ tptp.nth_d Xsi) I5))) (let ((_let_4 (@ (@ tptp.nth_d Xs) I5))) (let ((_let_5 (@ tptp.size_size_list_d Xs))) (=> (@ (@ tptp.member_nat I5) I3) (=> (@ (@ tptp.ord_less_nat I5) _let_5) (=> (= _let_5 (@ tptp.size_size_list_d Xsi)) (and (= _let_4 _let_2) (= _let_3 _let_1) (= (@ (@ A _let_4) _let_3) (@ (@ A6 _let_2) _let_1)))))))))))) (= (@ (@ (@ (@ tptp.vEBT_L7260734717915818976sn_d_d I3) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L7260734717915818976sn_d_d I7) A6) Xs4) Xsi2))))))) (forall ((I3 tptp.set_nat) (I7 tptp.set_nat) (Xs tptp.list_d) (Xs4 tptp.list_d) (Xsi tptp.list_nat) (Xsi2 tptp.list_nat) (A (-> tptp.d tptp.nat tptp.assn)) (A6 (-> tptp.d tptp.nat tptp.assn))) (=> (= I3 I7) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_d Xs4)) (=> (= (@ tptp.size_size_list_nat Xsi) (@ tptp.size_size_list_nat Xsi2)) (=> (forall ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat Xsi2) I5))) (let ((_let_2 (@ (@ tptp.nth_d Xs4) I5))) (let ((_let_3 (@ (@ tptp.nth_nat Xsi) I5))) (let ((_let_4 (@ (@ tptp.nth_d Xs) I5))) (let ((_let_5 (@ tptp.size_size_list_d Xs))) (=> (@ (@ tptp.member_nat I5) I3) (=> (@ (@ tptp.ord_less_nat I5) _let_5) (=> (= _let_5 (@ tptp.size_size_list_nat Xsi)) (and (= _let_4 _let_2) (= _let_3 _let_1) (= (@ (@ A _let_4) _let_3) (@ (@ A6 _let_2) _let_1)))))))))))) (= (@ (@ (@ (@ tptp.vEBT_L7820616366081188145_d_nat I3) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L7820616366081188145_d_nat I7) A6) Xs4) Xsi2))))))) (forall ((I3 tptp.set_nat) (I7 tptp.set_nat) (Xs tptp.list_d) (Xs4 tptp.list_d) (Xsi tptp.list_int) (Xsi2 tptp.list_int) (A (-> tptp.d tptp.int tptp.assn)) (A6 (-> tptp.d tptp.int tptp.assn))) (=> (= I3 I7) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_d Xs4)) (=> (= (@ tptp.size_size_list_int Xsi) (@ tptp.size_size_list_int Xsi2)) (=> (forall ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_int Xsi2) I5))) (let ((_let_2 (@ (@ tptp.nth_d Xs4) I5))) (let ((_let_3 (@ (@ tptp.nth_int Xsi) I5))) (let ((_let_4 (@ (@ tptp.nth_d Xs) I5))) (let ((_let_5 (@ tptp.size_size_list_d Xs))) (=> (@ (@ tptp.member_nat I5) I3) (=> (@ (@ tptp.ord_less_nat I5) _let_5) (=> (= _let_5 (@ tptp.size_size_list_int Xsi)) (and (= _let_4 _let_2) (= _let_3 _let_1) (= (@ (@ A _let_4) _let_3) (@ (@ A6 _let_2) _let_1)))))))))))) (= (@ (@ (@ (@ tptp.vEBT_L7818125895572137869_d_int I3) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L7818125895572137869_d_int I7) A6) Xs4) Xsi2))))))) (forall ((I3 tptp.set_nat) (I7 tptp.set_nat) (Xs tptp.list_nat) (Xs4 tptp.list_nat) (Xsi tptp.list_c) (Xsi2 tptp.list_c) (A (-> tptp.nat tptp.c tptp.assn)) (A6 (-> tptp.nat tptp.c tptp.assn))) (=> (= I3 I7) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Xs4)) (=> (= (@ tptp.size_size_list_c Xsi) (@ tptp.size_size_list_c Xsi2)) (=> (forall ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_c Xsi2) I5))) (let ((_let_2 (@ (@ tptp.nth_nat Xs4) I5))) (let ((_let_3 (@ (@ tptp.nth_c Xsi) I5))) (let ((_let_4 (@ (@ tptp.nth_nat Xs) I5))) (let ((_let_5 (@ tptp.size_size_list_nat Xs))) (=> (@ (@ tptp.member_nat I5) I3) (=> (@ (@ tptp.ord_less_nat I5) _let_5) (=> (= _let_5 (@ tptp.size_size_list_c Xsi)) (and (= _let_4 _let_2) (= _let_3 _let_1) (= (@ (@ A _let_4) _let_3) (@ (@ A6 _let_2) _let_1)))))))))))) (= (@ (@ (@ (@ tptp.vEBT_L8146214880390291086_nat_c I3) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L8146214880390291086_nat_c I7) A6) Xs4) Xsi2))))))) (forall ((I3 tptp.set_nat) (I7 tptp.set_nat) (Xs tptp.list_nat) (Xs4 tptp.list_nat) (Xsi tptp.list_d) (Xsi2 tptp.list_d) (A (-> tptp.nat tptp.d tptp.assn)) (A6 (-> tptp.nat tptp.d tptp.assn))) (=> (= I3 I7) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Xs4)) (=> (= (@ tptp.size_size_list_d Xsi) (@ tptp.size_size_list_d Xsi2)) (=> (forall ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_d Xsi2) I5))) (let ((_let_2 (@ (@ tptp.nth_nat Xs4) I5))) (let ((_let_3 (@ (@ tptp.nth_d Xsi) I5))) (let ((_let_4 (@ (@ tptp.nth_nat Xs) I5))) (let ((_let_5 (@ tptp.size_size_list_nat Xs))) (=> (@ (@ tptp.member_nat I5) I3) (=> (@ (@ tptp.ord_less_nat I5) _let_5) (=> (= _let_5 (@ tptp.size_size_list_d Xsi)) (and (= _let_4 _let_2) (= _let_3 _let_1) (= (@ (@ A _let_4) _let_3) (@ (@ A6 _let_2) _let_1)))))))))))) (= (@ (@ (@ (@ tptp.vEBT_L8146214880390291087_nat_d I3) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L8146214880390291087_nat_d I7) A6) Xs4) Xsi2))))))) (forall ((I3 tptp.set_nat) (I7 tptp.set_nat) (Xs tptp.list_nat) (Xs4 tptp.list_nat) (Xsi tptp.list_nat) (Xsi2 tptp.list_nat) (A (-> tptp.nat tptp.nat tptp.assn)) (A6 (-> tptp.nat tptp.nat tptp.assn))) (=> (= I3 I7) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Xs4)) (=> (= (@ tptp.size_size_list_nat Xsi) (@ tptp.size_size_list_nat Xsi2)) (=> (forall ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat Xsi2) I5))) (let ((_let_2 (@ (@ tptp.nth_nat Xs4) I5))) (let ((_let_3 (@ (@ tptp.nth_nat Xsi) I5))) (let ((_let_4 (@ (@ tptp.nth_nat Xs) I5))) (let ((_let_5 (@ tptp.size_size_list_nat Xs))) (=> (@ (@ tptp.member_nat I5) I3) (=> (@ (@ tptp.ord_less_nat I5) _let_5) (=> (= _let_5 (@ tptp.size_size_list_nat Xsi)) (and (= _let_4 _let_2) (= _let_3 _let_1) (= (@ (@ A _let_4) _let_3) (@ (@ A6 _let_2) _let_1)))))))))))) (= (@ (@ (@ (@ tptp.vEBT_L7892069108621897922at_nat I3) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L7892069108621897922at_nat I7) A6) Xs4) Xsi2))))))) (forall ((I3 tptp.set_nat) (I7 tptp.set_nat) (A (-> tptp.c tptp.c tptp.assn)) (A6 (-> tptp.c tptp.c tptp.assn)) (Xs tptp.list_c) (Xs4 tptp.list_c) (Xsi tptp.list_c) (Xsi2 tptp.list_c)) (=> (= I3 I7) (=> (= A A6) (=> (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_c Xs4)) (=> (= (@ tptp.size_size_list_c Xsi) (@ tptp.size_size_list_c Xsi2)) (=> (forall ((I5 tptp.nat)) (let ((_let_1 (@ tptp.size_size_list_c Xs))) (=> (@ (@ tptp.member_nat I5) I3) (=> (@ (@ tptp.ord_less_nat I5) _let_1) (=> (= _let_1 (@ tptp.size_size_list_c Xsi)) (and (= (@ (@ tptp.nth_c Xs) I5) (@ (@ tptp.nth_c Xs4) I5)) (= (@ (@ tptp.nth_c Xsi) I5) (@ (@ tptp.nth_c Xsi2) I5)))))))) (= (@ (@ (@ (@ tptp.vEBT_L824818263033719200sn_c_c I3) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L824818263033719200sn_c_c I7) A6) Xs4) Xsi2)))))))) (forall ((I3 tptp.set_nat) (I7 tptp.set_nat) (A (-> tptp.c tptp.nat tptp.assn)) (A6 (-> tptp.c tptp.nat tptp.assn)) (Xs tptp.list_c) (Xs4 tptp.list_c) (Xsi tptp.list_nat) (Xsi2 tptp.list_nat)) (=> (= I3 I7) (=> (= A A6) (=> (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_c Xs4)) (=> (= (@ tptp.size_size_list_nat Xsi) (@ tptp.size_size_list_nat Xsi2)) (=> (forall ((I5 tptp.nat)) (let ((_let_1 (@ tptp.size_size_list_c Xs))) (=> (@ (@ tptp.member_nat I5) I3) (=> (@ (@ tptp.ord_less_nat I5) _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Xsi)) (and (= (@ (@ tptp.nth_c Xs) I5) (@ (@ tptp.nth_c Xs4) I5)) (= (@ (@ tptp.nth_nat Xsi) I5) (@ (@ tptp.nth_nat Xsi2) I5)))))))) (= (@ (@ (@ (@ tptp.vEBT_L6585172037124793648_c_nat I3) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L6585172037124793648_c_nat I7) A6) Xs4) Xsi2)))))))) (forall ((I3 tptp.set_nat) (I7 tptp.set_nat) (A (-> tptp.c tptp.int tptp.assn)) (A6 (-> tptp.c tptp.int tptp.assn)) (Xs tptp.list_c) (Xs4 tptp.list_c) (Xsi tptp.list_int) (Xsi2 tptp.list_int)) (=> (= I3 I7) (=> (= A A6) (=> (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_c Xs4)) (=> (= (@ tptp.size_size_list_int Xsi) (@ tptp.size_size_list_int Xsi2)) (=> (forall ((I5 tptp.nat)) (let ((_let_1 (@ tptp.size_size_list_c Xs))) (=> (@ (@ tptp.member_nat I5) I3) (=> (@ (@ tptp.ord_less_nat I5) _let_1) (=> (= _let_1 (@ tptp.size_size_list_int Xsi)) (and (= (@ (@ tptp.nth_c Xs) I5) (@ (@ tptp.nth_c Xs4) I5)) (= (@ (@ tptp.nth_int Xsi) I5) (@ (@ tptp.nth_int Xsi2) I5)))))))) (= (@ (@ (@ (@ tptp.vEBT_L6582681566615743372_c_int I3) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L6582681566615743372_c_int I7) A6) Xs4) Xsi2)))))))) (forall ((I3 tptp.set_nat) (I7 tptp.set_nat) (A (-> tptp.d tptp.c tptp.assn)) (A6 (-> tptp.d tptp.c tptp.assn)) (Xs tptp.list_d) (Xs4 tptp.list_d) (Xsi tptp.list_c) (Xsi2 tptp.list_c)) (=> (= I3 I7) (=> (= A A6) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_d Xs4)) (=> (= (@ tptp.size_size_list_c Xsi) (@ tptp.size_size_list_c Xsi2)) (=> (forall ((I5 tptp.nat)) (let ((_let_1 (@ tptp.size_size_list_d Xs))) (=> (@ (@ tptp.member_nat I5) I3) (=> (@ (@ tptp.ord_less_nat I5) _let_1) (=> (= _let_1 (@ tptp.size_size_list_c Xsi)) (and (= (@ (@ tptp.nth_d Xs) I5) (@ (@ tptp.nth_d Xs4) I5)) (= (@ (@ tptp.nth_c Xsi) I5) (@ (@ tptp.nth_c Xsi2) I5)))))))) (= (@ (@ (@ (@ tptp.vEBT_L7260734717915818975sn_d_c I3) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L7260734717915818975sn_d_c I7) A6) Xs4) Xsi2)))))))) (forall ((I3 tptp.set_nat) (I7 tptp.set_nat) (A (-> tptp.d tptp.d tptp.assn)) (A6 (-> tptp.d tptp.d tptp.assn)) (Xs tptp.list_d) (Xs4 tptp.list_d) (Xsi tptp.list_d) (Xsi2 tptp.list_d)) (=> (= I3 I7) (=> (= A A6) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_d Xs4)) (=> (= (@ tptp.size_size_list_d Xsi) (@ tptp.size_size_list_d Xsi2)) (=> (forall ((I5 tptp.nat)) (let ((_let_1 (@ tptp.size_size_list_d Xs))) (=> (@ (@ tptp.member_nat I5) I3) (=> (@ (@ tptp.ord_less_nat I5) _let_1) (=> (= _let_1 (@ tptp.size_size_list_d Xsi)) (and (= (@ (@ tptp.nth_d Xs) I5) (@ (@ tptp.nth_d Xs4) I5)) (= (@ (@ tptp.nth_d Xsi) I5) (@ (@ tptp.nth_d Xsi2) I5)))))))) (= (@ (@ (@ (@ tptp.vEBT_L7260734717915818976sn_d_d I3) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L7260734717915818976sn_d_d I7) A6) Xs4) Xsi2)))))))) (forall ((I3 tptp.set_nat) (I7 tptp.set_nat) (A (-> tptp.d tptp.nat tptp.assn)) (A6 (-> tptp.d tptp.nat tptp.assn)) (Xs tptp.list_d) (Xs4 tptp.list_d) (Xsi tptp.list_nat) (Xsi2 tptp.list_nat)) (=> (= I3 I7) (=> (= A A6) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_d Xs4)) (=> (= (@ tptp.size_size_list_nat Xsi) (@ tptp.size_size_list_nat Xsi2)) (=> (forall ((I5 tptp.nat)) (let ((_let_1 (@ tptp.size_size_list_d Xs))) (=> (@ (@ tptp.member_nat I5) I3) (=> (@ (@ tptp.ord_less_nat I5) _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Xsi)) (and (= (@ (@ tptp.nth_d Xs) I5) (@ (@ tptp.nth_d Xs4) I5)) (= (@ (@ tptp.nth_nat Xsi) I5) (@ (@ tptp.nth_nat Xsi2) I5)))))))) (= (@ (@ (@ (@ tptp.vEBT_L7820616366081188145_d_nat I3) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L7820616366081188145_d_nat I7) A6) Xs4) Xsi2)))))))) (forall ((I3 tptp.set_nat) (I7 tptp.set_nat) (A (-> tptp.d tptp.int tptp.assn)) (A6 (-> tptp.d tptp.int tptp.assn)) (Xs tptp.list_d) (Xs4 tptp.list_d) (Xsi tptp.list_int) (Xsi2 tptp.list_int)) (=> (= I3 I7) (=> (= A A6) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_d Xs4)) (=> (= (@ tptp.size_size_list_int Xsi) (@ tptp.size_size_list_int Xsi2)) (=> (forall ((I5 tptp.nat)) (let ((_let_1 (@ tptp.size_size_list_d Xs))) (=> (@ (@ tptp.member_nat I5) I3) (=> (@ (@ tptp.ord_less_nat I5) _let_1) (=> (= _let_1 (@ tptp.size_size_list_int Xsi)) (and (= (@ (@ tptp.nth_d Xs) I5) (@ (@ tptp.nth_d Xs4) I5)) (= (@ (@ tptp.nth_int Xsi) I5) (@ (@ tptp.nth_int Xsi2) I5)))))))) (= (@ (@ (@ (@ tptp.vEBT_L7818125895572137869_d_int I3) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L7818125895572137869_d_int I7) A6) Xs4) Xsi2)))))))) (forall ((I3 tptp.set_nat) (I7 tptp.set_nat) (A (-> tptp.nat tptp.c tptp.assn)) (A6 (-> tptp.nat tptp.c tptp.assn)) (Xs tptp.list_nat) (Xs4 tptp.list_nat) (Xsi tptp.list_c) (Xsi2 tptp.list_c)) (=> (= I3 I7) (=> (= A A6) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Xs4)) (=> (= (@ tptp.size_size_list_c Xsi) (@ tptp.size_size_list_c Xsi2)) (=> (forall ((I5 tptp.nat)) (let ((_let_1 (@ tptp.size_size_list_nat Xs))) (=> (@ (@ tptp.member_nat I5) I3) (=> (@ (@ tptp.ord_less_nat I5) _let_1) (=> (= _let_1 (@ tptp.size_size_list_c Xsi)) (and (= (@ (@ tptp.nth_nat Xs) I5) (@ (@ tptp.nth_nat Xs4) I5)) (= (@ (@ tptp.nth_c Xsi) I5) (@ (@ tptp.nth_c Xsi2) I5)))))))) (= (@ (@ (@ (@ tptp.vEBT_L8146214880390291086_nat_c I3) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L8146214880390291086_nat_c I7) A6) Xs4) Xsi2)))))))) (forall ((I3 tptp.set_nat) (I7 tptp.set_nat) (A (-> tptp.nat tptp.d tptp.assn)) (A6 (-> tptp.nat tptp.d tptp.assn)) (Xs tptp.list_nat) (Xs4 tptp.list_nat) (Xsi tptp.list_d) (Xsi2 tptp.list_d)) (=> (= I3 I7) (=> (= A A6) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Xs4)) (=> (= (@ tptp.size_size_list_d Xsi) (@ tptp.size_size_list_d Xsi2)) (=> (forall ((I5 tptp.nat)) (let ((_let_1 (@ tptp.size_size_list_nat Xs))) (=> (@ (@ tptp.member_nat I5) I3) (=> (@ (@ tptp.ord_less_nat I5) _let_1) (=> (= _let_1 (@ tptp.size_size_list_d Xsi)) (and (= (@ (@ tptp.nth_nat Xs) I5) (@ (@ tptp.nth_nat Xs4) I5)) (= (@ (@ tptp.nth_d Xsi) I5) (@ (@ tptp.nth_d Xsi2) I5)))))))) (= (@ (@ (@ (@ tptp.vEBT_L8146214880390291087_nat_d I3) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L8146214880390291087_nat_d I7) A6) Xs4) Xsi2)))))))) (forall ((I3 tptp.set_nat) (I7 tptp.set_nat) (A (-> tptp.nat tptp.nat tptp.assn)) (A6 (-> tptp.nat tptp.nat tptp.assn)) (Xs tptp.list_nat) (Xs4 tptp.list_nat) (Xsi tptp.list_nat) (Xsi2 tptp.list_nat)) (=> (= I3 I7) (=> (= A A6) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Xs4)) (=> (= (@ tptp.size_size_list_nat Xsi) (@ tptp.size_size_list_nat Xsi2)) (=> (forall ((I5 tptp.nat)) (let ((_let_1 (@ tptp.size_size_list_nat Xs))) (=> (@ (@ tptp.member_nat I5) I3) (=> (@ (@ tptp.ord_less_nat I5) _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Xsi)) (and (= (@ (@ tptp.nth_nat Xs) I5) (@ (@ tptp.nth_nat Xs4) I5)) (= (@ (@ tptp.nth_nat Xsi) I5) (@ (@ tptp.nth_nat Xsi2) I5)))))))) (= (@ (@ (@ (@ tptp.vEBT_L7892069108621897922at_nat I3) A) Xs) Xsi) (@ (@ (@ (@ tptp.vEBT_L7892069108621897922at_nat I7) A6) Xs4) Xsi2)))))))) (forall ((A2 tptp.rat) (C tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A2))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 C)) B2) (@ (@ tptp.minus_minus_rat (@ _let_1 B2)) C)))) (forall ((A2 tptp.nat) (C tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 C)) B2) (@ (@ tptp.minus_minus_nat (@ _let_1 B2)) C)))) (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A2))) (= (@ (@ tptp.minus_minus_int (@ _let_1 C)) B2) (@ (@ tptp.minus_minus_int (@ _let_1 B2)) C)))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A2) B2) (@ (@ tptp.minus_minus_rat C) D2)) (= (= A2 B2) (= C D2)))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int) (D2 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A2) B2) (@ (@ tptp.minus_minus_int C) D2)) (= (= A2 B2) (= C D2)))) (forall ((A tptp.set_Pr4329608150637261639at_nat)) (=> (@ tptp.is_sin2937591304547752795at_nat A) (not (forall ((X3 tptp.produc3843707927480180839at_nat)) (not (= A (@ (@ tptp.insert9069300056098147895at_nat X3) tptp.bot_bo228742789529271731at_nat))))))) (forall ((A tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.is_sin2850979758926227957at_nat A) (not (forall ((X3 tptp.product_prod_nat_nat)) (not (= A (@ (@ tptp.insert8211810215607154385at_nat X3) tptp.bot_bo2099793752762293965at_nat))))))) (forall ((A tptp.set_o)) (=> (@ tptp.is_singleton_o A) (not (forall ((X3 Bool)) (not (= A (@ (@ tptp.insert_o2 X3) tptp.bot_bot_set_o))))))) (forall ((A tptp.set_nat)) (=> (@ tptp.is_singleton_nat A) (not (forall ((X3 tptp.nat)) (not (= A (@ (@ tptp.insert_nat2 X3) tptp.bot_bot_set_nat))))))) (forall ((A tptp.set_int)) (=> (@ tptp.is_singleton_int A) (not (forall ((X3 tptp.int)) (not (= A (@ (@ tptp.insert_int2 X3) tptp.bot_bot_set_int))))))) (= tptp.is_sin2937591304547752795at_nat (lambda ((A5 tptp.set_Pr4329608150637261639at_nat)) (exists ((X2 tptp.produc3843707927480180839at_nat)) (= A5 (@ (@ tptp.insert9069300056098147895at_nat X2) tptp.bot_bo228742789529271731at_nat))))) (= tptp.is_sin2850979758926227957at_nat (lambda ((A5 tptp.set_Pr1261947904930325089at_nat)) (exists ((X2 tptp.product_prod_nat_nat)) (= A5 (@ (@ tptp.insert8211810215607154385at_nat X2) tptp.bot_bo2099793752762293965at_nat))))) (= tptp.is_singleton_o (lambda ((A5 tptp.set_o)) (exists ((X2 Bool)) (= A5 (@ (@ tptp.insert_o2 X2) tptp.bot_bot_set_o))))) (= tptp.is_singleton_nat (lambda ((A5 tptp.set_nat)) (exists ((X2 tptp.nat)) (= A5 (@ (@ tptp.insert_nat2 X2) tptp.bot_bot_set_nat))))) (= tptp.is_singleton_int (lambda ((A5 tptp.set_int)) (exists ((X2 tptp.int)) (= A5 (@ (@ tptp.insert_int2 X2) tptp.bot_bot_set_int))))) (forall ((I tptp.nat) (I3 tptp.set_nat) (Xs tptp.list_c) (A (-> tptp.c tptp.nat tptp.assn)) (Xsi tptp.list_nat)) (=> (not (@ (@ tptp.member_nat I) I3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_c Xs)) (= (@ (@ (@ (@ tptp.vEBT_L6585172037124793648_c_nat (@ (@ tptp.insert_nat2 I) I3)) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_c Xs) I)) (@ (@ tptp.nth_nat Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L6585172037124793648_c_nat I3) A) Xs) Xsi)))))) (forall ((I tptp.nat) (I3 tptp.set_nat) (Xs tptp.list_c) (A (-> tptp.c tptp.int tptp.assn)) (Xsi tptp.list_int)) (=> (not (@ (@ tptp.member_nat I) I3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_c Xs)) (= (@ (@ (@ (@ tptp.vEBT_L6582681566615743372_c_int (@ (@ tptp.insert_nat2 I) I3)) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_c Xs) I)) (@ (@ tptp.nth_int Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L6582681566615743372_c_int I3) A) Xs) Xsi)))))) (forall ((I tptp.nat) (I3 tptp.set_nat) (Xs tptp.list_d) (A (-> tptp.d tptp.nat tptp.assn)) (Xsi tptp.list_nat)) (=> (not (@ (@ tptp.member_nat I) I3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_d Xs)) (= (@ (@ (@ (@ tptp.vEBT_L7820616366081188145_d_nat (@ (@ tptp.insert_nat2 I) I3)) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_d Xs) I)) (@ (@ tptp.nth_nat Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7820616366081188145_d_nat I3) A) Xs) Xsi)))))) (forall ((I tptp.nat) (I3 tptp.set_nat) (Xs tptp.list_d) (A (-> tptp.d tptp.int tptp.assn)) (Xsi tptp.list_int)) (=> (not (@ (@ tptp.member_nat I) I3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_d Xs)) (= (@ (@ (@ (@ tptp.vEBT_L7818125895572137869_d_int (@ (@ tptp.insert_nat2 I) I3)) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_d Xs) I)) (@ (@ tptp.nth_int Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7818125895572137869_d_int I3) A) Xs) Xsi)))))) (forall ((I tptp.nat) (I3 tptp.set_nat) (Xs tptp.list_nat) (A (-> tptp.nat tptp.nat tptp.assn)) (Xsi tptp.list_nat)) (=> (not (@ (@ tptp.member_nat I) I3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs)) (= (@ (@ (@ (@ tptp.vEBT_L7892069108621897922at_nat (@ (@ tptp.insert_nat2 I) I3)) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_nat Xs) I)) (@ (@ tptp.nth_nat Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7892069108621897922at_nat I3) A) Xs) Xsi)))))) (forall ((I tptp.nat) (I3 tptp.set_nat) (Xs tptp.list_nat) (A (-> tptp.nat tptp.int tptp.assn)) (Xsi tptp.list_int)) (=> (not (@ (@ tptp.member_nat I) I3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs)) (= (@ (@ (@ (@ tptp.vEBT_L7889578638112847646at_int (@ (@ tptp.insert_nat2 I) I3)) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_nat Xs) I)) (@ (@ tptp.nth_int Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L7889578638112847646at_int I3) A) Xs) Xsi)))))) (forall ((I tptp.nat) (I3 tptp.set_nat) (Xs tptp.list_int) (A (-> tptp.int tptp.nat tptp.assn)) (Xsi tptp.list_nat)) (=> (not (@ (@ tptp.member_nat I) I3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs)) (= (@ (@ (@ (@ tptp.vEBT_L8891422820522952478nt_nat (@ (@ tptp.insert_nat2 I) I3)) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_int Xs) I)) (@ (@ tptp.nth_nat Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L8891422820522952478nt_nat I3) A) Xs) Xsi)))))) (forall ((I tptp.nat) (I3 tptp.set_nat) (Xs tptp.list_int) (A (-> tptp.int tptp.int tptp.assn)) (Xsi tptp.list_int)) (=> (not (@ (@ tptp.member_nat I) I3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs)) (= (@ (@ (@ (@ tptp.vEBT_L8888932350013902202nt_int (@ (@ tptp.insert_nat2 I) I3)) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_int Xs) I)) (@ (@ tptp.nth_int Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L8888932350013902202nt_int I3) A) Xs) Xsi)))))) (forall ((I tptp.nat) (I3 tptp.set_nat) (Xs tptp.list_c) (A (-> tptp.c tptp.d tptp.assn)) (Xsi tptp.list_d)) (=> (not (@ (@ tptp.member_nat I) I3)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_c Xs)) (= (@ (@ (@ (@ tptp.vEBT_L824818263033719201sn_c_d (@ (@ tptp.insert_nat2 I) I3)) A) Xs) Xsi) (@ (@ tptp.times_times_assn (@ (@ A (@ (@ tptp.nth_c Xs) I)) (@ (@ tptp.nth_d Xsi) I))) (@ (@ (@ (@ tptp.vEBT_L824818263033719201sn_c_d I3) A) Xs) Xsi)))))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A2) C)) (@ (@ tptp.minus_minus_rat B2) C)))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.minus_8373710615458151222nteger A2) C)) (@ (@ tptp.minus_8373710615458151222nteger B2) C)))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A2) C)) (@ (@ tptp.minus_minus_int B2) C)))) (forall ((B2 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat C))) (=> (@ (@ tptp.ord_less_rat B2) A2) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B2))))) (forall ((B2 tptp.code_integer) (A2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) A2) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B2))))) (forall ((B2 tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int C))) (=> (@ (@ tptp.ord_less_int B2) A2) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2))))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A2) B2) (@ (@ tptp.minus_minus_rat C) D2)) (= (@ (@ tptp.ord_less_rat A2) B2) (@ (@ tptp.ord_less_rat C) D2)))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (= (@ (@ tptp.minus_8373710615458151222nteger A2) B2) (@ (@ tptp.minus_8373710615458151222nteger C) D2)) (= (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (@ (@ tptp.ord_le6747313008572928689nteger C) D2)))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int) (D2 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A2) B2) (@ (@ tptp.minus_minus_int C) D2)) (= (@ (@ tptp.ord_less_int A2) B2) (@ (@ tptp.ord_less_int C) D2)))) (= tptp.bot_bo7963750851167320836at_o_o (lambda ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (@ (@ tptp.member6576561426505652726_nat_o X2) tptp.bot_bo7824918357723582233_nat_o))) (= tptp.bot_bo6829958733157050602_nat_o (lambda ((X2 tptp.produc3843707927480180839at_nat)) (@ (@ tptp.member8757157785044589968at_nat X2) tptp.bot_bo228742789529271731at_nat))) (= tptp.bot_bo482883023278783056_nat_o (lambda ((X2 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X2) tptp.bot_bo2099793752762293965at_nat))) (= tptp.bot_bot_o_o (lambda ((X2 Bool)) (@ (@ tptp.member_o X2) tptp.bot_bot_set_o))) (= tptp.bot_bot_nat_o (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) tptp.bot_bot_set_nat))) (= tptp.bot_bot_int_o (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) tptp.bot_bot_set_int))) (forall ((P (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (= (= (@ tptp.collec939566748876313656_nat_o P) tptp.bot_bo7824918357723582233_nat_o) (= P tptp.bot_bo7963750851167320836at_o_o))) (forall ((P (-> tptp.produc3843707927480180839at_nat Bool))) (= (= (@ tptp.collec6321179662152712658at_nat P) tptp.bot_bo228742789529271731at_nat) (= P tptp.bot_bo6829958733157050602_nat_o))) (forall ((P (-> tptp.product_prod_nat_nat Bool))) (= (= (@ tptp.collec3392354462482085612at_nat P) tptp.bot_bo2099793752762293965at_nat) (= P tptp.bot_bo482883023278783056_nat_o))) (forall ((P (-> Bool Bool))) (= (= (@ tptp.collect_o P) tptp.bot_bot_set_o) (= P tptp.bot_bot_o_o))) (forall ((P (-> tptp.nat Bool))) (= (= (@ tptp.collect_nat P) tptp.bot_bot_set_nat) (= P tptp.bot_bot_nat_o))) (forall ((P (-> tptp.int Bool))) (= (= (@ tptp.collect_int P) tptp.bot_bot_set_int) (= P tptp.bot_bot_int_o))) _let_179 _let_178 _let_177 _let_176 _let_175 (forall ((I tptp.nat) (L tptp.list_P6011104703257516679at_nat) (X tptp.product_prod_nat_nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s5460976970255530739at_nat L)) (= (@ (@ tptp.insert8211810215607154385at_nat (@ (@ tptp.nth_Pr7617993195940197384at_nat L) I)) (@ tptp.set_Pr5648618587558075414at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat L) I) X))) (@ (@ tptp.insert8211810215607154385at_nat X) (@ tptp.set_Pr5648618587558075414at_nat L))))) (forall ((I tptp.nat) (L tptp.list_P5464809261938338413at_nat) (X tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s1588839187904960729at_nat L)) (= (@ (@ tptp.insert9069300056098147895at_nat (@ (@ tptp.nth_Pr1239524528086697198at_nat L) I)) (@ tptp.set_Pr3765526544606949372at_nat (@ (@ (@ tptp.list_u4696772448584712917at_nat L) I) X))) (@ (@ tptp.insert9069300056098147895at_nat X) (@ tptp.set_Pr3765526544606949372at_nat L))))) (forall ((I tptp.nat) (L tptp.list_o) (X Bool)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o L)) (= (@ (@ tptp.insert_o2 (@ (@ tptp.nth_o L) I)) (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o L) I) X))) (@ (@ tptp.insert_o2 X) (@ tptp.set_o2 L))))) (forall ((I tptp.nat) (L tptp.list_P8527749157015355191n_assn) (X tptp.produc6575502325842934193n_assn)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6829681357464350627n_assn L)) (= (@ (@ tptp.insert5290817439147925377n_assn (@ (@ tptp.nth_Pr1769885009046257848n_assn L) I)) (@ tptp.set_Pr1139785259514867910n_assn (@ (@ (@ tptp.list_u4534839942911652127n_assn L) I) X))) (@ (@ tptp.insert5290817439147925377n_assn X) (@ tptp.set_Pr1139785259514867910n_assn L))))) (forall ((I tptp.nat) (L tptp.list_c) (X tptp.c)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_c L)) (= (@ (@ tptp.insert_c (@ (@ tptp.nth_c L) I)) (@ tptp.set_c2 (@ (@ (@ tptp.list_update_c L) I) X))) (@ (@ tptp.insert_c X) (@ tptp.set_c2 L))))) (forall ((I tptp.nat) (L tptp.list_d) (X tptp.d)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_d L)) (= (@ (@ tptp.insert_d (@ (@ tptp.nth_d L) I)) (@ tptp.set_d2 (@ (@ (@ tptp.list_update_d L) I) X))) (@ (@ tptp.insert_d X) (@ tptp.set_d2 L))))) (forall ((I tptp.nat) (L tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat L)) (= (@ (@ tptp.insert_nat2 (@ (@ tptp.nth_nat L) I)) (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat L) I) X))) (@ (@ tptp.insert_nat2 X) (@ tptp.set_nat2 L))))) (forall ((I tptp.nat) (L tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int L)) (= (@ (@ tptp.insert_int2 (@ (@ tptp.nth_int L) I)) (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int L) I) X))) (@ (@ tptp.insert_int2 X) (@ tptp.set_int2 L))))) (forall ((I tptp.nat) (Xs tptp.list_P8527749157015355191n_assn) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_Pr1769885009046257848n_assn Xs))) (let ((_let_2 (@ tptp.size_s6829681357464350627n_assn Xs))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_Pr1139785259514867910n_assn (@ (@ (@ tptp.list_u4534839942911652127n_assn (@ (@ (@ tptp.list_u4534839942911652127n_assn Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.set_Pr1139785259514867910n_assn Xs))))))) (forall ((I tptp.nat) (Xs tptp.list_c) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_c Xs))) (let ((_let_2 (@ tptp.size_size_list_c Xs))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_c2 (@ (@ (@ tptp.list_update_c (@ (@ (@ tptp.list_update_c Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.set_c2 Xs))))))) (forall ((I tptp.nat) (Xs tptp.list_d) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_d Xs))) (let ((_let_2 (@ tptp.size_size_list_d Xs))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_d2 (@ (@ (@ tptp.list_update_d (@ (@ (@ tptp.list_update_d Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.set_d2 Xs))))))) (forall ((I tptp.nat) (Xs tptp.list_nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (let ((_let_2 (@ tptp.size_size_list_nat Xs))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat (@ (@ (@ tptp.list_update_nat Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.set_nat2 Xs))))))) (forall ((I tptp.nat) (Xs tptp.list_int) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs))) (let ((_let_2 (@ tptp.size_size_list_int Xs))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int (@ (@ (@ tptp.list_update_int Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.set_int2 Xs))))))) _let_174 _let_173 _let_172 _let_171 _let_170 (forall ((I tptp.nat) (Xs tptp.list_c) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_c Xs))) (let ((_let_2 (@ tptp.size_size_list_c Xs))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.distinct_c (@ (@ (@ tptp.list_update_c (@ (@ (@ tptp.list_update_c Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.distinct_c Xs))))))) (forall ((I tptp.nat) (Xs tptp.list_d) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_d Xs))) (let ((_let_2 (@ tptp.size_size_list_d Xs))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.distinct_d (@ (@ (@ tptp.list_update_d (@ (@ (@ tptp.list_update_d Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.distinct_d Xs))))))) (forall ((I tptp.nat) (Xs tptp.list_nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (let ((_let_2 (@ tptp.size_size_list_nat Xs))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.distinct_nat (@ (@ (@ tptp.list_update_nat (@ (@ (@ tptp.list_update_nat Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.distinct_nat Xs))))))) (forall ((I tptp.nat) (Xs tptp.list_int) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs))) (let ((_let_2 (@ tptp.size_size_list_int Xs))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.distinct_int (@ (@ (@ tptp.list_update_int (@ (@ (@ tptp.list_update_int Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.distinct_int Xs))))))) _let_169 _let_168 _let_167 _let_166 (forall ((P tptp.assn) (Q tptp.assn) (B2 Bool)) (let ((_let_1 (@ tptp.entails P))) (= (@ _let_1 (@ (@ tptp.times_times_assn Q) (@ tptp.pure_assn B2))) (and (forall ((H3 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P) H3) B2)) (@ _let_1 Q))))) (forall ((P Bool) (Q Bool)) (= (= (@ tptp.pure_assn P) (@ tptp.pure_assn Q)) (= P Q))) (forall ((X tptp.produc3843707927480180839at_nat) (Y tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat X))) (= (@ _let_1 (@ (@ tptp.remove5300788332298244428at_nat Y) A)) (and (@ _let_1 A) (not (= X Y)))))) (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X))) (= (@ _let_1 (@ (@ tptp.remove6466555014256735590at_nat Y) A)) (and (@ _let_1 A) (not (= X Y)))))) (forall ((X tptp.nat) (Y tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat X))) (= (@ _let_1 (@ (@ tptp.remove_nat Y) A)) (and (@ _let_1 A) (not (= X Y)))))) (forall ((X tptp.int) (Y tptp.int) (A tptp.set_int)) (let ((_let_1 (@ tptp.member_int X))) (= (@ _let_1 (@ (@ tptp.remove_int Y) A)) (and (@ _let_1 A) (not (= X Y)))))) (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Y (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o X))) (= (@ _let_1 (@ (@ tptp.remove4651630035290841522_nat_o Y) A)) (and (@ _let_1 A) (not (= 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As)))))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (S tptp.set_Pr4329608150637261639at_nat) (P (-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool))) (let ((_let_1 (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat A2) B2)) S))) (=> _let_1 (=> (=> _let_1 (@ (@ P A2) B2)) (exists ((A4 tptp.set_Pr1261947904930325089at_nat) (B4 tptp.set_Pr1261947904930325089at_nat)) (and (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat A4) B4)) S) (@ (@ P A4) B4))))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (S tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.nat tptp.nat Bool))) (let ((_let_1 (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B2)) S))) (=> _let_1 (=> (=> _let_1 (@ (@ P A2) B2)) (exists ((A4 tptp.nat) (B4 tptp.nat)) (and (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A4) B4)) S) (@ (@ 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(@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A2) B2)) S))) (=> _let_1 (=> (=> _let_1 (@ (@ P A2) B2)) (exists ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.produc3658429121746597890et_nat)) (and (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A4) B4)) S) (@ (@ P A4) B4))))))) (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.produc3925858234332021118et_nat) (S tptp.set_Pr8536935166611901872et_nat) (P (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat Bool))) (let ((_let_1 (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A2) B2)) S))) (=> _let_1 (=> (=> _let_1 (@ (@ P A2) B2)) (exists ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.produc3925858234332021118et_nat)) (and (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A4) B4)) S) (@ (@ P A4) B4))))))) (forall ((A2 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B2 tptp.product_prod_int_int) (S tptp.set_Pr9222295170931077689nt_int) (P (-> (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool))) (let ((_let_1 (@ (@ tptp.member7618704894036264090nt_int (@ (@ tptp.produc5700946648718959541nt_int A2) B2)) S))) (=> _let_1 (=> (=> _let_1 (@ (@ P A2) B2)) (exists ((A4 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B4 tptp.product_prod_int_int)) (and (@ (@ tptp.member7618704894036264090nt_int (@ (@ tptp.produc5700946648718959541nt_int A4) B4)) S) (@ (@ P A4) B4))))))) (forall ((A2 (-> tptp.int tptp.option6357759511663192854e_term)) (B2 tptp.product_prod_int_int) (S tptp.set_Pr1872883991513573699nt_int) (P (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool))) (let ((_let_1 (@ (@ tptp.member7034335876925520548nt_int (@ (@ 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tptp.vEBT_L74593716426352029nt_int A) Xs) Xsi) (@ (@ (@ tptp.vEBT_L74593716426352029nt_int A6) Xs4) Xsi2)))))) (forall ((Xs tptp.list_int) (Xs4 tptp.list_int) (Xsi tptp.list_nat) (Xsi2 tptp.list_nat) (A (-> tptp.int tptp.nat tptp.assn)) (A6 (-> tptp.int tptp.nat tptp.assn))) (=> (= Xs Xs4) (=> (= Xsi Xsi2) (=> (forall ((X3 tptp.int) (Xi tptp.nat)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs4)) (=> (@ (@ tptp.member_nat Xi) (@ tptp.set_nat2 Xsi2)) (= (@ (@ A X3) Xi) (@ (@ A6 X3) Xi))))) (= (@ (@ (@ tptp.vEBT_L77084186935402305nt_nat A) Xs) Xsi) (@ (@ (@ tptp.vEBT_L77084186935402305nt_nat A6) Xs4) Xsi2)))))) (forall ((Xs tptp.list_nat) (Xs4 tptp.list_nat) (Xsi tptp.list_int) (Xsi2 tptp.list_int) (A (-> tptp.nat tptp.int tptp.assn)) (A6 (-> tptp.nat tptp.int tptp.assn))) (=> (= Xs Xs4) (=> (= Xsi Xsi2) (=> (forall ((X3 tptp.nat) (Xi tptp.int)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs4)) (=> (@ (@ tptp.member_int Xi) (@ tptp.set_int2 Xsi2)) (= (@ (@ A X3) Xi) (@ (@ A6 X3) Xi))))) (= (@ (@ (@ tptp.vEBT_L8298612041380073281at_int A) Xs) Xsi) (@ (@ (@ tptp.vEBT_L8298612041380073281at_int A6) Xs4) Xsi2)))))) (forall ((Xs tptp.list_nat) (Xs4 tptp.list_nat) (Xsi tptp.list_nat) (Xsi2 tptp.list_nat) (A (-> tptp.nat tptp.nat tptp.assn)) (A6 (-> tptp.nat tptp.nat tptp.assn))) (=> (= Xs Xs4) (=> (= Xsi Xsi2) (=> (forall ((X3 tptp.nat) (Xi tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs4)) (=> (@ (@ tptp.member_nat Xi) (@ tptp.set_nat2 Xsi2)) (= (@ (@ A X3) Xi) (@ (@ A6 X3) Xi))))) (= (@ (@ (@ tptp.vEBT_L8301102511889123557at_nat A) Xs) Xsi) (@ (@ (@ tptp.vEBT_L8301102511889123557at_nat A6) Xs4) Xsi2)))))) (forall ((Xs tptp.list_P6011104703257516679at_nat) (Xs4 tptp.list_P6011104703257516679at_nat) (Xsi tptp.list_int) (Xsi2 tptp.list_int) (A (-> tptp.product_prod_nat_nat tptp.int tptp.assn)) (A6 (-> tptp.product_prod_nat_nat tptp.int tptp.assn))) (=> (= Xs Xs4) (=> (= Xsi Xsi2) (=> (forall ((X3 tptp.product_prod_nat_nat) (Xi tptp.int)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) (@ tptp.set_Pr5648618587558075414at_nat Xs4)) (=> (@ (@ tptp.member_int Xi) (@ tptp.set_int2 Xsi2)) (= (@ (@ A X3) Xi) (@ (@ A6 X3) Xi))))) (= (@ (@ (@ tptp.vEBT_L6295016686126367274at_int A) Xs) Xsi) (@ (@ (@ tptp.vEBT_L6295016686126367274at_int A6) Xs4) Xsi2)))))) (forall ((Xs tptp.list_P6011104703257516679at_nat) (Xs4 tptp.list_P6011104703257516679at_nat) (Xsi tptp.list_nat) (Xsi2 tptp.list_nat) (A (-> tptp.product_prod_nat_nat tptp.nat tptp.assn)) (A6 (-> tptp.product_prod_nat_nat tptp.nat tptp.assn))) (=> (= Xs Xs4) (=> (= Xsi Xsi2) (=> (forall ((X3 tptp.product_prod_nat_nat) (Xi tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) (@ tptp.set_Pr5648618587558075414at_nat Xs4)) (=> (@ (@ tptp.member_nat Xi) (@ tptp.set_nat2 Xsi2)) (= (@ (@ A X3) Xi) (@ (@ A6 X3) Xi))))) (= (@ (@ (@ tptp.vEBT_L6297507156635417550at_nat A) Xs) Xsi) (@ (@ (@ tptp.vEBT_L6297507156635417550at_nat A6) Xs4) Xsi2)))))) (forall ((Xs tptp.list_int) (Xs4 tptp.list_int) (Xsi tptp.list_P6011104703257516679at_nat) (Xsi2 tptp.list_P6011104703257516679at_nat) (A (-> tptp.int tptp.product_prod_nat_nat tptp.assn)) (A6 (-> tptp.int tptp.product_prod_nat_nat tptp.assn))) (=> (= Xs Xs4) (=> (= Xsi Xsi2) (=> (forall ((X3 tptp.int) (Xi tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs4)) (=> (@ (@ tptp.member8440522571783428010at_nat Xi) (@ tptp.set_Pr5648618587558075414at_nat Xsi2)) (= (@ (@ A X3) Xi) (@ (@ A6 X3) Xi))))) (= (@ (@ (@ tptp.vEBT_L3472024597287490640at_nat A) Xs) Xsi) (@ (@ (@ tptp.vEBT_L3472024597287490640at_nat A6) Xs4) Xsi2)))))) (forall ((Xs tptp.list_int) (Xs4 tptp.list_int) (Xsi tptp.list_P8527749157015355191n_assn) (Xsi2 tptp.list_P8527749157015355191n_assn) (A (-> tptp.int tptp.produc6575502325842934193n_assn tptp.assn)) (A6 (-> tptp.int tptp.produc6575502325842934193n_assn tptp.assn))) (=> (= Xs Xs4) (=> (= Xsi Xsi2) (=> (forall ((X3 tptp.int) (Xi tptp.produc6575502325842934193n_assn)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs4)) (=> (@ (@ tptp.member7957490590177025114n_assn Xi) (@ tptp.set_Pr1139785259514867910n_assn Xsi2)) (= (@ (@ A X3) Xi) (@ (@ A6 X3) Xi))))) (= (@ (@ (@ tptp.vEBT_L1620274777744359680n_assn A) Xs) Xsi) (@ (@ (@ tptp.vEBT_L1620274777744359680n_assn A6) Xs4) Xsi2)))))) (forall ((Xs tptp.list_nat) (Xs4 tptp.list_nat) (Xsi tptp.list_P6011104703257516679at_nat) (Xsi2 tptp.list_P6011104703257516679at_nat) (A (-> tptp.nat tptp.product_prod_nat_nat tptp.assn)) (A6 (-> tptp.nat tptp.product_prod_nat_nat tptp.assn))) (=> (= Xs Xs4) (=> (= Xsi Xsi2) (=> (forall ((X3 tptp.nat) (Xi tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs4)) (=> (@ (@ tptp.member8440522571783428010at_nat Xi) (@ tptp.set_Pr5648618587558075414at_nat Xsi2)) (= (@ (@ A X3) Xi) (@ (@ A6 X3) Xi))))) (= (@ (@ (@ tptp.vEBT_L434182512823356844at_nat A) Xs) Xsi) (@ (@ (@ tptp.vEBT_L434182512823356844at_nat A6) Xs4) Xsi2)))))) (forall ((Xs tptp.list_nat) (Xs4 tptp.list_nat) (Xsi tptp.list_P8527749157015355191n_assn) (Xsi2 tptp.list_P8527749157015355191n_assn) (A (-> tptp.nat tptp.produc6575502325842934193n_assn tptp.assn)) (A6 (-> tptp.nat tptp.produc6575502325842934193n_assn tptp.assn))) (=> (= Xs Xs4) (=> (= Xsi Xsi2) (=> (forall ((X3 tptp.nat) (Xi tptp.produc6575502325842934193n_assn)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs4)) (=> (@ (@ tptp.member7957490590177025114n_assn Xi) (@ tptp.set_Pr1139785259514867910n_assn Xsi2)) (= (@ (@ A X3) Xi) (@ (@ A6 X3) Xi))))) (= (@ (@ (@ tptp.vEBT_L9083610150846024284n_assn A) Xs) Xsi) (@ (@ (@ tptp.vEBT_L9083610150846024284n_assn A6) Xs4) Xsi2)))))) (forall ((Xs tptp.list_P5464809261938338413at_nat) (X tptp.produc3843707927480180839at_nat)) (=> (@ tptp.distin5355857245021852384at_nat Xs) (=> (@ (@ tptp.member8757157785044589968at_nat X) (@ tptp.set_Pr3765526544606949372at_nat Xs)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.ord_less_nat X3) (@ tptp.size_s1588839187904960729at_nat Xs)) (= (@ (@ tptp.nth_Pr1239524528086697198at_nat Xs) X3) X) (forall ((Y3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat Y3) (@ tptp.size_s1588839187904960729at_nat Xs)) (= (@ (@ tptp.nth_Pr1239524528086697198at_nat Xs) Y3) X)) (= Y3 X3)))))))) (forall ((Xs tptp.list_P6011104703257516679at_nat) (X tptp.product_prod_nat_nat)) (=> (@ tptp.distin6923225563576452346at_nat Xs) (=> (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.ord_less_nat X3) (@ tptp.size_s5460976970255530739at_nat Xs)) (= (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) X3) X) (forall ((Y3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat Y3) (@ tptp.size_s5460976970255530739at_nat Xs)) (= (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) Y3) X)) (= Y3 X3)))))))) (forall ((Xs tptp.list_P7985473006766602707_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.distin299582740263731014_nat_o Xs) (=> (@ (@ tptp.member6576561426505652726_nat_o X) (@ tptp.set_Pr400311997697478754_nat_o Xs)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.ord_less_nat X3) (@ tptp.size_s8908918004648414271_nat_o Xs)) (= (@ (@ tptp.nth_Pr6840583978799713108_nat_o Xs) X3) X) (forall ((Y3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat Y3) (@ tptp.size_s8908918004648414271_nat_o Xs)) (= (@ (@ tptp.nth_Pr6840583978799713108_nat_o Xs) Y3) X)) (= Y3 X3)))))))) (forall ((Xs tptp.list_P8527749157015355191n_assn) (X tptp.produc6575502325842934193n_assn)) (=> (@ tptp.distin4809818325527169450n_assn Xs) (=> (@ (@ tptp.member7957490590177025114n_assn X) (@ tptp.set_Pr1139785259514867910n_assn Xs)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.ord_less_nat X3) (@ tptp.size_s6829681357464350627n_assn Xs)) (= (@ (@ tptp.nth_Pr1769885009046257848n_assn Xs) X3) X) (forall ((Y3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat Y3) (@ tptp.size_s6829681357464350627n_assn Xs)) (= (@ (@ tptp.nth_Pr1769885009046257848n_assn Xs) Y3) X)) (= Y3 X3)))))))) (forall ((Xs tptp.list_c) (X tptp.c)) (=> (@ tptp.distinct_c Xs) (=> (@ (@ tptp.member_c X) (@ tptp.set_c2 Xs)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.ord_less_nat X3) (@ tptp.size_size_list_c Xs)) (= (@ (@ tptp.nth_c Xs) X3) X) (forall ((Y3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat Y3) (@ tptp.size_size_list_c Xs)) (= (@ (@ tptp.nth_c Xs) Y3) X)) (= Y3 X3)))))))) (forall ((Xs tptp.list_d) (X tptp.d)) (=> (@ tptp.distinct_d Xs) (=> (@ (@ tptp.member_d X) (@ tptp.set_d2 Xs)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.ord_less_nat X3) (@ tptp.size_size_list_d Xs)) (= (@ (@ tptp.nth_d Xs) X3) X) (forall ((Y3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat Y3) (@ tptp.size_size_list_d Xs)) (= (@ (@ tptp.nth_d Xs) Y3) X)) (= Y3 X3)))))))) (forall ((Xs tptp.list_nat) (X tptp.nat)) (=> (@ tptp.distinct_nat Xs) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.ord_less_nat X3) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) X3) X) (forall ((Y3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat Y3) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) Y3) X)) (= Y3 X3)))))))) (forall ((Xs tptp.list_int) (X tptp.int)) (=> (@ tptp.distinct_int Xs) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.ord_less_nat X3) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int Xs) X3) X) (forall ((Y3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat Y3) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int Xs) Y3) X)) (= Y3 X3)))))))) (forall ((P tptp.assn) (H2 tptp.heap_e7401611519738050253t_unit) (H4 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ tptp.rep_assn P))) (= (@ _let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) tptp.bot_bot_set_nat)) (@ _let_1 (@ (@ tptp.produc7507926704131184380et_nat H4) tptp.bot_bot_set_nat))))) (forall ((Xs tptp.list_P7985473006766602707_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (I tptp.nat)) (=> (@ tptp.distin299582740263731014_nat_o Xs) (=> (not (@ (@ tptp.member6576561426505652726_nat_o A2) (@ (@ tptp.minus_1801376950450012436_nat_o (@ tptp.set_Pr400311997697478754_nat_o Xs)) (@ (@ tptp.insert5175938949040314269_nat_o (@ (@ tptp.nth_Pr6840583978799713108_nat_o Xs) I)) tptp.bot_bo7824918357723582233_nat_o)))) (@ tptp.distin299582740263731014_nat_o (@ (@ (@ tptp.list_u6943956310655620667_nat_o Xs) I) A2))))) (forall ((Xs tptp.list_P8527749157015355191n_assn) (A2 tptp.produc6575502325842934193n_assn) (I tptp.nat)) (=> (@ tptp.distin4809818325527169450n_assn Xs) (=> (not (@ (@ tptp.member7957490590177025114n_assn A2) (@ (@ tptp.minus_2301194108115264760n_assn (@ tptp.set_Pr1139785259514867910n_assn Xs)) (@ (@ tptp.insert5290817439147925377n_assn (@ (@ tptp.nth_Pr1769885009046257848n_assn Xs) I)) tptp.bot_bo1176836662018730877n_assn)))) (@ tptp.distin4809818325527169450n_assn (@ (@ (@ tptp.list_u4534839942911652127n_assn Xs) I) A2))))) (forall ((Xs tptp.list_c) (A2 tptp.c) (I tptp.nat)) (=> (@ tptp.distinct_c Xs) (=> (not (@ (@ tptp.member_c A2) (@ (@ tptp.minus_minus_set_c (@ tptp.set_c2 Xs)) (@ (@ tptp.insert_c (@ (@ tptp.nth_c Xs) I)) tptp.bot_bot_set_c)))) (@ tptp.distinct_c (@ (@ (@ tptp.list_update_c Xs) I) A2))))) (forall ((Xs tptp.list_d) (A2 tptp.d) (I tptp.nat)) (=> (@ tptp.distinct_d Xs) (=> (not (@ (@ tptp.member_d A2) (@ (@ tptp.minus_minus_set_d (@ tptp.set_d2 Xs)) (@ (@ tptp.insert_d (@ (@ tptp.nth_d Xs) I)) tptp.bot_bot_set_d)))) (@ tptp.distinct_d (@ (@ (@ tptp.list_update_d Xs) I) A2))))) (forall ((Xs tptp.list_P5464809261938338413at_nat) (A2 tptp.produc3843707927480180839at_nat) (I tptp.nat)) (=> (@ tptp.distin5355857245021852384at_nat Xs) (=> (not (@ (@ tptp.member8757157785044589968at_nat A2) (@ (@ tptp.minus_3314409938677909166at_nat (@ tptp.set_Pr3765526544606949372at_nat Xs)) (@ (@ tptp.insert9069300056098147895at_nat (@ (@ tptp.nth_Pr1239524528086697198at_nat Xs) I)) tptp.bot_bo228742789529271731at_nat)))) (@ tptp.distin5355857245021852384at_nat (@ (@ (@ tptp.list_u4696772448584712917at_nat Xs) I) A2))))) (forall ((Xs tptp.list_P6011104703257516679at_nat) (A2 tptp.product_prod_nat_nat) (I tptp.nat)) (=> (@ tptp.distin6923225563576452346at_nat Xs) (=> (not (@ (@ tptp.member8440522571783428010at_nat A2) (@ (@ tptp.minus_1356011639430497352at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs)) (@ (@ tptp.insert8211810215607154385at_nat (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) I)) tptp.bot_bo2099793752762293965at_nat)))) (@ tptp.distin6923225563576452346at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat Xs) I) A2))))) (forall ((Xs tptp.list_o) (A2 Bool) (I tptp.nat)) (=> (@ tptp.distinct_o Xs) (=> (not (@ (@ tptp.member_o A2) (@ (@ tptp.minus_minus_set_o (@ tptp.set_o2 Xs)) (@ (@ tptp.insert_o2 (@ (@ tptp.nth_o Xs) I)) tptp.bot_bot_set_o)))) (@ tptp.distinct_o (@ (@ (@ tptp.list_update_o Xs) I) A2))))) (forall ((Xs tptp.list_int) (A2 tptp.int) (I tptp.nat)) (=> (@ tptp.distinct_int Xs) (=> (not (@ (@ tptp.member_int A2) (@ (@ tptp.minus_minus_set_int (@ tptp.set_int2 Xs)) (@ (@ tptp.insert_int2 (@ (@ tptp.nth_int Xs) I)) tptp.bot_bot_set_int)))) (@ tptp.distinct_int (@ (@ (@ tptp.list_update_int Xs) I) A2))))) (forall ((Xs tptp.list_nat) (A2 tptp.nat) (I tptp.nat)) (=> (@ tptp.distinct_nat Xs) (=> (not (@ (@ tptp.member_nat A2) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_nat2 Xs)) (@ (@ tptp.insert_nat2 (@ (@ tptp.nth_nat Xs) I)) tptp.bot_bot_set_nat)))) (@ tptp.distinct_nat (@ (@ (@ tptp.list_update_nat Xs) I) A2))))) _let_164 _let_163 _let_162 _let_161 (forall ((Xs tptp.list_c) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_c Xs))) (let ((_let_2 (@ tptp.size_size_list_c Xs))) (=> (@ tptp.distinct_c Xs) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (= (@ _let_1 I) (@ _let_1 J)) (= I J)))))))) (forall ((Xs tptp.list_d) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_d Xs))) (let ((_let_2 (@ tptp.size_size_list_d Xs))) (=> (@ tptp.distinct_d Xs) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (= (@ _let_1 I) (@ _let_1 J)) (= I J)))))))) (forall ((Xs tptp.list_nat) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (let ((_let_2 (@ tptp.size_size_list_nat Xs))) (=> (@ tptp.distinct_nat Xs) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (= (@ _let_1 I) (@ _let_1 J)) (= I J)))))))) (forall ((Xs tptp.list_int) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs))) (let ((_let_2 (@ tptp.size_size_list_int Xs))) (=> (@ tptp.distinct_int Xs) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (= (@ _let_1 I) (@ _let_1 J)) (= I J)))))))) (forall ((L tptp.list_P8527749157015355191n_assn) (P (-> tptp.produc6575502325842934193n_assn Bool))) (= (forall ((X2 tptp.produc6575502325842934193n_assn)) (=> (@ (@ tptp.member7957490590177025114n_assn X2) (@ tptp.set_Pr1139785259514867910n_assn L)) (@ P X2))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6829681357464350627n_assn L)) (@ P (@ (@ tptp.nth_Pr1769885009046257848n_assn L) I4)))))) (forall ((L tptp.list_c) (P (-> tptp.c Bool))) (= (forall ((X2 tptp.c)) (=> (@ (@ tptp.member_c X2) (@ tptp.set_c2 L)) (@ P X2))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_c L)) (@ P (@ (@ tptp.nth_c L) I4)))))) (forall ((L tptp.list_d) (P (-> tptp.d Bool))) (= (forall ((X2 tptp.d)) (=> (@ (@ tptp.member_d X2) (@ tptp.set_d2 L)) (@ P X2))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_d L)) (@ P (@ (@ tptp.nth_d L) I4)))))) (forall ((L tptp.list_nat) (P (-> tptp.nat Bool))) (= (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 L)) (@ P X2))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat L)) (@ P (@ (@ tptp.nth_nat L) I4)))))) (forall ((L tptp.list_int) (P (-> tptp.int Bool))) (= (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) (@ tptp.set_int2 L)) (@ P X2))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int L)) (@ P (@ (@ tptp.nth_int L) I4)))))) (forall ((N tptp.nat) (Xs tptp.list_P5464809261938338413at_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s1588839187904960729at_nat Xs)) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.nth_Pr1239524528086697198at_nat Xs) N)) (@ tptp.set_Pr3765526544606949372at_nat Xs)))) (forall ((N tptp.nat) (Xs tptp.list_P6011104703257516679at_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s5460976970255530739at_nat Xs)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) N)) (@ tptp.set_Pr5648618587558075414at_nat Xs)))) (forall ((N tptp.nat) (Xs tptp.list_P7985473006766602707_nat_o)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s8908918004648414271_nat_o Xs)) (@ (@ tptp.member6576561426505652726_nat_o (@ (@ tptp.nth_Pr6840583978799713108_nat_o Xs) N)) (@ tptp.set_Pr400311997697478754_nat_o Xs)))) (forall ((N tptp.nat) (Xs tptp.list_P8527749157015355191n_assn)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6829681357464350627n_assn Xs)) (@ (@ tptp.member7957490590177025114n_assn (@ (@ tptp.nth_Pr1769885009046257848n_assn Xs) N)) (@ tptp.set_Pr1139785259514867910n_assn Xs)))) (forall ((N tptp.nat) (Xs tptp.list_c)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_c Xs)) (@ (@ tptp.member_c (@ (@ tptp.nth_c Xs) N)) (@ tptp.set_c2 Xs)))) (forall ((N tptp.nat) (Xs tptp.list_d)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_d Xs)) (@ (@ tptp.member_d (@ (@ tptp.nth_d Xs) N)) (@ tptp.set_d2 Xs)))) (forall ((N tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.member_nat (@ (@ tptp.nth_nat Xs) N)) (@ tptp.set_nat2 Xs)))) (forall ((N tptp.nat) (Xs tptp.list_int)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs)) (@ (@ tptp.member_int (@ (@ tptp.nth_int Xs) N)) (@ tptp.set_int2 Xs)))) (forall ((N tptp.nat) (Xs tptp.list_P8527749157015355191n_assn) (P (-> tptp.produc6575502325842934193n_assn Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6829681357464350627n_assn Xs)) (=> (forall ((X3 tptp.produc6575502325842934193n_assn)) (=> (@ (@ tptp.member7957490590177025114n_assn X3) (@ tptp.set_Pr1139785259514867910n_assn Xs)) (@ P X3))) (@ P (@ (@ tptp.nth_Pr1769885009046257848n_assn Xs) N))))) (forall ((N tptp.nat) (Xs tptp.list_c) (P (-> tptp.c Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_c Xs)) (=> (forall ((X3 tptp.c)) (=> (@ (@ tptp.member_c X3) (@ tptp.set_c2 Xs)) (@ P X3))) (@ P (@ (@ tptp.nth_c Xs) N))))) (forall ((N tptp.nat) (Xs tptp.list_d) (P (-> tptp.d Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_d Xs)) (=> (forall ((X3 tptp.d)) (=> (@ (@ tptp.member_d X3) (@ tptp.set_d2 Xs)) (@ P X3))) (@ P (@ (@ tptp.nth_d Xs) N))))) (forall ((N tptp.nat) (Xs tptp.list_nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ 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tptp.list_d)) (= (@ (@ tptp.member_d X) (@ tptp.set_d2 Xs)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_d Xs)) (= (@ (@ tptp.nth_d Xs) I4) X))))) (forall ((X tptp.nat) (Xs tptp.list_nat)) (= (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I4) X))))) (forall ((X tptp.int) (Xs tptp.list_int)) (= (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int Xs) I4) X))))) (forall ((Xs tptp.list_P5464809261938338413at_nat) (P (-> tptp.produc3843707927480180839at_nat Bool)) (X tptp.produc3843707927480180839at_nat)) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_s1588839187904960729at_nat Xs)) (@ P (@ (@ tptp.nth_Pr1239524528086697198at_nat Xs) I5)))) (=> (@ (@ tptp.member8757157785044589968at_nat X) (@ tptp.set_Pr3765526544606949372at_nat Xs)) (@ P X)))) (forall ((Xs tptp.list_P6011104703257516679at_nat) (P (-> tptp.product_prod_nat_nat Bool)) (X tptp.product_prod_nat_nat)) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_s5460976970255530739at_nat Xs)) (@ P (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) I5)))) (=> (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs)) (@ P X)))) (forall ((Xs tptp.list_P7985473006766602707_nat_o) (P (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool)) (X (-> tptp.produc3658429121746597890et_nat Bool))) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_s8908918004648414271_nat_o Xs)) (@ P (@ (@ tptp.nth_Pr6840583978799713108_nat_o Xs) I5)))) (=> (@ (@ tptp.member6576561426505652726_nat_o X) (@ tptp.set_Pr400311997697478754_nat_o Xs)) (@ P X)))) (forall ((Xs tptp.list_P8527749157015355191n_assn) (P (-> tptp.produc6575502325842934193n_assn Bool)) (X 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tptp.member_nat X) (@ tptp.set_nat2 Xs)) (@ P X)))) (forall ((Xs tptp.list_int) (P (-> tptp.int Bool)) (X tptp.int)) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_int Xs)) (@ P (@ (@ tptp.nth_int Xs) I5)))) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs)) (@ P X)))) (forall ((Xs tptp.list_P8527749157015355191n_assn) (P (-> tptp.produc6575502325842934193n_assn Bool))) (= (forall ((X2 tptp.produc6575502325842934193n_assn)) (=> (@ (@ tptp.member7957490590177025114n_assn X2) (@ tptp.set_Pr1139785259514867910n_assn Xs)) (@ P X2))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6829681357464350627n_assn Xs)) (@ P (@ (@ tptp.nth_Pr1769885009046257848n_assn Xs) I4)))))) (forall ((Xs tptp.list_c) (P (-> tptp.c Bool))) (= (forall ((X2 tptp.c)) (=> (@ (@ tptp.member_c X2) (@ tptp.set_c2 Xs)) (@ P X2))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_c Xs)) (@ P (@ (@ tptp.nth_c Xs) I4)))))) (forall ((Xs tptp.list_d) (P (-> tptp.d Bool))) (= (forall ((X2 tptp.d)) (=> (@ (@ tptp.member_d X2) (@ tptp.set_d2 Xs)) (@ P X2))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_d Xs)) (@ P (@ (@ tptp.nth_d Xs) I4)))))) (forall ((Xs tptp.list_nat) (P (-> tptp.nat Bool))) (= (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Xs)) (@ P X2))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs)) (@ P (@ (@ tptp.nth_nat Xs) I4)))))) (forall ((Xs tptp.list_int) (P (-> tptp.int Bool))) (= (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) (@ tptp.set_int2 Xs)) (@ P X2))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs)) (@ P (@ (@ tptp.nth_int Xs) I4)))))) (forall ((I tptp.nat) (L tptp.list_P5464809261938338413at_nat) (X tptp.produc3843707927480180839at_nat) (Y tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s1588839187904960729at_nat L)) (= (@ (@ tptp.member8757157785044589968at_nat X) (@ tptp.set_Pr3765526544606949372at_nat (@ (@ (@ tptp.list_u4696772448584712917at_nat L) I) Y))) (or (= X Y) (forall ((Y5 tptp.produc3843707927480180839at_nat)) (@ (@ tptp.member8757157785044589968at_nat X) (@ tptp.set_Pr3765526544606949372at_nat (@ (@ (@ tptp.list_u4696772448584712917at_nat L) I) Y5)))))))) (forall ((I tptp.nat) (L tptp.list_P6011104703257516679at_nat) (X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s5460976970255530739at_nat L)) (= (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat L) I) Y))) (or (= X Y) (forall ((Y5 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat L) I) Y5)))))))) (forall ((I tptp.nat) (L tptp.list_P7985473006766602707_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Y (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s8908918004648414271_nat_o L)) (= (@ (@ tptp.member6576561426505652726_nat_o X) (@ tptp.set_Pr400311997697478754_nat_o (@ (@ (@ tptp.list_u6943956310655620667_nat_o L) I) Y))) (or (= X Y) (forall ((Y5 (-> tptp.produc3658429121746597890et_nat Bool))) (@ (@ tptp.member6576561426505652726_nat_o X) (@ tptp.set_Pr400311997697478754_nat_o (@ (@ (@ tptp.list_u6943956310655620667_nat_o L) I) Y5)))))))) (forall ((I tptp.nat) (L tptp.list_P8527749157015355191n_assn) (X tptp.produc6575502325842934193n_assn) (Y tptp.produc6575502325842934193n_assn)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6829681357464350627n_assn L)) (= (@ (@ tptp.member7957490590177025114n_assn X) (@ tptp.set_Pr1139785259514867910n_assn (@ (@ (@ tptp.list_u4534839942911652127n_assn L) I) Y))) (or (= X Y) (forall ((Y5 tptp.produc6575502325842934193n_assn)) (@ (@ tptp.member7957490590177025114n_assn X) (@ tptp.set_Pr1139785259514867910n_assn (@ (@ (@ tptp.list_u4534839942911652127n_assn L) I) Y5)))))))) (forall ((I tptp.nat) (L tptp.list_c) (X tptp.c) (Y tptp.c)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_c L)) (= (@ (@ tptp.member_c X) (@ tptp.set_c2 (@ (@ (@ tptp.list_update_c L) I) Y))) (or (= X Y) (forall ((Y5 tptp.c)) (@ (@ tptp.member_c X) (@ tptp.set_c2 (@ (@ (@ tptp.list_update_c L) I) Y5)))))))) (forall ((I tptp.nat) (L tptp.list_d) (X tptp.d) (Y tptp.d)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_d L)) (= (@ (@ tptp.member_d X) (@ tptp.set_d2 (@ (@ (@ tptp.list_update_d L) I) Y))) (or (= X Y) (forall ((Y5 tptp.d)) (@ (@ tptp.member_d X) (@ tptp.set_d2 (@ (@ (@ tptp.list_update_d L) I) Y5)))))))) (forall ((I tptp.nat) (L tptp.list_nat) (X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat L)) (= (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat L) I) Y))) (or (= X Y) (forall ((Y5 tptp.nat)) (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat L) I) Y5)))))))) (forall ((I tptp.nat) (L tptp.list_int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int L)) (= (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int L) I) Y))) (or (= X Y) (forall ((Y5 tptp.int)) (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int L) I) Y5)))))))) (forall ((X tptp.produc3843707927480180839at_nat) (L tptp.list_P5464809261938338413at_nat) (I tptp.nat) (Y tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat X))) (=> (@ _let_1 (@ tptp.set_Pr3765526544606949372at_nat (@ (@ (@ tptp.list_u4696772448584712917at_nat L) I) Y))) (=> (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s1588839187904960729at_nat L)) (not (= X Y))) (@ _let_1 (@ tptp.set_Pr3765526544606949372at_nat L)))))) (forall ((X tptp.product_prod_nat_nat) (L tptp.list_P6011104703257516679at_nat) (I tptp.nat) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X))) (=> (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat L) I) Y))) (=> (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s5460976970255530739at_nat L)) (not (= X Y))) (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat L)))))) (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (L tptp.list_P7985473006766602707_nat_o) (I tptp.nat) (Y (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o X))) (=> (@ _let_1 (@ tptp.set_Pr400311997697478754_nat_o (@ (@ (@ tptp.list_u6943956310655620667_nat_o L) I) Y))) (=> (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s8908918004648414271_nat_o L)) (not (= X Y))) (@ _let_1 (@ tptp.set_Pr400311997697478754_nat_o L)))))) (forall ((X tptp.produc6575502325842934193n_assn) (L tptp.list_P8527749157015355191n_assn) (I tptp.nat) (Y tptp.produc6575502325842934193n_assn)) (let ((_let_1 (@ tptp.member7957490590177025114n_assn X))) (=> (@ _let_1 (@ tptp.set_Pr1139785259514867910n_assn (@ (@ (@ tptp.list_u4534839942911652127n_assn L) I) Y))) (=> (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6829681357464350627n_assn L)) (not (= X Y))) (@ _let_1 (@ tptp.set_Pr1139785259514867910n_assn L)))))) (forall ((X tptp.c) (L tptp.list_c) (I tptp.nat) (Y tptp.c)) (let ((_let_1 (@ tptp.member_c X))) (=> (@ _let_1 (@ tptp.set_c2 (@ (@ (@ tptp.list_update_c L) I) Y))) (=> (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_c L)) (not (= X Y))) (@ _let_1 (@ tptp.set_c2 L)))))) (forall ((X tptp.d) (L tptp.list_d) (I tptp.nat) (Y tptp.d)) (let ((_let_1 (@ tptp.member_d X))) (=> (@ _let_1 (@ tptp.set_d2 (@ (@ (@ tptp.list_update_d L) I) Y))) (=> (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_d L)) (not (= X Y))) (@ _let_1 (@ tptp.set_d2 L)))))) (forall ((X tptp.nat) (L tptp.list_nat) (I tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (=> (@ _let_1 (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat L) I) Y))) (=> (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat L)) (not (= X Y))) (@ _let_1 (@ tptp.set_nat2 L)))))) (forall ((X tptp.int) (L tptp.list_int) (I tptp.nat) (Y tptp.int)) (let ((_let_1 (@ tptp.member_int X))) (=> (@ _let_1 (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int L) I) Y))) (=> (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int L)) (not (= X Y))) (@ _let_1 (@ tptp.set_int2 L)))))) (forall ((I tptp.nat) (L tptp.list_P5464809261938338413at_nat) (X tptp.produc3843707927480180839at_nat) (Y tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat X))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s1588839187904960729at_nat L)) (= (@ _let_1 (@ tptp.set_Pr3765526544606949372at_nat (@ (@ (@ tptp.list_u4696772448584712917at_nat L) I) Y))) (or (= X Y) (and (@ _let_1 (@ tptp.set_Pr3765526544606949372at_nat L)) (forall ((Y5 tptp.produc3843707927480180839at_nat)) (@ (@ tptp.member8757157785044589968at_nat X) (@ tptp.set_Pr3765526544606949372at_nat (@ (@ (@ tptp.list_u4696772448584712917at_nat L) I) Y5)))))))))) (forall ((I tptp.nat) (L tptp.list_P6011104703257516679at_nat) (X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s5460976970255530739at_nat L)) (= (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat L) I) Y))) (or (= X Y) (and (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat L)) (forall ((Y5 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat L) I) Y5)))))))))) (forall ((I tptp.nat) (L tptp.list_P7985473006766602707_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Y (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o X))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s8908918004648414271_nat_o L)) (= (@ _let_1 (@ tptp.set_Pr400311997697478754_nat_o (@ (@ (@ tptp.list_u6943956310655620667_nat_o L) I) Y))) (or (= X Y) (and (@ _let_1 (@ tptp.set_Pr400311997697478754_nat_o L)) (forall ((Y5 (-> tptp.produc3658429121746597890et_nat Bool))) (@ (@ tptp.member6576561426505652726_nat_o X) (@ tptp.set_Pr400311997697478754_nat_o (@ (@ (@ tptp.list_u6943956310655620667_nat_o L) I) Y5)))))))))) (forall ((I tptp.nat) (L tptp.list_P8527749157015355191n_assn) (X tptp.produc6575502325842934193n_assn) (Y tptp.produc6575502325842934193n_assn)) (let ((_let_1 (@ tptp.member7957490590177025114n_assn X))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6829681357464350627n_assn L)) (= (@ _let_1 (@ tptp.set_Pr1139785259514867910n_assn (@ (@ (@ tptp.list_u4534839942911652127n_assn L) I) Y))) (or (= X Y) (and (@ _let_1 (@ tptp.set_Pr1139785259514867910n_assn L)) (forall ((Y5 tptp.produc6575502325842934193n_assn)) (@ (@ tptp.member7957490590177025114n_assn X) (@ tptp.set_Pr1139785259514867910n_assn (@ (@ (@ tptp.list_u4534839942911652127n_assn L) I) Y5)))))))))) (forall ((I tptp.nat) (L tptp.list_c) (X tptp.c) (Y tptp.c)) (let ((_let_1 (@ tptp.member_c X))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_c L)) (= (@ _let_1 (@ tptp.set_c2 (@ (@ (@ tptp.list_update_c L) I) Y))) (or (= X Y) (and (@ _let_1 (@ tptp.set_c2 L)) (forall ((Y5 tptp.c)) (@ (@ tptp.member_c X) (@ tptp.set_c2 (@ (@ (@ tptp.list_update_c L) I) Y5)))))))))) (forall ((I tptp.nat) (L tptp.list_d) (X tptp.d) (Y tptp.d)) (let ((_let_1 (@ tptp.member_d X))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_d L)) (= (@ _let_1 (@ tptp.set_d2 (@ (@ (@ tptp.list_update_d L) I) Y))) (or (= X Y) (and (@ _let_1 (@ tptp.set_d2 L)) (forall ((Y5 tptp.d)) (@ (@ tptp.member_d X) (@ tptp.set_d2 (@ (@ (@ tptp.list_update_d L) I) Y5)))))))))) (forall ((I tptp.nat) (L tptp.list_nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat L)) (= (@ _let_1 (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat L) I) Y))) (or (= X Y) (and (@ _let_1 (@ tptp.set_nat2 L)) (forall ((Y5 tptp.nat)) (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat L) I) Y5)))))))))) (forall ((I tptp.nat) (L tptp.list_int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.member_int X))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int L)) (= (@ _let_1 (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int L) I) Y))) (or (= X Y) (and (@ _let_1 (@ tptp.set_int2 L)) (forall ((Y5 tptp.int)) (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int L) I) Y5)))))))))) (forall ((N tptp.nat) (Xs tptp.list_P5464809261938338413at_nat) (X tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s1588839187904960729at_nat Xs)) (@ (@ tptp.member8757157785044589968at_nat X) (@ tptp.set_Pr3765526544606949372at_nat (@ (@ (@ tptp.list_u4696772448584712917at_nat Xs) N) X))))) (forall ((N tptp.nat) (Xs tptp.list_P6011104703257516679at_nat) (X tptp.product_prod_nat_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s5460976970255530739at_nat Xs)) (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat Xs) N) X))))) (forall ((N tptp.nat) (Xs tptp.list_P7985473006766602707_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s8908918004648414271_nat_o Xs)) (@ (@ tptp.member6576561426505652726_nat_o X) (@ tptp.set_Pr400311997697478754_nat_o (@ (@ (@ tptp.list_u6943956310655620667_nat_o Xs) N) X))))) (forall ((N tptp.nat) (Xs tptp.list_P8527749157015355191n_assn) (X tptp.produc6575502325842934193n_assn)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6829681357464350627n_assn Xs)) (@ (@ tptp.member7957490590177025114n_assn X) (@ tptp.set_Pr1139785259514867910n_assn (@ (@ (@ tptp.list_u4534839942911652127n_assn Xs) N) X))))) (forall ((N tptp.nat) (Xs tptp.list_c) (X tptp.c)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_c Xs)) (@ (@ tptp.member_c X) (@ tptp.set_c2 (@ (@ (@ tptp.list_update_c Xs) N) X))))) (forall ((N tptp.nat) (Xs tptp.list_d) (X tptp.d)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_d Xs)) (@ (@ tptp.member_d X) (@ tptp.set_d2 (@ (@ (@ tptp.list_update_d Xs) N) X))))) (forall ((N tptp.nat) (Xs tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs) N) X))))) (forall ((N tptp.nat) (Xs tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs)) (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs) N) X))))) (forall ((Xs tptp.list_P8527749157015355191n_assn) (N tptp.nat) (X tptp.produc6575502325842934193n_assn)) (=> (@ tptp.distin4809818325527169450n_assn Xs) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6829681357464350627n_assn Xs)) (= (@ tptp.set_Pr1139785259514867910n_assn (@ (@ (@ tptp.list_u4534839942911652127n_assn Xs) N) X)) (@ (@ tptp.insert5290817439147925377n_assn X) (@ (@ tptp.minus_2301194108115264760n_assn (@ tptp.set_Pr1139785259514867910n_assn Xs)) (@ (@ tptp.insert5290817439147925377n_assn (@ (@ tptp.nth_Pr1769885009046257848n_assn Xs) N)) tptp.bot_bo1176836662018730877n_assn))))))) (forall ((Xs tptp.list_c) (N tptp.nat) (X tptp.c)) (=> (@ tptp.distinct_c Xs) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_c Xs)) (= (@ tptp.set_c2 (@ (@ (@ tptp.list_update_c Xs) N) X)) (@ (@ tptp.insert_c X) (@ (@ tptp.minus_minus_set_c (@ tptp.set_c2 Xs)) (@ (@ tptp.insert_c (@ (@ tptp.nth_c Xs) N)) tptp.bot_bot_set_c))))))) (forall ((Xs tptp.list_d) (N tptp.nat) (X tptp.d)) (=> (@ tptp.distinct_d Xs) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_d Xs)) (= (@ tptp.set_d2 (@ (@ (@ tptp.list_update_d Xs) N) X)) (@ (@ tptp.insert_d X) (@ (@ tptp.minus_minus_set_d (@ tptp.set_d2 Xs)) (@ (@ tptp.insert_d (@ (@ tptp.nth_d Xs) N)) tptp.bot_bot_set_d))))))) (forall ((Xs tptp.list_P5464809261938338413at_nat) (N tptp.nat) (X tptp.produc3843707927480180839at_nat)) (=> (@ tptp.distin5355857245021852384at_nat Xs) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s1588839187904960729at_nat Xs)) (= (@ tptp.set_Pr3765526544606949372at_nat (@ (@ (@ tptp.list_u4696772448584712917at_nat Xs) N) X)) (@ (@ tptp.insert9069300056098147895at_nat X) (@ (@ tptp.minus_3314409938677909166at_nat (@ tptp.set_Pr3765526544606949372at_nat Xs)) (@ (@ tptp.insert9069300056098147895at_nat (@ (@ tptp.nth_Pr1239524528086697198at_nat Xs) N)) tptp.bot_bo228742789529271731at_nat))))))) (forall ((Xs tptp.list_P6011104703257516679at_nat) (N tptp.nat) (X tptp.product_prod_nat_nat)) (=> (@ tptp.distin6923225563576452346at_nat Xs) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s5460976970255530739at_nat Xs)) (= (@ tptp.set_Pr5648618587558075414at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat Xs) N) X)) (@ (@ tptp.insert8211810215607154385at_nat X) (@ (@ tptp.minus_1356011639430497352at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs)) (@ (@ tptp.insert8211810215607154385at_nat (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) N)) tptp.bot_bo2099793752762293965at_nat))))))) (forall ((Xs tptp.list_o) (N tptp.nat) (X Bool)) (=> (@ tptp.distinct_o Xs) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs)) (= (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o Xs) N) X)) (@ (@ tptp.insert_o2 X) (@ (@ tptp.minus_minus_set_o (@ tptp.set_o2 Xs)) (@ (@ tptp.insert_o2 (@ (@ tptp.nth_o Xs) N)) tptp.bot_bot_set_o))))))) (forall ((Xs tptp.list_int) (N tptp.nat) (X tptp.int)) (=> (@ tptp.distinct_int Xs) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs)) (= (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs) N) X)) (@ (@ tptp.insert_int2 X) (@ (@ tptp.minus_minus_set_int (@ tptp.set_int2 Xs)) (@ (@ tptp.insert_int2 (@ (@ tptp.nth_int Xs) N)) tptp.bot_bot_set_int))))))) (forall ((Xs tptp.list_nat) (N tptp.nat) (X tptp.nat)) (=> (@ tptp.distinct_nat Xs) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (= (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs) N) X)) (@ (@ tptp.insert_nat2 X) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_nat2 Xs)) (@ (@ tptp.insert_nat2 (@ (@ tptp.nth_nat Xs) N)) tptp.bot_bot_set_nat))))))) (forall ((X1 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (X22 tptp.produc8923325533196201883nteger) (Y1 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (Y22 tptp.produc8923325533196201883nteger)) (= (= (@ (@ tptp.produc8603105652947943368nteger X1) X22) (@ (@ tptp.produc8603105652947943368nteger Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))) (forall ((X1 (-> tptp.produc3658429121746597890et_nat Bool)) (X22 tptp.produc3658429121746597890et_nat) (Y1 (-> tptp.produc3658429121746597890et_nat Bool)) (Y22 tptp.produc3658429121746597890et_nat)) (= (= (@ (@ tptp.produc5001842942810119800et_nat X1) X22) (@ (@ tptp.produc5001842942810119800et_nat Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))) (forall ((X1 (-> tptp.produc3658429121746597890et_nat Bool)) (X22 tptp.produc3925858234332021118et_nat) (Y1 (-> tptp.produc3658429121746597890et_nat Bool)) (Y22 tptp.produc3925858234332021118et_nat)) (= (= (@ (@ tptp.produc2245416461498447860et_nat X1) X22) (@ (@ tptp.produc2245416461498447860et_nat Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))) (forall ((X1 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (X22 tptp.product_prod_int_int) (Y1 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y22 tptp.product_prod_int_int)) (= (= (@ (@ tptp.produc5700946648718959541nt_int X1) X22) (@ (@ tptp.produc5700946648718959541nt_int Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))) (forall ((X1 (-> tptp.int tptp.option6357759511663192854e_term)) (X22 tptp.product_prod_int_int) (Y1 (-> tptp.int tptp.option6357759511663192854e_term)) (Y22 tptp.product_prod_int_int)) (= (= (@ (@ tptp.produc4305682042979456191nt_int X1) X22) (@ (@ tptp.produc4305682042979456191nt_int Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))) (forall ((A2 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B2 tptp.produc8923325533196201883nteger) (A7 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B6 tptp.produc8923325533196201883nteger)) (= (= (@ (@ tptp.produc8603105652947943368nteger A2) B2) (@ (@ tptp.produc8603105652947943368nteger A7) B6)) (and (= A2 A7) (= B2 B6)))) (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.produc3658429121746597890et_nat) (A7 (-> tptp.produc3658429121746597890et_nat Bool)) (B6 tptp.produc3658429121746597890et_nat)) (= (= (@ (@ tptp.produc5001842942810119800et_nat A2) B2) (@ (@ tptp.produc5001842942810119800et_nat A7) B6)) (and (= A2 A7) (= B2 B6)))) (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.produc3925858234332021118et_nat) (A7 (-> tptp.produc3658429121746597890et_nat Bool)) (B6 tptp.produc3925858234332021118et_nat)) (= (= (@ (@ tptp.produc2245416461498447860et_nat A2) B2) (@ (@ tptp.produc2245416461498447860et_nat A7) B6)) (and (= A2 A7) (= B2 B6)))) (forall ((A2 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B2 tptp.product_prod_int_int) (A7 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B6 tptp.product_prod_int_int)) (= (= (@ (@ tptp.produc5700946648718959541nt_int A2) B2) (@ (@ tptp.produc5700946648718959541nt_int A7) B6)) (and (= A2 A7) (= B2 B6)))) (forall ((A2 (-> tptp.int tptp.option6357759511663192854e_term)) (B2 tptp.product_prod_int_int) (A7 (-> tptp.int tptp.option6357759511663192854e_term)) (B6 tptp.product_prod_int_int)) (= (= (@ (@ tptp.produc4305682042979456191nt_int A2) B2) (@ (@ tptp.produc4305682042979456191nt_int A7) B6)) (and (= A2 A7) (= B2 B6)))) (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (= (@ tptp.distinct_int (@ (@ tptp.union_int Xs) Ys)) (@ tptp.distinct_int Ys))) (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (= (@ tptp.distinct_nat (@ (@ tptp.union_nat Xs) Ys)) (@ tptp.distinct_nat Ys))) (forall ((Xs tptp.list_P8527749157015355191n_assn) (X tptp.produc6575502325842934193n_assn)) (=> (@ tptp.distin4809818325527169450n_assn Xs) (= (@ tptp.set_Pr1139785259514867910n_assn (@ (@ tptp.remove1670527618125605709n_assn X) Xs)) (@ (@ tptp.minus_2301194108115264760n_assn (@ tptp.set_Pr1139785259514867910n_assn Xs)) (@ (@ tptp.insert5290817439147925377n_assn X) tptp.bot_bo1176836662018730877n_assn))))) (forall ((Xs tptp.list_P5464809261938338413at_nat) (X tptp.produc3843707927480180839at_nat)) (=> (@ tptp.distin5355857245021852384at_nat Xs) (= (@ tptp.set_Pr3765526544606949372at_nat (@ (@ tptp.remove8895909992688781315at_nat X) Xs)) (@ (@ tptp.minus_3314409938677909166at_nat (@ tptp.set_Pr3765526544606949372at_nat Xs)) (@ (@ tptp.insert9069300056098147895at_nat X) tptp.bot_bo228742789529271731at_nat))))) (forall ((Xs tptp.list_P6011104703257516679at_nat) (X tptp.product_prod_nat_nat)) (=> (@ tptp.distin6923225563576452346at_nat Xs) (= (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.remove5766854097993331357at_nat X) Xs)) (@ (@ tptp.minus_1356011639430497352at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs)) (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat))))) (forall ((Xs tptp.list_o) (X Bool)) (=> (@ tptp.distinct_o Xs) (= (@ tptp.set_o2 (@ (@ tptp.remove1_o X) Xs)) (@ (@ tptp.minus_minus_set_o (@ tptp.set_o2 Xs)) (@ (@ tptp.insert_o2 X) tptp.bot_bot_set_o))))) (forall ((Xs tptp.list_int) (X tptp.int)) (=> (@ tptp.distinct_int Xs) (= (@ tptp.set_int2 (@ (@ tptp.remove1_int X) Xs)) (@ (@ tptp.minus_minus_set_int (@ tptp.set_int2 Xs)) (@ (@ tptp.insert_int2 X) tptp.bot_bot_set_int))))) (forall ((Xs tptp.list_nat) (X tptp.nat)) (=> (@ tptp.distinct_nat Xs) (= (@ tptp.set_nat2 (@ (@ tptp.remove1_nat X) Xs)) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_nat2 Xs)) (@ (@ tptp.insert_nat2 X) tptp.bot_bot_set_nat))))) (forall ((Xs tptp.list_int)) (= (@ tptp.is_empty_int (@ tptp.set_int2 Xs)) (@ tptp.null_int Xs))) (forall ((Xs tptp.list_nat)) (= (@ tptp.is_empty_nat (@ tptp.set_nat2 Xs)) (@ tptp.null_nat Xs))) (forall ((Xs tptp.list_P8527749157015355191n_assn)) (= (@ tptp.is_emp7749065762491207043n_assn (@ tptp.set_Pr1139785259514867910n_assn Xs)) (@ tptp.null_P7596217980778516671n_assn Xs))) (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (= (@ tptp.set_Pr1139785259514867910n_assn (@ (@ tptp.remove1763081955827946941n_assn X) Xs)) (@ (@ tptp.minus_2301194108115264760n_assn (@ tptp.set_Pr1139785259514867910n_assn Xs)) (@ (@ tptp.insert5290817439147925377n_assn X) tptp.bot_bo1176836662018730877n_assn)))) (forall ((X tptp.produc3843707927480180839at_nat) (Xs tptp.list_P5464809261938338413at_nat)) (= (@ tptp.set_Pr3765526544606949372at_nat (@ (@ tptp.remove4908499291543849587at_nat X) Xs)) (@ (@ tptp.minus_3314409938677909166at_nat (@ tptp.set_Pr3765526544606949372at_nat Xs)) (@ (@ tptp.insert9069300056098147895at_nat X) tptp.bot_bo228742789529271731at_nat)))) (forall ((X tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (= (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.remove3673390508374433037at_nat X) Xs)) (@ (@ tptp.minus_1356011639430497352at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs)) (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat)))) (forall ((X Bool) (Xs tptp.list_o)) (= (@ tptp.set_o2 (@ (@ tptp.removeAll_o X) Xs)) (@ (@ tptp.minus_minus_set_o (@ tptp.set_o2 Xs)) (@ (@ tptp.insert_o2 X) tptp.bot_bot_set_o)))) (forall ((X tptp.int) (Xs tptp.list_int)) (= (@ tptp.set_int2 (@ (@ tptp.removeAll_int X) Xs)) (@ (@ tptp.minus_minus_set_int (@ tptp.set_int2 Xs)) (@ (@ tptp.insert_int2 X) tptp.bot_bot_set_int)))) (forall ((X tptp.nat) (Xs tptp.list_nat)) (= (@ tptp.set_nat2 (@ (@ tptp.removeAll_nat X) Xs)) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_nat2 Xs)) (@ (@ tptp.insert_nat2 X) tptp.bot_bot_set_nat)))) (forall ((Xs tptp.list_s1210847774152347623at_nat) (Ys tptp.list_s1210847774152347623at_nat) (R2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat Xs) Ys)) (@ tptp.listre8180072825634266816at_nat R2)) (exists ((Y5 tptp.set_Pr1261947904930325089at_nat) (N2 tptp.nat)) (and (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ (@ tptp.nth_se5679702624988424552at_nat Xs) N2)) Y5)) R2) (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s8736152011456118867at_nat Xs)) (= Ys (@ (@ (@ tptp.list_u8444657558853818831at_nat Xs) N2) Y5)))))) (forall ((Xs tptp.list_c) (Ys tptp.list_c) (R2 tptp.set_Product_prod_c_c)) (= (@ (@ tptp.member7012247553653173456list_c (@ (@ tptp.produc5515445818230282391list_c Xs) Ys)) (@ tptp.listrel1_c R2)) (exists ((Y5 tptp.c) (N2 tptp.nat)) (and (@ (@ tptp.member5074992359041316560od_c_c (@ (@ tptp.product_Pair_c_c (@ (@ tptp.nth_c Xs) N2)) Y5)) R2) (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_c Xs)) (= Ys (@ (@ (@ tptp.list_update_c Xs) N2) Y5)))))) (forall ((Xs tptp.list_d) (Ys tptp.list_d) (R2 tptp.set_Product_prod_d_d)) (= (@ (@ tptp.member1810801192463332112list_d (@ (@ tptp.produc242965421297323863list_d Xs) Ys)) (@ tptp.listrel1_d R2)) (exists ((Y5 tptp.d) (N2 tptp.nat)) (and (@ (@ tptp.member2287536781371869328od_d_d (@ (@ tptp.product_Pair_d_d (@ (@ tptp.nth_d Xs) N2)) Y5)) R2) (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_d Xs)) (= Ys (@ (@ (@ tptp.list_update_d Xs) N2) Y5)))))) (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Xs) Ys)) (@ tptp.listrel1_nat R2)) (exists ((Y5 tptp.nat) (N2 tptp.nat)) (and (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.nth_nat Xs) N2)) Y5)) R2) (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs)) (= Ys (@ (@ (@ tptp.list_update_nat Xs) N2) Y5)))))) (forall ((Xs tptp.list_int) (Ys tptp.list_int) (R2 tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Xs) Ys)) (@ tptp.listrel1_int R2)) (exists ((Y5 tptp.int) (N2 tptp.nat)) (and (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int (@ (@ tptp.nth_int Xs) N2)) Y5)) R2) (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_int Xs)) (= Ys (@ (@ (@ tptp.list_update_int Xs) N2) Y5)))))) (forall ((X tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (= (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.insert8944034826898310173at_nat X) Xs)) (@ (@ tptp.insert8211810215607154385at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs)))) (forall ((X tptp.produc3843707927480180839at_nat) (Xs tptp.list_P5464809261938338413at_nat)) (= (@ tptp.set_Pr3765526544606949372at_nat (@ (@ tptp.insert4149901806602606979at_nat X) Xs)) (@ (@ tptp.insert9069300056098147895at_nat X) (@ tptp.set_Pr3765526544606949372at_nat Xs)))) (forall ((X Bool) (Xs tptp.list_o)) (= (@ tptp.set_o2 (@ (@ tptp.insert_o X) Xs)) (@ (@ tptp.insert_o2 X) (@ tptp.set_o2 Xs)))) (forall ((X tptp.int) (Xs tptp.list_int)) (= (@ tptp.set_int2 (@ (@ tptp.insert_int X) Xs)) (@ (@ tptp.insert_int2 X) (@ tptp.set_int2 Xs)))) (forall ((X tptp.nat) (Xs tptp.list_nat)) (= (@ tptp.set_nat2 (@ (@ tptp.insert_nat X) Xs)) (@ (@ tptp.insert_nat2 X) (@ tptp.set_nat2 Xs)))) (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (= (@ tptp.set_Pr1139785259514867910n_assn (@ (@ tptp.insert3246601298802261197n_assn X) Xs)) (@ (@ tptp.insert5290817439147925377n_assn X) (@ tptp.set_Pr1139785259514867910n_assn Xs)))) (forall ((Xs tptp.list_c) (Ys tptp.list_c) (R2 tptp.set_Product_prod_c_c)) (= (@ (@ tptp.member7012247553653173456list_c (@ (@ tptp.produc5515445818230282391list_c Xs) Ys)) (@ tptp.listrel_c_c R2)) (and (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_c Ys)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_c Xs)) (@ (@ tptp.member5074992359041316560od_c_c (@ (@ tptp.product_Pair_c_c (@ (@ tptp.nth_c Xs) N2)) (@ (@ tptp.nth_c Ys) N2))) R2)))))) (forall ((Xs tptp.list_c) (Ys tptp.list_d) (R2 tptp.set_Product_prod_c_d)) (= (@ (@ tptp.member7083281593699519441list_d (@ (@ tptp.produc5515445822533511192list_d Xs) Ys)) (@ tptp.listrel_c_d R2)) (and (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_d Ys)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_c Xs)) (@ (@ tptp.member5074992363344545361od_c_d (@ (@ tptp.product_Pair_c_d (@ (@ tptp.nth_c Xs) N2)) (@ (@ tptp.nth_d Ys) N2))) R2)))))) (forall ((Xs tptp.list_c) (Ys tptp.list_nat) (R2 tptp.set_Pr6903500605879609269_c_nat)) (= (@ (@ tptp.member6184937725913850668st_nat (@ (@ tptp.produc6126748735280710287st_nat Xs) Ys)) (@ tptp.listrel_c_nat R2)) (and (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_nat Ys)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_c Xs)) (@ (@ tptp.member8195077246299207702_c_nat (@ (@ tptp.product_Pair_c_nat (@ (@ tptp.nth_c Xs) N2)) (@ (@ tptp.nth_nat Ys) N2))) R2)))))) (forall ((Xs tptp.list_c) (Ys tptp.list_int) (R2 tptp.set_Pr4413417460947882513_c_int)) (= (@ (@ tptp.member3694854580982123912st_int (@ (@ tptp.produc1948897715771513579st_int Xs) Ys)) (@ tptp.listrel_c_int R2)) (and (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_int Ys)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_c Xs)) (@ (@ tptp.member4017226226790010994_c_int (@ (@ tptp.product_Pair_c_int (@ (@ tptp.nth_c Xs) N2)) (@ (@ tptp.nth_int Ys) N2))) R2)))))) (forall ((Xs tptp.list_d) (Ys tptp.list_c) (R2 tptp.set_Product_prod_d_c)) (= (@ (@ tptp.member1739767152416986127list_c (@ (@ tptp.produc242965416994095062list_c Xs) Ys)) (@ tptp.listrel_d_c R2)) (and (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_c Ys)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_d Xs)) (@ (@ tptp.member2287536777068640527od_d_c (@ (@ tptp.product_Pair_d_c (@ (@ tptp.nth_d Xs) N2)) (@ (@ tptp.nth_c Ys) N2))) R2)))))) (forall ((Xs tptp.list_d) (Ys tptp.list_d) (R2 tptp.set_Product_prod_d_d)) (= (@ (@ tptp.member1810801192463332112list_d (@ (@ tptp.produc242965421297323863list_d Xs) Ys)) (@ tptp.listrel_d_d R2)) (and (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_d Ys)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_d Xs)) (@ (@ tptp.member2287536781371869328od_d_d (@ (@ tptp.product_Pair_d_d (@ (@ tptp.nth_d Xs) N2)) (@ (@ tptp.nth_d Ys) N2))) R2)))))) (forall ((Xs tptp.list_d) (Ys tptp.list_nat) (R2 tptp.set_Pr3276347184212964150_d_nat)) (= (@ (@ tptp.member6851837201453759021st_nat (@ (@ tptp.produc6793648210820618640st_nat Xs) Ys)) (@ tptp.listrel_d_nat R2)) (and (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_nat Ys)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_d Xs)) (@ (@ tptp.member207149538400826391_d_nat (@ (@ tptp.product_Pair_d_nat (@ (@ tptp.nth_d Xs) N2)) (@ (@ tptp.nth_nat Ys) N2))) R2)))))) (forall ((Xs tptp.list_d) (Ys tptp.list_int) (R2 tptp.set_Pr786264039281237394_d_int)) (= (@ (@ tptp.member4361754056522032265st_int (@ (@ tptp.produc2615797191311421932st_int Xs) Ys)) (@ tptp.listrel_d_int R2)) (and (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_int Ys)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_d Xs)) (@ (@ tptp.member5252670555746405491_d_int (@ (@ tptp.product_Pair_d_int (@ (@ tptp.nth_d Xs) N2)) (@ (@ tptp.nth_int Ys) N2))) R2)))))) (forall ((Xs tptp.list_nat) (Ys tptp.list_c) (R2 tptp.set_Pr4335409928928841947_nat_c)) (= (@ (@ tptp.member6074218473364765234list_c (@ (@ tptp.produc7723716018658481613list_c Xs) Ys)) (@ tptp.listrel_nat_c R2)) (and (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_c Ys)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.member8962352060716553276_nat_c (@ (@ tptp.product_Pair_nat_c (@ (@ tptp.nth_nat Xs) N2)) (@ (@ tptp.nth_c Ys) N2))) R2)))))) (forall ((Xs tptp.list_nat) (Ys tptp.list_d) (R2 tptp.set_Pr4406443968975187932_nat_d)) (= (@ (@ tptp.member6145252513411111219list_d (@ (@ tptp.produc7723716022961710414list_d Xs) Ys)) (@ tptp.listrel_nat_d R2)) (and (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_d Ys)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.member8962352065019782077_nat_d (@ (@ tptp.product_Pair_nat_d (@ (@ tptp.nth_nat Xs) N2)) (@ (@ tptp.nth_d Ys) N2))) R2)))))) (forall ((P tptp.assn) (B2 Bool)) (let ((_let_1 (@ tptp.entails P))) (= (@ _let_1 (@ tptp.pure_assn B2)) (and (forall ((H3 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P) H3) B2)) (@ _let_1 tptp.one_one_assn))))) (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger tptp.one_one_Code_integer) A2) A2)) (forall ((A2 tptp.assn)) (= (@ (@ tptp.times_times_assn tptp.one_one_assn) A2) A2)) (forall ((A2 tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A2) A2)) (forall ((A2 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A2) A2)) (forall ((A2 tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A2) A2)) (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger A2) tptp.one_one_Code_integer) A2)) (forall ((A2 tptp.assn)) (= (@ (@ tptp.times_times_assn A2) tptp.one_one_assn) A2)) (forall ((A2 tptp.rat)) (= (@ (@ tptp.times_times_rat A2) tptp.one_one_rat) A2)) (forall ((A2 tptp.nat)) (= (@ (@ tptp.times_times_nat A2) tptp.one_one_nat) A2)) (forall ((A2 tptp.int)) (= (@ (@ tptp.times_times_int A2) tptp.one_one_int) A2)) (forall ((A2 tptp.produc3843707927480180839at_nat) (B2 tptp.produc3843707927480180839at_nat) (Xs tptp.list_P5464809261938338413at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat A2))) (=> (not (= A2 B2)) (= (@ _let_1 (@ tptp.set_Pr3765526544606949372at_nat (@ (@ tptp.remove8895909992688781315at_nat B2) Xs))) (@ _let_1 (@ tptp.set_Pr3765526544606949372at_nat Xs)))))) (forall ((A2 tptp.product_prod_nat_nat) (B2 tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat A2))) (=> (not (= A2 B2)) (= (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.remove5766854097993331357at_nat B2) Xs))) (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat Xs)))))) (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 (-> tptp.produc3658429121746597890et_nat Bool)) (Xs tptp.list_P7985473006766602707_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o A2))) (=> (not (= A2 B2)) (= (@ _let_1 (@ tptp.set_Pr400311997697478754_nat_o (@ (@ tptp.remove4235003712227595625_nat_o B2) Xs))) (@ _let_1 (@ tptp.set_Pr400311997697478754_nat_o Xs)))))) (forall ((A2 tptp.int) (B2 tptp.int) (Xs tptp.list_int)) (let ((_let_1 (@ tptp.member_int A2))) (=> (not (= A2 B2)) (= (@ _let_1 (@ tptp.set_int2 (@ (@ tptp.remove1_int B2) Xs))) (@ _let_1 (@ tptp.set_int2 Xs)))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ tptp.member_nat A2))) (=> (not (= A2 B2)) (= (@ _let_1 (@ tptp.set_nat2 (@ (@ tptp.remove1_nat B2) Xs))) (@ _let_1 (@ tptp.set_nat2 Xs)))))) (forall ((A2 tptp.produc6575502325842934193n_assn) (B2 tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ tptp.member7957490590177025114n_assn A2))) (=> (not (= A2 B2)) (= (@ _let_1 (@ tptp.set_Pr1139785259514867910n_assn (@ (@ tptp.remove1670527618125605709n_assn B2) Xs))) (@ _let_1 (@ tptp.set_Pr1139785259514867910n_assn Xs)))))) (forall ((X tptp.produc3843707927480180839at_nat) (Xs tptp.list_P5464809261938338413at_nat)) (=> (not (@ (@ tptp.member8757157785044589968at_nat X) (@ tptp.set_Pr3765526544606949372at_nat Xs))) (= (@ (@ tptp.remove4908499291543849587at_nat X) Xs) Xs))) (forall ((X tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (=> (not (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs))) (= (@ (@ tptp.remove3673390508374433037at_nat X) Xs) Xs))) (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xs tptp.list_P7985473006766602707_nat_o)) (=> (not (@ (@ tptp.member6576561426505652726_nat_o X) (@ tptp.set_Pr400311997697478754_nat_o Xs))) (= (@ (@ tptp.remove7604696131425036249_nat_o X) Xs) Xs))) (forall ((X tptp.int) (Xs tptp.list_int)) (=> (not (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs))) (= (@ (@ tptp.removeAll_int X) Xs) Xs))) (forall ((X tptp.nat) (Xs tptp.list_nat)) (=> (not (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs))) (= (@ (@ tptp.removeAll_nat X) Xs) Xs))) (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (=> (not (@ (@ tptp.member7957490590177025114n_assn X) (@ tptp.set_Pr1139785259514867910n_assn Xs))) (= (@ (@ tptp.remove1763081955827946941n_assn X) Xs) Xs))) _let_160 (forall ((P Bool)) (= (= (@ tptp.pure_assn P) tptp.one_one_assn) P)) (forall ((A tptp.assn)) (@ (@ tptp.entailst A) tptp.one_one_assn)) (forall ((X tptp.produc3843707927480180839at_nat) (Xs tptp.list_P5464809261938338413at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X) (@ tptp.set_Pr3765526544606949372at_nat Xs)) (= (@ (@ tptp.insert4149901806602606979at_nat X) Xs) Xs))) (forall ((X tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (=> 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(R2 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Xs) Ys)) (@ tptp.listrel1_int R2)) (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys)))) (forall ((Xs tptp.list_c) (Ys tptp.list_c) (R2 tptp.set_Product_prod_c_c)) (=> (@ (@ tptp.member7012247553653173456list_c (@ (@ tptp.produc5515445818230282391list_c Xs) Ys)) (@ tptp.listrel_c_c R2)) (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_c Ys)))) (forall ((Xs tptp.list_c) (Ys tptp.list_d) (R2 tptp.set_Product_prod_c_d)) (=> (@ (@ tptp.member7083281593699519441list_d (@ (@ tptp.produc5515445822533511192list_d Xs) Ys)) (@ tptp.listrel_c_d R2)) (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_d Ys)))) (forall ((Xs tptp.list_c) (Ys tptp.list_nat) (R2 tptp.set_Pr6903500605879609269_c_nat)) (=> (@ (@ tptp.member6184937725913850668st_nat (@ (@ tptp.produc6126748735280710287st_nat Xs) Ys)) (@ tptp.listrel_c_nat R2)) (= (@ 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(@ (@ tptp.produc6793648210820618640st_nat Xs) Ys)) (@ tptp.listrel_d_nat R2)) (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_nat Ys)))) (forall ((Xs tptp.list_d) (Ys tptp.list_int) (R2 tptp.set_Pr786264039281237394_d_int)) (=> (@ (@ tptp.member4361754056522032265st_int (@ (@ tptp.produc2615797191311421932st_int Xs) Ys)) (@ tptp.listrel_d_int R2)) (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_int Ys)))) (forall ((Xs tptp.list_nat) (Ys tptp.list_c) (R2 tptp.set_Pr4335409928928841947_nat_c)) (=> (@ (@ tptp.member6074218473364765234list_c (@ (@ tptp.produc7723716018658481613list_c Xs) Ys)) (@ tptp.listrel_nat_c R2)) (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_c Ys)))) (forall ((Xs tptp.list_nat) (Ys tptp.list_d) (R2 tptp.set_Pr4406443968975187932_nat_d)) (=> (@ (@ tptp.member6145252513411111219list_d (@ (@ tptp.produc7723716022961710414list_d Xs) Ys)) (@ tptp.listrel_nat_d R2)) (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_d Ys)))) (forall ((Xs tptp.list_int) (X tptp.int)) (=> (@ tptp.distinct_int Xs) (= (@ (@ tptp.remove1_int X) Xs) (@ (@ tptp.removeAll_int X) Xs)))) (forall ((Xs tptp.list_nat) (X tptp.nat)) (=> (@ tptp.distinct_nat Xs) (= (@ (@ tptp.remove1_nat X) Xs) (@ (@ tptp.removeAll_nat X) Xs)))) (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger A2) tptp.one_one_Code_integer) A2)) (forall ((A2 tptp.assn)) (= (@ (@ tptp.times_times_assn A2) tptp.one_one_assn) A2)) (forall ((A2 tptp.rat)) (= (@ (@ tptp.times_times_rat A2) tptp.one_one_rat) A2)) (forall ((A2 tptp.nat)) (= (@ (@ tptp.times_times_nat A2) tptp.one_one_nat) A2)) (forall ((A2 tptp.int)) (= (@ (@ tptp.times_times_int A2) tptp.one_one_int) A2)) (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger tptp.one_one_Code_integer) A2) A2)) (forall ((A2 tptp.assn)) (= (@ (@ tptp.times_times_assn tptp.one_one_assn) A2) A2)) (forall ((A2 tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A2) A2)) (forall ((A2 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A2) A2)) (forall ((A2 tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A2) A2)) (forall ((P tptp.assn)) (= (@ (@ tptp.times_times_assn tptp.one_one_assn) P) P)) (forall ((A2 tptp.assn)) (= (@ (@ tptp.times_times_assn tptp.one_one_assn) A2) A2)) (forall ((A2 tptp.assn)) (= (@ (@ tptp.times_times_assn A2) tptp.one_one_assn) A2)) (forall ((X tptp.produc3843707927480180839at_nat) (Xs tptp.list_P5464809261938338413at_nat)) (=> (not (@ (@ tptp.member8757157785044589968at_nat X) (@ tptp.set_Pr3765526544606949372at_nat Xs))) (= (@ (@ tptp.remove8895909992688781315at_nat X) Xs) Xs))) (forall ((X tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (=> (not (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs))) (= (@ (@ tptp.remove5766854097993331357at_nat X) Xs) Xs))) (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xs tptp.list_P7985473006766602707_nat_o)) (=> (not (@ (@ tptp.member6576561426505652726_nat_o X) (@ tptp.set_Pr400311997697478754_nat_o Xs))) (= (@ (@ tptp.remove4235003712227595625_nat_o X) Xs) Xs))) (forall ((X tptp.int) (Xs tptp.list_int)) (=> (not (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs))) (= (@ (@ tptp.remove1_int X) Xs) Xs))) (forall ((X tptp.nat) (Xs tptp.list_nat)) (=> (not (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs))) (= (@ (@ tptp.remove1_nat X) Xs) Xs))) (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (=> (not (@ (@ tptp.member7957490590177025114n_assn X) (@ tptp.set_Pr1139785259514867910n_assn Xs))) (= (@ (@ tptp.remove1670527618125605709n_assn X) Xs) Xs))) (forall ((X tptp.produc3843707927480180839at_nat) (Xs tptp.list_P5464809261938338413at_nat) (Y tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat X))) (=> (not (@ _let_1 (@ tptp.set_Pr3765526544606949372at_nat Xs))) (not (@ _let_1 (@ tptp.set_Pr3765526544606949372at_nat (@ (@ tptp.remove8895909992688781315at_nat Y) Xs))))))) (forall ((X tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X))) (=> (not (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat Xs))) (not (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.remove5766854097993331357at_nat Y) Xs))))))) (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xs tptp.list_P7985473006766602707_nat_o) (Y (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o X))) (=> (not (@ _let_1 (@ tptp.set_Pr400311997697478754_nat_o Xs))) (not (@ _let_1 (@ tptp.set_Pr400311997697478754_nat_o (@ (@ tptp.remove4235003712227595625_nat_o Y) Xs))))))) (forall ((X tptp.int) (Xs tptp.list_int) (Y tptp.int)) (let ((_let_1 (@ tptp.member_int X))) (=> (not (@ _let_1 (@ tptp.set_int2 Xs))) (not (@ _let_1 (@ tptp.set_int2 (@ (@ tptp.remove1_int Y) Xs))))))) (forall ((X tptp.nat) (Xs tptp.list_nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (=> (not (@ _let_1 (@ tptp.set_nat2 Xs))) (not (@ _let_1 (@ tptp.set_nat2 (@ (@ tptp.remove1_nat Y) Xs))))))) (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn) (Y tptp.produc6575502325842934193n_assn)) (let ((_let_1 (@ tptp.member7957490590177025114n_assn X))) (=> (not (@ _let_1 (@ tptp.set_Pr1139785259514867910n_assn Xs))) (not (@ _let_1 (@ tptp.set_Pr1139785259514867910n_assn (@ (@ tptp.remove1670527618125605709n_assn Y) Xs))))))) (forall ((Xs tptp.list_int) (X tptp.int)) (=> (@ tptp.distinct_int Xs) (@ tptp.distinct_int (@ (@ tptp.remove1_int X) Xs)))) (forall ((Xs tptp.list_nat) (X tptp.nat)) (=> (@ tptp.distinct_nat Xs) (@ tptp.distinct_nat (@ (@ tptp.remove1_nat X) Xs)))) (forall ((Xs tptp.list_int) (X tptp.int)) (=> (@ tptp.distinct_int Xs) (@ tptp.distinct_int (@ (@ tptp.removeAll_int X) Xs)))) (forall ((Xs tptp.list_nat) (X tptp.nat)) (=> (@ tptp.distinct_nat Xs) (@ tptp.distinct_nat (@ (@ tptp.removeAll_nat X) Xs)))) (forall ((M2 tptp.rat) (N tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_rat M2) N)))))) (forall ((M2 tptp.code_integer) (N tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger M2) N)))))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_nat M2) N)))))) (forall ((M2 tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_int M2) N)))))) (forall ((P tptp.assn) (Q tptp.assn)) (=> (@ (@ (@ tptp.fI_QUERY P) Q) tptp.one_one_assn) (@ (@ tptp.entails P) Q))) (forall ((P (-> tptp.produc2732055786443039994et_nat Bool)) (X tptp.produc2732055786443039994et_nat)) (=> (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 (-> tptp.produc3658429121746597890et_nat Bool)) (C4 tptp.heap_e7401611519738050253t_unit) (D3 tptp.set_nat)) (@ P (@ (@ tptp.produc2245416461498447860et_nat A4) (@ (@ tptp.produc5001842942810119800et_nat B4) (@ (@ tptp.produc7507926704131184380et_nat C4) D3))))) (@ P X))) (forall ((P (-> tptp.produc1908205239877642774nteger Bool)) (X tptp.produc1908205239877642774nteger)) (=> (forall ((A4 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B4 tptp.code_integer) (C4 tptp.code_integer)) (@ P (@ (@ tptp.produc8603105652947943368nteger A4) (@ (@ tptp.produc1086072967326762835nteger B4) C4)))) (@ P X))) (forall ((P (-> tptp.produc3925858234332021118et_nat Bool)) (X tptp.produc3925858234332021118et_nat)) (=> (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.heap_e7401611519738050253t_unit) (C4 tptp.set_nat)) (@ P (@ (@ tptp.produc5001842942810119800et_nat A4) (@ (@ tptp.produc7507926704131184380et_nat B4) C4)))) (@ P X))) (forall ((P (-> tptp.produc2732055786443039994et_nat Bool)) (X tptp.produc2732055786443039994et_nat)) (=> (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 (-> tptp.produc3658429121746597890et_nat Bool)) (C4 tptp.produc3658429121746597890et_nat)) (@ P (@ (@ tptp.produc2245416461498447860et_nat A4) (@ (@ tptp.produc5001842942810119800et_nat B4) C4)))) (@ P X))) (forall ((P (-> tptp.produc2285326912895808259nt_int Bool)) (X tptp.produc2285326912895808259nt_int)) (=> (forall ((A4 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B4 tptp.int) (C4 tptp.int)) (@ P (@ (@ tptp.produc5700946648718959541nt_int A4) (@ (@ tptp.product_Pair_int_int B4) C4)))) (@ P X))) (forall ((P (-> tptp.produc7773217078559923341nt_int Bool)) (X tptp.produc7773217078559923341nt_int)) (=> (forall ((A4 (-> tptp.int 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(= (@ (@ tptp.produc2245416461498447860et_nat A2) B2) (@ (@ tptp.produc2245416461498447860et_nat A7) B6)) (not (=> (= A2 A7) (not (= B2 B6)))))) (forall ((A2 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B2 tptp.product_prod_int_int) (A7 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B6 tptp.product_prod_int_int)) (=> (= (@ (@ tptp.produc5700946648718959541nt_int A2) B2) (@ (@ tptp.produc5700946648718959541nt_int A7) B6)) (not (=> (= A2 A7) (not (= B2 B6)))))) (forall ((A2 (-> tptp.int tptp.option6357759511663192854e_term)) (B2 tptp.product_prod_int_int) (A7 (-> tptp.int tptp.option6357759511663192854e_term)) (B6 tptp.product_prod_int_int)) (=> (= (@ (@ tptp.produc4305682042979456191nt_int A2) B2) (@ (@ tptp.produc4305682042979456191nt_int A7) B6)) (not (=> (= A2 A7) (not (= B2 B6)))))) (forall ((P (-> tptp.produc1908205239877642774nteger Bool)) (P6 tptp.produc1908205239877642774nteger)) (=> (forall ((A4 (-> 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X3) Y2)))) (forall ((P6 tptp.produc2285326912895808259nt_int)) (exists ((X3 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y2 tptp.product_prod_int_int)) (= P6 (@ (@ tptp.produc5700946648718959541nt_int X3) Y2)))) (forall ((P6 tptp.produc7773217078559923341nt_int)) (exists ((X3 (-> tptp.int tptp.option6357759511663192854e_term)) (Y2 tptp.product_prod_int_int)) (= P6 (@ (@ tptp.produc4305682042979456191nt_int X3) Y2)))) (forall ((Y tptp.produc1908205239877642774nteger)) (not (forall ((A4 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B4 tptp.produc8923325533196201883nteger)) (not (= Y (@ (@ tptp.produc8603105652947943368nteger A4) B4)))))) (forall ((Y tptp.produc3925858234332021118et_nat)) (not (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.produc3658429121746597890et_nat)) (not (= Y (@ (@ tptp.produc5001842942810119800et_nat A4) B4)))))) (forall ((Y tptp.produc2732055786443039994et_nat)) (not (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.produc3925858234332021118et_nat)) (not (= Y (@ (@ tptp.produc2245416461498447860et_nat A4) B4)))))) (forall ((Y tptp.produc2285326912895808259nt_int)) (not (forall ((A4 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B4 tptp.product_prod_int_int)) (not (= Y (@ (@ tptp.produc5700946648718959541nt_int A4) B4)))))) (forall ((Y tptp.produc7773217078559923341nt_int)) (not (forall ((A4 (-> tptp.int tptp.option6357759511663192854e_term)) (B4 tptp.product_prod_int_int)) (not (= Y (@ (@ tptp.produc4305682042979456191nt_int A4) B4)))))) (forall ((X tptp.int) (Xs tptp.list_int)) (= (@ (@ tptp.remove_int X) (@ tptp.set_int2 Xs)) (@ tptp.set_int2 (@ (@ tptp.removeAll_int X) Xs)))) (forall ((X tptp.nat) (Xs tptp.list_nat)) (= (@ (@ tptp.remove_nat X) (@ tptp.set_nat2 Xs)) (@ tptp.set_nat2 (@ (@ tptp.removeAll_nat X) Xs)))) (forall ((X tptp.produc6575502325842934193n_assn) (Xs 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Xs)))) (forall ((X tptp.d) (Xs tptp.list_d)) (=> (@ (@ tptp.member_d X) (@ tptp.set_d2 Xs)) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_d (@ (@ tptp.removeAll_d X) Xs))) (@ tptp.size_size_list_d Xs)))) (forall ((X tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs)) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat (@ (@ tptp.removeAll_nat X) Xs))) (@ tptp.size_size_list_nat Xs)))) (forall ((X tptp.int) (Xs tptp.list_int)) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs)) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_int (@ (@ tptp.removeAll_int X) Xs))) (@ tptp.size_size_list_int Xs)))) (not (@ _let_117 tptp.one_one_rat)) (not (@ _let_116 tptp.one_one_Code_integer)) (not (@ _let_115 tptp.one_one_nat)) (not (@ _let_114 tptp.one_one_int)) (forall ((X Bool) (Xa tptp.produc3658429121746597890et_nat)) (=> (not (@ (@ tptp.pure_a825153325127701367it_nat X) Xa)) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (= Xa (@ (@ tptp.produc7507926704131184380et_nat H) As)) (and (= As tptp.bot_bot_set_nat) X)))))) (forall ((X Bool) (Xa tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.pure_a825153325127701367it_nat X) Xa) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (= Xa (@ (@ tptp.produc7507926704131184380et_nat H) As)) (not (and (= As tptp.bot_bot_set_nat) X))))))) (forall ((X Bool) (Xa tptp.produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ (@ tptp.pure_a825153325127701367it_nat X) Xa) Y) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (= Xa (@ (@ tptp.produc7507926704131184380et_nat H) As)) (= Y (not (and (= As tptp.bot_bot_set_nat) X)))))))) (forall ((B2 Bool) (H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (= (@ (@ tptp.pure_a825153325127701367it_nat B2) (@ (@ tptp.produc7507926704131184380et_nat H2) As2)) (and (= As2 tptp.bot_bot_set_nat) B2))) (forall ((I tptp.nat) (Xs tptp.list_c) (Ys tptp.list_c)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 (@ tptp.size_size_list_c Xs)) (=> (@ _let_1 (@ tptp.size_size_list_c Ys)) (= (@ (@ tptp.nth_Product_prod_c_c (@ (@ tptp.zip_c_c Xs) Ys)) I) (@ (@ tptp.product_Pair_c_c (@ (@ tptp.nth_c Xs) I)) (@ (@ tptp.nth_c Ys) I))))))) (forall ((I tptp.nat) (Xs tptp.list_c) (Ys tptp.list_d)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 (@ tptp.size_size_list_c Xs)) (=> (@ _let_1 (@ tptp.size_size_list_d Ys)) (= (@ (@ tptp.nth_Product_prod_c_d (@ (@ tptp.zip_c_d Xs) Ys)) I) (@ (@ tptp.product_Pair_c_d (@ (@ tptp.nth_c Xs) I)) (@ (@ tptp.nth_d Ys) I))))))) (forall ((I tptp.nat) (Xs tptp.list_c) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 (@ tptp.size_size_list_c Xs)) (=> (@ _let_1 (@ tptp.size_size_list_nat Ys)) (= (@ (@ tptp.nth_Pr1708982275578427192_c_nat (@ (@ tptp.zip_c_nat Xs) Ys)) I) (@ (@ tptp.product_Pair_c_nat (@ (@ tptp.nth_c Xs) I)) (@ (@ tptp.nth_nat Ys) I))))))) (forall ((I tptp.nat) (Xs tptp.list_c) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 (@ tptp.size_size_list_c Xs)) (=> (@ _let_1 (@ tptp.size_size_list_int Ys)) (= (@ (@ tptp.nth_Pr6754503292924006292_c_int (@ (@ tptp.zip_c_int Xs) Ys)) I) (@ (@ tptp.product_Pair_c_int (@ (@ tptp.nth_c Xs) I)) (@ (@ tptp.nth_int Ys) I))))))) (forall ((I tptp.nat) (Xs tptp.list_d) (Ys tptp.list_c)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 (@ tptp.size_size_list_d Xs)) (=> (@ _let_1 (@ tptp.size_size_list_c Ys)) (= (@ (@ tptp.nth_Product_prod_d_c (@ (@ tptp.zip_d_c Xs) Ys)) I) (@ (@ tptp.product_Pair_d_c (@ (@ tptp.nth_d Xs) I)) (@ (@ tptp.nth_c Ys) I))))))) (forall ((I tptp.nat) (Xs tptp.list_d) (Ys tptp.list_d)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 (@ tptp.size_size_list_d Xs)) (=> (@ _let_1 (@ tptp.size_size_list_d Ys)) (= (@ (@ tptp.nth_Product_prod_d_d (@ (@ tptp.zip_d_d Xs) Ys)) I) (@ (@ tptp.product_Pair_d_d (@ (@ tptp.nth_d Xs) I)) (@ (@ tptp.nth_d Ys) I))))))) (forall ((I tptp.nat) (Xs tptp.list_d) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 (@ tptp.size_size_list_d Xs)) (=> (@ _let_1 (@ tptp.size_size_list_nat Ys)) (= (@ (@ tptp.nth_Pr2944426604534821689_d_nat (@ (@ tptp.zip_d_nat Xs) Ys)) I) (@ (@ tptp.product_Pair_d_nat (@ (@ tptp.nth_d Xs) I)) (@ (@ tptp.nth_nat Ys) I))))))) (forall ((I tptp.nat) (Xs tptp.list_d) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 (@ tptp.size_size_list_d Xs)) (=> (@ _let_1 (@ tptp.size_size_list_int Ys)) (= (@ (@ tptp.nth_Pr7989947621880400789_d_int (@ (@ tptp.zip_d_int Xs) Ys)) I) (@ (@ tptp.product_Pair_d_int (@ (@ tptp.nth_d Xs) I)) (@ (@ tptp.nth_int Ys) I))))))) (forall ((I tptp.nat) (Xs tptp.list_nat) (Ys tptp.list_c)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 (@ tptp.size_size_list_nat Xs)) (=> (@ _let_1 (@ tptp.size_size_list_c Ys)) (= (@ (@ tptp.nth_Pr2476257089995772766_nat_c (@ (@ tptp.zip_nat_c Xs) Ys)) I) (@ (@ tptp.product_Pair_nat_c (@ (@ tptp.nth_nat Xs) I)) (@ (@ tptp.nth_c Ys) I))))))) (forall ((I tptp.nat) (Xs tptp.list_nat) (Ys tptp.list_d)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 (@ tptp.size_size_list_nat Xs)) (=> (@ _let_1 (@ tptp.size_size_list_d Ys)) (= (@ (@ tptp.nth_Pr2476257094299001567_nat_d (@ (@ tptp.zip_nat_d Xs) Ys)) I) (@ (@ tptp.product_Pair_nat_d (@ (@ tptp.nth_nat Xs) I)) (@ (@ tptp.nth_d Ys) I))))))) (forall ((F4 (-> tptp.produc1908205239877642774nteger Bool)) (A2 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B2 tptp.produc8923325533196201883nteger)) (=> (@ F4 (@ (@ tptp.produc8603105652947943368nteger A2) B2)) (@ (@ (@ tptp.produc1217013493180205570eger_o F4) A2) B2))) (forall ((F4 (-> tptp.produc3925858234332021118et_nat Bool)) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.produc3658429121746597890et_nat)) (=> (@ F4 (@ (@ tptp.produc5001842942810119800et_nat A2) B2)) (@ (@ (@ tptp.produc6216949301066131538_nat_o F4) A2) B2))) (forall ((F4 (-> tptp.produc2732055786443039994et_nat Bool)) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.produc3925858234332021118et_nat)) (=> (@ F4 (@ (@ tptp.produc2245416461498447860et_nat A2) B2)) (@ (@ (@ tptp.produc5101573711933517782_nat_o F4) A2) B2))) (forall ((F4 (-> tptp.produc2285326912895808259nt_int Bool)) (A2 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B2 tptp.product_prod_int_int)) (=> (@ F4 (@ (@ tptp.produc5700946648718959541nt_int A2) B2)) (@ (@ (@ tptp.produc730925184835016917_int_o F4) A2) B2))) (forall ((F4 (-> tptp.produc7773217078559923341nt_int Bool)) (A2 (-> tptp.int tptp.option6357759511663192854e_term)) (B2 tptp.product_prod_int_int)) (=> (@ F4 (@ (@ tptp.produc4305682042979456191nt_int A2) B2)) (@ (@ (@ tptp.produc9098658269643458507_int_o F4) A2) B2))) (forall ((A2 tptp.list_c) (B2 tptp.list_c) (A7 tptp.list_c) (B6 tptp.list_c)) (=> (= (@ tptp.size_size_list_c A2) (@ tptp.size_size_list_c B2)) (=> (= (@ 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(forall ((A2 tptp.list_d) (B2 tptp.list_int) (A7 tptp.list_d) (B6 tptp.list_int)) (=> (= (@ tptp.size_size_list_d A2) (@ tptp.size_size_list_int B2)) (=> (= (@ tptp.size_size_list_d A7) (@ tptp.size_size_list_int B6)) (= (= (@ (@ tptp.zip_d_int A2) B2) (@ (@ tptp.zip_d_int A7) B6)) (and (= A2 A7) (= B2 B6)))))) (forall ((A2 tptp.list_nat) (B2 tptp.list_c) (A7 tptp.list_nat) (B6 tptp.list_c)) (=> (= (@ tptp.size_size_list_nat A2) (@ tptp.size_size_list_c B2)) (=> (= (@ tptp.size_size_list_nat A7) (@ tptp.size_size_list_c B6)) (= (= (@ (@ tptp.zip_nat_c A2) B2) (@ (@ tptp.zip_nat_c A7) B6)) (and (= A2 A7) (= B2 B6)))))) (forall ((A2 tptp.list_nat) (B2 tptp.list_d) (A7 tptp.list_nat) (B6 tptp.list_d)) (=> (= (@ tptp.size_size_list_nat A2) (@ tptp.size_size_list_d B2)) (=> (= (@ tptp.size_size_list_nat A7) (@ tptp.size_size_list_d B6)) (= (= (@ (@ tptp.zip_nat_d A2) B2) (@ (@ tptp.zip_nat_d A7) B6)) (and (= A2 A7) (= B2 B6)))))) (forall ((A2 tptp.list_c) (B2 tptp.list_c) (A7 tptp.list_c) 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Ys) N)))) (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (R2 tptp.set_Pr1261947904930325089at_nat) (N tptp.nat)) (=> (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Xs) Ys)) (@ (@ tptp.lexn_nat R2) N)) (and (= (@ tptp.size_size_list_nat Xs) N) (= (@ tptp.size_size_list_nat Ys) N)))) (forall ((Xs tptp.list_int) (Ys tptp.list_int) (R2 tptp.set_Pr958786334691620121nt_int) (N tptp.nat)) (=> (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Xs) Ys)) (@ (@ tptp.lexn_int R2) N)) (and (= (@ tptp.size_size_list_int Xs) N) (= (@ tptp.size_size_list_int Ys) N)))) _let_159 _let_158 _let_157 _let_156 _let_155 (forall ((B2 Bool) (Q tptp.assn)) (let ((_let_1 (@ tptp.pure_assn B2))) (= (@ (@ tptp.inf_inf_assn _let_1) Q) (@ (@ tptp.times_times_assn (@ (@ tptp.inf_inf_assn tptp.one_one_assn) Q)) _let_1)))) (forall ((P tptp.assn) (B2 Bool)) (let ((_let_1 (@ tptp.pure_assn B2))) (= (@ (@ tptp.inf_inf_assn P) _let_1) (@ (@ 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(forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (= A B)))) (forall ((A2 tptp.assn)) (= (@ (@ tptp.inf_inf_assn A2) A2) A2)) (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A2) A2) A2)) (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A2) A2) A2)) (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn X) X) X)) (forall ((X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X) X) X)) (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat X) X) X)) (forall ((A2 tptp.assn) (B2 tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn A2))) (let ((_let_2 (@ _let_1 B2))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A2))) (let ((_let_2 (@ _let_1 B2))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 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tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2))) (= (@ (@ tptp.inf_in2572325071724192079at_nat _let_1) B2) _let_1))) (forall ((X tptp.assn) (Y tptp.assn)) (let ((_let_1 (@ (@ tptp.inf_inf_assn X) Y))) (= (@ (@ tptp.inf_inf_assn _let_1) Y) _let_1))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (let ((_let_1 (@ (@ tptp.inf_inf_set_nat X) Y))) (= (@ (@ tptp.inf_inf_set_nat _let_1) Y) _let_1))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ tptp.inf_in2572325071724192079at_nat X) Y))) (= (@ (@ tptp.inf_in2572325071724192079at_nat _let_1) Y) _let_1))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat X))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z)) (and (@ _let_1 Y) (@ _let_1 Z))))) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn X))) (= (@ _let_1 (@ (@ tptp.inf_inf_assn Y) Z)) (and (@ _let_1 Y) (@ _let_1 Z))))) (forall ((X tptp.filter_nat) (Y tptp.filter_nat) (Z tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_le2510731241096832064er_nat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_filter_nat Y) Z)) (and (@ _let_1 Y) (@ _let_1 Z))))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y) Z)) (and (@ _let_1 Y) (@ _let_1 Z))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z)) (and (@ _let_1 Y) (@ _let_1 Z))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (= (@ _let_1 (@ (@ tptp.inf_inf_int Y) Z)) (and (@ _let_1 Y) (@ _let_1 Z))))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A2))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B2) C)) (and (@ _let_1 B2) (@ _let_1 C))))) (forall ((A2 tptp.assn) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn A2))) (= (@ _let_1 (@ (@ tptp.inf_inf_assn B2) C)) (and (@ _let_1 B2) (@ _let_1 C))))) (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat) (C tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_le2510731241096832064er_nat A2))) (= (@ _let_1 (@ (@ tptp.inf_inf_filter_nat B2) C)) (and (@ _let_1 B2) (@ _let_1 C))))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat B2) C)) (and (@ _let_1 B2) (@ _let_1 C))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (= (@ _let_1 (@ (@ tptp.inf_inf_nat B2) C)) (and (@ _let_1 B2) (@ _let_1 C))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A2))) (= (@ _let_1 (@ (@ tptp.inf_inf_int B2) C)) (and (@ _let_1 B2) (@ _let_1 C))))) (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn X) tptp.bot_bot_assn) tptp.bot_bot_assn)) (forall ((X tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat X) tptp.bot_bo228742789529271731at_nat) tptp.bot_bo228742789529271731at_nat)) (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat X) tptp.bot_bo2099793752762293965at_nat) tptp.bot_bo2099793752762293965at_nat)) (forall ((X tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o X) tptp.bot_bot_set_o) tptp.bot_bot_set_o)) (forall ((X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X) tptp.bot_bot_set_nat) tptp.bot_bot_set_nat)) (forall ((X tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int X) tptp.bot_bot_set_int) tptp.bot_bot_set_int)) (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn tptp.bot_bot_assn) X) tptp.bot_bot_assn)) (forall ((X tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat tptp.bot_bo228742789529271731at_nat) X) tptp.bot_bo228742789529271731at_nat)) (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bot_bo2099793752762293965at_nat) X) tptp.bot_bo2099793752762293965at_nat)) (forall ((X tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o tptp.bot_bot_set_o) X) tptp.bot_bot_set_o)) (forall ((X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat tptp.bot_bot_set_nat) X) tptp.bot_bot_set_nat)) (forall ((X tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int tptp.bot_bot_set_int) X) tptp.bot_bot_set_int)) (forall ((A tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat A) tptp.bot_bo228742789529271731at_nat) (= A tptp.bot_bo228742789529271731at_nat))) (forall ((A tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat A) tptp.bot_bo2099793752762293965at_nat) (= A tptp.bot_bo2099793752762293965at_nat))) (forall ((A tptp.set_o)) (= (@ (@ tptp.ord_less_eq_set_o A) tptp.bot_bot_set_o) (= A tptp.bot_bot_set_o))) (forall ((A tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))) (forall ((A tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat) (= A tptp.bot_bot_set_nat))) (forall ((A tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat tptp.bot_bo228742789529271731at_nat) A)) (forall ((A tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat tptp.bot_bo2099793752762293965at_nat) A)) (forall ((A tptp.set_o)) (@ (@ tptp.ord_less_eq_set_o tptp.bot_bot_set_o) A)) (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A)) (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A)) (forall ((X Bool) (A tptp.set_o) (B tptp.set_o)) (= (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.insert_o2 X) A)) B) (and (@ (@ tptp.member_o X) B) (@ (@ tptp.ord_less_eq_set_o A) B)))) (forall ((X tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.insert9069300056098147895at_nat X) A)) B) (and (@ (@ tptp.member8757157785044589968at_nat X) B) (@ (@ tptp.ord_le1268244103169919719at_nat A) B)))) (forall ((X tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.insert8211810215607154385at_nat X) A)) B) (and (@ (@ tptp.member8440522571783428010at_nat X) B) (@ (@ tptp.ord_le3146513528884898305at_nat A) B)))) (forall ((X tptp.int) (A tptp.set_int) (B tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.insert_int2 X) A)) B) (and (@ (@ tptp.member_int X) B) (@ (@ tptp.ord_less_eq_set_int A) B)))) (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.ord_le2965882846123202637_nat_o (@ (@ tptp.insert5175938949040314269_nat_o X) A)) B) (and (@ (@ tptp.member6576561426505652726_nat_o X) B) (@ (@ tptp.ord_le2965882846123202637_nat_o A) B)))) (forall ((X tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.insert_nat2 X) A)) B) (and (@ (@ tptp.member_nat X) B) (@ (@ tptp.ord_less_eq_set_nat A) B)))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_set_nat A) B)))) (forall ((A2 Bool) (B2 Bool)) (= (@ (@ tptp.inf_inf_assn (@ tptp.pure_assn A2)) (@ tptp.pure_assn B2)) (@ tptp.pure_assn (and A2 B2)))) (forall ((B2 tptp.produc3843707927480180839at_nat) (A2 tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ (@ tptp.insert9069300056098147895at_nat B2) tptp.bot_bo228742789529271731at_nat))) (= (= _let_1 (@ (@ tptp.insert9069300056098147895at_nat A2) A)) (and (= A2 B2) (@ (@ tptp.ord_le1268244103169919719at_nat A) _let_1))))) (forall ((B2 tptp.product_prod_nat_nat) (A2 tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ tptp.insert8211810215607154385at_nat B2) tptp.bot_bo2099793752762293965at_nat))) (= (= _let_1 (@ (@ tptp.insert8211810215607154385at_nat A2) A)) (and (= A2 B2) (@ (@ tptp.ord_le3146513528884898305at_nat A) _let_1))))) (forall ((B2 Bool) (A2 Bool) (A tptp.set_o)) (let ((_let_1 (@ (@ tptp.insert_o2 B2) tptp.bot_bot_set_o))) (= (= _let_1 (@ (@ tptp.insert_o2 A2) A)) (and (= A2 B2) (@ (@ tptp.ord_less_eq_set_o A) _let_1))))) (forall ((B2 tptp.int) (A2 tptp.int) (A tptp.set_int)) (let ((_let_1 (@ (@ tptp.insert_int2 B2) tptp.bot_bot_set_int))) (= (= _let_1 (@ (@ tptp.insert_int2 A2) A)) (and (= A2 B2) (@ (@ tptp.ord_less_eq_set_int A) _let_1))))) (forall ((B2 tptp.nat) (A2 tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ (@ tptp.insert_nat2 B2) tptp.bot_bot_set_nat))) (= (= _let_1 (@ (@ tptp.insert_nat2 A2) A)) (and (= A2 B2) (@ (@ tptp.ord_less_eq_set_nat A) _let_1))))) (forall ((A2 tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B2 tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ (@ tptp.insert9069300056098147895at_nat B2) tptp.bot_bo228742789529271731at_nat))) (= (= (@ (@ tptp.insert9069300056098147895at_nat A2) A) _let_1) (and (= A2 B2) (@ (@ tptp.ord_le1268244103169919719at_nat A) _let_1))))) (forall ((A2 tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.insert8211810215607154385at_nat B2) tptp.bot_bo2099793752762293965at_nat))) (= (= (@ (@ tptp.insert8211810215607154385at_nat A2) A) _let_1) (and (= A2 B2) (@ (@ tptp.ord_le3146513528884898305at_nat A) _let_1))))) (forall ((A2 Bool) (A tptp.set_o) (B2 Bool)) (let ((_let_1 (@ (@ tptp.insert_o2 B2) tptp.bot_bot_set_o))) (= (= (@ (@ tptp.insert_o2 A2) A) _let_1) (and (= A2 B2) (@ (@ tptp.ord_less_eq_set_o A) _let_1))))) (forall ((A2 tptp.int) (A tptp.set_int) (B2 tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int2 B2) tptp.bot_bot_set_int))) (= (= (@ (@ tptp.insert_int2 A2) A) _let_1) (and (= A2 B2) (@ (@ tptp.ord_less_eq_set_int A) _let_1))))) (forall ((A2 tptp.nat) (A tptp.set_nat) (B2 tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat2 B2) tptp.bot_bot_set_nat))) (= (= (@ (@ tptp.insert_nat2 A2) A) _let_1) (and (= A2 B2) (@ (@ tptp.ord_less_eq_set_nat A) _let_1))))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (= (= (@ (@ tptp.minus_3314409938677909166at_nat A) B) tptp.bot_bo228742789529271731at_nat) (@ (@ tptp.ord_le1268244103169919719at_nat A) B))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.minus_1356011639430497352at_nat A) B) tptp.bot_bo2099793752762293965at_nat) (@ (@ tptp.ord_le3146513528884898305at_nat A) B))) (forall ((A tptp.set_o) (B tptp.set_o)) (= (= (@ (@ tptp.minus_minus_set_o A) B) tptp.bot_bot_set_o) (@ (@ tptp.ord_less_eq_set_o A) B))) (forall ((A tptp.set_int) (B tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int A) B) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int A) B))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat A) B) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat A) B))) (forall ((P tptp.assn) (Q tptp.assn) (B2 Bool)) (let ((_let_1 (@ tptp.pure_assn B2))) (let ((_let_2 (@ tptp.inf_inf_assn P))) (= (@ _let_2 (@ (@ tptp.times_times_assn Q) _let_1)) (@ (@ tptp.times_times_assn (@ _let_2 Q)) _let_1))))) (forall ((P tptp.assn) (B2 Bool) (Q tptp.assn)) (let ((_let_1 (@ tptp.pure_assn B2))) (= (@ (@ tptp.inf_inf_assn (@ (@ tptp.times_times_assn P) _let_1)) Q) (@ (@ tptp.times_times_assn (@ (@ tptp.inf_inf_assn P) Q)) _let_1)))) (forall ((P tptp.assn) (Q tptp.assn) (H2 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) tptp.bot_bot_set_nat))) (= (@ (@ tptp.rep_assn (@ (@ tptp.inf_inf_assn P) Q)) _let_1) (and (@ (@ tptp.rep_assn P) _let_1) (@ (@ tptp.rep_assn Q) _let_1))))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (X tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat X))) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A) B) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A) B) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((A tptp.set_int) (B tptp.set_int) (X tptp.int)) (let ((_let_1 (@ tptp.member_int X))) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o X))) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o A) B) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((A tptp.set_nat) (B tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (C tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A) B) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A) B) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o) (C (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o A) B) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (@ _let_1 A) (@ _let_1 B))))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (= A B) (not (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (not (@ (@ tptp.ord_less_eq_set_nat B) A)))))) (forall ((R (-> tptp.produc3843707927480180839at_nat tptp.produc3843707927480180839at_nat Bool)) (S tptp.set_Pr4329608150637261639at_nat) (X tptp.produc3843707927480180839at_nat) (Y tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.pairwi3222497012029234898at_nat R) S) (=> (@ (@ tptp.member8757157785044589968at_nat X) S) (=> (@ (@ tptp.member8757157785044589968at_nat Y) S) (=> (not (= X Y)) (@ (@ R X) Y)))))) (forall ((R (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (S tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (=> (@ (@ tptp.pairwi6357175311820755948at_nat R) S) (=> (@ (@ tptp.member8440522571783428010at_nat X) S) (=> (@ (@ tptp.member8440522571783428010at_nat Y) S) (=> (not (= X Y)) (@ (@ R X) Y)))))) (forall ((R (-> tptp.nat tptp.nat Bool)) (S tptp.set_nat) (X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.pairwise_nat R) S) (=> (@ (@ tptp.member_nat X) S) (=> (@ (@ tptp.member_nat Y) S) (=> (not (= X Y)) (@ (@ R X) Y)))))) (forall ((R (-> tptp.int tptp.int Bool)) (S tptp.set_int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.pairwise_int R) S) (=> (@ (@ tptp.member_int X) S) (=> (@ (@ tptp.member_int Y) S) (=> (not (= X Y)) (@ (@ R X) Y)))))) (forall ((R (-> (-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) Bool)) (S tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Y (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.pairwi2432143822833250616_nat_o R) S) (=> (@ (@ tptp.member6576561426505652726_nat_o X) S) (=> (@ (@ tptp.member6576561426505652726_nat_o Y) S) (=> (not (= X Y)) (@ (@ R X) Y)))))) (forall ((S tptp.set_Pr4329608150637261639at_nat) (R (-> tptp.produc3843707927480180839at_nat tptp.produc3843707927480180839at_nat Bool))) (=> (forall ((X3 tptp.produc3843707927480180839at_nat) (Y2 tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X3) S) (=> (@ (@ tptp.member8757157785044589968at_nat Y2) S) (=> (not (= X3 Y2)) (@ (@ R X3) Y2))))) (@ (@ tptp.pairwi3222497012029234898at_nat R) S))) (forall ((S tptp.set_Pr1261947904930325089at_nat) (R (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool))) (=> (forall ((X3 tptp.product_prod_nat_nat) (Y2 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) S) (=> (@ (@ tptp.member8440522571783428010at_nat Y2) S) (=> (not (= X3 Y2)) (@ (@ R X3) Y2))))) (@ (@ tptp.pairwi6357175311820755948at_nat R) S))) (forall ((S tptp.set_nat) (R (-> tptp.nat tptp.nat Bool))) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (=> (@ (@ tptp.member_nat Y2) S) (=> (not (= X3 Y2)) (@ (@ R X3) Y2))))) (@ (@ tptp.pairwise_nat R) S))) (forall ((S tptp.set_int) (R (-> tptp.int tptp.int Bool))) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.member_int X3) S) (=> (@ (@ tptp.member_int Y2) S) (=> (not (= X3 Y2)) (@ (@ R X3) Y2))))) (@ (@ tptp.pairwise_int R) S))) (forall ((S tptp.set_Pr4532377907799695533_nat_o) (R (-> (-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X3) S) (=> (@ (@ tptp.member6576561426505652726_nat_o Y2) S) (=> (not (= X3 Y2)) (@ (@ R X3) Y2))))) (@ (@ tptp.pairwi2432143822833250616_nat_o R) S))) _let_154 _let_153 _let_152 _let_151 _let_150 (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (= A B) (@ (@ tptp.ord_less_eq_set_nat A) B))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (= A B) (@ (@ tptp.ord_less_eq_set_nat B) A))) (= tptp.ord_le1268244103169919719at_nat (lambda ((A5 tptp.set_Pr4329608150637261639at_nat) (B7 tptp.set_Pr4329608150637261639at_nat)) (forall ((T2 tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat T2))) (=> (@ _let_1 A5) (@ _let_1 B7)))))) (= tptp.ord_le3146513528884898305at_nat (lambda ((A5 tptp.set_Pr1261947904930325089at_nat) (B7 tptp.set_Pr1261947904930325089at_nat)) (forall ((T2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat T2))) (=> (@ _let_1 A5) (@ _let_1 B7)))))) (= tptp.ord_less_eq_set_int (lambda ((A5 tptp.set_int) (B7 tptp.set_int)) (forall ((T2 tptp.int)) (let ((_let_1 (@ tptp.member_int T2))) (=> (@ _let_1 A5) (@ _let_1 B7)))))) (= tptp.ord_le2965882846123202637_nat_o (lambda ((A5 tptp.set_Pr4532377907799695533_nat_o) (B7 tptp.set_Pr4532377907799695533_nat_o)) (forall ((T2 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o T2))) (=> (@ _let_1 A5) (@ _let_1 B7)))))) (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B7 tptp.set_nat)) (forall ((T2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat T2))) (=> (@ _let_1 A5) (@ _let_1 B7)))))) (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A) A)) (forall ((P (-> tptp.product_prod_nat_nat Bool)) (Q (-> tptp.product_prod_nat_nat Bool))) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ P X3) (@ Q X3))) (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.collec3392354462482085612at_nat P)) (@ tptp.collec3392354462482085612at_nat Q)))) (forall ((P (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool)) (Q (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ P X3) (@ Q X3))) (@ (@ tptp.ord_le2965882846123202637_nat_o (@ tptp.collec939566748876313656_nat_o P)) (@ tptp.collec939566748876313656_nat_o Q)))) (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (=> (@ P X3) (@ Q X3))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat P)) (@ tptp.collect_nat Q)))) (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_nat B) C2) (@ _let_1 C2))))) (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.set_nat) (Q (-> tptp.nat tptp.nat Bool)) (B tptp.set_nat)) (=> (@ (@ tptp.pairwise_nat P) A) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ P X3) Y2) (@ (@ Q X3) Y2))) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (@ (@ tptp.pairwise_nat Q) B))))) (= (lambda ((Y4 tptp.set_nat) (Z2 tptp.set_nat)) (= Y4 Z2)) (lambda ((A5 tptp.set_nat) (B7 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A5) B7) (@ (@ tptp.ord_less_eq_set_nat B7) A5)))) (forall ((P (-> tptp.nat tptp.nat Bool)) (S tptp.set_nat) (T3 tptp.set_nat)) (let ((_let_1 (@ tptp.pairwise_nat P))) (=> (@ _let_1 S) (=> (@ (@ tptp.ord_less_eq_set_nat T3) S) (@ _let_1 T3))))) (forall ((P (-> tptp.product_prod_nat_nat Bool)) (Q (-> tptp.product_prod_nat_nat Bool))) (= (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.collec3392354462482085612at_nat P)) (@ tptp.collec3392354462482085612at_nat Q)) (forall ((X2 tptp.product_prod_nat_nat)) (=> (@ P X2) (@ Q X2))))) (forall ((P (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool)) (Q (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (= (@ (@ tptp.ord_le2965882846123202637_nat_o (@ tptp.collec939566748876313656_nat_o P)) (@ tptp.collec939566748876313656_nat_o Q)) (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ P X2) (@ Q X2))))) (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat P)) (@ tptp.collect_nat Q)) (forall ((X2 tptp.nat)) (=> (@ P X2) (@ Q X2))))) (forall ((A2 tptp.assn) (B2 tptp.assn) (C tptp.assn) (D2 tptp.assn)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_eq_assn B2) C) (=> (= C D2) (@ (@ tptp.ord_less_eq_assn A2) D2))))) (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat) (C tptp.filter_nat) (D2 tptp.filter_nat)) (=> (= A2 B2) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B2) C) (=> (= C D2) (@ (@ tptp.ord_le2510731241096832064er_nat A2) D2))))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (C tptp.set_nat) (D2 tptp.set_nat)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) C) (=> (= C D2) (@ (@ tptp.ord_less_eq_set_nat A2) D2))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (= C D2) (@ (@ tptp.ord_less_eq_nat A2) D2))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int) (D2 tptp.int)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_eq_int B2) C) (=> (= C D2) (@ (@ tptp.ord_less_eq_int A2) D2))))) (forall ((S tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.product_prod_nat_nat Bool))) (= (@ (@ tptp.ord_le3146513528884898305at_nat S) (@ tptp.collec3392354462482085612at_nat P)) (forall ((X2 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X2) S) (@ P X2))))) (forall ((S tptp.set_Pr4532377907799695533_nat_o) (P (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (= (@ (@ tptp.ord_le2965882846123202637_nat_o S) (@ tptp.collec939566748876313656_nat_o P)) (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X2) S) (@ P X2))))) (forall ((S tptp.set_nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_set_nat S) (@ tptp.collect_nat P)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) S) (@ P X2))))) (forall ((X tptp.assn) (Y tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (let ((_let_2 (@ tptp.inf_inf_assn Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (= tptp.inf_inf_assn (lambda ((X2 tptp.assn) (Y5 tptp.assn)) (@ (@ tptp.inf_inf_assn Y5) X2))) (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn X) X) X)) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (= (@ (@ tptp.inf_inf_assn (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_inf_assn Y) Z))))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat A2) B2)) (and (@ (@ tptp.ord_less_eq_nat B2) A2) (not (= B2 A2))))) (forall ((A2 tptp.int) (B2 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int A2) B2)) (and (@ (@ tptp.ord_less_eq_int B2) A2) (not (= B2 A2))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_int Z))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_int Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))) (= (lambda ((Y4 tptp.assn) (Z2 tptp.assn)) (= Y4 Z2)) (lambda ((X2 tptp.assn) (Y5 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn X2) Y5) (@ (@ tptp.ord_less_eq_assn Y5) X2)))) (= (lambda ((Y4 tptp.filter_nat) (Z2 tptp.filter_nat)) (= Y4 Z2)) (lambda ((X2 tptp.filter_nat) (Y5 tptp.filter_nat)) (and (@ (@ tptp.ord_le2510731241096832064er_nat X2) Y5) (@ (@ tptp.ord_le2510731241096832064er_nat Y5) X2)))) (= (lambda ((Y4 tptp.set_nat) (Z2 tptp.set_nat)) (= Y4 Z2)) (lambda ((X2 tptp.set_nat) (Y5 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat X2) Y5) (@ (@ tptp.ord_less_eq_set_nat Y5) X2)))) (= (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2)) (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X2) Y5) (@ (@ tptp.ord_less_eq_nat Y5) X2)))) (= (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2)) (lambda ((X2 tptp.int) (Y5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X2) Y5) (@ (@ tptp.ord_less_eq_int Y5) X2)))) (forall ((A2 tptp.assn) (B2 tptp.assn) (C tptp.assn)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_eq_assn B2) C) (@ (@ tptp.ord_less_eq_assn A2) C)))) (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat) (C tptp.filter_nat)) (=> (= A2 B2) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B2) C) (@ (@ tptp.ord_le2510731241096832064er_nat A2) C)))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (C tptp.set_nat)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) C) (@ (@ tptp.ord_less_eq_set_nat A2) C)))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (@ (@ tptp.ord_less_eq_nat A2) C)))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_eq_int B2) C) (@ (@ tptp.ord_less_eq_int A2) C)))) (forall ((A2 tptp.assn) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn A2))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))) (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat) (C tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_le2510731241096832064er_nat A2))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A2))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))) (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X) Y) (=> (@ (@ tptp.ord_less_eq_assn Y) X) (= X Y)))) (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat X) Y) (=> (@ (@ tptp.ord_le2510731241096832064er_nat Y) X) (= X Y)))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= X Y)))) (forall ((A2 tptp.assn) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_assn B2) C) (@ _let_1 C))))) (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat) (C tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_le2510731241096832064er_nat A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B2) C) (@ _let_1 C))))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) C) (@ _let_1 C))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (@ _let_1 C))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_int B2) C) (@ _let_1 C))))) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_assn Y) Z) (@ _let_1 Z))))) (forall ((X tptp.filter_nat) (Y tptp.filter_nat) (Z tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_le2510731241096832064er_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_le2510731241096832064er_nat Y) Z) (@ _let_1 Z))))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_nat Y) Z) (@ _let_1 Z))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z) (@ _let_1 Z))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ _let_1 Z))))) (forall ((P (-> tptp.nat tptp.nat Bool)) (A2 tptp.nat) (B2 tptp.nat)) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A4) B4) (@ (@ P A4) B4))) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (@ (@ P B4) A4) (@ (@ P A4) B4))) (@ (@ P A2) B2)))) (forall ((P (-> tptp.int tptp.int Bool)) (A2 tptp.int) (B2 tptp.int)) (=> (forall ((A4 tptp.int) (B4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A4) B4) (@ (@ P A4) B4))) (=> (forall ((A4 tptp.int) (B4 tptp.int)) (=> (@ (@ P B4) A4) (@ (@ P A4) B4))) (@ (@ P A2) B2)))) (= (lambda ((Y4 tptp.assn) (Z2 tptp.assn)) (= Y4 Z2)) (lambda ((A3 tptp.assn) (B3 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn B3) A3) (@ (@ tptp.ord_less_eq_assn A3) B3)))) (= (lambda ((Y4 tptp.filter_nat) (Z2 tptp.filter_nat)) (= Y4 Z2)) (lambda ((A3 tptp.filter_nat) (B3 tptp.filter_nat)) (and (@ (@ tptp.ord_le2510731241096832064er_nat B3) A3) (@ (@ tptp.ord_le2510731241096832064er_nat A3) B3)))) (= (lambda ((Y4 tptp.set_nat) (Z2 tptp.set_nat)) (= Y4 Z2)) (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B3) A3) (@ (@ tptp.ord_less_eq_set_nat A3) B3)))) (= (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2)) (lambda ((A3 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B3) A3) (@ (@ tptp.ord_less_eq_nat A3) B3)))) (= (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2)) (lambda ((A3 tptp.int) (B3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B3) A3) (@ (@ tptp.ord_less_eq_int A3) B3)))) (forall ((B2 tptp.assn) (A2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn B2) A2) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (= A2 B2)))) (forall ((B2 tptp.filter_nat) (A2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B2) A2) (=> (@ (@ tptp.ord_le2510731241096832064er_nat A2) B2) (= A2 B2)))) (forall ((B2 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A2) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (= A2 B2)))) (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= A2 B2)))) (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (= A2 B2)))) (forall ((B2 tptp.assn) (A2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn C))) (=> (@ (@ tptp.ord_less_eq_assn B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))) (forall ((B2 tptp.filter_nat) (A2 tptp.filter_nat) (C tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_le2510731241096832064er_nat C))) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))) (forall ((B2 tptp.set_nat) (A2 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C))) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))) (forall ((B2 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))) (forall ((B2 tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))) (forall ((A2 tptp.assn) (B2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (=> (@ (@ tptp.ord_less_eq_assn B2) A2) (= A2 B2)))) (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat A2) B2) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B2) A2) (= A2 B2)))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A2) (= A2 B2)))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (= A2 B2)))) (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (= A2 B2)))) (= (lambda ((Y4 tptp.assn) (Z2 tptp.assn)) (= Y4 Z2)) (lambda ((A3 tptp.assn) (B3 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn A3) B3) (@ (@ tptp.ord_less_eq_assn B3) A3)))) (= (lambda ((Y4 tptp.filter_nat) (Z2 tptp.filter_nat)) (= Y4 Z2)) (lambda ((A3 tptp.filter_nat) (B3 tptp.filter_nat)) (and (@ (@ tptp.ord_le2510731241096832064er_nat A3) B3) (@ (@ tptp.ord_le2510731241096832064er_nat B3) A3)))) (= (lambda ((Y4 tptp.set_nat) (Z2 tptp.set_nat)) (= Y4 Z2)) (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A3) B3) (@ (@ tptp.ord_less_eq_set_nat B3) A3)))) (= (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2)) (lambda ((A3 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B3) (@ (@ tptp.ord_less_eq_nat B3) A3)))) (= (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2)) (lambda ((A3 tptp.int) (B3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A3) B3) (@ (@ tptp.ord_less_eq_int B3) A3)))) (forall ((A2 tptp.assn) (F4 (-> tptp.assn tptp.assn)) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_assn B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((A2 tptp.assn) (F4 (-> tptp.nat tptp.assn)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_assn A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((A2 tptp.assn) (F4 (-> tptp.int tptp.assn)) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_assn A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_int B2) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y2) (@ (@ tptp.ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((A2 tptp.nat) (F4 (-> tptp.assn tptp.nat)) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_assn B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((A2 tptp.nat) (F4 (-> tptp.nat tptp.nat)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((A2 tptp.nat) (F4 (-> tptp.int tptp.nat)) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_int B2) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((A2 tptp.int) (F4 (-> tptp.assn tptp.int)) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_int A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_assn B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((A2 tptp.int) (F4 (-> tptp.nat tptp.int)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((A2 tptp.int) (F4 (-> tptp.int tptp.int)) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_int B2) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((A2 tptp.assn) (F4 (-> tptp.filter_nat tptp.assn)) (B2 tptp.filter_nat) (C tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_less_eq_assn A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B2) C) (=> (forall ((X3 tptp.filter_nat) (Y2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat X3) Y2) (@ (@ tptp.ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (=> (@ (@ tptp.ord_less_eq_assn (@ F4 B2)) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_assn (@ F4 A2)) C))))) (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (=> (@ (@ tptp.ord_less_eq_nat (@ F4 B2)) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_nat (@ F4 A2)) C))))) (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (=> (@ (@ tptp.ord_less_eq_int (@ F4 B2)) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_int (@ F4 A2)) C))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (F4 (-> tptp.nat tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_assn (@ F4 B2)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_assn (@ F4 A2)) C))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (F4 (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat (@ F4 B2)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_nat (@ F4 A2)) C))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (F4 (-> tptp.nat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_int (@ F4 B2)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_int (@ F4 A2)) C))))) (forall ((A2 tptp.int) (B2 tptp.int) (F4 (-> tptp.int tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_eq_assn (@ F4 B2)) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y2) (@ (@ tptp.ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_assn (@ F4 A2)) C))))) (forall ((A2 tptp.int) (B2 tptp.int) (F4 (-> tptp.int tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_eq_nat (@ F4 B2)) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_nat (@ F4 A2)) C))))) (forall ((A2 tptp.int) (B2 tptp.int) (F4 (-> tptp.int tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_eq_int (@ F4 B2)) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_int (@ F4 A2)) C))))) (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.filter_nat)) (C tptp.filter_nat)) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (=> (@ (@ tptp.ord_le2510731241096832064er_nat (@ F4 B2)) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_le2510731241096832064er_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le2510731241096832064er_nat (@ F4 A2)) C))))) (forall ((X tptp.assn) (Y tptp.assn)) (=> (= X Y) (@ (@ tptp.ord_less_eq_assn X) Y))) (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (=> (= X Y) (@ (@ tptp.ord_le2510731241096832064er_nat X) Y))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (= X Y) (@ (@ tptp.ord_less_eq_set_nat X) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (= X Y) (@ (@ tptp.ord_less_eq_nat X) Y))) (forall ((X tptp.int) (Y tptp.int)) (=> (= X Y) (@ (@ tptp.ord_less_eq_int X) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_eq_nat Y) X))) (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_eq_int X) Y) (@ (@ tptp.ord_less_eq_int Y) X))) (forall ((A2 tptp.assn) (F4 (-> tptp.assn tptp.assn)) (B2 tptp.assn) (C tptp.assn)) (=> (= A2 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_assn B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_assn A2) (@ F4 C)))))) (forall ((A2 tptp.nat) (F4 (-> tptp.assn tptp.nat)) (B2 tptp.assn) (C tptp.assn)) (=> (= A2 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_assn B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_nat A2) (@ F4 C)))))) (forall ((A2 tptp.int) (F4 (-> tptp.assn tptp.int)) (B2 tptp.assn) (C tptp.assn)) (=> (= A2 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_assn B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_int A2) (@ F4 C)))))) (forall ((A2 tptp.assn) (F4 (-> tptp.nat tptp.assn)) (B2 tptp.nat) (C tptp.nat)) (=> (= A2 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_assn A2) (@ F4 C)))))) (forall ((A2 tptp.nat) (F4 (-> tptp.nat tptp.nat)) (B2 tptp.nat) (C tptp.nat)) (=> (= A2 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_nat A2) (@ F4 C)))))) (forall ((A2 tptp.int) (F4 (-> tptp.nat tptp.int)) (B2 tptp.nat) (C tptp.nat)) (=> (= A2 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_int A2) (@ F4 C)))))) (forall ((A2 tptp.assn) (F4 (-> tptp.int tptp.assn)) (B2 tptp.int) (C tptp.int)) (=> (= A2 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_int B2) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y2) (@ (@ tptp.ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_assn A2) (@ F4 C)))))) (forall ((A2 tptp.nat) (F4 (-> tptp.int tptp.nat)) (B2 tptp.int) (C tptp.int)) (=> (= A2 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_int B2) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_nat A2) (@ F4 C)))))) (forall ((A2 tptp.int) (F4 (-> tptp.int tptp.int)) (B2 tptp.int) (C tptp.int)) (=> (= A2 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_int B2) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_int A2) (@ F4 C)))))) (forall ((A2 tptp.filter_nat) (F4 (-> tptp.assn tptp.filter_nat)) (B2 tptp.assn) (C tptp.assn)) (=> (= A2 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_assn B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_le2510731241096832064er_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le2510731241096832064er_nat A2) (@ F4 C)))))) (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_assn (@ F4 A2)) C))))) (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_nat (@ F4 A2)) C))))) (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_int (@ F4 A2)) C))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (F4 (-> tptp.nat tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_assn (@ F4 A2)) C))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (F4 (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_nat (@ F4 A2)) C))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (F4 (-> tptp.nat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_int (@ F4 A2)) C))))) (forall ((A2 tptp.int) (B2 tptp.int) (F4 (-> tptp.int tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y2) (@ (@ tptp.ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_assn (@ F4 A2)) C))))) (forall ((A2 tptp.int) (B2 tptp.int) (F4 (-> tptp.int tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_nat (@ F4 A2)) C))))) (forall ((A2 tptp.int) (B2 tptp.int) (F4 (-> tptp.int tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_eq_int (@ F4 A2)) C))))) (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.filter_nat)) (C tptp.filter_nat)) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (=> (= (@ F4 B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_le2510731241096832064er_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le2510731241096832064er_nat (@ F4 A2)) C))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))) (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))) (forall ((Y tptp.assn) (X tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn Y) X) (= (@ (@ tptp.ord_less_eq_assn X) Y) (= X Y)))) (forall ((Y tptp.filter_nat) (X tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat Y) X) (= (@ (@ tptp.ord_le2510731241096832064er_nat X) Y) (= X Y)))) (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (= (@ (@ tptp.ord_less_eq_set_nat X) Y) (= X Y)))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.ord_less_eq_nat X) Y) (= X Y)))) (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.ord_less_eq_int X) Y) (= X Y)))) (forall ((X tptp.assn) (Y tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (let ((_let_2 (@ tptp.inf_inf_assn Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (let ((_let_2 (@ tptp.inf_inf_set_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (let ((_let_2 (@ tptp.inf_in2572325071724192079at_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (= (@ (@ tptp.inf_inf_assn (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_inf_assn Y) Z))))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (= (@ (@ tptp.inf_inf_set_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y) Z))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z))))) (= tptp.inf_inf_assn (lambda ((X2 tptp.assn) (Y5 tptp.assn)) (@ (@ tptp.inf_inf_assn Y5) X2))) (= tptp.inf_inf_set_nat (lambda ((X2 tptp.set_nat) (Y5 tptp.set_nat)) (@ (@ tptp.inf_inf_set_nat Y5) X2))) (= tptp.inf_in2572325071724192079at_nat (lambda ((X2 tptp.set_Pr1261947904930325089at_nat) (Y5 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.inf_in2572325071724192079at_nat Y5) X2))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) Y)) (forall ((X tptp.assn) (Y tptp.assn)) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn X) Y)) Y)) (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.inf_inf_filter_nat X) Y)) Y)) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X) Y)) Y)) (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat X) Y)) Y)) (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int X) Y)) Y)) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) X)) (forall ((X tptp.assn) (Y tptp.assn)) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn X) Y)) X)) (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.inf_inf_filter_nat X) Y)) X)) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X) Y)) X)) (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat X) Y)) X)) (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int X) Y)) X)) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) X)) (forall ((X tptp.assn) (Y tptp.assn)) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn X) Y)) X)) (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.inf_inf_filter_nat X) Y)) X)) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X) Y)) X)) (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat X) Y)) X)) (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int X) Y)) X)) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) Y)) (forall ((X tptp.assn) (Y tptp.assn)) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn X) Y)) Y)) (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.inf_inf_filter_nat X) Y)) Y)) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X) Y)) Y)) (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat X) Y)) Y)) (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int X) Y)) Y)) (forall ((X tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat X))) (=> (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2)) (not (=> (@ _let_1 A2) (not (@ _let_1 B2))))))) (forall ((X tptp.assn) (A2 tptp.assn) (B2 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn X))) (=> (@ _let_1 (@ (@ tptp.inf_inf_assn A2) B2)) (not (=> (@ _let_1 A2) (not (@ _let_1 B2))))))) (forall ((X tptp.filter_nat) (A2 tptp.filter_nat) (B2 tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_le2510731241096832064er_nat X))) (=> (@ _let_1 (@ (@ tptp.inf_inf_filter_nat A2) B2)) (not (=> (@ _let_1 A2) (not (@ _let_1 B2))))))) (forall ((X tptp.set_nat) (A2 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat A2) B2)) (not (=> (@ _let_1 A2) (not (@ _let_1 B2))))))) (forall ((X tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 (@ (@ tptp.inf_inf_nat A2) B2)) (not (=> (@ _let_1 A2) (not (@ _let_1 B2))))))) (forall ((X tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 (@ (@ tptp.inf_inf_int A2) B2)) (not (=> (@ _let_1 A2) (not (@ _let_1 B2))))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat X))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2)))))) (forall ((X tptp.assn) (A2 tptp.assn) (B2 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn X))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.inf_inf_assn A2) B2)))))) (forall ((X tptp.filter_nat) (A2 tptp.filter_nat) (B2 tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_le2510731241096832064er_nat X))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.inf_inf_filter_nat A2) B2)))))) (forall ((X tptp.set_nat) (A2 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A2) B2)))))) (forall ((X tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.inf_inf_nat A2) B2)))))) (forall ((X tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.inf_inf_int A2) B2)))))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (D2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) C) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B2) D2) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2)) (@ (@ tptp.inf_in2572325071724192079at_nat C) D2))))) (forall ((A2 tptp.assn) (C tptp.assn) (B2 tptp.assn) (D2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A2) C) (=> (@ (@ tptp.ord_less_eq_assn B2) D2) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn A2) B2)) (@ (@ tptp.inf_inf_assn C) D2))))) (forall ((A2 tptp.filter_nat) (C tptp.filter_nat) (B2 tptp.filter_nat) (D2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat A2) C) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B2) D2) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.inf_inf_filter_nat A2) B2)) (@ (@ tptp.inf_inf_filter_nat C) D2))))) (forall ((A2 tptp.set_nat) (C tptp.set_nat) (B2 tptp.set_nat) (D2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) C) (=> (@ (@ tptp.ord_less_eq_set_nat B2) D2) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A2) B2)) (@ (@ tptp.inf_inf_set_nat C) D2))))) (forall ((A2 tptp.nat) (C tptp.nat) (B2 tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) C) (=> (@ (@ tptp.ord_less_eq_nat B2) D2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A2) B2)) (@ (@ tptp.inf_inf_nat C) D2))))) (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) C) (=> (@ (@ tptp.ord_less_eq_int B2) D2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A2) B2)) (@ (@ tptp.inf_inf_int C) D2))))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) X) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2)) X))) (forall ((A2 tptp.assn) (X tptp.assn) (B2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A2) X) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn A2) B2)) X))) (forall ((A2 tptp.filter_nat) (X tptp.filter_nat) (B2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat A2) X) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.inf_inf_filter_nat A2) B2)) X))) (forall ((A2 tptp.set_nat) (X tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) X) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A2) B2)) X))) (forall ((A2 tptp.nat) (X tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) X) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A2) B2)) X))) (forall ((A2 tptp.int) (X tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) X) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A2) B2)) X))) (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B2) X) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2)) X))) (forall ((B2 tptp.assn) (X tptp.assn) (A2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn B2) X) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn A2) B2)) X))) (forall ((B2 tptp.filter_nat) (X tptp.filter_nat) (A2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B2) X) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.inf_inf_filter_nat A2) B2)) X))) (forall ((B2 tptp.set_nat) (X tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B2) X) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A2) B2)) X))) (forall ((B2 tptp.nat) (X tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) X) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A2) B2)) X))) (forall ((B2 tptp.int) (X tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) X) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A2) B2)) X))) (forall ((A2 tptp.assn) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn A2))) (= (@ (@ tptp.inf_inf_assn (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.inf_inf_assn B2) C))))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A2))) (= (@ (@ tptp.inf_inf_set_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.inf_inf_set_nat B2) C))))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A2))) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B2) C))))) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (= (@ (@ tptp.inf_inf_assn (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_inf_assn Y) Z))))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (= (@ (@ tptp.inf_inf_set_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y) Z))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z))))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) B2) (= A2 (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2)))) (forall ((A2 tptp.assn) (B2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (= A2 (@ (@ tptp.inf_inf_assn A2) B2)))) (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat A2) B2) (= A2 (@ (@ tptp.inf_inf_filter_nat A2) B2)))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (= A2 (@ (@ tptp.inf_inf_set_nat A2) B2)))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= A2 (@ (@ tptp.inf_inf_nat A2) B2)))) (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (= A2 (@ (@ tptp.inf_inf_int A2) B2)))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (=> (= A2 (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2)) (@ (@ tptp.ord_le3146513528884898305at_nat A2) B2))) (forall ((A2 tptp.assn) (B2 tptp.assn)) (=> (= A2 (@ (@ tptp.inf_inf_assn A2) B2)) (@ (@ tptp.ord_less_eq_assn A2) B2))) (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat)) (=> (= A2 (@ (@ tptp.inf_inf_filter_nat A2) B2)) (@ (@ tptp.ord_le2510731241096832064er_nat A2) B2))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (= A2 (@ (@ tptp.inf_inf_set_nat A2) B2)) (@ (@ tptp.ord_less_eq_set_nat A2) B2))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (= A2 (@ (@ tptp.inf_inf_nat A2) B2)) (@ (@ tptp.ord_less_eq_nat A2) B2))) (forall ((A2 tptp.int) (B2 tptp.int)) (=> (= A2 (@ (@ tptp.inf_inf_int A2) B2)) (@ (@ tptp.ord_less_eq_int A2) B2))) (forall ((F4 (-> 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) (Y2 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ F4 X3) Y2)) X3)) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat) (Y2 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ F4 X3) Y2)) Y2)) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat) (Y2 tptp.set_Pr1261947904930325089at_nat) (Z4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat X3))) (=> (@ _let_1 Y2) (=> (@ _let_1 Z4) (@ _let_1 (@ (@ F4 Y2) Z4)))))) (= (@ (@ tptp.inf_in2572325071724192079at_nat X) Y) (@ (@ F4 X) Y)))))) (forall ((F4 (-> tptp.assn tptp.assn tptp.assn)) (X tptp.assn) (Y tptp.assn)) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (@ (@ tptp.ord_less_eq_assn (@ (@ F4 X3) Y2)) X3)) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (@ (@ tptp.ord_less_eq_assn (@ (@ F4 X3) Y2)) Y2)) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn) (Z4 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn X3))) (=> (@ _let_1 Y2) (=> (@ _let_1 Z4) (@ _let_1 (@ (@ F4 Y2) Z4)))))) (= (@ (@ tptp.inf_inf_assn X) Y) (@ (@ F4 X) Y)))))) (forall ((F4 (-> tptp.filter_nat tptp.filter_nat tptp.filter_nat)) (X tptp.filter_nat) (Y tptp.filter_nat)) (=> (forall ((X3 tptp.filter_nat) (Y2 tptp.filter_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ F4 X3) Y2)) X3)) (=> (forall ((X3 tptp.filter_nat) (Y2 tptp.filter_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ F4 X3) Y2)) Y2)) (=> (forall ((X3 tptp.filter_nat) (Y2 tptp.filter_nat) (Z4 tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_le2510731241096832064er_nat X3))) (=> (@ _let_1 Y2) (=> (@ _let_1 Z4) (@ _let_1 (@ (@ F4 Y2) Z4)))))) (= (@ (@ tptp.inf_inf_filter_nat X) Y) (@ (@ F4 X) Y)))))) (forall ((F4 (-> tptp.set_nat tptp.set_nat tptp.set_nat)) (X tptp.set_nat) (Y tptp.set_nat)) (=> (forall ((X3 tptp.set_nat) (Y2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ F4 X3) Y2)) X3)) (=> (forall ((X3 tptp.set_nat) (Y2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ F4 X3) Y2)) Y2)) (=> (forall ((X3 tptp.set_nat) (Y2 tptp.set_nat) (Z4 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X3))) (=> (@ _let_1 Y2) (=> (@ _let_1 Z4) (@ _let_1 (@ (@ F4 Y2) Z4)))))) (= (@ (@ tptp.inf_inf_set_nat X) Y) (@ (@ F4 X) Y)))))) (forall ((F4 (-> tptp.nat tptp.nat tptp.nat)) (X tptp.nat) (Y tptp.nat)) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ F4 X3) Y2)) X3)) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ F4 X3) Y2)) Y2)) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat) (Z4 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X3))) (=> (@ _let_1 Y2) (=> (@ _let_1 Z4) (@ _let_1 (@ (@ F4 Y2) Z4)))))) (= (@ (@ tptp.inf_inf_nat X) Y) (@ (@ F4 X) Y)))))) (forall ((F4 (-> tptp.int tptp.int tptp.int)) (X tptp.int) (Y tptp.int)) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ F4 X3) Y2)) X3)) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ F4 X3) Y2)) Y2)) (=> (forall ((X3 tptp.int) (Y2 tptp.int) (Z4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X3))) (=> (@ _let_1 Y2) (=> (@ _let_1 Z4) (@ _let_1 (@ (@ F4 Y2) Z4)))))) (= (@ (@ tptp.inf_inf_int X) Y) (@ (@ F4 X) Y)))))) (= tptp.ord_le3146513528884898305at_nat (lambda ((X2 tptp.set_Pr1261947904930325089at_nat) (Y5 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat X2) Y5) X2))) _let_149 _let_148 (= tptp.ord_less_eq_set_nat (lambda ((X2 tptp.set_nat) (Y5 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X2) Y5) X2))) _let_147 _let_146 (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) B2) (= (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2) A2))) (forall ((A2 tptp.assn) (B2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (= (@ (@ tptp.inf_inf_assn A2) B2) A2))) (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat A2) B2) (= (@ (@ tptp.inf_inf_filter_nat A2) B2) A2))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (= (@ (@ tptp.inf_inf_set_nat A2) B2) A2))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= (@ (@ tptp.inf_inf_nat A2) B2) A2))) (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (= (@ (@ tptp.inf_inf_int A2) B2) A2))) (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B2) A2) (= (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2) B2))) (forall ((B2 tptp.assn) (A2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn B2) A2) (= (@ (@ tptp.inf_inf_assn A2) B2) B2))) (forall ((B2 tptp.filter_nat) (A2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B2) A2) (= (@ (@ tptp.inf_inf_filter_nat A2) B2) B2))) (forall ((B2 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A2) (= (@ (@ tptp.inf_inf_set_nat A2) B2) B2))) (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (= (@ (@ tptp.inf_inf_nat A2) B2) B2))) (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (= (@ (@ tptp.inf_inf_int A2) B2) B2))) (= tptp.inf_inf_assn (lambda ((A3 tptp.assn) (B3 tptp.assn)) (@ (@ tptp.inf_inf_assn B3) A3))) (= tptp.inf_inf_set_nat (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (@ (@ tptp.inf_inf_set_nat B3) A3))) (= tptp.inf_in2572325071724192079at_nat (lambda ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.inf_in2572325071724192079at_nat B3) A3))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat X) Y) (= (@ (@ tptp.inf_in2572325071724192079at_nat X) Y) X))) (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X) Y) (= (@ (@ tptp.inf_inf_assn X) Y) X))) (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat X) Y) (= (@ (@ tptp.inf_inf_filter_nat X) Y) X))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (= (@ (@ tptp.inf_inf_set_nat X) Y) X))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (@ (@ tptp.inf_inf_nat X) Y) X))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (@ (@ tptp.inf_inf_int X) Y) X))) (forall ((Y tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat Y) X) (= (@ (@ tptp.inf_in2572325071724192079at_nat X) Y) Y))) (forall ((Y tptp.assn) (X tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn Y) X) (= (@ (@ tptp.inf_inf_assn X) Y) Y))) (forall ((Y tptp.filter_nat) (X tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat Y) X) (= (@ (@ tptp.inf_inf_filter_nat X) Y) Y))) (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (= (@ (@ tptp.inf_inf_set_nat X) Y) Y))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.inf_inf_nat X) Y) Y))) (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.inf_inf_int X) Y) Y))) (= tptp.inf_inf_assn (lambda ((X2 tptp.assn) (Y5 tptp.assn)) (@ (@ tptp.inf_inf_assn Y5) X2))) (= tptp.inf_inf_set_nat (lambda ((X2 tptp.set_nat) (Y5 tptp.set_nat)) (@ (@ tptp.inf_inf_set_nat Y5) X2))) (= tptp.inf_in2572325071724192079at_nat (lambda ((X2 tptp.set_Pr1261947904930325089at_nat) (Y5 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.inf_in2572325071724192079at_nat Y5) X2))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A2))) (=> (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B2) C)) (not (=> (@ _let_1 B2) (not (@ _let_1 C))))))) (forall ((A2 tptp.assn) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn A2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_assn B2) C)) (not (=> (@ _let_1 B2) (not (@ _let_1 C))))))) (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat) (C tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_le2510731241096832064er_nat A2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_filter_nat B2) C)) (not (=> (@ _let_1 B2) (not (@ _let_1 C))))))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat B2) C)) (not (=> (@ _let_1 B2) (not (@ _let_1 C))))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_nat B2) C)) (not (=> (@ _let_1 B2) (not (@ _let_1 C))))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_int B2) C)) (not (=> (@ _let_1 B2) (not (@ _let_1 C))))))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A2))) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B2) C)))))) (forall ((A2 tptp.assn) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn A2))) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.inf_inf_assn B2) C)))))) (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat) (C tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_le2510731241096832064er_nat A2))) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.inf_inf_filter_nat B2) C)))))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.inf_inf_set_nat B2) C)))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.inf_inf_nat B2) C)))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A2))) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.inf_inf_int B2) C)))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z)))))) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.inf_inf_assn Y) Z)))))) (forall ((X tptp.filter_nat) (Y tptp.filter_nat) (Z tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_le2510731241096832064er_nat X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.inf_inf_filter_nat Y) Z)))))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y) Z)))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z)))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.inf_inf_int Y) Z)))))) (= tptp.ord_le3146513528884898305at_nat (lambda ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= A3 (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)))) (= tptp.ord_less_eq_assn (lambda ((A3 tptp.assn) (B3 tptp.assn)) (= A3 (@ (@ tptp.inf_inf_assn A3) B3)))) (= tptp.ord_le2510731241096832064er_nat (lambda ((A3 tptp.filter_nat) (B3 tptp.filter_nat)) (= A3 (@ (@ tptp.inf_inf_filter_nat A3) B3)))) (= tptp.ord_less_eq_set_nat (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= A3 (@ (@ tptp.inf_inf_set_nat A3) B3)))) (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (= A3 (@ (@ tptp.inf_inf_nat A3) B3)))) (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B3 tptp.int)) (= A3 (@ (@ tptp.inf_inf_int A3) B3)))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2)) A2)) (forall ((A2 tptp.assn) (B2 tptp.assn)) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn A2) B2)) A2)) (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.inf_inf_filter_nat A2) B2)) A2)) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A2) B2)) A2)) (forall ((A2 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A2) B2)) A2)) (forall ((A2 tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A2) B2)) A2)) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2)) B2)) (forall ((A2 tptp.assn) (B2 tptp.assn)) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn A2) B2)) B2)) (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.inf_inf_filter_nat A2) B2)) B2)) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A2) B2)) B2)) (forall ((A2 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A2) B2)) B2)) (forall ((A2 tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A2) B2)) B2)) (= tptp.ord_le3146513528884898305at_nat (lambda ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3) A3))) (= tptp.ord_less_eq_assn (lambda ((A3 tptp.assn) (B3 tptp.assn)) (= (@ (@ tptp.inf_inf_assn A3) B3) A3))) (= tptp.ord_le2510731241096832064er_nat (lambda ((A3 tptp.filter_nat) (B3 tptp.filter_nat)) (= (@ (@ tptp.inf_inf_filter_nat A3) B3) A3))) (= tptp.ord_less_eq_set_nat (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A3) B3) A3))) (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.inf_inf_nat A3) B3) A3))) (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.inf_inf_int A3) B3) A3))) (= tptp.ord_le3146513528884898305at_nat (lambda ((B3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3) B3))) (= tptp.ord_less_eq_assn (lambda ((B3 tptp.assn) (A3 tptp.assn)) (= (@ (@ tptp.inf_inf_assn A3) B3) B3))) (= tptp.ord_le2510731241096832064er_nat (lambda ((B3 tptp.filter_nat) (A3 tptp.filter_nat)) (= (@ (@ tptp.inf_inf_filter_nat A3) B3) B3))) (= tptp.ord_less_eq_set_nat (lambda ((B3 tptp.set_nat) (A3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A3) B3) B3))) (= tptp.ord_less_eq_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (= (@ (@ tptp.inf_inf_nat A3) B3) B3))) (= tptp.ord_less_eq_int (lambda ((B3 tptp.int) (A3 tptp.int)) (= (@ (@ tptp.inf_inf_int A3) B3) B3))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) C) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2)) C))) (forall ((A2 tptp.assn) (C tptp.assn) (B2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A2) C) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn A2) B2)) C))) (forall ((A2 tptp.filter_nat) (C tptp.filter_nat) (B2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat A2) C) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.inf_inf_filter_nat A2) B2)) C))) (forall ((A2 tptp.set_nat) (C tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) C) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A2) B2)) C))) (forall ((A2 tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A2) B2)) C))) (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A2) B2)) C))) (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B2) C) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2)) C))) (forall ((B2 tptp.assn) (C tptp.assn) (A2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn B2) C) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn A2) B2)) C))) (forall ((B2 tptp.filter_nat) (C tptp.filter_nat) (A2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B2) C) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.inf_inf_filter_nat A2) B2)) C))) (forall ((B2 tptp.set_nat) (C tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B2) C) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A2) B2)) C))) (forall ((B2 tptp.nat) (C tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A2) B2)) C))) (forall ((B2 tptp.int) (C tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A2) B2)) C))) (forall ((B2 tptp.assn) (A2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn B2))) (let ((_let_2 (@ tptp.inf_inf_assn A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((B2 tptp.set_nat) (A2 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat B2))) (let ((_let_2 (@ tptp.inf_inf_set_nat A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat B2))) (let ((_let_2 (@ tptp.inf_in2572325071724192079at_nat A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (let ((_let_2 (@ tptp.inf_inf_assn Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (let ((_let_2 (@ tptp.inf_inf_set_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (let ((_let_2 (@ tptp.inf_in2572325071724192079at_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((B2 tptp.set_nat) (C tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B2) C) (@ (@ tptp.ord_less_set_nat (@ (@ tptp.inf_inf_set_nat A2) B2)) C))) (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat B2) C) (@ (@ tptp.ord_le7866589430770878221at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2)) C))) (forall ((B2 tptp.assn) (C tptp.assn) (A2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn B2) C) (@ (@ tptp.ord_less_assn (@ (@ tptp.inf_inf_assn A2) B2)) C))) (forall ((B2 tptp.nat) (C tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.inf_inf_nat A2) B2)) C))) (forall ((B2 tptp.int) (C tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int B2) C) (@ (@ tptp.ord_less_int (@ (@ tptp.inf_inf_int A2) B2)) C))) (forall ((A2 tptp.set_nat) (C tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) C) (@ (@ tptp.ord_less_set_nat (@ (@ tptp.inf_inf_set_nat A2) B2)) C))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat A2) C) (@ (@ tptp.ord_le7866589430770878221at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2)) C))) (forall ((A2 tptp.assn) (C tptp.assn) (B2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn A2) C) (@ (@ tptp.ord_less_assn (@ (@ tptp.inf_inf_assn A2) B2)) C))) (forall ((A2 tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (@ (@ 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(B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_nat B2) C)) (not (=> (@ _let_1 B2) (not (@ _let_1 C))))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_int B2) C)) (not (=> (@ _let_1 B2) (not (@ _let_1 C))))))) (forall ((B2 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B2) A2) (= (@ (@ tptp.inf_inf_set_nat A2) B2) B2))) (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat B2) A2) (= (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2) B2))) (forall ((B2 tptp.assn) (A2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn B2) A2) (= (@ (@ tptp.inf_inf_assn A2) B2) B2))) (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A2) (= (@ (@ tptp.inf_inf_nat A2) B2) B2))) (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A2) (= (@ (@ 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tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat B2) X) (@ (@ tptp.ord_le7866589430770878221at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2)) X))) (forall ((B2 tptp.assn) (X tptp.assn) (A2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn B2) X) (@ (@ tptp.ord_less_assn (@ (@ tptp.inf_inf_assn A2) B2)) X))) (forall ((B2 tptp.nat) (X tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) X) (@ (@ tptp.ord_less_nat (@ (@ tptp.inf_inf_nat A2) B2)) X))) (forall ((B2 tptp.int) (X tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int B2) X) (@ (@ tptp.ord_less_int (@ (@ tptp.inf_inf_int A2) B2)) X))) (forall ((A2 tptp.set_nat) (X tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) X) (@ (@ tptp.ord_less_set_nat (@ (@ tptp.inf_inf_set_nat A2) B2)) X))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat A2) X) (@ (@ tptp.ord_le7866589430770878221at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2)) X))) (forall ((A2 tptp.assn) (X tptp.assn) (B2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn A2) X) (@ (@ tptp.ord_less_assn (@ (@ tptp.inf_inf_assn A2) B2)) X))) (forall ((A2 tptp.nat) (X tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) X) (@ (@ tptp.ord_less_nat (@ (@ tptp.inf_inf_nat A2) B2)) X))) (forall ((A2 tptp.int) (X tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) X) (@ (@ tptp.ord_less_int (@ (@ tptp.inf_inf_int A2) B2)) X))) (forall ((T tptp.code_integer)) (exists ((Z4 tptp.code_integer)) (forall ((X7 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z4) X7) (not (@ (@ tptp.ord_le3102999989581377725nteger X7) T)))))) (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X7 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X7) (not (@ (@ tptp.ord_less_eq_num X7) T)))))) (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X7 tptp.nat)) (=> (@ (@ 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Z4) (not (@ (@ tptp.ord_less_eq_nat T) X7)))))) (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X7 tptp.int)) (=> (@ (@ tptp.ord_less_int X7) Z4) (not (@ (@ tptp.ord_less_eq_int T) X7)))))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger X) Y) (or (@ (@ tptp.ord_le6747313008572928689nteger X) Y) (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (or (@ (@ tptp.ord_less_num X) Y) (= X Y)))) (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X) Y) (or (@ (@ tptp.ord_less_assn X) Y) (= X Y)))) (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat X) Y) (or (@ (@ tptp.ord_less_filter_nat X) Y) (= X Y)))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (or (@ (@ tptp.ord_less_set_nat X) Y) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (or (@ (@ tptp.ord_less_nat 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tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 A2)) C))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (F4 (-> tptp.code_integer tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (@ (@ tptp.ord_less_eq_num (@ F4 B2)) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_num (@ F4 A2)) C))))) (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.code_integer)) (C tptp.code_integer)) (=> (@ (@ tptp.ord_less_assn A2) B2) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ F4 B2)) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 A2)) C))))) (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_assn A2) B2) (=> (@ (@ tptp.ord_less_eq_num (@ F4 B2)) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_num (@ F4 A2)) C))))) (forall ((A2 tptp.num) (B2 tptp.num) (F4 (-> tptp.num tptp.code_integer)) (C tptp.code_integer)) (=> (@ (@ tptp.ord_less_num A2) B2) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ F4 B2)) C) (=> (forall ((X3 tptp.num) (Y2 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 A2)) C))))) (forall ((A2 tptp.num) (B2 tptp.num) (F4 (-> tptp.num tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_num A2) B2) (=> (@ (@ tptp.ord_less_eq_num (@ F4 B2)) C) (=> (forall ((X3 tptp.num) (Y2 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y2) (@ (@ tptp.ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_num (@ F4 A2)) C))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (F4 (-> tptp.nat tptp.code_integer)) (C tptp.code_integer)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ F4 B2)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 A2)) C))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (F4 (-> tptp.nat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_num (@ F4 B2)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_num (@ F4 A2)) C))))) (forall ((A2 tptp.int) (B2 tptp.int) (F4 (-> tptp.int tptp.code_integer)) (C tptp.code_integer)) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ F4 B2)) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 A2)) C))))) (forall ((A2 tptp.int) (B2 tptp.int) (F4 (-> tptp.int tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ (@ tptp.ord_less_eq_num (@ F4 B2)) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y2) (@ (@ tptp.ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_num (@ F4 A2)) C))))) (forall ((A2 tptp.code_integer) (F4 (-> tptp.assn tptp.code_integer)) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_assn B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_le3102999989581377725nteger (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((A2 tptp.num) (F4 (-> tptp.assn tptp.num)) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_num A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_assn B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_less_eq_num (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((A2 tptp.assn) (F4 (-> tptp.assn tptp.assn)) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_assn B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((A2 tptp.nat) (F4 (-> tptp.assn tptp.nat)) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_assn B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((A2 tptp.int) (F4 (-> tptp.assn tptp.int)) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_int A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_assn B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((A2 tptp.code_integer) (F4 (-> tptp.nat tptp.code_integer)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_le3102999989581377725nteger (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((A2 tptp.num) (F4 (-> tptp.nat tptp.num)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_num A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_num (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((A2 tptp.assn) (F4 (-> tptp.nat tptp.assn)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_assn A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((A2 tptp.nat) (F4 (-> tptp.nat tptp.nat)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((A2 tptp.int) (F4 (-> tptp.nat tptp.int)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int A2))) (=> (@ _let_1 (@ F4 B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F4 X3)) (@ F4 Y2)))) (@ _let_1 (@ F4 C))))))) (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.code_integer)) (C tptp.code_integer)) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 B2)) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_le3102999989581377725nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 A2)) C))))) (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (=> (@ (@ tptp.ord_less_num (@ F4 B2)) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_less_eq_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_num (@ F4 A2)) C))))) (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (=> (@ (@ tptp.ord_less_assn (@ F4 B2)) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_assn (@ F4 A2)) C))))) (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (=> (@ (@ tptp.ord_less_nat (@ F4 B2)) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_nat (@ F4 A2)) C))))) (forall ((A2 tptp.assn) (B2 tptp.assn) (F4 (-> tptp.assn tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (=> (@ (@ tptp.ord_less_int (@ F4 B2)) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_int (@ F4 A2)) C))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (F4 (-> tptp.nat tptp.code_integer)) (C tptp.code_integer)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 B2)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_le3102999989581377725nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 A2)) C))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (F4 (-> tptp.nat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_num (@ F4 B2)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_num (@ F4 A2)) C))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (F4 (-> tptp.nat tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_assn (@ F4 B2)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_assn (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_assn (@ F4 A2)) C))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (F4 (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_nat (@ F4 B2)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_nat (@ F4 A2)) C))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (F4 (-> tptp.nat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_int (@ F4 B2)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_int (@ F4 A2)) C))))) (forall ((A2 tptp.code_integer) (F4 (-> tptp.code_integer tptp.code_integer)) (B2 tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) (@ F4 B2)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger A2) (@ F4 C)))))) (forall ((A2 tptp.num) (F4 (-> tptp.code_integer tptp.num)) (B2 tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_less_eq_num A2) (@ F4 B2)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_num A2) (@ F4 C)))))) (forall ((A2 tptp.code_integer) (F4 (-> tptp.assn tptp.code_integer)) (B2 tptp.assn) (C tptp.assn)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) (@ F4 B2)) (=> (@ (@ tptp.ord_less_assn B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger A2) (@ F4 C)))))) (forall ((A2 tptp.num) (F4 (-> tptp.assn tptp.num)) (B2 tptp.assn) (C tptp.assn)) (=> (@ (@ tptp.ord_less_eq_num A2) (@ F4 B2)) (=> (@ (@ tptp.ord_less_assn B2) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_num A2) (@ F4 C)))))) (forall ((A2 tptp.code_integer) (F4 (-> tptp.num tptp.code_integer)) (B2 tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) (@ F4 B2)) (=> (@ (@ tptp.ord_less_num B2) C) (=> (forall ((X3 tptp.num) (Y2 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger A2) (@ F4 C)))))) (forall ((A2 tptp.num) (F4 (-> tptp.num tptp.num)) (B2 tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A2) (@ F4 B2)) (=> (@ (@ tptp.ord_less_num B2) C) (=> (forall ((X3 tptp.num) (Y2 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y2) (@ (@ tptp.ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_num A2) (@ F4 C)))))) (forall ((A2 tptp.code_integer) (F4 (-> tptp.nat tptp.code_integer)) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) (@ F4 B2)) (=> (@ (@ tptp.ord_less_nat B2) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger A2) (@ F4 C)))))) (forall ((A2 tptp.num) (F4 (-> tptp.nat tptp.num)) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A2) (@ F4 B2)) (=> (@ (@ tptp.ord_less_nat B2) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_num A2) (@ F4 C)))))) (forall ((A2 tptp.code_integer) (F4 (-> tptp.int tptp.code_integer)) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) (@ F4 B2)) (=> (@ (@ tptp.ord_less_int B2) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger A2) (@ F4 C)))))) (forall ((A2 tptp.num) (F4 (-> tptp.int tptp.num)) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A2) (@ F4 B2)) (=> (@ (@ tptp.ord_less_int B2) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y2) (@ (@ tptp.ord_less_num (@ F4 X3)) (@ F4 Y2)))) (@ (@ tptp.ord_less_num A2) (@ F4 C)))))) (forall ((X tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_le3102999989581377725nteger Y) Z) (@ _let_1 Z))))) (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_num Y) Z) (@ _let_1 Z))))) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_assn Y) Z) (@ _let_1 Z))))) (forall ((X tptp.filter_nat) (Y tptp.filter_nat) (Z tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_less_filter_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_le2510731241096832064er_nat Y) Z) (@ _let_1 Z))))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_nat Y) Z) (@ _let_1 Z))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z) (@ _let_1 Z))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ _let_1 Z))))) (forall ((X tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger X) Y) (=> (@ (@ tptp.ord_le6747313008572928689nteger Y) Z) (@ (@ tptp.ord_le6747313008572928689nteger X) Z)))) (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (=> (@ (@ tptp.ord_less_num Y) Z) (@ (@ tptp.ord_less_num X) Z)))) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X) Y) (=> (@ (@ tptp.ord_less_assn Y) Z) (@ (@ tptp.ord_less_assn X) Z)))) (forall ((X tptp.filter_nat) (Y tptp.filter_nat) (Z tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat X) Y) (=> (@ (@ tptp.ord_less_filter_nat Y) Z) (@ (@ tptp.ord_less_filter_nat X) Z)))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (=> (@ (@ tptp.ord_less_set_nat Y) Z) (@ (@ tptp.ord_less_set_nat X) Z)))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (=> (@ (@ tptp.ord_less_nat Y) Z) (@ (@ tptp.ord_less_nat X) Z)))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ (@ tptp.ord_less_int X) Z)))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (not (= A2 B2)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B2) (@ (@ tptp.ord_le6747313008572928689nteger A2) B2)))) (forall ((A2 tptp.num) (B2 tptp.num)) (=> (not (= A2 B2)) (=> (@ (@ tptp.ord_less_eq_num A2) B2) (@ (@ tptp.ord_less_num A2) B2)))) (forall ((A2 tptp.assn) (B2 tptp.assn)) (=> (not (= A2 B2)) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (@ (@ tptp.ord_less_assn A2) B2)))) (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat)) (=> (not (= A2 B2)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat A2) B2) (@ (@ tptp.ord_less_filter_nat A2) B2)))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (not (= A2 B2)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (@ (@ tptp.ord_less_set_nat A2) B2)))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (not (= A2 B2)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (@ (@ tptp.ord_less_nat A2) B2)))) (forall ((A2 tptp.int) (B2 tptp.int)) (=> (not (= A2 B2)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (@ (@ tptp.ord_less_int A2) B2)))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B2) (=> (not (= A2 B2)) (@ (@ tptp.ord_le6747313008572928689nteger A2) B2)))) (forall ((A2 tptp.num) (B2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A2) B2) (=> (not (= A2 B2)) (@ (@ tptp.ord_less_num A2) B2)))) (forall ((A2 tptp.assn) (B2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (=> (not (= A2 B2)) (@ (@ tptp.ord_less_assn A2) B2)))) (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat A2) B2) (=> (not (= A2 B2)) (@ (@ tptp.ord_less_filter_nat A2) B2)))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (=> (not (= A2 B2)) (@ (@ tptp.ord_less_set_nat A2) B2)))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (not (= A2 B2)) (@ (@ tptp.ord_less_nat A2) B2)))) (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (not (= A2 B2)) (@ (@ tptp.ord_less_int A2) B2)))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X) Y) (@ (@ tptp.ord_le3102999989581377725nteger X) Y))) (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (@ (@ tptp.ord_less_eq_num X) Y))) (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_assn X) Y) (@ (@ tptp.ord_less_eq_assn X) Y))) (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (=> (@ (@ tptp.ord_less_filter_nat X) Y) (@ (@ tptp.ord_le2510731241096832064er_nat X) Y))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat X) Y) (@ (@ tptp.ord_less_eq_set_nat X) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_eq_nat X) Y))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (@ (@ tptp.ord_less_eq_int X) Y))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (not (@ (@ tptp.ord_le6747313008572928689nteger X) Y)) (@ (@ tptp.ord_le3102999989581377725nteger Y) X))) (forall ((X tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_num X) Y)) (@ (@ tptp.ord_less_eq_num Y) X))) (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))) (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (not (@ (@ tptp.ord_le3102999989581377725nteger X) Y)) (@ (@ tptp.ord_le6747313008572928689nteger Y) X))) (forall ((X tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num X) Y)) (@ (@ tptp.ord_less_num Y) X))) (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X))) (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int X) Y)) (@ (@ tptp.ord_less_int Y) X))) _let_140 _let_139 (= tptp.ord_less_assn (lambda ((X2 tptp.assn) (Y5 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn X2) Y5) (not (= X2 Y5))))) _let_138 (= tptp.ord_less_set_nat (lambda ((X2 tptp.set_nat) (Y5 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat X2) Y5) (not (= X2 Y5))))) (= tptp.ord_less_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X2) Y5) (not (= X2 Y5))))) (= tptp.ord_less_int (lambda ((X2 tptp.int) (Y5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X2) Y5) (not (= X2 Y5))))) (= tptp.ord_le3102999989581377725nteger (lambda ((X2 tptp.code_integer) (Y5 tptp.code_integer)) (or (@ (@ tptp.ord_le6747313008572928689nteger X2) Y5) (= X2 Y5)))) (= tptp.ord_less_eq_num (lambda ((X2 tptp.num) (Y5 tptp.num)) (or (@ (@ tptp.ord_less_num X2) Y5) (= X2 Y5)))) (= tptp.ord_less_eq_assn (lambda ((X2 tptp.assn) (Y5 tptp.assn)) (or (@ (@ tptp.ord_less_assn X2) Y5) (= X2 Y5)))) (= tptp.ord_le2510731241096832064er_nat (lambda ((X2 tptp.filter_nat) (Y5 tptp.filter_nat)) (or (@ (@ tptp.ord_less_filter_nat X2) Y5) (= X2 Y5)))) (= tptp.ord_less_eq_set_nat (lambda ((X2 tptp.set_nat) (Y5 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat X2) Y5) (= X2 Y5)))) (= tptp.ord_less_eq_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (or (@ (@ tptp.ord_less_nat X2) Y5) (= X2 Y5)))) (= tptp.ord_less_eq_int (lambda ((X2 tptp.int) (Y5 tptp.int)) (or (@ (@ tptp.ord_less_int X2) Y5) (= X2 Y5)))) (forall ((B2 tptp.code_integer) (A2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) A2) (@ (@ tptp.ord_le3102999989581377725nteger B2) A2))) (forall ((B2 tptp.num) (A2 tptp.num)) (=> (@ (@ tptp.ord_less_num B2) A2) (@ (@ tptp.ord_less_eq_num B2) A2))) (forall ((B2 tptp.assn) (A2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn B2) A2) (@ (@ tptp.ord_less_eq_assn B2) A2))) (forall ((B2 tptp.filter_nat) (A2 tptp.filter_nat)) (=> (@ (@ tptp.ord_less_filter_nat B2) A2) (@ (@ tptp.ord_le2510731241096832064er_nat B2) A2))) (forall ((B2 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B2) A2) (@ (@ tptp.ord_less_eq_set_nat B2) A2))) (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A2) (@ (@ tptp.ord_less_eq_nat B2) A2))) (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A2) (@ (@ tptp.ord_less_eq_int B2) A2))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (@ (@ tptp.ord_le3102999989581377725nteger A2) B2))) (forall ((A2 tptp.num) (B2 tptp.num)) (=> (@ (@ tptp.ord_less_num A2) B2) (@ (@ tptp.ord_less_eq_num A2) B2))) (forall ((A2 tptp.assn) (B2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn A2) B2) (@ (@ tptp.ord_less_eq_assn A2) B2))) (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat)) (=> (@ (@ tptp.ord_less_filter_nat A2) B2) (@ (@ tptp.ord_le2510731241096832064er_nat A2) B2))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) B2) (@ (@ tptp.ord_less_eq_set_nat A2) B2))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (@ (@ tptp.ord_less_eq_nat A2) B2))) (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (@ (@ tptp.ord_less_eq_int A2) B2))) (= tptp.ord_le6747313008572928689nteger (lambda ((B3 tptp.code_integer) (A3 tptp.code_integer)) (and (@ (@ tptp.ord_le3102999989581377725nteger B3) A3) (not (@ (@ tptp.ord_le3102999989581377725nteger A3) B3))))) (= tptp.ord_less_num (lambda ((B3 tptp.num) (A3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B3) A3) (not (@ (@ tptp.ord_less_eq_num A3) B3))))) (= tptp.ord_less_assn (lambda ((B3 tptp.assn) (A3 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn B3) A3) (not (@ (@ tptp.ord_less_eq_assn A3) B3))))) (= tptp.ord_less_filter_nat (lambda ((B3 tptp.filter_nat) (A3 tptp.filter_nat)) (and (@ (@ tptp.ord_le2510731241096832064er_nat B3) A3) (not (@ (@ tptp.ord_le2510731241096832064er_nat A3) B3))))) (= tptp.ord_less_set_nat (lambda ((B3 tptp.set_nat) (A3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B3) A3) (not (@ (@ tptp.ord_less_eq_set_nat A3) B3))))) (= tptp.ord_less_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B3) A3) (not (@ (@ tptp.ord_less_eq_nat A3) B3))))) (= tptp.ord_less_int (lambda ((B3 tptp.int) (A3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B3) A3) (not (@ (@ tptp.ord_less_eq_int A3) B3))))) (forall ((B2 tptp.code_integer) (A2 tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) A2) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) B2) (@ (@ tptp.ord_le6747313008572928689nteger C) A2)))) (forall ((B2 tptp.num) (A2 tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_num B2) A2) (=> (@ (@ tptp.ord_less_eq_num C) B2) (@ (@ tptp.ord_less_num C) A2)))) (forall ((B2 tptp.assn) (A2 tptp.assn) (C tptp.assn)) (=> (@ (@ tptp.ord_less_assn B2) A2) (=> (@ (@ tptp.ord_less_eq_assn C) B2) (@ (@ tptp.ord_less_assn C) A2)))) (forall ((B2 tptp.filter_nat) (A2 tptp.filter_nat) (C tptp.filter_nat)) (=> (@ (@ tptp.ord_less_filter_nat B2) A2) (=> (@ (@ tptp.ord_le2510731241096832064er_nat C) B2) (@ (@ tptp.ord_less_filter_nat C) A2)))) (forall ((B2 tptp.set_nat) (A2 tptp.set_nat) (C tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B2) A2) (=> (@ (@ tptp.ord_less_eq_set_nat C) B2) (@ (@ tptp.ord_less_set_nat C) A2)))) (forall ((B2 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A2) (=> (@ (@ tptp.ord_less_eq_nat C) B2) (@ (@ tptp.ord_less_nat C) A2)))) (forall ((B2 tptp.int) (A2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A2) (=> (@ (@ tptp.ord_less_eq_int C) B2) (@ (@ tptp.ord_less_int C) A2)))) (forall ((B2 tptp.code_integer) (A2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger C))) (=> (@ (@ tptp.ord_le3102999989581377725nteger B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))) (forall ((B2 tptp.num) (A2 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ (@ tptp.ord_less_eq_num B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))) (forall ((B2 tptp.assn) (A2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn C))) (=> (@ (@ tptp.ord_less_eq_assn B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))) (forall ((B2 tptp.filter_nat) (A2 tptp.filter_nat) (C tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_less_filter_nat C))) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))) (forall ((B2 tptp.set_nat) (A2 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat C))) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))) (forall ((B2 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))) (forall ((B2 tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))) (= tptp.ord_le6747313008572928689nteger (lambda ((B3 tptp.code_integer) (A3 tptp.code_integer)) (and (@ (@ tptp.ord_le3102999989581377725nteger B3) A3) (not (= A3 B3))))) (= tptp.ord_less_num (lambda ((B3 tptp.num) (A3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B3) A3) (not (= A3 B3))))) (= tptp.ord_less_assn (lambda ((B3 tptp.assn) (A3 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn B3) A3) (not (= A3 B3))))) (= tptp.ord_less_filter_nat (lambda ((B3 tptp.filter_nat) (A3 tptp.filter_nat)) (and (@ (@ tptp.ord_le2510731241096832064er_nat B3) A3) (not (= A3 B3))))) (= tptp.ord_less_set_nat (lambda ((B3 tptp.set_nat) (A3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B3) A3) (not (= A3 B3))))) (= tptp.ord_less_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B3) A3) (not (= A3 B3))))) (= tptp.ord_less_int (lambda ((B3 tptp.int) (A3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B3) A3) (not (= A3 B3))))) (= tptp.ord_le3102999989581377725nteger (lambda ((B3 tptp.code_integer) (A3 tptp.code_integer)) (or (@ (@ tptp.ord_le6747313008572928689nteger B3) A3) (= A3 B3)))) (= tptp.ord_less_eq_num (lambda ((B3 tptp.num) (A3 tptp.num)) (or (@ (@ tptp.ord_less_num B3) A3) (= A3 B3)))) (= tptp.ord_less_eq_assn (lambda ((B3 tptp.assn) (A3 tptp.assn)) (or (@ (@ tptp.ord_less_assn B3) A3) (= A3 B3)))) (= tptp.ord_le2510731241096832064er_nat (lambda ((B3 tptp.filter_nat) (A3 tptp.filter_nat)) (or (@ (@ tptp.ord_less_filter_nat B3) A3) (= A3 B3)))) (= tptp.ord_less_eq_set_nat (lambda ((B3 tptp.set_nat) (A3 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat B3) A3) (= A3 B3)))) (= tptp.ord_less_eq_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (or (@ (@ tptp.ord_less_nat B3) A3) (= A3 B3)))) (= tptp.ord_less_eq_int (lambda ((B3 tptp.int) (A3 tptp.int)) (or (@ (@ tptp.ord_less_int B3) A3) (= A3 B3)))) (= tptp.ord_le6747313008572928689nteger (lambda ((A3 tptp.code_integer) (B3 tptp.code_integer)) (and (@ (@ tptp.ord_le3102999989581377725nteger A3) B3) (not (@ (@ tptp.ord_le3102999989581377725nteger B3) A3))))) (= tptp.ord_less_num (lambda ((A3 tptp.num) (B3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A3) B3) (not (@ (@ tptp.ord_less_eq_num B3) A3))))) (= tptp.ord_less_assn (lambda ((A3 tptp.assn) (B3 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn A3) B3) (not (@ (@ tptp.ord_less_eq_assn B3) A3))))) (= tptp.ord_less_filter_nat (lambda ((A3 tptp.filter_nat) (B3 tptp.filter_nat)) (and (@ (@ tptp.ord_le2510731241096832064er_nat A3) B3) (not (@ (@ tptp.ord_le2510731241096832064er_nat B3) A3))))) (= tptp.ord_less_set_nat (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A3) B3) (not (@ (@ tptp.ord_less_eq_set_nat B3) A3))))) (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B3) (not (@ (@ tptp.ord_less_eq_nat B3) A3))))) (= tptp.ord_less_int (lambda ((A3 tptp.int) (B3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A3) B3) (not (@ (@ tptp.ord_less_eq_int B3) A3))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_le3102999989581377725nteger B2) C) (@ _let_1 C))))) (forall ((A2 tptp.num) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_num B2) C) (@ _let_1 C))))) (forall ((A2 tptp.assn) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_assn B2) C) (@ _let_1 C))))) (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat) (C tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_less_filter_nat A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B2) C) (@ _let_1 C))))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) C) (@ _let_1 C))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (@ _let_1 C))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_int B2) C) (@ _let_1 C))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) C) (@ (@ tptp.ord_le6747313008572928689nteger A2) C)))) (forall ((A2 tptp.num) (B2 tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A2) B2) (=> (@ (@ tptp.ord_less_num B2) C) (@ (@ tptp.ord_less_num A2) C)))) (forall ((A2 tptp.assn) (B2 tptp.assn) (C tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (=> (@ (@ tptp.ord_less_assn B2) C) (@ (@ tptp.ord_less_assn A2) C)))) (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat) (C tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat A2) B2) (=> (@ (@ tptp.ord_less_filter_nat B2) C) (@ (@ tptp.ord_less_filter_nat A2) C)))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (C tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (=> (@ (@ tptp.ord_less_set_nat B2) C) (@ (@ tptp.ord_less_set_nat A2) C)))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_nat B2) C) (@ (@ tptp.ord_less_nat A2) C)))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_int B2) C) (@ (@ tptp.ord_less_int A2) C)))) (= tptp.ord_le6747313008572928689nteger (lambda ((A3 tptp.code_integer) (B3 tptp.code_integer)) (and (@ (@ tptp.ord_le3102999989581377725nteger A3) B3) (not (= A3 B3))))) (= tptp.ord_less_num (lambda ((A3 tptp.num) (B3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A3) B3) (not (= A3 B3))))) (= tptp.ord_less_assn (lambda ((A3 tptp.assn) (B3 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn A3) B3) (not (= A3 B3))))) (= tptp.ord_less_filter_nat (lambda ((A3 tptp.filter_nat) (B3 tptp.filter_nat)) (and (@ (@ tptp.ord_le2510731241096832064er_nat A3) B3) (not (= A3 B3))))) (= tptp.ord_less_set_nat (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A3) B3) (not (= A3 B3))))) (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B3) (not (= A3 B3))))) (= tptp.ord_less_int (lambda ((A3 tptp.int) (B3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A3) B3) (not (= A3 B3))))) (= tptp.ord_le3102999989581377725nteger (lambda ((A3 tptp.code_integer) (B3 tptp.code_integer)) (or (@ (@ tptp.ord_le6747313008572928689nteger A3) B3) (= A3 B3)))) (= tptp.ord_less_eq_num (lambda ((A3 tptp.num) (B3 tptp.num)) (or (@ (@ tptp.ord_less_num A3) B3) (= A3 B3)))) (= tptp.ord_less_eq_assn (lambda ((A3 tptp.assn) (B3 tptp.assn)) (or (@ (@ tptp.ord_less_assn A3) B3) (= A3 B3)))) (= tptp.ord_le2510731241096832064er_nat (lambda ((A3 tptp.filter_nat) (B3 tptp.filter_nat)) (or (@ (@ tptp.ord_less_filter_nat A3) B3) (= A3 B3)))) (= tptp.ord_less_eq_set_nat (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat A3) B3) (= A3 B3)))) (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (or (@ (@ tptp.ord_less_nat A3) B3) (= A3 B3)))) (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B3 tptp.int)) (or (@ (@ tptp.ord_less_int A3) B3) (= A3 B3)))) (forall ((Y tptp.code_integer) (X tptp.code_integer)) (=> (not (@ (@ tptp.ord_le3102999989581377725nteger Y) X)) (@ (@ tptp.ord_le6747313008572928689nteger X) Y))) (forall ((Y tptp.num) (X tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num Y) X)) (@ (@ tptp.ord_less_num X) Y))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat Y) X)) (@ (@ tptp.ord_less_nat X) Y))) (forall ((Y tptp.int) (X tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int Y) X)) (@ (@ tptp.ord_less_int X) Y))) (= tptp.ord_le6747313008572928689nteger (lambda ((X2 tptp.code_integer) (Y5 tptp.code_integer)) (and (@ (@ tptp.ord_le3102999989581377725nteger X2) Y5) (not (@ (@ tptp.ord_le3102999989581377725nteger Y5) X2))))) (= tptp.ord_less_num (lambda ((X2 tptp.num) (Y5 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X2) Y5) (not (@ (@ tptp.ord_less_eq_num Y5) X2))))) (= tptp.ord_less_assn (lambda ((X2 tptp.assn) (Y5 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn X2) Y5) (not (@ (@ tptp.ord_less_eq_assn Y5) X2))))) (= tptp.ord_less_filter_nat (lambda ((X2 tptp.filter_nat) (Y5 tptp.filter_nat)) (and (@ (@ tptp.ord_le2510731241096832064er_nat X2) Y5) (not (@ (@ tptp.ord_le2510731241096832064er_nat Y5) X2))))) (= tptp.ord_less_set_nat (lambda ((X2 tptp.set_nat) (Y5 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat X2) Y5) (not (@ (@ tptp.ord_less_eq_set_nat Y5) X2))))) (= tptp.ord_less_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X2) Y5) (not (@ (@ tptp.ord_less_eq_nat Y5) X2))))) (= tptp.ord_less_int (lambda ((X2 tptp.int) (Y5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X2) Y5) (not (@ (@ tptp.ord_less_eq_int Y5) X2))))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger X) Y) (= (not (@ (@ tptp.ord_le6747313008572928689nteger X) Y)) (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (= (not (@ (@ tptp.ord_less_num X) Y)) (= X Y)))) (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X) Y) (= (not (@ (@ tptp.ord_less_assn X) Y)) (= X Y)))) (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat X) Y) (= (not (@ (@ tptp.ord_less_filter_nat X) Y)) (= X Y)))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (= (not (@ (@ tptp.ord_less_set_nat X) Y)) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (not (@ (@ tptp.ord_less_nat X) Y)) (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (not (@ (@ tptp.ord_less_int X) Y)) (= X Y)))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (not (@ (@ tptp.ord_le6747313008572928689nteger X) Y)) (= (@ (@ tptp.ord_le3102999989581377725nteger X) Y) (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (= (@ (@ tptp.ord_less_eq_num X) Y) (= X Y)))) (forall ((X tptp.assn) (Y tptp.assn)) (=> (not (@ (@ tptp.ord_less_assn X) Y)) (= (@ (@ tptp.ord_less_eq_assn X) Y) (= X Y)))) (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (=> (not (@ (@ tptp.ord_less_filter_nat X) Y)) (= (@ (@ tptp.ord_le2510731241096832064er_nat X) Y) (= X Y)))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (not (@ (@ tptp.ord_less_set_nat X) Y)) (= (@ (@ tptp.ord_less_eq_set_nat X) Y) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (= (@ (@ tptp.ord_less_eq_nat X) Y) (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (= (@ (@ tptp.ord_less_eq_int X) Y) (= X Y)))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (not (@ (@ tptp.ord_le6747313008572928689nteger A2) B2)) (or (not (@ (@ tptp.ord_le3102999989581377725nteger A2) B2)) (= A2 B2)))) (forall ((A2 tptp.num) (B2 tptp.num)) (= (not (@ (@ tptp.ord_less_num A2) B2)) (or (not (@ (@ tptp.ord_less_eq_num A2) B2)) (= A2 B2)))) (forall ((A2 tptp.assn) (B2 tptp.assn)) (= (not (@ (@ tptp.ord_less_assn A2) B2)) (or (not (@ (@ tptp.ord_less_eq_assn A2) B2)) (= A2 B2)))) (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat)) (= (not (@ (@ tptp.ord_less_filter_nat A2) B2)) (or (not (@ (@ tptp.ord_le2510731241096832064er_nat A2) B2)) (= A2 B2)))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (= (not (@ (@ tptp.ord_less_set_nat A2) B2)) (or (not (@ (@ tptp.ord_less_eq_set_nat A2) B2)) (= A2 B2)))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat A2) B2)) (or (not (@ (@ tptp.ord_less_eq_nat A2) B2)) (= A2 B2)))) (forall ((A2 tptp.int) (B2 tptp.int)) (= (not (@ (@ tptp.ord_less_int A2) B2)) (or (not (@ (@ tptp.ord_less_eq_int A2) B2)) (= A2 B2)))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (not (@ (@ tptp.ord_le6747313008572928689nteger X) Y)) (@ (@ tptp.ord_le3102999989581377725nteger Y) X))) (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (@ (@ tptp.ord_less_eq_num Y) X))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))) (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))) (forall ((Y tptp.code_integer) (X tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger Y) X) (not (@ (@ tptp.ord_le6747313008572928689nteger X) Y)))) (forall ((Y tptp.num) (X tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X) (not (@ (@ tptp.ord_less_num X) Y)))) (forall ((Y tptp.assn) (X tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn Y) X) (not (@ (@ tptp.ord_less_assn X) Y)))) (forall ((Y tptp.filter_nat) (X tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat Y) X) (not (@ (@ tptp.ord_less_filter_nat X) Y)))) (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (not (@ (@ tptp.ord_less_set_nat X) Y)))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (not (@ (@ tptp.ord_less_nat X) Y)))) (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (not (@ (@ tptp.ord_less_int X) Y)))) (forall ((A2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A2) tptp.bot_bo228742789529271731at_nat) (= A2 tptp.bot_bo228742789529271731at_nat))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) tptp.bot_bo2099793752762293965at_nat) (= A2 tptp.bot_bo2099793752762293965at_nat))) (forall ((A2 tptp.set_o)) (=> (@ (@ tptp.ord_less_eq_set_o A2) tptp.bot_bot_set_o) (= A2 tptp.bot_bot_set_o))) (forall ((A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) tptp.bot_bot_set_int) (= A2 tptp.bot_bot_set_int))) (forall ((A2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A2) tptp.bot_bot_assn) (= A2 tptp.bot_bot_assn))) (forall ((A2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat A2) tptp.bot_bot_filter_nat) (= A2 tptp.bot_bot_filter_nat))) (forall ((A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) tptp.bot_bot_set_nat) (= A2 tptp.bot_bot_set_nat))) (forall ((A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.bot_bot_nat) (= A2 tptp.bot_bot_nat))) (forall ((A2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat A2) tptp.bot_bo228742789529271731at_nat) (= A2 tptp.bot_bo228742789529271731at_nat))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat A2) tptp.bot_bo2099793752762293965at_nat) (= A2 tptp.bot_bo2099793752762293965at_nat))) (forall ((A2 tptp.set_o)) (= (@ (@ tptp.ord_less_eq_set_o A2) tptp.bot_bot_set_o) (= A2 tptp.bot_bot_set_o))) (forall ((A2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A2) tptp.bot_bot_set_int) (= A2 tptp.bot_bot_set_int))) (forall ((A2 tptp.assn)) (= (@ (@ tptp.ord_less_eq_assn A2) tptp.bot_bot_assn) (= A2 tptp.bot_bot_assn))) (forall ((A2 tptp.filter_nat)) (= (@ (@ tptp.ord_le2510731241096832064er_nat A2) tptp.bot_bot_filter_nat) (= A2 tptp.bot_bot_filter_nat))) (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A2) tptp.bot_bot_set_nat) (= A2 tptp.bot_bot_set_nat))) (forall ((A2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A2) tptp.bot_bot_nat) (= A2 tptp.bot_bot_nat))) (forall ((A2 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat tptp.bot_bo228742789529271731at_nat) A2)) (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat tptp.bot_bo2099793752762293965at_nat) A2)) (forall ((A2 tptp.set_o)) (@ (@ tptp.ord_less_eq_set_o tptp.bot_bot_set_o) A2)) (forall ((A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A2)) (forall ((A2 tptp.assn)) (@ (@ tptp.ord_less_eq_assn tptp.bot_bot_assn) A2)) (forall ((A2 tptp.filter_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat tptp.bot_bot_filter_nat) A2)) (forall ((A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A2)) (forall ((A2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.bot_bot_nat) A2)) (forall ((R2 tptp.set_Pr4329608150637261639at_nat) (S3 tptp.set_Pr4329608150637261639at_nat)) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat) (Y2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X3) Y2)))) (=> (@ _let_1 R2) (@ _let_1 S3)))) (@ (@ tptp.ord_le1268244103169919719at_nat R2) S3))) (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (S3 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) Y2)))) (=> (@ _let_1 R2) (@ _let_1 S3)))) (@ (@ tptp.ord_le3146513528884898305at_nat R2) S3))) (forall ((R2 tptp.set_Pr1281608226676607948nteger) (S3 tptp.set_Pr1281608226676607948nteger)) (=> (forall ((X3 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (Y2 tptp.produc8923325533196201883nteger)) (let ((_let_1 (@ tptp.member4164122664394876845nteger (@ (@ tptp.produc8603105652947943368nteger X3) Y2)))) (=> (@ _let_1 R2) (@ _let_1 S3)))) (@ (@ tptp.ord_le653643898420964396nteger R2) S3))) (forall ((R2 tptp.set_Pr3286484037609594932et_nat) (S3 tptp.set_Pr3286484037609594932et_nat)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 tptp.produc3658429121746597890et_nat)) (let ((_let_1 (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat X3) Y2)))) (=> (@ _let_1 R2) (@ _let_1 S3)))) (@ (@ tptp.ord_le5966269811547037844et_nat R2) S3))) (forall ((R2 tptp.set_Pr8536935166611901872et_nat) (S3 tptp.set_Pr8536935166611901872et_nat)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 tptp.produc3925858234332021118et_nat)) (let ((_let_1 (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat X3) Y2)))) (=> (@ _let_1 R2) (@ _let_1 S3)))) (@ (@ tptp.ord_le4763372923235995152et_nat R2) S3))) (forall ((R2 tptp.set_Pr9222295170931077689nt_int) (S3 tptp.set_Pr9222295170931077689nt_int)) (=> (forall ((X3 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y2 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.member7618704894036264090nt_int (@ (@ tptp.produc5700946648718959541nt_int X3) Y2)))) (=> (@ _let_1 R2) (@ _let_1 S3)))) (@ (@ tptp.ord_le8725513860283290265nt_int R2) S3))) (forall ((R2 tptp.set_Pr1872883991513573699nt_int) (S3 tptp.set_Pr1872883991513573699nt_int)) (=> (forall ((X3 (-> tptp.int tptp.option6357759511663192854e_term)) (Y2 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.member7034335876925520548nt_int (@ (@ tptp.produc4305682042979456191nt_int X3) Y2)))) (=> (@ _let_1 R2) (@ _let_1 S3)))) (@ (@ tptp.ord_le135402666524580259nt_int R2) S3))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A2) B2) (@ (@ tptp.minus_minus_rat C) D2)) (= (@ (@ tptp.ord_less_eq_rat A2) B2) (@ (@ tptp.ord_less_eq_rat C) D2)))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int) (D2 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A2) B2) (@ (@ tptp.minus_minus_int C) D2)) (= (@ (@ tptp.ord_less_eq_int A2) B2) (@ (@ tptp.ord_less_eq_int C) D2)))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A2) C)) (@ (@ tptp.minus_minus_rat B2) C)))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A2) C)) (@ (@ tptp.minus_minus_int B2) C)))) (forall ((B2 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B2) A2) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2))))) (forall ((B2 tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int C))) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2))))) (forall ((A2 tptp.rat) (B2 tptp.rat) (D2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_eq_rat D2) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A2) C)) (@ (@ tptp.minus_minus_rat B2) D2))))) (forall ((A2 tptp.int) (B2 tptp.int) (D2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_eq_int D2) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A2) C)) (@ (@ tptp.minus_minus_int B2) D2))))) (forall ((P tptp.assn) (Q tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn (@ (@ tptp.inf_inf_assn P) Q)) H2) (and (@ (@ tptp.rep_assn P) H2) (@ (@ tptp.rep_assn Q) H2)))) (forall ((A tptp.assn) (B tptp.assn) (C2 tptp.assn)) (let ((_let_1 (@ tptp.entails A))) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.inf_inf_assn B) C2)))))) (forall ((A tptp.assn) (C2 tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.entails A) C2) (@ (@ tptp.entails (@ (@ tptp.inf_inf_assn A) B)) C2))) (forall ((B tptp.assn) (C2 tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.entails B) C2) (@ (@ tptp.entails (@ (@ tptp.inf_inf_assn A) B)) C2))) (forall ((A tptp.set_int) (B tptp.set_int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert_int2 B2) B))))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (B2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat B2) B))))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (B2 tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.ord_le1268244103169919719at_nat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert9069300056098147895at_nat B2) B))))) (forall ((A tptp.set_o) (B tptp.set_o) (B2 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_set_o A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert_o2 B2) B))))) (forall ((A tptp.set_nat) (B tptp.set_nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert_nat2 B2) B))))) (forall ((B tptp.set_int) (A2 tptp.int)) (@ (@ tptp.ord_less_eq_set_int B) (@ (@ tptp.insert_int2 A2) B))) (forall ((B tptp.set_Pr1261947904930325089at_nat) (A2 tptp.product_prod_nat_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat B) (@ (@ tptp.insert8211810215607154385at_nat A2) B))) (forall ((B tptp.set_Pr4329608150637261639at_nat) (A2 tptp.produc3843707927480180839at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat B) (@ (@ tptp.insert9069300056098147895at_nat A2) B))) (forall ((B tptp.set_o) (A2 Bool)) (@ (@ tptp.ord_less_eq_set_o B) (@ (@ tptp.insert_o2 A2) B))) (forall ((B tptp.set_nat) (A2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat B) (@ (@ tptp.insert_nat2 A2) B))) (forall ((X Bool) (A tptp.set_o) (B tptp.set_o)) (let ((_let_1 (@ tptp.ord_less_eq_set_o A))) (=> (not (@ (@ tptp.member_o X) A)) (= (@ _let_1 (@ (@ tptp.insert_o2 X) B)) (@ _let_1 B))))) (forall ((X tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le1268244103169919719at_nat A))) (=> (not (@ (@ tptp.member8757157785044589968at_nat X) A)) (= (@ _let_1 (@ (@ tptp.insert9069300056098147895at_nat X) B)) (@ _let_1 B))))) (forall ((X tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A))) (=> (not (@ (@ tptp.member8440522571783428010at_nat X) A)) (= (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat X) B)) (@ _let_1 B))))) (forall ((X tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A))) (=> (not (@ (@ tptp.member_int X) A)) (= (@ _let_1 (@ (@ tptp.insert_int2 X) B)) (@ _let_1 B))))) (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.ord_le2965882846123202637_nat_o A))) (=> (not (@ (@ tptp.member6576561426505652726_nat_o X) A)) (= (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o X) B)) (@ _let_1 B))))) (forall ((X tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (=> (not (@ (@ tptp.member_nat X) A)) (= (@ _let_1 (@ (@ tptp.insert_nat2 X) B)) (@ _let_1 B))))) (forall ((C2 tptp.set_int) (D tptp.set_int) (A2 tptp.int)) (let ((_let_1 (@ tptp.insert_int2 A2))) (=> (@ (@ tptp.ord_less_eq_set_int C2) D) (@ (@ tptp.ord_less_eq_set_int (@ _let_1 C2)) (@ _let_1 D))))) (forall ((C2 tptp.set_Pr1261947904930325089at_nat) (D tptp.set_Pr1261947904930325089at_nat) (A2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A2))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat C2) D) (@ (@ tptp.ord_le3146513528884898305at_nat (@ _let_1 C2)) (@ _let_1 D))))) (forall ((C2 tptp.set_Pr4329608150637261639at_nat) (D tptp.set_Pr4329608150637261639at_nat) (A2 tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.insert9069300056098147895at_nat A2))) (=> (@ (@ tptp.ord_le1268244103169919719at_nat C2) D) (@ (@ tptp.ord_le1268244103169919719at_nat (@ _let_1 C2)) (@ _let_1 D))))) (forall ((C2 tptp.set_o) (D tptp.set_o) (A2 Bool)) (let ((_let_1 (@ tptp.insert_o2 A2))) (=> (@ (@ tptp.ord_less_eq_set_o C2) D) (@ (@ tptp.ord_less_eq_set_o (@ _let_1 C2)) (@ _let_1 D))))) (forall ((C2 tptp.set_nat) (D tptp.set_nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.insert_nat2 A2))) (=> (@ (@ tptp.ord_less_eq_set_nat C2) D) (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 C2)) (@ _let_1 D))))) (forall ((Xs tptp.list_P5464809261938338413at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat (@ tptp.set_Pr3765526544606949372at_nat Xs)) B) (forall ((X2 tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat X2))) (=> (@ _let_1 (@ tptp.set_Pr3765526544606949372at_nat Xs)) (@ _let_1 B)))))) (forall ((Xs tptp.list_P6011104703257516679at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs)) B) (forall ((X2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X2))) (=> (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat Xs)) (@ _let_1 B)))))) (forall ((Xs tptp.list_P7985473006766602707_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.ord_le2965882846123202637_nat_o (@ tptp.set_Pr400311997697478754_nat_o Xs)) B) (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o X2))) (=> (@ _let_1 (@ tptp.set_Pr400311997697478754_nat_o Xs)) (@ _let_1 B)))))) (forall ((Xs tptp.list_int) (B tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) B) (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.member_int X2))) (=> (@ _let_1 (@ tptp.set_int2 Xs)) (@ _let_1 B)))))) (forall ((Xs tptp.list_P8527749157015355191n_assn) (B tptp.set_Pr5949110396991348497n_assn)) (= (@ (@ tptp.ord_le171416862856029873n_assn (@ tptp.set_Pr1139785259514867910n_assn Xs)) B) (forall ((X2 tptp.produc6575502325842934193n_assn)) (let ((_let_1 (@ tptp.member7957490590177025114n_assn X2))) (=> (@ _let_1 (@ tptp.set_Pr1139785259514867910n_assn Xs)) (@ _let_1 B)))))) (forall ((Xs tptp.list_nat) (B tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) B) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X2))) (=> (@ _let_1 (@ tptp.set_nat2 Xs)) (@ _let_1 B)))))) (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (@ (@ tptp.ord_less_eq_set_nat B) C2) (= (@ (@ tptp.minus_minus_set_nat B) (@ (@ tptp.minus_minus_set_nat C2) A)) A)))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A) B)) A)) (forall ((A tptp.set_nat) (C2 tptp.set_nat) (D tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) C2) (=> (@ (@ tptp.ord_less_eq_set_nat D) B) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A) B)) (@ (@ tptp.minus_minus_set_nat C2) D))))) (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B7 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat A5) B7) (= A5 B7)))) (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (@ (@ tptp.ord_less_set_nat B) C2) (@ (@ tptp.ord_less_set_nat A) C2)))) (= tptp.ord_less_set_nat (lambda ((A5 tptp.set_nat) (B7 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A5) B7) (not (@ (@ tptp.ord_less_eq_set_nat B7) A5))))) (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_nat B) C2) (@ _let_1 C2))))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A) B) (@ (@ tptp.ord_less_eq_set_nat A) B))) (= tptp.ord_less_set_nat (lambda ((A5 tptp.set_nat) (B7 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A5) B7) (not (= A5 B7))))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A) B) (not (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (@ (@ tptp.ord_less_eq_set_nat B) A))))) (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn tptp.bot_bot_assn) X) tptp.bot_bot_assn)) (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn X) tptp.bot_bot_assn) tptp.bot_bot_assn)) (forall ((P (-> tptp.produc3843707927480180839at_nat tptp.produc3843707927480180839at_nat Bool))) (@ (@ tptp.pairwi3222497012029234898at_nat P) tptp.bot_bo228742789529271731at_nat)) (forall ((P (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool))) (@ (@ tptp.pairwi6357175311820755948at_nat P) tptp.bot_bo2099793752762293965at_nat)) (forall ((P (-> Bool Bool Bool))) (@ (@ tptp.pairwise_o P) tptp.bot_bot_set_o)) (forall ((P (-> tptp.nat tptp.nat Bool))) (@ (@ tptp.pairwise_nat P) tptp.bot_bot_set_nat)) (forall ((P (-> tptp.int tptp.int Bool))) (@ (@ tptp.pairwise_int P) tptp.bot_bot_set_int)) (forall ((R2 (-> Bool Bool Bool)) (X Bool) (S3 tptp.set_o)) (let ((_let_1 (@ tptp.pairwise_o R2))) (= (@ _let_1 (@ (@ tptp.insert_o2 X) S3)) (and (forall ((Y5 Bool)) (=> (and (@ (@ tptp.member_o Y5) S3) (not (= Y5 X))) (and (@ (@ R2 X) Y5) (@ (@ R2 Y5) X)))) (@ _let_1 S3))))) (forall ((R2 (-> tptp.produc3843707927480180839at_nat tptp.produc3843707927480180839at_nat Bool)) (X tptp.produc3843707927480180839at_nat) (S3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.pairwi3222497012029234898at_nat R2))) (= (@ _let_1 (@ (@ tptp.insert9069300056098147895at_nat X) S3)) (and (forall ((Y5 tptp.produc3843707927480180839at_nat)) (=> (and (@ (@ tptp.member8757157785044589968at_nat Y5) S3) (not (= Y5 X))) (and (@ (@ R2 X) Y5) (@ (@ R2 Y5) X)))) (@ _let_1 S3))))) (forall ((R2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (X tptp.product_prod_nat_nat) (S3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.pairwi6357175311820755948at_nat R2))) (= (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat X) S3)) (and (forall ((Y5 tptp.product_prod_nat_nat)) (=> (and (@ (@ tptp.member8440522571783428010at_nat Y5) S3) (not (= Y5 X))) (and (@ (@ R2 X) Y5) (@ (@ R2 Y5) X)))) (@ _let_1 S3))))) (forall ((R2 (-> tptp.nat tptp.nat Bool)) (X tptp.nat) (S3 tptp.set_nat)) (let ((_let_1 (@ tptp.pairwise_nat R2))) (= (@ _let_1 (@ (@ tptp.insert_nat2 X) S3)) (and (forall ((Y5 tptp.nat)) (=> (and (@ (@ tptp.member_nat Y5) S3) (not (= Y5 X))) (and (@ (@ R2 X) Y5) (@ (@ R2 Y5) X)))) (@ _let_1 S3))))) (forall ((R2 (-> tptp.int tptp.int Bool)) (X tptp.int) (S3 tptp.set_int)) (let ((_let_1 (@ tptp.pairwise_int R2))) (= (@ _let_1 (@ (@ tptp.insert_int2 X) S3)) (and (forall ((Y5 tptp.int)) (=> (and (@ (@ tptp.member_int Y5) S3) (not (= Y5 X))) (and (@ (@ R2 X) Y5) (@ (@ R2 Y5) X)))) (@ _let_1 S3))))) (forall ((R2 (-> (-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) Bool)) (X (-> tptp.produc3658429121746597890et_nat Bool)) (S3 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.pairwi2432143822833250616_nat_o R2))) (= (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o X) S3)) (and (forall ((Y5 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (and (@ (@ tptp.member6576561426505652726_nat_o Y5) S3) (not (= Y5 X))) (and (@ (@ R2 X) Y5) (@ (@ R2 Y5) X)))) (@ _let_1 S3))))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (X tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ (@ tptp.insert9069300056098147895at_nat X) tptp.bot_bo228742789529271731at_nat))) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A) _let_1) (or (= A tptp.bot_bo228742789529271731at_nat) (= A _let_1))))) (forall ((A 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 A) _let_1) (or (= A tptp.bot_bo2099793752762293965at_nat) (= A _let_1))))) (forall ((A tptp.set_o) (X Bool)) (let ((_let_1 (@ (@ tptp.insert_o2 X) tptp.bot_bot_set_o))) (=> (@ (@ tptp.ord_less_eq_set_o A) _let_1) (or (= A tptp.bot_bot_set_o) (= A _let_1))))) (forall ((A tptp.set_int) (X tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int2 X) tptp.bot_bot_set_int))) (=> (@ (@ tptp.ord_less_eq_set_int A) _let_1) (or (= A tptp.bot_bot_set_int) (= A _let_1))))) (forall ((A tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat2 X) tptp.bot_bot_set_nat))) (=> (@ (@ tptp.ord_less_eq_set_nat A) _let_1) (or (= A tptp.bot_bot_set_nat) (= A _let_1))))) (forall ((X4 tptp.set_Pr4329608150637261639at_nat) (A2 tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ (@ tptp.insert9069300056098147895at_nat A2) tptp.bot_bo228742789529271731at_nat))) (= (@ (@ tptp.ord_le1268244103169919719at_nat X4) _let_1) (or (= X4 tptp.bot_bo228742789529271731at_nat) (= X4 _let_1))))) (forall ((X4 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.insert8211810215607154385at_nat A2) tptp.bot_bo2099793752762293965at_nat))) (= (@ (@ tptp.ord_le3146513528884898305at_nat X4) _let_1) (or (= X4 tptp.bot_bo2099793752762293965at_nat) (= X4 _let_1))))) (forall ((X4 tptp.set_o) (A2 Bool)) (let ((_let_1 (@ (@ tptp.insert_o2 A2) tptp.bot_bot_set_o))) (= (@ (@ tptp.ord_less_eq_set_o X4) _let_1) (or (= X4 tptp.bot_bot_set_o) (= X4 _let_1))))) (forall ((X4 tptp.set_int) (A2 tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int2 A2) tptp.bot_bot_set_int))) (= (@ (@ tptp.ord_less_eq_set_int X4) _let_1) (or (= X4 tptp.bot_bot_set_int) (= X4 _let_1))))) (forall ((X4 tptp.set_nat) (A2 tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat2 A2) tptp.bot_bot_set_nat))) (= (@ (@ tptp.ord_less_eq_set_nat X4) _let_1) (or (= X4 tptp.bot_bot_set_nat) (= X4 _let_1))))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A) B) (= (@ (@ tptp.minus_3314409938677909166at_nat A) B) tptp.bot_bo228742789529271731at_nat))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A) B) (= (@ (@ tptp.minus_1356011639430497352at_nat A) B) tptp.bot_bo2099793752762293965at_nat))) (forall ((A tptp.set_o) (B tptp.set_o)) (=> (@ (@ tptp.ord_less_eq_set_o A) B) (= (@ (@ tptp.minus_minus_set_o A) B) tptp.bot_bot_set_o))) (forall ((A tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (= (@ (@ tptp.minus_minus_set_int A) B) tptp.bot_bot_set_int))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (= (@ (@ tptp.minus_minus_set_nat A) B) tptp.bot_bot_set_nat))) (forall ((A tptp.set_o) (B tptp.set_o) (X Bool) (C2 tptp.set_o)) (let ((_let_1 (@ tptp.minus_minus_set_o B))) (let ((_let_2 (@ tptp.ord_less_eq_set_o A))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_o2 X) C2))) (and (@ _let_2 (@ _let_1 C2)) (not (@ (@ tptp.member_o X) A))))))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (X tptp.produc3843707927480180839at_nat) (C2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.minus_3314409938677909166at_nat B))) (let ((_let_2 (@ tptp.ord_le1268244103169919719at_nat A))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert9069300056098147895at_nat X) C2))) (and (@ _let_2 (@ _let_1 C2)) (not (@ (@ tptp.member8757157785044589968at_nat X) A))))))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat B))) (let ((_let_2 (@ tptp.ord_le3146513528884898305at_nat A))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat X) C2))) (and (@ _let_2 (@ _let_1 C2)) (not (@ (@ tptp.member8440522571783428010at_nat X) A))))))) (forall ((A tptp.set_int) (B tptp.set_int) (X tptp.int) (C2 tptp.set_int)) (let ((_let_1 (@ tptp.minus_minus_set_int B))) (let ((_let_2 (@ tptp.ord_less_eq_set_int A))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_int2 X) C2))) (and (@ _let_2 (@ _let_1 C2)) (not (@ (@ tptp.member_int X) A))))))) (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool)) (C2 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.minus_1801376950450012436_nat_o B))) (let ((_let_2 (@ tptp.ord_le2965882846123202637_nat_o A))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o X) C2))) (and (@ _let_2 (@ _let_1 C2)) (not (@ (@ tptp.member6576561426505652726_nat_o X) A))))))) (forall ((A tptp.set_nat) (B tptp.set_nat) (X tptp.nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat B))) (let ((_let_2 (@ tptp.ord_less_eq_set_nat A))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_nat2 X) C2))) (and (@ _let_2 (@ _let_1 C2)) (not (@ (@ tptp.member_nat X) A))))))) (forall ((Xs tptp.list_P5464809261938338413at_nat) (A tptp.set_Pr4329608150637261639at_nat) (X tptp.produc3843707927480180839at_nat) (I tptp.nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat (@ tptp.set_Pr3765526544606949372at_nat Xs)) A) (=> (@ (@ tptp.member8757157785044589968at_nat X) A) (@ (@ tptp.ord_le1268244103169919719at_nat (@ tptp.set_Pr3765526544606949372at_nat (@ (@ (@ tptp.list_u4696772448584712917at_nat Xs) I) X))) A)))) (forall ((Xs tptp.list_P6011104703257516679at_nat) (A tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (I tptp.nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs)) A) (=> (@ (@ tptp.member8440522571783428010at_nat X) A) (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat Xs) I) X))) A)))) (forall ((Xs tptp.list_P7985473006766602707_nat_o) (A tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool)) (I tptp.nat)) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o (@ tptp.set_Pr400311997697478754_nat_o Xs)) A) (=> (@ (@ tptp.member6576561426505652726_nat_o X) A) (@ (@ tptp.ord_le2965882846123202637_nat_o (@ tptp.set_Pr400311997697478754_nat_o (@ (@ (@ tptp.list_u6943956310655620667_nat_o Xs) I) X))) A)))) (forall ((Xs tptp.list_int) (A tptp.set_int) (X tptp.int) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) A) (=> (@ (@ tptp.member_int X) A) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs) I) X))) A)))) (forall ((Xs tptp.list_P8527749157015355191n_assn) (A tptp.set_Pr5949110396991348497n_assn) (X tptp.produc6575502325842934193n_assn) (I tptp.nat)) (=> (@ (@ tptp.ord_le171416862856029873n_assn (@ tptp.set_Pr1139785259514867910n_assn Xs)) A) (=> (@ (@ tptp.member7957490590177025114n_assn X) A) (@ (@ tptp.ord_le171416862856029873n_assn (@ tptp.set_Pr1139785259514867910n_assn (@ (@ (@ tptp.list_u4534839942911652127n_assn Xs) I) X))) A)))) (forall ((Xs tptp.list_c) (A tptp.set_c) (X tptp.c) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_c (@ tptp.set_c2 Xs)) A) (=> (@ (@ tptp.member_c X) A) (@ (@ tptp.ord_less_eq_set_c (@ tptp.set_c2 (@ (@ (@ tptp.list_update_c Xs) I) X))) A)))) (forall ((Xs tptp.list_d) (A tptp.set_d) (X tptp.d) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_d (@ tptp.set_d2 Xs)) A) (=> (@ (@ tptp.member_d X) A) (@ (@ tptp.ord_less_eq_set_d (@ tptp.set_d2 (@ (@ (@ tptp.list_update_d Xs) I) X))) A)))) (forall ((Xs tptp.list_nat) (A tptp.set_nat) (X tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) A) (=> (@ (@ tptp.member_nat X) A) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs) I) X))) A)))) (forall ((X tptp.int) (Xs tptp.list_int)) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 (@ (@ tptp.remove1_int X) Xs))) (@ tptp.set_int2 Xs))) (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (@ (@ tptp.ord_le171416862856029873n_assn (@ tptp.set_Pr1139785259514867910n_assn (@ (@ tptp.remove1670527618125605709n_assn X) Xs))) (@ tptp.set_Pr1139785259514867910n_assn Xs))) (forall ((X tptp.nat) (Xs tptp.list_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 (@ (@ tptp.remove1_nat X) Xs))) (@ tptp.set_nat2 Xs))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (Ys tptp.list_P5464809261938338413at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat A) (@ tptp.coset_5307619257043544794at_nat Ys)) (forall ((X2 tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat X2))) (=> (@ _let_1 (@ tptp.set_Pr3765526544606949372at_nat Ys)) (not (@ _let_1 A))))))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (Ys tptp.list_P6011104703257516679at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat A) (@ tptp.coset_6809516720700967924at_nat Ys)) (forall ((X2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X2))) (=> (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat Ys)) (not (@ _let_1 A))))))) (forall ((A tptp.set_Pr4532377907799695533_nat_o) (Ys tptp.list_P7985473006766602707_nat_o)) (= (@ (@ tptp.ord_le2965882846123202637_nat_o A) (@ tptp.coset_9017067850271954240_nat_o Ys)) (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o X2))) (=> (@ _let_1 (@ tptp.set_Pr400311997697478754_nat_o Ys)) (not (@ _let_1 A))))))) (forall ((A tptp.set_int) (Ys tptp.list_int)) (= (@ (@ tptp.ord_less_eq_set_int A) (@ tptp.coset_int Ys)) (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.member_int X2))) (=> (@ _let_1 (@ tptp.set_int2 Ys)) (not (@ _let_1 A))))))) (forall ((A tptp.set_Pr5949110396991348497n_assn) (Ys tptp.list_P8527749157015355191n_assn)) (= (@ (@ tptp.ord_le171416862856029873n_assn A) (@ tptp.coset_703488708621576356n_assn Ys)) (forall ((X2 tptp.produc6575502325842934193n_assn)) (let ((_let_1 (@ tptp.member7957490590177025114n_assn X2))) (=> (@ _let_1 (@ tptp.set_Pr1139785259514867910n_assn Ys)) (not (@ _let_1 A))))))) (forall ((A tptp.set_nat) (Ys tptp.list_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A) (@ tptp.coset_nat Ys)) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X2))) (=> (@ _let_1 (@ tptp.set_nat2 Ys)) (not (@ _let_1 A))))))) (forall ((P (-> tptp.produc3843707927480180839at_nat tptp.produc3843707927480180839at_nat Bool)) (A tptp.produc3843707927480180839at_nat)) (@ (@ tptp.pairwi3222497012029234898at_nat P) (@ (@ tptp.insert9069300056098147895at_nat A) tptp.bot_bo228742789529271731at_nat))) (forall ((P (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (A tptp.product_prod_nat_nat)) (@ (@ tptp.pairwi6357175311820755948at_nat P) (@ (@ tptp.insert8211810215607154385at_nat A) tptp.bot_bo2099793752762293965at_nat))) (forall ((P (-> Bool Bool Bool)) (A Bool)) (@ (@ tptp.pairwise_o P) (@ (@ tptp.insert_o2 A) tptp.bot_bot_set_o))) (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat)) (@ (@ tptp.pairwise_nat P) (@ (@ tptp.insert_nat2 A) tptp.bot_bot_set_nat))) (forall ((P (-> tptp.int tptp.int Bool)) (A tptp.int)) (@ (@ tptp.pairwise_int P) (@ (@ tptp.insert_int2 A) tptp.bot_bot_set_int))) (forall ((A tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.ord_le2965882846123202637_nat_o A))) (let ((_let_2 (@ (@ tptp.member6576561426505652726_nat_o X) A))) (let ((_let_3 (@ tptp.insert5175938949040314269_nat_o X))) (= (@ _let_1 (@ _let_3 B)) (and (=> _let_2 (@ (@ tptp.ord_le2965882846123202637_nat_o (@ (@ tptp.minus_1801376950450012436_nat_o A) (@ _let_3 tptp.bot_bo7824918357723582233_nat_o))) B)) (=> (not _let_2) (@ _let_1 B)))))))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (X tptp.produc3843707927480180839at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le1268244103169919719at_nat A))) (let ((_let_2 (@ (@ tptp.member8757157785044589968at_nat X) A))) (let ((_let_3 (@ tptp.insert9069300056098147895at_nat X))) (= (@ _let_1 (@ _let_3 B)) (and (=> _let_2 (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.minus_3314409938677909166at_nat A) (@ _let_3 tptp.bot_bo228742789529271731at_nat))) B)) (=> (not _let_2) (@ _let_1 B)))))))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A))) (let ((_let_2 (@ (@ tptp.member8440522571783428010at_nat X) A))) (let ((_let_3 (@ tptp.insert8211810215607154385at_nat X))) (= (@ _let_1 (@ _let_3 B)) (and (=> _let_2 (@ (@ 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(let ((_let_2 (@ (@ tptp.member_nat X) A))) (let ((_let_3 (@ tptp.insert_nat2 X))) (= (@ _let_1 (@ _let_3 B)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A) (@ _let_3 tptp.bot_bot_set_nat))) B)) (=> (not _let_2) (@ _let_1 B)))))))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (X tptp.produc3843707927480180839at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.insert9069300056098147895at_nat X))) (=> (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.minus_3314409938677909166at_nat A) (@ _let_1 tptp.bot_bo228742789529271731at_nat))) B) (@ (@ tptp.ord_le1268244103169919719at_nat A) (@ _let_1 B))))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat X))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.minus_1356011639430497352at_nat A) (@ _let_1 tptp.bot_bo2099793752762293965at_nat))) B) (@ (@ 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tptp.list_u6180841689913720943at_nat Xs) I) X))) (@ (@ tptp.insert8211810215607154385at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs)))) (forall ((Xs tptp.list_P5464809261938338413at_nat) (I tptp.nat) (X tptp.produc3843707927480180839at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat (@ tptp.set_Pr3765526544606949372at_nat (@ (@ (@ tptp.list_u4696772448584712917at_nat Xs) I) X))) (@ (@ tptp.insert9069300056098147895at_nat X) (@ tptp.set_Pr3765526544606949372at_nat Xs)))) (forall ((Xs tptp.list_o) (I tptp.nat) (X Bool)) (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o Xs) I) X))) (@ (@ tptp.insert_o2 X) (@ tptp.set_o2 Xs)))) (forall ((Xs tptp.list_int) (I tptp.nat) (X tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs) I) X))) (@ (@ tptp.insert_int2 X) (@ tptp.set_int2 Xs)))) (forall ((Xs tptp.list_P8527749157015355191n_assn) (I tptp.nat) (X tptp.produc6575502325842934193n_assn)) (@ (@ tptp.ord_le171416862856029873n_assn (@ tptp.set_Pr1139785259514867910n_assn (@ (@ (@ tptp.list_u4534839942911652127n_assn Xs) I) X))) (@ (@ tptp.insert5290817439147925377n_assn X) (@ tptp.set_Pr1139785259514867910n_assn Xs)))) (forall ((Xs tptp.list_c) (I tptp.nat) (X tptp.c)) (@ (@ tptp.ord_less_eq_set_c (@ tptp.set_c2 (@ (@ (@ tptp.list_update_c Xs) I) X))) (@ (@ tptp.insert_c X) (@ tptp.set_c2 Xs)))) (forall ((Xs tptp.list_d) (I tptp.nat) (X tptp.d)) (@ (@ tptp.ord_less_eq_set_d (@ tptp.set_d2 (@ (@ (@ tptp.list_update_d Xs) I) X))) (@ (@ tptp.insert_d X) (@ tptp.set_d2 Xs)))) (forall ((Xs tptp.list_nat) (I tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs) I) X))) (@ (@ tptp.insert_nat2 X) (@ tptp.set_nat2 Xs)))) (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn X) tptp.bot_bot_assn) tptp.bot_bot_assn)) (forall ((X tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat X) tptp.bot_bo228742789529271731at_nat) tptp.bot_bo228742789529271731at_nat)) (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat X) tptp.bot_bo2099793752762293965at_nat) tptp.bot_bo2099793752762293965at_nat)) (forall ((X tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o X) tptp.bot_bot_set_o) tptp.bot_bot_set_o)) (forall ((X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X) tptp.bot_bot_set_nat) tptp.bot_bot_set_nat)) (forall ((X tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int X) tptp.bot_bot_set_int) tptp.bot_bot_set_int)) (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn tptp.bot_bot_assn) X) tptp.bot_bot_assn)) (forall ((X tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat tptp.bot_bo228742789529271731at_nat) X) tptp.bot_bo228742789529271731at_nat)) (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bot_bo2099793752762293965at_nat) X) tptp.bot_bo2099793752762293965at_nat)) (forall ((X tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o tptp.bot_bot_set_o) X) tptp.bot_bot_set_o)) (forall ((X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat tptp.bot_bot_set_nat) X) tptp.bot_bot_set_nat)) (forall ((X tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int tptp.bot_bot_set_int) X) tptp.bot_bot_set_int)) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (= (= (@ (@ tptp.minus_3314409938677909166at_nat X) Y) tptp.bot_bo228742789529271731at_nat) (@ (@ tptp.ord_le1268244103169919719at_nat X) Y))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.minus_1356011639430497352at_nat X) Y) tptp.bot_bo2099793752762293965at_nat) (@ (@ tptp.ord_le3146513528884898305at_nat X) Y))) (forall ((X tptp.set_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))) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int X) Y) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int X) Y))) (forall ((X tptp.assn) (Y tptp.assn)) (= (= (@ (@ tptp.minus_minus_assn X) Y) tptp.bot_bot_assn) (@ (@ tptp.ord_less_eq_assn X) Y))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat X) Y) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat X) Y))) (forall ((Xs tptp.list_c) (Ys tptp.list_c)) (= (@ tptp.size_s2756448709718749209od_c_c (@ (@ tptp.product_c_c Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_c Xs)) (@ tptp.size_size_list_c Ys)))) (forall ((Xs tptp.list_c) (Ys tptp.list_d)) (= (@ tptp.size_s2827482749765095194od_c_d (@ (@ tptp.product_c_d Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_c Xs)) (@ tptp.size_size_list_d Ys)))) (forall ((Xs tptp.list_c) (Ys tptp.list_nat)) (= (@ tptp.size_s2954062820725854115_c_nat (@ (@ tptp.product_c_nat Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_c Xs)) (@ tptp.size_size_list_nat Ys)))) (forall ((Xs tptp.list_c) (Ys tptp.list_int)) (= (@ tptp.size_s463979675794127359_c_int (@ (@ tptp.product_c_int Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_c Xs)) (@ tptp.size_size_list_int Ys)))) (forall ((Xs tptp.list_d) (Ys tptp.list_c)) (= (@ tptp.size_s2120799709113762520od_d_c (@ (@ tptp.product_d_c Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_d Xs)) (@ tptp.size_size_list_c Ys)))) (forall ((Xs tptp.list_d) (Ys tptp.list_d)) (= (@ tptp.size_s2191833749160108505od_d_d (@ (@ tptp.product_d_d Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_d Xs)) (@ tptp.size_size_list_d Ys)))) (forall ((Xs tptp.list_d) (Ys tptp.list_nat)) (= (@ tptp.size_s8550281435913984804_d_nat (@ (@ tptp.product_d_nat Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_d Xs)) (@ tptp.size_size_list_nat Ys)))) (forall ((Xs tptp.list_d) (Ys tptp.list_int)) (= (@ tptp.size_s6060198290982258048_d_int (@ (@ tptp.product_d_int Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_d Xs)) (@ tptp.size_size_list_int Ys)))) (forall ((Xs tptp.list_nat) (Ys tptp.list_c)) (= (@ tptp.size_s385972143775086793_nat_c (@ (@ tptp.product_nat_c Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs)) (@ tptp.size_size_list_c Ys)))) (forall ((Xs tptp.list_nat) (Ys tptp.list_d)) (= (@ tptp.size_s457006183821432778_nat_d (@ (@ tptp.product_nat_d Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs)) (@ tptp.size_size_list_d Ys)))) (forall ((J tptp.nat) (K3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) K3) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J) N)) K3))) (forall ((M2 tptp.nat) (N tptp.nat) (L tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (let ((_let_2 (@ tptp.ord_less_nat M2))) (=> (@ _let_2 N) (=> (@ _let_2 L) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 M2))))))) (forall ((X Bool) (A tptp.set_o) (X4 tptp.set_o)) (=> (@ (@ tptp.member_o X) A) (=> (@ (@ tptp.ord_less_eq_set_o X4) A) (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.insert_o2 X) X4)) A)))) (forall ((X tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (X4 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X) A) (=> (@ (@ tptp.ord_le1268244103169919719at_nat X4) A) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.insert9069300056098147895at_nat X) X4)) A)))) (forall ((X tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (X4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X) A) (=> (@ (@ tptp.ord_le3146513528884898305at_nat X4) A) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.insert8211810215607154385at_nat X) X4)) A)))) (forall ((X tptp.int) (A tptp.set_int) (X4 tptp.set_int)) (=> (@ (@ tptp.member_int X) A) (=> (@ (@ tptp.ord_less_eq_set_int X4) A) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.insert_int2 X) X4)) A)))) (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (X4 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.member6576561426505652726_nat_o X) A) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o X4) A) (@ (@ tptp.ord_le2965882846123202637_nat_o (@ (@ tptp.insert5175938949040314269_nat_o X) X4)) A)))) (forall ((X tptp.nat) (A tptp.set_nat) (X4 tptp.set_nat)) (=> (@ (@ tptp.member_nat X) A) (=> (@ (@ tptp.ord_less_eq_set_nat X4) A) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.insert_nat2 X) X4)) A)))) (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (not (@ (@ tptp.member6576561426505652726_nat_o X3) A))) (@ (@ tptp.ord_le2965882846123202637_nat_o A) tptp.bot_bo7824918357723582233_nat_o))) (forall ((A tptp.set_Pr4329608150637261639at_nat)) (=> (forall ((X3 tptp.produc3843707927480180839at_nat)) (not (@ (@ tptp.member8757157785044589968at_nat X3) A))) (@ (@ tptp.ord_le1268244103169919719at_nat A) tptp.bot_bo228742789529271731at_nat))) (forall ((A tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X3 tptp.product_prod_nat_nat)) (not (@ (@ tptp.member8440522571783428010at_nat X3) A))) (@ (@ tptp.ord_le3146513528884898305at_nat A) tptp.bot_bo2099793752762293965at_nat))) (forall ((A tptp.set_o)) (=> (forall ((X3 Bool)) (not (@ (@ tptp.member_o X3) A))) (@ (@ tptp.ord_less_eq_set_o A) tptp.bot_bot_set_o))) (forall ((A tptp.set_int)) (=> (forall ((X3 tptp.int)) (not (@ (@ tptp.member_int X3) A))) (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int))) (forall ((A tptp.set_nat)) (=> (forall ((X3 tptp.nat)) (not (@ (@ tptp.member_nat X3) A))) (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat))) (forall ((A2 tptp.nat) (B2 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ P A2) (=> (not (@ P B2)) (exists ((C4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A2) C4) (@ (@ tptp.ord_less_eq_nat C4) B2) (forall ((X7 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat A2) X7) (@ (@ tptp.ord_less_nat X7) C4)) (@ P X7))) (forall ((D4 tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat A2) X3) (@ (@ tptp.ord_less_nat X3) D4)) (@ P X3))) (@ (@ tptp.ord_less_eq_nat D4) C4))))))))) (forall ((A2 tptp.int) (B2 tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ P A2) (=> (not (@ P B2)) (exists ((C4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A2) C4) (@ (@ tptp.ord_less_eq_int C4) B2) (forall ((X7 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int A2) X7) (@ (@ tptp.ord_less_int X7) C4)) (@ P X7))) (forall ((D4 tptp.int)) (=> (forall ((X3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int A2) X3) (@ (@ tptp.ord_less_int X3) D4)) (@ P X3))) (@ (@ tptp.ord_less_eq_int D4) C4))))))))) (forall ((B6 tptp.code_integer) (A7 tptp.code_integer)) (= (not (@ (@ tptp.ord_le3102999989581377725nteger B6) A7)) (@ (@ tptp.ord_le6747313008572928689nteger A7) B6))) (forall ((B6 tptp.num) (A7 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num B6) A7)) (@ (@ tptp.ord_less_num A7) B6))) (forall ((B6 tptp.nat) (A7 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat B6) A7)) (@ (@ tptp.ord_less_nat A7) B6))) (forall ((B6 tptp.int) (A7 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int B6) A7)) (@ (@ tptp.ord_less_int A7) B6))) (forall ((C2 tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat C2))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) (and (@ _let_1 A) (@ _let_1 B))))) (forall ((C2 tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C2))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B)) (and (@ _let_1 A) (@ _let_1 B))))) (forall ((A2 Bool) (C2 tptp.set_o) (B tptp.set_o)) (=> (not (@ (@ tptp.member_o A2) C2)) (= (@ (@ tptp.inf_inf_set_o (@ (@ tptp.insert_o2 A2) B)) C2) (@ (@ tptp.inf_inf_set_o B) C2)))) (forall ((A2 tptp.produc3843707927480180839at_nat) (C2 tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (=> (not (@ (@ tptp.member8757157785044589968at_nat A2) C2)) (= (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.insert9069300056098147895at_nat A2) B)) C2) (@ (@ tptp.inf_in7913087082777306421at_nat B) C2)))) (forall ((A2 tptp.int) (C2 tptp.set_int) (B tptp.set_int)) (=> (not (@ (@ tptp.member_int A2) C2)) (= (@ (@ tptp.inf_inf_set_int (@ (@ tptp.insert_int2 A2) B)) C2) (@ (@ tptp.inf_inf_set_int B) C2)))) (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (C2 tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (=> (not (@ (@ tptp.member6576561426505652726_nat_o A2) C2)) (= (@ (@ tptp.inf_in1906310914598751387_nat_o (@ (@ tptp.insert5175938949040314269_nat_o A2) B)) C2) (@ (@ tptp.inf_in1906310914598751387_nat_o B) C2)))) (forall ((A2 tptp.nat) (C2 tptp.set_nat) (B tptp.set_nat)) (=> (not (@ (@ tptp.member_nat A2) C2)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.insert_nat2 A2) B)) C2) (@ (@ tptp.inf_inf_set_nat B) C2)))) (forall ((A2 tptp.product_prod_nat_nat) (C2 tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (=> (not (@ (@ tptp.member8440522571783428010at_nat A2) C2)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.insert8211810215607154385at_nat A2) B)) C2) (@ (@ tptp.inf_in2572325071724192079at_nat B) C2)))) (forall ((A2 Bool) (C2 tptp.set_o) (B tptp.set_o)) (let ((_let_1 (@ tptp.insert_o2 A2))) (=> (@ (@ tptp.member_o A2) C2) (= (@ (@ tptp.inf_inf_set_o (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.inf_inf_set_o B) C2)))))) (forall ((A2 tptp.produc3843707927480180839at_nat) (C2 tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.insert9069300056098147895at_nat A2))) (=> (@ (@ tptp.member8757157785044589968at_nat A2) C2) (= (@ (@ tptp.inf_in7913087082777306421at_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat B) C2)))))) (forall ((A2 tptp.int) (C2 tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.insert_int2 A2))) (=> (@ (@ tptp.member_int A2) C2) (= (@ (@ tptp.inf_inf_set_int (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.inf_inf_set_int B) C2)))))) (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (C2 tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.insert5175938949040314269_nat_o A2))) (=> (@ (@ tptp.member6576561426505652726_nat_o A2) C2) (= (@ (@ tptp.inf_in1906310914598751387_nat_o (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.inf_in1906310914598751387_nat_o B) C2)))))) (forall ((A2 tptp.nat) (C2 tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat2 A2))) (=> (@ (@ tptp.member_nat A2) C2) (= (@ (@ tptp.inf_inf_set_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.inf_inf_set_nat B) C2)))))) (forall ((A2 tptp.product_prod_nat_nat) (C2 tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A2))) (=> (@ (@ tptp.member8440522571783428010at_nat A2) C2) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B) C2)))))) (forall ((A2 tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.insert_int2 A2))) (= (@ (@ tptp.inf_inf_set_int (@ _let_1 A)) (@ _let_1 B)) (@ _let_1 (@ (@ tptp.inf_inf_set_int A) B))))) (forall ((A2 tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.insert9069300056098147895at_nat A2))) (= (@ (@ tptp.inf_in7913087082777306421at_nat (@ _let_1 A)) (@ _let_1 B)) (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat A) B))))) (forall ((A2 Bool) (A tptp.set_o) (B tptp.set_o)) (let ((_let_1 (@ tptp.insert_o2 A2))) (= (@ (@ tptp.inf_inf_set_o (@ _let_1 A)) (@ _let_1 B)) (@ _let_1 (@ (@ tptp.inf_inf_set_o A) B))))) (forall ((A2 tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat2 A2))) (= (@ (@ tptp.inf_inf_set_nat (@ _let_1 A)) (@ _let_1 B)) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B))))) (forall ((A2 tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A2))) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 A)) (@ _let_1 B)) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A) B))))) (forall ((A2 Bool) (A tptp.set_o) (B tptp.set_o)) (let ((_let_1 (@ tptp.inf_inf_set_o A))) (=> (not (@ (@ tptp.member_o A2) A)) (= (@ _let_1 (@ (@ tptp.insert_o2 A2) B)) (@ _let_1 B))))) (forall ((A2 tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.inf_in7913087082777306421at_nat A))) (=> (not (@ (@ tptp.member8757157785044589968at_nat A2) A)) (= (@ _let_1 (@ (@ tptp.insert9069300056098147895at_nat A2) B)) (@ _let_1 B))))) (forall ((A2 tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.inf_inf_set_int A))) (=> (not (@ (@ tptp.member_int A2) A)) (= (@ _let_1 (@ (@ tptp.insert_int2 A2) B)) (@ _let_1 B))))) (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.inf_in1906310914598751387_nat_o A))) (=> (not (@ (@ tptp.member6576561426505652726_nat_o A2) A)) (= (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o A2) B)) (@ _let_1 B))))) (forall ((A2 tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (=> (not (@ (@ tptp.member_nat A2) A)) (= (@ _let_1 (@ (@ tptp.insert_nat2 A2) B)) (@ _let_1 B))))) (forall ((A2 tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A))) (=> (not (@ (@ tptp.member8440522571783428010at_nat A2) A)) (= (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat A2) B)) (@ _let_1 B))))) (forall ((A2 Bool) (A tptp.set_o) (B tptp.set_o)) (let ((_let_1 (@ tptp.inf_inf_set_o A))) (let ((_let_2 (@ tptp.insert_o2 A2))) (=> (@ (@ tptp.member_o A2) A) (= (@ _let_1 (@ _let_2 B)) (@ _let_2 (@ _let_1 B))))))) (forall ((A2 tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.inf_in7913087082777306421at_nat A))) (let ((_let_2 (@ tptp.insert9069300056098147895at_nat A2))) (=> (@ (@ tptp.member8757157785044589968at_nat A2) A) (= (@ _let_1 (@ _let_2 B)) (@ _let_2 (@ _let_1 B))))))) (forall ((A2 tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.inf_inf_set_int A))) (let ((_let_2 (@ tptp.insert_int2 A2))) (=> (@ (@ tptp.member_int A2) A) (= (@ _let_1 (@ _let_2 B)) (@ _let_2 (@ _let_1 B))))))) (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.inf_in1906310914598751387_nat_o A))) (let ((_let_2 (@ tptp.insert5175938949040314269_nat_o A2))) (=> (@ (@ tptp.member6576561426505652726_nat_o A2) A) (= (@ _let_1 (@ _let_2 B)) (@ _let_2 (@ _let_1 B))))))) (forall ((A2 tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (let ((_let_2 (@ tptp.insert_nat2 A2))) (=> (@ (@ tptp.member_nat A2) A) (= (@ _let_1 (@ _let_2 B)) (@ _let_2 (@ _let_1 B))))))) (forall ((A2 tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A))) (let ((_let_2 (@ tptp.insert8211810215607154385at_nat A2))) (=> (@ (@ tptp.member8440522571783428010at_nat A2) A) (= (@ _let_1 (@ _let_2 B)) (@ _let_2 (@ _let_1 B))))))) (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (= (= (@ (@ tptp.inf_in1906310914598751387_nat_o (@ (@ tptp.insert5175938949040314269_nat_o A2) A)) B) tptp.bot_bo7824918357723582233_nat_o) (and (not (@ (@ tptp.member6576561426505652726_nat_o A2) B)) (= (@ (@ tptp.inf_in1906310914598751387_nat_o A) B) tptp.bot_bo7824918357723582233_nat_o)))) (forall ((A2 tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (= (= (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.insert9069300056098147895at_nat A2) A)) B) tptp.bot_bo228742789529271731at_nat) (and (not (@ (@ tptp.member8757157785044589968at_nat A2) B)) (= (@ (@ tptp.inf_in7913087082777306421at_nat A) B) tptp.bot_bo228742789529271731at_nat)))) (forall ((A2 tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.insert8211810215607154385at_nat A2) A)) B) tptp.bot_bo2099793752762293965at_nat) (and (not (@ (@ tptp.member8440522571783428010at_nat A2) B)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A) B) tptp.bot_bo2099793752762293965at_nat)))) (forall ((A2 Bool) (A tptp.set_o) (B tptp.set_o)) (= (= (@ (@ tptp.inf_inf_set_o (@ (@ tptp.insert_o2 A2) A)) B) tptp.bot_bot_set_o) (and (not (@ (@ tptp.member_o A2) B)) (= (@ (@ tptp.inf_inf_set_o A) B) tptp.bot_bot_set_o)))) (forall ((A2 tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.insert_nat2 A2) A)) B) tptp.bot_bot_set_nat) (and (not (@ (@ tptp.member_nat A2) B)) (= (@ (@ tptp.inf_inf_set_nat A) B) tptp.bot_bot_set_nat)))) (forall ((A2 tptp.int) (A tptp.set_int) (B tptp.set_int)) (= (= (@ (@ tptp.inf_inf_set_int (@ (@ tptp.insert_int2 A2) A)) B) tptp.bot_bot_set_int) (and (not (@ (@ tptp.member_int A2) B)) (= (@ (@ tptp.inf_inf_set_int A) B) tptp.bot_bot_set_int)))) (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (= (= tptp.bot_bo7824918357723582233_nat_o (@ (@ tptp.inf_in1906310914598751387_nat_o (@ (@ tptp.insert5175938949040314269_nat_o A2) A)) B)) (and (not (@ (@ tptp.member6576561426505652726_nat_o A2) B)) (= tptp.bot_bo7824918357723582233_nat_o (@ (@ tptp.inf_in1906310914598751387_nat_o A) B))))) (forall ((A2 tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (= (= tptp.bot_bo228742789529271731at_nat (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.insert9069300056098147895at_nat A2) A)) B)) (and (not (@ (@ tptp.member8757157785044589968at_nat A2) B)) (= tptp.bot_bo228742789529271731at_nat (@ (@ tptp.inf_in7913087082777306421at_nat A) B))))) (forall ((A2 tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (= tptp.bot_bo2099793752762293965at_nat (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.insert8211810215607154385at_nat A2) A)) B)) (and (not (@ (@ tptp.member8440522571783428010at_nat A2) B)) (= tptp.bot_bo2099793752762293965at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B))))) (forall ((A2 Bool) (A tptp.set_o) (B tptp.set_o)) (= (= tptp.bot_bot_set_o (@ (@ tptp.inf_inf_set_o (@ (@ tptp.insert_o2 A2) A)) B)) (and (not (@ (@ tptp.member_o A2) B)) (= tptp.bot_bot_set_o (@ (@ tptp.inf_inf_set_o A) B))))) (forall ((A2 tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (= (= tptp.bot_bot_set_nat (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.insert_nat2 A2) A)) B)) (and (not (@ (@ tptp.member_nat A2) B)) (= tptp.bot_bot_set_nat (@ (@ tptp.inf_inf_set_nat A) B))))) (forall ((A2 tptp.int) (A tptp.set_int) (B tptp.set_int)) (= (= tptp.bot_bot_set_int (@ (@ tptp.inf_inf_set_int (@ (@ tptp.insert_int2 A2) A)) B)) (and (not (@ (@ tptp.member_int A2) B)) (= tptp.bot_bot_set_int (@ (@ tptp.inf_inf_set_int A) B))))) (forall ((B tptp.set_Pr4532377907799695533_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.inf_in1906310914598751387_nat_o B))) (= (= (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o A2) A)) tptp.bot_bo7824918357723582233_nat_o) (and (not (@ (@ tptp.member6576561426505652726_nat_o A2) B)) (= (@ _let_1 A) tptp.bot_bo7824918357723582233_nat_o))))) (forall ((B tptp.set_Pr4329608150637261639at_nat) (A2 tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.inf_in7913087082777306421at_nat B))) (= (= (@ _let_1 (@ (@ tptp.insert9069300056098147895at_nat A2) A)) tptp.bot_bo228742789529271731at_nat) (and (not (@ (@ tptp.member8757157785044589968at_nat A2) B)) (= (@ _let_1 A) tptp.bot_bo228742789529271731at_nat))))) (forall ((B tptp.set_Pr1261947904930325089at_nat) (A2 tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat B))) (= (= (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat A2) A)) tptp.bot_bo2099793752762293965at_nat) (and (not (@ (@ tptp.member8440522571783428010at_nat A2) B)) (= (@ _let_1 A) tptp.bot_bo2099793752762293965at_nat))))) (forall ((B tptp.set_o) (A2 Bool) (A tptp.set_o)) (let ((_let_1 (@ tptp.inf_inf_set_o B))) (= (= (@ _let_1 (@ (@ tptp.insert_o2 A2) A)) tptp.bot_bot_set_o) (and (not (@ (@ tptp.member_o A2) B)) (= (@ _let_1 A) tptp.bot_bot_set_o))))) (forall ((B tptp.set_nat) (A2 tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat B))) (= (= (@ _let_1 (@ (@ tptp.insert_nat2 A2) A)) tptp.bot_bot_set_nat) (and (not (@ (@ tptp.member_nat A2) B)) (= (@ _let_1 A) tptp.bot_bot_set_nat))))) (forall ((B tptp.set_int) (A2 tptp.int) (A tptp.set_int)) (let ((_let_1 (@ tptp.inf_inf_set_int B))) (= (= (@ _let_1 (@ (@ tptp.insert_int2 A2) A)) tptp.bot_bot_set_int) (and (not (@ (@ tptp.member_int A2) B)) (= (@ _let_1 A) tptp.bot_bot_set_int))))) (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.inf_in1906310914598751387_nat_o A))) (= (= tptp.bot_bo7824918357723582233_nat_o (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o B2) B))) (and (not (@ (@ tptp.member6576561426505652726_nat_o B2) A)) (= tptp.bot_bo7824918357723582233_nat_o (@ _let_1 B)))))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B2 tptp.produc3843707927480180839at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.inf_in7913087082777306421at_nat A))) (= (= tptp.bot_bo228742789529271731at_nat (@ _let_1 (@ (@ tptp.insert9069300056098147895at_nat B2) B))) (and (not (@ (@ tptp.member8757157785044589968at_nat B2) A)) (= tptp.bot_bo228742789529271731at_nat (@ _let_1 B)))))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B2 tptp.product_prod_nat_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A))) (= (= tptp.bot_bo2099793752762293965at_nat (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat B2) B))) (and (not (@ (@ tptp.member8440522571783428010at_nat B2) A)) (= tptp.bot_bo2099793752762293965at_nat (@ _let_1 B)))))) (forall ((A tptp.set_o) (B2 Bool) (B tptp.set_o)) (let ((_let_1 (@ tptp.inf_inf_set_o A))) (= (= tptp.bot_bot_set_o (@ _let_1 (@ (@ tptp.insert_o2 B2) B))) (and (not (@ (@ tptp.member_o B2) A)) (= tptp.bot_bot_set_o (@ _let_1 B)))))) (forall ((A tptp.set_nat) (B2 tptp.nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (= (= tptp.bot_bot_set_nat (@ _let_1 (@ (@ tptp.insert_nat2 B2) B))) (and (not (@ (@ tptp.member_nat B2) A)) (= tptp.bot_bot_set_nat (@ _let_1 B)))))) (forall ((A tptp.set_int) (B2 tptp.int) (B tptp.set_int)) (let ((_let_1 (@ tptp.inf_inf_set_int A))) (= (= tptp.bot_bot_set_int (@ _let_1 (@ (@ tptp.insert_int2 B2) B))) (and (not (@ (@ tptp.member_int B2) A)) (= tptp.bot_bot_set_int (@ _let_1 B)))))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat A) (@ (@ tptp.minus_3314409938677909166at_nat B) A)) tptp.bot_bo228742789529271731at_nat)) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A) (@ (@ tptp.minus_1356011639430497352at_nat B) A)) tptp.bot_bo2099793752762293965at_nat)) (forall ((A tptp.set_o) (B tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o A) (@ (@ tptp.minus_minus_set_o B) A)) tptp.bot_bot_set_o)) (forall ((A tptp.set_int) (B tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int A) (@ (@ tptp.minus_minus_set_int B) A)) tptp.bot_bot_set_int)) (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A) (@ (@ tptp.minus_minus_set_nat B) A)) tptp.bot_bot_set_nat)) (forall ((Xs tptp.list_c) (I tptp.nat) (X tptp.c)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_c Xs)) I) (= (@ (@ (@ tptp.list_update_c Xs) I) X) Xs))) (forall ((Xs tptp.list_d) (I tptp.nat) (X tptp.d)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_d Xs)) I) (= (@ (@ (@ tptp.list_update_d Xs) I) X) Xs))) (forall ((Xs tptp.list_nat) (I tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) I) (= (@ (@ (@ tptp.list_update_nat Xs) I) X) Xs))) (forall ((Xs tptp.list_int) (I tptp.nat) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs)) I) (= (@ (@ (@ tptp.list_update_int Xs) I) X) Xs))) (= tptp.ord_less_nat (lambda ((M tptp.nat) (N2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M) N2) (not (= M N2))))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_eq_nat M2) N))) (= tptp.ord_less_eq_nat (lambda ((M tptp.nat) (N2 tptp.nat)) (or (@ (@ tptp.ord_less_nat M) N2) (= M N2)))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M2) N) (= M2 N)) (@ (@ tptp.ord_less_eq_nat M2) N))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (=> (not (= M2 N)) (@ (@ tptp.ord_less_nat M2) N)))) (forall ((F4 (-> tptp.nat tptp.nat)) (I tptp.nat) (J tptp.nat)) (=> (forall ((I5 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) J3) (@ (@ tptp.ord_less_nat (@ F4 I5)) (@ F4 J3)))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ F4 I)) (@ F4 J))))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (= (= (@ (@ tptp.inf_in7913087082777306421at_nat A) B) tptp.bot_bo228742789529271731at_nat) (forall ((X2 tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X2) A) (forall ((Y5 tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat Y5) B) (not (= X2 Y5)))))))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.inf_in2572325071724192079at_nat A) B) tptp.bot_bo2099793752762293965at_nat) (forall ((X2 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X2) A) (forall ((Y5 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat Y5) B) (not (= X2 Y5)))))))) (forall ((A tptp.set_o) (B tptp.set_o)) (= (= (@ (@ tptp.inf_inf_set_o A) B) tptp.bot_bot_set_o) (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) A) (forall ((Y5 Bool)) (=> (@ (@ tptp.member_o Y5) B) (= X2 (not Y5)))))))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat A) B) tptp.bot_bot_set_nat) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A) (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.member_nat Y5) B) (not (= X2 Y5)))))))) (forall ((A tptp.set_int) (B tptp.set_int)) (= (= (@ (@ tptp.inf_inf_set_int A) B) tptp.bot_bot_set_int) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A) (forall ((Y5 tptp.int)) (=> (@ (@ tptp.member_int Y5) B) (not (= X2 Y5)))))))) (forall ((A tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat A) tptp.bot_bo228742789529271731at_nat) tptp.bot_bo228742789529271731at_nat)) (forall ((A tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A) tptp.bot_bo2099793752762293965at_nat) tptp.bot_bo2099793752762293965at_nat)) (forall ((A tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o A) tptp.bot_bot_set_o) tptp.bot_bot_set_o)) (forall ((A tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A) tptp.bot_bot_set_nat) tptp.bot_bot_set_nat)) (forall ((A tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int A) tptp.bot_bot_set_int) tptp.bot_bot_set_int)) (forall ((B tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat tptp.bot_bo228742789529271731at_nat) B) tptp.bot_bo228742789529271731at_nat)) (forall ((B tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bot_bo2099793752762293965at_nat) B) tptp.bot_bo2099793752762293965at_nat)) (forall ((B tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o tptp.bot_bot_set_o) B) tptp.bot_bot_set_o)) (forall ((B tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat tptp.bot_bot_set_nat) B) tptp.bot_bot_set_nat)) (forall ((B tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int tptp.bot_bot_set_int) B) tptp.bot_bot_set_int)) (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (= (= (@ (@ tptp.inf_in1906310914598751387_nat_o A) B) tptp.bot_bo7824918357723582233_nat_o) (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o X2))) (=> (@ _let_1 A) (not (@ _let_1 B))))))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (= (= (@ (@ tptp.inf_in7913087082777306421at_nat A) B) tptp.bot_bo228742789529271731at_nat) (forall ((X2 tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat X2))) (=> (@ _let_1 A) (not (@ _let_1 B))))))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.inf_in2572325071724192079at_nat A) B) tptp.bot_bo2099793752762293965at_nat) (forall ((X2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X2))) (=> (@ _let_1 A) (not (@ _let_1 B))))))) (forall ((A tptp.set_o) (B tptp.set_o)) (= (= (@ (@ tptp.inf_inf_set_o A) B) tptp.bot_bot_set_o) (forall ((X2 Bool)) (let ((_let_1 (@ tptp.member_o X2))) (=> (@ _let_1 A) (not (@ _let_1 B))))))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat A) B) tptp.bot_bot_set_nat) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X2))) (=> (@ _let_1 A) (not (@ _let_1 B))))))) (forall ((A tptp.set_int) (B tptp.set_int)) (= (= (@ (@ tptp.inf_inf_set_int A) B) tptp.bot_bot_set_int) (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.member_int X2))) (=> (@ _let_1 A) (not (@ _let_1 B))))))) (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o X3))) (=> (@ _let_1 A) (not (@ _let_1 B))))) (= (@ (@ tptp.inf_in1906310914598751387_nat_o A) B) tptp.bot_bo7824918357723582233_nat_o))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (=> (forall ((X3 tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat X3))) (=> (@ _let_1 A) (not (@ _let_1 B))))) (= (@ (@ tptp.inf_in7913087082777306421at_nat A) B) tptp.bot_bo228742789529271731at_nat))) (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))) (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))) (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))) (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))) (forall ((A2 tptp.set_Pr4532377907799695533_nat_o) (B2 tptp.set_Pr4532377907799695533_nat_o)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o X3))) (=> (@ _let_1 A2) (not (@ _let_1 B2))))) (= (@ (@ tptp.inf_in1906310914598751387_nat_o A2) B2) tptp.bot_bo7824918357723582233_nat_o))) (forall ((A2 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (=> (forall ((X3 tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat X3))) (=> (@ _let_1 A2) (not (@ _let_1 B2))))) (= (@ (@ tptp.inf_in7913087082777306421at_nat A2) B2) tptp.bot_bo228742789529271731at_nat))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X3 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X3))) (=> (@ _let_1 A2) (not (@ _let_1 B2))))) (= (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2) tptp.bot_bo2099793752762293965at_nat))) (forall ((A2 tptp.set_o) (B2 tptp.set_o)) (=> (forall ((X3 Bool)) (let ((_let_1 (@ tptp.member_o X3))) (=> (@ _let_1 A2) (not (@ _let_1 B2))))) (= (@ (@ tptp.inf_inf_set_o A2) B2) tptp.bot_bot_set_o))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X3))) (=> (@ _let_1 A2) (not (@ _let_1 B2))))) (= (@ (@ tptp.inf_inf_set_nat A2) B2) tptp.bot_bot_set_nat))) (forall ((A2 tptp.set_int) (B2 tptp.set_int)) (=> (forall ((X3 tptp.int)) (let ((_let_1 (@ tptp.member_int X3))) (=> (@ _let_1 A2) (not (@ _let_1 B2))))) (= (@ (@ tptp.inf_inf_set_int A2) B2) tptp.bot_bot_set_int))) (forall ((S tptp.set_Pr1261947904930325089at_nat) (S4 tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat B))) (let ((_let_2 (@ tptp.inf_in2572325071724192079at_nat A))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat S) S4) (=> (= (@ _let_2 S4) (@ _let_1 S4)) (= (@ _let_2 S) (@ _let_1 S))))))) (forall ((S tptp.set_nat) (S4 tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat B))) (let ((_let_2 (@ tptp.inf_inf_set_nat A))) (=> (@ (@ tptp.ord_less_eq_set_nat S) S4) (=> (= (@ _let_2 S4) (@ _let_1 S4)) (= (@ _let_2 S) (@ _let_1 S))))))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (P (-> tptp.produc3843707927480180839at_nat Bool)) (Q (-> tptp.produc3843707927480180839at_nat Bool))) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A) B) (=> (forall ((X3 tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X3) A) (=> (@ P X3) (@ Q X3)))) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.inf_in7913087082777306421at_nat A) (@ tptp.collec6321179662152712658at_nat P))) (@ (@ tptp.inf_in7913087082777306421at_nat B) (@ tptp.collec6321179662152712658at_nat Q)))))) (forall ((A tptp.set_int) (B tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A) (=> (@ P X3) (@ Q X3)))) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int A) (@ tptp.collect_int P))) (@ (@ tptp.inf_inf_set_int B) (@ tptp.collect_int Q)))))) (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o) (P (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool)) (Q (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o A) B) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X3) A) (=> (@ P X3) (@ Q X3)))) (@ (@ tptp.ord_le2965882846123202637_nat_o (@ (@ tptp.inf_in1906310914598751387_nat_o A) (@ tptp.collec939566748876313656_nat_o P))) (@ (@ tptp.inf_in1906310914598751387_nat_o B) (@ tptp.collec939566748876313656_nat_o Q)))))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.product_prod_nat_nat Bool)) (Q (-> tptp.product_prod_nat_nat Bool))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A) B) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) A) (=> (@ P X3) (@ Q X3)))) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) (@ tptp.collec3392354462482085612at_nat P))) (@ (@ tptp.inf_in2572325071724192079at_nat B) (@ tptp.collec3392354462482085612at_nat Q)))))) (forall ((A tptp.set_nat) (B tptp.set_nat) (P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A) (=> (@ P X3) (@ Q X3)))) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A) (@ tptp.collect_nat P))) (@ (@ tptp.inf_inf_set_nat B) (@ tptp.collect_nat Q)))))) (forall ((C2 tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat C2))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A) B)))))) (forall ((C2 tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C2))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B)))))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A) B) (= (@ (@ tptp.inf_in2572325071724192079at_nat A) B) A))) (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))) (forall ((B tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B) A) (= (@ (@ tptp.inf_in2572325071724192079at_nat A) B) B))) (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))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) B)) (forall ((A tptp.set_nat) (B tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) B)) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) A)) (forall ((A tptp.set_nat) (B tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) A)) (forall ((A tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (D tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A) C2) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B) D) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) (@ (@ tptp.inf_in2572325071724192079at_nat C2) D))))) (forall ((A tptp.set_nat) (C2 tptp.set_nat) (B tptp.set_nat) (D tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) C2) (=> (@ (@ tptp.ord_less_eq_set_nat B) D) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) (@ (@ tptp.inf_inf_set_nat C2) D))))) (forall ((A2 Bool) (C2 tptp.set_o) (B tptp.set_o)) (let ((_let_1 (@ (@ tptp.inf_inf_set_o B) C2))) (let ((_let_2 (@ tptp.insert_o2 A2))) (let ((_let_3 (@ (@ tptp.inf_inf_set_o (@ _let_2 B)) C2))) (let ((_let_4 (@ (@ tptp.member_o A2) C2))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((A2 tptp.produc3843707927480180839at_nat) (C2 tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ (@ tptp.inf_in7913087082777306421at_nat B) C2))) (let ((_let_2 (@ tptp.insert9069300056098147895at_nat A2))) (let ((_let_3 (@ (@ tptp.inf_in7913087082777306421at_nat (@ _let_2 B)) C2))) (let ((_let_4 (@ (@ tptp.member8757157785044589968at_nat A2) C2))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((A2 tptp.int) (C2 tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ (@ tptp.inf_inf_set_int B) C2))) (let ((_let_2 (@ tptp.insert_int2 A2))) (let ((_let_3 (@ (@ tptp.inf_inf_set_int (@ _let_2 B)) C2))) (let ((_let_4 (@ (@ tptp.member_int A2) C2))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (C2 tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ (@ tptp.inf_in1906310914598751387_nat_o B) C2))) (let ((_let_2 (@ tptp.insert5175938949040314269_nat_o A2))) (let ((_let_3 (@ (@ tptp.inf_in1906310914598751387_nat_o (@ _let_2 B)) C2))) (let ((_let_4 (@ (@ tptp.member6576561426505652726_nat_o A2) C2))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((A2 tptp.nat) (C2 tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ (@ tptp.inf_inf_set_nat B) C2))) (let ((_let_2 (@ tptp.insert_nat2 A2))) (let ((_let_3 (@ (@ tptp.inf_inf_set_nat (@ _let_2 B)) C2))) (let ((_let_4 (@ (@ tptp.member_nat A2) C2))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((A2 tptp.product_prod_nat_nat) (C2 tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B) C2))) (let ((_let_2 (@ tptp.insert8211810215607154385at_nat A2))) (let ((_let_3 (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_2 B)) C2))) (let ((_let_4 (@ (@ tptp.member8440522571783428010at_nat A2) C2))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((A2 Bool) (A tptp.set_o) (B tptp.set_o)) (let ((_let_1 (@ tptp.inf_inf_set_o A))) (let ((_let_2 (@ _let_1 B))) (let ((_let_3 (@ tptp.insert_o2 A2))) (let ((_let_4 (@ _let_1 (@ _let_3 B)))) (let ((_let_5 (@ (@ tptp.member_o A2) A))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))) (forall ((A2 tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.inf_in7913087082777306421at_nat A))) (let ((_let_2 (@ _let_1 B))) (let ((_let_3 (@ tptp.insert9069300056098147895at_nat A2))) (let ((_let_4 (@ _let_1 (@ _let_3 B)))) (let ((_let_5 (@ (@ tptp.member8757157785044589968at_nat A2) A))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))) (forall ((A2 tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.inf_inf_set_int A))) (let ((_let_2 (@ _let_1 B))) (let ((_let_3 (@ tptp.insert_int2 A2))) (let ((_let_4 (@ _let_1 (@ _let_3 B)))) (let ((_let_5 (@ (@ tptp.member_int A2) A))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))) (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.inf_in1906310914598751387_nat_o A))) (let ((_let_2 (@ _let_1 B))) (let ((_let_3 (@ tptp.insert5175938949040314269_nat_o A2))) (let ((_let_4 (@ _let_1 (@ _let_3 B)))) (let ((_let_5 (@ (@ tptp.member6576561426505652726_nat_o A2) A))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))) (forall ((A2 tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (let ((_let_2 (@ _let_1 B))) (let ((_let_3 (@ tptp.insert_nat2 A2))) (let ((_let_4 (@ _let_1 (@ _let_3 B)))) (let ((_let_5 (@ (@ tptp.member_nat A2) A))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))) (forall ((A2 tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A))) (let ((_let_2 (@ _let_1 B))) (let ((_let_3 (@ tptp.insert8211810215607154385at_nat A2))) (let ((_let_4 (@ _let_1 (@ _let_3 B)))) (let ((_let_5 (@ (@ tptp.member8440522571783428010at_nat A2) A))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A))) (= (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat B) C2))))) (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (= (@ (@ tptp.minus_minus_set_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B) C2))))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) C2)))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B) C2)) (@ _let_1 B)))) (forall ((A tptp.set_nat) (C2 tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat (@ (@ tptp.inf_inf_set_nat A) C2)))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat B) C2)) (@ _let_1 B)))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.inf_in2572325071724192079at_nat A) B)))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.inf_inf_set_nat A) B)))) (forall ((C2 tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat C2))) (= (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A) B)) (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_1 A)) (@ _let_1 B))))) (forall ((C2 tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat C2))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B)) (@ (@ tptp.minus_minus_set_nat (@ _let_1 A)) (@ _let_1 B))))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.minus_1356011639430497352at_nat A) B)) C2) (@ (@ tptp.minus_1356011639430497352at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) C2)) (@ (@ tptp.inf_in2572325071724192079at_nat B) C2)))) (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.minus_minus_set_nat A) B)) C2) (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.inf_inf_set_nat A) C2)) (@ (@ tptp.inf_inf_set_nat B) C2)))) (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (=> (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N3) N) (not (@ P N3)))) (@ P N)) (exists ((N4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat N4) N) (@ P N4))))) (= tptp.ord_less_eq_assn (lambda ((A3 tptp.assn) (B3 tptp.assn)) (= A3 (@ (@ tptp.inf_inf_assn A3) B3)))) (forall ((K3 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K3))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M2) K3)) (@ (@ tptp.minus_minus_nat N) K3)) (@ (@ tptp.ord_less_nat M2) N)))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat C) A2) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat A2) C)) (@ (@ tptp.minus_minus_nat B2) C))))) (forall ((A2 tptp.set_Pr4329608150637261639at_nat) (A7 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat) (B6 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A2) A7) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B2) B6) (=> (= (@ (@ tptp.inf_in7913087082777306421at_nat A7) B6) tptp.bot_bo228742789529271731at_nat) (= (@ (@ tptp.inf_in7913087082777306421at_nat A2) B2) tptp.bot_bo228742789529271731at_nat))))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (A7 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) A7) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B2) B6) (=> (= (@ (@ tptp.inf_in2572325071724192079at_nat A7) B6) tptp.bot_bo2099793752762293965at_nat) (= (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2) tptp.bot_bo2099793752762293965at_nat))))) (forall ((A2 tptp.set_o) (A7 tptp.set_o) (B2 tptp.set_o) (B6 tptp.set_o)) (=> (@ (@ tptp.ord_less_eq_set_o A2) A7) (=> (@ (@ tptp.ord_less_eq_set_o B2) B6) (=> (= (@ (@ tptp.inf_inf_set_o A7) B6) tptp.bot_bot_set_o) (= (@ (@ tptp.inf_inf_set_o A2) B2) tptp.bot_bot_set_o))))) (forall ((A2 tptp.set_int) (A7 tptp.set_int) (B2 tptp.set_int) (B6 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) A7) (=> (@ (@ tptp.ord_less_eq_set_int B2) B6) (=> (= (@ (@ tptp.inf_inf_set_int A7) B6) tptp.bot_bot_set_int) (= (@ (@ tptp.inf_inf_set_int A2) B2) tptp.bot_bot_set_int))))) (forall ((A2 tptp.set_nat) (A7 tptp.set_nat) (B2 tptp.set_nat) (B6 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) A7) (=> (@ (@ tptp.ord_less_eq_set_nat B2) B6) (=> (= (@ (@ tptp.inf_inf_set_nat A7) B6) tptp.bot_bot_set_nat) (= (@ (@ tptp.inf_inf_set_nat A2) B2) tptp.bot_bot_set_nat))))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (= (not (= (@ (@ tptp.minus_3314409938677909166at_nat A) B) A)) (not (= (@ (@ tptp.inf_in7913087082777306421at_nat A) B) tptp.bot_bo228742789529271731at_nat)))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (not (= (@ (@ tptp.minus_1356011639430497352at_nat A) B) A)) (not (= (@ (@ tptp.inf_in2572325071724192079at_nat A) B) tptp.bot_bo2099793752762293965at_nat)))) (forall ((A tptp.set_o) (B tptp.set_o)) (= (not (= (@ (@ tptp.minus_minus_set_o A) B) A)) (not (= (@ (@ tptp.inf_inf_set_o A) B) tptp.bot_bot_set_o)))) (forall ((A tptp.set_int) (B tptp.set_int)) (= (not (= (@ (@ tptp.minus_minus_set_int A) B) A)) (not (= (@ (@ tptp.inf_inf_set_int A) B) tptp.bot_bot_set_int)))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (not (= (@ (@ tptp.minus_minus_set_nat A) B) A)) (not (= (@ (@ tptp.inf_inf_set_nat A) B) tptp.bot_bot_set_nat)))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (= (= (@ (@ tptp.minus_3314409938677909166at_nat A) B) A) (= (@ (@ tptp.inf_in7913087082777306421at_nat A) B) tptp.bot_bo228742789529271731at_nat))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.minus_1356011639430497352at_nat A) B) A) (= (@ (@ tptp.inf_in2572325071724192079at_nat A) B) tptp.bot_bo2099793752762293965at_nat))) (forall ((A tptp.set_o) (B tptp.set_o)) (= (= (@ (@ tptp.minus_minus_set_o A) B) A) (= (@ (@ tptp.inf_inf_set_o A) B) tptp.bot_bot_set_o))) (forall ((A tptp.set_int) (B tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int A) B) A) (= (@ (@ tptp.inf_inf_set_int A) B) tptp.bot_bot_set_int))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat A) B) A) (= (@ (@ tptp.inf_inf_set_nat A) B) tptp.bot_bot_set_nat))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.inf_in7913087082777306421at_nat A) B)) (@ (@ tptp.minus_3314409938677909166at_nat A) B)) tptp.bot_bo228742789529271731at_nat)) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) (@ (@ tptp.minus_1356011639430497352at_nat A) B)) tptp.bot_bo2099793752762293965at_nat)) (forall ((A tptp.set_o) (B tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o (@ (@ tptp.inf_inf_set_o A) B)) (@ (@ tptp.minus_minus_set_o A) B)) tptp.bot_bot_set_o)) (forall ((A tptp.set_int) (B tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int (@ (@ tptp.inf_inf_set_int A) B)) (@ (@ tptp.minus_minus_set_int A) B)) tptp.bot_bot_set_int)) (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) (@ (@ tptp.minus_minus_set_nat A) B)) tptp.bot_bot_set_nat)) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (=> (= (@ (@ tptp.inf_in7913087082777306421at_nat A) B) tptp.bot_bo228742789529271731at_nat) (= (@ (@ tptp.minus_3314409938677909166at_nat A) B) A))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (=> (= (@ (@ tptp.inf_in2572325071724192079at_nat A) B) tptp.bot_bo2099793752762293965at_nat) (= (@ (@ tptp.minus_1356011639430497352at_nat A) B) A))) (forall ((A tptp.set_o) (B tptp.set_o)) (=> (= (@ (@ tptp.inf_inf_set_o A) B) tptp.bot_bot_set_o) (= (@ (@ tptp.minus_minus_set_o A) B) A))) (forall ((A tptp.set_int) (B tptp.set_int)) (=> (= (@ (@ tptp.inf_inf_set_int A) B) tptp.bot_bot_set_int) (= (@ (@ tptp.minus_minus_set_int A) B) A))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (= (@ (@ tptp.inf_inf_set_nat A) B) tptp.bot_bot_set_nat) (= (@ (@ tptp.minus_minus_set_nat A) B) A))) (forall ((X tptp.code_integer) (Zs tptp.list_Code_integer)) (let ((_let_1 (@ tptp.foldl_1542389171486570077nteger tptp.times_3573771949741848930nteger))) (= (@ (@ tptp.times_3573771949741848930nteger X) (@ (@ _let_1 tptp.one_one_Code_integer) Zs)) (@ (@ _let_1 X) Zs)))) (forall ((X tptp.assn) (Zs tptp.list_assn)) (let ((_let_1 (@ tptp.foldl_assn_assn tptp.times_times_assn))) (= (@ (@ tptp.times_times_assn X) (@ (@ _let_1 tptp.one_one_assn) Zs)) (@ (@ _let_1 X) Zs)))) (forall ((X tptp.rat) (Zs tptp.list_rat)) (let ((_let_1 (@ tptp.foldl_rat_rat tptp.times_times_rat))) (= (@ (@ tptp.times_times_rat X) (@ (@ _let_1 tptp.one_one_rat) Zs)) (@ (@ _let_1 X) Zs)))) (forall ((X tptp.nat) (Zs tptp.list_nat)) (let ((_let_1 (@ tptp.foldl_nat_nat tptp.times_times_nat))) (= (@ (@ tptp.times_times_nat X) (@ (@ _let_1 tptp.one_one_nat) Zs)) (@ (@ _let_1 X) Zs)))) (forall ((X tptp.int) (Zs tptp.list_int)) (let ((_let_1 (@ tptp.foldl_int_int tptp.times_times_int))) (= (@ (@ tptp.times_times_int X) (@ (@ _let_1 tptp.one_one_int) Zs)) (@ (@ _let_1 X) Zs)))) (forall ((X tptp.c) (Xs tptp.list_c)) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_c (@ (@ tptp.removeAll_c X) Xs))) (@ tptp.size_size_list_c Xs))) (forall ((X tptp.d) (Xs tptp.list_d)) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_d (@ (@ tptp.removeAll_d X) Xs))) (@ tptp.size_size_list_d Xs))) (forall ((X tptp.nat) (Xs tptp.list_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat (@ (@ tptp.removeAll_nat X) Xs))) (@ tptp.size_size_list_nat Xs))) (forall ((X tptp.int) (Xs tptp.list_int)) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int (@ (@ tptp.removeAll_int X) Xs))) (@ tptp.size_size_list_int Xs))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le2604355607129572851at_nat (@ (@ tptp.minus_3314409938677909166at_nat A) B)) A) (not (= (@ (@ tptp.inf_in7913087082777306421at_nat A) B) tptp.bot_bo228742789529271731at_nat)))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le7866589430770878221at_nat (@ (@ tptp.minus_1356011639430497352at_nat A) B)) A) (not (= (@ (@ tptp.inf_in2572325071724192079at_nat A) B) tptp.bot_bo2099793752762293965at_nat)))) (forall ((A tptp.set_o) (B tptp.set_o)) (= (@ (@ tptp.ord_less_set_o (@ (@ tptp.minus_minus_set_o A) B)) A) (not (= (@ (@ tptp.inf_inf_set_o A) B) tptp.bot_bot_set_o)))) (forall ((A tptp.set_int) (B tptp.set_int)) (= (@ (@ tptp.ord_less_set_int (@ (@ tptp.minus_minus_set_int A) B)) A) (not (= (@ (@ tptp.inf_inf_set_int A) B) tptp.bot_bot_set_int)))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (@ (@ tptp.ord_less_set_nat (@ (@ tptp.minus_minus_set_nat A) B)) A) (not (= (@ (@ tptp.inf_inf_set_nat A) B) tptp.bot_bot_set_nat)))) (forall ((A2 tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger A2) A2))) (forall ((A2 tptp.assn)) (not (@ (@ tptp.ord_less_assn A2) A2))) (forall ((A2 tptp.num)) (not (@ (@ tptp.ord_less_num A2) A2))) (forall ((A2 tptp.nat)) (not (@ (@ tptp.ord_less_nat A2) A2))) (forall ((A2 tptp.int)) (not (@ (@ tptp.ord_less_int A2) A2))) (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (S3 tptp.set_Pr1261947904930325089at_nat) (R tptp.set_Pr4329608150637261639at_nat) (S5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.produc2922128104949294807at_nat R2))) (=> (@ (@ tptp.member8757157785044589968at_nat (@ _let_1 S3)) R) (=> (= S5 S3) (@ (@ tptp.member8757157785044589968at_nat (@ _let_1 S5)) R))))) (forall ((R2 tptp.nat) (S3 tptp.nat) (R tptp.set_Pr1261947904930325089at_nat) (S5 tptp.nat)) (let ((_let_1 (@ tptp.product_Pair_nat_nat R2))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 S3)) R) (=> (= S5 S3) (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 S5)) R))))) (forall ((R2 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (S3 tptp.produc8923325533196201883nteger) (R tptp.set_Pr1281608226676607948nteger) (S5 tptp.produc8923325533196201883nteger)) (let ((_let_1 (@ tptp.produc8603105652947943368nteger R2))) (=> (@ (@ tptp.member4164122664394876845nteger (@ _let_1 S3)) R) (=> (= S5 S3) (@ (@ tptp.member4164122664394876845nteger (@ _let_1 S5)) R))))) (forall ((R2 (-> tptp.produc3658429121746597890et_nat Bool)) (S3 tptp.produc3658429121746597890et_nat) (R tptp.set_Pr3286484037609594932et_nat) (S5 tptp.produc3658429121746597890et_nat)) (let ((_let_1 (@ tptp.produc5001842942810119800et_nat R2))) (=> (@ (@ tptp.member1996754912294343701et_nat (@ _let_1 S3)) R) (=> (= S5 S3) (@ (@ tptp.member1996754912294343701et_nat (@ _let_1 S5)) R))))) (forall ((R2 (-> tptp.produc3658429121746597890et_nat Bool)) (S3 tptp.produc3925858234332021118et_nat) (R tptp.set_Pr8536935166611901872et_nat) (S5 tptp.produc3925858234332021118et_nat)) (let ((_let_1 (@ tptp.produc2245416461498447860et_nat R2))) (=> (@ (@ tptp.member6124377750444531601et_nat (@ _let_1 S3)) R) (=> (= S5 S3) (@ (@ tptp.member6124377750444531601et_nat (@ _let_1 S5)) R))))) (forall ((R2 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (S3 tptp.product_prod_int_int) (R tptp.set_Pr9222295170931077689nt_int) (S5 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.produc5700946648718959541nt_int R2))) (=> (@ (@ tptp.member7618704894036264090nt_int (@ _let_1 S3)) R) (=> (= S5 S3) (@ (@ tptp.member7618704894036264090nt_int (@ _let_1 S5)) R))))) (forall ((R2 (-> tptp.int tptp.option6357759511663192854e_term)) (S3 tptp.product_prod_int_int) (R tptp.set_Pr1872883991513573699nt_int) (S5 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.produc4305682042979456191nt_int R2))) (=> (@ (@ tptp.member7034335876925520548nt_int (@ _let_1 S3)) R) (=> (= S5 S3) (@ (@ tptp.member7034335876925520548nt_int (@ _let_1 S5)) R))))) (forall ((Ys tptp.list_P8527749157015355191n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (=> (@ tptp.distin4809818325527169450n_assn Ys) (=> (= (@ tptp.set_Pr1139785259514867910n_assn Ys) (@ tptp.set_Pr1139785259514867910n_assn Xs)) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6829681357464350627n_assn Ys)) (@ tptp.size_s6829681357464350627n_assn Xs))))) (forall ((Ys tptp.list_c) (Xs tptp.list_c)) (=> (@ tptp.distinct_c Ys) (=> (= (@ tptp.set_c2 Ys) (@ tptp.set_c2 Xs)) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_c Ys)) (@ tptp.size_size_list_c Xs))))) (forall ((Ys tptp.list_d) (Xs tptp.list_d)) (=> (@ tptp.distinct_d Ys) (=> (= (@ tptp.set_d2 Ys) (@ tptp.set_d2 Xs)) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_d Ys)) (@ tptp.size_size_list_d Xs))))) (forall ((Ys tptp.list_nat) (Xs tptp.list_nat)) (=> (@ tptp.distinct_nat Ys) (=> (= (@ tptp.set_nat2 Ys) (@ tptp.set_nat2 Xs)) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Ys)) (@ tptp.size_size_list_nat Xs))))) (forall ((Ys tptp.list_int) (Xs tptp.list_int)) (=> (@ tptp.distinct_int Ys) (=> (= (@ tptp.set_int2 Ys) (@ tptp.set_int2 Xs)) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Ys)) (@ tptp.size_size_list_int Xs))))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (not (= M2 N)) (or (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_nat N) M2)))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))) (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M2) (not (= M2 N)))) (forall ((S3 tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S3) T) (not (= S3 T)))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))) (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N5 tptp.nat)) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M3) N5) (@ P M3))) (@ P N5))) (@ P N))) (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N5 tptp.nat)) (=> (not (@ P N5)) (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N5) (not (@ P M3)))))) (@ P N))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))) (forall ((X tptp.list_c) (Y tptp.list_c)) (=> (not (= (@ tptp.size_size_list_c X) (@ tptp.size_size_list_c Y))) (not (= X Y)))) (forall ((X tptp.list_d) (Y tptp.list_d)) (=> (not (= (@ tptp.size_size_list_d X) (@ tptp.size_size_list_d Y))) (not (= X Y)))) (forall ((X tptp.list_nat) (Y tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat X) (@ tptp.size_size_list_nat Y))) (not (= X Y)))) (forall ((X tptp.list_int) (Y tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int X) (@ tptp.size_size_list_int Y))) (not (= X Y)))) (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (=> (@ tptp.distinct_int Xs) (=> (@ tptp.distinct_int Ys) (@ tptp.distin3744728255968310194nt_int (@ (@ tptp.product_int_int Xs) Ys))))) (forall ((Xs tptp.list_int) (Ys tptp.list_nat)) (=> (@ tptp.distinct_int Xs) (=> (@ tptp.distinct_nat Ys) (@ tptp.distin7922579275477506902nt_nat (@ (@ tptp.product_int_nat Xs) Ys))))) (forall ((Xs tptp.list_nat) (Ys tptp.list_int)) (=> (@ tptp.distinct_nat Xs) (=> (@ tptp.distinct_int Ys) (@ tptp.distin2745374544067255638at_int (@ (@ tptp.product_nat_int Xs) Ys))))) (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (@ tptp.distinct_nat Xs) (=> (@ tptp.distinct_nat Ys) (@ tptp.distin6923225563576452346at_nat (@ (@ tptp.product_nat_nat Xs) Ys))))) (forall ((L tptp.list_Code_integer) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_Code_integer L))) (=> (@ (@ tptp.sorted710888440204495920nteger tptp.ord_le3102999989581377725nteger) L) (=> (@ tptp.distin1543349897113766820nteger L) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_s3445333598471063425nteger L)) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 I)) (@ _let_1 J)))))))) (forall ((L tptp.list_num) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_num L))) (=> (@ (@ tptp.sorted_wrt_num tptp.ord_less_eq_num) L) (=> (@ tptp.distinct_num L) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_num L)) (@ (@ tptp.ord_less_num (@ _let_1 I)) (@ _let_1 J)))))))) (forall ((L tptp.list_nat) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat L))) (=> (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) L) (=> (@ tptp.distinct_nat L) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat L)) (@ (@ tptp.ord_less_nat (@ _let_1 I)) (@ _let_1 J)))))))) (forall ((L tptp.list_int) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_int L))) (=> (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) L) (=> (@ tptp.distinct_int L) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_int L)) (@ (@ tptp.ord_less_int (@ _let_1 I)) (@ _let_1 J)))))))) (forall ((L tptp.list_Code_integer) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (let ((_let_2 (@ tptp.nth_Code_integer L))) (let ((_let_3 (@ tptp.size_s3445333598471063425nteger L))) (=> (@ tptp.distin1543349897113766820nteger L) (=> (@ (@ tptp.sorted710888440204495920nteger tptp.ord_le3102999989581377725nteger) L) (=> (@ _let_1 _let_3) (=> (@ (@ tptp.ord_less_nat J) _let_3) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_2 I)) (@ _let_2 J)) (@ _let_1 J)))))))))) (forall ((L tptp.list_num) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (let ((_let_2 (@ tptp.nth_num L))) (let ((_let_3 (@ tptp.size_size_list_num L))) (=> (@ tptp.distinct_num L) (=> (@ (@ tptp.sorted_wrt_num tptp.ord_less_eq_num) L) (=> (@ _let_1 _let_3) (=> (@ (@ tptp.ord_less_nat J) _let_3) (= (@ (@ tptp.ord_less_num (@ _let_2 I)) (@ _let_2 J)) (@ _let_1 J)))))))))) (forall ((L tptp.list_nat) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (let ((_let_2 (@ tptp.nth_nat L))) (let ((_let_3 (@ tptp.size_size_list_nat L))) (=> (@ tptp.distinct_nat L) (=> (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) L) (=> (@ _let_1 _let_3) (=> (@ (@ tptp.ord_less_nat J) _let_3) (= (@ (@ tptp.ord_less_nat (@ _let_2 I)) (@ _let_2 J)) (@ _let_1 J)))))))))) (forall ((L tptp.list_int) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (let ((_let_2 (@ tptp.nth_int L))) (let ((_let_3 (@ tptp.size_size_list_int L))) (=> (@ tptp.distinct_int L) (=> (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) L) (=> (@ _let_1 _let_3) (=> (@ (@ tptp.ord_less_nat J) _let_3) (= (@ (@ tptp.ord_less_int (@ _let_2 I)) (@ _let_2 J)) (@ _let_1 J)))))))))) (forall ((From tptp.nat) (To tptp.nat) (Xs tptp.list_c)) (=> (@ (@ tptp.ord_less_eq_nat From) To) (=> (@ (@ tptp.ord_less_eq_nat To) (@ tptp.size_size_list_c Xs)) (= (@ tptp.size_size_list_c (@ (@ (@ tptp.slice_c From) To) Xs)) (@ (@ tptp.minus_minus_nat To) From))))) (forall ((From tptp.nat) (To tptp.nat) (Xs tptp.list_d)) (=> (@ (@ tptp.ord_less_eq_nat From) To) (=> (@ (@ tptp.ord_less_eq_nat To) (@ tptp.size_size_list_d Xs)) (= (@ tptp.size_size_list_d (@ (@ (@ tptp.slice_d From) To) Xs)) (@ (@ tptp.minus_minus_nat To) From))))) (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))))) (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))))) (forall ((K3 tptp.nat) (Xs tptp.list_c) (Y tptp.c)) (let ((_let_1 (@ tptp.size_size_list_c Xs))) (=> (@ (@ tptp.ord_less_nat K3) _let_1) (= (@ tptp.rev_c (@ (@ (@ tptp.list_update_c Xs) K3) Y)) (@ (@ (@ tptp.list_update_c (@ tptp.rev_c Xs)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat _let_1) K3)) tptp.one_one_nat)) Y))))) (forall ((K3 tptp.nat) (Xs tptp.list_d) (Y tptp.d)) (let ((_let_1 (@ tptp.size_size_list_d Xs))) (=> (@ (@ tptp.ord_less_nat K3) _let_1) (= (@ tptp.rev_d (@ (@ (@ tptp.list_update_d Xs) K3) Y)) (@ (@ (@ tptp.list_update_d (@ tptp.rev_d Xs)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat _let_1) K3)) tptp.one_one_nat)) Y))))) (forall ((K3 tptp.nat) (Xs tptp.list_nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.size_size_list_nat Xs))) (=> (@ (@ tptp.ord_less_nat K3) _let_1) (= (@ tptp.rev_nat (@ (@ (@ tptp.list_update_nat Xs) K3) Y)) (@ (@ (@ tptp.list_update_nat (@ tptp.rev_nat Xs)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat _let_1) K3)) tptp.one_one_nat)) Y))))) (forall ((K3 tptp.nat) (Xs tptp.list_int) (Y tptp.int)) (let ((_let_1 (@ tptp.size_size_list_int Xs))) (=> (@ (@ tptp.ord_less_nat K3) _let_1) (= (@ tptp.rev_int (@ (@ (@ tptp.list_update_int Xs) K3) Y)) (@ (@ (@ tptp.list_update_int (@ tptp.rev_int Xs)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat _let_1) K3)) tptp.one_one_nat)) Y))))) (forall ((K3 tptp.nat) (Xs tptp.list_c) (X tptp.c)) (let ((_let_1 (@ tptp.butlast_c Xs))) (let ((_let_2 (@ tptp.butlast_c (@ (@ (@ tptp.list_update_c Xs) K3) X)))) (let ((_let_3 (= K3 (@ (@ tptp.minus_minus_nat (@ tptp.size_size_list_c Xs)) tptp.one_one_nat)))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ (@ tptp.list_update_c _let_1) K3) X)))))))) (forall ((K3 tptp.nat) (Xs tptp.list_d) (X tptp.d)) (let ((_let_1 (@ tptp.butlast_d Xs))) (let ((_let_2 (@ tptp.butlast_d (@ (@ (@ tptp.list_update_d Xs) K3) X)))) (let ((_let_3 (= K3 (@ (@ tptp.minus_minus_nat (@ tptp.size_size_list_d Xs)) tptp.one_one_nat)))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ (@ tptp.list_update_d _let_1) K3) X)))))))) (forall ((K3 tptp.nat) (Xs tptp.list_nat) (X tptp.nat)) (let ((_let_1 (@ tptp.butlast_nat Xs))) (let ((_let_2 (@ tptp.butlast_nat (@ (@ (@ tptp.list_update_nat Xs) K3) X)))) (let ((_let_3 (= K3 (@ (@ tptp.minus_minus_nat (@ tptp.size_size_list_nat Xs)) tptp.one_one_nat)))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ (@ tptp.list_update_nat _let_1) K3) X)))))))) (forall ((K3 tptp.nat) (Xs tptp.list_int) (X tptp.int)) (let ((_let_1 (@ tptp.butlast_int Xs))) (let ((_let_2 (@ tptp.butlast_int (@ (@ (@ tptp.list_update_int Xs) K3) X)))) (let ((_let_3 (= K3 (@ (@ tptp.minus_minus_nat (@ tptp.size_size_list_int Xs)) tptp.one_one_nat)))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ (@ tptp.list_update_int _let_1) K3) X)))))))) (forall ((L tptp.list_nat) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat L))) (let ((_let_2 (@ tptp.size_size_list_nat L))) (=> (@ tptp.distinct_nat L) (=> (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) L) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 I)) (@ _let_1 J)) (@ (@ tptp.ord_less_eq_nat I) J))))))))) (forall ((L tptp.list_int) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_int L))) (let ((_let_2 (@ tptp.size_size_list_int L))) (=> (@ tptp.distinct_int L) (=> (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) L) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 I)) (@ _let_1 J)) (@ (@ tptp.ord_less_eq_nat I) J))))))))) (forall ((Xs tptp.list_c) (Ys tptp.list_c)) (= (@ tptp.size_s2756448709718749209od_c_c (@ (@ tptp.zip_c_c Xs) Ys)) (@ (@ tptp.ord_min_nat (@ tptp.size_size_list_c Xs)) (@ tptp.size_size_list_c Ys)))) (forall ((Xs tptp.list_c) (Ys tptp.list_d)) (= (@ tptp.size_s2827482749765095194od_c_d (@ (@ tptp.zip_c_d Xs) Ys)) (@ (@ tptp.ord_min_nat (@ tptp.size_size_list_c Xs)) (@ tptp.size_size_list_d Ys)))) (forall ((Xs tptp.list_c) (Ys tptp.list_nat)) (= (@ tptp.size_s2954062820725854115_c_nat (@ (@ tptp.zip_c_nat Xs) Ys)) (@ (@ tptp.ord_min_nat (@ tptp.size_size_list_c Xs)) (@ tptp.size_size_list_nat Ys)))) (forall ((Xs tptp.list_c) (Ys tptp.list_int)) (= (@ tptp.size_s463979675794127359_c_int (@ (@ tptp.zip_c_int Xs) Ys)) (@ (@ tptp.ord_min_nat (@ tptp.size_size_list_c Xs)) (@ tptp.size_size_list_int Ys)))) (forall ((Xs tptp.list_d) (Ys tptp.list_c)) (= (@ tptp.size_s2120799709113762520od_d_c (@ (@ tptp.zip_d_c Xs) Ys)) (@ (@ tptp.ord_min_nat (@ tptp.size_size_list_d Xs)) (@ tptp.size_size_list_c Ys)))) (forall ((Xs tptp.list_d) (Ys tptp.list_d)) (= (@ tptp.size_s2191833749160108505od_d_d (@ (@ tptp.zip_d_d Xs) Ys)) (@ (@ tptp.ord_min_nat (@ tptp.size_size_list_d Xs)) (@ tptp.size_size_list_d Ys)))) (forall ((Xs tptp.list_d) (Ys tptp.list_nat)) (= (@ tptp.size_s8550281435913984804_d_nat (@ (@ tptp.zip_d_nat Xs) Ys)) (@ (@ tptp.ord_min_nat (@ tptp.size_size_list_d Xs)) (@ tptp.size_size_list_nat Ys)))) (forall ((Xs tptp.list_d) (Ys tptp.list_int)) (= (@ tptp.size_s6060198290982258048_d_int (@ (@ tptp.zip_d_int Xs) Ys)) (@ (@ tptp.ord_min_nat (@ tptp.size_size_list_d Xs)) (@ tptp.size_size_list_int Ys)))) (forall ((Xs tptp.list_nat) (Ys tptp.list_c)) (= (@ tptp.size_s385972143775086793_nat_c (@ (@ tptp.zip_nat_c Xs) Ys)) (@ (@ tptp.ord_min_nat (@ tptp.size_size_list_nat Xs)) (@ tptp.size_size_list_c Ys)))) (forall ((Xs tptp.list_nat) (Ys tptp.list_d)) (= (@ tptp.size_s457006183821432778_nat_d (@ (@ tptp.zip_nat_d Xs) Ys)) (@ (@ tptp.ord_min_nat (@ tptp.size_size_list_nat Xs)) (@ tptp.size_size_list_d Ys)))) (forall ((P tptp.assn) (H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat) (Q tptp.assn) (As3 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H2))) (=> (@ (@ tptp.rep_assn P) (@ _let_1 As2)) (=> (@ (@ tptp.rep_assn Q) (@ _let_1 As3)) (=> (= (@ (@ tptp.inf_inf_set_nat As2) As3) tptp.bot_bot_set_nat) (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn P) Q)) (@ _let_1 (@ (@ tptp.sup_sup_set_nat As2) As3)))))))) (forall ((A tptp.assn) (B tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn A) B)) H2) (exists ((Hr tptp.heap_e7401611519738050253t_unit) (As1 tptp.set_nat) (As22 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat Hr))) (and (= H2 (@ _let_1 (@ (@ tptp.sup_sup_set_nat As1) As22))) (= (@ (@ tptp.inf_inf_set_nat As1) As22) tptp.bot_bot_set_nat) (@ (@ tptp.rep_assn A) (@ _let_1 As1)) (@ (@ tptp.rep_assn B) (@ _let_1 As22))))))) (forall ((Xs tptp.list_c)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_c Xs)) tptp.one_one_nat) (= (@ tptp.rotate1_c Xs) Xs))) (forall ((Xs tptp.list_d)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_d Xs)) tptp.one_one_nat) (= (@ tptp.rotate1_d Xs) Xs))) (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))) (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))) (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A2) A2) A2)) (forall ((A2 tptp.assn)) (= (@ (@ tptp.sup_sup_assn A2) A2) A2)) (forall ((A2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat A2) A2) A2)) (forall ((X tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat X) X) X)) (forall ((X tptp.assn)) (= (@ (@ tptp.sup_sup_assn X) X) X)) (forall ((X tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat X) X) X)) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A2))) (let ((_let_2 (@ _let_1 B2))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A2 tptp.assn) (B2 tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn A2))) (let ((_let_2 (@ _let_1 B2))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A2 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat A2))) (let ((_let_2 (@ _let_1 B2))) (= (@ _let_1 _let_2) _let_2)))) (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)))) (forall ((X tptp.assn) (Y tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))) (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)))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.sup_sup_set_nat A2) B2))) (= (@ (@ tptp.sup_sup_set_nat _let_1) B2) _let_1))) (forall ((A2 tptp.assn) (B2 tptp.assn)) (let ((_let_1 (@ (@ tptp.sup_sup_assn A2) B2))) (= (@ (@ tptp.sup_sup_assn _let_1) B2) _let_1))) (forall ((A2 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2))) (= (@ (@ tptp.sup_su5525570899277871387at_nat _let_1) B2) _let_1))) (forall ((C tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat A) B)))))) (forall ((C tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.inf_inf_set_int A) B)))))) (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.inf_in1906310914598751387_nat_o A) B)))))) (forall ((C tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B)))))) (forall ((C tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A) B)))))) (forall ((C tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (= (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat A) B)) (and (@ _let_1 A) (@ _let_1 B))))) (forall ((C tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_int A) B)) (and (@ _let_1 A) (@ _let_1 B))))) (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (= (@ _let_1 (@ (@ tptp.inf_in1906310914598751387_nat_o A) B)) (and (@ _let_1 A) (@ _let_1 B))))) (forall ((C tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B)) (and (@ _let_1 A) (@ _let_1 B))))) (forall ((C tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) (and (@ _let_1 A) (@ _let_1 B))))) (forall ((C tptp.product_prod_nat_nat) (B tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (=> (not (@ _let_1 B)) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat A) B))))) (forall ((C tptp.int) (B tptp.set_int) (A tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (=> (not (@ _let_1 B)) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.sup_sup_set_int A) B))))) (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.set_Pr4532377907799695533_nat_o) (A tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (=> (not (@ _let_1 B)) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.sup_su5209123915105501825_nat_o A) B))))) (forall ((C tptp.nat) (B tptp.set_nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (=> (not (@ _let_1 B)) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B))))) (forall ((C tptp.produc3843707927480180839at_nat) (B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (=> (=> (not (@ _let_1 B)) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A) B))))) (forall ((C tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat A) B)) (or (@ _let_1 A) (@ _let_1 B))))) (forall ((C tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A) B)) (or (@ _let_1 A) (@ _let_1 B))))) (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (= (@ _let_1 (@ (@ tptp.sup_su5209123915105501825_nat_o A) B)) (or (@ _let_1 A) (@ _let_1 B))))) (forall ((C tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B)) (or (@ _let_1 A) (@ _let_1 B))))) (forall ((C tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (= (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A) B)) (or (@ _let_1 A) (@ _let_1 B))))) (forall ((A2 tptp.nat)) (= (@ (@ tptp.ord_min_nat A2) A2) A2)) (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_min_nat A2))) (let ((_let_2 (@ _let_1 B2))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_min_nat A2) B2))) (= (@ (@ tptp.ord_min_nat _let_1) B2) _let_1))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat X) Y)) Z) (and (@ (@ tptp.ord_le1268244103169919719at_nat X) Z) (@ (@ tptp.ord_le1268244103169919719at_nat Y) Z)))) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (= (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.sup_sup_assn X) Y)) Z) (and (@ (@ tptp.ord_less_eq_assn X) Z) (@ (@ tptp.ord_less_eq_assn Y) Z)))) (forall ((X tptp.filter_nat) (Y tptp.filter_nat) (Z tptp.filter_nat)) (= (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.sup_sup_filter_nat X) Y)) Z) (and (@ (@ tptp.ord_le2510731241096832064er_nat X) Z) (@ (@ tptp.ord_le2510731241096832064er_nat Y) Z)))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat X) Y)) Z) (and (@ (@ tptp.ord_less_eq_set_nat X) Z) (@ (@ tptp.ord_less_eq_set_nat Y) Z)))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat X) Y)) Z) (and (@ (@ tptp.ord_less_eq_nat X) Z) (@ (@ tptp.ord_less_eq_nat Y) Z)))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int X) Y)) Z) (and (@ (@ tptp.ord_less_eq_int X) Z) (@ (@ tptp.ord_less_eq_int Y) Z)))) (forall ((B2 tptp.set_Pr4329608150637261639at_nat) (C tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat B2) C)) A2) (and (@ (@ tptp.ord_le1268244103169919719at_nat B2) A2) (@ (@ tptp.ord_le1268244103169919719at_nat C) A2)))) (forall ((B2 tptp.assn) (C tptp.assn) (A2 tptp.assn)) (= (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.sup_sup_assn B2) C)) A2) (and (@ (@ tptp.ord_less_eq_assn B2) A2) (@ (@ tptp.ord_less_eq_assn C) A2)))) (forall ((B2 tptp.filter_nat) (C tptp.filter_nat) (A2 tptp.filter_nat)) (= (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.sup_sup_filter_nat B2) C)) A2) (and (@ (@ tptp.ord_le2510731241096832064er_nat B2) A2) (@ (@ tptp.ord_le2510731241096832064er_nat C) A2)))) (forall ((B2 tptp.set_nat) (C tptp.set_nat) (A2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat B2) C)) A2) (and (@ (@ tptp.ord_less_eq_set_nat B2) A2) (@ (@ tptp.ord_less_eq_set_nat C) A2)))) (forall ((B2 tptp.nat) (C tptp.nat) (A2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat B2) C)) A2) (and (@ (@ tptp.ord_less_eq_nat B2) A2) (@ (@ tptp.ord_less_eq_nat C) A2)))) (forall ((B2 tptp.int) (C tptp.int) (A2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int B2) C)) A2) (and (@ (@ tptp.ord_less_eq_int B2) A2) (@ (@ tptp.ord_less_eq_int C) A2)))) (forall ((A2 tptp.assn)) (= (@ (@ tptp.sup_sup_assn A2) tptp.bot_bot_assn) A2)) (forall ((A2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat A2) tptp.bot_bo228742789529271731at_nat) A2)) (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat A2) tptp.bot_bo2099793752762293965at_nat) A2)) (forall ((A2 tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o A2) tptp.bot_bot_set_o) A2)) (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A2) tptp.bot_bot_set_nat) A2)) (forall ((A2 tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int A2) tptp.bot_bot_set_int) A2)) (forall ((A2 tptp.assn) (B2 tptp.assn)) (= (= tptp.bot_bot_assn (@ (@ tptp.sup_sup_assn A2) B2)) (and (= A2 tptp.bot_bot_assn) (= B2 tptp.bot_bot_assn)))) (forall ((A2 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (= (= tptp.bot_bo228742789529271731at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2)) (and (= A2 tptp.bot_bo228742789529271731at_nat) (= B2 tptp.bot_bo228742789529271731at_nat)))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (= (= tptp.bot_bo2099793752762293965at_nat (@ (@ tptp.sup_su6327502436637775413at_nat A2) B2)) (and (= A2 tptp.bot_bo2099793752762293965at_nat) (= B2 tptp.bot_bo2099793752762293965at_nat)))) (forall ((A2 tptp.set_o) (B2 tptp.set_o)) (= (= tptp.bot_bot_set_o (@ (@ tptp.sup_sup_set_o A2) B2)) (and (= A2 tptp.bot_bot_set_o) (= B2 tptp.bot_bot_set_o)))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (= (= tptp.bot_bot_set_nat (@ (@ tptp.sup_sup_set_nat A2) B2)) (and (= A2 tptp.bot_bot_set_nat) (= B2 tptp.bot_bot_set_nat)))) (forall ((A2 tptp.set_int) (B2 tptp.set_int)) (= (= tptp.bot_bot_set_int (@ (@ tptp.sup_sup_set_int A2) B2)) (and (= A2 tptp.bot_bot_set_int) (= B2 tptp.bot_bot_set_int)))) (forall ((A2 tptp.assn)) (= (@ (@ tptp.sup_sup_assn tptp.bot_bot_assn) A2) A2)) (forall ((A2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat tptp.bot_bo228742789529271731at_nat) A2) A2)) (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat tptp.bot_bo2099793752762293965at_nat) A2) A2)) (forall ((A2 tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o tptp.bot_bot_set_o) A2) A2)) (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat tptp.bot_bot_set_nat) A2) A2)) (forall ((A2 tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int tptp.bot_bot_set_int) A2) A2)) (forall ((A2 tptp.assn) (B2 tptp.assn)) (= (= (@ (@ tptp.sup_sup_assn A2) B2) tptp.bot_bot_assn) (and (= A2 tptp.bot_bot_assn) (= B2 tptp.bot_bot_assn)))) (forall ((A2 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (= (= (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2) tptp.bot_bo228742789529271731at_nat) (and (= A2 tptp.bot_bo228742789529271731at_nat) (= B2 tptp.bot_bo228742789529271731at_nat)))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.sup_su6327502436637775413at_nat A2) B2) tptp.bot_bo2099793752762293965at_nat) (and (= A2 tptp.bot_bo2099793752762293965at_nat) (= B2 tptp.bot_bo2099793752762293965at_nat)))) (forall ((A2 tptp.set_o) (B2 tptp.set_o)) (= (= (@ (@ tptp.sup_sup_set_o A2) B2) tptp.bot_bot_set_o) (and (= A2 tptp.bot_bot_set_o) (= B2 tptp.bot_bot_set_o)))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (= (= (@ (@ tptp.sup_sup_set_nat A2) B2) tptp.bot_bot_set_nat) (and (= A2 tptp.bot_bot_set_nat) (= B2 tptp.bot_bot_set_nat)))) (forall ((A2 tptp.set_int) (B2 tptp.set_int)) (= (= (@ (@ tptp.sup_sup_set_int A2) B2) tptp.bot_bot_set_int) (and (= A2 tptp.bot_bot_set_int) (= B2 tptp.bot_bot_set_int)))) (forall ((X tptp.assn) (Y tptp.assn)) (= (= (@ (@ tptp.sup_sup_assn X) Y) tptp.bot_bot_assn) (and (= X tptp.bot_bot_assn) (= Y tptp.bot_bot_assn)))) (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)))) (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)))) (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)))) (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)))) (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)))) (forall ((X tptp.assn) (Y tptp.assn)) (= (= tptp.bot_bot_assn (@ (@ tptp.sup_sup_assn X) Y)) (and (= X tptp.bot_bot_assn) (= Y tptp.bot_bot_assn)))) (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)))) (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)))) (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)))) (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)))) (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)))) (forall ((X tptp.assn)) (= (@ (@ tptp.sup_sup_assn X) tptp.bot_bot_assn) X)) (forall ((X tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat X) tptp.bot_bo228742789529271731at_nat) X)) (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat X) tptp.bot_bo2099793752762293965at_nat) X)) (forall ((X tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o X) tptp.bot_bot_set_o) X)) (forall ((X tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat X) tptp.bot_bot_set_nat) X)) (forall ((X tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int X) tptp.bot_bot_set_int) X)) (forall ((X tptp.assn)) (= (@ (@ tptp.sup_sup_assn tptp.bot_bot_assn) X) X)) (forall ((X tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat tptp.bot_bo228742789529271731at_nat) X) X)) (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat tptp.bot_bo2099793752762293965at_nat) X) X)) (forall ((X tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o tptp.bot_bot_set_o) X) X)) (forall ((X tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat tptp.bot_bot_set_nat) X) X)) (forall ((X tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int tptp.bot_bot_set_int) X) X)) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat X) (@ (@ tptp.sup_su6327502436637775413at_nat X) Y)) X)) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X) (@ (@ tptp.sup_sup_set_nat X) Y)) X)) (forall ((X tptp.assn) (Y tptp.assn)) (= (@ (@ tptp.inf_inf_assn X) (@ (@ tptp.sup_sup_assn X) Y)) X)) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat X) (@ (@ tptp.sup_su5525570899277871387at_nat X) Y)) X)) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat X) (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) X)) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat X) (@ (@ tptp.inf_inf_set_nat X) Y)) X)) (forall ((X tptp.assn) (Y tptp.assn)) (= (@ (@ tptp.sup_sup_assn X) (@ (@ tptp.inf_inf_assn X) Y)) X)) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat X) (@ (@ tptp.inf_in7913087082777306421at_nat X) Y)) X)) (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)))) (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)))) (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)))) (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)))) (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)))) (forall ((M2 tptp.assn) (N tptp.assn)) (let ((_let_1 (@ (@ tptp.ord_min_assn M2) N))) (= (@ (@ tptp.ord_less_eq_assn M2) _let_1) (= _let_1 M2)))) (forall ((M2 tptp.filter_nat) (N tptp.filter_nat)) (let ((_let_1 (@ (@ tptp.ord_min_filter_nat M2) N))) (= (@ (@ tptp.ord_le2510731241096832064er_nat M2) _let_1) (= _let_1 M2)))) (forall ((M2 tptp.set_nat) (N tptp.set_nat)) (let ((_let_1 (@ (@ tptp.ord_min_set_nat M2) N))) (= (@ (@ tptp.ord_less_eq_set_nat M2) _let_1) (= _let_1 M2)))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_min_nat M2) N))) (= (@ (@ tptp.ord_less_eq_nat M2) _let_1) (= _let_1 M2)))) (forall ((M2 tptp.int) (N tptp.int)) (let ((_let_1 (@ (@ tptp.ord_min_int M2) N))) (= (@ (@ tptp.ord_less_eq_int M2) _let_1) (= _let_1 M2)))) (forall ((N tptp.assn) (M2 tptp.assn)) (let ((_let_1 (@ (@ tptp.ord_min_assn M2) N))) (= (@ (@ tptp.ord_less_eq_assn N) _let_1) (= _let_1 N)))) (forall ((N tptp.filter_nat) (M2 tptp.filter_nat)) (let ((_let_1 (@ (@ tptp.ord_min_filter_nat M2) N))) (= (@ (@ tptp.ord_le2510731241096832064er_nat N) _let_1) (= _let_1 N)))) (forall ((N tptp.set_nat) (M2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.ord_min_set_nat M2) N))) (= (@ (@ tptp.ord_less_eq_set_nat N) _let_1) (= _let_1 N)))) (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_min_nat M2) N))) (= (@ (@ tptp.ord_less_eq_nat N) _let_1) (= _let_1 N)))) (forall ((N tptp.int) (M2 tptp.int)) (let ((_let_1 (@ (@ tptp.ord_min_int M2) N))) (= (@ (@ tptp.ord_less_eq_int N) _let_1) (= _let_1 N)))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.ord_min_nat M2) N) N) (@ (@ tptp.ord_less_eq_nat N) M2))) (forall ((M2 tptp.int) (N tptp.int)) (= (= (@ (@ tptp.ord_min_int M2) N) N) (@ (@ tptp.ord_less_eq_int N) M2))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.ord_min_nat M2) N) M2) (@ (@ tptp.ord_less_eq_nat M2) N))) (forall ((M2 tptp.int) (N tptp.int)) (= (= (@ (@ tptp.ord_min_int M2) N) M2) (@ (@ tptp.ord_less_eq_int M2) N))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= (@ (@ tptp.ord_min_nat A2) B2) A2))) (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (= (@ (@ tptp.ord_min_int A2) B2) A2))) (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (= (@ (@ tptp.ord_min_nat A2) B2) B2))) (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (= (@ (@ tptp.ord_min_int A2) B2) B2))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (= (@ _let_1 (@ (@ tptp.ord_min_nat B2) C)) (and (@ _let_1 B2) (@ _let_1 C))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A2))) (= (@ _let_1 (@ (@ tptp.ord_min_int B2) C)) (and (@ _let_1 B2) (@ _let_1 C))))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A) B)) C2) (and (@ (@ tptp.ord_le1268244103169919719at_nat A) C2) (@ (@ tptp.ord_le1268244103169919719at_nat B) C2)))) (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat A) B)) C2) (and (@ (@ tptp.ord_less_eq_set_nat A) C2) (@ (@ tptp.ord_less_eq_set_nat B) C2)))) (forall ((A tptp.set_int) (A2 tptp.int) (B tptp.set_int)) (let ((_let_1 (@ tptp.sup_sup_set_int A))) (let ((_let_2 (@ tptp.insert_int2 A2))) (= (@ _let_1 (@ _let_2 B)) (@ _let_2 (@ _let_1 B)))))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (A2 tptp.product_prod_nat_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.sup_su6327502436637775413at_nat A))) (let ((_let_2 (@ tptp.insert8211810215607154385at_nat A2))) (= (@ _let_1 (@ _let_2 B)) (@ _let_2 (@ _let_1 B)))))) (forall ((A tptp.set_o) (A2 Bool) (B tptp.set_o)) (let ((_let_1 (@ tptp.sup_sup_set_o A))) (let ((_let_2 (@ tptp.insert_o2 A2))) (= (@ _let_1 (@ _let_2 B)) (@ _let_2 (@ _let_1 B)))))) (forall ((A tptp.set_nat) (A2 tptp.nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A))) (let ((_let_2 (@ tptp.insert_nat2 A2))) (= (@ _let_1 (@ _let_2 B)) (@ _let_2 (@ _let_1 B)))))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (A2 tptp.produc3843707927480180839at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat A))) (let ((_let_2 (@ tptp.insert9069300056098147895at_nat A2))) (= (@ _let_1 (@ _let_2 B)) (@ _let_2 (@ _let_1 B)))))) (forall ((A2 tptp.int) (B tptp.set_int) (C2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int2 A2))) (= (@ (@ tptp.sup_sup_set_int (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.sup_sup_set_int B) C2))))) (forall ((A2 tptp.product_prod_nat_nat) (B tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A2))) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat B) C2))))) (forall ((A2 Bool) (B tptp.set_o) (C2 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o2 A2))) (= (@ (@ tptp.sup_sup_set_o (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.sup_sup_set_o B) C2))))) (forall ((A2 tptp.nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat2 A2))) (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.sup_sup_set_nat B) C2))))) (forall ((A2 tptp.produc3843707927480180839at_nat) (B tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.insert9069300056098147895at_nat A2))) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat B) C2))))) (forall ((Z tptp.code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger Z))) (= (@ _let_1 (@ (@ tptp.ord_min_Code_integer X) Y)) (and (@ _let_1 X) (@ _let_1 Y))))) (forall ((Z tptp.num) (X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.ord_less_num Z))) (= (@ _let_1 (@ (@ tptp.ord_min_num X) Y)) (and (@ _let_1 X) (@ _let_1 Y))))) (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat Z))) (= (@ _let_1 (@ (@ tptp.ord_min_nat X) Y)) (and (@ _let_1 X) (@ _let_1 Y))))) (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_int Z))) (= (@ _let_1 (@ (@ tptp.ord_min_int X) Y)) (and (@ _let_1 X) (@ _let_1 Y))))) (forall ((B2 tptp.code_integer) (A2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) A2) (= (@ (@ tptp.ord_min_Code_integer A2) B2) B2))) (forall ((B2 tptp.num) (A2 tptp.num)) (=> (@ (@ tptp.ord_less_num B2) A2) (= (@ (@ tptp.ord_min_num A2) B2) B2))) (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A2) (= (@ (@ tptp.ord_min_nat A2) B2) B2))) (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A2) (= (@ (@ tptp.ord_min_int A2) B2) B2))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (= (@ (@ tptp.ord_min_Code_integer A2) B2) A2))) (forall ((A2 tptp.num) (B2 tptp.num)) (=> (@ (@ tptp.ord_less_num A2) B2) (= (@ (@ tptp.ord_min_num A2) B2) A2))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (= (@ (@ tptp.ord_min_nat A2) B2) A2))) (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (= (@ (@ tptp.ord_min_int A2) B2) A2))) (forall ((M2 tptp.code_integer) (N tptp.code_integer)) (let ((_let_1 (@ (@ tptp.ord_min_Code_integer M2) N))) (= (not (@ (@ tptp.ord_le6747313008572928689nteger _let_1) M2)) (= _let_1 M2)))) (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ (@ tptp.ord_min_num M2) N))) (= (not (@ (@ tptp.ord_less_num _let_1) M2)) (= _let_1 M2)))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_min_nat M2) N))) (= (not (@ (@ tptp.ord_less_nat _let_1) M2)) (= _let_1 M2)))) (forall ((M2 tptp.int) (N tptp.int)) (let ((_let_1 (@ (@ tptp.ord_min_int M2) N))) (= (not (@ (@ tptp.ord_less_int _let_1) M2)) (= _let_1 M2)))) (forall ((M2 tptp.code_integer) (N tptp.code_integer)) (let ((_let_1 (@ (@ tptp.ord_min_Code_integer M2) N))) (= (not (@ (@ tptp.ord_le6747313008572928689nteger _let_1) N)) (= _let_1 N)))) (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ (@ tptp.ord_min_num M2) N))) (= (not (@ (@ tptp.ord_less_num _let_1) N)) (= _let_1 N)))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_min_nat M2) N))) (= (not (@ (@ tptp.ord_less_nat _let_1) N)) (= _let_1 N)))) (forall ((M2 tptp.int) (N tptp.int)) (let ((_let_1 (@ (@ tptp.ord_min_int M2) N))) (= (not (@ (@ tptp.ord_less_int _let_1) N)) (= _let_1 N)))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.ord_min_Code_integer A2) B2)) A2) (@ (@ tptp.ord_le6747313008572928689nteger B2) A2))) (forall ((A2 tptp.num) (B2 tptp.num)) (= (@ (@ tptp.ord_less_num (@ (@ tptp.ord_min_num A2) B2)) A2) (@ (@ tptp.ord_less_num B2) A2))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_min_nat A2) B2)) A2) (@ (@ tptp.ord_less_nat B2) A2))) (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.ord_min_int A2) B2)) A2) (@ (@ tptp.ord_less_int B2) A2))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.ord_min_Code_integer A2) B2)) B2) (@ (@ tptp.ord_le6747313008572928689nteger A2) B2))) (forall ((A2 tptp.num) (B2 tptp.num)) (= (@ (@ tptp.ord_less_num (@ (@ tptp.ord_min_num A2) B2)) B2) (@ (@ tptp.ord_less_num A2) B2))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_min_nat A2) B2)) B2) (@ (@ tptp.ord_less_nat A2) B2))) (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.ord_min_int A2) B2)) B2) (@ (@ tptp.ord_less_int A2) B2))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (= (@ (@ tptp.ord_min_Code_integer A2) B2) A2))) (forall ((A2 tptp.assn) (B2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn A2) B2) (= (@ (@ tptp.ord_min_assn A2) B2) A2))) (forall ((A2 tptp.num) (B2 tptp.num)) (=> (@ (@ tptp.ord_less_num A2) B2) (= (@ (@ tptp.ord_min_num A2) B2) A2))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (= (@ (@ tptp.ord_min_nat A2) B2) A2))) (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (= (@ (@ tptp.ord_min_int A2) B2) A2))) (forall ((B2 tptp.code_integer) (A2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) A2) (= (@ (@ tptp.ord_min_Code_integer A2) B2) B2))) (forall ((B2 tptp.assn) (A2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn B2) A2) (= (@ (@ tptp.ord_min_assn A2) B2) B2))) (forall ((B2 tptp.num) (A2 tptp.num)) (=> (@ (@ tptp.ord_less_num B2) A2) (= (@ (@ tptp.ord_min_num A2) B2) B2))) (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A2) (= (@ (@ tptp.ord_min_nat A2) B2) B2))) (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A2) (= (@ (@ tptp.ord_min_int A2) B2) B2))) (forall ((X tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_mi6693596345299712430at_nat X) tptp.bot_bo228742789529271731at_nat) tptp.bot_bo228742789529271731at_nat)) (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_mi4194197829855655752at_nat X) tptp.bot_bo2099793752762293965at_nat) tptp.bot_bo2099793752762293965at_nat)) (forall ((X tptp.set_o)) (= (@ (@ tptp.ord_min_set_o X) tptp.bot_bot_set_o) tptp.bot_bot_set_o)) (forall ((X tptp.set_nat)) (= (@ (@ tptp.ord_min_set_nat X) tptp.bot_bot_set_nat) tptp.bot_bot_set_nat)) (forall ((X tptp.set_int)) (= (@ (@ tptp.ord_min_set_int X) tptp.bot_bot_set_int) tptp.bot_bot_set_int)) (forall ((X tptp.nat)) (= (@ (@ tptp.ord_min_nat X) tptp.bot_bot_nat) tptp.bot_bot_nat)) (forall ((X tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_mi6693596345299712430at_nat tptp.bot_bo228742789529271731at_nat) X) tptp.bot_bo228742789529271731at_nat)) (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_mi4194197829855655752at_nat tptp.bot_bo2099793752762293965at_nat) X) tptp.bot_bo2099793752762293965at_nat)) (forall ((X tptp.set_o)) (= (@ (@ tptp.ord_min_set_o tptp.bot_bot_set_o) X) tptp.bot_bot_set_o)) (forall ((X tptp.set_nat)) (= (@ (@ tptp.ord_min_set_nat tptp.bot_bot_set_nat) X) tptp.bot_bot_set_nat)) (forall ((X tptp.set_int)) (= (@ (@ tptp.ord_min_set_int tptp.bot_bot_set_int) X) tptp.bot_bot_set_int)) (forall ((X tptp.nat)) (= (@ (@ tptp.ord_min_nat tptp.bot_bot_nat) X) tptp.bot_bot_nat)) (forall ((T3 tptp.set_Pr1261947904930325089at_nat) (S tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat T3) (@ (@ tptp.inf_in2572325071724192079at_nat S) T3)) T3)) (forall ((T3 tptp.set_nat) (S tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat T3) (@ (@ tptp.inf_inf_set_nat S) T3)) T3)) (forall ((T3 tptp.set_Pr4329608150637261639at_nat) (S tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat T3) (@ (@ tptp.inf_in7913087082777306421at_nat S) T3)) T3)) (forall ((S tptp.set_Pr1261947904930325089at_nat) (T3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat S) (@ (@ tptp.inf_in2572325071724192079at_nat S) T3)) S)) (forall ((S tptp.set_nat) (T3 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat S) (@ (@ tptp.inf_inf_set_nat S) T3)) S)) (forall ((S tptp.set_Pr4329608150637261639at_nat) (T3 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat S) (@ (@ tptp.inf_in7913087082777306421at_nat S) T3)) S)) (forall ((S tptp.set_Pr1261947904930325089at_nat) (T3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat S) T3)) T3) T3)) (forall ((S tptp.set_nat) (T3 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat S) T3)) T3) T3)) (forall ((S tptp.set_Pr4329608150637261639at_nat) (T3 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat S) T3)) T3) T3)) (forall ((S tptp.set_Pr1261947904930325089at_nat) (T3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat S) T3)) S) S)) (forall ((S tptp.set_nat) (T3 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat S) T3)) S) S)) (forall ((S tptp.set_Pr4329608150637261639at_nat) (T3 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat S) T3)) S) S)) (forall ((T3 tptp.set_Pr1261947904930325089at_nat) (S tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat T3) (@ (@ tptp.sup_su6327502436637775413at_nat S) T3)) T3)) (forall ((T3 tptp.set_nat) (S tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat T3) (@ (@ tptp.sup_sup_set_nat S) T3)) T3)) (forall ((T3 tptp.set_Pr4329608150637261639at_nat) (S tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat T3) (@ (@ tptp.sup_su5525570899277871387at_nat S) T3)) T3)) (forall ((S tptp.set_Pr1261947904930325089at_nat) (T3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat S) (@ (@ tptp.sup_su6327502436637775413at_nat S) T3)) S)) (forall ((S tptp.set_nat) (T3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat S) (@ (@ tptp.sup_sup_set_nat S) T3)) S)) (forall ((S tptp.set_Pr4329608150637261639at_nat) (T3 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat S) (@ (@ tptp.sup_su5525570899277871387at_nat S) T3)) S)) (forall ((S tptp.set_Pr1261947904930325089at_nat) (T3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat S) T3)) T3) T3)) (forall ((S tptp.set_nat) (T3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat S) T3)) T3) T3)) (forall ((S tptp.set_Pr4329608150637261639at_nat) (T3 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.sup_su5525570899277871387at_nat S) T3)) T3) T3)) (forall ((S tptp.set_Pr1261947904930325089at_nat) (T3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat S) T3)) S) S)) (forall ((S tptp.set_nat) (T3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat S) T3)) S) S)) (forall ((S tptp.set_Pr4329608150637261639at_nat) (T3 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.sup_su5525570899277871387at_nat S) T3)) S) S)) (forall ((B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.minus_3314409938677909166at_nat B) A)) A) (@ (@ tptp.sup_su5525570899277871387at_nat B) A))) (forall ((B tptp.set_nat) (A tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.minus_minus_set_nat B) A)) A) (@ (@ tptp.sup_sup_set_nat B) A))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat A))) (= (@ _let_1 (@ (@ tptp.minus_3314409938677909166at_nat B) A)) (@ _let_1 B)))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat B) A)) (@ _let_1 B)))) (forall ((Xs tptp.list_int)) (= (@ tptp.set_int2 (@ tptp.rev_int Xs)) (@ tptp.set_int2 Xs))) (forall ((Xs tptp.list_nat)) (= (@ tptp.set_nat2 (@ tptp.rev_nat Xs)) (@ tptp.set_nat2 Xs))) (forall ((Xs tptp.list_P8527749157015355191n_assn)) (= (@ tptp.set_Pr1139785259514867910n_assn (@ tptp.rev_Pr4855572775806611735n_assn Xs)) (@ tptp.set_Pr1139785259514867910n_assn Xs))) (forall ((Xs tptp.list_c)) (= (@ tptp.size_size_list_c (@ tptp.rev_c Xs)) (@ tptp.size_size_list_c Xs))) (forall ((Xs tptp.list_d)) (= (@ tptp.size_size_list_d (@ tptp.rev_d Xs)) (@ tptp.size_size_list_d Xs))) (forall ((Xs tptp.list_nat)) (= (@ tptp.size_size_list_nat (@ tptp.rev_nat Xs)) (@ tptp.size_size_list_nat Xs))) (forall ((Xs tptp.list_int)) (= (@ tptp.size_size_list_int (@ tptp.rev_int Xs)) (@ tptp.size_size_list_int Xs))) (forall ((Xs tptp.list_int)) (= (@ tptp.distinct_int (@ tptp.rev_int Xs)) (@ tptp.distinct_int Xs))) (forall ((Xs tptp.list_nat)) (= (@ tptp.distinct_nat (@ tptp.rev_nat Xs)) (@ tptp.distinct_nat Xs))) (forall ((Xs tptp.list_int)) (= (@ tptp.set_int2 (@ tptp.rotate1_int Xs)) (@ tptp.set_int2 Xs))) (forall ((Xs tptp.list_nat)) (= (@ tptp.set_nat2 (@ tptp.rotate1_nat Xs)) (@ tptp.set_nat2 Xs))) (forall ((Xs tptp.list_P8527749157015355191n_assn)) (= (@ tptp.set_Pr1139785259514867910n_assn (@ tptp.rotate328796349445179396n_assn Xs)) (@ tptp.set_Pr1139785259514867910n_assn Xs))) (forall ((Xs tptp.list_c)) (= (@ tptp.size_size_list_c (@ tptp.rotate1_c Xs)) (@ tptp.size_size_list_c Xs))) (forall ((Xs tptp.list_d)) (= (@ tptp.size_size_list_d (@ tptp.rotate1_d Xs)) (@ tptp.size_size_list_d Xs))) (forall ((Xs tptp.list_nat)) (= (@ tptp.size_size_list_nat (@ tptp.rotate1_nat Xs)) (@ tptp.size_size_list_nat Xs))) (forall ((Xs tptp.list_int)) (= (@ tptp.size_size_list_int (@ tptp.rotate1_int Xs)) (@ tptp.size_size_list_int Xs))) (forall ((Xs tptp.list_int)) (= (@ tptp.distinct_int (@ tptp.rotate1_int Xs)) (@ tptp.distinct_int Xs))) (forall ((Xs tptp.list_nat)) (= (@ tptp.distinct_nat (@ tptp.rotate1_nat Xs)) (@ tptp.distinct_nat Xs))) (forall ((P (-> tptp.int Bool)) (Xs tptp.list_int)) (let ((_let_1 (@ tptp.list_ex_int P))) (= (@ _let_1 (@ tptp.rev_int Xs)) (@ _let_1 Xs)))) (forall ((P (-> tptp.nat Bool)) (Xs tptp.list_nat)) (let ((_let_1 (@ tptp.list_ex_nat P))) (= (@ _let_1 (@ tptp.rev_nat Xs)) (@ _let_1 Xs)))) (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (= (@ tptp.set_int2 (@ (@ tptp.union_int Xs) Ys)) (@ (@ tptp.sup_sup_set_int (@ tptp.set_int2 Xs)) (@ tptp.set_int2 Ys)))) (forall ((Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_P8527749157015355191n_assn)) (= (@ tptp.set_Pr1139785259514867910n_assn (@ (@ tptp.union_944050417204428971n_assn Xs) Ys)) (@ (@ tptp.sup_su1735938885662425829n_assn (@ tptp.set_Pr1139785259514867910n_assn Xs)) (@ tptp.set_Pr1139785259514867910n_assn Ys)))) (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (= (@ tptp.set_nat2 (@ (@ tptp.union_nat Xs) Ys)) (@ (@ tptp.sup_sup_set_nat (@ tptp.set_nat2 Xs)) (@ tptp.set_nat2 Ys)))) (forall ((Xs tptp.list_P5464809261938338413at_nat) (Ys tptp.list_P5464809261938338413at_nat)) (= (@ tptp.set_Pr3765526544606949372at_nat (@ (@ tptp.union_4462254032241401953at_nat Xs) Ys)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ tptp.set_Pr3765526544606949372at_nat Xs)) (@ tptp.set_Pr3765526544606949372at_nat Ys)))) (forall ((Xs tptp.list_c)) (= (@ tptp.size_size_list_c (@ tptp.butlast_c Xs)) (@ (@ tptp.minus_minus_nat (@ tptp.size_size_list_c Xs)) tptp.one_one_nat))) (forall ((Xs tptp.list_d)) (= (@ tptp.size_size_list_d (@ tptp.butlast_d Xs)) (@ (@ tptp.minus_minus_nat (@ tptp.size_size_list_d Xs)) tptp.one_one_nat))) (forall ((Xs tptp.list_nat)) (= (@ tptp.size_size_list_nat (@ tptp.butlast_nat Xs)) (@ (@ tptp.minus_minus_nat (@ tptp.size_size_list_nat Xs)) tptp.one_one_nat))) (forall ((Xs tptp.list_int)) (= (@ tptp.size_size_list_int (@ tptp.butlast_int Xs)) (@ (@ tptp.minus_minus_nat (@ tptp.size_size_list_int Xs)) tptp.one_one_nat))) (forall ((C tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat A) B)) (not (=> (@ _let_1 A) (not (@ _let_1 B))))))) (forall ((C tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_int A) B)) (not (=> (@ _let_1 A) (not (@ _let_1 B))))))) (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ _let_1 (@ (@ tptp.inf_in1906310914598751387_nat_o A) B)) (not (=> (@ _let_1 A) (not (@ _let_1 B))))))) (forall ((C tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B)) (not (=> (@ _let_1 A) (not (@ _let_1 B))))))) (forall ((C tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) (not (=> (@ _let_1 A) (not (@ _let_1 B))))))) (forall ((C tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat A) B)) (@ _let_1 A)))) (forall ((C tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_int A) B)) (@ _let_1 A)))) (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ _let_1 (@ (@ tptp.inf_in1906310914598751387_nat_o A) B)) (@ _let_1 A)))) (forall ((C tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B)) (@ _let_1 A)))) (forall ((C tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) (@ _let_1 A)))) (forall ((C tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat A) B)) (@ _let_1 B)))) (forall ((C tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_int A) B)) (@ _let_1 B)))) (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ _let_1 (@ (@ tptp.inf_in1906310914598751387_nat_o A) B)) (@ _let_1 B)))) (forall ((C tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B)) (@ _let_1 B)))) (forall ((C tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) (@ _let_1 B)))) (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (= (@ (@ tptp.inf_inf_set_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.inf_inf_set_nat B) C2))))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A))) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B) C2))))) (forall ((A tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A) A) A)) (forall ((A tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A) A) A)) (= tptp.inf_inf_set_nat (lambda ((A5 tptp.set_nat) (B7 tptp.set_nat)) (@ (@ tptp.inf_inf_set_nat B7) A5))) (= tptp.inf_in2572325071724192079at_nat (lambda ((A5 tptp.set_Pr1261947904930325089at_nat) (B7 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.inf_in2572325071724192079at_nat B7) A5))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) (@ (@ tptp.inf_in2572325071724192079at_nat B) C2))) (@ (@ tptp.inf_in2572325071724192079at_nat C2) A)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat A) B)) (@ (@ tptp.sup_su6327502436637775413at_nat B) C2))) (@ (@ tptp.sup_su6327502436637775413at_nat C2) A)))) (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) (@ (@ tptp.inf_inf_set_nat B) C2))) (@ (@ tptp.inf_inf_set_nat C2) A)) (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat A) B)) (@ (@ tptp.sup_sup_set_nat B) C2))) (@ (@ tptp.sup_sup_set_nat C2) A)))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat A) B)) (@ (@ tptp.inf_in7913087082777306421at_nat B) C2))) (@ (@ tptp.inf_in7913087082777306421at_nat C2) A)) (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A) B)) (@ (@ tptp.sup_su5525570899277871387at_nat B) C2))) (@ (@ tptp.sup_su5525570899277871387at_nat C2) A)))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A))) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat B) C2)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 B)) (@ _let_1 C2))))) (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat B) C2)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 B)) (@ _let_1 C2))))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.inf_in7913087082777306421at_nat A))) (= (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat B) C2)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 B)) (@ _let_1 C2))))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.sup_su6327502436637775413at_nat A))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B) C2)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 B)) (@ _let_1 C2))))) (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat B) C2)) (@ (@ tptp.inf_inf_set_nat (@ _let_1 B)) (@ _let_1 C2))))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat A))) (= (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat B) C2)) (@ (@ tptp.inf_in7913087082777306421at_nat (@ _let_1 B)) (@ _let_1 C2))))) (forall ((B tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat B) C2)) A) (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat B) A)) (@ (@ tptp.inf_in2572325071724192079at_nat C2) A)))) (forall ((B tptp.set_nat) (C2 tptp.set_nat) (A tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat B) C2)) A) (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat B) A)) (@ (@ tptp.inf_inf_set_nat C2) A)))) (forall ((B tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.sup_su5525570899277871387at_nat B) C2)) A) (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat B) A)) (@ (@ tptp.inf_in7913087082777306421at_nat C2) A)))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))) (forall ((B tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat B) C2)) A) (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat B) A)) (@ (@ tptp.sup_su6327502436637775413at_nat C2) A)))) (forall ((B tptp.set_nat) (C2 tptp.set_nat) (A tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat B) C2)) A) (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat B) A)) (@ (@ tptp.sup_sup_set_nat C2) A)))) (forall ((B tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat B) C2)) A) (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.sup_su5525570899277871387at_nat B) A)) (@ (@ tptp.sup_su5525570899277871387at_nat C2) A)))) (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (let ((_let_2 (@ tptp.inf_inf_set_nat B))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A))) (let ((_let_2 (@ tptp.inf_in2572325071724192079at_nat B))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))) (= tptp.ord_less_assn (lambda ((A3 tptp.assn) (B3 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn A3) B3) (not (= A3 B3))))) (forall ((C tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat A) B)) (=> (not (@ _let_1 A)) (@ _let_1 B))))) (forall ((C tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.sup_sup_set_int A) B)) (=> (not (@ _let_1 A)) (@ _let_1 B))))) (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ _let_1 (@ (@ tptp.sup_su5209123915105501825_nat_o A) B)) (=> (not (@ _let_1 A)) (@ _let_1 B))))) (forall ((C tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B)) (=> (not (@ _let_1 A)) (@ _let_1 B))))) (forall ((C tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (=> (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A) B)) (=> (not (@ _let_1 A)) (@ _let_1 B))))) (forall ((C tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat A) B))))) (forall ((C tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_set_int A) B))))) (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su5209123915105501825_nat_o A) B))))) (forall ((C tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B))))) (forall ((C tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A) B))))) (forall ((C tptp.product_prod_nat_nat) (B tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat A) B))))) (forall ((C tptp.int) (B tptp.set_int) (A tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_set_int A) B))))) (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.set_Pr4532377907799695533_nat_o) (A tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su5209123915105501825_nat_o A) B))))) (forall ((C tptp.nat) (B tptp.set_nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B))))) (forall ((C tptp.produc3843707927480180839at_nat) (B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A) B))))) (forall ((A tptp.set_nat) (B tptp.set_nat) (P (-> tptp.nat Bool))) (= (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) (@ (@ tptp.sup_sup_set_nat A) B)) (@ P X2))) (or (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A) (@ P X2))) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) B) (@ P X2)))))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (P (-> tptp.produc3843707927480180839at_nat Bool))) (= (exists ((X2 tptp.produc3843707927480180839at_nat)) (and (@ (@ tptp.member8757157785044589968at_nat X2) (@ (@ tptp.sup_su5525570899277871387at_nat A) B)) (@ P X2))) (or (exists ((X2 tptp.produc3843707927480180839at_nat)) (and (@ (@ tptp.member8757157785044589968at_nat X2) A) (@ P X2))) (exists ((X2 tptp.produc3843707927480180839at_nat)) (and (@ (@ tptp.member8757157785044589968at_nat X2) B) (@ P X2)))))) (forall ((A tptp.set_nat) (B tptp.set_nat) (P (-> tptp.nat Bool))) (= (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.sup_sup_set_nat A) B)) (@ P X2))) (and (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A) (@ P X2))) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) B) (@ P X2)))))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (P (-> tptp.produc3843707927480180839at_nat Bool))) (= (forall ((X2 tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X2) (@ (@ tptp.sup_su5525570899277871387at_nat A) B)) (@ P X2))) (and (forall ((X2 tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X2) A) (@ P X2))) (forall ((X2 tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X2) B) (@ P X2)))))) (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))))) (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))))) (forall ((A tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A) A) A)) (forall ((A tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat A) A) A)) (= tptp.sup_sup_set_nat (lambda ((A5 tptp.set_nat) (B7 tptp.set_nat)) (@ (@ tptp.sup_sup_set_nat B7) A5))) (= tptp.sup_su5525570899277871387at_nat (lambda ((A5 tptp.set_Pr4329608150637261639at_nat) (B7 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.sup_su5525570899277871387at_nat B7) A5))) (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)))) (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)))) (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A))) (let ((_let_2 (@ tptp.sup_sup_set_nat B))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat A))) (let ((_let_2 (@ tptp.sup_su5525570899277871387at_nat B))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))) (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)))) (forall ((X tptp.assn) (Y tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))) (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)))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (let ((_let_2 (@ tptp.sup_sup_set_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (let ((_let_2 (@ tptp.sup_sup_assn Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat X))) (let ((_let_2 (@ tptp.sup_su5525570899277871387at_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_sup_set_nat Y) Z))))) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (= (@ (@ tptp.sup_sup_assn (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_sup_assn Y) Z))))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat X))) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat Y) Z))))) (= tptp.sup_sup_set_nat (lambda ((X2 tptp.set_nat) (Y5 tptp.set_nat)) (@ (@ tptp.sup_sup_set_nat Y5) X2))) (= tptp.sup_sup_assn (lambda ((X2 tptp.assn) (Y5 tptp.assn)) (@ (@ tptp.sup_sup_assn Y5) X2))) (= tptp.sup_su5525570899277871387at_nat (lambda ((X2 tptp.set_Pr4329608150637261639at_nat) (Y5 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.sup_su5525570899277871387at_nat Y5) X2))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_min_nat A2))) (= (@ (@ tptp.ord_min_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.ord_min_nat B2) C))))) (= tptp.ord_min_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.ord_min_nat B3) A3))) (forall ((B2 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_min_nat B2))) (let ((_let_2 (@ tptp.ord_min_nat A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A2))) (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.sup_sup_set_nat B2) C))))) (forall ((A2 tptp.assn) (B2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn A2))) (= (@ (@ tptp.sup_sup_assn (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.sup_sup_assn B2) C))))) (forall ((A2 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat) (C tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat A2))) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat B2) C))))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_sup_set_nat Y) Z))))) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (= (@ (@ tptp.sup_sup_assn (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_sup_assn Y) Z))))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat X))) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat Y) Z))))) (= tptp.sup_sup_set_nat (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (@ (@ tptp.sup_sup_set_nat B3) A3))) (= tptp.sup_sup_assn (lambda ((A3 tptp.assn) (B3 tptp.assn)) (@ (@ tptp.sup_sup_assn B3) A3))) (= tptp.sup_su5525570899277871387at_nat (lambda ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.sup_su5525570899277871387at_nat B3) A3))) (= tptp.sup_sup_set_nat (lambda ((X2 tptp.set_nat) (Y5 tptp.set_nat)) (@ (@ tptp.sup_sup_set_nat Y5) X2))) (= tptp.sup_sup_assn (lambda ((X2 tptp.assn) (Y5 tptp.assn)) (@ (@ tptp.sup_sup_assn Y5) X2))) (= tptp.sup_su5525570899277871387at_nat (lambda ((X2 tptp.set_Pr4329608150637261639at_nat) (Y5 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.sup_su5525570899277871387at_nat Y5) X2))) (forall ((B2 tptp.set_nat) (A2 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat B2))) (let ((_let_2 (@ tptp.sup_sup_set_nat A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((B2 tptp.assn) (A2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn B2))) (let ((_let_2 (@ tptp.sup_sup_assn A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((B2 tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat) (C tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat B2))) (let ((_let_2 (@ tptp.sup_su5525570899277871387at_nat A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (let ((_let_2 (@ tptp.sup_sup_set_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (let ((_let_2 (@ tptp.sup_sup_assn Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat X))) (let ((_let_2 (@ tptp.sup_su5525570899277871387at_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((Xs tptp.list_c) (Ys tptp.list_c)) (=> (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_c Ys)) (= (@ (@ tptp.zip_c_c (@ tptp.rev_c Xs)) (@ tptp.rev_c Ys)) (@ tptp.rev_Product_prod_c_c (@ (@ tptp.zip_c_c Xs) Ys))))) (forall ((Xs tptp.list_c) (Ys tptp.list_d)) (=> (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_d Ys)) (= (@ (@ tptp.zip_c_d (@ tptp.rev_c Xs)) (@ tptp.rev_d Ys)) (@ tptp.rev_Product_prod_c_d (@ (@ tptp.zip_c_d Xs) Ys))))) (forall ((Xs tptp.list_c) (Ys tptp.list_nat)) (=> (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_nat Ys)) (= (@ (@ tptp.zip_c_nat (@ tptp.rev_c Xs)) (@ tptp.rev_nat Ys)) (@ tptp.rev_Pr3799340238495523993_c_nat (@ (@ tptp.zip_c_nat Xs) Ys))))) (forall ((Xs tptp.list_c) (Ys tptp.list_int)) (=> (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_int Ys)) (= (@ (@ tptp.zip_c_int (@ tptp.rev_c Xs)) (@ tptp.rev_int Ys)) (@ tptp.rev_Pr8844861255841103093_c_int (@ (@ tptp.zip_c_int Xs) Ys))))) (forall ((Xs tptp.list_d) (Ys tptp.list_c)) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_c Ys)) (= (@ (@ tptp.zip_d_c (@ tptp.rev_d Xs)) (@ tptp.rev_c Ys)) (@ tptp.rev_Product_prod_d_c (@ (@ tptp.zip_d_c Xs) Ys))))) (forall ((Xs tptp.list_d) (Ys tptp.list_d)) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_d Ys)) (= (@ (@ tptp.zip_d_d (@ tptp.rev_d Xs)) (@ tptp.rev_d Ys)) (@ tptp.rev_Product_prod_d_d (@ (@ tptp.zip_d_d Xs) Ys))))) (forall ((Xs tptp.list_d) (Ys tptp.list_nat)) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_nat Ys)) (= (@ (@ tptp.zip_d_nat (@ tptp.rev_d Xs)) (@ tptp.rev_nat Ys)) (@ tptp.rev_Pr5034784567451918490_d_nat (@ (@ tptp.zip_d_nat Xs) Ys))))) (forall ((Xs tptp.list_d) (Ys tptp.list_int)) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_int Ys)) (= (@ (@ tptp.zip_d_int (@ tptp.rev_d Xs)) (@ tptp.rev_int Ys)) (@ tptp.rev_Pr856933547942721782_d_int (@ (@ tptp.zip_d_int Xs) Ys))))) (forall ((Xs tptp.list_nat) (Ys tptp.list_c)) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_c Ys)) (= (@ (@ tptp.zip_nat_c (@ tptp.rev_nat Xs)) (@ tptp.rev_c Ys)) (@ tptp.rev_Pr4566615052912869567_nat_c (@ (@ tptp.zip_nat_c Xs) Ys))))) (forall ((Xs tptp.list_nat) (Ys tptp.list_d)) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_d Ys)) (= (@ (@ tptp.zip_nat_d (@ tptp.rev_nat Xs)) (@ tptp.rev_d Ys)) (@ tptp.rev_Pr4566615057216098368_nat_d (@ (@ tptp.zip_nat_d Xs) Ys))))) (forall ((Ns tptp.list_nat) (I tptp.nat)) (=> (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) Ns) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Ns)) (@ (@ tptp.ord_less_eq_nat I) (@ (@ tptp.nth_nat Ns) I))))) (forall ((Xs tptp.list_P5464809261938338413at_nat) (P (-> tptp.produc3843707927480180839at_nat tptp.produc3843707927480180839at_nat Bool)) (Q (-> tptp.produc3843707927480180839at_nat tptp.produc3843707927480180839at_nat Bool))) (=> (forall ((X3 tptp.produc3843707927480180839at_nat) (Y2 tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.set_Pr3765526544606949372at_nat Xs))) (=> (@ (@ tptp.member8757157785044589968at_nat X3) _let_1) (=> (@ (@ tptp.member8757157785044589968at_nat Y2) _let_1) (=> (@ (@ P X3) Y2) (@ (@ Q X3) Y2)))))) (=> (@ (@ tptp.sorted8831241538929206612at_nat P) Xs) (@ (@ tptp.sorted8831241538929206612at_nat Q) Xs)))) (forall ((Xs tptp.list_P6011104703257516679at_nat) (P (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (Q (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool))) (=> (forall ((X3 tptp.product_prod_nat_nat) (Y2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.set_Pr5648618587558075414at_nat Xs))) (=> (@ (@ tptp.member8440522571783428010at_nat X3) _let_1) (=> (@ (@ tptp.member8440522571783428010at_nat Y2) _let_1) (=> (@ (@ P X3) Y2) (@ (@ Q X3) Y2)))))) (=> (@ (@ tptp.sorted5214655850825725294at_nat P) Xs) (@ (@ tptp.sorted5214655850825725294at_nat Q) Xs)))) (forall ((Xs tptp.list_P7985473006766602707_nat_o) (P (-> (-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) Bool)) (Q (-> (-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.set_Pr400311997697478754_nat_o Xs))) (=> (@ (@ tptp.member6576561426505652726_nat_o X3) _let_1) (=> (@ (@ tptp.member6576561426505652726_nat_o Y2) _let_1) (=> (@ (@ P X3) Y2) (@ (@ Q X3) Y2)))))) (=> (@ (@ tptp.sorted9199660237762088378_nat_o P) Xs) (@ (@ tptp.sorted9199660237762088378_nat_o Q) Xs)))) (forall ((Xs tptp.list_P8527749157015355191n_assn) (P (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn Bool)) (Q (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn Bool))) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Y2 tptp.produc6575502325842934193n_assn)) (let ((_let_1 (@ tptp.set_Pr1139785259514867910n_assn Xs))) (=> (@ (@ tptp.member7957490590177025114n_assn X3) _let_1) (=> (@ (@ tptp.member7957490590177025114n_assn Y2) _let_1) (=> (@ (@ P X3) Y2) (@ (@ Q X3) Y2)))))) (=> (@ (@ tptp.sorted3986126766855596574n_assn P) Xs) (@ (@ tptp.sorted3986126766855596574n_assn Q) Xs)))) (forall ((Xs tptp.list_nat) (P (-> tptp.nat tptp.nat Bool)) (Q (-> tptp.nat tptp.nat Bool))) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.set_nat2 Xs))) (=> (@ (@ tptp.member_nat X3) _let_1) (=> (@ (@ tptp.member_nat Y2) _let_1) (=> (@ (@ P X3) Y2) (@ (@ Q X3) Y2)))))) (=> (@ (@ tptp.sorted_wrt_nat P) Xs) (@ (@ tptp.sorted_wrt_nat Q) Xs)))) (forall ((Xs tptp.list_int) (P (-> tptp.int tptp.int Bool)) (Q (-> tptp.int tptp.int Bool))) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.set_int2 Xs))) (=> (@ (@ tptp.member_int X3) _let_1) (=> (@ (@ tptp.member_int Y2) _let_1) (=> (@ (@ P X3) Y2) (@ (@ Q X3) Y2)))))) (=> (@ (@ tptp.sorted_wrt_int P) Xs) (@ (@ tptp.sorted_wrt_int Q) Xs)))) _let_137 _let_136 _let_135 _let_134 _let_133 (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X) Y) (= (@ (@ tptp.ord_min_assn X) Y) X))) (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat X) Y) (= (@ (@ tptp.ord_min_filter_nat X) Y) X))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (= (@ (@ tptp.ord_min_set_nat X) Y) X))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (@ (@ tptp.ord_min_nat X) Y) X))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (@ (@ tptp.ord_min_int X) Y) X))) (forall ((Y tptp.assn) (X tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn Y) X) (= (@ (@ tptp.ord_min_assn X) Y) Y))) (forall ((Y tptp.filter_nat) (X tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat Y) X) (= (@ (@ tptp.ord_min_filter_nat X) Y) Y))) (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (= (@ (@ tptp.ord_min_set_nat X) Y) Y))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.ord_min_nat X) Y) Y))) (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.ord_min_int X) Y) Y))) (forall ((A2 tptp.nat) (C tptp.nat) (B2 tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) C) (=> (@ (@ tptp.ord_less_eq_nat B2) D2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_min_nat A2) B2)) (@ (@ tptp.ord_min_nat C) D2))))) (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) C) (=> (@ (@ tptp.ord_less_eq_int B2) D2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_min_int A2) B2)) (@ (@ tptp.ord_min_int C) D2))))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= A2 (@ (@ tptp.ord_min_nat A2) B2)))) (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (= A2 (@ (@ tptp.ord_min_int A2) B2)))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (= A2 (@ (@ tptp.ord_min_nat A2) B2)) (@ (@ tptp.ord_less_eq_nat A2) B2))) (forall ((A2 tptp.int) (B2 tptp.int)) (=> (= A2 (@ (@ tptp.ord_min_int A2) B2)) (@ (@ tptp.ord_less_eq_int A2) B2))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 (@ (@ tptp.ord_min_nat B2) C)) (not (=> (@ _let_1 B2) (not (@ _let_1 C))))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A2))) (=> (@ _let_1 (@ (@ tptp.ord_min_int B2) C)) (not (=> (@ _let_1 B2) (not (@ _let_1 C))))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.ord_min_nat B2) C)))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A2))) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.ord_min_int B2) C)))))) (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (= A3 (@ (@ tptp.ord_min_nat A3) B3)))) (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B3 tptp.int)) (= A3 (@ (@ tptp.ord_min_int A3) B3)))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_min_nat A2) B2)) A2)) (forall ((A2 tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_min_int A2) B2)) A2)) (forall ((A2 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_min_nat A2) B2)) B2)) (forall ((A2 tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_min_int A2) B2)) B2)) (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.ord_min_nat A3) B3) A3))) (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.ord_min_int A3) B3) A3))) (= tptp.ord_less_eq_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (= (@ (@ tptp.ord_min_nat A3) B3) B3))) (= tptp.ord_less_eq_int (lambda ((B3 tptp.int) (A3 tptp.int)) (= (@ (@ tptp.ord_min_int A3) B3) B3))) (forall ((A2 tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_min_nat A2) B2)) C))) (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_min_int A2) B2)) C))) (forall ((B2 tptp.nat) (C tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_min_nat A2) B2)) C))) (forall ((B2 tptp.int) (C tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_min_int A2) B2)) C))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_min_nat X) Y)) Z) (or (@ (@ tptp.ord_less_eq_nat X) Z) (@ (@ tptp.ord_less_eq_nat Y) Z)))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_min_int X) Y)) Z) (or (@ (@ tptp.ord_less_eq_int X) Z) (@ (@ tptp.ord_less_eq_int Y) Z)))) (forall ((B2 tptp.code_integer) (C tptp.code_integer) (A2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.ord_min_Code_integer A2) B2)) C))) (forall ((B2 tptp.num) (C tptp.num) (A2 tptp.num)) (=> (@ (@ tptp.ord_less_num B2) C) (@ (@ tptp.ord_less_num (@ (@ tptp.ord_min_num A2) B2)) C))) (forall ((B2 tptp.nat) (C tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_min_nat A2) B2)) C))) (forall ((B2 tptp.int) (C tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int B2) C) (@ (@ tptp.ord_less_int (@ (@ tptp.ord_min_int A2) B2)) C))) (forall ((A2 tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.ord_min_Code_integer A2) B2)) C))) (forall ((A2 tptp.num) (C tptp.num) (B2 tptp.num)) (=> (@ (@ tptp.ord_less_num A2) C) (@ (@ tptp.ord_less_num (@ (@ tptp.ord_min_num A2) B2)) C))) (forall ((A2 tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_min_nat A2) B2)) C))) (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) C) (@ (@ tptp.ord_less_int (@ (@ tptp.ord_min_int A2) B2)) C))) (= tptp.ord_le6747313008572928689nteger (lambda ((A3 tptp.code_integer) (B3 tptp.code_integer)) (and (= A3 (@ (@ tptp.ord_min_Code_integer A3) B3)) (not (= A3 B3))))) (= tptp.ord_less_num (lambda ((A3 tptp.num) (B3 tptp.num)) (and (= A3 (@ (@ tptp.ord_min_num A3) B3)) (not (= A3 B3))))) (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (and (= A3 (@ (@ tptp.ord_min_nat A3) B3)) (not (= A3 B3))))) (= tptp.ord_less_int (lambda ((A3 tptp.int) (B3 tptp.int)) (and (= A3 (@ (@ tptp.ord_min_int A3) B3)) (not (= A3 B3))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A2))) (=> (@ _let_1 (@ (@ tptp.ord_min_Code_integer B2) C)) (not (=> (@ _let_1 B2) (not (@ _let_1 C))))))) (forall ((A2 tptp.num) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A2))) (=> (@ _let_1 (@ (@ tptp.ord_min_num B2) C)) (not (=> (@ _let_1 B2) (not (@ _let_1 C))))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 (@ (@ tptp.ord_min_nat B2) C)) (not (=> (@ _let_1 B2) (not (@ _let_1 C))))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A2))) (=> (@ _let_1 (@ (@ tptp.ord_min_int B2) C)) (not (=> (@ _let_1 B2) (not (@ _let_1 C))))))) (forall ((X tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.ord_min_Code_integer X) Y)) Z) (or (@ (@ tptp.ord_le6747313008572928689nteger X) Z) (@ (@ tptp.ord_le6747313008572928689nteger Y) Z)))) (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (= (@ (@ tptp.ord_less_num (@ (@ tptp.ord_min_num X) Y)) Z) (or (@ (@ tptp.ord_less_num X) Z) (@ (@ tptp.ord_less_num Y) Z)))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_min_nat X) Y)) Z) (or (@ (@ tptp.ord_less_nat X) Z) (@ (@ tptp.ord_less_nat Y) Z)))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.ord_min_int X) Y)) Z) (or (@ (@ tptp.ord_less_int X) Z) (@ (@ tptp.ord_less_int Y) Z)))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.ord_min_rat X) Y)) Z) (@ (@ tptp.ord_min_rat (@ (@ tptp.minus_minus_rat X) Z)) (@ (@ tptp.minus_minus_rat Y) Z)))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.ord_min_int X) Y)) Z) (@ (@ tptp.ord_min_int (@ (@ tptp.minus_minus_int X) Z)) (@ (@ tptp.minus_minus_int Y) Z)))) (forall ((Y tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat Y) (@ (@ tptp.sup_su5525570899277871387at_nat X) Y))) (forall ((Y tptp.assn) (X tptp.assn)) (@ (@ tptp.ord_less_eq_assn Y) (@ (@ tptp.sup_sup_assn X) Y))) (forall ((Y tptp.filter_nat) (X tptp.filter_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat Y) (@ (@ tptp.sup_sup_filter_nat X) Y))) (forall ((Y tptp.set_nat) (X tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat Y) (@ (@ tptp.sup_sup_set_nat X) Y))) (forall ((Y tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y) (@ (@ tptp.sup_sup_nat X) Y))) (forall ((Y tptp.int) (X tptp.int)) (@ (@ tptp.ord_less_eq_int Y) (@ (@ tptp.sup_sup_int X) Y))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat X) (@ (@ tptp.sup_su5525570899277871387at_nat X) Y))) (forall ((X tptp.assn) (Y tptp.assn)) (@ (@ tptp.ord_less_eq_assn X) (@ (@ tptp.sup_sup_assn X) Y))) (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat X) (@ (@ tptp.sup_sup_filter_nat X) Y))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X) (@ (@ tptp.sup_sup_set_nat X) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.sup_sup_nat X) Y))) (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.sup_sup_int X) Y))) (forall ((A2 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2)) X) (not (=> (@ (@ tptp.ord_le1268244103169919719at_nat A2) X) (not (@ (@ tptp.ord_le1268244103169919719at_nat B2) X)))))) (forall ((A2 tptp.assn) (B2 tptp.assn) (X tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.sup_sup_assn A2) B2)) X) (not (=> (@ (@ tptp.ord_less_eq_assn A2) X) (not (@ (@ tptp.ord_less_eq_assn B2) X)))))) (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat) (X tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.sup_sup_filter_nat A2) B2)) X) (not (=> (@ (@ tptp.ord_le2510731241096832064er_nat A2) X) (not (@ (@ tptp.ord_le2510731241096832064er_nat B2) X)))))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat A2) B2)) X) (not (=> (@ (@ tptp.ord_less_eq_set_nat A2) X) (not (@ (@ tptp.ord_less_eq_set_nat B2) X)))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat A2) B2)) X) (not (=> (@ (@ tptp.ord_less_eq_nat A2) X) (not (@ (@ tptp.ord_less_eq_nat B2) X)))))) (forall ((A2 tptp.int) (B2 tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int A2) B2)) X) (not (=> (@ (@ tptp.ord_less_eq_int A2) X) (not (@ (@ tptp.ord_less_eq_int B2) X)))))) (forall ((A2 tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A2) X) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B2) X) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2)) X)))) (forall ((A2 tptp.assn) (X tptp.assn) (B2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A2) X) (=> (@ (@ tptp.ord_less_eq_assn B2) X) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.sup_sup_assn A2) B2)) X)))) (forall ((A2 tptp.filter_nat) (X tptp.filter_nat) (B2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat A2) X) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B2) X) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.sup_sup_filter_nat A2) B2)) X)))) (forall ((A2 tptp.set_nat) (X tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) X) (=> (@ (@ tptp.ord_less_eq_set_nat B2) X) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat A2) B2)) X)))) (forall ((A2 tptp.nat) (X tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) X) (=> (@ (@ tptp.ord_less_eq_nat B2) X) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat A2) B2)) X)))) (forall ((A2 tptp.int) (X tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) X) (=> (@ (@ tptp.ord_less_eq_int B2) X) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int A2) B2)) X)))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat X) (@ (@ tptp.sup_su5525570899277871387at_nat X) Y))) (forall ((X tptp.assn) (Y tptp.assn)) (@ (@ tptp.ord_less_eq_assn X) (@ (@ tptp.sup_sup_assn X) Y))) (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat X) (@ (@ tptp.sup_sup_filter_nat X) Y))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X) (@ (@ tptp.sup_sup_set_nat X) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.sup_sup_nat X) Y))) (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.sup_sup_int X) Y))) (forall ((Y tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat Y) (@ (@ tptp.sup_su5525570899277871387at_nat X) Y))) (forall ((Y tptp.assn) (X tptp.assn)) (@ (@ tptp.ord_less_eq_assn Y) (@ (@ tptp.sup_sup_assn X) Y))) (forall ((Y tptp.filter_nat) (X tptp.filter_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat Y) (@ (@ tptp.sup_sup_filter_nat X) Y))) (forall ((Y tptp.set_nat) (X tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat Y) (@ (@ tptp.sup_sup_set_nat X) Y))) (forall ((Y tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y) (@ (@ tptp.sup_sup_nat X) Y))) (forall ((Y tptp.int) (X tptp.int)) (@ (@ tptp.ord_less_eq_int Y) (@ (@ tptp.sup_sup_int X) Y))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le1268244103169919719at_nat X))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2))))) (forall ((X tptp.assn) (A2 tptp.assn) (B2 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn X))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_assn A2) B2))))) (forall ((X tptp.filter_nat) (A2 tptp.filter_nat) (B2 tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_le2510731241096832064er_nat X))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_filter_nat A2) B2))))) (forall ((X tptp.set_nat) (A2 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A2) B2))))) (forall ((X tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_nat A2) B2))))) (forall ((X tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_int A2) B2))))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le1268244103169919719at_nat X))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2))))) (forall ((X tptp.assn) (B2 tptp.assn) (A2 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn X))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_assn A2) B2))))) (forall ((X tptp.filter_nat) (B2 tptp.filter_nat) (A2 tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_le2510731241096832064er_nat X))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_filter_nat A2) B2))))) (forall ((X tptp.set_nat) (B2 tptp.set_nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A2) B2))))) (forall ((X tptp.nat) (B2 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_nat A2) B2))))) (forall ((X tptp.int) (B2 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_int A2) B2))))) (forall ((C tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat) (D2 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat C) A2) (=> (@ (@ tptp.ord_le1268244103169919719at_nat D2) B2) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat C) D2)) (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2))))) (forall ((C tptp.assn) (A2 tptp.assn) (D2 tptp.assn) (B2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn C) A2) (=> (@ (@ tptp.ord_less_eq_assn D2) B2) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.sup_sup_assn C) D2)) (@ (@ tptp.sup_sup_assn A2) B2))))) (forall ((C tptp.filter_nat) (A2 tptp.filter_nat) (D2 tptp.filter_nat) (B2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat C) A2) (=> (@ (@ tptp.ord_le2510731241096832064er_nat D2) B2) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.sup_sup_filter_nat C) D2)) (@ (@ tptp.sup_sup_filter_nat A2) B2))))) (forall ((C tptp.set_nat) (A2 tptp.set_nat) (D2 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat C) A2) (=> (@ (@ tptp.ord_less_eq_set_nat D2) B2) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat C) D2)) (@ (@ tptp.sup_sup_set_nat A2) B2))))) (forall ((C tptp.nat) (A2 tptp.nat) (D2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) A2) (=> (@ (@ tptp.ord_less_eq_nat D2) B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat C) D2)) (@ (@ tptp.sup_sup_nat A2) B2))))) (forall ((C tptp.int) (A2 tptp.int) (D2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) A2) (=> (@ (@ tptp.ord_less_eq_int D2) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int C) D2)) (@ (@ tptp.sup_sup_int A2) B2))))) (forall ((A2 tptp.set_Pr4329608150637261639at_nat) (C tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat) (D2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A2) C) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B2) D2) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2)) (@ (@ tptp.sup_su5525570899277871387at_nat C) D2))))) (forall ((A2 tptp.assn) (C tptp.assn) (B2 tptp.assn) (D2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A2) C) (=> (@ (@ tptp.ord_less_eq_assn B2) D2) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.sup_sup_assn A2) B2)) (@ (@ tptp.sup_sup_assn C) D2))))) (forall ((A2 tptp.filter_nat) (C tptp.filter_nat) (B2 tptp.filter_nat) (D2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat A2) C) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B2) D2) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.sup_sup_filter_nat A2) B2)) (@ (@ tptp.sup_sup_filter_nat C) D2))))) (forall ((A2 tptp.set_nat) (C tptp.set_nat) (B2 tptp.set_nat) (D2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) C) (=> (@ (@ tptp.ord_less_eq_set_nat B2) D2) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat A2) B2)) (@ (@ tptp.sup_sup_set_nat C) D2))))) (forall ((A2 tptp.nat) (C tptp.nat) (B2 tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) C) (=> (@ (@ tptp.ord_less_eq_nat B2) D2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat A2) B2)) (@ (@ tptp.sup_sup_nat C) D2))))) (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) C) (=> (@ (@ tptp.ord_less_eq_int B2) D2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int A2) B2)) (@ (@ tptp.sup_sup_int C) D2))))) (forall ((Y tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat Y) X) (=> (@ (@ tptp.ord_le1268244103169919719at_nat Z) X) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat Y) Z)) X)))) (forall ((Y tptp.assn) (X tptp.assn) (Z tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn Y) X) (=> (@ (@ tptp.ord_less_eq_assn Z) X) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.sup_sup_assn Y) Z)) X)))) (forall ((Y tptp.filter_nat) (X tptp.filter_nat) (Z tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat Y) X) (=> (@ (@ tptp.ord_le2510731241096832064er_nat Z) X) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.sup_sup_filter_nat Y) Z)) X)))) (forall ((Y tptp.set_nat) (X tptp.set_nat) (Z tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (=> (@ (@ tptp.ord_less_eq_set_nat Z) X) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat Y) Z)) X)))) (forall ((Y tptp.nat) (X tptp.nat) (Z tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (=> (@ (@ tptp.ord_less_eq_nat Z) X) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat Y) Z)) X)))) (forall ((Y tptp.int) (X tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (=> (@ (@ tptp.ord_less_eq_int Z) X) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int Y) Z)) X)))) (= tptp.ord_le1268244103169919719at_nat (lambda ((X2 tptp.set_Pr4329608150637261639at_nat) (Y5 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat X2) Y5) Y5))) (= tptp.ord_less_eq_assn (lambda ((X2 tptp.assn) (Y5 tptp.assn)) (= (@ (@ tptp.sup_sup_assn X2) Y5) Y5))) (= tptp.ord_le2510731241096832064er_nat (lambda ((X2 tptp.filter_nat) (Y5 tptp.filter_nat)) (= (@ (@ tptp.sup_sup_filter_nat X2) Y5) Y5))) (= tptp.ord_less_eq_set_nat (lambda ((X2 tptp.set_nat) (Y5 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat X2) Y5) Y5))) (= tptp.ord_less_eq_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (= (@ (@ tptp.sup_sup_nat X2) Y5) Y5))) (= tptp.ord_less_eq_int (lambda ((X2 tptp.int) (Y5 tptp.int)) (= (@ (@ tptp.sup_sup_int X2) Y5) Y5))) (forall ((B2 tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B2) A2) (= A2 (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2)))) (forall ((B2 tptp.assn) (A2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn B2) A2) (= A2 (@ (@ tptp.sup_sup_assn A2) B2)))) (forall ((B2 tptp.filter_nat) (A2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B2) A2) (= A2 (@ (@ tptp.sup_sup_filter_nat A2) B2)))) (forall ((B2 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A2) (= A2 (@ (@ tptp.sup_sup_set_nat A2) B2)))) (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (= A2 (@ (@ tptp.sup_sup_nat A2) B2)))) (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (= A2 (@ (@ tptp.sup_sup_int A2) B2)))) (forall ((A2 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (=> (= A2 (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2)) (@ (@ tptp.ord_le1268244103169919719at_nat B2) A2))) (forall ((A2 tptp.assn) (B2 tptp.assn)) (=> (= A2 (@ (@ tptp.sup_sup_assn A2) B2)) (@ (@ tptp.ord_less_eq_assn B2) A2))) (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat)) (=> (= A2 (@ (@ tptp.sup_sup_filter_nat A2) B2)) (@ (@ tptp.ord_le2510731241096832064er_nat B2) A2))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (= A2 (@ (@ tptp.sup_sup_set_nat A2) B2)) (@ (@ tptp.ord_less_eq_set_nat B2) A2))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (= A2 (@ (@ tptp.sup_sup_nat A2) B2)) (@ (@ tptp.ord_less_eq_nat B2) A2))) (forall ((A2 tptp.int) (B2 tptp.int)) (=> (= A2 (@ (@ tptp.sup_sup_int A2) B2)) (@ (@ tptp.ord_less_eq_int B2) A2))) (forall ((F4 (-> 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) (Y2 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat X3) (@ (@ F4 X3) Y2))) (=> (forall ((X3 tptp.set_Pr4329608150637261639at_nat) (Y2 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat Y2) (@ (@ F4 X3) Y2))) (=> (forall ((X3 tptp.set_Pr4329608150637261639at_nat) (Y2 tptp.set_Pr4329608150637261639at_nat) (Z4 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat Y2) X3) (=> (@ (@ tptp.ord_le1268244103169919719at_nat Z4) X3) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ F4 Y2) Z4)) X3)))) (= (@ (@ tptp.sup_su5525570899277871387at_nat X) Y) (@ (@ F4 X) Y)))))) (forall ((F4 (-> tptp.assn tptp.assn tptp.assn)) (X tptp.assn) (Y tptp.assn)) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (@ (@ tptp.ord_less_eq_assn X3) (@ (@ F4 X3) Y2))) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (@ (@ tptp.ord_less_eq_assn Y2) (@ (@ F4 X3) Y2))) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn) (Z4 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn Y2) X3) (=> (@ (@ tptp.ord_less_eq_assn Z4) X3) (@ (@ tptp.ord_less_eq_assn (@ (@ F4 Y2) Z4)) X3)))) (= (@ (@ tptp.sup_sup_assn X) Y) (@ (@ F4 X) Y)))))) (forall ((F4 (-> tptp.filter_nat tptp.filter_nat tptp.filter_nat)) (X tptp.filter_nat) (Y tptp.filter_nat)) (=> (forall ((X3 tptp.filter_nat) (Y2 tptp.filter_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat X3) (@ (@ F4 X3) Y2))) (=> (forall ((X3 tptp.filter_nat) (Y2 tptp.filter_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat Y2) (@ (@ F4 X3) Y2))) (=> (forall ((X3 tptp.filter_nat) (Y2 tptp.filter_nat) (Z4 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat Y2) X3) (=> (@ (@ tptp.ord_le2510731241096832064er_nat Z4) X3) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ F4 Y2) Z4)) X3)))) (= (@ (@ tptp.sup_sup_filter_nat X) Y) (@ (@ F4 X) Y)))))) (forall ((F4 (-> tptp.set_nat tptp.set_nat tptp.set_nat)) (X tptp.set_nat) (Y tptp.set_nat)) (=> (forall ((X3 tptp.set_nat) (Y2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X3) (@ (@ F4 X3) Y2))) (=> (forall ((X3 tptp.set_nat) (Y2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat Y2) (@ (@ F4 X3) Y2))) (=> (forall ((X3 tptp.set_nat) (Y2 tptp.set_nat) (Z4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y2) X3) (=> (@ (@ tptp.ord_less_eq_set_nat Z4) X3) (@ (@ tptp.ord_less_eq_set_nat (@ (@ F4 Y2) Z4)) X3)))) (= (@ (@ tptp.sup_sup_set_nat X) Y) (@ (@ F4 X) Y)))))) (forall ((F4 (-> tptp.nat tptp.nat tptp.nat)) (X tptp.nat) (Y tptp.nat)) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X3) (@ (@ F4 X3) Y2))) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y2) (@ (@ F4 X3) Y2))) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat) (Z4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y2) X3) (=> (@ (@ tptp.ord_less_eq_nat Z4) X3) (@ (@ tptp.ord_less_eq_nat (@ (@ F4 Y2) Z4)) X3)))) (= (@ (@ tptp.sup_sup_nat X) Y) (@ (@ F4 X) Y)))))) (forall ((F4 (-> tptp.int tptp.int tptp.int)) (X tptp.int) (Y tptp.int)) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (@ (@ tptp.ord_less_eq_int X3) (@ (@ F4 X3) Y2))) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (@ (@ tptp.ord_less_eq_int Y2) (@ (@ F4 X3) Y2))) (=> (forall ((X3 tptp.int) (Y2 tptp.int) (Z4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y2) X3) (=> (@ (@ tptp.ord_less_eq_int Z4) X3) (@ (@ tptp.ord_less_eq_int (@ (@ F4 Y2) Z4)) X3)))) (= (@ (@ tptp.sup_sup_int X) Y) (@ (@ F4 X) Y)))))) (forall ((B2 tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B2) A2) (= (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2) A2))) (forall ((B2 tptp.assn) (A2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn B2) A2) (= (@ (@ tptp.sup_sup_assn A2) B2) A2))) (forall ((B2 tptp.filter_nat) (A2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B2) A2) (= (@ (@ tptp.sup_sup_filter_nat A2) B2) A2))) (forall ((B2 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A2) (= (@ (@ tptp.sup_sup_set_nat A2) B2) A2))) (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (= (@ (@ tptp.sup_sup_nat A2) B2) A2))) (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (= (@ (@ tptp.sup_sup_int A2) B2) A2))) (forall ((A2 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A2) B2) (= (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2) B2))) (forall ((A2 tptp.assn) (B2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A2) B2) (= (@ (@ tptp.sup_sup_assn A2) B2) B2))) (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat A2) B2) (= (@ (@ tptp.sup_sup_filter_nat A2) B2) B2))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (= (@ (@ tptp.sup_sup_set_nat A2) B2) B2))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= (@ (@ tptp.sup_sup_nat A2) B2) B2))) (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (= (@ (@ tptp.sup_sup_int A2) B2) B2))) (forall ((Y tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat Y) X) (= (@ (@ tptp.sup_su5525570899277871387at_nat X) Y) X))) (forall ((Y tptp.assn) (X tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn Y) X) (= (@ (@ tptp.sup_sup_assn X) Y) X))) (forall ((Y tptp.filter_nat) (X tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat Y) X) (= (@ (@ tptp.sup_sup_filter_nat X) Y) X))) (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (= (@ (@ tptp.sup_sup_set_nat X) Y) X))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.sup_sup_nat X) Y) X))) (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.sup_sup_int X) Y) X))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat X) Y) (= (@ (@ tptp.sup_su5525570899277871387at_nat X) Y) Y))) (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X) Y) (= (@ (@ tptp.sup_sup_assn X) Y) Y))) (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat X) Y) (= (@ (@ tptp.sup_sup_filter_nat X) Y) Y))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (= (@ (@ tptp.sup_sup_set_nat X) Y) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (@ (@ tptp.sup_sup_nat X) Y) Y))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (@ (@ tptp.sup_sup_int X) Y) Y))) (forall ((B2 tptp.set_Pr4329608150637261639at_nat) (C tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat B2) C)) A2) (not (=> (@ (@ tptp.ord_le1268244103169919719at_nat B2) A2) (not (@ (@ tptp.ord_le1268244103169919719at_nat C) A2)))))) (forall ((B2 tptp.assn) (C tptp.assn) (A2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.sup_sup_assn B2) C)) A2) (not (=> (@ (@ tptp.ord_less_eq_assn B2) A2) (not (@ (@ tptp.ord_less_eq_assn C) A2)))))) (forall ((B2 tptp.filter_nat) (C tptp.filter_nat) (A2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.sup_sup_filter_nat B2) C)) A2) (not (=> (@ (@ tptp.ord_le2510731241096832064er_nat B2) A2) (not (@ (@ tptp.ord_le2510731241096832064er_nat C) A2)))))) (forall ((B2 tptp.set_nat) (C tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat B2) C)) A2) (not (=> (@ (@ tptp.ord_less_eq_set_nat B2) A2) (not (@ (@ tptp.ord_less_eq_set_nat C) A2)))))) (forall ((B2 tptp.nat) (C tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat B2) C)) A2) (not (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (not (@ (@ tptp.ord_less_eq_nat C) A2)))))) (forall ((B2 tptp.int) (C tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int B2) C)) A2) (not (=> (@ (@ tptp.ord_less_eq_int B2) A2) (not (@ (@ tptp.ord_less_eq_int C) A2)))))) (forall ((B2 tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat) (C tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B2) A2) (=> (@ (@ tptp.ord_le1268244103169919719at_nat C) A2) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat B2) C)) A2)))) (forall ((B2 tptp.assn) (A2 tptp.assn) (C tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn B2) A2) (=> (@ (@ tptp.ord_less_eq_assn C) A2) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.sup_sup_assn B2) C)) A2)))) (forall ((B2 tptp.filter_nat) (A2 tptp.filter_nat) (C tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B2) A2) (=> (@ (@ tptp.ord_le2510731241096832064er_nat C) A2) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.sup_sup_filter_nat B2) C)) A2)))) (forall ((B2 tptp.set_nat) (A2 tptp.set_nat) (C tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A2) (=> (@ (@ tptp.ord_less_eq_set_nat C) A2) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat B2) C)) A2)))) (forall ((B2 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (=> (@ (@ tptp.ord_less_eq_nat C) A2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat B2) C)) A2)))) (forall ((B2 tptp.int) (A2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (=> (@ (@ tptp.ord_less_eq_int C) A2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int B2) C)) A2)))) (= tptp.ord_le1268244103169919719at_nat (lambda ((B3 tptp.set_Pr4329608150637261639at_nat) (A3 tptp.set_Pr4329608150637261639at_nat)) (= A3 (@ (@ tptp.sup_su5525570899277871387at_nat A3) B3)))) (= tptp.ord_less_eq_assn (lambda ((B3 tptp.assn) (A3 tptp.assn)) (= A3 (@ (@ tptp.sup_sup_assn A3) B3)))) (= tptp.ord_le2510731241096832064er_nat (lambda ((B3 tptp.filter_nat) (A3 tptp.filter_nat)) (= A3 (@ (@ tptp.sup_sup_filter_nat A3) B3)))) (= tptp.ord_less_eq_set_nat (lambda ((B3 tptp.set_nat) (A3 tptp.set_nat)) (= A3 (@ (@ tptp.sup_sup_set_nat A3) B3)))) (= tptp.ord_less_eq_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (= A3 (@ (@ tptp.sup_sup_nat A3) B3)))) (= tptp.ord_less_eq_int (lambda ((B3 tptp.int) (A3 tptp.int)) (= A3 (@ (@ tptp.sup_sup_int A3) B3)))) (forall ((A2 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat A2) (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2))) (forall ((A2 tptp.assn) (B2 tptp.assn)) (@ (@ tptp.ord_less_eq_assn A2) (@ (@ tptp.sup_sup_assn A2) B2))) (forall ((A2 tptp.filter_nat) (B2 tptp.filter_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat A2) (@ (@ tptp.sup_sup_filter_nat A2) B2))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A2) (@ (@ tptp.sup_sup_set_nat A2) B2))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat A2) (@ (@ tptp.sup_sup_nat A2) B2))) (forall ((A2 tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_eq_int A2) (@ (@ tptp.sup_sup_int A2) B2))) (forall ((B2 tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat B2) (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2))) (forall ((B2 tptp.assn) (A2 tptp.assn)) (@ (@ tptp.ord_less_eq_assn B2) (@ (@ tptp.sup_sup_assn A2) B2))) (forall ((B2 tptp.filter_nat) (A2 tptp.filter_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat B2) (@ (@ tptp.sup_sup_filter_nat A2) B2))) (forall ((B2 tptp.set_nat) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat B2) (@ (@ tptp.sup_sup_set_nat A2) B2))) (forall ((B2 tptp.nat) (A2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat B2) (@ (@ tptp.sup_sup_nat A2) B2))) (forall ((B2 tptp.int) (A2 tptp.int)) (@ (@ tptp.ord_less_eq_int B2) (@ (@ tptp.sup_sup_int A2) B2))) (= tptp.ord_le1268244103169919719at_nat (lambda ((B3 tptp.set_Pr4329608150637261639at_nat) (A3 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat A3) B3) A3))) (= tptp.ord_less_eq_assn (lambda ((B3 tptp.assn) (A3 tptp.assn)) (= (@ (@ tptp.sup_sup_assn A3) B3) A3))) (= tptp.ord_le2510731241096832064er_nat (lambda ((B3 tptp.filter_nat) (A3 tptp.filter_nat)) (= (@ (@ tptp.sup_sup_filter_nat A3) B3) A3))) (= tptp.ord_less_eq_set_nat (lambda ((B3 tptp.set_nat) (A3 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A3) B3) A3))) (= tptp.ord_less_eq_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (= (@ (@ tptp.sup_sup_nat A3) B3) A3))) (= tptp.ord_less_eq_int (lambda ((B3 tptp.int) (A3 tptp.int)) (= (@ (@ tptp.sup_sup_int A3) B3) A3))) (= tptp.ord_le1268244103169919719at_nat (lambda ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat A3) B3) B3))) (= tptp.ord_less_eq_assn (lambda ((A3 tptp.assn) (B3 tptp.assn)) (= (@ (@ tptp.sup_sup_assn A3) B3) B3))) (= tptp.ord_le2510731241096832064er_nat (lambda ((A3 tptp.filter_nat) (B3 tptp.filter_nat)) (= (@ (@ tptp.sup_sup_filter_nat A3) B3) B3))) (= tptp.ord_less_eq_set_nat (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A3) B3) B3))) (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.sup_sup_nat A3) B3) B3))) (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.sup_sup_int A3) B3) B3))) (forall ((C tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le1268244103169919719at_nat C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2))))) (forall ((C tptp.assn) (A2 tptp.assn) (B2 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_assn A2) B2))))) (forall ((C tptp.filter_nat) (A2 tptp.filter_nat) (B2 tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_le2510731241096832064er_nat C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_filter_nat A2) B2))))) (forall ((C tptp.set_nat) (A2 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A2) B2))))) (forall ((C tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_nat A2) B2))))) (forall ((C tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_int A2) B2))))) (forall ((C tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le1268244103169919719at_nat C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2))))) (forall ((C tptp.assn) (B2 tptp.assn) (A2 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_assn A2) B2))))) (forall ((C tptp.filter_nat) (B2 tptp.filter_nat) (A2 tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_le2510731241096832064er_nat C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_filter_nat A2) B2))))) (forall ((C tptp.set_nat) (B2 tptp.set_nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A2) B2))))) (forall ((C tptp.nat) (B2 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_nat A2) B2))))) (forall ((C tptp.int) (B2 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_int A2) B2))))) (= tptp.inf_inf_nat tptp.ord_min_nat) (forall ((C tptp.set_nat) (B2 tptp.set_nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A2) B2))))) (forall ((C tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le2604355607129572851at_nat C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2))))) (forall ((C tptp.assn) (B2 tptp.assn) (A2 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_assn A2) B2))))) (forall ((C tptp.nat) (B2 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_nat A2) B2))))) (forall ((C tptp.int) (B2 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_int A2) B2))))) (forall ((C tptp.set_nat) (A2 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A2) B2))))) (forall ((C tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le2604355607129572851at_nat C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2))))) (forall ((C tptp.assn) (A2 tptp.assn) (B2 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_assn A2) B2))))) (forall ((C tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_nat A2) B2))))) (forall ((C tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_int A2) B2))))) (= tptp.ord_less_set_nat (lambda ((B3 tptp.set_nat) (A3 tptp.set_nat)) (and (= A3 (@ (@ tptp.sup_sup_set_nat A3) B3)) (not (= A3 B3))))) _let_132 (= tptp.ord_less_assn (lambda ((B3 tptp.assn) (A3 tptp.assn)) (and (= A3 (@ (@ tptp.sup_sup_assn A3) B3)) (not (= A3 B3))))) (= tptp.ord_less_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (and (= A3 (@ (@ tptp.sup_sup_nat A3) B3)) (not (= A3 B3))))) (= tptp.ord_less_int (lambda ((B3 tptp.int) (A3 tptp.int)) (and (= A3 (@ (@ tptp.sup_sup_int A3) B3)) (not (= A3 B3))))) (forall ((B2 tptp.set_nat) (C tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat (@ (@ tptp.sup_sup_set_nat B2) C)) A2) (not (=> (@ (@ tptp.ord_less_set_nat B2) A2) (not (@ (@ tptp.ord_less_set_nat C) A2)))))) (forall ((B2 tptp.set_Pr4329608150637261639at_nat) (C tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le2604355607129572851at_nat (@ (@ tptp.sup_su5525570899277871387at_nat B2) C)) A2) (not (=> (@ (@ tptp.ord_le2604355607129572851at_nat B2) A2) (not (@ (@ tptp.ord_le2604355607129572851at_nat C) A2)))))) (forall ((B2 tptp.assn) (C tptp.assn) (A2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn (@ (@ tptp.sup_sup_assn B2) C)) A2) (not (=> (@ (@ tptp.ord_less_assn B2) A2) (not (@ (@ tptp.ord_less_assn C) A2)))))) (forall ((B2 tptp.nat) (C tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.sup_sup_nat B2) C)) A2) (not (=> (@ (@ tptp.ord_less_nat B2) A2) (not (@ (@ tptp.ord_less_nat C) A2)))))) (forall ((B2 tptp.int) (C tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.sup_sup_int B2) C)) A2) (not (=> (@ (@ tptp.ord_less_int B2) A2) (not (@ (@ tptp.ord_less_int C) A2)))))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) B2) (= (@ (@ tptp.sup_sup_set_nat A2) B2) B2))) (forall ((A2 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le2604355607129572851at_nat A2) B2) (= (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2) B2))) (forall ((A2 tptp.assn) (B2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn A2) B2) (= (@ (@ tptp.sup_sup_assn A2) B2) B2))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (= (@ (@ tptp.sup_sup_nat A2) B2) B2))) (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (= (@ (@ tptp.sup_sup_int A2) B2) B2))) (forall ((B2 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B2) A2) (= (@ (@ tptp.sup_sup_set_nat A2) B2) A2))) (forall ((B2 tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le2604355607129572851at_nat B2) A2) (= (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2) A2))) (forall ((B2 tptp.assn) (A2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn B2) A2) (= (@ (@ tptp.sup_sup_assn A2) B2) A2))) (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A2) (= (@ (@ tptp.sup_sup_nat A2) B2) A2))) (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A2) (= (@ (@ tptp.sup_sup_int A2) B2) A2))) (forall ((X tptp.set_nat) (B2 tptp.set_nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat X))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A2) B2))))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le2604355607129572851at_nat X))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2))))) (forall ((X tptp.assn) (B2 tptp.assn) (A2 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn X))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_assn A2) B2))))) (forall ((X tptp.nat) (B2 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_nat A2) B2))))) (forall ((X tptp.int) (B2 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_sup_int A2) B2))))) (forall ((X tptp.set_nat) (A2 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat X))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A2) B2))))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (A2 tptp.set_Pr4329608150637261639at_nat) (B2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le2604355607129572851at_nat X))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A2) B2))))) (forall ((X tptp.assn) (A2 tptp.assn) (B2 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn X))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_assn A2) B2))))) (forall ((X tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_nat A2) B2))))) (forall ((X tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_sup_int A2) B2))))) (forall ((X tptp.assn)) (= (@ (@ tptp.sup_sup_assn X) tptp.bot_bot_assn) X)) (forall ((X tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat X) tptp.bot_bo228742789529271731at_nat) X)) (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat X) tptp.bot_bo2099793752762293965at_nat) X)) (forall ((X tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o X) tptp.bot_bot_set_o) X)) (forall ((X tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat X) tptp.bot_bot_set_nat) X)) (forall ((X tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int X) tptp.bot_bot_set_int) X)) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.sup_su6327502436637775413at_nat X))) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat) (Y2 tptp.set_Pr1261947904930325089at_nat) (Z4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X3))) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat Y2) Z4)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 Y2)) (@ _let_1 Z4))))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 Y)) (@ _let_1 Z)))))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (=> (forall ((X3 tptp.set_nat) (Y2 tptp.set_nat) (Z4 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X3))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat Y2) Z4)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 Y2)) (@ _let_1 Z4))))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y) Z)) (@ (@ tptp.inf_inf_set_nat (@ _let_1 Y)) (@ _let_1 Z)))))) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn) (Z4 tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X3))) (= (@ _let_1 (@ (@ tptp.sup_sup_assn Y2) Z4)) (@ (@ tptp.sup_sup_assn (@ _let_1 Y2)) (@ _let_1 Z4))))) (= (@ _let_1 (@ (@ tptp.inf_inf_assn Y) Z)) (@ (@ tptp.inf_inf_assn (@ _let_1 Y)) (@ _let_1 Z)))))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat X))) (=> (forall ((X3 tptp.set_Pr4329608150637261639at_nat) (Y2 tptp.set_Pr4329608150637261639at_nat) (Z4 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.inf_in7913087082777306421at_nat X3))) (= (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat Y2) Z4)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 Y2)) (@ _let_1 Z4))))) (= (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat Y) Z)) (@ (@ tptp.inf_in7913087082777306421at_nat (@ _let_1 Y)) (@ _let_1 Z)))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat) (Y2 tptp.set_Pr1261947904930325089at_nat) (Z4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.sup_su6327502436637775413at_nat X3))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y2) Z4)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 Y2)) (@ _let_1 Z4))))) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat Y) Z)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 Y)) (@ _let_1 Z)))))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (=> (forall ((X3 tptp.set_nat) (Y2 tptp.set_nat) (Z4 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X3))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y2) Z4)) (@ (@ tptp.inf_inf_set_nat (@ _let_1 Y2)) (@ _let_1 Z4))))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat Y) Z)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 Y)) (@ _let_1 Z)))))) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn) (Z4 tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X3))) (= (@ _let_1 (@ (@ tptp.inf_inf_assn Y2) Z4)) (@ (@ tptp.inf_inf_assn (@ _let_1 Y2)) (@ _let_1 Z4))))) (= (@ _let_1 (@ (@ tptp.sup_sup_assn Y) Z)) (@ (@ tptp.sup_sup_assn (@ _let_1 Y)) (@ _let_1 Z)))))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.inf_in7913087082777306421at_nat X))) (=> (forall ((X3 tptp.set_Pr4329608150637261639at_nat) (Y2 tptp.set_Pr4329608150637261639at_nat) (Z4 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat X3))) (= (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat Y2) Z4)) (@ (@ tptp.inf_in7913087082777306421at_nat (@ _let_1 Y2)) (@ _let_1 Z4))))) (= (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat Y) Z)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 Y)) (@ _let_1 Z)))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat Y) Z)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 Y)) (@ _let_1 Z))))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat Y) Z)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 Y)) (@ _let_1 Z))))) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (= (@ _let_1 (@ (@ tptp.sup_sup_assn Y) Z)) (@ (@ tptp.sup_sup_assn (@ _let_1 Y)) (@ _let_1 Z))))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.inf_in7913087082777306421at_nat X))) (= (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat Y) Z)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 Y)) (@ _let_1 Z))))) (forall ((Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat Y) Z)) X) (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat Y) X)) (@ (@ tptp.inf_in2572325071724192079at_nat Z) X)))) (forall ((Y tptp.set_nat) (Z tptp.set_nat) (X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat Y) Z)) X) (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat Y) X)) (@ (@ tptp.inf_inf_set_nat Z) X)))) (forall ((Y tptp.assn) (Z tptp.assn) (X tptp.assn)) (= (@ (@ tptp.inf_inf_assn (@ (@ tptp.sup_sup_assn Y) Z)) X) (@ (@ tptp.sup_sup_assn (@ (@ tptp.inf_inf_assn Y) X)) (@ (@ tptp.inf_inf_assn Z) X)))) (forall ((Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.sup_su5525570899277871387at_nat Y) Z)) X) (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat Y) X)) (@ (@ tptp.inf_in7913087082777306421at_nat Z) X)))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.sup_su6327502436637775413at_nat X))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 Y)) (@ _let_1 Z))))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y) Z)) (@ (@ tptp.inf_inf_set_nat (@ _let_1 Y)) (@ _let_1 Z))))) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (= (@ _let_1 (@ (@ tptp.inf_inf_assn Y) Z)) (@ (@ tptp.inf_inf_assn (@ _let_1 Y)) (@ _let_1 Z))))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat X))) (= (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat Y) Z)) (@ (@ tptp.inf_in7913087082777306421at_nat (@ _let_1 Y)) (@ _let_1 Z))))) (forall ((Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z)) X) (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat Y) X)) (@ (@ tptp.sup_su6327502436637775413at_nat Z) X)))) (forall ((Y tptp.set_nat) (Z tptp.set_nat) (X tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat Y) Z)) X) (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat Y) X)) (@ (@ tptp.sup_sup_set_nat Z) X)))) (forall ((Y tptp.assn) (Z tptp.assn) (X tptp.assn)) (= (@ (@ tptp.sup_sup_assn (@ (@ tptp.inf_inf_assn Y) Z)) X) (@ (@ tptp.inf_inf_assn (@ (@ tptp.sup_sup_assn Y) X)) (@ (@ tptp.sup_sup_assn Z) X)))) (forall ((Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat Y) Z)) X) (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.sup_su5525570899277871387at_nat Y) X)) (@ (@ tptp.sup_su5525570899277871387at_nat Z) X)))) (forall ((B tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat tptp.bot_bo228742789529271731at_nat) B) B)) (forall ((B tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat tptp.bot_bo2099793752762293965at_nat) B) B)) (forall ((B tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o tptp.bot_bot_set_o) B) B)) (forall ((B tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat tptp.bot_bot_set_nat) B) B)) (forall ((B tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int tptp.bot_bot_set_int) B) B)) (forall ((A tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat A) tptp.bot_bo228742789529271731at_nat) A)) (forall ((A tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat A) tptp.bot_bo2099793752762293965at_nat) A)) (forall ((A tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o A) tptp.bot_bot_set_o) A)) (forall ((A tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A) tptp.bot_bot_set_nat) A)) (forall ((A tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int A) tptp.bot_bot_set_int) A)) (forall ((I tptp.set_Pr4329608150637261639at_nat) (Ww tptp.list_s4242580248156217677at_nat)) (let ((_let_1 (@ tptp.foldl_4541198706405875041at_nat tptp.sup_su5525570899277871387at_nat))) (= (@ (@ _let_1 I) Ww) (@ (@ tptp.sup_su5525570899277871387at_nat I) (@ (@ _let_1 tptp.bot_bo228742789529271731at_nat) Ww))))) (forall ((I tptp.set_Pr1261947904930325089at_nat) (Ww tptp.list_s1210847774152347623at_nat)) (let ((_let_1 (@ tptp.foldl_5307762784932486881at_nat tptp.sup_su6327502436637775413at_nat))) (= (@ (@ _let_1 I) Ww) (@ (@ tptp.sup_su6327502436637775413at_nat I) (@ (@ _let_1 tptp.bot_bo2099793752762293965at_nat) Ww))))) (forall ((I tptp.set_o) (Ww tptp.list_set_o)) (let ((_let_1 (@ tptp.foldl_set_o_set_o tptp.sup_sup_set_o))) (= (@ (@ _let_1 I) Ww) (@ (@ tptp.sup_sup_set_o I) (@ (@ _let_1 tptp.bot_bot_set_o) Ww))))) (forall ((I tptp.set_nat) (Ww tptp.list_set_nat)) (let ((_let_1 (@ tptp.foldl_4988731653086973103et_nat tptp.sup_sup_set_nat))) (= (@ (@ _let_1 I) Ww) (@ (@ tptp.sup_sup_set_nat I) (@ (@ _let_1 tptp.bot_bot_set_nat) Ww))))) (forall ((I tptp.set_int) (Ww tptp.list_set_int)) (let ((_let_1 (@ tptp.foldl_6819690284573351271et_int tptp.sup_sup_set_int))) (= (@ (@ _let_1 I) Ww) (@ (@ tptp.sup_sup_set_int I) (@ (@ _let_1 tptp.bot_bot_set_int) Ww))))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (D tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A) C2) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B) D) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A) B)) (@ (@ tptp.sup_su5525570899277871387at_nat C2) D))))) (forall ((A tptp.set_nat) (C2 tptp.set_nat) (B tptp.set_nat) (D tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) C2) (=> (@ (@ tptp.ord_less_eq_set_nat B) D) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat A) B)) (@ (@ tptp.sup_sup_set_nat C2) D))))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A) C2) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B) C2) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A) B)) C2)))) (forall ((A tptp.set_nat) (C2 tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) C2) (=> (@ (@ tptp.ord_less_eq_set_nat B) C2) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat A) B)) C2)))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat A) (@ (@ tptp.sup_su5525570899277871387at_nat A) B))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A) (@ (@ tptp.sup_sup_set_nat A) B))) (forall ((B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat B) (@ (@ tptp.sup_su5525570899277871387at_nat A) B))) (forall ((B tptp.set_nat) (A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat B) (@ (@ tptp.sup_sup_set_nat A) B))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A) B) (= (@ (@ tptp.sup_su5525570899277871387at_nat A) B) B))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (= (@ (@ tptp.sup_sup_set_nat A) B) B))) (forall ((B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B) A) (= (@ (@ tptp.sup_su5525570899277871387at_nat A) B) A))) (forall ((B tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (= (@ (@ tptp.sup_sup_set_nat A) B) A))) (forall ((C2 tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat C2) (@ (@ tptp.sup_su5525570899277871387at_nat A) B)) (not (forall ((A8 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A8) A) (forall ((B8 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B8) B) (not (= C2 (@ (@ tptp.sup_su5525570899277871387at_nat A8) B8)))))))))) (forall ((C2 tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat C2) (@ (@ tptp.sup_sup_set_nat A) B)) (not (forall ((A8 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A8) A) (forall ((B8 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B8) B) (not (= C2 (@ (@ tptp.sup_sup_set_nat A8) B8)))))))))) (= tptp.ord_le1268244103169919719at_nat (lambda ((A5 tptp.set_Pr4329608150637261639at_nat) (B7 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat A5) B7) B7))) (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B7 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A5) B7) B7))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A))) (= (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat B) C2))) (@ (@ tptp.ord_le3146513528884898305at_nat C2) A)))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.inf_in7913087082777306421at_nat A))) (= (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat B) C2))) (@ (@ tptp.ord_le1268244103169919719at_nat C2) A)))) (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (= (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.sup_sup_set_nat B) C2))) (@ (@ tptp.ord_less_eq_set_nat C2) A)))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.minus_3314409938677909166at_nat A))) (= (@ (@ tptp.minus_3314409938677909166at_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat B) C2))))) (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A))) (= (@ (@ tptp.minus_minus_set_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.sup_sup_set_nat B) C2))))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.minus_3314409938677909166at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A) B)) C2) (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.minus_3314409938677909166at_nat A) C2)) (@ (@ tptp.minus_3314409938677909166at_nat B) C2)))) (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.sup_sup_set_nat A) B)) C2) (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.minus_minus_set_nat A) C2)) (@ (@ tptp.minus_minus_set_nat B) C2)))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat A))) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat B) C2)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 B)) (@ _let_1 C2))))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.minus_3314409938677909166at_nat A))) (= (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat B) C2)) (@ (@ tptp.inf_in7913087082777306421at_nat (@ _let_1 B)) (@ _let_1 C2))))) (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat B) C2)) (@ (@ tptp.inf_inf_set_nat (@ _let_1 B)) (@ _let_1 C2))))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat A))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B) C2)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 B)) (@ _let_1 C2))))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.minus_3314409938677909166at_nat A))) (= (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat B) C2)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 B)) (@ _let_1 C2))))) (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat B) C2)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 B)) (@ _let_1 C2))))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) (@ (@ tptp.minus_1356011639430497352at_nat A) B)) A)) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat A) B)) (@ (@ tptp.minus_3314409938677909166at_nat A) B)) A)) (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) (@ (@ tptp.minus_minus_set_nat A) B)) A)) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.minus_1356011639430497352at_nat A) B)) (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) A)) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.minus_3314409938677909166at_nat A) B)) (@ (@ tptp.inf_in7913087082777306421at_nat A) B)) A)) (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.minus_minus_set_nat A) B)) (@ (@ tptp.inf_inf_set_nat A) B)) A)) (forall ((X tptp.produc3843707927480180839at_nat) (Xs tptp.list_P5464809261938338413at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat X))) (=> (@ _let_1 (@ tptp.set_Pr3765526544606949372at_nat (@ tptp.butlas2561766218336428473at_nat Xs))) (@ _let_1 (@ tptp.set_Pr3765526544606949372at_nat Xs))))) (forall ((X tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X))) (=> (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat (@ tptp.butlas5569151904373679443at_nat Xs))) (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat Xs))))) (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xs tptp.list_P7985473006766602707_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o X))) (=> (@ _let_1 (@ tptp.set_Pr400311997697478754_nat_o (@ tptp.butlas8287983287669047583_nat_o Xs))) (@ _let_1 (@ tptp.set_Pr400311997697478754_nat_o Xs))))) (forall ((X tptp.int) (Xs tptp.list_int)) (let ((_let_1 (@ tptp.member_int X))) (=> (@ _let_1 (@ tptp.set_int2 (@ tptp.butlast_int Xs))) (@ _let_1 (@ tptp.set_int2 Xs))))) (forall ((X tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ tptp.member_nat X))) (=> (@ _let_1 (@ tptp.set_nat2 (@ tptp.butlast_nat Xs))) (@ _let_1 (@ tptp.set_nat2 Xs))))) (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ tptp.member7957490590177025114n_assn X))) (=> (@ _let_1 (@ tptp.set_Pr1139785259514867910n_assn (@ tptp.butlas3012047794866324995n_assn Xs))) (@ _let_1 (@ tptp.set_Pr1139785259514867910n_assn Xs))))) (forall ((Xs tptp.list_int)) (=> (@ tptp.distinct_int Xs) (@ tptp.distinct_int (@ tptp.butlast_int Xs)))) (forall ((Xs tptp.list_nat)) (=> (@ tptp.distinct_nat Xs) (@ tptp.distinct_nat (@ tptp.butlast_nat Xs)))) (forall ((L tptp.list_nat) (I tptp.nat) (X tptp.nat)) (= (@ (@ (@ tptp.list_update_nat (@ tptp.butlast_nat L)) I) X) (@ tptp.butlast_nat (@ (@ (@ tptp.list_update_nat L) I) X)))) (forall ((L tptp.list_c) (I tptp.nat) (X tptp.c)) (= (@ (@ (@ tptp.list_update_c (@ tptp.butlast_c L)) I) X) (@ tptp.butlast_c (@ (@ (@ tptp.list_update_c L) I) X)))) (forall ((L tptp.list_d) (I tptp.nat) (X tptp.d)) (= (@ (@ (@ tptp.list_update_d (@ tptp.butlast_d L)) I) X) (@ tptp.butlast_d (@ (@ (@ tptp.list_update_d L) I) X)))) (forall ((Xs tptp.list_nat)) (= (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) (@ tptp.rev_nat Xs)) (forall ((I4 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (=> (@ (@ tptp.ord_less_eq_nat I4) J2) (=> (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.ord_less_eq_nat (@ _let_1 J2)) (@ _let_1 I4)))))))) (forall ((Xs tptp.list_int)) (= (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) (@ tptp.rev_int Xs)) (forall ((I4 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs))) (=> (@ (@ tptp.ord_less_eq_nat I4) J2) (=> (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_int Xs)) (@ (@ tptp.ord_less_eq_int (@ _let_1 J2)) (@ _let_1 I4)))))))) (forall ((Xs tptp.list_nat) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (=> (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) (@ tptp.rev_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 J)) (@ _let_1 I))))))) (forall ((Xs tptp.list_int) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs))) (=> (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) (@ tptp.rev_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 J)) (@ _let_1 I))))))) (forall ((Xs tptp.list_Code_integer)) (=> (@ (@ tptp.sorted710888440204495920nteger tptp.ord_le6747313008572928689nteger) Xs) (@ (@ tptp.sorted710888440204495920nteger tptp.ord_le3102999989581377725nteger) Xs))) (forall ((Xs tptp.list_num)) (=> (@ (@ tptp.sorted_wrt_num tptp.ord_less_num) Xs) (@ (@ tptp.sorted_wrt_num tptp.ord_less_eq_num) Xs))) (forall ((Xs tptp.list_nat)) (=> (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) Xs) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) Xs))) (forall ((Xs tptp.list_int)) (=> (@ (@ tptp.sorted_wrt_int tptp.ord_less_int) Xs) (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) Xs))) (forall ((Xs tptp.list_Code_integer) (Ys tptp.list_Code_integer)) (let ((_let_1 (@ tptp.sorted710888440204495920nteger tptp.ord_le6747313008572928689nteger))) (=> (@ _let_1 Xs) (=> (@ _let_1 Ys) (=> (= (@ tptp.set_Code_integer2 Ys) (@ tptp.set_Code_integer2 Xs)) (= Ys Xs)))))) (forall ((Xs tptp.list_num) (Ys tptp.list_num)) (let ((_let_1 (@ tptp.sorted_wrt_num tptp.ord_less_num))) (=> (@ _let_1 Xs) (=> (@ _let_1 Ys) (=> (= (@ tptp.set_num2 Ys) (@ tptp.set_num2 Xs)) (= Ys Xs)))))) (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.sorted_wrt_nat tptp.ord_less_nat))) (=> (@ _let_1 Xs) (=> (@ _let_1 Ys) (=> (= (@ tptp.set_nat2 Ys) (@ tptp.set_nat2 Xs)) (= Ys Xs)))))) (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.sorted_wrt_int tptp.ord_less_int))) (=> (@ _let_1 Xs) (=> (@ _let_1 Ys) (=> (= (@ tptp.set_int2 Ys) (@ tptp.set_int2 Xs)) (= Ys Xs)))))) (forall ((Xs tptp.list_c) (P (-> tptp.c tptp.c Bool))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_c Xs)) tptp.one_one_nat) (@ (@ tptp.sorted_wrt_c P) Xs))) (forall ((Xs tptp.list_d) (P (-> tptp.d tptp.d Bool))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_d Xs)) tptp.one_one_nat) (@ (@ tptp.sorted_wrt_d P) Xs))) (forall ((Xs tptp.list_nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) tptp.one_one_nat) (@ (@ tptp.sorted_wrt_nat P) Xs))) (forall ((Xs tptp.list_int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs)) tptp.one_one_nat) (@ (@ tptp.sorted_wrt_int P) Xs))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 Y)) (@ _let_1 Z))) (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat Y) Z))))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z 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 Z))) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat Y) Z))))) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.sup_sup_assn (@ _let_1 Y)) (@ _let_1 Z))) (@ _let_1 (@ (@ tptp.sup_sup_assn Y) Z))))) (forall ((X tptp.filter_nat) (Y tptp.filter_nat) (Z tptp.filter_nat)) (let ((_let_1 (@ tptp.inf_inf_filter_nat X))) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.sup_sup_filter_nat (@ _let_1 Y)) (@ _let_1 Z))) (@ _let_1 (@ (@ tptp.sup_sup_filter_nat Y) Z))))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat (@ _let_1 Y)) (@ _let_1 Z))) (@ _let_1 (@ (@ tptp.sup_sup_set_nat Y) Z))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat (@ _let_1 Y)) (@ _let_1 Z))) (@ _let_1 (@ (@ tptp.sup_sup_nat Y) Z))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.inf_inf_int X))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int (@ _let_1 Y)) (@ _let_1 Z))) (@ _let_1 (@ (@ tptp.sup_sup_int Y) Z))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.sup_su6327502436637775413at_nat X))) (@ (@ tptp.ord_le3146513528884898305at_nat (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z))) (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 Y)) (@ _let_1 Z))))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat X))) (@ (@ tptp.ord_le1268244103169919719at_nat (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat Y) Z))) (@ (@ tptp.inf_in7913087082777306421at_nat (@ _let_1 Y)) (@ _let_1 Z))))) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (@ (@ tptp.ord_less_eq_assn (@ _let_1 (@ (@ tptp.inf_inf_assn Y) Z))) (@ (@ tptp.inf_inf_assn (@ _let_1 Y)) (@ _let_1 Z))))) (forall ((X tptp.filter_nat) (Y tptp.filter_nat) (Z tptp.filter_nat)) (let ((_let_1 (@ tptp.sup_sup_filter_nat X))) (@ (@ tptp.ord_le2510731241096832064er_nat (@ _let_1 (@ (@ tptp.inf_inf_filter_nat Y) Z))) (@ (@ tptp.inf_inf_filter_nat (@ _let_1 Y)) (@ _let_1 Z))))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y) Z))) (@ (@ tptp.inf_inf_set_nat (@ _let_1 Y)) (@ _let_1 Z))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z))) (@ (@ tptp.inf_inf_nat (@ _let_1 Y)) (@ _let_1 Z))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.sup_sup_int X))) (@ (@ tptp.ord_less_eq_int (@ _let_1 (@ (@ tptp.inf_inf_int Y) Z))) (@ (@ tptp.inf_inf_int (@ _let_1 Y)) (@ _let_1 Z))))) (forall ((Xs tptp.list_nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat))) (=> (@ _let_1 Xs) (@ _let_1 (@ (@ tptp.remove1_nat A2) Xs))))) (forall ((Xs tptp.list_int) (A2 tptp.int)) (let ((_let_1 (@ tptp.sorted_wrt_int tptp.ord_less_eq_int))) (=> (@ _let_1 Xs) (@ _let_1 (@ (@ tptp.remove1_int A2) Xs))))) (= tptp.insert9069300056098147895at_nat (lambda ((A3 tptp.produc3843707927480180839at_nat) (__flatten_var_0 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.insert9069300056098147895at_nat A3) tptp.bot_bo228742789529271731at_nat)) __flatten_var_0))) (= tptp.insert8211810215607154385at_nat (lambda ((A3 tptp.product_prod_nat_nat) (__flatten_var_0 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.insert8211810215607154385at_nat A3) tptp.bot_bo2099793752762293965at_nat)) __flatten_var_0))) (= tptp.insert_o2 (lambda ((A3 Bool) (__flatten_var_0 tptp.set_o)) (@ (@ tptp.sup_sup_set_o (@ (@ tptp.insert_o2 A3) tptp.bot_bot_set_o)) __flatten_var_0))) (= tptp.insert_nat2 (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.set_nat)) (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.insert_nat2 A3) tptp.bot_bot_set_nat)) __flatten_var_0))) (= tptp.insert_int2 (lambda ((A3 tptp.int) (__flatten_var_0 tptp.set_int)) (@ (@ tptp.sup_sup_set_int (@ (@ tptp.insert_int2 A3) tptp.bot_bot_set_int)) __flatten_var_0))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (X tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ (@ tptp.insert9069300056098147895at_nat X) tptp.bot_bo228742789529271731at_nat))) (let ((_let_2 (= B _let_1))) (let ((_let_3 (= A _let_1))) (= (= (@ (@ tptp.sup_su5525570899277871387at_nat A) B) _let_1) (or (and (= A tptp.bot_bo228742789529271731at_nat) _let_2) (and _let_3 (= B tptp.bot_bo228742789529271731at_nat)) (and _let_3 _let_2))))))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat))) (let ((_let_2 (= B _let_1))) (let ((_let_3 (= A _let_1))) (= (= (@ (@ tptp.sup_su6327502436637775413at_nat A) B) _let_1) (or (and (= A tptp.bot_bo2099793752762293965at_nat) _let_2) (and _let_3 (= B tptp.bot_bo2099793752762293965at_nat)) (and _let_3 _let_2))))))) (forall ((A tptp.set_o) (B tptp.set_o) (X Bool)) (let ((_let_1 (@ (@ tptp.insert_o2 X) tptp.bot_bot_set_o))) (let ((_let_2 (= B _let_1))) (let ((_let_3 (= A _let_1))) (= (= (@ (@ tptp.sup_sup_set_o A) B) _let_1) (or (and (= A tptp.bot_bot_set_o) _let_2) (and _let_3 (= B tptp.bot_bot_set_o)) (and _let_3 _let_2))))))) (forall ((A tptp.set_nat) (B tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat2 X) tptp.bot_bot_set_nat))) (let ((_let_2 (= B _let_1))) (let ((_let_3 (= A _let_1))) (= (= (@ (@ tptp.sup_sup_set_nat A) B) _let_1) (or (and (= A tptp.bot_bot_set_nat) _let_2) (and _let_3 (= B tptp.bot_bot_set_nat)) (and _let_3 _let_2))))))) (forall ((A tptp.set_int) (B tptp.set_int) (X tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int2 X) tptp.bot_bot_set_int))) (let ((_let_2 (= B _let_1))) (let ((_let_3 (= A _let_1))) (= (= (@ (@ tptp.sup_sup_set_int A) B) _let_1) (or (and (= A tptp.bot_bot_set_int) _let_2) (and _let_3 (= B tptp.bot_bot_set_int)) (and _let_3 _let_2))))))) (forall ((X tptp.produc3843707927480180839at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ (@ tptp.insert9069300056098147895at_nat X) tptp.bot_bo228742789529271731at_nat))) (let ((_let_2 (= B _let_1))) (let ((_let_3 (= A _let_1))) (= (= _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A) B)) (or (and (= A tptp.bot_bo228742789529271731at_nat) _let_2) (and _let_3 (= B tptp.bot_bo228742789529271731at_nat)) (and _let_3 _let_2))))))) (forall ((X tptp.product_prod_nat_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat))) (let ((_let_2 (= B _let_1))) (let ((_let_3 (= A _let_1))) (= (= _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat A) B)) (or (and (= A tptp.bot_bo2099793752762293965at_nat) _let_2) (and _let_3 (= B tptp.bot_bo2099793752762293965at_nat)) (and _let_3 _let_2))))))) (forall ((X Bool) (A tptp.set_o) (B tptp.set_o)) (let ((_let_1 (@ (@ tptp.insert_o2 X) tptp.bot_bot_set_o))) (let ((_let_2 (= B _let_1))) (let ((_let_3 (= A _let_1))) (= (= _let_1 (@ (@ tptp.sup_sup_set_o A) B)) (or (and (= A tptp.bot_bot_set_o) _let_2) (and _let_3 (= B tptp.bot_bot_set_o)) (and _let_3 _let_2))))))) (forall ((X tptp.nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ (@ tptp.insert_nat2 X) tptp.bot_bot_set_nat))) (let ((_let_2 (= B _let_1))) (let ((_let_3 (= A _let_1))) (= (= _let_1 (@ (@ tptp.sup_sup_set_nat A) B)) (or (and (= A tptp.bot_bot_set_nat) _let_2) (and _let_3 (= B tptp.bot_bot_set_nat)) (and _let_3 _let_2))))))) (forall ((X tptp.int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ (@ tptp.insert_int2 X) tptp.bot_bot_set_int))) (let ((_let_2 (= B _let_1))) (let ((_let_3 (= A _let_1))) (= (= _let_1 (@ (@ tptp.sup_sup_set_int A) B)) (or (and (= A tptp.bot_bot_set_int) _let_2) (and _let_3 (= B tptp.bot_bot_set_int)) (and _let_3 _let_2))))))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A) B) (= (@ (@ tptp.sup_su5525570899277871387at_nat A) (@ (@ tptp.minus_3314409938677909166at_nat B) A)) B))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (= (@ (@ tptp.sup_sup_set_nat A) (@ (@ tptp.minus_minus_set_nat B) A)) B))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.minus_3314409938677909166at_nat A) B)) C2) (@ (@ tptp.ord_le1268244103169919719at_nat A) (@ (@ tptp.sup_su5525570899277871387at_nat B) C2)))) (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A) B)) C2) (@ (@ tptp.ord_less_eq_set_nat A) (@ (@ tptp.sup_sup_set_nat B) C2)))) (forall ((L tptp.list_Code_integer)) (= (@ (@ tptp.sorted710888440204495920nteger tptp.ord_le6747313008572928689nteger) L) (and (@ (@ tptp.sorted710888440204495920nteger tptp.ord_le3102999989581377725nteger) L) (@ tptp.distin1543349897113766820nteger L)))) (forall ((L tptp.list_num)) (= (@ (@ tptp.sorted_wrt_num tptp.ord_less_num) L) (and (@ (@ tptp.sorted_wrt_num tptp.ord_less_eq_num) L) (@ tptp.distinct_num L)))) (forall ((L tptp.list_nat)) (= (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) L) (and (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) L) (@ tptp.distinct_nat L)))) (forall ((L tptp.list_int)) (= (@ (@ tptp.sorted_wrt_int tptp.ord_less_int) L) (and (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) L) (@ tptp.distinct_int L)))) (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))) (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))) (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat))) (=> (@ _let_1 Xs) (=> (@ tptp.distinct_nat Xs) (=> (@ _let_1 Ys) (=> (@ tptp.distinct_nat Ys) (=> (= (@ tptp.set_nat2 Xs) (@ tptp.set_nat2 Ys)) (= Xs Ys)))))))) (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.sorted_wrt_int tptp.ord_less_eq_int))) (=> (@ _let_1 Xs) (=> (@ tptp.distinct_int Xs) (=> (@ _let_1 Ys) (=> (@ tptp.distinct_int Ys) (=> (= (@ tptp.set_int2 Xs) (@ tptp.set_int2 Ys)) (= Xs Ys)))))))) _let_131 _let_130 _let_129 _let_128 (forall ((P (-> tptp.c tptp.c Bool)) (Xs tptp.list_c) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_c Xs))) (=> (@ (@ tptp.sorted_wrt_c P) Xs) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_c Xs)) (@ (@ P (@ _let_1 I)) (@ _let_1 J))))))) (forall ((P (-> tptp.d tptp.d Bool)) (Xs tptp.list_d) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_d Xs))) (=> (@ (@ tptp.sorted_wrt_d P) Xs) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_d Xs)) (@ (@ P (@ _let_1 I)) (@ _let_1 J))))))) (forall ((P (-> tptp.nat tptp.nat Bool)) (Xs tptp.list_nat) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (=> (@ (@ tptp.sorted_wrt_nat P) Xs) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs)) (@ (@ P (@ _let_1 I)) (@ _let_1 J))))))) (forall ((P (-> tptp.int tptp.int Bool)) (Xs tptp.list_int) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs))) (=> (@ (@ tptp.sorted_wrt_int P) Xs) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_int Xs)) (@ (@ P (@ _let_1 I)) (@ _let_1 J))))))) (forall ((N tptp.nat) (Xs tptp.list_c)) (let ((_let_1 (@ tptp.butlast_c Xs))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_c _let_1)) (= (@ (@ tptp.nth_c _let_1) N) (@ (@ tptp.nth_c Xs) N))))) (forall ((N tptp.nat) (Xs tptp.list_d)) (let ((_let_1 (@ tptp.butlast_d Xs))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_d _let_1)) (= (@ (@ tptp.nth_d _let_1) N) (@ (@ tptp.nth_d Xs) N))))) (forall ((N tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ tptp.butlast_nat Xs))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat _let_1)) (= (@ (@ tptp.nth_nat _let_1) N) (@ (@ tptp.nth_nat Xs) N))))) (forall ((N tptp.nat) (Xs tptp.list_int)) (let ((_let_1 (@ tptp.butlast_int Xs))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int _let_1)) (= (@ (@ tptp.nth_int _let_1) N) (@ (@ tptp.nth_int Xs) N))))) (forall ((Xs tptp.list_nat)) (= (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) Xs) (forall ((I4 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (=> (@ (@ tptp.ord_less_eq_nat I4) J2) (=> (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I4)) (@ _let_1 J2)))))))) (forall ((Xs tptp.list_int)) (= (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) Xs) (forall ((I4 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs))) (=> (@ (@ tptp.ord_less_eq_nat I4) J2) (=> (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_int Xs)) (@ (@ tptp.ord_less_eq_int (@ _let_1 I4)) (@ _let_1 J2)))))))) (forall ((Xs tptp.list_nat) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (=> (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) Xs) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I)) (@ _let_1 J))))))) (forall ((Xs tptp.list_int) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs))) (=> (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) Xs) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_int Xs)) (@ (@ tptp.ord_less_eq_int (@ _let_1 I)) (@ _let_1 J))))))) (forall ((Xs tptp.list_nat)) (= (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) Xs) (forall ((I4 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (=> (@ (@ tptp.ord_less_nat I4) J2) (=> (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I4)) (@ _let_1 J2)))))))) (forall ((Xs tptp.list_int)) (= (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) Xs) (forall ((I4 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs))) (=> (@ (@ tptp.ord_less_nat I4) J2) (=> (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_int Xs)) (@ (@ tptp.ord_less_eq_int (@ _let_1 I4)) (@ _let_1 J2)))))))) (forall ((L tptp.list_nat)) (let ((_let_1 (@ tptp.merges1656613366846331073ps_nat L))) (and (@ tptp.distinct_nat _let_1) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) _let_1) (= (@ tptp.set_nat2 _let_1) (@ tptp.set_nat2 L))))) (forall ((L tptp.list_int)) (let ((_let_1 (@ tptp.merges1654122896337280797ps_int L))) (and (@ tptp.distinct_int _let_1) (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) _let_1) (= (@ tptp.set_int2 _let_1) (@ tptp.set_int2 L))))) (forall ((P (-> tptp.produc3658429121746597890et_nat Bool)) (Q (-> tptp.produc3658429121746597890et_nat Bool)) (H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (= (@ (@ (@ tptp.times_assn_raw P) Q) (@ (@ tptp.produc7507926704131184380et_nat H2) As2)) (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) (@ P (@ _let_1 As1)) (@ Q (@ _let_1 As22))))))) (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 ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (= Xb (@ (@ tptp.produc7507926704131184380et_nat H) As)) (= Y (not (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) (@ X (@ _let_1 As1)) (@ Xa (@ _let_1 As22)))))))))))) (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat)) (=> (@ (@ (@ tptp.times_assn_raw X) Xa) Xb) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (= Xb (@ (@ tptp.produc7507926704131184380et_nat H) As)) (not (exists ((As12 tptp.set_nat) (As23 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H))) (and (= As (@ (@ 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))))))))))) (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 ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (= Xb (@ (@ tptp.produc7507926704131184380et_nat H) As)) (exists ((As13 tptp.set_nat) (As24 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H))) (and (= As (@ (@ 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)))))))))) (forall ((N tptp.nat) (P (-> tptp.nat Bool)) (M2 tptp.nat)) (=> (forall ((K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (@ P K))) (=> (forall ((K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (=> (forall ((I6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) I6) (@ P I6))) (@ P K)))) (@ P M2)))) (forall ((L12 tptp.list_nat) (L23 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.merge_nat L12) L23))) (let ((_let_2 (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat))) (=> (and (@ tptp.distinct_nat L12) (@ _let_2 L12)) (=> (and (@ tptp.distinct_nat L23) (@ _let_2 L23)) (and (@ tptp.distinct_nat _let_1) (@ _let_2 _let_1) (= (@ tptp.set_nat2 _let_1) (@ (@ tptp.sup_sup_set_nat (@ tptp.set_nat2 L12)) (@ tptp.set_nat2 L23))))))))) (forall ((L12 tptp.list_int) (L23 tptp.list_int)) (let ((_let_1 (@ (@ tptp.merge_int L12) L23))) (let ((_let_2 (@ tptp.sorted_wrt_int tptp.ord_less_eq_int))) (=> (and (@ tptp.distinct_int L12) (@ _let_2 L12)) (=> (and (@ tptp.distinct_int L23) (@ _let_2 L23)) (and (@ tptp.distinct_int _let_1) (@ _let_2 _let_1) (= (@ tptp.set_int2 _let_1) (@ (@ tptp.sup_sup_set_int (@ tptp.set_int2 L12)) (@ tptp.set_int2 L23))))))))) (forall ((From tptp.nat) (To tptp.nat) (Xs tptp.list_c) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat From) To) (=> (@ (@ tptp.ord_less_eq_nat To) (@ tptp.size_size_list_c Xs)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.minus_minus_nat To) From)) (= (@ (@ tptp.nth_c (@ (@ (@ tptp.slice_c From) To) Xs)) I) (@ (@ tptp.nth_c Xs) (@ (@ tptp.plus_plus_nat From) I))))))) (forall ((From tptp.nat) (To tptp.nat) (Xs tptp.list_d) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat From) To) (=> (@ (@ tptp.ord_less_eq_nat To) (@ tptp.size_size_list_d Xs)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.minus_minus_nat To) From)) (= (@ (@ tptp.nth_d (@ (@ (@ tptp.slice_d From) To) Xs)) I) (@ (@ tptp.nth_d Xs) (@ (@ tptp.plus_plus_nat From) I))))))) (forall ((From tptp.nat) (To tptp.nat) (Xs tptp.list_nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat From) To) (=> (@ (@ tptp.ord_less_eq_nat To) (@ tptp.size_size_list_nat Xs)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.minus_minus_nat To) From)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.slice_nat From) To) Xs)) I) (@ (@ tptp.nth_nat Xs) (@ (@ tptp.plus_plus_nat From) I))))))) (forall ((From tptp.nat) (To tptp.nat) (Xs tptp.list_int) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat From) To) (=> (@ (@ tptp.ord_less_eq_nat To) (@ tptp.size_size_list_int Xs)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.minus_minus_nat To) From)) (= (@ (@ tptp.nth_int (@ (@ (@ tptp.slice_int From) To) Xs)) I) (@ (@ tptp.nth_int Xs) (@ (@ tptp.plus_plus_nat From) I))))))) (forall ((Xs tptp.list_nat)) (= (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) (@ tptp.rev_nat Xs)) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (let ((_let_2 (@ tptp.suc I4))) (=> (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.ord_less_eq_nat (@ _let_1 _let_2)) (@ _let_1 I4)))))))) (forall ((Xs tptp.list_int)) (= (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) (@ tptp.rev_int Xs)) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs))) (let ((_let_2 (@ tptp.suc I4))) (=> (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_size_list_int Xs)) (@ (@ tptp.ord_less_eq_int (@ _let_1 _let_2)) (@ _let_1 I4)))))))) (forall ((B2 tptp.multis2468970476368604999at_nat) (A2 tptp.multis2468970476368604999at_nat) (C tptp.multis2468970476368604999at_nat)) (= (= (@ (@ tptp.plus_p7104986032573967614at_nat B2) A2) (@ (@ tptp.plus_p7104986032573967614at_nat C) A2)) (= B2 C))) (forall ((B2 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B2) A2) (@ (@ tptp.plus_plus_rat C) A2)) (= B2 C))) (forall ((B2 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B2) A2) (@ (@ tptp.plus_plus_nat C) A2)) (= B2 C))) (forall ((B2 tptp.int) (A2 tptp.int) (C tptp.int)) (= (= (@ (@ tptp.plus_plus_int B2) A2) (@ (@ tptp.plus_plus_int C) A2)) (= B2 C))) (forall ((A2 tptp.multis2468970476368604999at_nat) (B2 tptp.multis2468970476368604999at_nat) (C tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.plus_p7104986032573967614at_nat A2))) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A2))) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A2))) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A2))) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))) (forall ((P tptp.assn) (Q tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn (@ (@ tptp.sup_sup_assn P) Q)) H2) (or (@ (@ tptp.rep_assn P) H2) (@ (@ tptp.rep_assn Q) H2)))) (forall ((A2 Bool) (B2 Bool)) (= (@ (@ tptp.sup_sup_assn (@ tptp.pure_assn A2)) (@ tptp.pure_assn B2)) (@ tptp.pure_assn (or A2 B2)))) (forall ((A2 tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B2) C)) (@ (@ tptp.ord_less_eq_rat A2) B2))) (forall ((A2 tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B2) C)) (@ (@ tptp.ord_less_eq_nat A2) B2))) (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.ord_less_eq_int A2) B2))) (forall ((C tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_rat A2) B2)))) (forall ((C tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_nat A2) B2)))) (forall ((C tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_int A2) B2)))) (forall ((C tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_rat A2) B2)))) (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger C))) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_le6747313008572928689nteger A2) B2)))) (forall ((C tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_nat A2) B2)))) (forall ((C tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_int A2) B2)))) (forall ((A2 tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B2) C)) (@ (@ tptp.ord_less_rat A2) B2))) (forall ((A2 tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) C)) (@ (@ tptp.plus_p5714425477246183910nteger B2) C)) (@ (@ tptp.ord_le6747313008572928689nteger A2) B2))) (forall ((A2 tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B2) C)) (@ (@ tptp.ord_less_nat A2) B2))) (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.ord_less_int A2) B2))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A2) B2)) B2) A2)) (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A2) B2)) B2) A2)) (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A2) B2)) B2) A2)) (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A2) B2)) B2) A2)) (forall ((C tptp.multis2468970476368604999at_nat) (A2 tptp.multis2468970476368604999at_nat) (B2 tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.plus_p7104986032573967614at_nat C))) (= (@ (@ tptp.minus_4286766774447292334at_nat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.minus_4286766774447292334at_nat A2) B2)))) (forall ((C tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.minus_minus_rat A2) B2)))) (forall ((C tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.minus_minus_nat A2) B2)))) (forall ((C tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.minus_minus_int (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.minus_minus_int A2) B2)))) (forall ((A2 tptp.multis2468970476368604999at_nat) (B2 tptp.multis2468970476368604999at_nat)) (= (@ (@ tptp.minus_4286766774447292334at_nat (@ (@ tptp.plus_p7104986032573967614at_nat A2) B2)) A2) B2)) (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A2) B2)) A2) B2)) (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A2) B2)) A2) B2)) (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A2) B2)) A2) B2)) (forall ((A2 tptp.multis2468970476368604999at_nat) (C tptp.multis2468970476368604999at_nat) (B2 tptp.multis2468970476368604999at_nat)) (= (@ (@ tptp.minus_4286766774447292334at_nat (@ (@ tptp.plus_p7104986032573967614at_nat A2) C)) (@ (@ tptp.plus_p7104986032573967614at_nat B2) C)) (@ (@ tptp.minus_4286766774447292334at_nat A2) B2))) (forall ((A2 tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B2) C)) (@ (@ tptp.minus_minus_rat A2) B2))) (forall ((A2 tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B2) C)) (@ (@ tptp.minus_minus_nat A2) B2))) (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.minus_minus_int A2) B2))) (forall ((A2 tptp.multis2468970476368604999at_nat) (B2 tptp.multis2468970476368604999at_nat)) (= (@ (@ tptp.minus_4286766774447292334at_nat (@ (@ tptp.plus_p7104986032573967614at_nat A2) B2)) B2) A2)) (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A2) B2)) B2) A2)) (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A2) B2)) B2) A2)) (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A2) B2)) B2) A2)) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc N))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_nat (@ tptp.suc M2)) (@ tptp.suc N)))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M2)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M2) N))) (forall ((K3 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K3))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M2) N)))) (forall ((B2 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B2) A2) (= (@ (@ tptp.plus_plus_rat B2) (@ (@ tptp.minus_minus_rat A2) B2)) A2))) (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (= (@ (@ tptp.plus_plus_nat B2) (@ (@ tptp.minus_minus_nat A2) B2)) A2))) (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (= (@ (@ tptp.plus_plus_int B2) (@ (@ tptp.minus_minus_int A2) B2)) A2))) (forall ((B2 tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B2) A2) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A2) B2)) B2) A2))) (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat A2) B2)) B2) A2))) (forall ((B2 tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A2) B2)) B2) A2))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.suc A2))) (=> (@ (@ tptp.ord_less_nat A2) B2) (= (@ (@ tptp.ord_min_nat _let_1) B2) _let_1)))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.suc A2))) (=> (@ (@ tptp.ord_less_nat A2) B2) (= (@ (@ tptp.ord_min_nat B2) _let_1) _let_1)))) (forall ((P tptp.assn) (Q tptp.assn) (H2 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) tptp.bot_bot_set_nat))) (= (@ (@ tptp.rep_assn (@ (@ tptp.sup_sup_assn P) Q)) _let_1) (or (@ (@ tptp.rep_assn P) _let_1) (@ (@ tptp.rep_assn Q) _let_1))))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M2) (= (@ tptp.suc (@ _let_1 M2)) (@ _let_1 (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat))))))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (not (forall ((Q5 tptp.nat)) (not (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) Q5)))))))) (forall ((I tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) M2)))) (forall ((I tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) I)))) (= tptp.ord_less_nat (lambda ((M tptp.nat) (N2 tptp.nat)) (exists ((K4 tptp.nat)) (= N2 (@ tptp.suc (@ (@ tptp.plus_plus_nat M) K4)))))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (exists ((K tptp.nat)) (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) K)))))) (forall ((B2 tptp.multis2468970476368604999at_nat) (A2 tptp.multis2468970476368604999at_nat) (C tptp.multis2468970476368604999at_nat)) (=> (= (@ (@ tptp.plus_p7104986032573967614at_nat B2) A2) (@ (@ tptp.plus_p7104986032573967614at_nat C) A2)) (= B2 C))) (forall ((B2 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat B2) A2) (@ (@ tptp.plus_plus_rat C) A2)) (= B2 C))) (forall ((B2 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat B2) A2) (@ (@ tptp.plus_plus_nat C) A2)) (= B2 C))) (forall ((B2 tptp.int) (A2 tptp.int) (C tptp.int)) (=> (= (@ (@ tptp.plus_plus_int B2) A2) (@ (@ tptp.plus_plus_int C) A2)) (= B2 C))) (forall ((A2 tptp.multis2468970476368604999at_nat) (B2 tptp.multis2468970476368604999at_nat) (C tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.plus_p7104986032573967614at_nat A2))) (=> (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A2))) (=> (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A2))) (=> (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A2))) (=> (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))) (forall ((B2 tptp.multis2468970476368604999at_nat) (A2 tptp.multis2468970476368604999at_nat) (C tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.plus_p7104986032573967614at_nat B2))) (let ((_let_2 (@ tptp.plus_p7104986032573967614at_nat A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((B2 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat B2))) (let ((_let_2 (@ tptp.plus_plus_rat A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((B2 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat B2))) (let ((_let_2 (@ tptp.plus_plus_nat A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((B2 tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int B2))) (let ((_let_2 (@ tptp.plus_plus_int A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (= tptp.plus_p7104986032573967614at_nat (lambda ((A3 tptp.multis2468970476368604999at_nat) (B3 tptp.multis2468970476368604999at_nat)) (@ (@ tptp.plus_p7104986032573967614at_nat B3) A3))) (= tptp.plus_plus_rat (lambda ((A3 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.plus_plus_rat B3) A3))) (= tptp.plus_plus_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.plus_plus_nat B3) A3))) (= tptp.plus_plus_int (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ tptp.plus_plus_int B3) A3))) (forall ((B2 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B2) A2) (@ (@ tptp.plus_plus_rat C) A2)) (= B2 C))) (forall ((B2 tptp.int) (A2 tptp.int) (C tptp.int)) (= (= (@ (@ tptp.plus_plus_int B2) A2) (@ (@ tptp.plus_plus_int C) A2)) (= B2 C))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A2))) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A2))) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))) (forall ((A2 tptp.multis2468970476368604999at_nat) (B2 tptp.multis2468970476368604999at_nat) (C tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.plus_p7104986032573967614at_nat A2))) (= (@ (@ tptp.plus_p7104986032573967614at_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_p7104986032573967614at_nat B2) C))))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A2))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B2) C))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A2))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B2) C))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A2))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B2) C))))) (forall ((B tptp.multis2468970476368604999at_nat) (K3 tptp.multis2468970476368604999at_nat) (B2 tptp.multis2468970476368604999at_nat) (A2 tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.plus_p7104986032573967614at_nat A2))) (let ((_let_2 (@ tptp.plus_p7104986032573967614at_nat K3))) (=> (= B (@ _let_2 B2)) (= (@ _let_1 B) (@ _let_2 (@ _let_1 B2))))))) (forall ((B tptp.rat) (K3 tptp.rat) (B2 tptp.rat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A2))) (let ((_let_2 (@ tptp.plus_plus_rat K3))) (=> (= B (@ _let_2 B2)) (= (@ _let_1 B) (@ _let_2 (@ _let_1 B2))))))) (forall ((B tptp.nat) (K3 tptp.nat) (B2 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A2))) (let ((_let_2 (@ tptp.plus_plus_nat K3))) (=> (= B (@ _let_2 B2)) (= (@ _let_1 B) (@ _let_2 (@ _let_1 B2))))))) (forall ((B tptp.int) (K3 tptp.int) (B2 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A2))) (let ((_let_2 (@ tptp.plus_plus_int K3))) (=> (= B (@ _let_2 B2)) (= (@ _let_1 B) (@ _let_2 (@ _let_1 B2))))))) (forall ((A tptp.multis2468970476368604999at_nat) (K3 tptp.multis2468970476368604999at_nat) (A2 tptp.multis2468970476368604999at_nat) (B2 tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.plus_p7104986032573967614at_nat K3))) (=> (= A (@ _let_1 A2)) (= (@ (@ tptp.plus_p7104986032573967614at_nat A) B2) (@ _let_1 (@ (@ tptp.plus_p7104986032573967614at_nat A2) B2)))))) (forall ((A tptp.rat) (K3 tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat K3))) (=> (= A (@ _let_1 A2)) (= (@ (@ tptp.plus_plus_rat A) B2) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) B2)))))) (forall ((A tptp.nat) (K3 tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K3))) (=> (= A (@ _let_1 A2)) (= (@ (@ tptp.plus_plus_nat A) B2) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) B2)))))) (forall ((A tptp.int) (K3 tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K3))) (=> (= A (@ _let_1 A2)) (= (@ (@ tptp.plus_plus_int A) B2) (@ _let_1 (@ (@ tptp.plus_plus_int A2) B2)))))) (forall ((I tptp.rat) (J tptp.rat) (K3 tptp.rat) (L tptp.rat)) (=> (and (= I J) (= K3 L)) (= (@ (@ tptp.plus_plus_rat I) K3) (@ (@ tptp.plus_plus_rat J) L)))) (forall ((I tptp.nat) (J tptp.nat) (K3 tptp.nat) (L tptp.nat)) (=> (and (= I J) (= K3 L)) (= (@ (@ tptp.plus_plus_nat I) K3) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((I tptp.int) (J tptp.int) (K3 tptp.int) (L tptp.int)) (=> (and (= I J) (= K3 L)) (= (@ (@ tptp.plus_plus_int I) K3) (@ (@ tptp.plus_plus_int J) L)))) (forall ((A2 tptp.rat) (C tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B2) C)) (@ (@ tptp.ord_less_eq_rat A2) B2))) (forall ((A2 tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B2) C)) (@ (@ tptp.ord_less_eq_nat A2) B2))) (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.ord_less_eq_int A2) B2))) (forall ((C tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_rat A2) B2)))) (forall ((C tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_nat A2) B2)))) (forall ((C tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_int A2) B2)))) (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (exists ((C5 tptp.nat)) (= B3 (@ (@ tptp.plus_plus_nat A3) C5))))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B2) C)))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B2) C)))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B2) C)))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (not (forall ((C4 tptp.nat)) (not (= B2 (@ (@ tptp.plus_plus_nat A2) C4))))))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B2))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2))))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_eq_rat C) D2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B2) D2))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B2) D2))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_eq_int C) D2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B2) D2))))) (forall ((I tptp.rat) (J tptp.rat) (K3 tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I) J) (@ (@ tptp.ord_less_eq_rat K3) L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K3)) (@ (@ tptp.plus_plus_rat J) L)))) (forall ((I tptp.nat) (J tptp.nat) (K3 tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat K3) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K3)) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((I tptp.int) (J tptp.int) (K3 tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I) J) (@ (@ tptp.ord_less_eq_int K3) L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K3)) (@ (@ tptp.plus_plus_int J) L)))) (forall ((I tptp.rat) (J tptp.rat) (K3 tptp.rat) (L tptp.rat)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_rat K3) L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K3)) (@ (@ tptp.plus_plus_rat J) L)))) (forall ((I tptp.nat) (J tptp.nat) (K3 tptp.nat) (L tptp.nat)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_nat K3) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K3)) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((I tptp.int) (J tptp.int) (K3 tptp.int) (L tptp.int)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_int K3) L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K3)) (@ (@ tptp.plus_plus_int J) L)))) (forall ((I tptp.rat) (J tptp.rat) (K3 tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I) J) (= K3 L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K3)) (@ (@ tptp.plus_plus_rat J) L)))) (forall ((I tptp.nat) (J tptp.nat) (K3 tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (= K3 L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K3)) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((I tptp.int) (J tptp.int) (K3 tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I) J) (= K3 L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K3)) (@ (@ tptp.plus_plus_int J) L)))) (forall ((I tptp.rat) (J tptp.rat) (K3 tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I) J) (@ (@ tptp.ord_less_rat K3) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K3)) (@ (@ tptp.plus_plus_rat J) L)))) (forall ((I tptp.code_integer) (J tptp.code_integer) (K3 tptp.code_integer) (L tptp.code_integer)) (=> (and (@ (@ tptp.ord_le6747313008572928689nteger I) J) (@ (@ tptp.ord_le6747313008572928689nteger K3) L)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger I) K3)) (@ (@ tptp.plus_p5714425477246183910nteger J) L)))) (forall ((I tptp.nat) (J tptp.nat) (K3 tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_nat K3) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K3)) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((I tptp.int) (J tptp.int) (K3 tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I) J) (@ (@ tptp.ord_less_int K3) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K3)) (@ (@ tptp.plus_plus_int J) L)))) (forall ((I tptp.rat) (J tptp.rat) (K3 tptp.rat) (L tptp.rat)) (=> (and (= I J) (@ (@ tptp.ord_less_rat K3) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K3)) (@ (@ tptp.plus_plus_rat J) L)))) (forall ((I tptp.code_integer) (J tptp.code_integer) (K3 tptp.code_integer) (L tptp.code_integer)) (=> (and (= I J) (@ (@ tptp.ord_le6747313008572928689nteger K3) L)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger I) K3)) (@ (@ tptp.plus_p5714425477246183910nteger J) L)))) (forall ((I tptp.nat) (J tptp.nat) (K3 tptp.nat) (L tptp.nat)) (=> (and (= I J) (@ (@ tptp.ord_less_nat K3) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K3)) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((I tptp.int) (J tptp.int) (K3 tptp.int) (L tptp.int)) (=> (and (= I J) (@ (@ tptp.ord_less_int K3) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K3)) (@ (@ tptp.plus_plus_int J) L)))) (forall ((I tptp.rat) (J tptp.rat) (K3 tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I) J) (= K3 L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K3)) (@ (@ tptp.plus_plus_rat J) L)))) (forall ((I tptp.code_integer) (J tptp.code_integer) (K3 tptp.code_integer) (L tptp.code_integer)) (=> (and (@ (@ tptp.ord_le6747313008572928689nteger I) J) (= K3 L)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger I) K3)) (@ (@ tptp.plus_p5714425477246183910nteger J) L)))) (forall ((I tptp.nat) (J tptp.nat) (K3 tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (= K3 L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K3)) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((I tptp.int) (J tptp.int) (K3 tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I) J) (= K3 L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K3)) (@ (@ tptp.plus_plus_int J) L)))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (@ (@ tptp.ord_less_rat C) D2) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B2) D2))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) D2) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) C)) (@ (@ tptp.plus_p5714425477246183910nteger B2) D2))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_nat C) D2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B2) D2))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ (@ tptp.ord_less_int C) D2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B2) D2))))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_rat A2) B2) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B2))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B2))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_nat A2) B2) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B2))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_int A2) B2) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2))))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B2) C)))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) C)) (@ (@ tptp.plus_p5714425477246183910nteger B2) C)))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B2) C)))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B2) C)))) (forall ((C tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_rat A2) B2)))) (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_le6747313008572928689nteger A2) B2)))) (forall ((C tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_nat A2) B2)))) (forall ((C tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_int A2) B2)))) (forall ((A2 tptp.rat) (C tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B2) C)) (@ (@ tptp.ord_less_rat A2) B2))) (forall ((A2 tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) C)) (@ (@ tptp.plus_p5714425477246183910nteger B2) C)) (@ (@ tptp.ord_le6747313008572928689nteger A2) B2))) (forall ((A2 tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B2) C)) (@ (@ tptp.ord_less_nat A2) B2))) (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.ord_less_int A2) B2))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B2) C)))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A2) B2)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B2) C)))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A2) B2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B2) C)))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A2))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B2) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 B2)) (@ _let_1 C))))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B2) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B2)) (@ _let_1 C))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B2)) (@ _let_1 C))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B2) C)))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A2) B2)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B2) C)))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A2) B2)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B2) C)))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A2) B2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B2) C)))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A2))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B2) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 B2)) (@ _let_1 C))))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B2) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B2)) (@ _let_1 C))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B2) C)) (@ (@ tptp.plus_plus_nat (@ _let_1 B2)) (@ _let_1 C))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B2)) (@ _let_1 C))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B2) C)))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A2) B2)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B2) C)))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A2) B2)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B2) C)))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A2) B2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B2) C)))) (forall ((A2 tptp.code_integer) (E tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A2) E)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B2) E)) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)) E)) C))) (forall ((A2 tptp.rat) (E tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) E)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B2) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A2) B2)) E)) C))) (forall ((A2 tptp.nat) (E tptp.nat) (B2 tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A2) E)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B2) E)) C)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A2) B2)) E)) C))) (forall ((A2 tptp.int) (E tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) E)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A2) B2)) E)) C))) (forall ((A tptp.rat) (K3 tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat K3))) (=> (= A (@ _let_1 A2)) (= (@ (@ tptp.minus_minus_rat A) B2) (@ _let_1 (@ (@ tptp.minus_minus_rat A2) B2)))))) (forall ((A tptp.int) (K3 tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K3))) (=> (= A (@ _let_1 A2)) (= (@ (@ tptp.minus_minus_int A) B2) (@ _let_1 (@ (@ tptp.minus_minus_int A2) B2)))))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.minus_minus_rat A2) B2) C) (= A2 (@ (@ tptp.plus_plus_rat C) B2)))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (= (= (@ (@ tptp.minus_minus_int A2) B2) C) (= A2 (@ (@ tptp.plus_plus_int C) B2)))) (forall ((A2 tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (= A2 (@ (@ tptp.minus_minus_rat C) B2)) (= (@ (@ tptp.plus_plus_rat A2) B2) C))) (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int)) (= (= A2 (@ (@ tptp.minus_minus_int C) B2)) (= (@ (@ tptp.plus_plus_int A2) B2) C))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B2) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B2)) C)))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B2) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B2)) C)))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.minus_minus_rat A2) (@ (@ tptp.minus_minus_rat B2) C)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A2) C)) B2))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.minus_minus_int A2) (@ (@ tptp.minus_minus_int B2) C)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A2) C)) B2))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A2) B2)) C) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A2) C)) B2))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A2) B2)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A2) C)) B2))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B2) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 C)) B2)))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.minus_minus_int (@ _let_1 C)) B2)))) (forall ((C tptp.multis2468970476368604999at_nat) (B2 tptp.multis2468970476368604999at_nat) (A2 tptp.multis2468970476368604999at_nat)) (=> (= (@ (@ tptp.plus_p7104986032573967614at_nat C) B2) A2) (= C (@ (@ tptp.minus_4286766774447292334at_nat A2) B2)))) (forall ((C tptp.rat) (B2 tptp.rat) (A2 tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat C) B2) A2) (= C (@ (@ tptp.minus_minus_rat A2) B2)))) (forall ((C tptp.nat) (B2 tptp.nat) (A2 tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat C) B2) A2) (= C (@ (@ tptp.minus_minus_nat A2) B2)))) (forall ((C tptp.int) (B2 tptp.int) (A2 tptp.int)) (=> (= (@ (@ tptp.plus_plus_int C) B2) A2) (= C (@ (@ tptp.minus_minus_int A2) B2)))) (forall ((A2 tptp.multis2468970476368604999at_nat) (B2 tptp.multis2468970476368604999at_nat) (C tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.minus_4286766774447292334at_nat A2))) (= (@ (@ tptp.minus_4286766774447292334at_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_p7104986032573967614at_nat B2) C))))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A2))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B2) C))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B2) C))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A2))) (= (@ (@ tptp.minus_minus_int (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B2) C))))) (forall ((A tptp.assn) (B tptp.assn) (C2 tptp.assn)) (= (@ (@ tptp.times_times_assn (@ (@ tptp.sup_sup_assn A) B)) C2) (@ (@ tptp.sup_sup_assn (@ (@ tptp.times_times_assn A) C2)) (@ (@ tptp.times_times_assn B) C2)))) (forall ((C2 tptp.assn) (A tptp.assn) (B tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn C2))) (= (@ _let_1 (@ (@ tptp.sup_sup_assn A) B)) (@ (@ tptp.sup_sup_assn (@ _let_1 A)) (@ _let_1 B))))) (forall ((I tptp.nat) (K3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K3) (=> (not (= K3 (@ tptp.suc I))) (not (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J3) (not (= K3 (@ tptp.suc J3))))))))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M2)) N) (@ (@ tptp.ord_less_nat M2) N))) (forall ((I tptp.nat) (K3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K3) (not (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J3) (not (= K3 (@ tptp.suc J3)))))))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc M2))) (=> (@ (@ tptp.ord_less_nat M2) N) (=> (not (= _let_1 N)) (@ (@ tptp.ord_less_nat _let_1) N))))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M2))) (=> (@ _let_1 (@ tptp.suc N)) (=> (not (@ _let_1 N)) (= M2 N))))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M2))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))) (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N)) (@ P I4))) (or (@ P N) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) N) (@ P I4)))))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M2))) (= (@ _let_1 (@ tptp.suc N)) (or (@ _let_1 N) (= M2 N))))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M2) N)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc M2)))) (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N)) (@ P I4))) (and (@ P N) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N) (@ P I4)))))) (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N)) M2) (exists ((M4 tptp.nat)) (and (= M2 (@ tptp.suc M4)) (@ (@ tptp.ord_less_nat N) M4))))) (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M2)) (=> (@ _let_1 (@ tptp.suc M2)) (= M2 N))))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M2)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M2) N))) (forall ((I tptp.nat) (J tptp.nat) (K3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) K3) (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K3)))) (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (forall ((I5 tptp.nat)) (@ (@ P I5) (@ tptp.suc I5))) (=> (forall ((I5 tptp.nat) (J3 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ P I5))) (=> (@ (@ tptp.ord_less_nat I5) J3) (=> (@ (@ tptp.ord_less_nat J3) K) (=> (@ _let_1 J3) (=> (@ (@ P J3) K) (@ _let_1 K))))))) (@ (@ P I) J))))) (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (forall ((I5 tptp.nat)) (=> (= J (@ tptp.suc I5)) (@ P I5))) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) J) (=> (@ P (@ tptp.suc I5)) (@ P I5)))) (@ P I))))) (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M2)) (= (@ _let_1 (@ tptp.suc M2)) (= N M2))))) (forall ((I tptp.nat) (J tptp.nat) (K3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) K3) (@ (@ tptp.ord_less_nat I) K3))) (forall ((I tptp.nat) (J tptp.nat) (K3 tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat K3) L) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K3)) (@ (@ tptp.plus_plus_nat J) L))))) (forall ((I tptp.nat) (J tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) I))) (forall ((J tptp.nat) (I tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J) I)) I))) (forall ((I tptp.nat) (J tptp.nat) (K3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K3)) (@ (@ tptp.plus_plus_nat J) K3)))) (forall ((I tptp.nat) (J tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M2))))) (forall ((I tptp.nat) (J tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M2) J))))) (forall ((K3 tptp.nat) (L tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat K3) L) (=> (= (@ (@ tptp.plus_plus_nat M2) L) (@ (@ tptp.plus_plus_nat K3) N)) (@ (@ tptp.ord_less_nat M2) N)))) (forall ((B tptp.assn) (A tptp.assn)) (@ (@ tptp.entails B) (@ (@ tptp.sup_sup_assn A) B))) (forall ((A tptp.assn) (B tptp.assn)) (@ (@ tptp.entails A) (@ (@ tptp.sup_sup_assn A) B))) (forall ((A tptp.assn) (C2 tptp.assn) (B tptp.assn)) (let ((_let_1 (@ tptp.entails A))) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.sup_sup_assn B) C2))))) (forall ((A tptp.assn) (B tptp.assn) (C2 tptp.assn)) (let ((_let_1 (@ tptp.entails A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_assn B) C2))))) (forall ((P tptp.assn) (Q tptp.assn) (R tptp.assn)) (=> (@ (@ tptp.entails (@ (@ tptp.sup_sup_assn P) Q)) R) (@ (@ tptp.entails Q) R))) (forall ((P tptp.assn) (Q tptp.assn) (R tptp.assn)) (=> (@ (@ tptp.entails (@ (@ tptp.sup_sup_assn P) Q)) R) (@ (@ tptp.entails P) R))) (forall ((A tptp.assn) (C2 tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.entails A) C2) (=> (@ (@ tptp.entails B) C2) (@ (@ tptp.entails (@ (@ tptp.sup_sup_assn A) B)) C2)))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat X))) (= (@ _let_1 (@ (@ tptp.ord_min_rat Y) Z)) (@ (@ 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tptp.plus_plus_nat Y) Z)))) (forall ((A tptp.assn) (M5 tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.entailst A) M5) (=> (@ (@ tptp.entailst B) M5) (@ (@ tptp.entailst (@ (@ tptp.sup_sup_assn A) B)) M5)))) (forall ((A tptp.assn) (B tptp.assn) (C2 tptp.assn)) (=> (@ (@ tptp.entailst (@ (@ tptp.sup_sup_assn A) B)) C2) (@ (@ tptp.entailst A) C2))) (forall ((A tptp.assn) (B tptp.assn) (C2 tptp.assn)) (=> (@ (@ tptp.entailst (@ (@ tptp.sup_sup_assn A) B)) C2) (@ (@ tptp.entailst B) C2))) (forall ((A tptp.assn) (B tptp.assn) (C2 tptp.assn)) (let ((_let_1 (@ tptp.entailst A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_assn B) C2))))) (forall ((A tptp.assn) (C2 tptp.assn) (B tptp.assn)) (let ((_let_1 (@ tptp.entailst A))) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.sup_sup_assn B) C2))))) (forall ((A tptp.assn) (B tptp.assn)) (@ (@ tptp.entailst A) (@ (@ tptp.sup_sup_assn A) B))) (forall ((B tptp.assn) (A tptp.assn)) (@ (@ tptp.entailst B) (@ (@ tptp.sup_sup_assn A) B))) (forall ((X tptp.assn)) (= (@ (@ tptp.sup_sup_assn X) tptp.bot_bot_assn) X)) (forall ((X tptp.assn)) (= (@ (@ tptp.sup_sup_assn tptp.bot_bot_assn) X) X)) (forall ((I tptp.rat) (J tptp.rat) (K3 tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I) J) (@ (@ tptp.ord_less_rat K3) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K3)) (@ (@ tptp.plus_plus_rat J) L)))) (forall ((I tptp.code_integer) (J tptp.code_integer) (K3 tptp.code_integer) (L tptp.code_integer)) (=> (and (@ (@ tptp.ord_le3102999989581377725nteger I) J) (@ (@ tptp.ord_le6747313008572928689nteger K3) L)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger I) K3)) (@ (@ tptp.plus_p5714425477246183910nteger J) L)))) (forall ((I tptp.nat) (J tptp.nat) (K3 tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_nat K3) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K3)) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((I tptp.int) (J tptp.int) (K3 tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I) J) (@ (@ tptp.ord_less_int K3) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K3)) (@ (@ tptp.plus_plus_int J) L)))) (forall ((I tptp.rat) (J tptp.rat) (K3 tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I) J) (@ (@ tptp.ord_less_eq_rat K3) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K3)) (@ (@ tptp.plus_plus_rat J) L)))) (forall ((I tptp.code_integer) (J tptp.code_integer) (K3 tptp.code_integer) (L tptp.code_integer)) (=> (and (@ (@ tptp.ord_le6747313008572928689nteger I) J) (@ (@ tptp.ord_le3102999989581377725nteger K3) L)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger I) K3)) (@ (@ tptp.plus_p5714425477246183910nteger J) L)))) (forall ((I tptp.nat) (J tptp.nat) (K3 tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_eq_nat K3) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K3)) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((I tptp.int) (J tptp.int) (K3 tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I) J) (@ (@ tptp.ord_less_eq_int K3) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K3)) (@ (@ tptp.plus_plus_int J) L)))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_rat C) D2) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B2) D2))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) D2) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) C)) (@ (@ tptp.plus_p5714425477246183910nteger B2) D2))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_nat C) D2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B2) D2))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_int C) D2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B2) D2))))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (@ (@ tptp.ord_less_eq_rat C) D2) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B2) D2))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) D2) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) C)) (@ (@ tptp.plus_p5714425477246183910nteger B2) D2))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B2) D2))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ (@ tptp.ord_less_eq_int C) D2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B2) D2))))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A2) B2)) C) (@ (@ tptp.ord_less_eq_rat A2) (@ (@ tptp.plus_plus_rat C) B2)))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A2) B2)) C) (@ (@ tptp.ord_less_eq_int A2) (@ (@ tptp.plus_plus_int C) B2)))) (forall ((A2 tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A2) (@ (@ tptp.minus_minus_rat C) B2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) B2)) C))) (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int A2) (@ (@ tptp.minus_minus_int C) B2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) B2)) C))) (forall ((I tptp.rat) (K3 tptp.rat) (N tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K3)) N) (@ (@ tptp.ord_less_eq_rat I) (@ (@ tptp.minus_minus_rat N) K3)))) (forall ((I tptp.nat) (K3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K3)) N) (@ (@ tptp.ord_less_eq_nat I) (@ (@ tptp.minus_minus_nat N) K3)))) (forall ((I tptp.int) (K3 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K3)) N) (@ (@ tptp.ord_less_eq_int I) (@ (@ tptp.minus_minus_int N) K3)))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B2) A2)) A2) B2))) (forall ((I tptp.rat) (K3 tptp.rat) (N tptp.rat) (J tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_rat N) (@ (@ tptp.plus_plus_rat J) K3)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K3)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat N) K3)) J)))))))) (forall ((I tptp.nat) (K3 tptp.nat) (N tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat J) K3)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K3)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat N) K3)) J)))))))) (forall ((I tptp.int) (K3 tptp.int) (N tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int N) (@ (@ tptp.plus_plus_int J) K3)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K3)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int N) K3)) J)))))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (@ (@ tptp.ord_less_eq_nat C) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B2) C)) A2)))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= (@ (@ tptp.ord_less_eq_nat C) (@ (@ tptp.minus_minus_nat B2) A2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat C) A2)) B2)))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat B2) A2)) (@ (@ tptp.minus_minus_nat (@ _let_1 B2)) A2))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B2)) A2) (@ _let_1 (@ (@ tptp.minus_minus_nat B2) A2)))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B2) A2)) C) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B2) C)) A2)))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B2) C)) A2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B2) A2)) C)))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= (@ (@ tptp.minus_minus_nat C) (@ (@ tptp.minus_minus_nat B2) A2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat C) A2)) B2)))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= (@ (@ tptp.plus_plus_nat A2) (@ (@ tptp.minus_minus_nat B2) A2)) B2))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat A2) B2))) (=> _let_1 (=> _let_1 (= (= (@ (@ tptp.minus_minus_nat B2) A2) C) (= B2 (@ (@ tptp.plus_plus_nat C) A2))))))) (forall ((A2 tptp.rat)) (@ (@ tptp.ord_less_rat A2) (@ (@ tptp.plus_plus_rat A2) tptp.one_one_rat))) (forall ((A2 tptp.code_integer)) (@ (@ tptp.ord_le6747313008572928689nteger A2) (@ (@ tptp.plus_p5714425477246183910nteger A2) tptp.one_one_Code_integer))) (forall ((A2 tptp.nat)) (@ (@ tptp.ord_less_nat A2) (@ (@ tptp.plus_plus_nat A2) tptp.one_one_nat))) (forall ((A2 tptp.int)) (@ (@ tptp.ord_less_int A2) (@ (@ tptp.plus_plus_int A2) tptp.one_one_int))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) tptp.one_one_rat)) (@ (@ tptp.plus_plus_rat B2) tptp.one_one_rat)))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) tptp.one_one_Code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger B2) tptp.one_one_Code_integer)))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat B2) tptp.one_one_nat)))) (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) tptp.one_one_int)) (@ (@ tptp.plus_plus_int B2) tptp.one_one_int)))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A2) B2)) C) (@ (@ tptp.ord_less_rat A2) (@ (@ tptp.plus_plus_rat C) B2)))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.minus_8373710615458151222nteger A2) B2)) C) (@ (@ tptp.ord_le6747313008572928689nteger A2) (@ (@ tptp.plus_p5714425477246183910nteger C) B2)))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A2) B2)) C) (@ (@ tptp.ord_less_int A2) (@ (@ tptp.plus_plus_int C) B2)))) (forall ((A2 tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat A2) (@ (@ tptp.minus_minus_rat C) B2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) B2)) C))) (forall ((A2 tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A2) (@ (@ tptp.minus_8373710615458151222nteger C) B2)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)) C))) (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int A2) (@ (@ tptp.minus_minus_int C) B2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) B2)) C))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat A2) B2)) (= (@ (@ tptp.plus_plus_rat B2) (@ (@ tptp.minus_minus_rat A2) B2)) A2))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (not (@ (@ tptp.ord_le6747313008572928689nteger A2) B2)) (= (@ (@ tptp.plus_p5714425477246183910nteger B2) (@ (@ tptp.minus_8373710615458151222nteger A2) B2)) A2))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat A2) B2)) (= (@ (@ tptp.plus_plus_nat B2) (@ (@ tptp.minus_minus_nat A2) B2)) A2))) (forall ((A2 tptp.int) (B2 tptp.int)) (=> (not (@ (@ tptp.ord_less_int A2) B2)) (= (@ (@ tptp.plus_plus_int B2) (@ (@ tptp.minus_minus_int A2) B2)) A2))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.times_3573771949741848930nteger X) X)) (@ (@ tptp.times_3573771949741848930nteger Y) Y)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger X) Y)) (@ (@ tptp.minus_8373710615458151222nteger X) Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X) Y)) (@ (@ tptp.minus_minus_rat X) Y)))) (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X) Y)) (@ (@ tptp.minus_minus_int X) Y)))) (forall ((A2 tptp.code_integer) (E tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer) (D2 tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A2) E)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B2) E)) D2)) (= C (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger B2) A2)) E)) D2)))) (forall ((A2 tptp.rat) (E tptp.rat) (C tptp.rat) (B2 tptp.rat) (D2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) E)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B2) E)) D2)) (= C (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B2) A2)) E)) D2)))) (forall ((A2 tptp.int) (E tptp.int) (C tptp.int) (B2 tptp.int) (D2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) E)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) E)) D2)) (= C (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B2) A2)) E)) D2)))) (forall ((A2 tptp.code_integer) (E tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer) (D2 tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A2) E)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B2) E)) D2)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger A2) B2)) E)) C) D2))) (forall ((A2 tptp.rat) (E tptp.rat) (C tptp.rat) (B2 tptp.rat) (D2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) E)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B2) E)) D2)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A2) B2)) E)) C) D2))) (forall ((A2 tptp.int) (E tptp.int) (C tptp.int) (B2 tptp.int) (D2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) E)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) E)) D2)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A2) B2)) E)) C) D2))) (forall ((F4 (-> tptp.nat tptp.code_integer)) (N tptp.nat) (N6 tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 N5)) (@ F4 (@ tptp.suc N5)))) (=> (@ (@ tptp.ord_less_nat N) N6) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 N)) (@ F4 N6))))) (forall ((F4 (-> tptp.nat tptp.assn)) (N tptp.nat) (N6 tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_assn (@ F4 N5)) (@ F4 (@ tptp.suc N5)))) (=> (@ (@ tptp.ord_less_nat N) N6) (@ (@ tptp.ord_less_assn (@ F4 N)) (@ F4 N6))))) (forall ((F4 (-> tptp.nat tptp.num)) (N tptp.nat) (N6 tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_num (@ F4 N5)) (@ F4 (@ tptp.suc N5)))) (=> (@ (@ tptp.ord_less_nat N) N6) (@ (@ tptp.ord_less_num (@ F4 N)) (@ F4 N6))))) (forall ((F4 (-> tptp.nat tptp.nat)) (N tptp.nat) (N6 tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F4 N5)) (@ F4 (@ tptp.suc N5)))) (=> (@ (@ tptp.ord_less_nat N) N6) (@ (@ tptp.ord_less_nat (@ F4 N)) (@ F4 N6))))) (forall ((F4 (-> tptp.nat tptp.int)) (N tptp.nat) (N6 tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_int (@ F4 N5)) (@ F4 (@ tptp.suc N5)))) (=> (@ (@ tptp.ord_less_nat N) N6) (@ (@ tptp.ord_less_int (@ F4 N)) (@ F4 N6))))) (forall ((F4 (-> tptp.nat tptp.code_integer)) (N tptp.nat) (M2 tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 N5)) (@ F4 (@ tptp.suc N5)))) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ F4 N)) (@ F4 M2)) (@ (@ tptp.ord_less_nat N) M2)))) (forall ((F4 (-> tptp.nat tptp.assn)) (N tptp.nat) (M2 tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_assn (@ F4 N5)) (@ F4 (@ tptp.suc N5)))) (= (@ (@ tptp.ord_less_assn (@ F4 N)) (@ F4 M2)) (@ (@ tptp.ord_less_nat N) M2)))) (forall ((F4 (-> tptp.nat tptp.num)) (N tptp.nat) (M2 tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_num (@ F4 N5)) (@ F4 (@ tptp.suc N5)))) (= (@ (@ tptp.ord_less_num (@ F4 N)) (@ F4 M2)) (@ (@ tptp.ord_less_nat N) M2)))) (forall ((F4 (-> tptp.nat tptp.nat)) (N tptp.nat) (M2 tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F4 N5)) (@ F4 (@ tptp.suc N5)))) (= (@ (@ tptp.ord_less_nat (@ F4 N)) (@ F4 M2)) (@ (@ tptp.ord_less_nat N) M2)))) (forall ((F4 (-> tptp.nat tptp.int)) (N tptp.nat) (M2 tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_int (@ F4 N5)) (@ F4 (@ tptp.suc N5)))) (= (@ (@ tptp.ord_less_int (@ F4 N)) (@ F4 M2)) (@ (@ tptp.ord_less_nat N) M2)))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N) (@ (@ tptp.ord_less_nat M2) N))) (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ P I) (=> (forall ((N5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N5) (=> (@ (@ tptp.ord_less_nat N5) J) (=> (@ P N5) (@ P (@ tptp.suc N5)))))) (@ P J))))) (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ P J) (=> (forall ((N5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N5) (=> (@ (@ tptp.ord_less_nat N5) J) (=> (@ P (@ tptp.suc N5)) (@ P N5))))) (@ P I))))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N) (@ (@ tptp.ord_less_nat M2) N))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc M2)) (= N M2)))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M2) (@ tptp.suc N)) (@ (@ tptp.ord_less_eq_nat M2) N))) (= tptp.ord_less_nat (lambda ((N2 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) __flatten_var_0))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_nat M2) (@ tptp.suc N)))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.suc A2))) (= (and (@ (@ tptp.ord_less_nat A2) B2) (@ (@ tptp.ord_less_eq_nat B2) _let_1)) (= B2 _let_1)))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (and (@ (@ tptp.ord_less_eq_nat A2) B2) (@ (@ tptp.ord_less_nat B2) (@ tptp.suc A2))) (= B2 A2))) (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M2))) (=> (@ (@ tptp.ord_less_nat N) M2) (= (@ tptp.suc (@ _let_1 (@ tptp.suc N))) (@ _let_1 N))))) (forall ((M2 tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M2) N)) (@ tptp.suc M2))) (forall ((F4 (-> tptp.nat tptp.nat)) (M2 tptp.nat) (K3 tptp.nat)) (=> (forall ((M6 tptp.nat) (N5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M6) N5) (@ (@ tptp.ord_less_nat (@ F4 M6)) (@ F4 N5)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ F4 M2)) K3)) (@ F4 (@ (@ tptp.plus_plus_nat M2) K3))))) (forall ((K3 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K3)))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M2) N)))) (forall ((I tptp.nat) (J tptp.nat) (K3 tptp.nat)) (= (@ (@ tptp.ord_less_nat I) (@ (@ tptp.minus_minus_nat J) K3)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K3)) J))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M2) N)) (= (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.minus_minus_nat M2) N)) M2))) (forall ((A2 tptp.nat) (A tptp.nat) (B2 tptp.nat) (N7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) A) (=> (@ (@ tptp.ord_less_nat B2) N7) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A2) N7)) B2)) (@ (@ tptp.times_times_nat A) N7))))) (forall ((A2 tptp.nat) (A7 tptp.nat) (B2 tptp.nat) (N7 tptp.nat) (B6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) A7) (=> (@ (@ tptp.ord_less_nat B2) N7) (=> (@ (@ tptp.ord_less_nat B6) N7) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A2) N7)) B2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A7) N7)) B6)))))) (forall ((A2 tptp.nat) (A7 tptp.nat) (B2 tptp.nat) (B6 tptp.nat) (N7 tptp.nat)) (=> (= A2 A7) (=> (@ (@ tptp.ord_less_nat B2) B6) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A2) N7)) B2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A7) N7)) B6))))) (forall ((A2 tptp.nat) (A7 tptp.nat) (B2 tptp.nat) (B6 tptp.nat) (N7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) A7) (=> (@ (@ tptp.ord_less_eq_nat B2) B6) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A2) N7)) B2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A7) N7)) B6))))) (forall ((A2 tptp.code_integer) (E tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer) (D2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A2) E)) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B2) E)) D2)) (@ (@ tptp.ord_le3102999989581377725nteger C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger B2) A2)) E)) D2)))) (forall ((A2 tptp.rat) (E tptp.rat) (C tptp.rat) (B2 tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B2) E)) D2)) (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B2) A2)) E)) D2)))) (forall ((A2 tptp.int) (E tptp.int) (C tptp.int) (B2 tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) E)) D2)) (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B2) A2)) E)) D2)))) (forall ((A2 tptp.code_integer) (E tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer) (D2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A2) E)) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B2) E)) D2)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger A2) B2)) E)) C)) D2))) (forall ((A2 tptp.rat) (E tptp.rat) (C tptp.rat) (B2 tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B2) E)) D2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A2) B2)) E)) C)) D2))) (forall ((A2 tptp.int) (E tptp.int) (C tptp.int) (B2 tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) E)) D2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A2) B2)) E)) C)) D2))) (forall ((A2 tptp.rat) (E tptp.rat) (C tptp.rat) (B2 tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B2) E)) D2)) (@ (@ tptp.ord_less_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B2) A2)) E)) D2)))) (forall ((A2 tptp.code_integer) (E tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer) (D2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A2) E)) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B2) E)) D2)) (@ (@ tptp.ord_le6747313008572928689nteger C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger B2) A2)) E)) D2)))) (forall ((A2 tptp.int) (E tptp.int) (C tptp.int) (B2 tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) E)) D2)) (@ (@ tptp.ord_less_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B2) A2)) E)) D2)))) (forall ((A2 tptp.rat) (E tptp.rat) (C tptp.rat) (B2 tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B2) E)) D2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A2) B2)) E)) C)) D2))) (forall ((A2 tptp.code_integer) (E tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer) (D2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A2) E)) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B2) E)) D2)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger A2) B2)) E)) C)) D2))) (forall ((A2 tptp.int) (E tptp.int) (C tptp.int) (B2 tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) E)) D2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A2) B2)) E)) C)) D2))) (forall ((X tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.times_3573771949741848930nteger X) X)) tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger X) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger X) tptp.one_one_Code_integer)))) (forall ((X tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) X)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X) tptp.one_one_rat)) (@ (@ tptp.minus_minus_rat X) tptp.one_one_rat)))) (forall ((X tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X) X)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) (@ (@ tptp.minus_minus_int X) tptp.one_one_int)))) (forall ((K3 tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J) K3)) I) (@ (@ tptp.ord_less_nat J) (@ (@ tptp.plus_plus_nat I) K3))))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) M2) (= (@ tptp.suc (@ _let_1 M2)) (@ _let_1 (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat))))))) (forall ((Xs tptp.list_nat)) (= (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) Xs) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.suc I4))) (let ((_let_2 (@ tptp.nth_nat Xs))) (=> (@ (@ tptp.ord_less_nat _let_1) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.ord_less_eq_nat (@ _let_2 I4)) (@ _let_2 _let_1)))))))) (forall ((Xs tptp.list_int)) (= (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) Xs) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.suc I4))) (let ((_let_2 (@ tptp.nth_int Xs))) (=> (@ (@ tptp.ord_less_nat _let_1) (@ tptp.size_size_list_int Xs)) (@ (@ tptp.ord_less_eq_int (@ _let_2 I4)) (@ _let_2 _let_1)))))))) (forall ((N tptp.nat) (Xs tptp.list_c)) (let ((_let_1 (@ tptp.size_size_list_c Xs))) (=> (@ (@ tptp.ord_less_nat N) _let_1) (= (@ (@ tptp.nth_c (@ tptp.rev_c Xs)) N) (@ (@ tptp.nth_c Xs) (@ (@ tptp.minus_minus_nat _let_1) (@ tptp.suc N))))))) (forall ((N tptp.nat) (Xs tptp.list_d)) (let ((_let_1 (@ tptp.size_size_list_d Xs))) (=> (@ (@ tptp.ord_less_nat N) _let_1) (= (@ (@ tptp.nth_d (@ tptp.rev_d Xs)) N) (@ (@ tptp.nth_d Xs) (@ (@ tptp.minus_minus_nat _let_1) (@ tptp.suc N))))))) (forall ((N tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Xs))) (=> (@ (@ tptp.ord_less_nat N) _let_1) (= (@ (@ tptp.nth_nat (@ tptp.rev_nat Xs)) N) (@ (@ tptp.nth_nat Xs) (@ (@ tptp.minus_minus_nat _let_1) (@ tptp.suc N))))))) (forall ((N tptp.nat) (Xs tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Xs))) (=> (@ (@ tptp.ord_less_nat N) _let_1) (= (@ (@ tptp.nth_int (@ tptp.rev_int Xs)) N) (@ (@ tptp.nth_int Xs) (@ (@ tptp.minus_minus_nat _let_1) (@ tptp.suc N))))))) (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I) J)) U)) M2)) N)))) (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N))))) (= tptp.ord_le6747313008572928689nteger (lambda ((A3 tptp.code_integer) (__flatten_var_0 tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A3) tptp.one_one_Code_integer)) __flatten_var_0))) (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A3) tptp.one_one_nat)) __flatten_var_0))) (= tptp.ord_less_int (lambda ((A3 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A3) tptp.one_one_int)) __flatten_var_0))) (forall ((I tptp.nat) (J tptp.nat) (L tptp.list_Code_integer) (X tptp.code_integer)) (let ((_let_1 (@ tptp.nth_Code_integer L))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) I) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_s3445333598471063425nteger L)) (=> (@ (@ tptp.sorted710888440204495920nteger tptp.ord_le3102999989581377725nteger) L) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 I)) X) (=> (@ (@ tptp.ord_le6747313008572928689nteger X) (@ _let_1 J)) (not (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.nth_Code_integer L))) (=> (@ (@ tptp.ord_less_eq_nat I) K) (=> (@ (@ tptp.ord_less_nat K) J) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 K)) X) (not (@ (@ tptp.ord_le6747313008572928689nteger X) (@ _let_1 (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))))))))))))))) (forall ((I tptp.nat) (J tptp.nat) (L tptp.list_num) (X tptp.num)) (let ((_let_1 (@ tptp.nth_num L))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) I) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_num L)) (=> (@ (@ tptp.sorted_wrt_num tptp.ord_less_eq_num) L) (=> (@ (@ tptp.ord_less_eq_num (@ _let_1 I)) X) (=> (@ (@ tptp.ord_less_num X) (@ _let_1 J)) (not (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.nth_num L))) (=> (@ (@ tptp.ord_less_eq_nat I) K) (=> (@ (@ tptp.ord_less_nat K) J) (=> (@ (@ 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)))))))))))))))))) (forall ((I tptp.nat) (J tptp.nat) (L tptp.list_nat) (X tptp.nat)) (let ((_let_1 (@ tptp.nth_nat L))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) I) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat L)) (=> (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) L) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 I)) X) (=> (@ (@ tptp.ord_less_nat X) (@ _let_1 J)) (not (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.nth_nat L))) (=> (@ (@ tptp.ord_less_eq_nat I) K) (=> (@ (@ tptp.ord_less_nat K) J) (=> (@ (@ 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)))))))))))))))))) (forall ((I tptp.nat) (J tptp.nat) (L tptp.list_int) (X tptp.int)) (let ((_let_1 (@ tptp.nth_int L))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) I) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_int L)) (=> (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) L) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 I)) X) (=> (@ (@ tptp.ord_less_int X) (@ _let_1 J)) (not (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.nth_int L))) (=> (@ (@ tptp.ord_less_eq_nat I) K) (=> (@ (@ tptp.ord_less_nat K) J) (=> (@ (@ 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)))))))))))))))))) (forall ((W tptp.code_integer) (Y tptp.code_integer) (X tptp.code_integer) (Z tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger X))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger W))) (= (= (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X) (= Y Z)))))) (forall ((W tptp.rat) (Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X))) (let ((_let_2 (@ tptp.times_times_rat W))) (= (= (@ (@ tptp.plus_plus_rat (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_rat (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X) (= Y Z)))))) (forall ((W tptp.nat) (Y tptp.nat) (X tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat X))) (let ((_let_2 (@ tptp.times_times_nat W))) (= (= (@ (@ tptp.plus_plus_nat (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_nat (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X) (= Y Z)))))) (forall ((W tptp.int) (Y tptp.int) (X tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.times_times_int X))) (let ((_let_2 (@ tptp.times_times_int W))) (= (= (@ (@ tptp.plus_plus_int (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_int (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X) (= Y Z)))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger B2))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger A2))) (= (and (not (= A2 B2)) (not (= C D2))) (not (= (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 C)) (@ _let_1 D2)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 D2)) (@ _let_1 C)))))))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat B2))) (let ((_let_2 (@ tptp.times_times_rat A2))) (= (and (not (= A2 B2)) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_rat (@ _let_2 C)) (@ _let_1 D2)) (@ (@ tptp.plus_plus_rat (@ _let_2 D2)) (@ _let_1 C)))))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B2))) (let ((_let_2 (@ tptp.times_times_nat A2))) (= (and (not (= A2 B2)) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_nat (@ _let_2 C)) (@ _let_1 D2)) (@ (@ tptp.plus_plus_nat (@ _let_2 D2)) (@ _let_1 C)))))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int B2))) (let ((_let_2 (@ tptp.times_times_int A2))) (= (and (not (= A2 B2)) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_int (@ _let_2 C)) (@ _let_1 D2)) (@ (@ tptp.plus_plus_int (@ _let_2 D2)) (@ _let_1 C)))))))) (forall ((Xs tptp.list_s1210847774152347623at_nat) (R tptp.set_Pr4329608150637261639at_nat) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.nth_se5679702624988424552at_nat Xs))) (=> (forall ((N5 tptp.nat)) (let ((_let_1 (@ tptp.nth_se5679702624988424552at_nat Xs))) (=> (@ (@ tptp.ord_less_nat N5) (@ (@ tptp.minus_minus_nat (@ tptp.size_s8736152011456118867at_nat Xs)) tptp.one_one_nat)) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ _let_1 (@ tptp.suc N5))) (@ _let_1 N5))) R)))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s8736152011456118867at_nat Xs)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ _let_1 N)) (@ _let_1 M2))) (@ tptp.transi2703068831062848130at_nat R))))))) (forall ((Xs tptp.list_c) (R tptp.set_Product_prod_c_c) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.nth_c Xs))) (=> (forall ((N5 tptp.nat)) (let ((_let_1 (@ tptp.nth_c Xs))) (=> (@ (@ tptp.ord_less_nat N5) (@ (@ tptp.minus_minus_nat (@ tptp.size_size_list_c Xs)) tptp.one_one_nat)) (@ (@ tptp.member5074992359041316560od_c_c (@ (@ tptp.product_Pair_c_c (@ _let_1 (@ tptp.suc N5))) (@ _let_1 N5))) R)))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_c Xs)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.member5074992359041316560od_c_c (@ (@ tptp.product_Pair_c_c (@ _let_1 N)) (@ _let_1 M2))) (@ tptp.transitive_trancl_c R))))))) (forall ((Xs tptp.list_d) (R tptp.set_Product_prod_d_d) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.nth_d Xs))) (=> (forall ((N5 tptp.nat)) (let ((_let_1 (@ tptp.nth_d Xs))) (=> (@ (@ tptp.ord_less_nat N5) (@ (@ tptp.minus_minus_nat (@ tptp.size_size_list_d Xs)) tptp.one_one_nat)) (@ (@ tptp.member2287536781371869328od_d_d (@ (@ tptp.product_Pair_d_d (@ _let_1 (@ tptp.suc N5))) (@ _let_1 N5))) R)))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_d Xs)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.member2287536781371869328od_d_d (@ (@ tptp.product_Pair_d_d (@ _let_1 N)) (@ _let_1 M2))) (@ tptp.transitive_trancl_d R))))))) (forall ((Xs tptp.list_int) (R tptp.set_Pr958786334691620121nt_int) (N tptp.nat) (M2 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))) R)))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int (@ _let_1 N)) (@ _let_1 M2))) (@ tptp.transi6261509568448316235cl_int R))))))) (forall ((Xs tptp.list_nat) (R tptp.set_Pr1261947904930325089at_nat) (N tptp.nat) (M2 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))) R)))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat (@ _let_1 N)) (@ _let_1 M2))) (@ tptp.transi6264000038957366511cl_nat R))))))) _let_127 _let_126 _let_125 (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))) (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))) (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A2) tptp.zero_z3403309356797280102nteger) A2)) (forall ((A2 tptp.multis2468970476368604999at_nat)) (= (@ (@ tptp.plus_p7104986032573967614at_nat A2) tptp.zero_z1048942125864253310at_nat) A2)) (forall ((A2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat A2) tptp.zero_zero_rat) A2)) (forall ((A2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat A2) tptp.zero_zero_nat) A2)) (forall ((A2 tptp.int)) (= (@ (@ tptp.plus_plus_int A2) tptp.zero_zero_int) A2)) (forall ((A2 tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) A2)) (= A2 tptp.zero_z3403309356797280102nteger))) (forall ((A2 tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.plus_plus_rat A2) A2)) (= A2 tptp.zero_zero_rat))) (forall ((A2 tptp.int)) (= (= tptp.zero_zero_int (@ (@ tptp.plus_plus_int A2) A2)) (= A2 tptp.zero_zero_int))) (forall ((B2 tptp.code_integer) (A2 tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger B2) A2) A2) (= B2 tptp.zero_z3403309356797280102nteger))) (forall ((B2 tptp.multis2468970476368604999at_nat) (A2 tptp.multis2468970476368604999at_nat)) (= (= (@ (@ tptp.plus_p7104986032573967614at_nat B2) A2) A2) (= B2 tptp.zero_z1048942125864253310at_nat))) (forall ((B2 tptp.rat) (A2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B2) A2) A2) (= B2 tptp.zero_zero_rat))) (forall ((B2 tptp.nat) (A2 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B2) A2) A2) (= B2 tptp.zero_zero_nat))) (forall ((B2 tptp.int) (A2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int B2) A2) A2) (= B2 tptp.zero_zero_int))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger A2) B2) A2) (= B2 tptp.zero_z3403309356797280102nteger))) (forall ((A2 tptp.multis2468970476368604999at_nat) (B2 tptp.multis2468970476368604999at_nat)) (= (= (@ (@ tptp.plus_p7104986032573967614at_nat A2) B2) A2) (= B2 tptp.zero_z1048942125864253310at_nat))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A2) B2) A2) (= B2 tptp.zero_zero_rat))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat A2) B2) A2) (= B2 tptp.zero_zero_nat))) (forall ((A2 tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int A2) B2) A2) (= B2 tptp.zero_zero_int))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (= A2 (@ (@ tptp.plus_p5714425477246183910nteger B2) A2)) (= B2 tptp.zero_z3403309356797280102nteger))) (forall ((A2 tptp.multis2468970476368604999at_nat) (B2 tptp.multis2468970476368604999at_nat)) (= (= A2 (@ (@ tptp.plus_p7104986032573967614at_nat B2) A2)) (= B2 tptp.zero_z1048942125864253310at_nat))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (= A2 (@ (@ tptp.plus_plus_rat B2) A2)) (= B2 tptp.zero_zero_rat))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (= A2 (@ (@ tptp.plus_plus_nat B2) A2)) (= B2 tptp.zero_zero_nat))) (forall ((A2 tptp.int) (B2 tptp.int)) (= (= A2 (@ (@ tptp.plus_plus_int B2) A2)) (= B2 tptp.zero_zero_int))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (= A2 (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)) (= B2 tptp.zero_z3403309356797280102nteger))) (forall ((A2 tptp.multis2468970476368604999at_nat) (B2 tptp.multis2468970476368604999at_nat)) (= (= A2 (@ (@ tptp.plus_p7104986032573967614at_nat A2) B2)) (= B2 tptp.zero_z1048942125864253310at_nat))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (= A2 (@ (@ tptp.plus_plus_rat A2) B2)) (= B2 tptp.zero_zero_rat))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (= A2 (@ (@ tptp.plus_plus_nat A2) B2)) (= B2 tptp.zero_zero_nat))) (forall ((A2 tptp.int) (B2 tptp.int)) (= (= A2 (@ (@ tptp.plus_plus_int A2) B2)) (= B2 tptp.zero_zero_int))) (forall ((X tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.plus_plus_nat X) Y)) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))) (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.zero_z3403309356797280102nteger) A2) A2)) (forall ((A2 tptp.multis2468970476368604999at_nat)) (= (@ (@ tptp.plus_p7104986032573967614at_nat tptp.zero_z1048942125864253310at_nat) A2) A2)) (forall ((A2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A2) A2)) (forall ((A2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A2) A2)) (forall ((A2 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A2) A2)) (forall ((A2 tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger A2) C) (@ (@ tptp.times_3573771949741848930nteger B2) C)) (or (= C tptp.zero_z3403309356797280102nteger) (= A2 B2)))) (forall ((A2 tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (= (@ (@ tptp.times_times_rat A2) C) (@ (@ tptp.times_times_rat B2) C)) (or (= C tptp.zero_zero_rat) (= A2 B2)))) (forall ((A2 tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat A2) C) (@ (@ tptp.times_times_nat B2) C)) (or (= C tptp.zero_zero_nat) (= A2 B2)))) (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.times_times_int A2) C) (@ (@ tptp.times_times_int B2) C)) (or (= C tptp.zero_zero_int) (= A2 B2)))) (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (= (@ _let_1 A2) (@ _let_1 B2)) (or (= C tptp.zero_z3403309356797280102nteger) (= A2 B2))))) (forall ((C tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (= (@ _let_1 A2) (@ _let_1 B2)) (or (= C tptp.zero_zero_rat) (= A2 B2))))) (forall ((C tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (= (= (@ _let_1 A2) (@ _let_1 B2)) (or (= C tptp.zero_zero_nat) (= A2 B2))))) (forall ((C tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (= (@ _let_1 A2) (@ _let_1 B2)) (or (= C tptp.zero_zero_int) (= A2 B2))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger A2) B2) tptp.zero_z3403309356797280102nteger) (or (= A2 tptp.zero_z3403309356797280102nteger) (= B2 tptp.zero_z3403309356797280102nteger)))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (= (@ (@ tptp.times_times_rat A2) B2) tptp.zero_zero_rat) (or (= A2 tptp.zero_zero_rat) (= B2 tptp.zero_zero_rat)))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat A2) B2) tptp.zero_zero_nat) (or (= A2 tptp.zero_zero_nat) (= B2 tptp.zero_zero_nat)))) (forall ((A2 tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.times_times_int A2) B2) tptp.zero_zero_int) (or (= A2 tptp.zero_zero_int) (= B2 tptp.zero_zero_int)))) (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger A2) tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)) (forall ((A2 tptp.rat)) (= (@ (@ tptp.times_times_rat A2) tptp.zero_zero_rat) tptp.zero_zero_rat)) (forall ((A2 tptp.nat)) (= (@ (@ tptp.times_times_nat A2) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((A2 tptp.int)) (= (@ (@ tptp.times_times_int A2) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger tptp.zero_z3403309356797280102nteger) A2) tptp.zero_z3403309356797280102nteger)) (forall ((A2 tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.zero_zero_rat) A2) tptp.zero_zero_rat)) (forall ((A2 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) A2) tptp.zero_zero_nat)) (forall ((A2 tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) A2) tptp.zero_zero_int)) (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A2) A2) tptp.zero_z3403309356797280102nteger)) (forall ((A2 tptp.multis2468970476368604999at_nat)) (= (@ (@ tptp.minus_4286766774447292334at_nat A2) A2) tptp.zero_z1048942125864253310at_nat)) (forall ((A2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A2) A2) tptp.zero_zero_rat)) (forall ((A2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat A2) A2) tptp.zero_zero_nat)) (forall ((A2 tptp.int)) (= (@ (@ tptp.minus_minus_int A2) A2) tptp.zero_zero_int)) (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A2) tptp.zero_z3403309356797280102nteger) A2)) (forall ((A2 tptp.multis2468970476368604999at_nat)) (= (@ (@ tptp.minus_4286766774447292334at_nat A2) tptp.zero_z1048942125864253310at_nat) A2)) (forall ((A2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A2) tptp.zero_zero_rat) A2)) (forall ((A2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat A2) tptp.zero_zero_nat) A2)) (forall ((A2 tptp.int)) (= (@ (@ tptp.minus_minus_int A2) tptp.zero_zero_int) A2)) (forall ((A2 tptp.multis2468970476368604999at_nat)) (= (@ (@ tptp.minus_4286766774447292334at_nat tptp.zero_z1048942125864253310at_nat) A2) tptp.zero_z1048942125864253310at_nat)) (forall ((A2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) A2) tptp.zero_zero_nat)) (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A2) tptp.zero_z3403309356797280102nteger) A2)) (forall ((A2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A2) tptp.zero_zero_rat) A2)) (forall ((A2 tptp.int)) (= (@ (@ tptp.minus_minus_int A2) tptp.zero_zero_int) A2)) (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A2) A2) tptp.zero_z3403309356797280102nteger)) (forall ((A2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A2) A2) tptp.zero_zero_rat)) (forall ((A2 tptp.int)) (= (@ (@ tptp.minus_minus_int A2) A2) tptp.zero_zero_int)) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))) (forall ((N tptp.nat)) (= (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (forall ((A2 tptp.nat)) (= (not (= A2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A2))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ tptp.insert9069300056098147895at_nat (@ (@ tptp.produc2922128104949294807at_nat A2) B2)) tptp.bot_bo228742789529271731at_nat))) (= (@ tptp.transi2703068831062848130at_nat _let_1) _let_1))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ (@ tptp.insert8211810215607154385at_nat (@ (@ tptp.product_Pair_nat_nat A2) B2)) tptp.bot_bo2099793752762293965at_nat))) (= (@ tptp.transi6264000038957366511cl_nat _let_1) _let_1))) (forall ((B2 tptp.code_integer) (A2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger B2) A2)) B2) (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger))) (forall ((B2 tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat B2) A2)) B2) (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat))) (forall ((B2 tptp.nat) (A2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat B2) A2)) B2) (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat))) (forall ((B2 tptp.int) (A2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int B2) A2)) B2) (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)) B2) (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) B2)) B2) (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) B2)) B2) (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat))) (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) B2)) B2) (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger A2) (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B2))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A2) (@ (@ tptp.plus_plus_rat A2) B2)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B2))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A2) (@ (@ tptp.plus_plus_nat A2) B2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B2))) (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int A2) (@ (@ tptp.plus_plus_int A2) B2)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger A2) (@ (@ tptp.plus_p5714425477246183910nteger B2) A2)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B2))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A2) (@ (@ tptp.plus_plus_rat B2) A2)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B2))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A2) (@ (@ tptp.plus_plus_nat B2) A2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B2))) (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int A2) (@ (@ tptp.plus_plus_int B2) A2)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2))) (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) A2)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger))) (forall ((A2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) A2)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat))) (forall ((A2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) A2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int))) (forall ((A2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A2) A2)) (@ _let_1 A2)))) (forall ((A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat A2) A2)) (@ _let_1 A2)))) (forall ((A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A2) A2)) (@ _let_1 A2)))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.minus_8373710615458151222nteger A2) B2)) (@ (@ tptp.ord_le3102999989581377725nteger B2) A2))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.minus_minus_rat A2) B2)) (@ (@ tptp.ord_less_eq_rat B2) A2))) (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A2) B2)) (@ (@ tptp.ord_less_eq_int B2) A2))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.minus_8373710615458151222nteger A2) B2)) (@ (@ tptp.ord_le3102999989581377725nteger B2) A2))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.minus_minus_rat A2) B2)) (@ (@ tptp.ord_less_eq_rat B2) A2))) (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A2) B2)) (@ (@ tptp.ord_less_eq_int B2) A2))) (forall ((A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat A2) A2)) (@ _let_1 A2)))) (forall ((A2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A2) A2)) (@ _let_1 A2)))) (forall ((A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A2) A2)) (@ _let_1 A2)))) (forall ((A2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) A2)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat))) (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) A2)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.zero_z3403309356797280102nteger))) (forall ((A2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) A2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat A2) (@ (@ tptp.plus_plus_rat B2) A2)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B2))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A2) (@ (@ tptp.plus_p5714425477246183910nteger B2) A2)) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B2))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_nat A2) (@ (@ tptp.plus_plus_nat B2) A2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2))) (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int A2) (@ (@ tptp.plus_plus_int B2) A2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat A2) (@ (@ tptp.plus_plus_rat A2) B2)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B2))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A2) (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B2))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_nat A2) (@ (@ tptp.plus_plus_nat A2) B2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2))) (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int A2) (@ (@ tptp.plus_plus_int A2) B2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) B2)) B2) (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)) B2) (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.zero_z3403309356797280102nteger))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) B2)) B2) (@ (@ tptp.ord_less_nat A2) tptp.zero_zero_nat))) (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) B2)) B2) (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int))) (forall ((B2 tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat B2) A2)) B2) (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat))) (forall ((B2 tptp.code_integer) (A2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger B2) A2)) B2) (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.zero_z3403309356797280102nteger))) (forall ((B2 tptp.nat) (A2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat B2) A2)) B2) (@ (@ tptp.ord_less_nat A2) tptp.zero_zero_nat))) (forall ((B2 tptp.int) (A2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int B2) A2)) B2) (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.minus_minus_rat A2) B2)) (@ (@ tptp.ord_less_rat B2) A2))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.minus_8373710615458151222nteger A2) B2)) (@ (@ tptp.ord_le6747313008572928689nteger B2) A2))) (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A2) B2)) (@ (@ tptp.ord_less_int B2) A2))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.minus_minus_rat A2) B2)) (@ (@ tptp.ord_less_rat B2) A2))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.minus_8373710615458151222nteger A2) B2)) (@ (@ tptp.ord_le6747313008572928689nteger B2) A2))) (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A2) B2)) (@ (@ tptp.ord_less_int B2) A2))) (forall ((C tptp.code_integer) (B2 tptp.code_integer)) (= (= C (@ (@ tptp.times_3573771949741848930nteger C) B2)) (or (= C tptp.zero_z3403309356797280102nteger) (= B2 tptp.one_one_Code_integer)))) (forall ((C tptp.rat) (B2 tptp.rat)) (= (= C (@ (@ tptp.times_times_rat C) B2)) (or (= C tptp.zero_zero_rat) (= B2 tptp.one_one_rat)))) (forall ((C tptp.int) (B2 tptp.int)) (= (= C (@ (@ tptp.times_times_int C) B2)) (or (= C tptp.zero_zero_int) (= B2 tptp.one_one_int)))) (forall ((C tptp.code_integer) (A2 tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger C) A2) C) (or (= C tptp.zero_z3403309356797280102nteger) (= A2 tptp.one_one_Code_integer)))) (forall ((C tptp.rat) (A2 tptp.rat)) (= (= (@ (@ tptp.times_times_rat C) A2) C) (or (= C tptp.zero_zero_rat) (= A2 tptp.one_one_rat)))) (forall ((C tptp.int) (A2 tptp.int)) (= (= (@ (@ tptp.times_times_int C) A2) C) (or (= C tptp.zero_zero_int) (= A2 tptp.one_one_int)))) (forall ((C tptp.code_integer) (B2 tptp.code_integer)) (= (= C (@ (@ tptp.times_3573771949741848930nteger B2) C)) (or (= C tptp.zero_z3403309356797280102nteger) (= B2 tptp.one_one_Code_integer)))) (forall ((C tptp.rat) (B2 tptp.rat)) (= (= C (@ (@ tptp.times_times_rat B2) C)) (or (= C tptp.zero_zero_rat) (= B2 tptp.one_one_rat)))) (forall ((C tptp.int) (B2 tptp.int)) (= (= C (@ (@ tptp.times_times_int B2) C)) (or (= C tptp.zero_zero_int) (= B2 tptp.one_one_int)))) (forall ((A2 tptp.code_integer) (C tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger A2) C) C) (or (= C tptp.zero_z3403309356797280102nteger) (= A2 tptp.one_one_Code_integer)))) (forall ((A2 tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.times_times_rat A2) C) C) (or (= C tptp.zero_zero_rat) (= A2 tptp.one_one_rat)))) (forall ((A2 tptp.int) (C tptp.int)) (= (= (@ (@ tptp.times_times_int A2) C) C) (or (= C tptp.zero_zero_int) (= A2 tptp.one_one_int)))) (forall ((A2 tptp.multis2468970476368604999at_nat) (B2 tptp.multis2468970476368604999at_nat)) (= (@ (@ tptp.minus_4286766774447292334at_nat A2) (@ (@ tptp.plus_p7104986032573967614at_nat A2) B2)) tptp.zero_z1048942125864253310at_nat)) (forall ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat A2) (@ (@ tptp.plus_plus_nat A2) B2)) tptp.zero_zero_nat)) _let_124 _let_123 _let_122 (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc tptp.zero_zero_nat)) (= N tptp.zero_zero_nat))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)) (or (@ _let_1 M2) (@ _let_1 N))))) (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) M2)) (@ (@ tptp.ord_less_nat M2) N))) (forall ((K3 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K3))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (@ (@ tptp.ord_less_nat M2) N))))) (forall ((M2 tptp.nat) (K3 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat M2) K3)) (@ (@ tptp.times_times_nat N) K3)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (@ (@ tptp.ord_less_nat M2) N)))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.times_times_nat M2) N)) (and (@ _let_1 M2) (@ _let_1 N))))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) tptp.one_one_nat) (= N tptp.zero_zero_nat))) (forall ((Xs tptp.list_c)) (= (@ (@ (@ tptp.slice_c tptp.zero_zero_nat) (@ tptp.size_size_list_c Xs)) Xs) Xs)) (forall ((Xs tptp.list_d)) (= (@ (@ (@ tptp.slice_d tptp.zero_zero_nat) (@ tptp.size_size_list_d Xs)) Xs) Xs)) (forall ((Xs tptp.list_nat)) (= (@ (@ (@ tptp.slice_nat tptp.zero_zero_nat) (@ tptp.size_size_list_nat Xs)) Xs) Xs)) (forall ((Xs tptp.list_int)) (= (@ (@ (@ tptp.slice_int tptp.zero_zero_nat) (@ tptp.size_size_list_int Xs)) Xs) Xs)) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) N))) (forall ((K3 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K3))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M2)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (@ (@ tptp.ord_less_eq_nat M2) N))))) (forall ((M2 tptp.nat) (K3 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M2) K3)) (@ (@ tptp.times_times_nat N) K3)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (@ (@ tptp.ord_less_eq_nat M2) N)))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) N))) (forall ((X tptp.assn) (Y tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (let ((_let_2 (@ tptp.sup_sup_assn Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (= tptp.sup_sup_assn (lambda ((X2 tptp.assn) (Y5 tptp.assn)) (@ (@ tptp.sup_sup_assn Y5) X2))) (forall ((X tptp.assn)) (= (@ (@ tptp.sup_sup_assn X) X) X)) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (= (@ (@ tptp.sup_sup_assn (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_sup_assn Y) Z))))) (forall ((X tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger X) (= X tptp.zero_z3403309356797280102nteger))) (forall ((X tptp.multis2468970476368604999at_nat)) (= (= tptp.zero_z1048942125864253310at_nat X) (= X tptp.zero_z1048942125864253310at_nat))) (forall ((X tptp.rat)) (= (= tptp.zero_zero_rat X) (= X tptp.zero_zero_rat))) (forall ((X tptp.nat)) (= (= tptp.zero_zero_nat X) (= X tptp.zero_zero_nat))) (forall ((X tptp.int)) (= (= tptp.zero_zero_int X) (= X tptp.zero_zero_int))) (forall ((U2 tptp.set_Pr4329608150637261639at_nat) (V tptp.set_Pr4329608150637261639at_nat) (X tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat X))) (=> (@ (@ tptp.ord_le1268244103169919719at_nat U2) V) (=> (@ _let_1 (@ tptp.transi2703068831062848130at_nat U2)) (@ _let_1 (@ tptp.transi2703068831062848130at_nat V)))))) (forall ((U2 tptp.set_Pr1261947904930325089at_nat) (V tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat U2) V) (=> (@ _let_1 (@ tptp.transi6264000038957366511cl_nat U2)) (@ _let_1 (@ tptp.transi6264000038957366511cl_nat V)))))) (forall ((R tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat R) (@ tptp.transi6264000038957366511cl_nat R))) (forall ((R tptp.set_Pr4329608150637261639at_nat) (X tptp.produc3843707927480180839at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat (@ tptp.transi2703068831062848130at_nat R)) (@ tptp.transi2703068831062848130at_nat (@ (@ tptp.insert9069300056098147895at_nat X) R)))) (forall ((R tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.transi6264000038957366511cl_nat R)) (@ tptp.transi6264000038957366511cl_nat (@ (@ tptp.insert8211810215607154385at_nat X) R)))) (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X)) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (not (= N tptp.zero_zero_nat)))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (not (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))) (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (not (@ _let_109 tptp.zero_zero_rat)) (not (@ _let_108 tptp.zero_z3403309356797280102nteger)) (not (@ _let_107 tptp.zero_zero_nat)) (not (@ _let_106 tptp.zero_zero_int)) (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.zero_z3403309356797280102nteger) A2) A2)) (forall ((A2 tptp.multis2468970476368604999at_nat)) (= (@ (@ tptp.plus_p7104986032573967614at_nat tptp.zero_z1048942125864253310at_nat) A2) A2)) (forall ((A2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A2) A2)) (forall ((A2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A2) A2)) (forall ((A2 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A2) A2)) (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A2) tptp.zero_z3403309356797280102nteger) A2)) (forall ((A2 tptp.multis2468970476368604999at_nat)) (= (@ (@ tptp.plus_p7104986032573967614at_nat A2) tptp.zero_z1048942125864253310at_nat) A2)) (forall ((A2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat A2) tptp.zero_zero_rat) A2)) (forall ((A2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat A2) tptp.zero_zero_nat) A2)) (forall ((A2 tptp.int)) (= (@ (@ tptp.plus_plus_int A2) tptp.zero_zero_int) A2)) (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.zero_z3403309356797280102nteger) A2) A2)) (forall ((A2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A2) A2)) (forall ((A2 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A2) A2)) (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (= (= (@ (@ tptp.times_3573771949741848930nteger A2) C) (@ (@ tptp.times_3573771949741848930nteger B2) C)) (= A2 B2)))) (forall ((C tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ (@ tptp.times_times_rat A2) C) (@ (@ tptp.times_times_rat B2) C)) (= A2 B2)))) (forall ((C tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (= (= (@ (@ tptp.times_times_nat A2) C) (@ (@ tptp.times_times_nat B2) C)) (= A2 B2)))) (forall ((C tptp.int) (A2 tptp.int) (B2 tptp.int)) (=> (not (= C tptp.zero_zero_int)) (= (= (@ (@ tptp.times_times_int A2) C) (@ (@ tptp.times_times_int B2) C)) (= A2 B2)))) (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (= (= (@ _let_1 A2) (@ _let_1 B2)) (= A2 B2))))) (forall ((C tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ _let_1 A2) (@ _let_1 B2)) (= A2 B2))))) (forall ((C tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (not (= C tptp.zero_zero_nat)) (= (= (@ _let_1 A2) (@ _let_1 B2)) (= A2 B2))))) (forall ((C tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (= (@ _let_1 A2) (@ _let_1 B2)) (= A2 B2))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (not (= A2 tptp.zero_z3403309356797280102nteger)) (=> (not (= B2 tptp.zero_z3403309356797280102nteger)) (not (= (@ (@ tptp.times_3573771949741848930nteger A2) B2) tptp.zero_z3403309356797280102nteger))))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (not (= A2 tptp.zero_zero_rat)) (=> (not (= B2 tptp.zero_zero_rat)) (not (= (@ (@ tptp.times_times_rat A2) B2) tptp.zero_zero_rat))))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (not (= A2 tptp.zero_zero_nat)) (=> (not (= B2 tptp.zero_zero_nat)) (not (= (@ (@ tptp.times_times_nat A2) B2) tptp.zero_zero_nat))))) (forall ((A2 tptp.int) (B2 tptp.int)) (=> (not (= A2 tptp.zero_zero_int)) (=> (not (= B2 tptp.zero_zero_int)) (not (= (@ (@ tptp.times_times_int A2) B2) tptp.zero_zero_int))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (= (@ (@ tptp.times_3573771949741848930nteger A2) B2) tptp.zero_z3403309356797280102nteger) (or (= A2 tptp.zero_z3403309356797280102nteger) (= B2 tptp.zero_z3403309356797280102nteger)))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (= (@ (@ tptp.times_times_rat A2) B2) tptp.zero_zero_rat) (or (= A2 tptp.zero_zero_rat) (= B2 tptp.zero_zero_rat)))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (= (@ (@ tptp.times_times_nat A2) B2) tptp.zero_zero_nat) (or (= A2 tptp.zero_zero_nat) (= B2 tptp.zero_zero_nat)))) (forall ((A2 tptp.int) (B2 tptp.int)) (=> (= (@ (@ tptp.times_times_int A2) B2) tptp.zero_zero_int) (or (= A2 tptp.zero_zero_int) (= B2 tptp.zero_zero_int)))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (not (= (@ (@ tptp.times_3573771949741848930nteger A2) B2) tptp.zero_z3403309356797280102nteger)) (and (not (= A2 tptp.zero_z3403309356797280102nteger)) (not (= B2 tptp.zero_z3403309356797280102nteger))))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (not (= (@ (@ tptp.times_times_rat A2) B2) tptp.zero_zero_rat)) (and (not (= A2 tptp.zero_zero_rat)) (not (= B2 tptp.zero_zero_rat))))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (not (= (@ (@ tptp.times_times_nat A2) B2) tptp.zero_zero_nat)) (and (not (= A2 tptp.zero_zero_nat)) (not (= B2 tptp.zero_zero_nat))))) (forall ((A2 tptp.int) (B2 tptp.int)) (=> (not (= (@ (@ tptp.times_times_int A2) B2) tptp.zero_zero_int)) (and (not (= A2 tptp.zero_zero_int)) (not (= B2 tptp.zero_zero_int))))) (not (= tptp.zero_z3403309356797280102nteger tptp.one_one_Code_integer)) (not (= tptp.zero_zero_rat tptp.one_one_rat)) (not (= tptp.zero_zero_nat tptp.one_one_nat)) (not (= tptp.zero_zero_int tptp.one_one_int)) (= (lambda ((Y4 tptp.code_integer) (Z2 tptp.code_integer)) (= Y4 Z2)) (lambda ((A3 tptp.code_integer) (B3 tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A3) B3) tptp.zero_z3403309356797280102nteger))) (= (lambda ((Y4 tptp.rat) (Z2 tptp.rat)) (= Y4 Z2)) (lambda ((A3 tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A3) B3) tptp.zero_zero_rat))) (= (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2)) (lambda ((A3 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.minus_minus_int A3) B3) tptp.zero_zero_int))) (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N5) (=> (not (@ P N5)) (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N5) (not (@ P M3))))))) (@ P N)))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (not (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))) (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))) (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (forall ((A2 tptp.nat)) (not (@ (@ tptp.ord_less_nat A2) tptp.zero_zero_nat))) (forall ((R2 tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger R2))) (=> (not (= R2 tptp.zero_z3403309356797280102nteger)) (=> (and (= A2 B2) (not (= C D2))) (not (= (@ (@ tptp.plus_p5714425477246183910nteger A2) (@ _let_1 C)) (@ (@ tptp.plus_p5714425477246183910nteger B2) (@ _let_1 D2)))))))) (forall ((R2 tptp.rat) (A2 tptp.rat) (B2 tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat R2))) (=> (not (= R2 tptp.zero_zero_rat)) (=> (and (= A2 B2) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_rat A2) (@ _let_1 C)) (@ (@ tptp.plus_plus_rat B2) (@ _let_1 D2)))))))) (forall ((R2 tptp.nat) (A2 tptp.nat) (B2 tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat R2))) (=> (not (= R2 tptp.zero_zero_nat)) (=> (and (= A2 B2) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_nat A2) (@ _let_1 C)) (@ (@ tptp.plus_plus_nat B2) (@ _let_1 D2)))))))) (forall ((R2 tptp.int) (A2 tptp.int) (B2 tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int R2))) (=> (not (= R2 tptp.zero_zero_int)) (=> (and (= A2 B2) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_int A2) (@ _let_1 C)) (@ (@ tptp.plus_plus_int B2) (@ _let_1 D2)))))))) (forall ((K3 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K3))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (= (= (@ _let_1 M2) (@ _let_1 N)) (= M2 N))))) (forall ((K3 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K3))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (= (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M2) N))))) (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)))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.zero_zero_rat) (= (= (@ (@ tptp.plus_plus_rat X) Y) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat Y) tptp.zero_zero_nat) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.zero_zero_int) (= (= (@ (@ tptp.plus_plus_int X) Y) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))) (forall ((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))))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_rat X) Y) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat))))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_int X) Y) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le3102999989581377725nteger B2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)) tptp.zero_z3403309356797280102nteger)))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) B2)) tptp.zero_zero_rat)))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) B2)) tptp.zero_zero_nat)))) (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) B2)) tptp.zero_zero_int)))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)))))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) B2)))))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) B2)))))) (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_int A2) B2)))))) (forall ((C tptp.code_integer) (B2 tptp.code_integer) (A2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger B2))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A2) C)))))) (forall ((C tptp.rat) (B2 tptp.rat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat B2))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) C)))))) (forall ((C tptp.nat) (B2 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) C)))))) (forall ((C tptp.int) (B2 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int B2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.plus_plus_int A2) C)))))) (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B2) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) C)) B2)))) (forall ((C tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) C)) B2)))) (forall ((C tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) C)) B2)))) (forall ((C tptp.int) (A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) C)) B2)))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger B2))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A2) C)))))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat B2))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) C)))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) C)))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int B2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A2) C)))))) (forall ((A2 tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) B2) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) C)) B2)))) (forall ((A2 tptp.rat) (C tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat C) B2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) C)) B2)))) (forall ((A2 tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat C) B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) C)) B2)))) (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int C) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) C)) B2)))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B2) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) D2) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B2) D2)))))))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_eq_rat C) D2) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B2) D2)))))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B2) D2)))))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_eq_int C) D2) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B2) D2)))))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B2) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) D2) (=> (@ _let_1 A2) (=> (@ _let_1 C) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B2) D2)))))))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_eq_rat C) D2) (=> (@ _let_1 A2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B2) D2)))))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (=> (@ _let_1 A2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B2) D2)))))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_eq_int C) D2) (=> (@ _let_1 A2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B2) D2)))))))) (forall ((A2 tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.times_3573771949741848930nteger A2) A2))) (forall ((A2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A2) A2))) (forall ((A2 tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A2) A2))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (or (and (@ _let_1 A2) (@ _let_1 B2)) (and (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B2) tptp.zero_z3403309356797280102nteger))) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A2) B2))))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (or (and (@ _let_1 A2) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat))) (@ _let_1 (@ (@ tptp.times_times_rat A2) B2))))) (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A2) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int))) (@ _let_1 (@ (@ tptp.times_times_int A2) B2))))) (forall ((B2 tptp.code_integer) (A2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le3102999989581377725nteger B2) A2) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A2)) (@ _let_1 B2)))))) (forall ((B2 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B2) A2) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2)))))) (forall ((B2 tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le3102999989581377725nteger B2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.times_3573771949741848930nteger A2) B2))))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A2) B2))))) (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A2) B2))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B2) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A2)) (@ _let_1 B2)))))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2)))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B2)))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)))))) (forall ((B2 tptp.code_integer) (A2 tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger B2) A2) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B2) C))))) (forall ((B2 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B2) A2) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B2) C))))) (forall ((B2 tptp.int) (A2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A2) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B2) C))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B2) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B2) C))))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B2) C))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B2) C))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B2) C))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A2) B2)) tptp.zero_z3403309356797280102nteger) (or (and (@ _let_1 A2) (@ (@ tptp.ord_le3102999989581377725nteger B2) tptp.zero_z3403309356797280102nteger)) (and (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger) (@ _let_1 B2)))))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) B2)) tptp.zero_zero_rat) (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (@ _let_1 B2)))))) (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) B2)) tptp.zero_zero_int) (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (@ _let_1 B2)))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (or (and (@ _let_1 A2) (@ (@ tptp.ord_le3102999989581377725nteger B2) tptp.zero_z3403309356797280102nteger)) (and (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger) (@ _let_1 B2))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A2) B2)) tptp.zero_z3403309356797280102nteger)))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (@ _let_1 B2))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) B2)) tptp.zero_zero_rat)))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_nat B2) tptp.zero_zero_nat)) (and (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat) (@ _let_1 B2))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) B2)) tptp.zero_zero_nat)))) (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (@ _let_1 B2))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) B2)) tptp.zero_zero_int)))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A2) B2)))))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_rat A2) B2)))))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_nat A2) B2)))))) (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_int A2) B2)))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ (@ tptp.ord_le3102999989581377725nteger B2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A2) B2)) tptp.zero_z3403309356797280102nteger)))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) B2)) tptp.zero_zero_rat)))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_eq_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) B2)) tptp.zero_zero_nat)))) (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) B2)) tptp.zero_zero_int)))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B2) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A2) B2)) tptp.zero_z3403309356797280102nteger)))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) B2)) tptp.zero_zero_rat)))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) B2)) tptp.zero_zero_nat)))) (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) B2)) tptp.zero_zero_int)))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ (@ tptp.ord_le3102999989581377725nteger B2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger B2) A2)) tptp.zero_z3403309356797280102nteger)))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat B2) A2)) tptp.zero_zero_rat)))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_eq_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat B2) A2)) tptp.zero_zero_nat)))) (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int B2) A2)) tptp.zero_zero_int)))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A2) B2)) (or (and (@ _let_1 A2) (@ _let_1 B2)) (and (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B2) tptp.zero_z3403309356797280102nteger)))))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.times_times_rat A2) B2)) (or (and (@ _let_1 A2) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat)))))) (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.times_times_int A2) B2)) (or (and (@ _let_1 A2) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int)))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B2) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A2)) (@ _let_1 B2)))))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2)))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B2)))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)))))) _let_121 _let_120 _let_119 _let_118 _let_121 _let_120 _let_119 _let_118 (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)) (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.zero_zero_rat)) (not (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.zero_zero_nat)) (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.zero_zero_int)) (= tptp.ord_le3102999989581377725nteger (lambda ((A3 tptp.code_integer) (B3 tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger A3) B3)) tptp.zero_z3403309356797280102nteger))) (= tptp.ord_less_eq_rat (lambda ((A3 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A3) B3)) tptp.zero_zero_rat))) (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A3) B3)) tptp.zero_zero_int))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat X) Y)) tptp.zero_zero_rat) (or (@ (@ tptp.ord_less_rat X) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat)))) (forall ((X tptp.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)))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X) Y)) tptp.zero_zero_int) (or (@ (@ tptp.ord_less_int X) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Y) tptp.zero_zero_int)))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) B2)) tptp.zero_zero_rat)))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)) tptp.zero_z3403309356797280102nteger)))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) B2)) tptp.zero_zero_nat)))) (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) B2)) tptp.zero_zero_int)))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) B2)))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)))))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) B2)))))) (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_int A2) B2)))))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (not (forall ((C4 tptp.nat)) (=> (= B2 (@ (@ tptp.plus_plus_nat A2) C4)) (= C4 tptp.zero_zero_nat)))))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B2))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) C)))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger B2))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A2) C)))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) C)))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A2) C)))))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A2) B2))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.times_3573771949741848930nteger A2) B2))))) (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A2) B2))))) (forall ((A2 tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) A2)) tptp.zero_zero_rat))) (forall ((A2 tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) A2)) tptp.zero_z3403309356797280102nteger))) (forall ((A2 tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) A2)) tptp.zero_zero_int))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) B2)) tptp.zero_zero_rat) (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_rat B2) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (@ _let_1 B2)))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) B2)) tptp.zero_z3403309356797280102nteger) (or (and (@ _let_1 A2) (@ (@ tptp.ord_le6747313008572928689nteger B2) tptp.zero_z3403309356797280102nteger)) (and (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.zero_z3403309356797280102nteger) (@ _let_1 B2)))))) (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) B2)) tptp.zero_zero_int) (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int) (@ _let_1 B2)))))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B2) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) B2)) tptp.zero_zero_rat)))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B2) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) B2)) tptp.zero_z3403309356797280102nteger)))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) B2)) tptp.zero_zero_nat)))) (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) B2)) tptp.zero_zero_int)))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) B2)) tptp.zero_zero_rat)))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) B2)) tptp.zero_z3403309356797280102nteger)))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) B2)) tptp.zero_zero_nat)))) (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) B2)) tptp.zero_zero_int)))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_rat A2) B2)))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A2) B2)))))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_nat A2) B2)))))) (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_int A2) B2)))))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat B2) A2)) tptp.zero_zero_rat)))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger B2) A2)) tptp.zero_z3403309356797280102nteger)))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat B2) A2)) tptp.zero_zero_nat)))) (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int B2) A2)) tptp.zero_zero_int)))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.times_times_rat A2) B2)) (or (and (@ _let_1 A2) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B2) tptp.zero_zero_rat)))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A2) B2)) (or (and (@ _let_1 A2) (@ _let_1 B2)) (and (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B2) tptp.zero_z3403309356797280102nteger)))))) (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.times_times_int A2) B2)) (or (and (@ _let_1 A2) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int)))))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.times_times_rat A2) B2)) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A2) B2)) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat A2) B2)) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.times_times_int A2) B2)) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((B2 tptp.rat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.times_times_rat B2) A2)) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((B2 tptp.code_integer) (A2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B2) A2)) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((B2 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat B2) A2)) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((B2 tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.times_times_int B2) A2)) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((C tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_rat B2) A2))))) (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_le6747313008572928689nteger B2) A2))))) (forall ((C tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_int B2) A2))))) (forall ((C tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_rat A2) B2))))) (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_le6747313008572928689nteger A2) B2))))) (forall ((C tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (= (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_int A2) B2))))) (forall ((B2 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat B2) A2) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B2)))))) (forall ((B2 tptp.code_integer) (A2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) A2) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B2)))))) (forall ((B2 tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int B2) A2) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2)))))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B2)))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B2)))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B2)))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2)))))) (forall ((C tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B2)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A2) B2)) (and (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B2) A2)))))) (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B2)) (or (and (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A2) B2)) (and (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B2) A2)))))) (forall ((C tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A2) B2)) (and (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) A2)))))) (forall ((B2 tptp.rat) (A2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat B2) A2) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B2) C))))) (forall ((B2 tptp.code_integer) (A2 tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) A2) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B2) C))))) (forall ((B2 tptp.int) (A2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A2) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B2) C))))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B2) C))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B2) C))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B2) C))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B2) C))))) (forall ((A2 tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B2) C)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A2) B2)) (and (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B2) A2))))) (forall ((A2 tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B2) C)) (or (and (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A2) B2)) (and (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B2) A2))))) (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B2) C)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A2) B2)) (and (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) A2))))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B2)))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B2)))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B2)))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2)))))) (not (@ _let_117 tptp.zero_zero_rat)) (not (@ _let_116 tptp.zero_z3403309356797280102nteger)) (not (@ _let_115 tptp.zero_zero_nat)) (not (@ _let_114 tptp.zero_zero_int)) _let_113 _let_112 _let_111 _let_110 _let_113 _let_112 _let_111 _let_110 (= tptp.ord_less_rat (lambda ((A3 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A3) B3)) tptp.zero_zero_rat))) (= tptp.ord_le6747313008572928689nteger (lambda ((A3 tptp.code_integer) (B3 tptp.code_integer)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.minus_8373710615458151222nteger A3) B3)) tptp.zero_z3403309356797280102nteger))) (= tptp.ord_less_int (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A3) B3)) tptp.zero_zero_int))) (forall ((K3 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K3))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M2) N))))) (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N)) (@ P I4))) (or (@ P tptp.zero_zero_nat) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) N) (@ P (@ tptp.suc I4))))))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M tptp.nat)) (= N (@ tptp.suc M))))) (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N)) (@ P I4))) (and (@ P tptp.zero_zero_nat) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N) (@ P (@ tptp.suc I4))))))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M6 tptp.nat)) (= N (@ tptp.suc M6))))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M2) (@ tptp.suc N)) (or (= M2 tptp.zero_zero_nat) (exists ((J2 tptp.nat)) (and (= M2 (@ tptp.suc J2)) (@ (@ tptp.ord_less_nat J2) N)))))) (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N5 tptp.nat)) (=> (forall ((Nn tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Nn) N5) (@ P Nn))) (@ P (@ tptp.suc N5)))) (@ P N)))) (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N5 tptp.nat)) (=> (forall ((Nn tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Nn) N5) (@ P Nn))) (@ P (@ tptp.suc N5)))) (@ P N)))) (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P N) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat K) N) (forall ((I6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I6) K) (not (@ P I6)))) (@ P K)))))) (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (exists ((K tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.plus_plus_nat I) K) J))))) (forall ((N tptp.nat) (M2 tptp.nat)) (=> (= (@ tptp.suc N) M2) (= N (@ (@ tptp.minus_minus_nat M2) (@ tptp.suc tptp.zero_zero_nat))))) (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (=> (@ _let_1 M2) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M2) N)) M2))))) (forall ((I tptp.nat) (J tptp.nat) (K3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat I) K3)) (@ (@ tptp.times_times_nat J) K3))))) (forall ((I tptp.nat) (J tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K3))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (@ (@ tptp.ord_less_nat (@ _let_1 I)) (@ _let_1 J)))))) (forall ((X tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) X) (not (= X tptp.zero_zero_nat)))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) B2)) tptp.zero_zero_rat)))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le3102999989581377725nteger B2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)) tptp.zero_z3403309356797280102nteger)))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) B2)) tptp.zero_zero_nat)))) (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) B2)) tptp.zero_zero_int)))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) B2)))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)))))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) B2)))))) (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_int A2) B2)))))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) B2)) tptp.zero_zero_rat)))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)) tptp.zero_z3403309356797280102nteger)))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) B2)) tptp.zero_zero_nat)))) (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) B2)) tptp.zero_zero_int)))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B2) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) B2)))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B2) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)))))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B2) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) B2)))))) (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2) (@ _let_1 (@ (@ tptp.plus_plus_int A2) B2)))))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_eq_rat B2) C) (@ (@ tptp.ord_less_rat B2) (@ (@ tptp.plus_plus_rat A2) C))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ (@ tptp.ord_le3102999989581377725nteger B2) C) (@ (@ tptp.ord_le6747313008572928689nteger B2) (@ (@ tptp.plus_p5714425477246183910nteger A2) C))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (@ (@ tptp.ord_less_nat B2) (@ (@ tptp.plus_plus_nat A2) C))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_eq_int B2) C) (@ (@ tptp.ord_less_int B2) (@ (@ tptp.plus_plus_int A2) C))))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B2))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) C)))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger B2))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A2) C)))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) C)))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A2) C)))))) (forall ((C tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A2) B2)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B2) A2)))))) (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A2)) (@ _let_1 B2)) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger A2) B2)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B2) A2)))))) (forall ((C tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A2) B2)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B2) A2)))))) (forall ((A2 tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B2) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A2) B2)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B2) A2))))) (forall ((A2 tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B2) C)) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger A2) B2)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B2) A2))))) (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B2) C)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A2) B2)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B2) A2))))) (forall ((C tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A2) B2))))) (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A2) B2))))) (forall ((C tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat A2) B2))))) (forall ((C tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A2) B2))))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (@ (@ tptp.ord_less_rat C) D2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B2) D2))))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) D2) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B2) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B2) D2))))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_nat C) D2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B2) D2))))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ (@ tptp.ord_less_int C) D2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B2) D2))))))) (forall ((C tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B2)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A2) B2)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B2) A2)))))) (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B2)) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A2) B2)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B2) A2)))))) (forall ((C tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A2) B2)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) A2)))))) (forall ((A2 tptp.rat) (C tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B2) C)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A2) B2)))) (forall ((A2 tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B2) C)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A2) B2)))) (forall ((A2 tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B2) C)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat A2) B2)))) (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B2) C)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A2) B2)))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (@ (@ tptp.ord_less_rat C) D2) (=> (@ _let_1 A2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B2) D2)))))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) D2) (=> (@ _let_1 A2) (=> (@ _let_1 C) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B2) D2)))))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_nat C) D2) (=> (@ _let_1 A2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B2) D2)))))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ (@ tptp.ord_less_int C) D2) (=> (@ _let_1 A2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B2) D2)))))))) (forall ((A2 tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B2) C)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A2) B2)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B2) A2))))) (forall ((A2 tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B2) C)) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A2) B2)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B2) A2))))) (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B2) C)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A2) B2)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) A2))))) (forall ((C tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_rat B2) A2))))) (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_le3102999989581377725nteger B2) A2))))) (forall ((C tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_int B2) A2))))) (forall ((C tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_rat A2) B2))))) (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_le3102999989581377725nteger A2) B2))))) (forall ((C tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_int A2) B2))))) (forall ((C tptp.rat) (A2 tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A2) B2))))) (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A2)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger A2) B2))))) (forall ((C tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat A2) B2))))) (forall ((C tptp.int) (A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A2) B2))))) (forall ((A2 tptp.rat) (C tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B2) C)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A2) B2)))) (forall ((A2 tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B2) C)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger A2) B2)))) (forall ((A2 tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B2) C)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat A2) B2)))) (forall ((A2 tptp.int) (C tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B2) C)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A2) B2)))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B2) (=> (@ (@ tptp.ord_less_rat C) D2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B2) D2))))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) D2) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B2) D2))))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_nat C) D2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B2) D2))))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_int C) D2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B2) D2))))))) (forall ((A2 tptp.rat) (B2 tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B2) (=> (@ (@ tptp.ord_less_eq_rat C) D2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B2) D2))))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B2) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) D2) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B2) D2))))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B2) D2))))))) (forall ((A2 tptp.int) (B2 tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ (@ tptp.ord_less_eq_int C) D2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B2) D2))))))) (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)))) (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y)))) (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)))) (forall ((C tptp.code_integer) (A2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.one_one_Code_integer) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) A2)))) (forall ((C tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.one_one_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C)) A2)))) (forall ((C tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) tptp.one_one_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) C)) A2)))) (forall ((C tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.one_one_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) C)) A2)))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.one_one_Code_integer) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B2) (=> (@ (@ tptp.ord_le3102999989581377725nteger B2) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A2) B2)) tptp.one_one_Code_integer))))) (forall ((A2 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) tptp.one_one_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B2) (=> (@ (@ tptp.ord_less_eq_rat B2) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) B2)) tptp.one_one_rat))))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.one_one_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B2) (=> (@ (@ tptp.ord_less_eq_nat B2) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) B2)) tptp.one_one_nat))))) (forall ((A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.one_one_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_eq_int B2) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) B2)) tptp.one_one_int))))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_le3102999989581377725nteger Y) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger X) Y)) X)))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X) Y)) X)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X) Y)) X)))))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_le3102999989581377725nteger Y) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger Y) X)) X)))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Y) X)) X)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int Y) X)) X)))))) (forall ((X tptp.rat) (Y tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y))) tptp.zero_zero_rat))) (forall ((X tptp.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))) (forall ((X tptp.int) (Y tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) tptp.zero_zero_int))) (@ _let_109 (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)) (@ _let_108 (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) tptp.one_one_Code_integer)) (@ _let_107 (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)) (@ _let_106 (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)) (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P N) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K tptp.nat)) (and (@ (@ tptp.ord_less_nat K) N) (forall ((I6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I6) K) (not (@ P I6)))) (@ P (@ tptp.suc K))))))) (forall ((X tptp.produc3843707927480180839at_nat) (Xs tptp.list_P5464809261938338413at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X) (@ tptp.set_Pr3765526544606949372at_nat Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s1588839187904960729at_nat Xs)))) (forall ((X tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s5460976970255530739at_nat Xs)))) (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xs tptp.list_P7985473006766602707_nat_o)) (=> (@ (@ tptp.member6576561426505652726_nat_o X) (@ tptp.set_Pr400311997697478754_nat_o Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s8908918004648414271_nat_o Xs)))) (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (=> (@ (@ tptp.member7957490590177025114n_assn X) (@ tptp.set_Pr1139785259514867910n_assn Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s6829681357464350627n_assn Xs)))) (forall ((X tptp.c) (Xs tptp.list_c)) (=> (@ (@ tptp.member_c X) (@ tptp.set_c2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_c Xs)))) (forall ((X tptp.d) (Xs tptp.list_d)) (=> (@ (@ tptp.member_d X) (@ tptp.set_d2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_d Xs)))) (forall ((X tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_nat Xs)))) (forall ((X tptp.int) (Xs tptp.list_int)) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_int Xs)))) (forall ((N tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I))) N))) (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M2) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat N) M2))))) (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M2) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat M2) N))))) (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 N) (=> (@ _let_1 M2) (@ _let_1 (@ (@ tptp.times_times_nat M2) N)))))) (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ P tptp.one_one_nat) (=> (forall ((N5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N5) (=> (@ P N5) (@ P (@ tptp.suc N5))))) (@ P N))))) (forall ((P (-> tptp.nat Bool)) (A2 tptp.nat) (B2 tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A2) B2)) (and (=> (@ (@ tptp.ord_less_nat A2) B2) (@ P tptp.zero_zero_nat)) (forall ((D5 tptp.nat)) (=> (= A2 (@ (@ tptp.plus_plus_nat B2) D5)) (@ P D5)))))) (forall ((P (-> tptp.nat Bool)) (A2 tptp.nat) (B2 tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A2) B2)) (not (or (and (@ (@ tptp.ord_less_nat A2) B2) (not (@ P tptp.zero_zero_nat))) (exists ((D5 tptp.nat)) (and (= A2 (@ (@ tptp.plus_plus_nat B2) D5)) (not (@ P D5)))))))) (forall ((C tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.times_times_rat C) B2)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) B2)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B2) tptp.one_one_rat))))) (forall ((C tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger C) (@ (@ tptp.times_3573771949741848930nteger C) B2)) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) B2)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B2) tptp.one_one_Code_integer))))) (forall ((C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.times_times_int C) B2)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) B2)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B2) tptp.one_one_int))))) (forall ((C tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat C) A2)) C) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A2) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A2))))) (forall ((C tptp.code_integer) (A2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger C) A2)) C) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.one_one_Code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) A2))))) (forall ((C tptp.int) (A2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int C) A2)) C) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A2) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A2))))) (forall ((C tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.times_times_rat B2) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) B2)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B2) tptp.one_one_rat))))) (forall ((C tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger C) (@ (@ tptp.times_3573771949741848930nteger B2) C)) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) B2)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B2) tptp.one_one_Code_integer))))) (forall ((C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.times_times_int B2) C)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) B2)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B2) tptp.one_one_int))))) (forall ((A2 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C)) C) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A2) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A2))))) (forall ((A2 tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) C) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.one_one_Code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) A2))))) (forall ((A2 tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) C)) C) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A2) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A2))))) (forall ((C tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat C) (@ (@ tptp.times_times_rat C) B2)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat tptp.one_one_rat) B2)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B2) tptp.one_one_rat))))) (forall ((C tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger C) (@ (@ tptp.times_3573771949741848930nteger C) B2)) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) B2)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B2) tptp.one_one_Code_integer))))) (forall ((C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int C) (@ (@ tptp.times_times_int C) B2)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int tptp.one_one_int) B2)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) tptp.one_one_int))))) (forall ((C tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat C) A2)) C) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A2) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) A2))))) (forall ((C tptp.code_integer) (A2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger C) A2)) C) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.one_one_Code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A2))))) (forall ((C tptp.int) (A2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int C) A2)) C) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A2) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) A2))))) (forall ((C tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat C) (@ (@ tptp.times_times_rat B2) C)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat tptp.one_one_rat) B2)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B2) tptp.one_one_rat))))) (forall ((C tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger C) (@ (@ tptp.times_3573771949741848930nteger B2) C)) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) B2)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B2) tptp.one_one_Code_integer))))) (forall ((C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int C) (@ (@ tptp.times_times_int B2) C)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int tptp.one_one_int) B2)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) tptp.one_one_int))))) (forall ((A2 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) C) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A2) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) A2))))) (forall ((A2 tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) C) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.one_one_Code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A2))))) (forall ((A2 tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C)) C) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A2) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) A2))))) (forall ((X tptp.code_integer) (A2 tptp.code_integer) (Y tptp.code_integer) (U tptp.code_integer) (V2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_le3102999989581377725nteger X) A2) (=> (@ (@ tptp.ord_le3102999989581377725nteger Y) A2) (=> (@ _let_1 U) (=> (@ _let_1 V2) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger U) V2) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger U) X)) (@ (@ tptp.times_3573771949741848930nteger V2) Y))) A2)))))))) (forall ((X tptp.rat) (A2 tptp.rat) (Y tptp.rat) (U tptp.rat) (V2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat X) A2) (=> (@ (@ tptp.ord_less_eq_rat Y) A2) (=> (@ _let_1 U) (=> (@ _let_1 V2) (=> (= (@ (@ tptp.plus_plus_rat U) V2) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat U) X)) (@ (@ tptp.times_times_rat V2) Y))) A2)))))))) (forall ((X tptp.int) (A2 tptp.int) (Y tptp.int) (U tptp.int) (V2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int X) A2) (=> (@ (@ tptp.ord_less_eq_int Y) A2) (=> (@ _let_1 U) (=> (@ _let_1 V2) (=> (= (@ (@ tptp.plus_plus_int U) V2) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X)) (@ (@ tptp.times_times_int V2) Y))) A2)))))))) (forall ((K3 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (=> (@ (@ tptp.ord_less_eq_nat K3) M2) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat K3) (@ tptp.suc tptp.zero_zero_nat))) M2)))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= N (@ tptp.suc (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))) (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M2)) N) (@ (@ tptp.minus_minus_nat M2) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))) (forall ((X tptp.rat) (A2 tptp.rat) (Y tptp.rat) (U tptp.rat) (V2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat X) A2) (=> (@ (@ tptp.ord_less_rat Y) A2) (=> (@ _let_1 U) (=> (@ _let_1 V2) (=> (= (@ (@ tptp.plus_plus_rat U) V2) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat U) X)) (@ (@ tptp.times_times_rat V2) Y))) A2)))))))) (forall ((X tptp.code_integer) (A2 tptp.code_integer) (Y tptp.code_integer) (U tptp.code_integer) (V2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X) A2) (=> (@ (@ tptp.ord_le6747313008572928689nteger Y) A2) (=> (@ _let_1 U) (=> (@ _let_1 V2) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger U) V2) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger U) X)) (@ (@ tptp.times_3573771949741848930nteger V2) Y))) A2)))))))) (forall ((X tptp.int) (A2 tptp.int) (Y tptp.int) (U tptp.int) (V2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int X) A2) (=> (@ (@ tptp.ord_less_int Y) A2) (=> (@ _let_1 U) (=> (@ _let_1 V2) (=> (= (@ (@ tptp.plus_plus_int U) V2) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X)) (@ (@ tptp.times_times_int V2) Y))) A2)))))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (forall ((Z4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z4) (=> (@ (@ tptp.ord_less_rat Z4) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z4) X)) Y)))) (@ (@ tptp.ord_less_eq_rat X) Y))) (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y))) (or (not (= X tptp.zero_zero_rat)) (not (= Y tptp.zero_zero_rat))))) (forall ((X tptp.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))))) (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) (or (not (= X tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int))))) (forall ((X tptp.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)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y))) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))) (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat Y) Z)) (@ (@ tptp.ord_less_eq_rat X) Y)))) (forall ((Z tptp.code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) Z) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger X) Z)) (@ (@ tptp.times_3573771949741848930nteger Y) Z)) (@ (@ tptp.ord_le3102999989581377725nteger X) Y)))) (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X) Z)) (@ (@ tptp.times_times_int Y) Z)) (@ (@ tptp.ord_less_eq_int X) Y)))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat Z))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_rat X) Y))))) (forall ((Z tptp.code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger Z))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) Z) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_le3102999989581377725nteger X) Y))))) (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.times_times_int Z))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_int X) Y))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (forall ((E2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.plus_plus_rat Y) E2)))) (@ (@ tptp.ord_less_eq_rat X) Y))) (forall ((Q6 tptp.code_integer) (R2 tptp.code_integer)) (= (@ tptp.unique5706413561485394159nteger (@ (@ tptp.produc1086072967326762835nteger Q6) R2)) (= R2 tptp.zero_z3403309356797280102nteger))) (forall ((Q6 tptp.nat) (R2 tptp.nat)) (= (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.product_Pair_nat_nat Q6) R2)) (= R2 tptp.zero_zero_nat))) (forall ((Q6 tptp.int) (R2 tptp.int)) (= (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.product_Pair_int_int Q6) R2)) (= R2 tptp.zero_zero_int))) (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)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y)) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))) (forall ((X tptp.int) (Y tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat Y) Z)) (@ (@ tptp.ord_less_rat X) Y)))) (forall ((Z tptp.code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) Z) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger X) Z)) (@ (@ tptp.times_3573771949741848930nteger Y) Z)) (@ (@ tptp.ord_le6747313008572928689nteger X) Y)))) (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int X) Z)) (@ (@ tptp.times_times_int Y) Z)) (@ (@ tptp.ord_less_int X) Y)))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (R2 tptp.set_Pr4329608150637261639at_nat) (P (-> tptp.set_Pr1261947904930325089at_nat Bool))) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat A2) B2)) (@ tptp.transi2703068831062848130at_nat R2)) (=> (forall ((Y2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat Y2) B2)) R2) (@ P Y2))) (=> (forall ((Y2 tptp.set_Pr1261947904930325089at_nat) (Z4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat Y2) Z4)) R2) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat Z4) B2)) (@ tptp.transi2703068831062848130at_nat R2)) (=> (@ P Z4) (@ P Y2))))) (@ P A2))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B2)) (@ tptp.transi6264000038957366511cl_nat R2)) (=> (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y2) B2)) R2) (@ P Y2))) (=> (forall ((Y2 tptp.nat) (Z4 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y2) Z4)) R2) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Z4) B2)) (@ tptp.transi6264000038957366511cl_nat R2)) (=> (@ P Z4) (@ P Y2))))) (@ P A2))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (R2 tptp.set_Pr4329608150637261639at_nat) (P (-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool))) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Y)) (@ tptp.transi2703068831062848130at_nat R2)) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat) (Y2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X3) Y2)) R2) (@ (@ P X3) Y2))) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat) (Y2 tptp.set_Pr1261947904930325089at_nat) (Z4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ P X3))) (let ((_let_2 (@ tptp.transi2703068831062848130at_nat R2))) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X3) Y2)) _let_2) (=> (@ _let_1 Y2) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat Y2) Z4)) _let_2) (=> (@ (@ P Y2) Z4) (@ _let_1 Z4)))))))) (@ (@ P X) Y))))) (forall ((X tptp.nat) (Y tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ tptp.transi6264000038957366511cl_nat R2)) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) Y2)) R2) (@ (@ P X3) Y2))) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat) (Z4 tptp.nat)) (let ((_let_1 (@ P X3))) (let ((_let_2 (@ tptp.transi6264000038957366511cl_nat R2))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) Y2)) _let_2) (=> (@ _let_1 Y2) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y2) Z4)) _let_2) (=> (@ (@ P Y2) Z4) (@ _let_1 Z4)))))))) (@ (@ P X) Y))))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (R2 tptp.set_Pr4329608150637261639at_nat) (C tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.transi2703068831062848130at_nat R2))) (let ((_let_2 (@ tptp.produc2922128104949294807at_nat A2))) (=> (@ (@ tptp.member8757157785044589968at_nat (@ _let_2 B2)) R2) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat B2) C)) _let_1) (@ (@ tptp.member8757157785044589968at_nat (@ _let_2 C)) _let_1)))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.transi6264000038957366511cl_nat R2))) (let ((_let_2 (@ tptp.product_Pair_nat_nat A2))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ _let_2 B2)) R2) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B2) C)) _let_1) (@ (@ tptp.member8440522571783428010at_nat (@ _let_2 C)) _let_1)))))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (R2 tptp.set_Pr4329608150637261639at_nat) (C tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.transi2703068831062848130at_nat R2))) (let ((_let_2 (@ tptp.produc2922128104949294807at_nat A2))) (=> (@ (@ tptp.member8757157785044589968at_nat (@ _let_2 B2)) _let_1) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat B2) C)) R2) (@ (@ tptp.member8757157785044589968at_nat (@ _let_2 C)) _let_1)))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.transi6264000038957366511cl_nat R2))) (let ((_let_2 (@ tptp.product_Pair_nat_nat A2))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ _let_2 B2)) _let_1) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B2) C)) R2) (@ (@ tptp.member8440522571783428010at_nat (@ _let_2 C)) _let_1)))))) (forall ((R2 tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat)) (not (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X3) X3)) (@ tptp.transi2703068831062848130at_nat R2)))) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Y)) R2) (not (= X Y))))) (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))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat) (R2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Z)))) (=> (@ _let_1 (@ tptp.transi2703068831062848130at_nat R2)) (=> (not (@ _let_1 R2)) (not (forall ((Y2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Y2)) R2) (not (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat Y2) Z)) (@ tptp.transi2703068831062848130at_nat R2)))))))))) (forall ((X tptp.nat) (Z tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Z)))) (=> (@ _let_1 (@ tptp.transi6264000038957366511cl_nat R2)) (=> (not (@ _let_1 R2)) (not (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y2)) R2) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y2) Z)) (@ tptp.transi6264000038957366511cl_nat R2)))))))))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (R tptp.set_Pr4329608150637261639at_nat) (C tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.produc2922128104949294807at_nat A2))) (=> (@ (@ tptp.member8757157785044589968at_nat (@ _let_1 B2)) R) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat B2) C)) R) (@ (@ tptp.member8757157785044589968at_nat (@ _let_1 C)) (@ tptp.transi2703068831062848130at_nat R)))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (R tptp.set_Pr1261947904930325089at_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.product_Pair_nat_nat A2))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 B2)) R) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B2) C)) R) (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 C)) (@ tptp.transi6264000038957366511cl_nat R)))))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (R2 tptp.set_Pr4329608150637261639at_nat) (P (-> tptp.set_Pr1261947904930325089at_nat Bool))) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat A2) B2)) (@ tptp.transi2703068831062848130at_nat R2)) (=> (forall ((Y2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat A2) Y2)) R2) (@ P Y2))) (=> (forall ((Y2 tptp.set_Pr1261947904930325089at_nat) (Z4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat A2) Y2)) (@ tptp.transi2703068831062848130at_nat R2)) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat Y2) Z4)) R2) (=> (@ P Y2) (@ P Z4))))) (@ P B2))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B2)) (@ tptp.transi6264000038957366511cl_nat R2)) (=> (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) Y2)) R2) (@ P Y2))) (=> (forall ((Y2 tptp.nat) (Z4 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) Y2)) (@ tptp.transi6264000038957366511cl_nat R2)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y2) Z4)) R2) (=> (@ P Y2) (@ P Z4))))) (@ P B2))))) (forall ((Ax (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (Ay tptp.produc8923325533196201883nteger) (Bx (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (By tptp.produc8923325533196201883nteger) (R2 tptp.set_Pr1722956316086891245nteger) (P (-> (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger Bool))) (=> (@ (@ tptp.member2446009503569356342nteger (@ (@ tptp.produc7954516348491987909nteger (@ (@ tptp.produc8603105652947943368nteger Ax) Ay)) (@ (@ tptp.produc8603105652947943368nteger Bx) By))) (@ tptp.transi6228740973808232501nteger R2)) (=> (forall ((A4 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B4 tptp.produc8923325533196201883nteger)) (=> (@ (@ tptp.member2446009503569356342nteger (@ (@ tptp.produc7954516348491987909nteger (@ (@ tptp.produc8603105652947943368nteger Ax) Ay)) (@ (@ tptp.produc8603105652947943368nteger A4) B4))) R2) (@ (@ P A4) B4))) (=> (forall ((A4 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B4 tptp.produc8923325533196201883nteger) (Aa (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (Ba tptp.produc8923325533196201883nteger)) (let ((_let_1 (@ (@ tptp.produc8603105652947943368nteger A4) B4))) (=> (@ (@ tptp.member2446009503569356342nteger (@ (@ tptp.produc7954516348491987909nteger (@ (@ tptp.produc8603105652947943368nteger Ax) Ay)) _let_1)) (@ tptp.transi6228740973808232501nteger R2)) (=> (@ (@ tptp.member2446009503569356342nteger (@ (@ tptp.produc7954516348491987909nteger _let_1) (@ (@ tptp.produc8603105652947943368nteger Aa) Ba))) R2) (=> (@ (@ P A4) B4) (@ (@ P Aa) Ba)))))) (@ (@ P Bx) By))))) (forall ((Ax (-> tptp.produc3658429121746597890et_nat Bool)) (Ay tptp.produc3658429121746597890et_nat) (Bx (-> tptp.produc3658429121746597890et_nat Bool)) (By tptp.produc3658429121746597890et_nat) (R2 tptp.set_Pr7928877670098842301et_nat) (P (-> (-> 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 ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.member4763271486408492550et_nat (@ (@ tptp.produc8599840265553166229et_nat (@ (@ tptp.produc5001842942810119800et_nat Ax) Ay)) (@ (@ tptp.produc5001842942810119800et_nat A4) B4))) R2) (@ (@ P A4) B4))) (=> (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.produc3658429121746597890et_nat) (Aa (-> tptp.produc3658429121746597890et_nat Bool)) (Ba tptp.produc3658429121746597890et_nat)) (let ((_let_1 (@ (@ tptp.produc5001842942810119800et_nat A4) B4))) (=> (@ (@ 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 Aa) Ba))) R2) (=> (@ (@ P A4) B4) (@ (@ P Aa) Ba)))))) (@ (@ P Bx) By))))) (forall ((Ax (-> tptp.produc3658429121746597890et_nat Bool)) (Ay tptp.produc3925858234332021118et_nat) (Bx (-> tptp.produc3658429121746597890et_nat Bool)) (By tptp.produc3925858234332021118et_nat) (R2 tptp.set_Pr3444600963470892981et_nat) (P (-> (-> 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 ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.produc3925858234332021118et_nat)) (=> (@ (@ tptp.member6341495586645257982et_nat (@ (@ tptp.produc1940133919992309389et_nat (@ (@ tptp.produc2245416461498447860et_nat Ax) Ay)) (@ (@ tptp.produc2245416461498447860et_nat A4) B4))) R2) (@ (@ P A4) B4))) (=> (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.produc3925858234332021118et_nat) (Aa (-> tptp.produc3658429121746597890et_nat Bool)) (Ba tptp.produc3925858234332021118et_nat)) (let ((_let_1 (@ (@ tptp.produc2245416461498447860et_nat A4) B4))) (=> (@ (@ 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 Aa) Ba))) R2) (=> (@ (@ P A4) B4) (@ (@ P Aa) Ba)))))) (@ (@ P Bx) By))))) (forall ((Ax (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Ay tptp.product_prod_int_int) (Bx (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (By tptp.product_prod_int_int) (R2 tptp.set_Pr4708930517165415495nt_int) (P (-> (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.member6582457606847315088nt_int (@ (@ tptp.produc7601053194514725023nt_int (@ (@ tptp.produc5700946648718959541nt_int Ax) Ay)) (@ (@ tptp.produc5700946648718959541nt_int Bx) By))) (@ tptp.transi7434818091516421410nt_int R2)) (=> (forall ((A4 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B4 tptp.product_prod_int_int)) (=> (@ (@ tptp.member6582457606847315088nt_int (@ (@ tptp.produc7601053194514725023nt_int (@ (@ tptp.produc5700946648718959541nt_int Ax) Ay)) (@ (@ tptp.produc5700946648718959541nt_int A4) B4))) R2) (@ (@ P A4) B4))) (=> (forall ((A4 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B4 tptp.product_prod_int_int) (Aa (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Ba tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.produc5700946648718959541nt_int A4) B4))) (=> (@ (@ tptp.member6582457606847315088nt_int (@ (@ tptp.produc7601053194514725023nt_int (@ (@ tptp.produc5700946648718959541nt_int Ax) Ay)) _let_1)) (@ tptp.transi7434818091516421410nt_int R2)) (=> (@ (@ tptp.member6582457606847315088nt_int (@ (@ tptp.produc7601053194514725023nt_int _let_1) (@ (@ tptp.produc5700946648718959541nt_int Aa) Ba))) R2) (=> (@ (@ P A4) B4) (@ (@ P Aa) Ba)))))) (@ (@ P Bx) By))))) (forall ((Ax (-> tptp.int tptp.option6357759511663192854e_term)) (Ay tptp.product_prod_int_int) (Bx (-> tptp.int tptp.option6357759511663192854e_term)) (By tptp.product_prod_int_int) (R2 tptp.set_Pr8634505666381077339nt_int) (P (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.member4085533954029916580nt_int (@ (@ tptp.produc8406175334058502835nt_int (@ (@ tptp.produc4305682042979456191nt_int Ax) Ay)) (@ (@ tptp.produc4305682042979456191nt_int Bx) By))) (@ tptp.transi4533545184864474924nt_int R2)) (=> (forall ((A4 (-> tptp.int tptp.option6357759511663192854e_term)) (B4 tptp.product_prod_int_int)) (=> (@ (@ tptp.member4085533954029916580nt_int (@ (@ tptp.produc8406175334058502835nt_int (@ (@ tptp.produc4305682042979456191nt_int Ax) Ay)) (@ (@ tptp.produc4305682042979456191nt_int A4) B4))) R2) (@ (@ P A4) B4))) (=> (forall ((A4 (-> tptp.int tptp.option6357759511663192854e_term)) (B4 tptp.product_prod_int_int) (Aa (-> tptp.int tptp.option6357759511663192854e_term)) (Ba tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.produc4305682042979456191nt_int A4) B4))) (=> (@ (@ tptp.member4085533954029916580nt_int (@ (@ tptp.produc8406175334058502835nt_int (@ (@ tptp.produc4305682042979456191nt_int Ax) Ay)) _let_1)) (@ tptp.transi4533545184864474924nt_int R2)) (=> (@ (@ tptp.member4085533954029916580nt_int (@ (@ tptp.produc8406175334058502835nt_int _let_1) (@ (@ tptp.produc4305682042979456191nt_int Aa) Ba))) R2) (=> (@ (@ P A4) B4) (@ (@ P Aa) Ba)))))) (@ (@ P Bx) By))))) (forall ((A1 tptp.set_Pr1261947904930325089at_nat) (A22 tptp.set_Pr1261947904930325089at_nat) (R2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat A1) A22)))) (=> (@ _let_1 (@ tptp.transi2703068831062848130at_nat R2)) (=> (not (@ _let_1 R2)) (not (forall ((B4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat A1) B4)) (@ tptp.transi2703068831062848130at_nat R2)) (not (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat B4) A22)) R2))))))))) (forall ((A1 tptp.nat) (A22 tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A1) A22)))) (=> (@ _let_1 (@ tptp.transi6264000038957366511cl_nat R2)) (=> (not (@ _let_1 R2)) (not (forall ((B4 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A1) B4)) (@ tptp.transi6264000038957366511cl_nat R2)) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B4) A22)) R2))))))))) (forall ((A1 tptp.set_Pr1261947904930325089at_nat) (A22 tptp.set_Pr1261947904930325089at_nat) (R2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat A1) A22)) (@ tptp.transi2703068831062848130at_nat R2)) (or (exists ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (and (= A1 A3) (= A22 B3) (@ (@ tptp.member8757157785044589968at_nat (@ (@ 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tptp.transi2703068831062848130at_nat R2)) (=> (not (@ _let_1 R2)) (not (forall ((C4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat A2) C4)) (@ tptp.transi2703068831062848130at_nat R2)) (not (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat C4) B2)) R2))))))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B2)))) (=> (@ _let_1 (@ tptp.transi6264000038957366511cl_nat R2)) (=> (not (@ _let_1 R2)) (not (forall ((C4 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) C4)) (@ tptp.transi6264000038957366511cl_nat R2)) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat C4) B2)) R2))))))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (R2 tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.transi2703068831062848130at_nat R2))) (let ((_let_2 (@ tptp.produc2922128104949294807at_nat X))) (=> (@ (@ tptp.member8757157785044589968at_nat (@ _let_2 Y)) _let_1) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat Y) Z)) _let_1) (@ (@ tptp.member8757157785044589968at_nat (@ _let_2 Z)) _let_1)))))) (forall ((X tptp.nat) (Y tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (Z 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) Z)) _let_1) (@ (@ tptp.member8440522571783428010at_nat (@ _let_2 Z)) _let_1)))))) (forall ((S tptp.multis2468970476368604999at_nat)) (= (not (= S tptp.zero_z1048942125864253310at_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s8510653225128441779at_nat S)))) (@ tptp.biject3388518990857851981at_nat tptp.bot_bo228742789529271731at_nat) (@ tptp.bijective_nat_nat tptp.bot_bo2099793752762293965at_nat) (forall ((X tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.total_7212417256332265445at_nat (@ (@ tptp.insert9200635055090092081at_nat X) tptp.bot_bo3083307316010499117at_nat)) (@ (@ tptp.insert9069300056098147895at_nat (@ (@ tptp.produc2922128104949294807at_nat X) X)) tptp.bot_bo228742789529271731at_nat))) (forall ((X tptp.produc3843707927480180839at_nat)) (@ (@ tptp.total_1513685709984341995at_nat (@ (@ tptp.insert9069300056098147895at_nat X) tptp.bot_bo228742789529271731at_nat)) (@ (@ tptp.insert398606708087465655at_nat (@ (@ tptp.produc2335810615602371415at_nat X) X)) tptp.bot_bo7193250159860175667at_nat))) (forall ((X tptp.product_prod_nat_nat)) (@ (@ tptp.total_3592101749530773125at_nat (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat)) (@ (@ tptp.insert5050368324300391991at_nat (@ (@ tptp.produc6161850002892822231at_nat X) X)) tptp.bot_bo5327735625951526323at_nat))) (forall ((X Bool)) (@ (@ tptp.total_on_o (@ (@ tptp.insert_o2 X) tptp.bot_bot_set_o)) (@ (@ tptp.insert6201435330877294327od_o_o (@ (@ tptp.product_Pair_o_o X) X)) tptp.bot_bo7073875226086086771od_o_o))) (forall ((X tptp.nat)) (@ (@ tptp.total_on_nat (@ (@ tptp.insert_nat2 X) tptp.bot_bot_set_nat)) (@ (@ tptp.insert8211810215607154385at_nat (@ (@ tptp.product_Pair_nat_nat X) X)) tptp.bot_bo2099793752762293965at_nat))) (forall ((X tptp.int)) (@ (@ tptp.total_on_int (@ (@ tptp.insert_int2 X) tptp.bot_bot_set_int)) (@ (@ tptp.insert5033312907999012233nt_int (@ (@ tptp.product_Pair_int_int X) X)) tptp.bot_bo1796632182523588997nt_int))) (forall ((N tptp.nat) (X tptp.int) (Xs tptp.list_int)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.nth_int (@ (@ tptp.cons_int X) Xs)) N) (@ (@ tptp.nth_int Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))) (forall ((N tptp.nat) (X tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X) Xs)) N) (@ (@ tptp.nth_nat Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))) (forall ((N tptp.nat) (X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.nth_Pr1769885009046257848n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) N) (@ (@ tptp.nth_Pr1769885009046257848n_assn Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (R2 tptp.set_Pr4329608150637261639at_nat)) (= (@ tptp.field_3145993188331922222at_nat (@ (@ tptp.insert9069300056098147895at_nat (@ (@ tptp.produc2922128104949294807at_nat A2) B2)) R2)) (@ (@ tptp.sup_su3642409539654194069at_nat (@ (@ tptp.insert9200635055090092081at_nat A2) (@ (@ tptp.insert9200635055090092081at_nat B2) tptp.bot_bo3083307316010499117at_nat))) (@ tptp.field_3145993188331922222at_nat R2)))) (forall ((A2 tptp.produc3843707927480180839at_nat) (B2 tptp.produc3843707927480180839at_nat) (R2 tptp.set_Pr5564308138774400199at_nat)) (= (@ tptp.field_2862844103579723188at_nat (@ (@ tptp.insert398606708087465655at_nat (@ (@ tptp.produc2335810615602371415at_nat A2) B2)) R2)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.insert9069300056098147895at_nat A2) (@ (@ tptp.insert9069300056098147895at_nat B2) tptp.bot_bo228742789529271731at_nat))) (@ tptp.field_2862844103579723188at_nat R2)))) (forall ((A2 tptp.product_prod_nat_nat) (B2 tptp.product_prod_nat_nat) (R2 tptp.set_Pr8693737435421807431at_nat)) (= (@ tptp.field_4706345496283612622at_nat (@ (@ tptp.insert5050368324300391991at_nat (@ (@ tptp.produc6161850002892822231at_nat A2) B2)) R2)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.insert8211810215607154385at_nat A2) (@ (@ tptp.insert8211810215607154385at_nat B2) tptp.bot_bo2099793752762293965at_nat))) (@ tptp.field_4706345496283612622at_nat R2)))) (forall ((A2 Bool) (B2 Bool) (R2 tptp.set_Product_prod_o_o)) (= (@ tptp.field_o (@ (@ tptp.insert6201435330877294327od_o_o (@ (@ tptp.product_Pair_o_o A2) B2)) R2)) (@ (@ tptp.sup_sup_set_o (@ (@ tptp.insert_o2 A2) (@ (@ tptp.insert_o2 B2) tptp.bot_bot_set_o))) (@ tptp.field_o R2)))) (forall ((A2 tptp.nat) (B2 tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.field_nat (@ (@ tptp.insert8211810215607154385at_nat (@ (@ tptp.product_Pair_nat_nat A2) B2)) R2)) (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.insert_nat2 A2) (@ (@ tptp.insert_nat2 B2) tptp.bot_bot_set_nat))) (@ tptp.field_nat R2)))) (forall ((A2 tptp.int) (B2 tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (= (@ tptp.field_int (@ (@ tptp.insert5033312907999012233nt_int (@ (@ tptp.product_Pair_int_int A2) B2)) R2)) (@ (@ tptp.sup_sup_set_int (@ (@ tptp.insert_int2 A2) (@ (@ tptp.insert_int2 B2) tptp.bot_bot_set_int))) (@ tptp.field_int R2)))) (forall ((M2 tptp.nat) (Xs tptp.list_c) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) (@ tptp.size_size_list_c Xs)) (= (@ (@ tptp.nth_Pr2476257089995772766_nat_c (@ (@ tptp.enumerate_c N) Xs)) M2) (@ (@ tptp.product_Pair_nat_c (@ (@ tptp.plus_plus_nat N) M2)) (@ (@ tptp.nth_c Xs) M2))))) (forall ((M2 tptp.nat) (Xs tptp.list_d) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) (@ tptp.size_size_list_d Xs)) (= (@ (@ tptp.nth_Pr2476257094299001567_nat_d (@ (@ tptp.enumerate_d N) Xs)) M2) (@ (@ tptp.product_Pair_nat_d (@ (@ tptp.plus_plus_nat N) M2)) (@ (@ tptp.nth_d Xs) M2))))) (forall ((M2 tptp.nat) (Xs tptp.list_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_Pr7617993195940197384at_nat (@ (@ tptp.enumerate_nat N) Xs)) M2) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat N) M2)) (@ (@ tptp.nth_nat Xs) M2))))) (forall ((M2 tptp.nat) (Xs tptp.list_int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_Pr3440142176431000676at_int (@ (@ tptp.enumerate_int N) Xs)) M2) (@ (@ tptp.product_Pair_nat_int (@ (@ tptp.plus_plus_nat N) M2)) (@ (@ tptp.nth_int Xs) M2))))) (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 ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As))) (=> (= Xb _let_1) (=> (@ (@ tptp.accp_P1862375125659990705et_nat tptp.times_assn_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) _let_1))) (exists ((As13 tptp.set_nat) (As24 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H))) (and (= As (@ (@ 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))))))))))))) (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 ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As))) (=> (= Xb _let_1) (=> (@ (@ tptp.accp_P1862375125659990705et_nat tptp.times_assn_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) _let_1))) (not (exists ((As12 tptp.set_nat) (As23 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H))) (and (= As (@ (@ 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)))))))))))))) (forall ((X21 tptp.int) (X222 tptp.list_int) (Y21 tptp.int) (Y222 tptp.list_int)) (= (= (@ (@ tptp.cons_int X21) X222) (@ (@ tptp.cons_int Y21) Y222)) (and (= X21 Y21) (= X222 Y222)))) (forall ((X21 tptp.nat) (X222 tptp.list_nat) (Y21 tptp.nat) (Y222 tptp.list_nat)) (= (= (@ (@ tptp.cons_nat X21) X222) (@ (@ tptp.cons_nat Y21) Y222)) (and (= X21 Y21) (= X222 Y222)))) (forall ((X21 tptp.produc6575502325842934193n_assn) (X222 tptp.list_P8527749157015355191n_assn) (Y21 tptp.produc6575502325842934193n_assn) (Y222 tptp.list_P8527749157015355191n_assn)) (= (= (@ (@ tptp.cons_P2971678138204555879n_assn X21) X222) (@ (@ tptp.cons_P2971678138204555879n_assn Y21) Y222)) (and (= X21 Y21) (= X222 Y222)))) (forall ((R2 tptp.set_Product_prod_o_o) (S3 tptp.set_Product_prod_o_o)) (= (@ tptp.field_o (@ (@ tptp.sup_su5769328420594410459od_o_o R2) S3)) (@ (@ tptp.sup_sup_set_o (@ tptp.field_o R2)) (@ tptp.field_o S3)))) (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (S3 tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.field_nat (@ (@ tptp.sup_su6327502436637775413at_nat R2) S3)) (@ (@ tptp.sup_sup_set_nat (@ tptp.field_nat R2)) (@ tptp.field_nat S3)))) (forall ((R2 tptp.set_Pr5564308138774400199at_nat) (S3 tptp.set_Pr5564308138774400199at_nat)) (= (@ tptp.field_2862844103579723188at_nat (@ (@ tptp.sup_su6664651903789602459at_nat R2) S3)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ tptp.field_2862844103579723188at_nat R2)) (@ tptp.field_2862844103579723188at_nat S3)))) (forall ((R2 tptp.set_Pr4329608150637261639at_nat) (S3 tptp.set_Pr4329608150637261639at_nat)) (= (@ tptp.field_3145993188331922222at_nat (@ (@ tptp.sup_su5525570899277871387at_nat R2) S3)) (@ (@ tptp.sup_su3642409539654194069at_nat (@ tptp.field_3145993188331922222at_nat R2)) (@ tptp.field_3145993188331922222at_nat S3)))) (forall ((P (-> tptp.int Bool)) (X tptp.int) (Xs tptp.list_int)) (let ((_let_1 (@ tptp.list_ex_int P))) (= (@ _let_1 (@ (@ tptp.cons_int X) Xs)) (or (@ P X) (@ _let_1 Xs))))) (forall ((P (-> tptp.nat Bool)) (X tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ tptp.list_ex_nat P))) (= (@ _let_1 (@ (@ tptp.cons_nat X) Xs)) (or (@ P X) (@ _let_1 Xs))))) (forall ((P (-> tptp.produc6575502325842934193n_assn Bool)) (X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ tptp.list_e1087220904399170805n_assn P))) (= (@ _let_1 (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) (or (@ P X) (@ _let_1 Xs))))) (forall ((N tptp.nat) (Xs tptp.list_c)) (= (@ tptp.size_s385972143775086793_nat_c (@ (@ tptp.enumerate_c N) Xs)) (@ tptp.size_size_list_c Xs))) (forall ((N tptp.nat) (Xs tptp.list_d)) (= (@ tptp.size_s457006183821432778_nat_d (@ (@ tptp.enumerate_d N) Xs)) (@ tptp.size_size_list_d Xs))) (forall ((N tptp.nat) (Xs tptp.list_nat)) (= (@ tptp.size_s5460976970255530739at_nat (@ (@ tptp.enumerate_nat N) Xs)) (@ tptp.size_size_list_nat Xs))) (forall ((N tptp.nat) (Xs tptp.list_int)) (= (@ tptp.size_s2970893825323803983at_int (@ (@ tptp.enumerate_int N) Xs)) (@ tptp.size_size_list_int Xs))) (forall ((X21 tptp.product_prod_nat_nat) (X222 tptp.list_P6011104703257516679at_nat)) (= (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.cons_P6512896166579812791at_nat X21) X222)) (@ (@ tptp.insert8211810215607154385at_nat X21) (@ tptp.set_Pr5648618587558075414at_nat X222)))) (forall ((X21 tptp.produc3843707927480180839at_nat) (X222 tptp.list_P5464809261938338413at_nat)) (= (@ tptp.set_Pr3765526544606949372at_nat (@ (@ tptp.cons_P3940603068885512221at_nat X21) X222)) (@ (@ tptp.insert9069300056098147895at_nat X21) (@ tptp.set_Pr3765526544606949372at_nat X222)))) (forall ((X21 Bool) (X222 tptp.list_o)) (= (@ tptp.set_o2 (@ (@ tptp.cons_o X21) X222)) (@ (@ tptp.insert_o2 X21) (@ tptp.set_o2 X222)))) (forall ((X21 tptp.int) (X222 tptp.list_int)) (= (@ tptp.set_int2 (@ (@ tptp.cons_int X21) X222)) (@ (@ tptp.insert_int2 X21) (@ tptp.set_int2 X222)))) (forall ((X21 tptp.nat) (X222 tptp.list_nat)) (= (@ tptp.set_nat2 (@ (@ tptp.cons_nat X21) X222)) (@ (@ tptp.insert_nat2 X21) (@ tptp.set_nat2 X222)))) (forall ((X21 tptp.produc6575502325842934193n_assn) (X222 tptp.list_P8527749157015355191n_assn)) (= (@ tptp.set_Pr1139785259514867910n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X21) X222)) (@ (@ tptp.insert5290817439147925377n_assn X21) (@ tptp.set_Pr1139785259514867910n_assn X222)))) (forall ((X tptp.int) (Xs tptp.list_int)) (= (@ (@ tptp.nth_int (@ (@ tptp.cons_int X) Xs)) tptp.zero_zero_nat) X)) (forall ((X tptp.nat) (Xs tptp.list_nat)) (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X) Xs)) tptp.zero_zero_nat) X)) (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (= (@ (@ tptp.nth_Pr1769885009046257848n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) tptp.zero_zero_nat) X)) (forall ((X tptp.int) (Xs tptp.list_int) (N tptp.nat)) (= (@ (@ tptp.nth_int (@ (@ tptp.cons_int X) Xs)) (@ tptp.suc N)) (@ (@ tptp.nth_int Xs) N))) (forall ((X tptp.nat) (Xs tptp.list_nat) (N tptp.nat)) (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X) Xs)) (@ tptp.suc N)) (@ (@ tptp.nth_nat Xs) N))) (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn) (N tptp.nat)) (= (@ (@ tptp.nth_Pr1769885009046257848n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) (@ tptp.suc N)) (@ (@ tptp.nth_Pr1769885009046257848n_assn Xs) N))) (forall ((X tptp.assn) (Xs tptp.list_assn) (Y tptp.assn) (Ys tptp.list_assn)) (= (@ (@ tptp.zip_assn_assn (@ (@ tptp.cons_assn X) Xs)) (@ (@ tptp.cons_assn Y) Ys)) (@ (@ tptp.cons_P2971678138204555879n_assn (@ (@ tptp.produc118845697133431529n_assn X) Y)) (@ (@ tptp.zip_assn_assn Xs) Ys)))) (forall ((X tptp.int) (Xs tptp.list_int) (Y tptp.int) (Ys tptp.list_int)) (= (@ (@ tptp.zip_int_int (@ (@ tptp.cons_int X) Xs)) (@ (@ tptp.cons_int Y) Ys)) (@ (@ tptp.cons_P3334398858971670639nt_int (@ (@ tptp.product_Pair_int_int X) Y)) (@ (@ tptp.zip_int_int Xs) Ys)))) (forall ((X tptp.int) (Xs tptp.list_int) (Y tptp.nat) (Ys tptp.list_nat)) (= (@ (@ tptp.zip_int_nat (@ (@ tptp.cons_int X) Xs)) (@ (@ tptp.cons_nat Y) Ys)) (@ (@ tptp.cons_P7512249878480867347nt_nat (@ (@ tptp.product_Pair_int_nat X) Y)) (@ (@ tptp.zip_int_nat Xs) Ys)))) (forall ((X tptp.nat) (Xs tptp.list_nat) (Y tptp.int) (Ys tptp.list_int)) (= (@ (@ tptp.zip_nat_int (@ (@ tptp.cons_nat X) Xs)) (@ (@ tptp.cons_int Y) Ys)) (@ (@ tptp.cons_P2335045147070616083at_int (@ (@ tptp.product_Pair_nat_int X) Y)) (@ (@ tptp.zip_nat_int Xs) Ys)))) (forall ((X tptp.nat) (Xs tptp.list_nat) (Y tptp.nat) (Ys tptp.list_nat)) (= (@ (@ tptp.zip_nat_nat (@ (@ tptp.cons_nat X) Xs)) (@ (@ tptp.cons_nat Y) Ys)) (@ (@ tptp.cons_P6512896166579812791at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ (@ tptp.zip_nat_nat Xs) Ys)))) (forall ((X tptp.int) (Xs tptp.list_int) (Y tptp.produc6575502325842934193n_assn) (Ys tptp.list_P8527749157015355191n_assn)) (= (@ (@ tptp.zip_in7098856637274830732n_assn (@ (@ tptp.cons_int X) Xs)) (@ (@ tptp.cons_P2971678138204555879n_assn Y) Ys)) (@ (@ tptp.cons_P8828502514829229636n_assn (@ (@ tptp.produc3313821056773121708n_assn X) Y)) (@ (@ tptp.zip_in7098856637274830732n_assn Xs) Ys)))) (forall ((X tptp.nat) (Xs tptp.list_nat) (Y tptp.produc6575502325842934193n_assn) (Ys tptp.list_P8527749157015355191n_assn)) (= (@ (@ tptp.zip_na5338819973521719528n_assn (@ (@ tptp.cons_nat X) Xs)) (@ (@ tptp.cons_P2971678138204555879n_assn Y) Ys)) (@ (@ tptp.cons_P7068465851076118432n_assn (@ (@ tptp.produc1553784393020010504n_assn X) Y)) (@ (@ tptp.zip_na5338819973521719528n_assn Xs) Ys)))) (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn) (Y tptp.int) (Ys tptp.list_int)) (= (@ (@ tptp.zip_Pr1015554993053626726sn_int (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) (@ (@ tptp.cons_int Y) Ys)) (@ (@ tptp.cons_P5155970366129889750sn_int (@ (@ tptp.produc6453891449406693510sn_int X) Y)) (@ (@ tptp.zip_Pr1015554993053626726sn_int Xs) Ys)))) (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn) (Y tptp.nat) (Ys tptp.list_nat)) (= (@ (@ tptp.zip_Pr1018045463562677002sn_nat (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) (@ (@ tptp.cons_nat Y) Ys)) (@ (@ tptp.cons_P110449348784310650sn_nat (@ (@ tptp.produc6456381919915743786sn_nat X) Y)) (@ (@ tptp.zip_Pr1018045463562677002sn_nat Xs) Ys)))) (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn) (Y tptp.produc6575502325842934193n_assn) (Ys tptp.list_P8527749157015355191n_assn)) (= (@ (@ tptp.zip_Pr8806919808394484215n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) (@ (@ tptp.cons_P2971678138204555879n_assn Y) Ys)) (@ (@ tptp.cons_P9150528168557782045n_assn (@ (@ tptp.produc6128706242671166167n_assn X) Y)) (@ (@ tptp.zip_Pr8806919808394484215n_assn Xs) Ys)))) (= (@ tptp.field_2862844103579723188at_nat tptp.bot_bo7193250159860175667at_nat) tptp.bot_bo228742789529271731at_nat) (= (@ tptp.field_4706345496283612622at_nat tptp.bot_bo5327735625951526323at_nat) tptp.bot_bo2099793752762293965at_nat) (= (@ tptp.field_o tptp.bot_bo7073875226086086771od_o_o) tptp.bot_bot_set_o) (= (@ tptp.field_int tptp.bot_bo1796632182523588997nt_int) tptp.bot_bot_set_int) _let_105 (= (@ tptp.field_nat tptp.bot_bo2099793752762293965at_nat) tptp.bot_bot_set_nat) (forall ((X tptp.produc3843707927480180839at_nat) (Xs tptp.list_P5464809261938338413at_nat)) (=> (not (@ (@ tptp.member8757157785044589968at_nat X) (@ tptp.set_Pr3765526544606949372at_nat Xs))) (= (@ (@ tptp.insert4149901806602606979at_nat X) Xs) (@ (@ tptp.cons_P3940603068885512221at_nat X) Xs)))) (forall ((X tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (=> (not (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs))) (= (@ (@ tptp.insert8944034826898310173at_nat X) Xs) (@ (@ tptp.cons_P6512896166579812791at_nat X) Xs)))) (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xs tptp.list_P7985473006766602707_nat_o)) (=> (not (@ (@ tptp.member6576561426505652726_nat_o X) (@ tptp.set_Pr400311997697478754_nat_o Xs))) (= (@ (@ tptp.insert8021100735160035049_nat_o X) Xs) (@ (@ tptp.cons_P6219271836124797827_nat_o X) Xs)))) (forall ((X tptp.int) (Xs tptp.list_int)) (=> (not (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs))) (= (@ (@ tptp.insert_int X) Xs) (@ (@ tptp.cons_int X) Xs)))) (forall ((X tptp.nat) (Xs tptp.list_nat)) (=> (not (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs))) (= (@ (@ tptp.insert_nat X) Xs) (@ (@ tptp.cons_nat X) Xs)))) (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (=> (not (@ (@ tptp.member7957490590177025114n_assn X) (@ tptp.set_Pr1139785259514867910n_assn Xs))) (= (@ (@ tptp.insert3246601298802261197n_assn X) Xs) (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Xs tptp.list_s1210847774152347623at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Ys tptp.list_s1210847774152347623at_nat) (R2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.listre8180072825634266816at_nat R2))) (= (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat (@ (@ tptp.cons_s6881495754146722583at_nat X) Xs)) (@ (@ tptp.cons_s6881495754146722583at_nat Y) Ys))) _let_1) (or (and (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Y)) R2) (= Xs Ys)) (and (= X Y) (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat Xs) Ys)) _let_1)))))) (forall ((X tptp.int) (Xs tptp.list_int) (Y tptp.int) (Ys tptp.list_int) (R2 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.listrel1_int R2))) (= (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int (@ (@ tptp.cons_int X) Xs)) (@ (@ tptp.cons_int Y) Ys))) _let_1) (or (and (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) R2) (= Xs Ys)) (and (= X Y) (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Xs) Ys)) _let_1)))))) (forall ((X tptp.nat) (Xs tptp.list_nat) (Y tptp.nat) (Ys tptp.list_nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.listrel1_nat R2))) (= (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat (@ (@ tptp.cons_nat X) Xs)) (@ (@ tptp.cons_nat Y) Ys))) _let_1) (or (and (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) R2) (= Xs Ys)) (and (= X Y) (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Xs) Ys)) _let_1)))))) (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn) (Y tptp.produc6575502325842934193n_assn) (Ys tptp.list_P8527749157015355191n_assn) (R2 tptp.set_Pr8116311503512020807n_assn)) (let ((_let_1 (@ tptp.listre4270255209692100112n_assn R2))) (= (@ (@ tptp.member3994142547374651152n_assn (@ (@ tptp.produc3014731801419794263n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) (@ (@ tptp.cons_P2971678138204555879n_assn Y) Ys))) _let_1) (or (and (@ (@ tptp.member4743710847862083984n_assn (@ (@ tptp.produc6128706242671166167n_assn X) Y)) R2) (= Xs Ys)) (and (= X Y) (@ (@ tptp.member3994142547374651152n_assn (@ (@ tptp.produc3014731801419794263n_assn Xs) Ys)) _let_1)))))) (forall ((N tptp.nat) (X tptp.int) (Xs tptp.list_int)) (= (@ (@ tptp.enumerate_int N) (@ (@ tptp.cons_int X) Xs)) (@ (@ tptp.cons_P2335045147070616083at_int (@ (@ tptp.product_Pair_nat_int N) X)) (@ (@ tptp.enumerate_int (@ tptp.suc N)) Xs)))) (forall ((N tptp.nat) (X tptp.nat) (Xs tptp.list_nat)) (= (@ (@ tptp.enumerate_nat N) (@ (@ tptp.cons_nat X) Xs)) (@ (@ tptp.cons_P6512896166579812791at_nat (@ (@ tptp.product_Pair_nat_nat N) X)) (@ (@ tptp.enumerate_nat (@ tptp.suc N)) Xs)))) (forall ((N tptp.nat) (X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (= (@ (@ tptp.enumer9200277086812776726n_assn N) (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) (@ (@ tptp.cons_P7068465851076118432n_assn (@ (@ tptp.produc1553784393020010504n_assn N) X)) (@ (@ tptp.enumer9200277086812776726n_assn (@ tptp.suc N)) Xs)))) (forall ((X tptp.int) (Xs tptp.list_int)) (not (= (@ (@ tptp.cons_int X) Xs) Xs))) (forall ((X tptp.nat) (Xs tptp.list_nat)) (not (= (@ (@ tptp.cons_nat X) Xs) Xs))) (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (not (= (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs) Xs))) (forall ((N1 tptp.int) (R1 tptp.list_int) (N22 tptp.int) (R22 tptp.list_int)) (=> (= (@ (@ tptp.cons_int N1) R1) (@ (@ tptp.cons_int N22) R22)) (and (= N1 N22) (= R1 R22)))) (forall ((N1 tptp.nat) (R1 tptp.list_nat) (N22 tptp.nat) (R22 tptp.list_nat)) (=> (= (@ (@ tptp.cons_nat N1) R1) (@ (@ tptp.cons_nat N22) R22)) (and (= N1 N22) (= R1 R22)))) (forall ((N1 tptp.produc6575502325842934193n_assn) (R1 tptp.list_P8527749157015355191n_assn) (N22 tptp.produc6575502325842934193n_assn) (R22 tptp.list_P8527749157015355191n_assn)) (=> (= (@ (@ tptp.cons_P2971678138204555879n_assn N1) R1) (@ (@ tptp.cons_P2971678138204555879n_assn N22) R22)) (and (= N1 N22) (= R1 R22)))) (forall ((C2 tptp.multis2468970476368604999at_nat) (B tptp.multis2468970476368604999at_nat) (A tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.plus_p7104986032573967614at_nat A))) (=> (= (@ (@ tptp.minus_4286766774447292334at_nat C2) B) tptp.zero_z1048942125864253310at_nat) (= (@ (@ tptp.minus_4286766774447292334at_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.minus_4286766774447292334at_nat B) C2)))))) (forall ((Xs tptp.list_int) (Ys tptp.list_int) (Xy tptp.product_prod_int_int) (Xys tptp.list_P5707943133018811711nt_int)) (=> (= (@ (@ tptp.zip_int_int Xs) Ys) (@ (@ tptp.cons_P3334398858971670639nt_int Xy) Xys)) (not (forall ((X3 tptp.int) (Xs5 tptp.list_int)) (=> (= Xs (@ (@ tptp.cons_int X3) Xs5)) (forall ((Y2 tptp.int) (Ys4 tptp.list_int)) (=> (= Ys (@ (@ tptp.cons_int Y2) Ys4)) (=> (= Xy (@ (@ tptp.product_Pair_int_int X3) Y2)) (not (= Xys (@ (@ tptp.zip_int_int Xs5) Ys4))))))))))) (forall ((Xs tptp.list_int) (Ys tptp.list_nat) (Xy tptp.product_prod_int_nat) (Xys tptp.list_P8198026277950538467nt_nat)) (=> (= (@ (@ tptp.zip_int_nat Xs) Ys) (@ (@ tptp.cons_P7512249878480867347nt_nat Xy) Xys)) (not (forall ((X3 tptp.int) (Xs5 tptp.list_int)) (=> (= Xs (@ (@ tptp.cons_int X3) Xs5)) (forall ((Y2 tptp.nat) (Ys4 tptp.list_nat)) (=> (= Ys (@ (@ tptp.cons_nat Y2) Ys4)) (=> (= Xy (@ (@ tptp.product_Pair_int_nat X3) Y2)) (not (= Xys (@ (@ tptp.zip_int_nat Xs5) Ys4))))))))))) (forall ((Xs tptp.list_nat) (Ys tptp.list_int) (Xy tptp.product_prod_nat_int) (Xys tptp.list_P3521021558325789923at_int)) (=> (= (@ (@ tptp.zip_nat_int Xs) Ys) (@ (@ tptp.cons_P2335045147070616083at_int Xy) Xys)) (not (forall ((X3 tptp.nat) (Xs5 tptp.list_nat)) (=> (= Xs (@ (@ tptp.cons_nat X3) Xs5)) (forall ((Y2 tptp.int) (Ys4 tptp.list_int)) (=> (= Ys (@ (@ tptp.cons_int Y2) Ys4)) (=> (= Xy (@ (@ tptp.product_Pair_nat_int X3) Y2)) (not (= Xys (@ (@ tptp.zip_nat_int Xs5) Ys4))))))))))) (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (Xy tptp.product_prod_nat_nat) (Xys tptp.list_P6011104703257516679at_nat)) (=> (= (@ (@ tptp.zip_nat_nat Xs) Ys) (@ (@ tptp.cons_P6512896166579812791at_nat Xy) Xys)) (not (forall ((X3 tptp.nat) (Xs5 tptp.list_nat)) (=> (= Xs (@ (@ tptp.cons_nat X3) Xs5)) (forall ((Y2 tptp.nat) (Ys4 tptp.list_nat)) (=> (= Ys (@ (@ tptp.cons_nat Y2) Ys4)) (=> (= Xy (@ (@ tptp.product_Pair_nat_nat X3) Y2)) (not (= Xys (@ (@ tptp.zip_nat_nat Xs5) Ys4))))))))))) (forall ((Xs tptp.list_assn) (Ys tptp.list_assn) (Xy tptp.produc6575502325842934193n_assn) (Xys tptp.list_P8527749157015355191n_assn)) (=> (= (@ (@ tptp.zip_assn_assn Xs) Ys) (@ (@ tptp.cons_P2971678138204555879n_assn Xy) Xys)) (not (forall ((X3 tptp.assn) (Xs5 tptp.list_assn)) (=> (= Xs (@ (@ tptp.cons_assn X3) Xs5)) (forall ((Y2 tptp.assn) (Ys4 tptp.list_assn)) (=> (= Ys (@ (@ tptp.cons_assn Y2) Ys4)) (=> (= Xy (@ (@ tptp.produc118845697133431529n_assn X3) Y2)) (not (= Xys (@ (@ tptp.zip_assn_assn Xs5) Ys4))))))))))) (forall ((Xs tptp.list_int) (Ys tptp.list_P8527749157015355191n_assn) (Xy tptp.produc3167338625816234618n_assn) (Xys tptp.list_P1495281457390866698n_assn)) (=> (= (@ (@ tptp.zip_in7098856637274830732n_assn Xs) Ys) (@ (@ tptp.cons_P8828502514829229636n_assn Xy) Xys)) (not (forall ((X3 tptp.int) (Xs5 tptp.list_int)) (=> (= Xs (@ (@ tptp.cons_int X3) Xs5)) (forall ((Y2 tptp.produc6575502325842934193n_assn) (Ys4 tptp.list_P8527749157015355191n_assn)) (=> (= Ys (@ (@ tptp.cons_P2971678138204555879n_assn Y2) Ys4)) (=> (= Xy (@ (@ tptp.produc3313821056773121708n_assn X3) Y2)) (not (= Xys (@ (@ tptp.zip_in7098856637274830732n_assn Xs5) Ys4))))))))))) (forall ((Xs tptp.list_nat) (Ys tptp.list_P8527749157015355191n_assn) (Xy tptp.produc1407301962063123414n_assn) (Xys tptp.list_P7711101519850957926n_assn)) (=> (= (@ (@ tptp.zip_na5338819973521719528n_assn Xs) Ys) (@ (@ tptp.cons_P7068465851076118432n_assn Xy) Xys)) (not (forall ((X3 tptp.nat) (Xs5 tptp.list_nat)) (=> (= Xs (@ (@ tptp.cons_nat X3) Xs5)) (forall ((Y2 tptp.produc6575502325842934193n_assn) (Ys4 tptp.list_P8527749157015355191n_assn)) (=> (= Ys (@ (@ tptp.cons_P2971678138204555879n_assn Y2) Ys4)) (=> (= Xy (@ (@ tptp.produc1553784393020010504n_assn X3) Y2)) (not (= Xys (@ (@ tptp.zip_na5338819973521719528n_assn Xs5) Ys4))))))))))) (forall ((Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_int) (Xy tptp.produc8718178513971670540sn_int) (Xys tptp.list_P421884338359569308sn_int)) (=> (= (@ (@ tptp.zip_Pr1015554993053626726sn_int Xs) Ys) (@ (@ 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Y2)) (not (= Xys (@ (@ tptp.zip_Pr1018045463562677002sn_nat Xs5) Ys4))))))))))) (forall ((Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_P8527749157015355191n_assn) (Xy tptp.produc9053633027152450663n_assn) (Xys tptp.list_P28140577958321773n_assn)) (=> (= (@ (@ tptp.zip_Pr8806919808394484215n_assn Xs) Ys) (@ (@ tptp.cons_P9150528168557782045n_assn Xy) Xys)) (not (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs5 tptp.list_P8527749157015355191n_assn)) (=> (= Xs (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs5)) (forall ((Y2 tptp.produc6575502325842934193n_assn) (Ys4 tptp.list_P8527749157015355191n_assn)) (=> (= Ys (@ (@ tptp.cons_P2971678138204555879n_assn Y2) Ys4)) (=> (= Xy (@ (@ tptp.produc6128706242671166167n_assn X3) Y2)) (not (= Xys (@ (@ tptp.zip_Pr8806919808394484215n_assn Xs5) Ys4))))))))))) (forall ((I tptp.produc3843707927480180839at_nat) (J tptp.produc3843707927480180839at_nat) (R tptp.set_Pr5564308138774400199at_nat)) (=> (@ (@ 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tptp.field_81821745747897882_nat_o R)))) (forall ((I tptp.set_Pr1261947904930325089at_nat) (J tptp.set_Pr1261947904930325089at_nat) (R tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat I) J)) R) (@ (@ tptp.member2643936169264416010at_nat I) (@ tptp.field_3145993188331922222at_nat R)))) (forall ((I tptp.nat) (J tptp.nat) (R tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat I) J)) R) (@ (@ tptp.member_nat I) (@ tptp.field_nat R)))) (forall ((I Bool) (J Bool) (R tptp.set_Product_prod_o_o)) (=> (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o I) J)) R) (@ (@ tptp.member_o I) (@ tptp.field_o R)))) (forall ((I tptp.produc3843707927480180839at_nat) (J tptp.produc3843707927480180839at_nat) (R tptp.set_Pr5564308138774400199at_nat)) (=> (@ (@ tptp.member6009668390874684176at_nat (@ (@ tptp.produc2335810615602371415at_nat I) J)) R) (@ (@ tptp.member8757157785044589968at_nat J) (@ tptp.field_2862844103579723188at_nat R)))) (forall ((I tptp.product_prod_nat_nat) (J tptp.product_prod_nat_nat) (R tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat I) J)) R) (@ (@ tptp.member8440522571783428010at_nat J) (@ tptp.field_4706345496283612622at_nat R)))) (forall ((I tptp.int) (J tptp.int) (R tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int I) J)) R) (@ (@ tptp.member_int J) (@ tptp.field_int R)))) (forall ((I (-> tptp.produc3658429121746597890et_nat Bool)) (J (-> tptp.produc3658429121746597890et_nat Bool)) (R tptp.set_Pr2161125870931222855_nat_o)) (=> (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o I) J)) R) (@ (@ tptp.member6576561426505652726_nat_o J) (@ tptp.field_81821745747897882_nat_o R)))) (forall ((I 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tptp.cons_P3940603068885512221at_nat X) Xs))) (or (= Y X) (@ _let_1 (@ tptp.set_Pr3765526544606949372at_nat Xs)))))) (forall ((Y tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat Y))) (=> (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.cons_P6512896166579812791at_nat X) Xs))) (or (= Y X) (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat Xs)))))) (forall ((Y (-> tptp.produc3658429121746597890et_nat Bool)) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Xs tptp.list_P7985473006766602707_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o Y))) (=> (@ _let_1 (@ tptp.set_Pr400311997697478754_nat_o (@ (@ tptp.cons_P6219271836124797827_nat_o X) Xs))) (or (= Y X) (@ _let_1 (@ tptp.set_Pr400311997697478754_nat_o Xs)))))) (forall ((Y tptp.int) (X tptp.int) (Xs tptp.list_int)) (let ((_let_1 (@ tptp.member_int Y))) (=> (@ _let_1 (@ tptp.set_int2 (@ (@ tptp.cons_int X) 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tptp.set_nat2 Z22))))))))) (forall ((E tptp.produc6575502325842934193n_assn) (A2 tptp.list_P8527749157015355191n_assn)) (=> (@ (@ tptp.member7957490590177025114n_assn E) (@ tptp.set_Pr1139785259514867910n_assn A2)) (=> (forall ((Z22 tptp.list_P8527749157015355191n_assn)) (not (= A2 (@ (@ tptp.cons_P2971678138204555879n_assn E) Z22)))) (not (forall ((Z1 tptp.produc6575502325842934193n_assn) (Z22 tptp.list_P8527749157015355191n_assn)) (=> (= A2 (@ (@ tptp.cons_P2971678138204555879n_assn Z1) Z22)) (not (@ (@ tptp.member7957490590177025114n_assn E) (@ tptp.set_Pr1139785259514867910n_assn Z22))))))))) (forall ((X21 tptp.produc3843707927480180839at_nat) (X222 tptp.list_P5464809261938338413at_nat)) (@ (@ tptp.member8757157785044589968at_nat X21) (@ tptp.set_Pr3765526544606949372at_nat (@ (@ tptp.cons_P3940603068885512221at_nat X21) X222)))) (forall ((X21 tptp.product_prod_nat_nat) (X222 tptp.list_P6011104703257516679at_nat)) (@ (@ tptp.member8440522571783428010at_nat X21) (@ 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tptp.member8757157785044589968at_nat Y))) (=> (@ _let_1 (@ tptp.set_Pr3765526544606949372at_nat X222)) (@ _let_1 (@ tptp.set_Pr3765526544606949372at_nat (@ (@ tptp.cons_P3940603068885512221at_nat X21) X222)))))) (forall ((Y tptp.product_prod_nat_nat) (X222 tptp.list_P6011104703257516679at_nat) (X21 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat Y))) (=> (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat X222)) (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.cons_P6512896166579812791at_nat X21) X222)))))) (forall ((Y (-> tptp.produc3658429121746597890et_nat Bool)) (X222 tptp.list_P7985473006766602707_nat_o) (X21 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o Y))) (=> (@ _let_1 (@ tptp.set_Pr400311997697478754_nat_o X222)) (@ _let_1 (@ tptp.set_Pr400311997697478754_nat_o (@ (@ tptp.cons_P6219271836124797827_nat_o X21) X222)))))) (forall ((Y tptp.int) (X222 tptp.list_int) (X21 tptp.int)) (let ((_let_1 (@ tptp.member_int Y))) (=> (@ _let_1 (@ tptp.set_int2 X222)) (@ _let_1 (@ tptp.set_int2 (@ (@ tptp.cons_int X21) X222)))))) (forall ((Y tptp.nat) (X222 tptp.list_nat) (X21 tptp.nat)) (let ((_let_1 (@ tptp.member_nat Y))) (=> (@ _let_1 (@ tptp.set_nat2 X222)) (@ _let_1 (@ tptp.set_nat2 (@ (@ tptp.cons_nat X21) X222)))))) (forall ((Y tptp.produc6575502325842934193n_assn) (X222 tptp.list_P8527749157015355191n_assn) (X21 tptp.produc6575502325842934193n_assn)) (let ((_let_1 (@ tptp.member7957490590177025114n_assn Y))) (=> (@ _let_1 (@ tptp.set_Pr1139785259514867910n_assn X222)) (@ _let_1 (@ tptp.set_Pr1139785259514867910n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X21) X222)))))) (forall ((A2 tptp.int) (B2 tptp.int) (Xs tptp.list_int)) (let ((_let_1 (@ (@ tptp.cons_int B2) Xs))) (let ((_let_2 (@ tptp.cons_int A2))) (= (@ tptp.distinct_int (@ _let_2 _let_1)) (and (not (= A2 B2)) (@ tptp.distinct_int (@ _let_2 Xs)) (@ tptp.distinct_int _let_1)))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat B2) Xs))) (let ((_let_2 (@ tptp.cons_nat A2))) (= (@ tptp.distinct_nat (@ _let_2 _let_1)) (and (not (= A2 B2)) (@ tptp.distinct_nat (@ _let_2 Xs)) (@ tptp.distinct_nat _let_1)))))) (forall ((A2 tptp.produc6575502325842934193n_assn) (B2 tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ (@ tptp.cons_P2971678138204555879n_assn B2) Xs))) (let ((_let_2 (@ tptp.cons_P2971678138204555879n_assn A2))) (= (@ tptp.distin4809818325527169450n_assn (@ _let_2 _let_1)) (and (not (= A2 B2)) (@ tptp.distin4809818325527169450n_assn (@ _let_2 Xs)) (@ tptp.distin4809818325527169450n_assn _let_1)))))) (forall ((X tptp.int) (Y tptp.int) (Xs tptp.list_int)) (let ((_let_1 (@ tptp.remove1_int X))) (let ((_let_2 (@ tptp.cons_int Y))) (let ((_let_3 (@ _let_1 (@ _let_2 Xs)))) (let ((_let_4 (= X Y))) (and (=> _let_4 (= _let_3 Xs)) (=> (not _let_4) (= _let_3 (@ _let_2 (@ _let_1 Xs)))))))))) (forall ((X tptp.nat) (Y tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ tptp.remove1_nat X))) (let ((_let_2 (@ tptp.cons_nat Y))) (let ((_let_3 (@ _let_1 (@ _let_2 Xs)))) (let ((_let_4 (= X Y))) (and (=> _let_4 (= _let_3 Xs)) (=> (not _let_4) (= _let_3 (@ _let_2 (@ _let_1 Xs)))))))))) (forall ((X tptp.produc6575502325842934193n_assn) (Y tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ tptp.remove1670527618125605709n_assn X))) (let ((_let_2 (@ tptp.cons_P2971678138204555879n_assn Y))) (let ((_let_3 (@ _let_1 (@ _let_2 Xs)))) (let ((_let_4 (= X Y))) (and (=> _let_4 (= _let_3 Xs)) (=> (not _let_4) (= _let_3 (@ _let_2 (@ _let_1 Xs)))))))))) (forall ((A tptp.set_se7855581050983116737at_nat) (R2 tptp.set_Pr4329608150637261639at_nat)) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat) (Y2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member2643936169264416010at_nat X3) A) (=> (@ (@ tptp.member2643936169264416010at_nat Y2) A) (=> (not (= X3 Y2)) (or (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X3) Y2)) R2) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat Y2) X3)) R2)))))) (@ (@ tptp.total_7212417256332265445at_nat A) R2))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (R2 tptp.set_Pr5564308138774400199at_nat)) (=> (forall ((X3 tptp.produc3843707927480180839at_nat) (Y2 tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X3) A) (=> (@ (@ tptp.member8757157785044589968at_nat Y2) A) (=> (not (= X3 Y2)) (or (@ (@ tptp.member6009668390874684176at_nat (@ (@ tptp.produc2335810615602371415at_nat X3) Y2)) R2) (@ (@ tptp.member6009668390874684176at_nat (@ (@ tptp.produc2335810615602371415at_nat Y2) X3)) R2)))))) (@ (@ tptp.total_1513685709984341995at_nat A) R2))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (R2 tptp.set_Pr8693737435421807431at_nat)) (=> (forall ((X3 tptp.product_prod_nat_nat) (Y2 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) A) (=> (@ (@ tptp.member8440522571783428010at_nat Y2) A) (=> (not (= X3 Y2)) (or (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X3) Y2)) R2) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat Y2) X3)) R2)))))) (@ (@ tptp.total_3592101749530773125at_nat A) R2))) (forall ((A tptp.set_nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A) (=> (@ (@ tptp.member_nat Y2) A) (=> (not (= X3 Y2)) (or (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) Y2)) R2) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y2) X3)) R2)))))) (@ (@ tptp.total_on_nat A) R2))) (forall ((A tptp.set_int) (R2 tptp.set_Pr958786334691620121nt_int)) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.member_int X3) A) (=> (@ (@ tptp.member_int Y2) A) (=> (not (= X3 Y2)) (or (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X3) Y2)) R2) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y2) X3)) R2)))))) (@ (@ tptp.total_on_int A) R2))) (forall ((A tptp.set_Pr4532377907799695533_nat_o) (R2 tptp.set_Pr2161125870931222855_nat_o)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X3) A) (=> (@ (@ tptp.member6576561426505652726_nat_o Y2) A) (=> (not (= X3 Y2)) (or (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o X3) Y2)) R2) (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o Y2) X3)) R2)))))) (@ (@ tptp.total_7429123086324524369_nat_o A) R2))) _let_103 _let_102 (forall ((R2 tptp.set_Pr5564308138774400199at_nat)) (@ (@ tptp.total_1513685709984341995at_nat tptp.bot_bo228742789529271731at_nat) R2)) (forall ((R2 tptp.set_Pr8693737435421807431at_nat)) (@ (@ tptp.total_3592101749530773125at_nat tptp.bot_bo2099793752762293965at_nat) R2)) (forall ((R2 tptp.set_Product_prod_o_o)) (@ (@ tptp.total_on_o tptp.bot_bot_set_o) R2)) (forall ((R2 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.total_on_nat tptp.bot_bot_set_nat) R2)) (forall ((R2 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.total_on_int tptp.bot_bot_set_int) R2)) (forall ((X tptp.int) (Y tptp.int) (Xs tptp.list_int)) (let ((_let_1 (@ tptp.removeAll_int X))) (let ((_let_2 (@ _let_1 Xs))) (let ((_let_3 (@ tptp.cons_int Y))) (let ((_let_4 (@ _let_1 (@ _let_3 Xs)))) (let ((_let_5 (= X Y))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))) (forall ((X tptp.nat) (Y tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ tptp.removeAll_nat X))) (let ((_let_2 (@ _let_1 Xs))) (let ((_let_3 (@ tptp.cons_nat Y))) (let ((_let_4 (@ _let_1 (@ _let_3 Xs)))) (let ((_let_5 (= X Y))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))) (forall ((X tptp.produc6575502325842934193n_assn) (Y tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ tptp.remove1763081955827946941n_assn X))) (let ((_let_2 (@ _let_1 Xs))) (let ((_let_3 (@ tptp.cons_P2971678138204555879n_assn Y))) (let ((_let_4 (@ _let_1 (@ _let_3 Xs)))) (let ((_let_5 (= X Y))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))) (forall ((F4 (-> tptp.int tptp.int tptp.int)) (A2 tptp.int) (As2 tptp.list_int) (B2 tptp.int) (Bs tptp.list_int)) (let ((_let_1 (@ tptp.zipf_int_int_int F4))) (= (@ (@ _let_1 (@ (@ tptp.cons_int A2) As2)) (@ (@ tptp.cons_int B2) Bs)) (@ (@ tptp.cons_int (@ (@ F4 A2) B2)) (@ (@ _let_1 As2) Bs))))) (forall ((F4 (-> tptp.int tptp.int tptp.nat)) (A2 tptp.int) (As2 tptp.list_int) (B2 tptp.int) (Bs tptp.list_int)) (let ((_let_1 (@ tptp.zipf_int_int_nat F4))) (= (@ (@ _let_1 (@ (@ tptp.cons_int A2) As2)) (@ (@ tptp.cons_int B2) Bs)) (@ (@ tptp.cons_nat (@ (@ F4 A2) B2)) (@ (@ _let_1 As2) Bs))))) (forall ((F4 (-> tptp.int tptp.nat tptp.int)) (A2 tptp.int) (As2 tptp.list_int) (B2 tptp.nat) (Bs tptp.list_nat)) (let ((_let_1 (@ tptp.zipf_int_nat_int F4))) (= (@ (@ _let_1 (@ (@ tptp.cons_int A2) As2)) (@ (@ tptp.cons_nat B2) Bs)) (@ (@ tptp.cons_int (@ (@ F4 A2) B2)) (@ (@ _let_1 As2) Bs))))) (forall ((F4 (-> tptp.int tptp.nat tptp.nat)) (A2 tptp.int) (As2 tptp.list_int) (B2 tptp.nat) (Bs tptp.list_nat)) (let ((_let_1 (@ tptp.zipf_int_nat_nat F4))) (= (@ (@ _let_1 (@ (@ tptp.cons_int A2) As2)) (@ (@ tptp.cons_nat B2) Bs)) (@ (@ tptp.cons_nat (@ (@ F4 A2) B2)) (@ (@ _let_1 As2) Bs))))) (forall ((F4 (-> tptp.nat tptp.int tptp.int)) (A2 tptp.nat) (As2 tptp.list_nat) (B2 tptp.int) (Bs tptp.list_int)) (let ((_let_1 (@ tptp.zipf_nat_int_int F4))) (= (@ (@ _let_1 (@ (@ tptp.cons_nat A2) As2)) (@ (@ tptp.cons_int B2) Bs)) (@ (@ tptp.cons_int (@ (@ F4 A2) B2)) (@ (@ _let_1 As2) Bs))))) (forall ((F4 (-> tptp.nat tptp.int tptp.nat)) (A2 tptp.nat) (As2 tptp.list_nat) (B2 tptp.int) (Bs tptp.list_int)) (let ((_let_1 (@ tptp.zipf_nat_int_nat F4))) (= (@ (@ _let_1 (@ (@ tptp.cons_nat A2) As2)) (@ (@ tptp.cons_int B2) Bs)) (@ (@ tptp.cons_nat (@ (@ F4 A2) B2)) (@ (@ _let_1 As2) Bs))))) (forall ((F4 (-> tptp.nat tptp.nat tptp.int)) (A2 tptp.nat) (As2 tptp.list_nat) (B2 tptp.nat) (Bs tptp.list_nat)) (let ((_let_1 (@ tptp.zipf_nat_nat_int F4))) (= (@ (@ _let_1 (@ (@ tptp.cons_nat A2) As2)) (@ (@ tptp.cons_nat B2) Bs)) (@ (@ tptp.cons_int (@ (@ F4 A2) B2)) (@ (@ _let_1 As2) Bs))))) (forall ((F4 (-> tptp.nat tptp.nat tptp.nat)) (A2 tptp.nat) (As2 tptp.list_nat) (B2 tptp.nat) (Bs tptp.list_nat)) (let ((_let_1 (@ tptp.zipf_nat_nat_nat F4))) (= (@ (@ _let_1 (@ (@ tptp.cons_nat A2) As2)) (@ (@ tptp.cons_nat B2) Bs)) (@ (@ tptp.cons_nat (@ (@ F4 A2) B2)) (@ (@ _let_1 As2) Bs))))) (forall ((F4 (-> tptp.int tptp.int tptp.produc6575502325842934193n_assn)) (A2 tptp.int) (As2 tptp.list_int) (B2 tptp.int) (Bs tptp.list_int)) (let ((_let_1 (@ tptp.zipf_i7756021159461276697n_assn F4))) (= (@ (@ _let_1 (@ (@ tptp.cons_int A2) As2)) (@ (@ tptp.cons_int B2) Bs)) (@ (@ tptp.cons_P2971678138204555879n_assn (@ (@ F4 A2) B2)) (@ (@ _let_1 As2) Bs))))) (forall ((F4 (-> tptp.int tptp.nat tptp.produc6575502325842934193n_assn)) (A2 tptp.int) (As2 tptp.list_int) (B2 tptp.nat) (Bs tptp.list_nat)) (let ((_let_1 (@ tptp.zipf_i5995984495708165493n_assn F4))) (= (@ (@ _let_1 (@ (@ tptp.cons_int A2) As2)) (@ (@ tptp.cons_nat B2) Bs)) (@ (@ tptp.cons_P2971678138204555879n_assn (@ (@ F4 A2) B2)) (@ (@ _let_1 As2) Bs))))) (forall ((X tptp.int) (Xs tptp.list_int)) (not (@ tptp.null_int (@ (@ tptp.cons_int X) Xs)))) (forall ((X tptp.nat) (Xs tptp.list_nat)) (not (@ tptp.null_nat (@ (@ tptp.cons_nat X) Xs)))) (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (not (@ tptp.null_P7596217980778516671n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)))) (forall ((Xs tptp.list_P8527749157015355191n_assn) (N tptp.nat)) (= (= (@ tptp.size_s6829681357464350627n_assn Xs) (@ tptp.suc N)) (exists ((Y5 tptp.produc6575502325842934193n_assn) (Ys3 tptp.list_P8527749157015355191n_assn)) (and (= Xs (@ (@ tptp.cons_P2971678138204555879n_assn Y5) Ys3)) (= (@ tptp.size_s6829681357464350627n_assn Ys3) N))))) (forall ((Xs tptp.list_c) (N tptp.nat)) (= (= (@ tptp.size_size_list_c Xs) (@ tptp.suc N)) (exists ((Y5 tptp.c) (Ys3 tptp.list_c)) (and (= Xs (@ (@ tptp.cons_c Y5) Ys3)) (= (@ tptp.size_size_list_c Ys3) N))))) (forall ((Xs tptp.list_d) (N tptp.nat)) (= (= (@ tptp.size_size_list_d Xs) (@ tptp.suc N)) (exists ((Y5 tptp.d) (Ys3 tptp.list_d)) (and (= Xs (@ (@ tptp.cons_d Y5) Ys3)) (= (@ tptp.size_size_list_d Ys3) N))))) (forall ((Xs tptp.list_nat) (N tptp.nat)) (= (= (@ tptp.size_size_list_nat Xs) (@ tptp.suc N)) (exists ((Y5 tptp.nat) (Ys3 tptp.list_nat)) (and (= Xs (@ (@ tptp.cons_nat Y5) Ys3)) (= (@ tptp.size_size_list_nat Ys3) N))))) (forall ((Xs tptp.list_int) (N tptp.nat)) (= (= (@ tptp.size_size_list_int Xs) (@ tptp.suc N)) (exists ((Y5 tptp.int) (Ys3 tptp.list_int)) (and (= Xs (@ (@ tptp.cons_int Y5) Ys3)) (= (@ tptp.size_size_list_int Ys3) N))))) (forall ((N tptp.nat) (Xs tptp.list_P8527749157015355191n_assn)) (= (= (@ tptp.suc N) (@ tptp.size_s6829681357464350627n_assn Xs)) (exists ((Y5 tptp.produc6575502325842934193n_assn) (Ys3 tptp.list_P8527749157015355191n_assn)) (and (= Xs (@ (@ tptp.cons_P2971678138204555879n_assn Y5) Ys3)) (= (@ tptp.size_s6829681357464350627n_assn Ys3) N))))) (forall ((N tptp.nat) (Xs tptp.list_c)) (= (= (@ tptp.suc N) (@ tptp.size_size_list_c Xs)) (exists ((Y5 tptp.c) (Ys3 tptp.list_c)) (and (= Xs (@ (@ tptp.cons_c Y5) Ys3)) (= (@ tptp.size_size_list_c Ys3) N))))) (forall ((N tptp.nat) (Xs tptp.list_d)) (= (= (@ tptp.suc N) (@ tptp.size_size_list_d Xs)) (exists ((Y5 tptp.d) (Ys3 tptp.list_d)) (and (= Xs (@ (@ tptp.cons_d Y5) Ys3)) (= (@ tptp.size_size_list_d Ys3) N))))) (forall ((N tptp.nat) (Xs tptp.list_nat)) (= (= (@ tptp.suc N) (@ tptp.size_size_list_nat Xs)) (exists ((Y5 tptp.nat) (Ys3 tptp.list_nat)) (and (= Xs (@ (@ tptp.cons_nat Y5) Ys3)) (= (@ tptp.size_size_list_nat Ys3) N))))) (forall ((N tptp.nat) (Xs tptp.list_int)) (= (= (@ tptp.suc N) (@ tptp.size_size_list_int Xs)) (exists ((Y5 tptp.int) (Ys3 tptp.list_int)) (and (= Xs (@ (@ tptp.cons_int Y5) Ys3)) (= (@ tptp.size_size_list_int Ys3) N))))) (forall ((Xs tptp.list_int) (X tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) (@ tptp.set_int2 (@ (@ tptp.cons_int X) Xs)))) (forall ((Xs tptp.list_P8527749157015355191n_assn) (X tptp.produc6575502325842934193n_assn)) (@ (@ tptp.ord_le171416862856029873n_assn (@ tptp.set_Pr1139785259514867910n_assn Xs)) (@ tptp.set_Pr1139785259514867910n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)))) (forall ((Xs tptp.list_nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) (@ tptp.set_nat2 (@ (@ tptp.cons_nat X) Xs)))) (forall ((R2 tptp.set_Product_prod_o_o) (S3 tptp.set_Product_prod_o_o)) (=> (@ (@ tptp.ord_le192195778054999463od_o_o R2) S3) (@ (@ tptp.ord_less_eq_set_o (@ tptp.field_o R2)) (@ tptp.field_o S3)))) (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (S3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat R2) S3) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.field_nat R2)) (@ tptp.field_nat S3)))) (forall ((Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_P8527749157015355191n_assn) (X tptp.produc6575502325842934193n_assn)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6829681357464350627n_assn Xs)) (@ tptp.size_s6829681357464350627n_assn Ys)) (not (= Xs (@ (@ tptp.cons_P2971678138204555879n_assn X) Ys))))) (forall ((Xs tptp.list_c) (Ys tptp.list_c) (X tptp.c)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_c Xs)) (@ tptp.size_size_list_c Ys)) (not (= Xs (@ (@ tptp.cons_c X) Ys))))) (forall ((Xs tptp.list_d) (Ys tptp.list_d) (X tptp.d)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_d Xs)) (@ tptp.size_size_list_d Ys)) (not (= Xs (@ (@ tptp.cons_d X) Ys))))) (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) (@ tptp.size_size_list_nat Ys)) (not (= Xs (@ (@ tptp.cons_nat X) Ys))))) (forall ((Xs tptp.list_int) (Ys tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs)) (@ tptp.size_size_list_int Ys)) (not (= Xs (@ (@ tptp.cons_int X) Ys))))) (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)))))) (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)))))) (forall ((X tptp.produc3843707927480180839at_nat) (Xs tptp.list_P5464809261938338413at_nat)) (= (@ tptp.distin5355857245021852384at_nat (@ (@ tptp.cons_P3940603068885512221at_nat X) Xs)) (and (not (@ (@ tptp.member8757157785044589968at_nat X) (@ tptp.set_Pr3765526544606949372at_nat Xs))) (@ tptp.distin5355857245021852384at_nat Xs)))) (forall ((X tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (= (@ tptp.distin6923225563576452346at_nat (@ (@ tptp.cons_P6512896166579812791at_nat X) Xs)) (and (not (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs))) (@ tptp.distin6923225563576452346at_nat Xs)))) (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xs tptp.list_P7985473006766602707_nat_o)) (= (@ tptp.distin299582740263731014_nat_o (@ (@ tptp.cons_P6219271836124797827_nat_o X) Xs)) (and (not (@ (@ tptp.member6576561426505652726_nat_o X) (@ tptp.set_Pr400311997697478754_nat_o Xs))) (@ tptp.distin299582740263731014_nat_o Xs)))) (forall ((X tptp.int) (Xs tptp.list_int)) (= (@ tptp.distinct_int (@ (@ tptp.cons_int X) Xs)) (and (not (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs))) (@ tptp.distinct_int Xs)))) (forall ((X tptp.nat) (Xs tptp.list_nat)) (= (@ tptp.distinct_nat (@ (@ tptp.cons_nat X) Xs)) (and (not (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs))) (@ tptp.distinct_nat Xs)))) (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (= (@ tptp.distin4809818325527169450n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) (and (not (@ (@ tptp.member7957490590177025114n_assn X) (@ tptp.set_Pr1139785259514867910n_assn Xs))) (@ tptp.distin4809818325527169450n_assn Xs)))) (forall ((X tptp.int) (Xs tptp.list_int) (Y tptp.int)) (= (@ (@ (@ tptp.list_update_int (@ (@ tptp.cons_int X) Xs)) tptp.zero_zero_nat) Y) (@ (@ tptp.cons_int Y) Xs))) (forall ((X tptp.nat) (Xs tptp.list_nat) (Y tptp.nat)) (= (@ (@ (@ tptp.list_update_nat (@ (@ tptp.cons_nat X) Xs)) tptp.zero_zero_nat) Y) (@ (@ tptp.cons_nat Y) Xs))) (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn) (Y tptp.produc6575502325842934193n_assn)) (= (@ (@ (@ tptp.list_u4534839942911652127n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) tptp.zero_zero_nat) Y) (@ (@ tptp.cons_P2971678138204555879n_assn Y) Xs))) (forall ((X tptp.c) (Xs tptp.list_c) (Y tptp.c)) (= (@ (@ (@ tptp.list_update_c (@ (@ tptp.cons_c X) Xs)) tptp.zero_zero_nat) Y) (@ (@ tptp.cons_c Y) Xs))) (forall ((X tptp.d) (Xs tptp.list_d) (Y tptp.d)) (= (@ (@ (@ tptp.list_update_d (@ (@ tptp.cons_d X) Xs)) tptp.zero_zero_nat) Y) (@ (@ tptp.cons_d Y) Xs))) (forall ((X tptp.int) (Xs tptp.list_int) (I tptp.nat) (Y tptp.int)) (let ((_let_1 (@ tptp.cons_int X))) (= (@ (@ (@ tptp.list_update_int (@ _let_1 Xs)) (@ tptp.suc I)) Y) (@ _let_1 (@ (@ (@ tptp.list_update_int Xs) I) Y))))) (forall ((X tptp.nat) (Xs tptp.list_nat) (I tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.cons_nat X))) (= (@ (@ (@ tptp.list_update_nat (@ _let_1 Xs)) (@ tptp.suc I)) Y) (@ _let_1 (@ (@ (@ tptp.list_update_nat Xs) I) Y))))) (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn) (I tptp.nat) (Y tptp.produc6575502325842934193n_assn)) (let ((_let_1 (@ tptp.cons_P2971678138204555879n_assn X))) (= (@ (@ (@ tptp.list_u4534839942911652127n_assn (@ _let_1 Xs)) (@ tptp.suc I)) Y) (@ _let_1 (@ (@ (@ tptp.list_u4534839942911652127n_assn Xs) I) Y))))) (forall ((X tptp.c) (Xs tptp.list_c) (I tptp.nat) (Y tptp.c)) (let ((_let_1 (@ tptp.cons_c X))) (= (@ (@ (@ tptp.list_update_c (@ _let_1 Xs)) (@ tptp.suc I)) Y) (@ _let_1 (@ (@ (@ tptp.list_update_c Xs) I) Y))))) (forall ((X tptp.d) (Xs tptp.list_d) (I tptp.nat) (Y tptp.d)) (let ((_let_1 (@ tptp.cons_d X))) (= (@ (@ (@ tptp.list_update_d (@ _let_1 Xs)) (@ tptp.suc I)) Y) (@ _let_1 (@ (@ (@ tptp.list_update_d Xs) I) Y))))) (forall ((Xs tptp.list_int) (Ys tptp.list_int) (R2 tptp.set_Pr958786334691620121nt_int) (X tptp.int)) (let ((_let_1 (@ tptp.listrel1_int R2))) (let ((_let_2 (@ tptp.cons_int X))) (=> (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Xs) Ys)) _let_1) (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int (@ _let_2 Xs)) (@ _let_2 Ys))) _let_1))))) (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (R2 tptp.set_Pr1261947904930325089at_nat) (X tptp.nat)) (let ((_let_1 (@ tptp.listrel1_nat R2))) (let ((_let_2 (@ tptp.cons_nat X))) (=> (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Xs) Ys)) _let_1) (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat (@ _let_2 Xs)) (@ _let_2 Ys))) _let_1))))) (forall ((Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_P8527749157015355191n_assn) (R2 tptp.set_Pr8116311503512020807n_assn) (X tptp.produc6575502325842934193n_assn)) (let ((_let_1 (@ tptp.listre4270255209692100112n_assn R2))) (let ((_let_2 (@ tptp.cons_P2971678138204555879n_assn X))) (=> (@ (@ tptp.member3994142547374651152n_assn (@ (@ tptp.produc3014731801419794263n_assn Xs) Ys)) _let_1) (@ (@ tptp.member3994142547374651152n_assn (@ (@ tptp.produc3014731801419794263n_assn (@ _let_2 Xs)) (@ _let_2 Ys))) _let_1))))) (forall ((X1 tptp.code_integer) (X22 tptp.code_integer) (L12 tptp.list_Code_integer) (L23 tptp.list_Code_integer)) (let ((_let_1 (@ tptp.cons_Code_integer X1))) (let ((_let_2 (@ tptp.merge_Code_integer (@ _let_1 L12)))) (let ((_let_3 (@ tptp.cons_Code_integer X22))) (let ((_let_4 (@ _let_3 L23))) (let ((_let_5 (@ _let_2 _let_4))) (let ((_let_6 (= X1 X22))) (let ((_let_7 (@ tptp.merge_Code_integer L12))) (let ((_let_8 (@ (@ tptp.ord_le6747313008572928689nteger X1) X22))) (and (=> _let_8 (= _let_5 (@ _let_1 (@ _let_7 _let_4)))) (=> (not _let_8) (and (=> _let_6 (= _let_5 (@ _let_1 (@ _let_7 L23)))) (=> (not _let_6) (= _let_5 (@ _let_3 (@ _let_2 L23)))))))))))))))) (forall ((X1 tptp.num) (X22 tptp.num) (L12 tptp.list_num) (L23 tptp.list_num)) (let ((_let_1 (@ tptp.cons_num X1))) (let ((_let_2 (@ tptp.merge_num (@ _let_1 L12)))) (let ((_let_3 (@ tptp.cons_num X22))) (let ((_let_4 (@ _let_3 L23))) (let ((_let_5 (@ _let_2 _let_4))) (let ((_let_6 (= X1 X22))) (let ((_let_7 (@ tptp.merge_num L12))) (let ((_let_8 (@ (@ tptp.ord_less_num X1) X22))) (and (=> _let_8 (= _let_5 (@ _let_1 (@ _let_7 _let_4)))) (=> (not _let_8) (and (=> _let_6 (= _let_5 (@ _let_1 (@ _let_7 L23)))) (=> (not _let_6) (= _let_5 (@ _let_3 (@ _let_2 L23)))))))))))))))) (forall ((X1 tptp.nat) (X22 tptp.nat) (L12 tptp.list_nat) (L23 tptp.list_nat)) (let ((_let_1 (@ tptp.cons_nat X1))) (let ((_let_2 (@ tptp.merge_nat (@ _let_1 L12)))) (let ((_let_3 (@ tptp.cons_nat X22))) (let ((_let_4 (@ _let_3 L23))) (let ((_let_5 (@ _let_2 _let_4))) (let ((_let_6 (= X1 X22))) (let ((_let_7 (@ tptp.merge_nat L12))) (let ((_let_8 (@ (@ tptp.ord_less_nat X1) X22))) (and (=> _let_8 (= _let_5 (@ _let_1 (@ _let_7 _let_4)))) (=> (not _let_8) (and (=> _let_6 (= _let_5 (@ _let_1 (@ _let_7 L23)))) (=> (not _let_6) (= _let_5 (@ _let_3 (@ _let_2 L23)))))))))))))))) (forall ((X1 tptp.int) (X22 tptp.int) (L12 tptp.list_int) (L23 tptp.list_int)) (let ((_let_1 (@ tptp.cons_int X1))) (let ((_let_2 (@ tptp.merge_int (@ _let_1 L12)))) (let ((_let_3 (@ tptp.cons_int X22))) (let ((_let_4 (@ _let_3 L23))) (let ((_let_5 (@ _let_2 _let_4))) (let ((_let_6 (= X1 X22))) (let ((_let_7 (@ tptp.merge_int L12))) (let ((_let_8 (@ (@ tptp.ord_less_int X1) X22))) (and (=> _let_8 (= _let_5 (@ _let_1 (@ _let_7 _let_4)))) (=> (not _let_8) (and (=> _let_6 (= _let_5 (@ _let_1 (@ _let_7 L23)))) (=> (not _let_6) (= _let_5 (@ _let_3 (@ _let_2 L23)))))))))))))))) (forall ((P (-> tptp.int tptp.int tptp.assn)) (A2 tptp.int) (As2 tptp.list_int) (C tptp.int) (Cs tptp.list_int)) (let ((_let_1 (@ tptp.vEBT_L74593716426352029nt_int P))) (= (@ (@ _let_1 (@ (@ tptp.cons_int A2) As2)) (@ (@ tptp.cons_int C) Cs)) (@ (@ tptp.times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))) (forall ((P (-> tptp.int tptp.nat tptp.assn)) (A2 tptp.int) (As2 tptp.list_int) (C tptp.nat) (Cs tptp.list_nat)) (let ((_let_1 (@ tptp.vEBT_L77084186935402305nt_nat P))) (= (@ (@ _let_1 (@ (@ tptp.cons_int A2) As2)) (@ (@ tptp.cons_nat C) Cs)) (@ (@ tptp.times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))) (forall ((P (-> tptp.int tptp.produc6575502325842934193n_assn tptp.assn)) (A2 tptp.int) (As2 tptp.list_int) (C tptp.produc6575502325842934193n_assn) (Cs tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ tptp.vEBT_L1620274777744359680n_assn P))) (= (@ (@ _let_1 (@ (@ tptp.cons_int A2) As2)) (@ (@ tptp.cons_P2971678138204555879n_assn C) Cs)) (@ (@ tptp.times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))) (forall ((P (-> tptp.nat tptp.int tptp.assn)) (A2 tptp.nat) (As2 tptp.list_nat) (C tptp.int) (Cs tptp.list_int)) (let ((_let_1 (@ tptp.vEBT_L8298612041380073281at_int P))) (= (@ (@ _let_1 (@ (@ tptp.cons_nat A2) As2)) (@ (@ tptp.cons_int C) Cs)) (@ (@ tptp.times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))) (forall ((P (-> tptp.nat tptp.nat tptp.assn)) (A2 tptp.nat) (As2 tptp.list_nat) (C tptp.nat) (Cs tptp.list_nat)) (let ((_let_1 (@ tptp.vEBT_L8301102511889123557at_nat P))) (= (@ (@ _let_1 (@ (@ tptp.cons_nat A2) As2)) (@ (@ tptp.cons_nat C) Cs)) (@ (@ tptp.times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))) (forall ((P (-> tptp.nat tptp.produc6575502325842934193n_assn tptp.assn)) (A2 tptp.nat) (As2 tptp.list_nat) (C tptp.produc6575502325842934193n_assn) (Cs tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ tptp.vEBT_L9083610150846024284n_assn P))) (= (@ (@ _let_1 (@ (@ tptp.cons_nat A2) As2)) (@ (@ tptp.cons_P2971678138204555879n_assn C) Cs)) (@ (@ tptp.times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))) (forall ((P (-> tptp.produc6575502325842934193n_assn tptp.int tptp.assn)) (A2 tptp.produc6575502325842934193n_assn) (As2 tptp.list_P8527749157015355191n_assn) (C tptp.int) (Cs tptp.list_int)) (let ((_let_1 (@ tptp.vEBT_L4760345170377931482sn_int P))) (= (@ (@ _let_1 (@ (@ tptp.cons_P2971678138204555879n_assn A2) As2)) (@ (@ tptp.cons_int C) Cs)) (@ (@ tptp.times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))) (forall ((P (-> tptp.produc6575502325842934193n_assn tptp.nat tptp.assn)) (A2 tptp.produc6575502325842934193n_assn) (As2 tptp.list_P8527749157015355191n_assn) (C tptp.nat) (Cs tptp.list_nat)) (let ((_let_1 (@ tptp.vEBT_L4762835640886981758sn_nat P))) (= (@ (@ _let_1 (@ (@ tptp.cons_P2971678138204555879n_assn A2) As2)) (@ (@ tptp.cons_nat C) Cs)) (@ (@ tptp.times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))) (forall ((P (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn tptp.assn)) (A2 tptp.produc6575502325842934193n_assn) (As2 tptp.list_P8527749157015355191n_assn) (C tptp.produc6575502325842934193n_assn) (Cs tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ tptp.vEBT_L3108143461992071043n_assn P))) (= (@ (@ _let_1 (@ (@ tptp.cons_P2971678138204555879n_assn A2) As2)) (@ (@ tptp.cons_P2971678138204555879n_assn C) Cs)) (@ (@ tptp.times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))) (forall ((P (-> tptp.int tptp.int tptp.assn)) (A2 tptp.int) (As2 tptp.list_int) (C tptp.int) (Cs tptp.list_int)) (let ((_let_1 (@ tptp.vEBT_L74593716426352029nt_int P))) (= (@ (@ _let_1 (@ (@ tptp.cons_int A2) As2)) (@ (@ tptp.cons_int C) Cs)) (@ (@ tptp.times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))) (forall ((P (-> tptp.int tptp.nat tptp.assn)) (A2 tptp.int) (As2 tptp.list_int) (C tptp.nat) (Cs tptp.list_nat)) (let ((_let_1 (@ tptp.vEBT_L77084186935402305nt_nat P))) (= (@ (@ _let_1 (@ (@ tptp.cons_int A2) As2)) (@ (@ tptp.cons_nat C) Cs)) (@ (@ tptp.times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))) (forall ((P (-> tptp.int tptp.produc6575502325842934193n_assn tptp.assn)) (A2 tptp.int) (As2 tptp.list_int) (C tptp.produc6575502325842934193n_assn) (Cs tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ tptp.vEBT_L1620274777744359680n_assn P))) (= (@ (@ _let_1 (@ (@ tptp.cons_int A2) As2)) (@ (@ tptp.cons_P2971678138204555879n_assn C) Cs)) (@ (@ tptp.times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))) (forall ((P (-> tptp.nat tptp.int tptp.assn)) (A2 tptp.nat) (As2 tptp.list_nat) (C tptp.int) (Cs tptp.list_int)) (let ((_let_1 (@ tptp.vEBT_L8298612041380073281at_int P))) (= (@ (@ _let_1 (@ (@ tptp.cons_nat A2) As2)) (@ (@ tptp.cons_int C) Cs)) (@ (@ tptp.times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))) (forall ((P (-> tptp.nat tptp.nat tptp.assn)) (A2 tptp.nat) (As2 tptp.list_nat) (C tptp.nat) (Cs tptp.list_nat)) (let ((_let_1 (@ tptp.vEBT_L8301102511889123557at_nat P))) (= (@ (@ _let_1 (@ (@ tptp.cons_nat A2) As2)) (@ (@ tptp.cons_nat C) Cs)) (@ (@ tptp.times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))) (forall ((P (-> tptp.nat tptp.produc6575502325842934193n_assn tptp.assn)) (A2 tptp.nat) (As2 tptp.list_nat) (C tptp.produc6575502325842934193n_assn) (Cs tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ tptp.vEBT_L9083610150846024284n_assn P))) (= (@ (@ _let_1 (@ (@ tptp.cons_nat A2) As2)) (@ (@ tptp.cons_P2971678138204555879n_assn C) Cs)) (@ (@ tptp.times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))) (forall ((P (-> tptp.produc6575502325842934193n_assn tptp.int tptp.assn)) (A2 tptp.produc6575502325842934193n_assn) (As2 tptp.list_P8527749157015355191n_assn) (C tptp.int) (Cs tptp.list_int)) (let ((_let_1 (@ tptp.vEBT_L4760345170377931482sn_int P))) (= (@ (@ _let_1 (@ (@ tptp.cons_P2971678138204555879n_assn A2) As2)) (@ (@ tptp.cons_int C) Cs)) (@ (@ tptp.times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))) (forall ((P (-> tptp.produc6575502325842934193n_assn tptp.nat tptp.assn)) (A2 tptp.produc6575502325842934193n_assn) (As2 tptp.list_P8527749157015355191n_assn) (C tptp.nat) (Cs tptp.list_nat)) (let ((_let_1 (@ tptp.vEBT_L4762835640886981758sn_nat P))) (= (@ (@ _let_1 (@ (@ tptp.cons_P2971678138204555879n_assn A2) As2)) (@ (@ tptp.cons_nat C) Cs)) (@ (@ tptp.times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))) (forall ((P (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn tptp.assn)) (A2 tptp.produc6575502325842934193n_assn) (As2 tptp.list_P8527749157015355191n_assn) (C tptp.produc6575502325842934193n_assn) (Cs tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ tptp.vEBT_L3108143461992071043n_assn P))) (= (@ (@ _let_1 (@ (@ tptp.cons_P2971678138204555879n_assn A2) As2)) (@ (@ tptp.cons_P2971678138204555879n_assn C) Cs)) (@ (@ tptp.times_times_assn (@ (@ P A2) C)) (@ (@ _let_1 As2) Cs))))) _let_101 _let_100 _let_99 _let_98 _let_97 _let_96 (forall ((N tptp.nat) (Xs tptp.list_P8527749157015355191n_assn)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.size_s6829681357464350627n_assn Xs)) (exists ((X2 tptp.produc6575502325842934193n_assn) (Ys3 tptp.list_P8527749157015355191n_assn)) (and (= Xs (@ (@ tptp.cons_P2971678138204555879n_assn X2) Ys3)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_s6829681357464350627n_assn Ys3)))))) (forall ((N tptp.nat) (Xs tptp.list_c)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.size_size_list_c Xs)) (exists ((X2 tptp.c) (Ys3 tptp.list_c)) (and (= Xs (@ (@ tptp.cons_c X2) Ys3)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_c Ys3)))))) (forall ((N tptp.nat) (Xs tptp.list_d)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.size_size_list_d Xs)) (exists ((X2 tptp.d) (Ys3 tptp.list_d)) (and (= Xs (@ (@ tptp.cons_d X2) Ys3)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_d Ys3)))))) (forall ((N tptp.nat) (Xs tptp.list_nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.size_size_list_nat Xs)) (exists ((X2 tptp.nat) (Ys3 tptp.list_nat)) (and (= Xs (@ (@ tptp.cons_nat X2) Ys3)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_nat Ys3)))))) (forall ((N tptp.nat) (Xs tptp.list_int)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.size_size_list_int Xs)) (exists ((X2 tptp.int) (Ys3 tptp.list_int)) (and (= Xs (@ (@ tptp.cons_int X2) Ys3)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_int Ys3)))))) (forall ((X tptp.nat) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat))) (= (@ _let_1 (@ (@ tptp.cons_nat X) Ys)) (and (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Ys)) (@ (@ tptp.ord_less_eq_nat X) X2))) (@ _let_1 Ys))))) (forall ((X tptp.int) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.sorted_wrt_int tptp.ord_less_eq_int))) (= (@ _let_1 (@ (@ tptp.cons_int X) Ys)) (and (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) (@ tptp.set_int2 Ys)) (@ (@ tptp.ord_less_eq_int X) X2))) (@ _let_1 Ys))))) (forall ((X tptp.code_integer) (Ys tptp.list_Code_integer)) (let ((_let_1 (@ tptp.sorted710888440204495920nteger tptp.ord_le6747313008572928689nteger))) (= (@ _let_1 (@ (@ tptp.cons_Code_integer X) Ys)) (and (forall ((X2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X2) (@ tptp.set_Code_integer2 Ys)) (@ (@ tptp.ord_le6747313008572928689nteger X) X2))) (@ _let_1 Ys))))) (forall ((X tptp.num) (Ys tptp.list_num)) (let ((_let_1 (@ tptp.sorted_wrt_num tptp.ord_less_num))) (= (@ _let_1 (@ (@ tptp.cons_num X) Ys)) (and (forall ((X2 tptp.num)) (=> (@ (@ tptp.member_num X2) (@ tptp.set_num2 Ys)) (@ (@ tptp.ord_less_num X) X2))) (@ _let_1 Ys))))) (forall ((X tptp.nat) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.sorted_wrt_nat tptp.ord_less_nat))) (= (@ _let_1 (@ (@ tptp.cons_nat X) Ys)) (and (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Ys)) (@ (@ tptp.ord_less_nat X) X2))) (@ _let_1 Ys))))) (forall ((X tptp.int) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.sorted_wrt_int tptp.ord_less_int))) (= (@ _let_1 (@ (@ tptp.cons_int X) Ys)) (and (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) (@ tptp.set_int2 Ys)) (@ (@ tptp.ord_less_int X) X2))) (@ _let_1 Ys))))) _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 (forall ((Xs tptp.list_s1210847774152347623at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Ys tptp.list_s1210847774152347623at_nat) (R2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat Xs) (@ (@ tptp.cons_s6881495754146722583at_nat Y) Ys))) (@ tptp.listre8180072825634266816at_nat R2)) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat)) (=> (= Xs (@ (@ tptp.cons_s6881495754146722583at_nat X3) Ys)) (not (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X3) Y)) R2)))) (not (forall ((Zs2 tptp.list_s1210847774152347623at_nat)) (=> (= Xs (@ (@ tptp.cons_s6881495754146722583at_nat Y) Zs2)) (not (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat Zs2) Ys)) (@ tptp.listre8180072825634266816at_nat R2))))))))) (forall ((Xs tptp.list_int) (Y tptp.int) (Ys tptp.list_int) (R2 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Xs) (@ (@ tptp.cons_int Y) Ys))) (@ tptp.listrel1_int R2)) (=> (forall ((X3 tptp.int)) (=> (= Xs (@ (@ tptp.cons_int X3) Ys)) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X3) Y)) R2)))) (not (forall ((Zs2 tptp.list_int)) (=> (= Xs (@ (@ tptp.cons_int Y) Zs2)) (not (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Zs2) Ys)) (@ tptp.listrel1_int R2))))))))) (forall ((Xs tptp.list_nat) (Y tptp.nat) (Ys tptp.list_nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Xs) (@ (@ tptp.cons_nat Y) Ys))) (@ tptp.listrel1_nat R2)) (=> (forall ((X3 tptp.nat)) (=> (= Xs (@ (@ tptp.cons_nat X3) Ys)) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) Y)) R2)))) (not (forall ((Zs2 tptp.list_nat)) (=> (= Xs (@ (@ tptp.cons_nat Y) Zs2)) (not (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Zs2) Ys)) (@ tptp.listrel1_nat R2))))))))) (forall ((Xs tptp.list_P8527749157015355191n_assn) (Y tptp.produc6575502325842934193n_assn) (Ys tptp.list_P8527749157015355191n_assn) (R2 tptp.set_Pr8116311503512020807n_assn)) (=> (@ (@ tptp.member3994142547374651152n_assn (@ (@ tptp.produc3014731801419794263n_assn Xs) (@ (@ tptp.cons_P2971678138204555879n_assn Y) Ys))) (@ tptp.listre4270255209692100112n_assn R2)) (=> (forall ((X3 tptp.produc6575502325842934193n_assn)) (=> (= Xs (@ (@ tptp.cons_P2971678138204555879n_assn X3) Ys)) (not (@ (@ tptp.member4743710847862083984n_assn (@ (@ tptp.produc6128706242671166167n_assn X3) Y)) R2)))) (not (forall ((Zs2 tptp.list_P8527749157015355191n_assn)) (=> (= Xs (@ (@ tptp.cons_P2971678138204555879n_assn Y) Zs2)) (not (@ (@ tptp.member3994142547374651152n_assn (@ (@ tptp.produc3014731801419794263n_assn Zs2) Ys)) (@ tptp.listre4270255209692100112n_assn R2))))))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Xs tptp.list_s1210847774152347623at_nat) (Ys tptp.list_s1210847774152347623at_nat) (R2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat (@ (@ tptp.cons_s6881495754146722583at_nat X) Xs)) Ys)) (@ tptp.listre8180072825634266816at_nat R2)) (=> (forall ((Y2 tptp.set_Pr1261947904930325089at_nat)) (=> (= Ys (@ (@ tptp.cons_s6881495754146722583at_nat Y2) Xs)) (not (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Y2)) R2)))) (not (forall ((Zs2 tptp.list_s1210847774152347623at_nat)) (=> (= Ys (@ (@ tptp.cons_s6881495754146722583at_nat X) Zs2)) (not (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat Xs) Zs2)) (@ tptp.listre8180072825634266816at_nat R2))))))))) (forall ((X tptp.int) (Xs tptp.list_int) (Ys tptp.list_int) (R2 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int (@ (@ tptp.cons_int X) Xs)) Ys)) (@ tptp.listrel1_int R2)) (=> (forall ((Y2 tptp.int)) (=> (= Ys (@ (@ tptp.cons_int Y2) Xs)) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y2)) R2)))) (not (forall ((Zs2 tptp.list_int)) (=> (= Ys (@ (@ tptp.cons_int X) Zs2)) (not (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Xs) Zs2)) (@ tptp.listrel1_int R2))))))))) (forall ((X tptp.nat) (Xs tptp.list_nat) (Ys tptp.list_nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat (@ (@ tptp.cons_nat X) Xs)) Ys)) (@ tptp.listrel1_nat R2)) (=> (forall ((Y2 tptp.nat)) (=> (= Ys (@ (@ tptp.cons_nat Y2) Xs)) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y2)) R2)))) (not (forall ((Zs2 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Zs2)) (@ tptp.listre4270255209692100112n_assn R2))))))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (R2 tptp.set_Pr4329608150637261639at_nat) (Xs tptp.list_s1210847774152347623at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Y)) R2) (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat (@ (@ tptp.cons_s6881495754146722583at_nat X) Xs)) (@ (@ tptp.cons_s6881495754146722583at_nat Y) Xs))) (@ tptp.listre8180072825634266816at_nat R2)))) (forall ((X tptp.int) (Y tptp.int) (R2 tptp.set_Pr958786334691620121nt_int) (Xs tptp.list_int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) R2) (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int (@ (@ tptp.cons_int X) Xs)) (@ (@ tptp.cons_int Y) Xs))) (@ tptp.listrel1_int R2)))) (forall ((X tptp.nat) (Y tptp.nat) (R2 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(=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat Y) Y2)) R2) (not (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat Ys) Ys5)) (@ tptp.listre2047417242196832561at_nat R2))))))))) (forall ((X tptp.int) (Y tptp.int) (R2 tptp.set_Pr958786334691620121nt_int) (Xs tptp.list_int) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.listrel_int_int R2))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) R2) (=> (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Xs) Ys)) _let_1) (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int (@ (@ tptp.cons_int X) Xs)) (@ (@ tptp.cons_int Y) Ys))) _let_1))))) (forall ((X tptp.int) (Y tptp.nat) (R2 tptp.set_Pr3448869479623346877nt_nat) (Xs tptp.list_int) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.listrel_int_nat R2))) (=> (@ (@ tptp.member216504246829706758nt_nat (@ (@ tptp.product_Pair_int_nat X) Y)) R2) (=> (@ (@ tptp.member9189046780804443046st_nat (@ (@ tptp.produc4542114716404682293st_nat Xs) Ys)) _let_1) (@ (@ tptp.member9189046780804443046st_nat (@ (@ tptp.produc4542114716404682293st_nat (@ (@ tptp.cons_int X) Xs)) (@ (@ tptp.cons_nat Y) Ys))) _let_1))))) (forall ((X tptp.nat) (Y tptp.int) (R2 tptp.set_Pr7995236796853374141at_int) (Xs tptp.list_nat) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.listrel_nat_int R2))) (=> (@ (@ tptp.member4262671552274231302at_int (@ (@ tptp.product_Pair_nat_int X) Y)) R2) (=> (@ (@ tptp.member4850886304473975718st_int (@ (@ tptp.produc7739558402351520821st_int Xs) Ys)) _let_1) (@ (@ tptp.member4850886304473975718st_int (@ (@ tptp.produc7739558402351520821st_int (@ (@ tptp.cons_nat X) Xs)) (@ (@ tptp.cons_int Y) Ys))) _let_1))))) (forall ((X tptp.nat) (Y tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (Xs tptp.list_nat) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.listrel_nat_nat R2))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) R2) (=> (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Xs) Ys)) _let_1) (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat (@ (@ tptp.cons_nat X) Xs)) (@ (@ tptp.cons_nat Y) Ys))) _let_1))))) (forall ((X tptp.int) (Y tptp.produc6575502325842934193n_assn) (R2 tptp.set_Pr3255386646789011632n_assn) (Xs tptp.list_int) (Ys tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ tptp.listre4888949683985722578n_assn R2))) (=> (@ (@ tptp.member241480614033477777n_assn (@ (@ tptp.produc3313821056773121708n_assn X) Y)) R2) (=> (@ (@ tptp.member490958779117458567n_assn (@ (@ tptp.produc4510294837168919970n_assn Xs) Ys)) _let_1) (@ (@ tptp.member490958779117458567n_assn (@ (@ tptp.produc4510294837168919970n_assn (@ (@ tptp.cons_int X) Xs)) (@ (@ tptp.cons_P2971678138204555879n_assn Y) Ys))) _let_1))))) (forall ((X tptp.nat) (Y tptp.produc6575502325842934193n_assn) (R2 tptp.set_Pr247834672394327052n_assn) (Xs tptp.list_nat) (Ys tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ tptp.listre3128913020232611374n_assn R2))) (=> (@ (@ tptp.member7704815987135142381n_assn (@ (@ tptp.produc1553784393020010504n_assn X) Y)) R2) (=> (@ (@ tptp.member3687432546746012131n_assn (@ (@ tptp.produc7706768604797473534n_assn Xs) Ys)) _let_1) (@ (@ tptp.member3687432546746012131n_assn (@ (@ tptp.produc7706768604797473534n_assn (@ (@ tptp.cons_nat X) Xs)) (@ (@ tptp.cons_P2971678138204555879n_assn Y) Ys))) _let_1))))) (forall ((X tptp.produc6575502325842934193n_assn) (Y tptp.int) (R2 tptp.set_Pr2181989527757714242sn_int) (Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.listre8029020076619294380sn_int R2))) (=> (@ (@ tptp.member5792320502188913699sn_int (@ (@ tptp.produc6453891449406693510sn_int X) Y)) R2) (=> (@ (@ tptp.member5295696281703116473st_int (@ (@ tptp.produc1996262876970182428st_int Xs) Ys)) _let_1) (@ (@ tptp.member5295696281703116473st_int (@ (@ tptp.produc1996262876970182428st_int (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) (@ (@ tptp.cons_int Y) Ys))) _let_1))))) (forall ((X tptp.produc6575502325842934193n_assn) (Y tptp.nat) (R2 tptp.set_Pr4672072672689440998sn_nat) (Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.listre8031510547128344656sn_nat R2))) (=> (@ (@ tptp.member746799484843334599sn_nat (@ (@ tptp.produc6456381919915743786sn_nat X) Y)) R2) (=> (@ (@ tptp.member7785779426634843229st_nat (@ (@ tptp.produc6174113896479379136st_nat Xs) Ys)) _let_1) (@ (@ tptp.member7785779426634843229st_nat (@ (@ tptp.produc6174113896479379136st_nat (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) (@ (@ tptp.cons_nat Y) Ys))) _let_1))))) (forall ((X tptp.produc6575502325842934193n_assn) (Y tptp.produc6575502325842934193n_assn) (R2 tptp.set_Pr8116311503512020807n_assn) (Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ tptp.listre5253995379918703921n_assn R2))) (=> (@ (@ tptp.member4743710847862083984n_assn (@ (@ tptp.produc6128706242671166167n_assn X) Y)) R2) (=> (@ (@ tptp.member3994142547374651152n_assn (@ (@ tptp.produc3014731801419794263n_assn Xs) Ys)) _let_1) (@ (@ tptp.member3994142547374651152n_assn (@ (@ tptp.produc3014731801419794263n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) (@ (@ tptp.cons_P2971678138204555879n_assn Y) Ys))) _let_1))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (R2 tptp.set_Pr4329608150637261639at_nat) (Xs tptp.list_s1210847774152347623at_nat) (Ys tptp.list_s1210847774152347623at_nat)) (let ((_let_1 (@ tptp.listre2047417242196832561at_nat R2))) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Y)) R2) (=> (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat Xs) Ys)) _let_1) (@ (@ tptp.member4080735728053443344at_nat (@ (@ tptp.produc7536900900485677911at_nat (@ (@ tptp.cons_s6881495754146722583at_nat X) Xs)) (@ (@ tptp.cons_s6881495754146722583at_nat Y) Ys))) _let_1))))) (forall ((X21 tptp.produc6575502325842934193n_assn) (X222 tptp.list_P8527749157015355191n_assn)) (= (@ tptp.size_s6829681357464350627n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X21) X222)) (@ (@ tptp.plus_plus_nat (@ tptp.size_s6829681357464350627n_assn X222)) (@ tptp.suc tptp.zero_zero_nat)))) (forall ((X21 tptp.c) (X222 tptp.list_c)) (= (@ tptp.size_size_list_c (@ (@ tptp.cons_c X21) X222)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_list_c X222)) (@ tptp.suc tptp.zero_zero_nat)))) (forall ((X21 tptp.d) (X222 tptp.list_d)) (= (@ tptp.size_size_list_d (@ (@ tptp.cons_d X21) X222)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_list_d X222)) (@ tptp.suc tptp.zero_zero_nat)))) (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)))) (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)))) (forall ((N tptp.nat) (X tptp.int) (Xs tptp.list_int)) (let ((_let_1 (@ (@ tptp.nth_int (@ (@ tptp.cons_int X) Xs)) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_int Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))) (forall ((N tptp.nat) (X tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X) Xs)) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_nat Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))) (forall ((N tptp.nat) (X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ (@ tptp.nth_Pr1769885009046257848n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_Pr1769885009046257848n_assn Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))) (forall ((X tptp.produc3843707927480180839at_nat) (Xs tptp.list_P5464809261938338413at_nat) (N tptp.nat)) (=> (not (@ (@ tptp.member8757157785044589968at_nat X) (@ tptp.set_Pr3765526544606949372at_nat Xs))) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_s1588839187904960729at_nat Xs)) (= (= (@ (@ tptp.nth_Pr1239524528086697198at_nat (@ (@ tptp.cons_P3940603068885512221at_nat X) Xs)) N) X) (= N tptp.zero_zero_nat))))) (forall ((X tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat) (N tptp.nat)) (=> (not (@ (@ tptp.member8440522571783428010at_nat X) (@ 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tptp.nth_Pr1769885009046257848n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) N) X) (= N tptp.zero_zero_nat))))) (forall ((X tptp.c) (Xs tptp.list_c) (N tptp.nat)) (=> (not (@ (@ tptp.member_c X) (@ tptp.set_c2 Xs))) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_c Xs)) (= (= (@ (@ tptp.nth_c (@ (@ tptp.cons_c X) Xs)) N) X) (= N tptp.zero_zero_nat))))) (forall ((X tptp.d) (Xs tptp.list_d) (N tptp.nat)) (=> (not (@ (@ tptp.member_d X) (@ tptp.set_d2 Xs))) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_d Xs)) (= (= (@ (@ tptp.nth_d (@ (@ tptp.cons_d X) Xs)) N) X) (= N tptp.zero_zero_nat))))) (forall ((X tptp.nat) (Xs tptp.list_nat) (N tptp.nat)) (=> (not (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs))) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_nat Xs)) (= (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X) Xs)) N) X) (= N tptp.zero_zero_nat))))) (forall ((X tptp.int) (Xs tptp.list_int) (N tptp.nat)) (=> (not (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs))) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_int Xs)) (= (= (@ (@ tptp.nth_int (@ (@ tptp.cons_int X) Xs)) N) X) (= N tptp.zero_zero_nat))))) (forall ((X tptp.int) (Y tptp.int) (Xs tptp.list_int) (N tptp.nat)) (=> (not (= X Y)) (= (= (@ (@ tptp.nth_int (@ (@ tptp.cons_int X) Xs)) N) Y) (and (= (@ (@ tptp.nth_int Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) Y) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))) (forall ((X tptp.nat) (Y tptp.nat) (Xs tptp.list_nat) (N tptp.nat)) (=> (not (= X Y)) (= (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X) Xs)) N) Y) (and (= (@ (@ tptp.nth_nat Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) Y) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))) (forall ((X tptp.produc6575502325842934193n_assn) (Y tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn) (N tptp.nat)) (=> (not (= X Y)) (= (= (@ (@ tptp.nth_Pr1769885009046257848n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) N) Y) (and (= (@ (@ tptp.nth_Pr1769885009046257848n_assn Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) Y) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))) (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)))))))))) (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)))))))))) (forall ((Begin tptp.nat) (End tptp.nat) (X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ (@ tptp.minus_minus_nat End) tptp.one_one_nat))) (let ((_let_2 (@ tptp.cons_P2971678138204555879n_assn X))) (let ((_let_3 (@ tptp.slice_7964966981652229398n_assn 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_7964966981652229398n_assn (@ (@ tptp.minus_minus_nat Begin) tptp.one_one_nat)) _let_1) Xs)))))))))) (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa 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Ys)) _let_1)))))) (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn) (Y tptp.produc6575502325842934193n_assn) (Ys tptp.list_P8527749157015355191n_assn) (R2 tptp.set_Pr8116311503512020807n_assn)) (let ((_let_1 (@ tptp.lex_Pr7559194461235888923n_assn R2))) (= (@ (@ tptp.member3994142547374651152n_assn (@ (@ tptp.produc3014731801419794263n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) (@ (@ tptp.cons_P2971678138204555879n_assn Y) Ys))) _let_1) (or (and (@ (@ tptp.member4743710847862083984n_assn (@ (@ tptp.produc6128706242671166167n_assn X) Y)) R2) (= (@ tptp.size_s6829681357464350627n_assn Xs) (@ tptp.size_s6829681357464350627n_assn Ys))) (and (= X Y) (@ (@ tptp.member3994142547374651152n_assn (@ (@ tptp.produc3014731801419794263n_assn Xs) Ys)) _let_1)))))) (forall ((X tptp.c) (Xs tptp.list_c) (Y tptp.c) (Ys tptp.list_c) (R2 tptp.set_Product_prod_c_c)) (let ((_let_1 (@ tptp.lex_c R2))) (= (@ (@ tptp.member7012247553653173456list_c (@ (@ 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(@ tptp.vEBT_L8301102511889123557at_nat X) Xa) Xb) Y) (=> (=> _let_2 (=> _let_3 (not (= Y tptp.one_one_assn)))) (=> (forall ((A4 tptp.nat) (As tptp.list_nat)) (=> (= Xa (@ (@ tptp.cons_nat A4) As)) (forall ((C4 tptp.nat) (Cs2 tptp.list_nat)) (=> (= Xb (@ (@ tptp.cons_nat C4) Cs2)) (not (= Y (@ (@ tptp.times_times_assn (@ (@ X A4) C4)) (@ (@ (@ tptp.vEBT_L8301102511889123557at_nat X) As) Cs2)))))))) (=> (=> (exists ((V3 tptp.nat) (Va tptp.list_nat)) (= Xa (@ (@ tptp.cons_nat V3) Va))) (=> _let_3 _let_1)) (not (=> _let_2 (=> (exists ((V3 tptp.nat) (Va tptp.list_nat)) (= Xb (@ (@ tptp.cons_nat V3) Va))) _let_1))))))))))) (forall ((X (-> tptp.nat tptp.produc6575502325842934193n_assn tptp.assn)) (Xa tptp.list_nat) (Xb tptp.list_P8527749157015355191n_assn) (Y tptp.assn)) (let ((_let_1 (not (= Y tptp.bot_bot_assn)))) (let ((_let_2 (= Xa tptp.nil_nat))) (let ((_let_3 (= Xb tptp.nil_Pr5671120429643327159n_assn))) (=> (= (@ (@ (@ tptp.vEBT_L9083610150846024284n_assn X) Xa) Xb) Y) (=> (=> _let_2 (=> _let_3 (not (= Y tptp.one_one_assn)))) (=> (forall ((A4 tptp.nat) (As tptp.list_nat)) (=> (= Xa (@ (@ tptp.cons_nat A4) As)) (forall ((C4 tptp.produc6575502325842934193n_assn) (Cs2 tptp.list_P8527749157015355191n_assn)) (=> (= Xb (@ (@ tptp.cons_P2971678138204555879n_assn C4) Cs2)) (not (= Y (@ (@ tptp.times_times_assn (@ (@ X A4) C4)) (@ (@ (@ tptp.vEBT_L9083610150846024284n_assn X) As) Cs2)))))))) (=> (=> (exists ((V3 tptp.nat) (Va tptp.list_nat)) (= Xa (@ (@ tptp.cons_nat V3) Va))) (=> _let_3 _let_1)) (not (=> _let_2 (=> (exists ((V3 tptp.produc6575502325842934193n_assn) (Va tptp.list_P8527749157015355191n_assn)) (= Xb (@ (@ tptp.cons_P2971678138204555879n_assn V3) Va))) _let_1))))))))))) (forall ((X (-> tptp.produc6575502325842934193n_assn tptp.int tptp.assn)) (Xa tptp.list_P8527749157015355191n_assn) (Xb tptp.list_int) (Y tptp.assn)) (let ((_let_1 (not (= Y tptp.bot_bot_assn)))) (let ((_let_2 (= Xa tptp.nil_Pr5671120429643327159n_assn))) (let ((_let_3 (= Xb tptp.nil_int))) (=> (= (@ (@ (@ tptp.vEBT_L4760345170377931482sn_int X) Xa) Xb) Y) (=> (=> _let_2 (=> _let_3 (not (= Y tptp.one_one_assn)))) (=> (forall ((A4 tptp.produc6575502325842934193n_assn) (As tptp.list_P8527749157015355191n_assn)) (=> (= Xa (@ (@ tptp.cons_P2971678138204555879n_assn A4) As)) (forall ((C4 tptp.int) (Cs2 tptp.list_int)) (=> (= Xb (@ (@ tptp.cons_int C4) Cs2)) (not (= Y (@ (@ tptp.times_times_assn (@ (@ X A4) C4)) (@ (@ (@ tptp.vEBT_L4760345170377931482sn_int X) As) Cs2)))))))) (=> (=> (exists ((V3 tptp.produc6575502325842934193n_assn) (Va tptp.list_P8527749157015355191n_assn)) (= Xa (@ (@ tptp.cons_P2971678138204555879n_assn V3) Va))) (=> _let_3 _let_1)) (not (=> _let_2 (=> (exists ((V3 tptp.int) (Va tptp.list_int)) (= Xb (@ (@ tptp.cons_int V3) Va))) _let_1))))))))))) (forall ((X (-> tptp.produc6575502325842934193n_assn tptp.nat tptp.assn)) (Xa tptp.list_P8527749157015355191n_assn) (Xb tptp.list_nat) (Y tptp.assn)) (let ((_let_1 (not (= Y tptp.bot_bot_assn)))) (let ((_let_2 (= Xa tptp.nil_Pr5671120429643327159n_assn))) (let ((_let_3 (= Xb tptp.nil_nat))) (=> (= (@ (@ (@ tptp.vEBT_L4762835640886981758sn_nat X) Xa) Xb) Y) (=> (=> _let_2 (=> _let_3 (not (= Y tptp.one_one_assn)))) (=> (forall ((A4 tptp.produc6575502325842934193n_assn) (As tptp.list_P8527749157015355191n_assn)) (=> (= Xa (@ (@ tptp.cons_P2971678138204555879n_assn A4) As)) (forall ((C4 tptp.nat) (Cs2 tptp.list_nat)) (=> (= Xb (@ (@ tptp.cons_nat C4) Cs2)) (not (= Y (@ (@ tptp.times_times_assn (@ (@ X A4) C4)) (@ (@ (@ tptp.vEBT_L4762835640886981758sn_nat X) As) Cs2)))))))) (=> (=> (exists ((V3 tptp.produc6575502325842934193n_assn) (Va tptp.list_P8527749157015355191n_assn)) (= Xa (@ (@ tptp.cons_P2971678138204555879n_assn V3) Va))) (=> _let_3 _let_1)) (not (=> _let_2 (=> (exists ((V3 tptp.nat) (Va tptp.list_nat)) (= Xb (@ (@ tptp.cons_nat V3) Va))) _let_1))))))))))) (forall ((X (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn tptp.assn)) (Xa tptp.list_P8527749157015355191n_assn) (Xb tptp.list_P8527749157015355191n_assn) (Y tptp.assn)) (let ((_let_1 (not (= Y tptp.bot_bot_assn)))) (let ((_let_2 (= Xa tptp.nil_Pr5671120429643327159n_assn))) (let ((_let_3 (= Xb tptp.nil_Pr5671120429643327159n_assn))) (=> (= (@ (@ (@ tptp.vEBT_L3108143461992071043n_assn X) Xa) Xb) Y) (=> (=> _let_2 (=> _let_3 (not (= Y tptp.one_one_assn)))) (=> (forall ((A4 tptp.produc6575502325842934193n_assn) (As tptp.list_P8527749157015355191n_assn)) (=> (= Xa (@ (@ tptp.cons_P2971678138204555879n_assn A4) As)) (forall ((C4 tptp.produc6575502325842934193n_assn) (Cs2 tptp.list_P8527749157015355191n_assn)) (=> (= Xb (@ (@ tptp.cons_P2971678138204555879n_assn C4) Cs2)) (not (= Y (@ (@ tptp.times_times_assn (@ (@ X A4) C4)) (@ (@ (@ tptp.vEBT_L3108143461992071043n_assn X) As) Cs2)))))))) (=> (=> (exists ((V3 tptp.produc6575502325842934193n_assn) (Va tptp.list_P8527749157015355191n_assn)) (= Xa (@ (@ tptp.cons_P2971678138204555879n_assn V3) Va))) (=> _let_3 _let_1)) (not (=> _let_2 (=> (exists ((V3 tptp.produc6575502325842934193n_assn) (Va tptp.list_P8527749157015355191n_assn)) (= Xb (@ (@ tptp.cons_P2971678138204555879n_assn V3) Va))) _let_1))))))))))) (forall ((X tptp.int) (Y tptp.int) (Xs tptp.list_int)) (let ((_let_1 (@ (@ tptp.count_list_int Xs) Y))) (let ((_let_2 (@ (@ tptp.count_list_int (@ (@ tptp.cons_int X) Xs)) Y))) (let ((_let_3 (= X Y))) (and (=> _let_3 (= _let_2 (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((X tptp.nat) (Y tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ (@ tptp.count_list_nat Xs) Y))) (let ((_let_2 (@ (@ tptp.count_list_nat (@ (@ tptp.cons_nat X) Xs)) Y))) (let ((_let_3 (= X Y))) (and (=> _let_3 (= _let_2 (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((X tptp.produc6575502325842934193n_assn) (Y tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ (@ tptp.count_2530312006313534765n_assn Xs) Y))) (let ((_let_2 (@ (@ tptp.count_2530312006313534765n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X) Xs)) Y))) (let ((_let_3 (= X Y))) (and (=> _let_3 (= _let_2 (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((X tptp.produc3843707927480180839at_nat) (Xs tptp.list_P5464809261938338413at_nat)) (=> (not (@ (@ tptp.member8757157785044589968at_nat X) (@ tptp.set_Pr3765526544606949372at_nat Xs))) (= (@ (@ tptp.count_1483299019173949923at_nat Xs) X) tptp.zero_zero_nat))) (forall ((X tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (=> (not (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs))) (= (@ (@ tptp.count_4203492906077236349at_nat Xs) X) tptp.zero_zero_nat))) (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xs tptp.list_P7985473006766602707_nat_o)) (=> (not (@ (@ tptp.member6576561426505652726_nat_o X) (@ tptp.set_Pr400311997697478754_nat_o Xs))) (= (@ (@ tptp.count_5695430372156137289_nat_o Xs) X) tptp.zero_zero_nat))) (forall ((X tptp.int) (Xs tptp.list_int)) (=> (not (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs))) (= (@ (@ tptp.count_list_int Xs) X) tptp.zero_zero_nat))) (forall ((X tptp.nat) (Xs tptp.list_nat)) (=> (not (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs))) (= (@ (@ tptp.count_list_nat Xs) X) tptp.zero_zero_nat))) (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (=> (not (@ (@ tptp.member7957490590177025114n_assn X) (@ tptp.set_Pr1139785259514867910n_assn Xs))) (= (@ (@ tptp.count_2530312006313534765n_assn Xs) X) tptp.zero_zero_nat))) (forall ((B2 tptp.rat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B2))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B2) (=> (@ (@ tptp.ord_less_rat B2) tptp.one_one_rat) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M2)))))) (forall ((B2 tptp.code_integer) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger B2))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) tptp.one_one_Code_integer) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M2)))))) (forall ((B2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (=> (@ (@ tptp.ord_less_nat B2) tptp.one_one_nat) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M2)))))) (forall ((B2 tptp.int) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_int B2) tptp.one_one_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M2)))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (F4 (-> tptp.set_Pr1261947904930325089at_nat tptp.nat)) (Fs tptp.list_s9130966667114977576at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Y)))) (let ((_let_2 (@ F4 Y))) (let ((_let_3 (@ F4 X))) (= (@ _let_1 (@ tptp.measur2694323259624372065at_nat (@ (@ tptp.cons_s2538900923071588440at_nat F4) Fs))) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ _let_1 (@ tptp.measur2694323259624372065at_nat Fs))))))))) (forall ((X tptp.nat) (Y tptp.nat) (F4 (-> tptp.nat tptp.nat)) (Fs tptp.list_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)))) (let ((_let_2 (@ F4 Y))) (let ((_let_3 (@ F4 X))) (= (@ _let_1 (@ tptp.measures_nat (@ (@ tptp.cons_nat_nat F4) Fs))) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ _let_1 (@ tptp.measures_nat Fs))))))))) (forall ((X tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat X) N)) (or (@ _let_1 X) (= N tptp.zero_zero_nat))))) (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (= (= (@ (@ tptp.zip_int_int Xs) Ys) tptp.nil_Pr2300489316682597567nt_int) (or (= Xs tptp.nil_int) (= Ys tptp.nil_int)))) (forall ((Xs tptp.list_int) (Ys tptp.list_nat)) (= (= (@ (@ tptp.zip_int_nat Xs) Ys) tptp.nil_Pr6478340336191794275nt_nat) (or (= Xs tptp.nil_int) (= Ys tptp.nil_nat)))) (forall ((Xs tptp.list_int) (Ys tptp.list_P8527749157015355191n_assn)) (= (= (@ (@ tptp.zip_in7098856637274830732n_assn Xs) Ys) tptp.nil_Pr2440414457004260852n_assn) (or (= Xs tptp.nil_int) (= Ys tptp.nil_Pr5671120429643327159n_assn)))) (forall ((Xs tptp.list_nat) (Ys tptp.list_int)) (= (= (@ (@ tptp.zip_nat_int Xs) Ys) tptp.nil_Pr1301135604781543011at_int) (or (= Xs tptp.nil_nat) (= Ys tptp.nil_int)))) (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (= (= (@ (@ tptp.zip_nat_nat Xs) Ys) tptp.nil_Pr5478986624290739719at_nat) (or (= Xs tptp.nil_nat) (= Ys tptp.nil_nat)))) (forall ((Xs tptp.list_nat) (Ys tptp.list_P8527749157015355191n_assn)) (= (= (@ (@ tptp.zip_na5338819973521719528n_assn Xs) Ys) tptp.nil_Pr680377793251149648n_assn) (or (= Xs tptp.nil_nat) (= Ys tptp.nil_Pr5671120429643327159n_assn)))) (forall ((Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_int)) (= (= (@ (@ tptp.zip_Pr1015554993053626726sn_int Xs) Ys) tptp.nil_Pr7991254345159696774sn_int) (or (= Xs tptp.nil_Pr5671120429643327159n_assn) (= Ys tptp.nil_int)))) (forall ((Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_nat)) (= (= (@ (@ tptp.zip_Pr1018045463562677002sn_nat Xs) Ys) tptp.nil_Pr2945733327814117674sn_nat) (or (= Xs tptp.nil_Pr5671120429643327159n_assn) (= Ys tptp.nil_nat)))) (forall ((Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_P8527749157015355191n_assn)) (= (= (@ (@ tptp.zip_Pr8806919808394484215n_assn Xs) Ys) tptp.nil_Pr4327835960982145133n_assn) (or (= Xs tptp.nil_Pr5671120429643327159n_assn) (= Ys tptp.nil_Pr5671120429643327159n_assn)))) (forall ((Xs tptp.list_assn) (Ys tptp.list_assn)) (= (= (@ (@ tptp.zip_assn_assn Xs) Ys) tptp.nil_Pr5671120429643327159n_assn) (or (= Xs tptp.nil_assn) (= Ys tptp.nil_assn)))) (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (= (= tptp.nil_Pr2300489316682597567nt_int (@ (@ tptp.zip_int_int Xs) Ys)) (or (= Xs tptp.nil_int) (= Ys tptp.nil_int)))) (forall ((Xs tptp.list_int) (Ys tptp.list_nat)) (= (= tptp.nil_Pr6478340336191794275nt_nat (@ (@ tptp.zip_int_nat Xs) Ys)) (or (= Xs tptp.nil_int) (= Ys tptp.nil_nat)))) (forall ((Xs tptp.list_int) (Ys tptp.list_P8527749157015355191n_assn)) (= (= tptp.nil_Pr2440414457004260852n_assn (@ (@ tptp.zip_in7098856637274830732n_assn Xs) Ys)) (or (= Xs tptp.nil_int) (= Ys tptp.nil_Pr5671120429643327159n_assn)))) (forall ((Xs tptp.list_nat) (Ys tptp.list_int)) (= (= tptp.nil_Pr1301135604781543011at_int (@ (@ tptp.zip_nat_int Xs) Ys)) (or (= Xs tptp.nil_nat) (= Ys tptp.nil_int)))) (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (= (= tptp.nil_Pr5478986624290739719at_nat (@ (@ tptp.zip_nat_nat Xs) Ys)) (or (= Xs tptp.nil_nat) (= Ys tptp.nil_nat)))) (forall ((Xs tptp.list_nat) (Ys tptp.list_P8527749157015355191n_assn)) (= (= tptp.nil_Pr680377793251149648n_assn (@ (@ tptp.zip_na5338819973521719528n_assn Xs) Ys)) (or (= Xs tptp.nil_nat) (= Ys tptp.nil_Pr5671120429643327159n_assn)))) (forall ((Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_int)) (= (= tptp.nil_Pr7991254345159696774sn_int (@ (@ tptp.zip_Pr1015554993053626726sn_int Xs) Ys)) (or (= Xs tptp.nil_Pr5671120429643327159n_assn) (= Ys tptp.nil_int)))) (forall ((Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_nat)) (= (= tptp.nil_Pr2945733327814117674sn_nat (@ (@ tptp.zip_Pr1018045463562677002sn_nat Xs) Ys)) (or (= Xs tptp.nil_Pr5671120429643327159n_assn) (= Ys tptp.nil_nat)))) (forall ((Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_P8527749157015355191n_assn)) (= (= tptp.nil_Pr4327835960982145133n_assn (@ (@ tptp.zip_Pr8806919808394484215n_assn Xs) Ys)) (or (= Xs tptp.nil_Pr5671120429643327159n_assn) (= Ys tptp.nil_Pr5671120429643327159n_assn)))) (forall ((Xs tptp.list_assn) (Ys tptp.list_assn)) (= (= tptp.nil_Pr5671120429643327159n_assn (@ (@ tptp.zip_assn_assn Xs) Ys)) (or (= Xs tptp.nil_assn) (= Ys tptp.nil_assn)))) (forall ((Ys tptp.list_assn)) (= (@ (@ tptp.zip_assn_assn tptp.nil_assn) Ys) tptp.nil_Pr5671120429643327159n_assn)) (forall ((Xs tptp.list_int)) (= (= tptp.nil_int (@ tptp.rev_int Xs)) (= Xs tptp.nil_int))) (forall ((Xs tptp.list_nat)) (= (= tptp.nil_nat (@ tptp.rev_nat Xs)) (= Xs tptp.nil_nat))) (forall ((Xs tptp.list_P8527749157015355191n_assn)) (= (= tptp.nil_Pr5671120429643327159n_assn (@ tptp.rev_Pr4855572775806611735n_assn Xs)) (= Xs tptp.nil_Pr5671120429643327159n_assn))) (forall ((Xs tptp.list_int)) (= (= (@ tptp.rev_int Xs) tptp.nil_int) (= Xs tptp.nil_int))) (forall ((Xs tptp.list_nat)) (= (= (@ tptp.rev_nat Xs) tptp.nil_nat) (= Xs tptp.nil_nat))) (forall ((Xs tptp.list_P8527749157015355191n_assn)) (= (= (@ tptp.rev_Pr4855572775806611735n_assn Xs) tptp.nil_Pr5671120429643327159n_assn) (= Xs tptp.nil_Pr5671120429643327159n_assn))) (forall ((Xs tptp.list_int) (K3 tptp.nat) (X tptp.int)) (= (= (@ (@ (@ tptp.list_update_int Xs) K3) X) tptp.nil_int) (= Xs tptp.nil_int))) (forall ((Xs tptp.list_nat) (K3 tptp.nat) (X tptp.nat)) (= (= (@ (@ (@ tptp.list_update_nat Xs) K3) X) tptp.nil_nat) (= Xs tptp.nil_nat))) (forall ((Xs tptp.list_P8527749157015355191n_assn) (K3 tptp.nat) (X tptp.produc6575502325842934193n_assn)) (= (= (@ (@ (@ tptp.list_u4534839942911652127n_assn Xs) K3) X) tptp.nil_Pr5671120429643327159n_assn) (= Xs tptp.nil_Pr5671120429643327159n_assn))) (forall ((Xs tptp.list_c) (K3 tptp.nat) (X tptp.c)) (= (= (@ (@ (@ tptp.list_update_c Xs) K3) X) tptp.nil_c) (= Xs tptp.nil_c))) (forall ((Xs tptp.list_d) (K3 tptp.nat) (X tptp.d)) (= (= (@ (@ (@ tptp.list_update_d Xs) K3) X) tptp.nil_d) (= Xs tptp.nil_d))) (forall ((N tptp.nat)) (= (@ (@ tptp.enumerate_int N) tptp.nil_int) tptp.nil_Pr1301135604781543011at_int)) (forall ((N tptp.nat)) (= (@ (@ tptp.enumerate_nat N) tptp.nil_nat) tptp.nil_Pr5478986624290739719at_nat)) (forall ((N tptp.nat)) (= (@ (@ tptp.enumer9200277086812776726n_assn N) tptp.nil_Pr5671120429643327159n_assn) tptp.nil_Pr680377793251149648n_assn)) (forall ((Xs tptp.list_int)) (= (= (@ tptp.rotate1_int Xs) tptp.nil_int) (= Xs tptp.nil_int))) (forall ((Xs tptp.list_nat)) (= (= (@ tptp.rotate1_nat Xs) tptp.nil_nat) (= Xs tptp.nil_nat))) (forall ((Xs tptp.list_P8527749157015355191n_assn)) (= (= (@ tptp.rotate328796349445179396n_assn Xs) tptp.nil_Pr5671120429643327159n_assn) (= Xs tptp.nil_Pr5671120429643327159n_assn))) (forall ((P (-> tptp.int Bool))) (not (@ (@ tptp.list_ex_int P) tptp.nil_int))) (forall ((P (-> tptp.nat Bool))) (not (@ (@ tptp.list_ex_nat P) tptp.nil_nat))) (forall ((P (-> tptp.produc6575502325842934193n_assn Bool))) (not (@ (@ tptp.list_e1087220904399170805n_assn P) tptp.nil_Pr5671120429643327159n_assn))) (forall ((Begin tptp.nat) (End tptp.nat)) (= (@ (@ (@ tptp.slice_int Begin) End) tptp.nil_int) tptp.nil_int)) (forall ((Begin tptp.nat) (End tptp.nat)) (= (@ (@ (@ tptp.slice_nat Begin) End) tptp.nil_nat) tptp.nil_nat)) (forall ((Begin tptp.nat) (End tptp.nat)) (= (@ (@ (@ tptp.slice_7964966981652229398n_assn Begin) End) tptp.nil_Pr5671120429643327159n_assn) tptp.nil_Pr5671120429643327159n_assn)) (forall ((I tptp.nat) (Xs tptp.list_int)) (= (@ (@ (@ tptp.slice_int I) I) Xs) tptp.nil_int)) (forall ((I tptp.nat) (Xs tptp.list_nat)) (= (@ (@ (@ tptp.slice_nat I) I) Xs) tptp.nil_nat)) (forall ((I tptp.nat) (Xs tptp.list_P8527749157015355191n_assn)) (= (@ (@ (@ tptp.slice_7964966981652229398n_assn I) I) Xs) tptp.nil_Pr5671120429643327159n_assn)) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (not (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X) Y)) (@ tptp.measur2694323259624372065at_nat tptp.nil_se7398569966080822440at_nat)))) (forall ((X tptp.nat) (Y tptp.nat)) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ tptp.measures_nat tptp.nil_nat_nat)))) (forall ((A2 tptp.rat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A2))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A2) (= (= (@ _let_1 M2) (@ _let_1 N)) (= M2 N))))) (forall ((A2 tptp.code_integer) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A2))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A2) (= (= (@ _let_1 M2) (@ _let_1 N)) (= M2 N))))) (forall ((A2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A2) (= (= (@ _let_1 M2) (@ _let_1 N)) (= M2 N))))) (forall ((A2 tptp.int) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A2))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A2) (= (= (@ _let_1 M2) (@ _let_1 N)) (= M2 N))))) (forall ((Xs tptp.list_P8527749157015355191n_assn)) (= (= (@ tptp.set_Pr1139785259514867910n_assn Xs) tptp.bot_bo1176836662018730877n_assn) (= Xs tptp.nil_Pr5671120429643327159n_assn))) (forall ((Xs tptp.list_P5464809261938338413at_nat)) (= (= (@ tptp.set_Pr3765526544606949372at_nat Xs) tptp.bot_bo228742789529271731at_nat) (= Xs tptp.nil_Pr8341282898164651117at_nat))) (forall ((Xs tptp.list_P6011104703257516679at_nat)) (= (= (@ tptp.set_Pr5648618587558075414at_nat Xs) tptp.bot_bo2099793752762293965at_nat) (= Xs tptp.nil_Pr5478986624290739719at_nat))) (forall ((Xs tptp.list_o)) (= (= (@ tptp.set_o2 Xs) tptp.bot_bot_set_o) (= Xs tptp.nil_o))) (forall ((Xs tptp.list_nat)) (= (= (@ tptp.set_nat2 Xs) tptp.bot_bot_set_nat) (= Xs tptp.nil_nat))) (forall ((Xs tptp.list_int)) (= (= (@ tptp.set_int2 Xs) tptp.bot_bot_set_int) (= Xs tptp.nil_int))) (forall ((Xs tptp.list_P8527749157015355191n_assn)) (= (= tptp.bot_bo1176836662018730877n_assn (@ tptp.set_Pr1139785259514867910n_assn Xs)) (= Xs tptp.nil_Pr5671120429643327159n_assn))) (forall ((Xs tptp.list_P5464809261938338413at_nat)) (= (= tptp.bot_bo228742789529271731at_nat (@ tptp.set_Pr3765526544606949372at_nat Xs)) (= Xs tptp.nil_Pr8341282898164651117at_nat))) (forall ((Xs tptp.list_P6011104703257516679at_nat)) (= (= tptp.bot_bo2099793752762293965at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs)) (= Xs tptp.nil_Pr5478986624290739719at_nat))) (forall ((Xs tptp.list_o)) (= (= tptp.bot_bot_set_o (@ tptp.set_o2 Xs)) (= Xs tptp.nil_o))) (forall ((Xs tptp.list_nat)) (= (= tptp.bot_bot_set_nat (@ tptp.set_nat2 Xs)) (= Xs tptp.nil_nat))) (forall ((Xs tptp.list_int)) (= (= tptp.bot_bot_set_int (@ tptp.set_int2 Xs)) (= Xs tptp.nil_int))) (forall ((Xs tptp.list_P8527749157015355191n_assn)) (= (= (@ tptp.size_s6829681357464350627n_assn Xs) tptp.zero_zero_nat) (= Xs tptp.nil_Pr5671120429643327159n_assn))) (forall ((Xs tptp.list_c)) (= (= (@ tptp.size_size_list_c Xs) tptp.zero_zero_nat) (= Xs tptp.nil_c))) (forall ((Xs tptp.list_d)) (= (= (@ tptp.size_size_list_d Xs) tptp.zero_zero_nat) (= Xs tptp.nil_d))) (forall ((Xs tptp.list_nat)) (= (= (@ tptp.size_size_list_nat Xs) tptp.zero_zero_nat) (= Xs tptp.nil_nat))) (forall ((Xs tptp.list_int)) (= (= (@ tptp.size_size_list_int Xs) tptp.zero_zero_nat) (= Xs tptp.nil_int))) (forall ((X tptp.int) (Xs tptp.list_int)) (let ((_let_1 (@ (@ tptp.cons_int X) tptp.nil_int))) (= (= _let_1 (@ tptp.rev_int Xs)) (= _let_1 Xs)))) (forall ((X tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat X) tptp.nil_nat))) (= (= _let_1 (@ tptp.rev_nat Xs)) (= _let_1 Xs)))) (forall ((X tptp.produc6575502325842934193n_assn) (Xs tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ (@ tptp.cons_P2971678138204555879n_assn X) tptp.nil_Pr5671120429643327159n_assn))) (= (= _let_1 (@ tptp.rev_Pr4855572775806611735n_assn Xs)) (= _let_1 Xs)))) (forall ((Xs tptp.list_int) (X tptp.int)) (let ((_let_1 (@ (@ tptp.cons_int X) tptp.nil_int))) (= (= (@ tptp.rev_int Xs) _let_1) (= Xs _let_1)))) (forall ((Xs tptp.list_nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.cons_nat X) tptp.nil_nat))) (= (= (@ tptp.rev_nat Xs) _let_1) (= Xs _let_1)))) (forall ((Xs tptp.list_P8527749157015355191n_assn) (X tptp.produc6575502325842934193n_assn)) (let ((_let_1 (@ (@ tptp.cons_P2971678138204555879n_assn X) tptp.nil_Pr5671120429643327159n_assn))) (= (= (@ tptp.rev_Pr4855572775806611735n_assn Xs) _let_1) (= Xs _let_1)))) (forall ((Ns tptp.list_int) (R2 tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int tptp.nil_int) Ns)) (@ tptp.lenlex_int R2)) (not (= Ns tptp.nil_int)))) (forall ((Ns tptp.list_nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat tptp.nil_nat) Ns)) (@ tptp.lenlex_nat R2)) (not (= Ns tptp.nil_nat)))) (forall ((Ns tptp.list_P8527749157015355191n_assn) (R2 tptp.set_Pr8116311503512020807n_assn)) (= (@ (@ tptp.member3994142547374651152n_assn (@ (@ tptp.produc3014731801419794263n_assn tptp.nil_Pr5671120429643327159n_assn) Ns)) (@ tptp.lenlex6671093235567761724n_assn R2)) (not (= Ns tptp.nil_Pr5671120429643327159n_assn)))) (forall ((X tptp.int)) (= (@ (@ tptp.insert_int X) tptp.nil_int) (@ (@ tptp.cons_int X) tptp.nil_int))) (forall ((X tptp.nat)) (= (@ (@ tptp.insert_nat X) tptp.nil_nat) (@ (@ tptp.cons_nat X) tptp.nil_nat))) (forall ((X tptp.produc6575502325842934193n_assn)) (= (@ (@ tptp.insert3246601298802261197n_assn X) tptp.nil_Pr5671120429643327159n_assn) (@ (@ tptp.cons_P2971678138204555879n_assn X) tptp.nil_Pr5671120429643327159n_assn))) (forall ((P (-> tptp.int tptp.int tptp.assn)) (L3 tptp.list_int)) (= (@ (@ (@ tptp.vEBT_L74593716426352029nt_int P) tptp.nil_int) L3) (@ tptp.pure_assn (= L3 tptp.nil_int)))) (forall ((P (-> tptp.int tptp.nat tptp.assn)) (L3 tptp.list_nat)) (= (@ (@ (@ tptp.vEBT_L77084186935402305nt_nat P) tptp.nil_int) L3) (@ tptp.pure_assn (= L3 tptp.nil_nat)))) (forall ((P (-> tptp.int tptp.produc6575502325842934193n_assn tptp.assn)) (L3 tptp.list_P8527749157015355191n_assn)) (= (@ (@ (@ tptp.vEBT_L1620274777744359680n_assn P) tptp.nil_int) L3) (@ tptp.pure_assn (= L3 tptp.nil_Pr5671120429643327159n_assn)))) (forall ((P (-> tptp.nat tptp.int tptp.assn)) (L3 tptp.list_int)) (= (@ (@ (@ tptp.vEBT_L8298612041380073281at_int P) tptp.nil_nat) L3) (@ tptp.pure_assn (= L3 tptp.nil_int)))) (forall ((P (-> tptp.nat tptp.nat tptp.assn)) (L3 tptp.list_nat)) (= (@ (@ (@ tptp.vEBT_L8301102511889123557at_nat P) tptp.nil_nat) L3) (@ tptp.pure_assn (= L3 tptp.nil_nat)))) (forall ((P (-> tptp.nat tptp.produc6575502325842934193n_assn tptp.assn)) (L3 tptp.list_P8527749157015355191n_assn)) (= (@ (@ (@ tptp.vEBT_L9083610150846024284n_assn P) tptp.nil_nat) L3) (@ tptp.pure_assn (= L3 tptp.nil_Pr5671120429643327159n_assn)))) (forall ((P (-> tptp.produc6575502325842934193n_assn tptp.int tptp.assn)) (L3 tptp.list_int)) (= (@ (@ (@ tptp.vEBT_L4760345170377931482sn_int P) tptp.nil_Pr5671120429643327159n_assn) L3) (@ tptp.pure_assn (= L3 tptp.nil_int)))) (forall ((P (-> tptp.produc6575502325842934193n_assn tptp.nat tptp.assn)) (L3 tptp.list_nat)) (= (@ (@ (@ tptp.vEBT_L4762835640886981758sn_nat P) tptp.nil_Pr5671120429643327159n_assn) L3) (@ tptp.pure_assn (= L3 tptp.nil_nat)))) (forall ((P (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn tptp.assn)) (L3 tptp.list_P8527749157015355191n_assn)) (= (@ (@ (@ tptp.vEBT_L3108143461992071043n_assn P) tptp.nil_Pr5671120429643327159n_assn) L3) (@ tptp.pure_assn (= L3 tptp.nil_Pr5671120429643327159n_assn)))) (forall ((P (-> tptp.int tptp.int tptp.assn)) (L tptp.list_int)) (= (@ (@ (@ tptp.vEBT_L74593716426352029nt_int P) L) tptp.nil_int) (@ tptp.pure_assn (= L tptp.nil_int)))) (forall ((P (-> tptp.nat tptp.int tptp.assn)) (L tptp.list_nat)) (= (@ (@ (@ tptp.vEBT_L8298612041380073281at_int P) L) tptp.nil_int) (@ tptp.pure_assn (= L tptp.nil_nat)))) (forall ((P (-> tptp.produc6575502325842934193n_assn tptp.int tptp.assn)) (L tptp.list_P8527749157015355191n_assn)) (= (@ (@ (@ tptp.vEBT_L4760345170377931482sn_int P) L) tptp.nil_int) (@ tptp.pure_assn (= L tptp.nil_Pr5671120429643327159n_assn)))) (forall ((P (-> tptp.int tptp.nat tptp.assn)) (L tptp.list_int)) (= (@ (@ (@ tptp.vEBT_L77084186935402305nt_nat P) L) tptp.nil_nat) (@ tptp.pure_assn (= L tptp.nil_int)))) (forall ((P (-> tptp.nat tptp.nat tptp.assn)) (L tptp.list_nat)) (= (@ (@ (@ tptp.vEBT_L8301102511889123557at_nat P) L) tptp.nil_nat) (@ tptp.pure_assn (= L tptp.nil_nat)))) (forall ((P (-> tptp.produc6575502325842934193n_assn tptp.nat tptp.assn)) (L tptp.list_P8527749157015355191n_assn)) (= (@ (@ (@ tptp.vEBT_L4762835640886981758sn_nat P) L) tptp.nil_nat) (@ tptp.pure_assn (= L tptp.nil_Pr5671120429643327159n_assn)))) (forall ((P (-> tptp.int tptp.produc6575502325842934193n_assn tptp.assn)) (L tptp.list_int)) (= (@ (@ (@ tptp.vEBT_L1620274777744359680n_assn P) L) tptp.nil_Pr5671120429643327159n_assn) (@ tptp.pure_assn (= L tptp.nil_int)))) (forall ((P (-> tptp.nat tptp.produc6575502325842934193n_assn tptp.assn)) (L tptp.list_nat)) (= (@ (@ (@ tptp.vEBT_L9083610150846024284n_assn P) L) tptp.nil_Pr5671120429643327159n_assn) (@ tptp.pure_assn (= L tptp.nil_nat)))) (forall ((P (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn tptp.assn)) (L tptp.list_P8527749157015355191n_assn)) (= (@ (@ (@ tptp.vEBT_L3108143461992071043n_assn P) L) tptp.nil_Pr5671120429643327159n_assn) (@ tptp.pure_assn (= L tptp.nil_Pr5671120429643327159n_assn)))) (forall ((B2 tptp.rat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B2))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) B2) (= (@ (@ tptp.ord_less_rat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))) (forall ((B2 tptp.code_integer) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger B2))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) B2) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))) (forall ((B2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B2) (= (@ (@ tptp.ord_less_nat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))) (forall ((B2 tptp.int) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B2))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B2) (= (@ (@ tptp.ord_less_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))) (forall ((A2 tptp.code_integer) (N tptp.nat)) (= (= (@ (@ tptp.power_8256067586552552935nteger A2) N) tptp.zero_z3403309356797280102nteger) (and (= A2 tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((A2 tptp.rat) (N tptp.nat)) (= (= (@ (@ tptp.power_power_rat A2) N) tptp.zero_zero_rat) (and (= A2 tptp.zero_zero_rat) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((A2 tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.power_power_nat A2) N) tptp.zero_zero_nat) (and (= A2 tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((A2 tptp.int) (N tptp.nat)) (= (= (@ (@ tptp.power_power_int A2) N) tptp.zero_zero_int) (and (= A2 tptp.zero_zero_int) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((Xs tptp.list_P8527749157015355191n_assn)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s6829681357464350627n_assn Xs)) (not (= Xs tptp.nil_Pr5671120429643327159n_assn)))) (forall ((Xs tptp.list_c)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_c Xs)) (not (= Xs tptp.nil_c)))) (forall ((Xs tptp.list_d)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_d Xs)) (not (= Xs tptp.nil_d)))) (forall ((Xs tptp.list_nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_nat Xs)) (not (= Xs tptp.nil_nat)))) (forall ((Xs tptp.list_int)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_int Xs)) (not (= Xs tptp.nil_int)))) (forall ((B2 tptp.rat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B2))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B2) (=> (@ (@ tptp.ord_less_rat B2) tptp.one_one_rat) (= (@ (@ tptp.ord_less_rat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M2)))))) (forall ((B2 tptp.code_integer) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger B2))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger B2) tptp.one_one_Code_integer) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M2)))))) (forall ((B2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (=> (@ (@ tptp.ord_less_nat B2) tptp.one_one_nat) (= (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M2)))))) (forall ((B2 tptp.int) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_int B2) tptp.one_one_int) (= (@ (@ tptp.ord_less_int (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M2)))))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A2) N)) (@ (@ tptp.power_8256067586552552935nteger B2) N)) (@ (@ tptp.ord_le3102999989581377725nteger A2) B2))))))) (forall ((A2 tptp.rat) (B2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A2) N)) (@ (@ tptp.power_power_rat B2) N)) (@ (@ tptp.ord_less_eq_rat A2) B2))))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A2) N)) (@ (@ tptp.power_power_nat B2) N)) (@ (@ tptp.ord_less_eq_nat A2) B2))))))) (forall ((A2 tptp.int) (B2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A2) N)) (@ (@ tptp.power_power_int B2) N)) (@ (@ tptp.ord_less_eq_int A2) B2))))))) (forall ((B2 tptp.rat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B2))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) B2) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))) (forall ((B2 tptp.code_integer) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger B2))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) B2) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))) (forall ((B2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B2) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))) (forall ((B2 tptp.int) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B2))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B2) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))) (forall ((L tptp.list_P8527749157015355191n_assn)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.size_s6829681357464350627n_assn L)) (not (= L tptp.nil_Pr5671120429643327159n_assn)))) (forall ((L tptp.list_c)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.size_size_list_c L)) (not (= L tptp.nil_c)))) (forall ((L tptp.list_d)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.size_size_list_d L)) (not (= L tptp.nil_d)))) (forall ((L tptp.list_nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.size_size_list_nat L)) (not (= L tptp.nil_nat)))) (forall ((L tptp.list_int)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.size_size_list_int L)) (not (= L tptp.nil_int)))) (forall ((X tptp.list_list_int)) (=> (not (= X tptp.nil_list_int)) (=> (forall ((Xss tptp.list_list_int)) (not (= X (@ (@ tptp.cons_list_int tptp.nil_int) Xss)))) (not (forall ((X3 tptp.int) (Xs2 tptp.list_int) (Xss tptp.list_list_int)) (not (= X (@ (@ tptp.cons_list_int (@ (@ tptp.cons_int X3) Xs2)) Xss)))))))) (forall ((X tptp.list_list_nat)) (=> (not (= X tptp.nil_list_nat)) (=> (forall ((Xss tptp.list_list_nat)) (not (= X (@ (@ tptp.cons_list_nat tptp.nil_nat) Xss)))) (not (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Xss tptp.list_list_nat)) (not (= X (@ (@ tptp.cons_list_nat (@ (@ tptp.cons_nat X3) Xs2)) Xss)))))))) (forall ((X tptp.list_l6351802567095793725n_assn)) (=> (not (= X tptp.nil_li5476096274760905021n_assn)) (=> (forall ((Xss tptp.list_l6351802567095793725n_assn)) (not (= X (@ (@ tptp.cons_l2423627976422276333n_assn tptp.nil_Pr5671120429643327159n_assn) Xss)))) (not (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn) (Xss tptp.list_l6351802567095793725n_assn)) (not (= X (@ (@ tptp.cons_l2423627976422276333n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)) Xss)))))))) (forall ((Ns tptp.list_int) (R2 tptp.set_Pr958786334691620121nt_int)) (not (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Ns) tptp.nil_int)) (@ tptp.lenlex_int R2)))) (forall ((Ns tptp.list_nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (not (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Ns) tptp.nil_nat)) (@ tptp.lenlex_nat R2)))) (forall ((Ns tptp.list_P8527749157015355191n_assn) (R2 tptp.set_Pr8116311503512020807n_assn)) (not (@ (@ tptp.member3994142547374651152n_assn (@ (@ tptp.produc3014731801419794263n_assn Ns) tptp.nil_Pr5671120429643327159n_assn)) (@ tptp.lenlex6671093235567761724n_assn R2)))) (forall ((Xs tptp.list_int) (R2 tptp.set_Pr958786334691620121nt_int)) (not (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Xs) tptp.nil_int)) (@ tptp.lex_int R2)))) (forall ((Xs tptp.list_nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (not (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Xs) tptp.nil_nat)) (@ tptp.lex_nat R2)))) (forall ((Xs tptp.list_P8527749157015355191n_assn) (R2 tptp.set_Pr8116311503512020807n_assn)) (not (@ (@ tptp.member3994142547374651152n_assn (@ (@ tptp.produc3014731801419794263n_assn Xs) tptp.nil_Pr5671120429643327159n_assn)) (@ tptp.lex_Pr7559194461235888923n_assn R2)))) (forall ((Ys tptp.list_int) (R2 tptp.set_Pr958786334691620121nt_int)) (not (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int tptp.nil_int) Ys)) (@ tptp.lex_int R2)))) (forall ((Ys tptp.list_nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (not (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat tptp.nil_nat) Ys)) (@ tptp.lex_nat R2)))) (forall ((Ys tptp.list_P8527749157015355191n_assn) (R2 tptp.set_Pr8116311503512020807n_assn)) (not (@ (@ tptp.member3994142547374651152n_assn (@ (@ tptp.produc3014731801419794263n_assn tptp.nil_Pr5671120429643327159n_assn) Ys)) (@ tptp.lex_Pr7559194461235888923n_assn R2)))) (forall ((Xs tptp.list_assn)) (= (@ (@ tptp.zip_assn_assn Xs) tptp.nil_assn) tptp.nil_Pr5671120429643327159n_assn)) (forall ((A tptp.multis2468970476368604999at_nat) (B tptp.multis2468970476368604999at_nat) (M5 tptp.multis2468970476368604999at_nat) (N7 tptp.multis2468970476368604999at_nat)) (=> (= (@ (@ tptp.plus_p7104986032573967614at_nat A) B) (@ (@ tptp.plus_p7104986032573967614at_nat M5) N7)) (not (forall ((Am tptp.multis2468970476368604999at_nat) (An tptp.multis2468970476368604999at_nat)) (=> (= A (@ (@ tptp.plus_p7104986032573967614at_nat Am) An)) (forall ((Bm tptp.multis2468970476368604999at_nat) (Bn tptp.multis2468970476368604999at_nat)) (=> (= B (@ (@ tptp.plus_p7104986032573967614at_nat Bm) Bn)) (=> (= M5 (@ (@ tptp.plus_p7104986032573967614at_nat Am) Bm)) (not (= N7 (@ (@ tptp.plus_p7104986032573967614at_nat An) Bn))))))))))) (forall ((Y tptp.int)) (= (@ (@ tptp.count_list_int tptp.nil_int) Y) tptp.zero_zero_nat)) (forall ((Y tptp.nat)) (= (@ (@ tptp.count_list_nat tptp.nil_nat) Y) tptp.zero_zero_nat)) (forall ((Y tptp.produc6575502325842934193n_assn)) (= (@ (@ tptp.count_2530312006313534765n_assn tptp.nil_Pr5671120429643327159n_assn) Y) tptp.zero_zero_nat)) (forall ((Uu tptp.list_assn)) (= (@ (@ tptp.product_assn_assn tptp.nil_assn) Uu) tptp.nil_Pr5671120429643327159n_assn)) (forall ((A2 tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger A2) N))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) A2) (@ (@ tptp.times_3573771949741848930nteger A2) _let_1)))) (forall ((A2 tptp.assn) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_assn A2) N))) (= (@ (@ tptp.times_times_assn _let_1) A2) (@ (@ tptp.times_times_assn A2) _let_1)))) (forall ((A2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A2) N))) (= (@ (@ tptp.times_times_rat _let_1) A2) (@ (@ tptp.times_times_rat A2) _let_1)))) (forall ((A2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A2) N))) (= (@ (@ tptp.times_times_nat _let_1) A2) (@ (@ tptp.times_times_nat A2) _let_1)))) (forall ((A2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A2) N))) (= (@ (@ tptp.times_times_int _let_1) A2) (@ (@ tptp.times_times_int A2) _let_1)))) (forall ((A2 tptp.code_integer) (B2 tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.times_3573771949741848930nteger A2) B2)) N) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger A2) N)) (@ (@ tptp.power_8256067586552552935nteger B2) N)))) (forall ((A2 tptp.assn) (B2 tptp.assn) (N tptp.nat)) (= (@ (@ tptp.power_power_assn (@ (@ tptp.times_times_assn A2) B2)) N) (@ (@ tptp.times_times_assn (@ (@ tptp.power_power_assn A2) N)) (@ (@ tptp.power_power_assn B2) N)))) (forall ((A2 tptp.rat) (B2 tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ (@ tptp.times_times_rat A2) B2)) N) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat A2) N)) (@ (@ tptp.power_power_rat B2) N)))) (forall ((A2 tptp.nat) (B2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.times_times_nat A2) B2)) N) (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat A2) N)) (@ (@ tptp.power_power_nat B2) N)))) (forall ((A2 tptp.int) (B2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.times_times_int A2) B2)) N) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int A2) N)) (@ (@ tptp.power_power_int B2) N)))) (forall ((X tptp.code_integer) (Y tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger X) N))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger Y))) (=> (= (@ (@ tptp.times_3573771949741848930nteger X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) Y) (@ _let_2 _let_1)))))) (forall ((X tptp.assn) (Y tptp.assn) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_assn X) N))) (let ((_let_2 (@ tptp.times_times_assn Y))) (=> (= (@ (@ tptp.times_times_assn X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_times_assn _let_1) Y) (@ _let_2 _let_1)))))) (forall ((X tptp.rat) (Y tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat X) N))) (let ((_let_2 (@ tptp.times_times_rat Y))) (=> (= (@ (@ tptp.times_times_rat X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_times_rat _let_1) Y) (@ _let_2 _let_1)))))) (forall ((X tptp.nat) (Y tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat X) N))) (let ((_let_2 (@ tptp.times_times_nat Y))) (=> (= (@ (@ tptp.times_times_nat X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_times_nat _let_1) Y) (@ _let_2 _let_1)))))) (forall ((X tptp.int) (Y tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int X) N))) (let ((_let_2 (@ tptp.times_times_int Y))) (=> (= (@ (@ tptp.times_times_int X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_times_int _let_1) Y) (@ _let_2 _let_1)))))) (forall ((X tptp.produc5834231552977413017st_int)) (=> (forall ((P5 (-> tptp.int tptp.int Bool))) (not (= X (@ (@ tptp.produc8618682346314911123st_int P5) tptp.nil_int)))) (=> (forall ((P5 (-> tptp.int tptp.int Bool)) (X3 tptp.int)) (not (= X (@ (@ tptp.produc8618682346314911123st_int P5) (@ (@ tptp.cons_int X3) tptp.nil_int))))) (not (forall ((P5 (-> tptp.int tptp.int Bool)) (X3 tptp.int) (Y2 tptp.int) (Xs2 tptp.list_int)) (not (= X (@ (@ tptp.produc8618682346314911123st_int P5) (@ (@ tptp.cons_int X3) (@ (@ tptp.cons_int Y2) Xs2)))))))))) (forall ((X tptp.produc254973753779126261st_nat)) (=> (forall ((P5 (-> tptp.nat tptp.nat Bool))) (not (= X (@ (@ tptp.produc4727192421694094319st_nat P5) tptp.nil_nat)))) (=> (forall ((P5 (-> tptp.nat tptp.nat Bool)) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc4727192421694094319st_nat P5) (@ (@ tptp.cons_nat X3) tptp.nil_nat))))) (not (forall ((P5 (-> tptp.nat tptp.nat Bool)) (X3 tptp.nat) (Y2 tptp.nat) (Xs2 tptp.list_nat)) (not (= X (@ (@ tptp.produc4727192421694094319st_nat P5) (@ (@ tptp.cons_nat X3) (@ (@ tptp.cons_nat Y2) Xs2)))))))))) (forall ((X tptp.produc4530688714081574576n_assn)) (=> (forall ((P5 (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn Bool))) (not (= X (@ (@ tptp.produc6115016301897879072n_assn P5) tptp.nil_Pr5671120429643327159n_assn)))) (=> (forall ((P5 (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn Bool)) (X3 tptp.produc6575502325842934193n_assn)) (not (= X (@ (@ tptp.produc6115016301897879072n_assn P5) (@ (@ tptp.cons_P2971678138204555879n_assn X3) tptp.nil_Pr5671120429643327159n_assn))))) (not (forall ((P5 (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn Bool)) (X3 tptp.produc6575502325842934193n_assn) (Y2 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn)) (not (= X (@ (@ tptp.produc6115016301897879072n_assn P5) (@ (@ tptp.cons_P2971678138204555879n_assn X3) (@ (@ tptp.cons_P2971678138204555879n_assn Y2) Xs2)))))))))) (forall ((X tptp.produc5834231552977413017st_int)) (=> (forall ((P5 (-> tptp.int tptp.int Bool))) (not (= X (@ (@ tptp.produc8618682346314911123st_int P5) tptp.nil_int)))) (not (forall ((P5 (-> tptp.int tptp.int Bool)) (X3 tptp.int) (Ys5 tptp.list_int)) (not (= X (@ (@ tptp.produc8618682346314911123st_int P5) (@ (@ tptp.cons_int X3) Ys5)))))))) (forall ((X tptp.produc254973753779126261st_nat)) (=> (forall ((P5 (-> tptp.nat tptp.nat Bool))) (not (= X (@ (@ tptp.produc4727192421694094319st_nat P5) tptp.nil_nat)))) (not (forall ((P5 (-> tptp.nat tptp.nat Bool)) (X3 tptp.nat) (Ys5 tptp.list_nat)) (not (= X (@ (@ tptp.produc4727192421694094319st_nat P5) (@ (@ tptp.cons_nat X3) Ys5)))))))) (forall ((X tptp.produc4530688714081574576n_assn)) (=> (forall ((P5 (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn Bool))) (not (= X (@ (@ tptp.produc6115016301897879072n_assn P5) tptp.nil_Pr5671120429643327159n_assn)))) (not (forall ((P5 (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn Bool)) (X3 tptp.produc6575502325842934193n_assn) (Ys5 tptp.list_P8527749157015355191n_assn)) (not (= X (@ (@ tptp.produc6115016301897879072n_assn P5) (@ (@ tptp.cons_P2971678138204555879n_assn X3) Ys5)))))))) (forall ((L tptp.list_int)) (=> (not (= L tptp.nil_int)) (not (forall ((X3 tptp.int) (Xs2 tptp.list_int)) (not (= L (@ (@ tptp.cons_int X3) Xs2))))))) (forall ((L tptp.list_nat)) (=> (not (= L tptp.nil_nat)) (not (forall ((X3 tptp.nat) (Xs2 tptp.list_nat)) (not (= L (@ (@ tptp.cons_nat X3) Xs2))))))) (forall ((L tptp.list_P8527749157015355191n_assn)) (=> (not (= L tptp.nil_Pr5671120429643327159n_assn)) (not (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn)) (not (= L (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2))))))) (forall ((P (-> tptp.list_int tptp.list_int Bool)) (W1 tptp.list_int) (W2 tptp.list_int)) (=> (@ (@ P tptp.nil_int) tptp.nil_int) (=> (forall ((E2 tptp.int) (W12 tptp.list_int) (W22 tptp.list_int)) (=> (@ (@ P W12) W22) (@ (@ P (@ (@ tptp.cons_int E2) W12)) W22))) (=> (forall ((E2 tptp.int) (W13 tptp.list_int) (W23 tptp.list_int)) (let ((_let_1 (@ P W13))) (=> (@ _let_1 W23) (@ _let_1 (@ (@ tptp.cons_int E2) W23))))) (@ (@ P W1) W2))))) (forall ((P (-> tptp.list_int tptp.list_nat Bool)) (W1 tptp.list_int) (W2 tptp.list_nat)) (=> (@ (@ P tptp.nil_int) tptp.nil_nat) (=> (forall ((E2 tptp.int) (W12 tptp.list_int) (W22 tptp.list_nat)) (=> (@ (@ P W12) W22) (@ (@ P (@ (@ tptp.cons_int E2) W12)) W22))) (=> (forall ((E2 tptp.nat) (W13 tptp.list_int) (W23 tptp.list_nat)) (let ((_let_1 (@ P W13))) (=> (@ _let_1 W23) (@ _let_1 (@ (@ tptp.cons_nat E2) W23))))) (@ (@ P W1) W2))))) (forall ((P (-> tptp.list_int tptp.list_P8527749157015355191n_assn Bool)) (W1 tptp.list_int) (W2 tptp.list_P8527749157015355191n_assn)) (=> (@ (@ P tptp.nil_int) tptp.nil_Pr5671120429643327159n_assn) (=> (forall ((E2 tptp.int) (W12 tptp.list_int) (W22 tptp.list_P8527749157015355191n_assn)) (=> (@ (@ P W12) W22) (@ (@ P (@ (@ tptp.cons_int E2) W12)) W22))) (=> (forall ((E2 tptp.produc6575502325842934193n_assn) (W13 tptp.list_int) (W23 tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ P W13))) (=> (@ _let_1 W23) (@ _let_1 (@ (@ tptp.cons_P2971678138204555879n_assn E2) W23))))) (@ (@ P W1) W2))))) (forall ((P (-> tptp.list_nat tptp.list_int Bool)) (W1 tptp.list_nat) (W2 tptp.list_int)) (=> (@ (@ P tptp.nil_nat) tptp.nil_int) (=> (forall ((E2 tptp.nat) (W12 tptp.list_nat) (W22 tptp.list_int)) (=> (@ (@ P W12) W22) (@ (@ P (@ (@ tptp.cons_nat E2) W12)) W22))) (=> (forall ((E2 tptp.int) (W13 tptp.list_nat) (W23 tptp.list_int)) (let ((_let_1 (@ P W13))) (=> (@ _let_1 W23) (@ _let_1 (@ (@ tptp.cons_int E2) W23))))) (@ (@ P W1) W2))))) (forall ((P (-> tptp.list_nat tptp.list_nat Bool)) (W1 tptp.list_nat) (W2 tptp.list_nat)) (=> (@ (@ P tptp.nil_nat) tptp.nil_nat) (=> (forall ((E2 tptp.nat) (W12 tptp.list_nat) (W22 tptp.list_nat)) (=> (@ (@ P W12) W22) (@ (@ P (@ (@ tptp.cons_nat E2) W12)) W22))) (=> (forall ((E2 tptp.nat) (W13 tptp.list_nat) (W23 tptp.list_nat)) (let ((_let_1 (@ P W13))) (=> (@ _let_1 W23) (@ _let_1 (@ (@ tptp.cons_nat E2) W23))))) (@ (@ P W1) W2))))) (forall ((P (-> tptp.list_nat tptp.list_P8527749157015355191n_assn Bool)) (W1 tptp.list_nat) (W2 tptp.list_P8527749157015355191n_assn)) (=> (@ (@ P tptp.nil_nat) tptp.nil_Pr5671120429643327159n_assn) (=> (forall ((E2 tptp.nat) (W12 tptp.list_nat) (W22 tptp.list_P8527749157015355191n_assn)) (=> (@ (@ P W12) W22) (@ (@ P (@ (@ tptp.cons_nat E2) W12)) W22))) (=> (forall ((E2 tptp.produc6575502325842934193n_assn) (W13 tptp.list_nat) (W23 tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ P W13))) (=> (@ _let_1 W23) (@ _let_1 (@ (@ tptp.cons_P2971678138204555879n_assn E2) W23))))) (@ (@ P W1) W2))))) (forall ((P (-> tptp.list_P8527749157015355191n_assn tptp.list_int Bool)) (W1 tptp.list_P8527749157015355191n_assn) (W2 tptp.list_int)) (=> (@ (@ P tptp.nil_Pr5671120429643327159n_assn) tptp.nil_int) (=> (forall ((E2 tptp.produc6575502325842934193n_assn) (W12 tptp.list_P8527749157015355191n_assn) (W22 tptp.list_int)) (=> (@ (@ P W12) W22) (@ (@ P (@ (@ tptp.cons_P2971678138204555879n_assn E2) W12)) W22))) (=> (forall ((E2 tptp.int) (W13 tptp.list_P8527749157015355191n_assn) (W23 tptp.list_int)) (let ((_let_1 (@ P W13))) (=> (@ _let_1 W23) (@ _let_1 (@ (@ tptp.cons_int E2) W23))))) (@ (@ P W1) W2))))) (forall ((P (-> tptp.list_P8527749157015355191n_assn tptp.list_nat Bool)) (W1 tptp.list_P8527749157015355191n_assn) (W2 tptp.list_nat)) (=> (@ (@ P tptp.nil_Pr5671120429643327159n_assn) tptp.nil_nat) (=> (forall ((E2 tptp.produc6575502325842934193n_assn) (W12 tptp.list_P8527749157015355191n_assn) (W22 tptp.list_nat)) (=> (@ (@ P W12) W22) (@ (@ P (@ (@ tptp.cons_P2971678138204555879n_assn E2) W12)) W22))) (=> (forall ((E2 tptp.nat) (W13 tptp.list_P8527749157015355191n_assn) (W23 tptp.list_nat)) (let ((_let_1 (@ P W13))) (=> (@ _let_1 W23) (@ _let_1 (@ (@ tptp.cons_nat E2) W23))))) (@ (@ P W1) W2))))) (forall ((P (-> tptp.list_P8527749157015355191n_assn tptp.list_P8527749157015355191n_assn Bool)) (W1 tptp.list_P8527749157015355191n_assn) (W2 tptp.list_P8527749157015355191n_assn)) (=> (@ (@ P tptp.nil_Pr5671120429643327159n_assn) tptp.nil_Pr5671120429643327159n_assn) (=> (forall ((E2 tptp.produc6575502325842934193n_assn) (W12 tptp.list_P8527749157015355191n_assn) (W22 tptp.list_P8527749157015355191n_assn)) (=> (@ (@ P W12) W22) (@ (@ P (@ (@ tptp.cons_P2971678138204555879n_assn E2) W12)) W22))) (=> (forall ((E2 tptp.produc6575502325842934193n_assn) (W13 tptp.list_P8527749157015355191n_assn) (W23 tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ P W13))) (=> (@ _let_1 W23) (@ _let_1 (@ (@ tptp.cons_P2971678138204555879n_assn E2) W23))))) (@ (@ P W1) W2))))) (forall ((P (-> tptp.list_int Bool)) (Xs tptp.list_int)) (=> (@ P tptp.nil_int) (=> (forall ((X3 tptp.int)) (@ P (@ (@ tptp.cons_int X3) tptp.nil_int))) (=> (forall ((X12 tptp.int) (X23 tptp.int) (Xs2 tptp.list_int)) (=> (@ P Xs2) (@ P (@ (@ tptp.cons_int X12) (@ (@ tptp.cons_int X23) Xs2))))) (@ P Xs))))) (forall ((P (-> tptp.list_nat Bool)) (Xs tptp.list_nat)) (=> (@ P tptp.nil_nat) (=> (forall ((X3 tptp.nat)) (@ P (@ (@ tptp.cons_nat X3) tptp.nil_nat))) (=> (forall ((X12 tptp.nat) (X23 tptp.nat) (Xs2 tptp.list_nat)) (=> (@ P Xs2) (@ P (@ (@ tptp.cons_nat X12) (@ (@ tptp.cons_nat X23) Xs2))))) (@ P Xs))))) (forall ((P (-> tptp.list_P8527749157015355191n_assn Bool)) (Xs tptp.list_P8527749157015355191n_assn)) (=> (@ P tptp.nil_Pr5671120429643327159n_assn) (=> (forall ((X3 tptp.produc6575502325842934193n_assn)) (@ P (@ (@ tptp.cons_P2971678138204555879n_assn X3) tptp.nil_Pr5671120429643327159n_assn))) (=> (forall ((X12 tptp.produc6575502325842934193n_assn) (X23 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn)) (=> (@ P Xs2) (@ P (@ (@ tptp.cons_P2971678138204555879n_assn X12) (@ (@ tptp.cons_P2971678138204555879n_assn X23) Xs2))))) (@ P Xs))))) (forall ((P (-> tptp.list_int tptp.list_int Bool)) (R (-> tptp.int tptp.int Bool)) (Xs tptp.list_int) (Ys tptp.list_int)) (=> (forall ((Xs2 tptp.list_int)) (@ (@ P Xs2) tptp.nil_int)) (=> (forall ((X_1 tptp.list_int)) (@ (@ P tptp.nil_int) X_1)) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int) (Y2 tptp.int) (Ys5 tptp.list_int)) (let ((_let_1 (@ (@ tptp.cons_int Y2) Ys5))) (=> (@ (@ R X3) Y2) (=> (@ (@ P Xs2) _let_1) (@ (@ P (@ (@ tptp.cons_int X3) Xs2)) _let_1))))) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int) (Y2 tptp.int) (Ys5 tptp.list_int)) (let ((_let_1 (@ P (@ (@ tptp.cons_int X3) Xs2)))) (=> (not (@ (@ R X3) Y2)) (=> (@ _let_1 Ys5) (@ _let_1 (@ (@ tptp.cons_int Y2) Ys5)))))) (@ (@ P Xs) Ys)))))) (forall ((P (-> tptp.list_nat tptp.list_int Bool)) (R (-> tptp.nat tptp.int Bool)) (Xs tptp.list_nat) (Ys tptp.list_int)) (=> (forall ((Xs2 tptp.list_nat)) (@ (@ P Xs2) tptp.nil_int)) (=> (forall ((X_1 tptp.list_int)) (@ (@ P tptp.nil_nat) X_1)) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.int) (Ys5 tptp.list_int)) (let ((_let_1 (@ (@ tptp.cons_int Y2) Ys5))) (=> (@ (@ R X3) Y2) (=> (@ (@ P Xs2) _let_1) (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) _let_1))))) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.int) (Ys5 tptp.list_int)) (let ((_let_1 (@ P (@ (@ tptp.cons_nat X3) Xs2)))) (=> (not (@ (@ R X3) Y2)) (=> (@ _let_1 Ys5) (@ _let_1 (@ (@ tptp.cons_int Y2) Ys5)))))) (@ (@ P Xs) Ys)))))) (forall ((P (-> tptp.list_P8527749157015355191n_assn tptp.list_int Bool)) (R (-> tptp.produc6575502325842934193n_assn tptp.int Bool)) (Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_int)) (=> (forall ((Xs2 tptp.list_P8527749157015355191n_assn)) (@ (@ P Xs2) tptp.nil_int)) (=> (forall ((X_1 tptp.list_int)) (@ (@ P tptp.nil_Pr5671120429643327159n_assn) X_1)) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn) (Y2 tptp.int) (Ys5 tptp.list_int)) (let ((_let_1 (@ (@ tptp.cons_int Y2) Ys5))) (=> (@ (@ R X3) Y2) (=> (@ (@ P Xs2) _let_1) (@ (@ P (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)) _let_1))))) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn) (Y2 tptp.int) (Ys5 tptp.list_int)) (let ((_let_1 (@ P (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)))) (=> (not (@ (@ R X3) Y2)) (=> (@ _let_1 Ys5) (@ _let_1 (@ (@ tptp.cons_int Y2) Ys5)))))) (@ (@ P Xs) Ys)))))) (forall ((P (-> tptp.list_int tptp.list_nat Bool)) (R (-> tptp.int tptp.nat Bool)) (Xs tptp.list_int) (Ys tptp.list_nat)) (=> (forall ((Xs2 tptp.list_int)) (@ (@ P Xs2) tptp.nil_nat)) (=> (forall ((X_1 tptp.list_nat)) (@ (@ P tptp.nil_int) X_1)) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int) (Y2 tptp.nat) (Ys5 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat Y2) Ys5))) (=> (@ (@ R X3) Y2) (=> (@ (@ P Xs2) _let_1) (@ (@ P (@ (@ tptp.cons_int X3) Xs2)) _let_1))))) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int) (Y2 tptp.nat) (Ys5 tptp.list_nat)) (let ((_let_1 (@ P (@ (@ tptp.cons_int X3) Xs2)))) (=> (not (@ (@ R X3) Y2)) (=> (@ _let_1 Ys5) (@ _let_1 (@ (@ tptp.cons_nat Y2) Ys5)))))) (@ (@ P Xs) Ys)))))) (forall ((P (-> tptp.list_nat tptp.list_nat Bool)) (R (-> tptp.nat tptp.nat Bool)) (Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (forall ((Xs2 tptp.list_nat)) (@ (@ P Xs2) tptp.nil_nat)) (=> (forall ((X_1 tptp.list_nat)) (@ (@ P tptp.nil_nat) X_1)) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.nat) (Ys5 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat Y2) Ys5))) (=> (@ (@ R X3) Y2) (=> (@ (@ P Xs2) _let_1) (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) _let_1))))) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.nat) (Ys5 tptp.list_nat)) (let ((_let_1 (@ P (@ (@ tptp.cons_nat X3) Xs2)))) (=> (not (@ (@ R X3) Y2)) (=> (@ _let_1 Ys5) (@ _let_1 (@ (@ tptp.cons_nat Y2) Ys5)))))) (@ (@ P Xs) Ys)))))) (forall ((P (-> tptp.list_P8527749157015355191n_assn tptp.list_nat Bool)) (R (-> tptp.produc6575502325842934193n_assn tptp.nat Bool)) (Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_nat)) (=> (forall ((Xs2 tptp.list_P8527749157015355191n_assn)) (@ (@ P Xs2) tptp.nil_nat)) (=> (forall ((X_1 tptp.list_nat)) (@ (@ P tptp.nil_Pr5671120429643327159n_assn) X_1)) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn) (Y2 tptp.nat) (Ys5 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat Y2) Ys5))) (=> (@ (@ R X3) Y2) (=> (@ (@ P Xs2) _let_1) (@ (@ P (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)) _let_1))))) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn) (Y2 tptp.nat) (Ys5 tptp.list_nat)) (let ((_let_1 (@ P (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)))) (=> (not (@ (@ R X3) Y2)) (=> (@ _let_1 Ys5) (@ _let_1 (@ (@ tptp.cons_nat Y2) Ys5)))))) (@ (@ P Xs) Ys)))))) (forall ((P (-> tptp.list_int tptp.list_P8527749157015355191n_assn Bool)) (R (-> tptp.int tptp.produc6575502325842934193n_assn Bool)) (Xs tptp.list_int) (Ys tptp.list_P8527749157015355191n_assn)) (=> (forall ((Xs2 tptp.list_int)) (@ (@ P Xs2) tptp.nil_Pr5671120429643327159n_assn)) (=> (forall ((X_1 tptp.list_P8527749157015355191n_assn)) (@ (@ P tptp.nil_int) X_1)) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int) (Y2 tptp.produc6575502325842934193n_assn) (Ys5 tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ (@ tptp.cons_P2971678138204555879n_assn Y2) Ys5))) (=> (@ (@ R X3) Y2) (=> (@ (@ P Xs2) _let_1) (@ (@ P (@ (@ tptp.cons_int X3) Xs2)) _let_1))))) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int) (Y2 tptp.produc6575502325842934193n_assn) (Ys5 tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ P (@ (@ tptp.cons_int X3) Xs2)))) (=> (not (@ (@ R X3) Y2)) (=> (@ _let_1 Ys5) (@ _let_1 (@ (@ tptp.cons_P2971678138204555879n_assn Y2) Ys5)))))) (@ (@ P Xs) Ys)))))) (forall ((P (-> tptp.list_nat tptp.list_P8527749157015355191n_assn Bool)) (R (-> tptp.nat tptp.produc6575502325842934193n_assn Bool)) (Xs tptp.list_nat) (Ys tptp.list_P8527749157015355191n_assn)) (=> (forall ((Xs2 tptp.list_nat)) (@ (@ P Xs2) tptp.nil_Pr5671120429643327159n_assn)) (=> (forall ((X_1 tptp.list_P8527749157015355191n_assn)) (@ (@ P tptp.nil_nat) X_1)) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.produc6575502325842934193n_assn) (Ys5 tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ (@ tptp.cons_P2971678138204555879n_assn Y2) Ys5))) (=> (@ (@ R X3) Y2) (=> (@ (@ P Xs2) _let_1) (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) _let_1))))) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.produc6575502325842934193n_assn) (Ys5 tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ P (@ (@ tptp.cons_nat X3) Xs2)))) (=> (not (@ (@ R X3) Y2)) (=> (@ _let_1 Ys5) (@ _let_1 (@ (@ tptp.cons_P2971678138204555879n_assn Y2) Ys5)))))) (@ (@ P Xs) Ys)))))) (forall ((P (-> tptp.list_P8527749157015355191n_assn tptp.list_P8527749157015355191n_assn Bool)) (R (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn Bool)) (Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_P8527749157015355191n_assn)) (=> (forall ((Xs2 tptp.list_P8527749157015355191n_assn)) (@ (@ P Xs2) tptp.nil_Pr5671120429643327159n_assn)) (=> (forall ((X_1 tptp.list_P8527749157015355191n_assn)) (@ (@ P tptp.nil_Pr5671120429643327159n_assn) X_1)) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn) (Y2 tptp.produc6575502325842934193n_assn) (Ys5 tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ (@ tptp.cons_P2971678138204555879n_assn Y2) Ys5))) (=> (@ (@ R X3) Y2) (=> (@ (@ P Xs2) _let_1) (@ (@ P (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)) _let_1))))) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn) (Y2 tptp.produc6575502325842934193n_assn) (Ys5 tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ P (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)))) (=> (not (@ (@ R X3) Y2)) (=> (@ _let_1 Ys5) (@ _let_1 (@ (@ tptp.cons_P2971678138204555879n_assn Y2) Ys5)))))) (@ (@ P Xs) Ys)))))) (forall ((X21 tptp.int) (X222 tptp.list_int)) (not (= tptp.nil_int (@ (@ tptp.cons_int X21) X222)))) (forall ((X21 tptp.nat) (X222 tptp.list_nat)) (not (= tptp.nil_nat (@ (@ tptp.cons_nat X21) X222)))) (forall ((X21 tptp.produc6575502325842934193n_assn) (X222 tptp.list_P8527749157015355191n_assn)) (not (= tptp.nil_Pr5671120429643327159n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X21) X222)))) (forall ((List tptp.list_int) (X21 tptp.int) (X222 tptp.list_int)) (=> (= List (@ (@ tptp.cons_int X21) X222)) (not (= List tptp.nil_int)))) (forall ((List tptp.list_nat) (X21 tptp.nat) (X222 tptp.list_nat)) (=> (= List (@ (@ tptp.cons_nat X21) X222)) (not (= List tptp.nil_nat)))) (forall ((List tptp.list_P8527749157015355191n_assn) (X21 tptp.produc6575502325842934193n_assn) (X222 tptp.list_P8527749157015355191n_assn)) (=> (= List (@ (@ tptp.cons_P2971678138204555879n_assn X21) X222)) (not (= List tptp.nil_Pr5671120429643327159n_assn)))) (forall ((Y tptp.list_int)) (=> (not (= Y tptp.nil_int)) (not (forall ((X212 tptp.int) (X223 tptp.list_int)) (not (= Y (@ (@ tptp.cons_int X212) X223))))))) (forall ((Y tptp.list_nat)) (=> (not (= Y tptp.nil_nat)) (not (forall ((X212 tptp.nat) (X223 tptp.list_nat)) (not (= Y (@ (@ tptp.cons_nat X212) X223))))))) (forall ((Y tptp.list_P8527749157015355191n_assn)) (=> (not (= Y tptp.nil_Pr5671120429643327159n_assn)) (not (forall ((X212 tptp.produc6575502325842934193n_assn) (X223 tptp.list_P8527749157015355191n_assn)) (not (= Y (@ (@ tptp.cons_P2971678138204555879n_assn X212) X223))))))) (forall ((X tptp.list_int)) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int)) (not (= X (@ (@ tptp.cons_int X3) Xs2)))) (= X tptp.nil_int))) (forall ((X tptp.list_nat)) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat)) (not (= X (@ (@ tptp.cons_nat X3) Xs2)))) (= X tptp.nil_nat))) (forall ((X tptp.list_int)) (=> (not (= X tptp.nil_int)) (=> (forall ((X3 tptp.int)) (not (= X (@ (@ tptp.cons_int X3) tptp.nil_int)))) (not (forall ((X3 tptp.int) (Y2 tptp.int) (Xs2 tptp.list_int)) (not (= X (@ (@ tptp.cons_int X3) (@ (@ tptp.cons_int Y2) Xs2))))))))) (forall ((X tptp.list_nat)) (=> (not (= X tptp.nil_nat)) (=> (forall ((X3 tptp.nat)) (not (= X (@ (@ tptp.cons_nat X3) tptp.nil_nat)))) (not (forall ((X3 tptp.nat) (Y2 tptp.nat) (Xs2 tptp.list_nat)) (not (= X (@ (@ tptp.cons_nat X3) (@ (@ tptp.cons_nat Y2) Xs2))))))))) (forall ((X tptp.list_P8527749157015355191n_assn)) (=> (not (= X tptp.nil_Pr5671120429643327159n_assn)) (=> (forall ((X3 tptp.produc6575502325842934193n_assn)) (not (= X (@ (@ tptp.cons_P2971678138204555879n_assn X3) tptp.nil_Pr5671120429643327159n_assn)))) (not (forall ((X3 tptp.produc6575502325842934193n_assn) (Y2 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn)) (not (= X (@ (@ tptp.cons_P2971678138204555879n_assn X3) (@ (@ tptp.cons_P2971678138204555879n_assn Y2) Xs2))))))))) (forall ((Xs tptp.list_int)) (= (not (= Xs tptp.nil_int)) (exists ((Y5 tptp.int) (Ys3 tptp.list_int)) (= Xs (@ (@ tptp.cons_int Y5) Ys3))))) (forall ((Xs tptp.list_nat)) (= (not (= Xs tptp.nil_nat)) (exists ((Y5 tptp.nat) (Ys3 tptp.list_nat)) (= Xs (@ (@ tptp.cons_nat Y5) Ys3))))) (forall ((Xs tptp.list_P8527749157015355191n_assn)) (= (not (= Xs tptp.nil_Pr5671120429643327159n_assn)) (exists ((Y5 tptp.produc6575502325842934193n_assn) (Ys3 tptp.list_P8527749157015355191n_assn)) (= Xs (@ (@ tptp.cons_P2971678138204555879n_assn Y5) Ys3))))) (forall ((P (-> tptp.list_int tptp.list_int Bool)) (Xs tptp.list_int) (Ys tptp.list_int)) (=> (@ (@ P tptp.nil_int) tptp.nil_int) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int)) (@ (@ P (@ (@ tptp.cons_int X3) Xs2)) tptp.nil_int)) (=> (forall ((Y2 tptp.int) (Ys5 tptp.list_int)) (@ (@ P tptp.nil_int) (@ (@ tptp.cons_int Y2) Ys5))) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int) (Y2 tptp.int) (Ys5 tptp.list_int)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ tptp.cons_int X3) Xs2)) (@ (@ tptp.cons_int Y2) Ys5)))) (@ (@ P Xs) Ys)))))) (forall ((P (-> tptp.list_int tptp.list_nat Bool)) (Xs tptp.list_int) (Ys tptp.list_nat)) (=> (@ (@ P tptp.nil_int) tptp.nil_nat) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int)) (@ (@ P (@ (@ tptp.cons_int X3) Xs2)) tptp.nil_nat)) (=> (forall ((Y2 tptp.nat) (Ys5 tptp.list_nat)) (@ (@ P tptp.nil_int) (@ (@ tptp.cons_nat Y2) Ys5))) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int) (Y2 tptp.nat) (Ys5 tptp.list_nat)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ tptp.cons_int X3) Xs2)) (@ (@ tptp.cons_nat Y2) Ys5)))) (@ (@ P Xs) Ys)))))) (forall ((P (-> tptp.list_int tptp.list_P8527749157015355191n_assn Bool)) (Xs tptp.list_int) (Ys tptp.list_P8527749157015355191n_assn)) (=> (@ (@ P tptp.nil_int) tptp.nil_Pr5671120429643327159n_assn) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int)) (@ (@ P (@ (@ tptp.cons_int X3) Xs2)) tptp.nil_Pr5671120429643327159n_assn)) (=> (forall ((Y2 tptp.produc6575502325842934193n_assn) (Ys5 tptp.list_P8527749157015355191n_assn)) (@ (@ P tptp.nil_int) (@ (@ tptp.cons_P2971678138204555879n_assn Y2) Ys5))) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int) (Y2 tptp.produc6575502325842934193n_assn) (Ys5 tptp.list_P8527749157015355191n_assn)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ tptp.cons_int X3) Xs2)) (@ (@ tptp.cons_P2971678138204555879n_assn Y2) Ys5)))) (@ (@ P Xs) Ys)))))) (forall ((P (-> tptp.list_nat tptp.list_int Bool)) (Xs tptp.list_nat) (Ys tptp.list_int)) (=> (@ (@ P tptp.nil_nat) tptp.nil_int) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat)) (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) tptp.nil_int)) (=> (forall ((Y2 tptp.int) (Ys5 tptp.list_int)) (@ (@ P tptp.nil_nat) (@ (@ tptp.cons_int Y2) Ys5))) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.int) (Ys5 tptp.list_int)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) (@ (@ tptp.cons_int Y2) Ys5)))) (@ (@ P Xs) Ys)))))) (forall ((P (-> tptp.list_nat tptp.list_nat Bool)) (Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (@ (@ P tptp.nil_nat) tptp.nil_nat) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat)) (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) tptp.nil_nat)) (=> (forall ((Y2 tptp.nat) (Ys5 tptp.list_nat)) (@ (@ P tptp.nil_nat) (@ (@ tptp.cons_nat Y2) Ys5))) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.nat) (Ys5 tptp.list_nat)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) (@ (@ tptp.cons_nat Y2) Ys5)))) (@ (@ P Xs) Ys)))))) (forall ((P (-> tptp.list_nat tptp.list_P8527749157015355191n_assn Bool)) (Xs tptp.list_nat) (Ys tptp.list_P8527749157015355191n_assn)) (=> (@ (@ P tptp.nil_nat) tptp.nil_Pr5671120429643327159n_assn) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat)) (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) tptp.nil_Pr5671120429643327159n_assn)) (=> (forall ((Y2 tptp.produc6575502325842934193n_assn) (Ys5 tptp.list_P8527749157015355191n_assn)) (@ (@ P tptp.nil_nat) (@ (@ tptp.cons_P2971678138204555879n_assn Y2) Ys5))) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.produc6575502325842934193n_assn) (Ys5 tptp.list_P8527749157015355191n_assn)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) (@ (@ tptp.cons_P2971678138204555879n_assn Y2) Ys5)))) (@ (@ P Xs) Ys)))))) (forall ((P (-> tptp.list_P8527749157015355191n_assn tptp.list_int Bool)) (Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_int)) (=> (@ (@ P tptp.nil_Pr5671120429643327159n_assn) tptp.nil_int) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn)) (@ (@ P (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)) tptp.nil_int)) (=> (forall ((Y2 tptp.int) (Ys5 tptp.list_int)) (@ (@ P tptp.nil_Pr5671120429643327159n_assn) (@ (@ tptp.cons_int Y2) Ys5))) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn) (Y2 tptp.int) (Ys5 tptp.list_int)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)) (@ (@ tptp.cons_int Y2) Ys5)))) (@ (@ P Xs) Ys)))))) (forall ((P (-> tptp.list_P8527749157015355191n_assn tptp.list_nat Bool)) (Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_nat)) (=> (@ (@ P tptp.nil_Pr5671120429643327159n_assn) tptp.nil_nat) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn)) (@ (@ P (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)) tptp.nil_nat)) (=> (forall ((Y2 tptp.nat) (Ys5 tptp.list_nat)) (@ (@ P tptp.nil_Pr5671120429643327159n_assn) (@ (@ tptp.cons_nat Y2) Ys5))) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn) (Y2 tptp.nat) (Ys5 tptp.list_nat)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)) (@ (@ tptp.cons_nat Y2) Ys5)))) (@ (@ P Xs) Ys)))))) (forall ((P (-> tptp.list_P8527749157015355191n_assn tptp.list_P8527749157015355191n_assn Bool)) (Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_P8527749157015355191n_assn)) (=> (@ (@ P tptp.nil_Pr5671120429643327159n_assn) tptp.nil_Pr5671120429643327159n_assn) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn)) (@ (@ P (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)) tptp.nil_Pr5671120429643327159n_assn)) (=> (forall ((Y2 tptp.produc6575502325842934193n_assn) (Ys5 tptp.list_P8527749157015355191n_assn)) (@ (@ P tptp.nil_Pr5671120429643327159n_assn) (@ (@ tptp.cons_P2971678138204555879n_assn Y2) Ys5))) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn) (Y2 tptp.produc6575502325842934193n_assn) (Ys5 tptp.list_P8527749157015355191n_assn)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)) (@ (@ tptp.cons_P2971678138204555879n_assn Y2) Ys5)))) (@ (@ P Xs) Ys)))))) (forall ((Xs tptp.list_int) (P (-> tptp.list_int Bool))) (=> (not (= Xs tptp.nil_int)) (=> (forall ((X3 tptp.int)) (@ P (@ (@ tptp.cons_int X3) tptp.nil_int))) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int)) (=> (not (= Xs2 tptp.nil_int)) (=> (@ P Xs2) (@ P (@ (@ tptp.cons_int X3) Xs2))))) (@ P Xs))))) (forall ((Xs tptp.list_nat) (P (-> tptp.list_nat Bool))) (=> (not (= Xs tptp.nil_nat)) (=> (forall ((X3 tptp.nat)) (@ P (@ (@ tptp.cons_nat X3) tptp.nil_nat))) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat)) (=> (not (= Xs2 tptp.nil_nat)) (=> (@ P Xs2) (@ P (@ (@ tptp.cons_nat X3) Xs2))))) (@ P Xs))))) (forall ((Xs tptp.list_P8527749157015355191n_assn) (P (-> tptp.list_P8527749157015355191n_assn Bool))) (=> (not (= Xs tptp.nil_Pr5671120429643327159n_assn)) (=> (forall ((X3 tptp.produc6575502325842934193n_assn)) (@ P (@ (@ tptp.cons_P2971678138204555879n_assn X3) tptp.nil_Pr5671120429643327159n_assn))) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn)) (=> (not (= Xs2 tptp.nil_Pr5671120429643327159n_assn)) (=> (@ P Xs2) (@ P (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2))))) (@ P Xs))))) (@ tptp.distinct_int tptp.nil_int) (@ tptp.distinct_nat tptp.nil_nat) (@ tptp.distin4809818325527169450n_assn tptp.nil_Pr5671120429643327159n_assn) (forall ((P (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn Bool))) (@ (@ tptp.sorted3986126766855596574n_assn P) tptp.nil_Pr5671120429643327159n_assn)) (forall ((P (-> tptp.nat tptp.nat Bool))) (@ (@ tptp.sorted_wrt_nat P) tptp.nil_nat)) (forall ((P (-> tptp.int tptp.int Bool))) (@ (@ tptp.sorted_wrt_int P) tptp.nil_int)) (= (@ tptp.rev_int tptp.nil_int) tptp.nil_int) (= (@ tptp.rev_nat tptp.nil_nat) tptp.nil_nat) (= (@ tptp.rev_Pr4855572775806611735n_assn tptp.nil_Pr5671120429643327159n_assn) tptp.nil_Pr5671120429643327159n_assn) (forall ((I tptp.nat) (V2 tptp.int)) (= (@ (@ (@ tptp.list_update_int tptp.nil_int) I) V2) tptp.nil_int)) (forall ((I tptp.nat) (V2 tptp.nat)) (= (@ (@ (@ tptp.list_update_nat tptp.nil_nat) I) V2) tptp.nil_nat)) (forall ((I tptp.nat) (V2 tptp.produc6575502325842934193n_assn)) (= (@ (@ (@ tptp.list_u4534839942911652127n_assn tptp.nil_Pr5671120429643327159n_assn) I) V2) tptp.nil_Pr5671120429643327159n_assn)) (forall ((I tptp.nat) (V2 tptp.c)) (= (@ (@ (@ tptp.list_update_c tptp.nil_c) I) V2) tptp.nil_c)) (forall ((I tptp.nat) (V2 tptp.d)) (= (@ (@ (@ tptp.list_update_d tptp.nil_d) I) V2) tptp.nil_d)) (forall ((I tptp.nat) (Y tptp.int)) (= (@ (@ (@ tptp.list_update_int tptp.nil_int) I) Y) tptp.nil_int)) (forall ((I tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.list_update_nat tptp.nil_nat) I) Y) tptp.nil_nat)) (forall ((I tptp.nat) (Y tptp.produc6575502325842934193n_assn)) (= (@ (@ (@ tptp.list_u4534839942911652127n_assn tptp.nil_Pr5671120429643327159n_assn) I) Y) tptp.nil_Pr5671120429643327159n_assn)) (forall ((I tptp.nat) (Y tptp.c)) (= (@ (@ (@ tptp.list_update_c tptp.nil_c) I) Y) tptp.nil_c)) (forall ((I tptp.nat) (Y tptp.d)) (= (@ (@ (@ tptp.list_update_d tptp.nil_d) I) Y) tptp.nil_d)) (= (@ tptp.butlast_int tptp.nil_int) tptp.nil_int) (= (@ tptp.butlast_nat tptp.nil_nat) tptp.nil_nat) (= (@ tptp.butlas3012047794866324995n_assn tptp.nil_Pr5671120429643327159n_assn) tptp.nil_Pr5671120429643327159n_assn) (forall ((X tptp.int)) (= (@ (@ tptp.remove1_int X) tptp.nil_int) tptp.nil_int)) (forall ((X tptp.nat)) (= (@ (@ tptp.remove1_nat X) tptp.nil_nat) tptp.nil_nat)) (forall ((X tptp.produc6575502325842934193n_assn)) (= (@ (@ tptp.remove1670527618125605709n_assn X) tptp.nil_Pr5671120429643327159n_assn) tptp.nil_Pr5671120429643327159n_assn)) (forall ((X tptp.int)) (= (@ (@ tptp.removeAll_int X) tptp.nil_int) tptp.nil_int)) (forall ((X tptp.nat)) (= (@ (@ tptp.removeAll_nat X) tptp.nil_nat) tptp.nil_nat)) (forall ((X tptp.produc6575502325842934193n_assn)) (= (@ (@ tptp.remove1763081955827946941n_assn X) tptp.nil_Pr5671120429643327159n_assn) tptp.nil_Pr5671120429643327159n_assn)) (forall ((L23 tptp.list_int)) (= (@ (@ tptp.merge_int tptp.nil_int) L23) L23)) (forall ((L23 tptp.list_nat)) (= (@ (@ tptp.merge_nat tptp.nil_nat) L23) L23)) (= (@ tptp.rotate1_int tptp.nil_int) tptp.nil_int) (= (@ tptp.rotate1_nat tptp.nil_nat) tptp.nil_nat) (= (@ tptp.rotate328796349445179396n_assn tptp.nil_Pr5671120429643327159n_assn) tptp.nil_Pr5671120429643327159n_assn) (forall ((F4 (-> tptp.int tptp.int tptp.int))) (= (@ (@ (@ tptp.zipf_int_int_int F4) tptp.nil_int) tptp.nil_int) tptp.nil_int)) (forall ((F4 (-> tptp.int tptp.int tptp.nat))) (= (@ (@ (@ tptp.zipf_int_int_nat F4) tptp.nil_int) tptp.nil_int) tptp.nil_nat)) (forall ((F4 (-> tptp.int tptp.nat tptp.int))) (= (@ (@ (@ tptp.zipf_int_nat_int F4) tptp.nil_int) tptp.nil_nat) tptp.nil_int)) (forall ((F4 (-> tptp.int tptp.nat tptp.nat))) (= (@ (@ (@ tptp.zipf_int_nat_nat F4) tptp.nil_int) tptp.nil_nat) tptp.nil_nat)) (forall ((F4 (-> tptp.nat tptp.int tptp.int))) (= (@ (@ (@ tptp.zipf_nat_int_int F4) tptp.nil_nat) tptp.nil_int) tptp.nil_int)) (forall ((F4 (-> tptp.nat tptp.int tptp.nat))) (= (@ (@ (@ tptp.zipf_nat_int_nat F4) tptp.nil_nat) tptp.nil_int) tptp.nil_nat)) (forall ((F4 (-> tptp.nat tptp.nat tptp.int))) (= (@ (@ (@ tptp.zipf_nat_nat_int F4) tptp.nil_nat) tptp.nil_nat) tptp.nil_int)) (forall ((F4 (-> tptp.nat tptp.nat tptp.nat))) (= (@ (@ (@ tptp.zipf_nat_nat_nat F4) tptp.nil_nat) tptp.nil_nat) tptp.nil_nat)) (forall ((F4 (-> tptp.int tptp.int tptp.produc6575502325842934193n_assn))) (= (@ (@ (@ tptp.zipf_i7756021159461276697n_assn F4) tptp.nil_int) tptp.nil_int) tptp.nil_Pr5671120429643327159n_assn)) (forall ((F4 (-> tptp.int tptp.nat tptp.produc6575502325842934193n_assn))) (= (@ (@ (@ tptp.zipf_i5995984495708165493n_assn F4) tptp.nil_int) tptp.nil_nat) tptp.nil_Pr5671120429643327159n_assn)) (@ tptp.null_int tptp.nil_int) (@ tptp.null_nat tptp.nil_nat) (@ tptp.null_P7596217980778516671n_assn tptp.nil_Pr5671120429643327159n_assn) (forall ((Xs tptp.list_int)) (= (= Xs tptp.nil_int) (@ tptp.null_int Xs))) (forall ((Xs tptp.list_nat)) (= (= Xs tptp.nil_nat) (@ tptp.null_nat Xs))) (forall ((Xs tptp.list_P8527749157015355191n_assn)) (= (= Xs tptp.nil_Pr5671120429643327159n_assn) (@ tptp.null_P7596217980778516671n_assn Xs))) (forall ((A2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.power_power_rat A2) N))))) (forall ((A2 tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A2) N))))) (forall ((A2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.power_power_nat A2) N))))) (forall ((A2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.power_power_int A2) N))))) (forall ((X tptp.code_integer) (Y tptp.code_integer) (N tptp.nat)) (=> (= (@ (@ tptp.times_3573771949741848930nteger X) Y) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger X) N)) (@ (@ tptp.power_8256067586552552935nteger Y) N)) tptp.one_one_Code_integer))) (forall ((X tptp.assn) (Y tptp.assn) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_assn X) Y) tptp.one_one_assn) (= (@ (@ tptp.times_times_assn (@ (@ tptp.power_power_assn X) N)) (@ (@ tptp.power_power_assn Y) N)) tptp.one_one_assn))) (forall ((X tptp.rat) (Y tptp.rat) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_rat X) Y) tptp.one_one_rat) (= (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X) N)) (@ (@ tptp.power_power_rat Y) N)) tptp.one_one_rat))) (forall ((X tptp.nat) (Y tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_nat X) Y) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat X) N)) (@ (@ tptp.power_power_nat Y) N)) tptp.one_one_nat))) (forall ((X tptp.int) (Y tptp.int) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_int X) Y) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X) N)) (@ (@ tptp.power_power_int Y) N)) tptp.one_one_int))) (forall ((A2 tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_3573771949741848930nteger A2) (@ _let_1 N))))) (forall ((A2 tptp.assn) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_assn A2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_assn A2) (@ _let_1 N))))) (forall ((A2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_rat A2) (@ _let_1 N))))) (forall ((A2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat A2) (@ _let_1 N))))) (forall ((A2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int A2) (@ _let_1 N))))) (forall ((A2 tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 N)) A2)))) (forall ((A2 tptp.assn) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_assn A2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_assn (@ _let_1 N)) A2)))) (forall ((A2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_rat (@ _let_1 N)) A2)))) (forall ((A2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat (@ _let_1 N)) A2)))) (forall ((A2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int (@ _let_1 N)) A2)))) (forall ((A2 tptp.code_integer) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 M2)) (@ _let_1 N))))) (forall ((A2 tptp.assn) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_assn A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.times_times_assn (@ _let_1 M2)) (@ _let_1 N))))) (forall ((A2 tptp.rat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.times_times_rat (@ _let_1 M2)) (@ _let_1 N))))) (forall ((A2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.times_times_nat (@ _let_1 M2)) (@ _let_1 N))))) (forall ((A2 tptp.int) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.times_times_int (@ _let_1 M2)) (@ _let_1 N))))) (forall ((I tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) I) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M2) N))))) (forall ((Xs tptp.list_c) (Ys tptp.list_c) (P (-> tptp.list_c tptp.list_c Bool))) (=> (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_c Ys)) (=> (@ (@ P tptp.nil_c) tptp.nil_c) (=> (forall ((X3 tptp.c) (Xs2 tptp.list_c) (Y2 tptp.c) (Ys5 tptp.list_c)) (=> (= (@ tptp.size_size_list_c Xs2) (@ tptp.size_size_list_c Ys5)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ tptp.cons_c X3) Xs2)) (@ (@ tptp.cons_c Y2) Ys5))))) (@ (@ P Xs) Ys))))) (forall ((Xs tptp.list_c) (Ys tptp.list_d) (P (-> tptp.list_c tptp.list_d Bool))) (=> (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_d Ys)) (=> (@ (@ P tptp.nil_c) tptp.nil_d) (=> (forall ((X3 tptp.c) (Xs2 tptp.list_c) (Y2 tptp.d) (Ys5 tptp.list_d)) (=> (= (@ tptp.size_size_list_c Xs2) (@ tptp.size_size_list_d Ys5)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ tptp.cons_c X3) Xs2)) (@ (@ tptp.cons_d Y2) Ys5))))) (@ (@ P Xs) Ys))))) (forall ((Xs tptp.list_c) (Ys tptp.list_nat) (P (-> tptp.list_c tptp.list_nat Bool))) (=> (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_nat Ys)) (=> (@ (@ P tptp.nil_c) tptp.nil_nat) (=> (forall ((X3 tptp.c) (Xs2 tptp.list_c) (Y2 tptp.nat) (Ys5 tptp.list_nat)) (=> (= (@ tptp.size_size_list_c Xs2) (@ tptp.size_size_list_nat Ys5)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ tptp.cons_c X3) Xs2)) (@ (@ tptp.cons_nat Y2) Ys5))))) (@ (@ P Xs) Ys))))) (forall ((Xs tptp.list_c) (Ys tptp.list_int) (P (-> tptp.list_c tptp.list_int Bool))) (=> (= (@ tptp.size_size_list_c Xs) (@ tptp.size_size_list_int Ys)) (=> (@ (@ P tptp.nil_c) tptp.nil_int) (=> (forall ((X3 tptp.c) (Xs2 tptp.list_c) (Y2 tptp.int) (Ys5 tptp.list_int)) (=> (= (@ tptp.size_size_list_c Xs2) (@ tptp.size_size_list_int Ys5)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ tptp.cons_c X3) Xs2)) (@ (@ tptp.cons_int Y2) Ys5))))) (@ (@ P Xs) Ys))))) (forall ((Xs tptp.list_d) (Ys tptp.list_c) (P (-> tptp.list_d tptp.list_c Bool))) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_c Ys)) (=> (@ (@ P tptp.nil_d) tptp.nil_c) (=> (forall ((X3 tptp.d) (Xs2 tptp.list_d) (Y2 tptp.c) (Ys5 tptp.list_c)) (=> (= (@ tptp.size_size_list_d Xs2) (@ tptp.size_size_list_c Ys5)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ tptp.cons_d X3) Xs2)) (@ (@ tptp.cons_c Y2) Ys5))))) (@ (@ P Xs) Ys))))) (forall ((Xs tptp.list_d) (Ys tptp.list_d) (P (-> tptp.list_d tptp.list_d Bool))) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_d Ys)) (=> (@ (@ P tptp.nil_d) tptp.nil_d) (=> (forall ((X3 tptp.d) (Xs2 tptp.list_d) (Y2 tptp.d) (Ys5 tptp.list_d)) (=> (= (@ tptp.size_size_list_d Xs2) (@ tptp.size_size_list_d Ys5)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ tptp.cons_d X3) Xs2)) (@ (@ tptp.cons_d Y2) Ys5))))) (@ (@ P Xs) Ys))))) (forall ((Xs tptp.list_d) (Ys tptp.list_nat) (P (-> tptp.list_d tptp.list_nat Bool))) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_nat Ys)) (=> (@ (@ P tptp.nil_d) tptp.nil_nat) (=> (forall ((X3 tptp.d) (Xs2 tptp.list_d) (Y2 tptp.nat) (Ys5 tptp.list_nat)) (=> (= (@ tptp.size_size_list_d Xs2) (@ tptp.size_size_list_nat Ys5)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ tptp.cons_d X3) Xs2)) (@ (@ tptp.cons_nat Y2) Ys5))))) (@ (@ P Xs) Ys))))) (forall ((Xs tptp.list_d) (Ys tptp.list_int) (P (-> tptp.list_d tptp.list_int Bool))) (=> (= (@ tptp.size_size_list_d Xs) (@ tptp.size_size_list_int Ys)) (=> (@ (@ P tptp.nil_d) tptp.nil_int) (=> (forall ((X3 tptp.d) (Xs2 tptp.list_d) (Y2 tptp.int) (Ys5 tptp.list_int)) (=> (= (@ tptp.size_size_list_d Xs2) (@ tptp.size_size_list_int Ys5)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ tptp.cons_d X3) Xs2)) (@ (@ tptp.cons_int Y2) Ys5))))) (@ (@ P Xs) Ys))))) (forall ((Xs tptp.list_nat) (Ys tptp.list_c) (P (-> tptp.list_nat tptp.list_c Bool))) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_c Ys)) (=> (@ (@ P tptp.nil_nat) tptp.nil_c) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.c) (Ys5 tptp.list_c)) (=> (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_size_list_c Ys5)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) (@ (@ tptp.cons_c Y2) Ys5))))) (@ (@ P Xs) Ys))))) (forall ((Xs tptp.list_nat) (Ys tptp.list_d) (P (-> tptp.list_nat tptp.list_d Bool))) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_d Ys)) (=> (@ (@ P tptp.nil_nat) tptp.nil_d) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.d) (Ys5 tptp.list_d)) (=> (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_size_list_d Ys5)) (=> (@ (@ P Xs2) Ys5) (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) (@ (@ tptp.cons_d Y2) Ys5))))) (@ (@ P Xs) Ys))))) (forall ((Xs tptp.list_c) (Ys tptp.list_c) (Zs tptp.list_c) (P (-> tptp.list_c tptp.list_c tptp.list_c Bool))) (let ((_let_1 (@ tptp.size_size_list_c Ys))) (=> (= (@ tptp.size_size_list_c Xs) _let_1) (=> (= _let_1 (@ tptp.size_size_list_c Zs)) (=> (@ (@ (@ P tptp.nil_c) tptp.nil_c) tptp.nil_c) (=> (forall ((X3 tptp.c) (Xs2 tptp.list_c) (Y2 tptp.c) (Ys5 tptp.list_c) (Z4 tptp.c) (Zs2 tptp.list_c)) (let ((_let_1 (@ tptp.size_size_list_c Ys5))) (=> (= (@ tptp.size_size_list_c Xs2) _let_1) (=> (= _let_1 (@ tptp.size_size_list_c Zs2)) (=> (@ (@ (@ P Xs2) Ys5) Zs2) (@ (@ (@ P (@ (@ tptp.cons_c X3) Xs2)) (@ (@ tptp.cons_c Y2) Ys5)) (@ (@ tptp.cons_c Z4) Zs2))))))) (@ (@ (@ P Xs) Ys) Zs))))))) (forall ((Xs tptp.list_c) (Ys tptp.list_c) (Zs tptp.list_d) (P (-> tptp.list_c tptp.list_c tptp.list_d Bool))) (let ((_let_1 (@ tptp.size_size_list_c Ys))) (=> (= (@ tptp.size_size_list_c Xs) _let_1) (=> (= _let_1 (@ tptp.size_size_list_d Zs)) (=> (@ (@ (@ P tptp.nil_c) tptp.nil_c) tptp.nil_d) (=> (forall ((X3 tptp.c) (Xs2 tptp.list_c) (Y2 tptp.c) (Ys5 tptp.list_c) (Z4 tptp.d) (Zs2 tptp.list_d)) (let ((_let_1 (@ tptp.size_size_list_c Ys5))) (=> (= (@ tptp.size_size_list_c Xs2) _let_1) (=> (= _let_1 (@ tptp.size_size_list_d Zs2)) (=> (@ (@ (@ P Xs2) Ys5) Zs2) (@ (@ (@ P (@ (@ tptp.cons_c X3) Xs2)) (@ (@ tptp.cons_c Y2) Ys5)) (@ (@ tptp.cons_d Z4) Zs2))))))) (@ (@ (@ P Xs) Ys) Zs))))))) (forall ((Xs tptp.list_c) (Ys tptp.list_c) (Zs tptp.list_nat) (P (-> tptp.list_c tptp.list_c tptp.list_nat Bool))) (let ((_let_1 (@ tptp.size_size_list_c Ys))) (=> (= (@ tptp.size_size_list_c Xs) _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Zs)) (=> (@ (@ (@ P tptp.nil_c) tptp.nil_c) tptp.nil_nat) (=> (forall ((X3 tptp.c) (Xs2 tptp.list_c) (Y2 tptp.c) (Ys5 tptp.list_c) (Z4 tptp.nat) (Zs2 tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_c Ys5))) (=> (= (@ tptp.size_size_list_c Xs2) _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Zs2)) (=> (@ (@ (@ P Xs2) Ys5) Zs2) (@ (@ (@ P (@ (@ tptp.cons_c X3) Xs2)) (@ (@ tptp.cons_c Y2) Ys5)) (@ (@ tptp.cons_nat Z4) Zs2))))))) (@ (@ (@ P Xs) Ys) Zs))))))) (forall ((Xs tptp.list_c) (Ys tptp.list_c) (Zs tptp.list_int) (P (-> tptp.list_c tptp.list_c tptp.list_int Bool))) (let ((_let_1 (@ tptp.size_size_list_c Ys))) (=> (= (@ tptp.size_size_list_c Xs) _let_1) (=> (= _let_1 (@ tptp.size_size_list_int Zs)) (=> (@ (@ (@ P tptp.nil_c) tptp.nil_c) tptp.nil_int) (=> (forall ((X3 tptp.c) (Xs2 tptp.list_c) (Y2 tptp.c) (Ys5 tptp.list_c) (Z4 tptp.int) (Zs2 tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_c Ys5))) (=> (= (@ tptp.size_size_list_c Xs2) _let_1) (=> (= _let_1 (@ tptp.size_size_list_int Zs2)) (=> (@ (@ (@ P Xs2) Ys5) Zs2) (@ (@ (@ P (@ (@ tptp.cons_c X3) Xs2)) (@ (@ tptp.cons_c Y2) Ys5)) (@ (@ tptp.cons_int Z4) Zs2))))))) (@ (@ (@ P Xs) Ys) Zs))))))) (forall ((Xs tptp.list_c) (Ys tptp.list_d) (Zs tptp.list_c) (P (-> tptp.list_c tptp.list_d tptp.list_c Bool))) (let ((_let_1 (@ tptp.size_size_list_d Ys))) (=> (= (@ tptp.size_size_list_c Xs) _let_1) (=> (= _let_1 (@ tptp.size_size_list_c Zs)) (=> (@ (@ (@ P tptp.nil_c) tptp.nil_d) tptp.nil_c) (=> (forall ((X3 tptp.c) (Xs2 tptp.list_c) (Y2 tptp.d) (Ys5 tptp.list_d) (Z4 tptp.c) (Zs2 tptp.list_c)) (let ((_let_1 (@ tptp.size_size_list_d Ys5))) (=> (= (@ tptp.size_size_list_c Xs2) _let_1) (=> (= _let_1 (@ tptp.size_size_list_c Zs2)) (=> (@ (@ (@ P Xs2) Ys5) Zs2) (@ (@ (@ P (@ (@ tptp.cons_c X3) Xs2)) (@ (@ tptp.cons_d Y2) Ys5)) (@ (@ tptp.cons_c Z4) Zs2))))))) (@ (@ (@ P Xs) Ys) Zs))))))) (forall ((Xs tptp.list_c) (Ys tptp.list_d) (Zs tptp.list_d) (P (-> tptp.list_c tptp.list_d tptp.list_d Bool))) (let ((_let_1 (@ tptp.size_size_list_d Ys))) (=> (= (@ tptp.size_size_list_c Xs) _let_1) (=> (= _let_1 (@ tptp.size_size_list_d Zs)) (=> (@ (@ (@ P tptp.nil_c) tptp.nil_d) tptp.nil_d) (=> (forall ((X3 tptp.c) (Xs2 tptp.list_c) (Y2 tptp.d) (Ys5 tptp.list_d) (Z4 tptp.d) (Zs2 tptp.list_d)) (let ((_let_1 (@ tptp.size_size_list_d Ys5))) (=> (= (@ tptp.size_size_list_c Xs2) _let_1) (=> (= _let_1 (@ tptp.size_size_list_d Zs2)) (=> (@ (@ (@ P Xs2) Ys5) Zs2) (@ (@ (@ P (@ (@ tptp.cons_c X3) Xs2)) (@ (@ tptp.cons_d Y2) Ys5)) (@ (@ tptp.cons_d Z4) Zs2))))))) (@ (@ (@ P Xs) Ys) Zs))))))) (forall ((Xs tptp.list_c) (Ys tptp.list_d) (Zs tptp.list_nat) (P (-> tptp.list_c tptp.list_d tptp.list_nat Bool))) (let ((_let_1 (@ tptp.size_size_list_d Ys))) (=> (= (@ tptp.size_size_list_c Xs) _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Zs)) (=> (@ (@ (@ P tptp.nil_c) tptp.nil_d) tptp.nil_nat) (=> (forall ((X3 tptp.c) (Xs2 tptp.list_c) (Y2 tptp.d) (Ys5 tptp.list_d) (Z4 tptp.nat) (Zs2 tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_d Ys5))) (=> (= (@ tptp.size_size_list_c Xs2) _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Zs2)) (=> (@ (@ (@ P Xs2) Ys5) Zs2) (@ (@ (@ P (@ (@ tptp.cons_c X3) Xs2)) (@ (@ tptp.cons_d Y2) Ys5)) (@ (@ tptp.cons_nat Z4) Zs2))))))) (@ (@ (@ P Xs) Ys) Zs))))))) (forall ((Xs tptp.list_c) (Ys tptp.list_d) (Zs tptp.list_int) (P (-> tptp.list_c tptp.list_d tptp.list_int Bool))) (let ((_let_1 (@ tptp.size_size_list_d Ys))) (=> (= (@ tptp.size_size_list_c Xs) _let_1) (=> (= _let_1 (@ tptp.size_size_list_int Zs)) (=> (@ (@ (@ P tptp.nil_c) tptp.nil_d) tptp.nil_int) (=> (forall ((X3 tptp.c) (Xs2 tptp.list_c) (Y2 tptp.d) (Ys5 tptp.list_d) (Z4 tptp.int) (Zs2 tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_d Ys5))) (=> (= (@ tptp.size_size_list_c Xs2) _let_1) (=> (= _let_1 (@ tptp.size_size_list_int Zs2)) (=> (@ (@ (@ P Xs2) Ys5) Zs2) (@ (@ (@ P (@ (@ tptp.cons_c X3) Xs2)) (@ (@ tptp.cons_d Y2) Ys5)) (@ (@ tptp.cons_int Z4) Zs2))))))) (@ (@ (@ P Xs) Ys) Zs))))))) (forall ((Xs tptp.list_c) (Ys tptp.list_nat) (Zs tptp.list_c) (P (-> tptp.list_c tptp.list_nat tptp.list_c Bool))) (let ((_let_1 (@ tptp.size_size_list_nat Ys))) (=> (= (@ tptp.size_size_list_c Xs) _let_1) (=> (= _let_1 (@ tptp.size_size_list_c Zs)) (=> (@ (@ (@ P tptp.nil_c) tptp.nil_nat) tptp.nil_c) (=> (forall ((X3 tptp.c) (Xs2 tptp.list_c) (Y2 tptp.nat) (Ys5 tptp.list_nat) (Z4 tptp.c) (Zs2 tptp.list_c)) (let ((_let_1 (@ tptp.size_size_list_nat Ys5))) (=> (= (@ tptp.size_size_list_c Xs2) _let_1) (=> (= _let_1 (@ tptp.size_size_list_c Zs2)) (=> (@ (@ (@ P Xs2) Ys5) Zs2) (@ (@ (@ P (@ (@ tptp.cons_c X3) Xs2)) (@ (@ tptp.cons_nat Y2) Ys5)) (@ (@ tptp.cons_c Z4) Zs2))))))) (@ (@ (@ P Xs) Ys) Zs))))))) (forall ((Xs tptp.list_c) (Ys tptp.list_nat) (Zs tptp.list_d) (P (-> tptp.list_c tptp.list_nat tptp.list_d Bool))) (let ((_let_1 (@ tptp.size_size_list_nat Ys))) (=> (= (@ tptp.size_size_list_c Xs) _let_1) (=> (= _let_1 (@ tptp.size_size_list_d Zs)) (=> (@ (@ (@ P tptp.nil_c) tptp.nil_nat) tptp.nil_d) (=> (forall ((X3 tptp.c) (Xs2 tptp.list_c) (Y2 tptp.nat) (Ys5 tptp.list_nat) (Z4 tptp.d) (Zs2 tptp.list_d)) (let ((_let_1 (@ tptp.size_size_list_nat Ys5))) (=> (= (@ tptp.size_size_list_c Xs2) _let_1) (=> (= _let_1 (@ tptp.size_size_list_d Zs2)) (=> (@ (@ (@ P Xs2) Ys5) Zs2) (@ (@ (@ P (@ (@ tptp.cons_c X3) Xs2)) (@ (@ tptp.cons_nat Y2) Ys5)) (@ (@ tptp.cons_d Z4) Zs2))))))) (@ (@ (@ P Xs) Ys) Zs))))))) (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (Zs tptp.list_int) (Ws tptp.list_c) (P (-> tptp.list_nat tptp.list_nat tptp.list_int tptp.list_c Bool))) (let ((_let_1 (@ tptp.size_size_list_int Zs))) (let ((_let_2 (@ tptp.size_size_list_nat Ys))) (=> (= (@ tptp.size_size_list_nat Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_c Ws)) (=> (@ (@ (@ (@ P tptp.nil_nat) tptp.nil_nat) tptp.nil_int) tptp.nil_c) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.nat) (Ys5 tptp.list_nat) (Z4 tptp.int) (Zs2 tptp.list_int) (W3 tptp.c) (Ws2 tptp.list_c)) (let ((_let_1 (@ tptp.size_size_list_int Zs2))) (let ((_let_2 (@ tptp.size_size_list_nat Ys5))) (=> (= (@ tptp.size_size_list_nat Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_c Ws2)) (=> (@ (@ (@ (@ P Xs2) Ys5) Zs2) Ws2) (@ (@ (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) (@ (@ tptp.cons_nat Y2) Ys5)) (@ (@ tptp.cons_int Z4) Zs2)) (@ (@ tptp.cons_c W3) Ws2))))))))) (@ (@ (@ (@ P Xs) Ys) Zs) Ws))))))))) (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (Zs tptp.list_int) (Ws tptp.list_d) (P (-> tptp.list_nat tptp.list_nat tptp.list_int tptp.list_d Bool))) (let ((_let_1 (@ tptp.size_size_list_int Zs))) (let ((_let_2 (@ tptp.size_size_list_nat Ys))) (=> (= (@ tptp.size_size_list_nat Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_d Ws)) (=> (@ (@ (@ (@ P tptp.nil_nat) tptp.nil_nat) tptp.nil_int) tptp.nil_d) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.nat) (Ys5 tptp.list_nat) (Z4 tptp.int) (Zs2 tptp.list_int) (W3 tptp.d) (Ws2 tptp.list_d)) (let ((_let_1 (@ tptp.size_size_list_int Zs2))) (let ((_let_2 (@ tptp.size_size_list_nat Ys5))) (=> (= (@ tptp.size_size_list_nat Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_d Ws2)) (=> (@ (@ (@ (@ P Xs2) Ys5) Zs2) Ws2) (@ (@ (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) (@ (@ tptp.cons_nat Y2) Ys5)) (@ (@ tptp.cons_int Z4) Zs2)) (@ (@ tptp.cons_d W3) Ws2))))))))) (@ (@ (@ (@ P Xs) Ys) Zs) Ws))))))))) (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (Zs tptp.list_int) (Ws tptp.list_nat) (P (-> tptp.list_nat tptp.list_nat tptp.list_int tptp.list_nat Bool))) (let ((_let_1 (@ tptp.size_size_list_int Zs))) (let ((_let_2 (@ tptp.size_size_list_nat Ys))) (=> (= (@ tptp.size_size_list_nat Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Ws)) (=> (@ (@ (@ (@ P tptp.nil_nat) tptp.nil_nat) tptp.nil_int) tptp.nil_nat) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.nat) (Ys5 tptp.list_nat) (Z4 tptp.int) (Zs2 tptp.list_int) (W3 tptp.nat) (Ws2 tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_int Zs2))) (let ((_let_2 (@ tptp.size_size_list_nat Ys5))) (=> (= (@ tptp.size_size_list_nat Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Ws2)) (=> (@ (@ (@ (@ P Xs2) Ys5) Zs2) Ws2) (@ (@ (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) (@ (@ tptp.cons_nat Y2) Ys5)) (@ (@ tptp.cons_int Z4) Zs2)) (@ (@ tptp.cons_nat W3) Ws2))))))))) (@ (@ (@ (@ P Xs) Ys) Zs) Ws))))))))) (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (Zs tptp.list_int) (Ws tptp.list_int) (P (-> tptp.list_nat tptp.list_nat tptp.list_int tptp.list_int Bool))) (let ((_let_1 (@ tptp.size_size_list_int Zs))) (let ((_let_2 (@ tptp.size_size_list_nat Ys))) (=> (= (@ tptp.size_size_list_nat Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_int Ws)) (=> (@ (@ (@ (@ P tptp.nil_nat) tptp.nil_nat) tptp.nil_int) tptp.nil_int) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.nat) (Ys5 tptp.list_nat) (Z4 tptp.int) (Zs2 tptp.list_int) (W3 tptp.int) (Ws2 tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Zs2))) (let ((_let_2 (@ tptp.size_size_list_nat Ys5))) (=> (= (@ tptp.size_size_list_nat Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_int Ws2)) (=> (@ (@ (@ (@ P Xs2) Ys5) Zs2) Ws2) (@ (@ (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) (@ (@ tptp.cons_nat Y2) Ys5)) (@ (@ tptp.cons_int Z4) Zs2)) (@ (@ tptp.cons_int W3) Ws2))))))))) (@ (@ (@ (@ P Xs) Ys) Zs) Ws))))))))) (forall ((Xs tptp.list_nat) (Ys tptp.list_int) (Zs tptp.list_c) (Ws tptp.list_c) (P (-> tptp.list_nat tptp.list_int tptp.list_c tptp.list_c Bool))) (let ((_let_1 (@ tptp.size_size_list_c Zs))) (let ((_let_2 (@ tptp.size_size_list_int Ys))) (=> (= (@ tptp.size_size_list_nat Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_c Ws)) (=> (@ (@ (@ (@ P tptp.nil_nat) tptp.nil_int) tptp.nil_c) tptp.nil_c) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.int) (Ys5 tptp.list_int) (Z4 tptp.c) (Zs2 tptp.list_c) (W3 tptp.c) (Ws2 tptp.list_c)) (let ((_let_1 (@ tptp.size_size_list_c Zs2))) (let ((_let_2 (@ tptp.size_size_list_int Ys5))) (=> (= (@ tptp.size_size_list_nat Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_c Ws2)) (=> (@ (@ (@ (@ P Xs2) Ys5) Zs2) Ws2) (@ (@ (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) (@ (@ tptp.cons_int Y2) Ys5)) (@ (@ tptp.cons_c Z4) Zs2)) (@ (@ tptp.cons_c W3) Ws2))))))))) (@ (@ (@ (@ P Xs) Ys) Zs) Ws))))))))) (forall ((Xs tptp.list_nat) (Ys tptp.list_int) (Zs tptp.list_c) (Ws tptp.list_d) (P (-> tptp.list_nat tptp.list_int tptp.list_c tptp.list_d Bool))) (let ((_let_1 (@ tptp.size_size_list_c Zs))) (let ((_let_2 (@ tptp.size_size_list_int Ys))) (=> (= (@ tptp.size_size_list_nat Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_d Ws)) (=> (@ (@ (@ (@ P tptp.nil_nat) tptp.nil_int) tptp.nil_c) tptp.nil_d) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.int) (Ys5 tptp.list_int) (Z4 tptp.c) (Zs2 tptp.list_c) (W3 tptp.d) (Ws2 tptp.list_d)) (let ((_let_1 (@ tptp.size_size_list_c Zs2))) (let ((_let_2 (@ tptp.size_size_list_int Ys5))) (=> (= (@ tptp.size_size_list_nat Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_d Ws2)) (=> (@ (@ (@ (@ P Xs2) Ys5) Zs2) Ws2) (@ (@ (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) (@ (@ tptp.cons_int Y2) Ys5)) (@ (@ tptp.cons_c Z4) Zs2)) (@ (@ tptp.cons_d W3) Ws2))))))))) (@ (@ (@ (@ P Xs) Ys) Zs) Ws))))))))) (forall ((Xs tptp.list_nat) (Ys tptp.list_int) (Zs tptp.list_c) (Ws tptp.list_nat) (P (-> tptp.list_nat tptp.list_int tptp.list_c tptp.list_nat Bool))) (let ((_let_1 (@ tptp.size_size_list_c Zs))) (let ((_let_2 (@ tptp.size_size_list_int Ys))) (=> (= (@ tptp.size_size_list_nat Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Ws)) (=> (@ (@ (@ (@ P tptp.nil_nat) tptp.nil_int) tptp.nil_c) tptp.nil_nat) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.int) (Ys5 tptp.list_int) (Z4 tptp.c) (Zs2 tptp.list_c) (W3 tptp.nat) (Ws2 tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_c Zs2))) (let ((_let_2 (@ tptp.size_size_list_int Ys5))) (=> (= (@ tptp.size_size_list_nat Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Ws2)) (=> (@ (@ (@ (@ P Xs2) Ys5) Zs2) Ws2) (@ (@ (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) (@ (@ tptp.cons_int Y2) Ys5)) (@ (@ tptp.cons_c Z4) Zs2)) (@ (@ tptp.cons_nat W3) Ws2))))))))) (@ (@ (@ (@ P Xs) Ys) Zs) Ws))))))))) (forall ((Xs tptp.list_nat) (Ys tptp.list_int) (Zs tptp.list_c) (Ws tptp.list_int) (P (-> tptp.list_nat tptp.list_int tptp.list_c tptp.list_int Bool))) (let ((_let_1 (@ tptp.size_size_list_c Zs))) (let ((_let_2 (@ tptp.size_size_list_int Ys))) (=> (= (@ tptp.size_size_list_nat Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_int Ws)) (=> (@ (@ (@ (@ P tptp.nil_nat) tptp.nil_int) tptp.nil_c) tptp.nil_int) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.int) (Ys5 tptp.list_int) (Z4 tptp.c) (Zs2 tptp.list_c) (W3 tptp.int) (Ws2 tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_c Zs2))) (let ((_let_2 (@ tptp.size_size_list_int Ys5))) (=> (= (@ tptp.size_size_list_nat Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_int Ws2)) (=> (@ (@ (@ (@ P Xs2) Ys5) Zs2) Ws2) (@ (@ (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) (@ (@ tptp.cons_int Y2) Ys5)) (@ (@ tptp.cons_c Z4) Zs2)) (@ (@ tptp.cons_int W3) Ws2))))))))) (@ (@ (@ (@ P Xs) Ys) Zs) Ws))))))))) (forall ((Xs tptp.list_nat) (Ys tptp.list_int) (Zs tptp.list_d) (Ws tptp.list_c) (P (-> tptp.list_nat tptp.list_int tptp.list_d tptp.list_c Bool))) (let ((_let_1 (@ tptp.size_size_list_d Zs))) (let ((_let_2 (@ tptp.size_size_list_int Ys))) (=> (= (@ tptp.size_size_list_nat Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_c Ws)) (=> (@ (@ (@ (@ P tptp.nil_nat) tptp.nil_int) tptp.nil_d) tptp.nil_c) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.int) (Ys5 tptp.list_int) (Z4 tptp.d) (Zs2 tptp.list_d) (W3 tptp.c) (Ws2 tptp.list_c)) (let ((_let_1 (@ tptp.size_size_list_d Zs2))) (let ((_let_2 (@ tptp.size_size_list_int Ys5))) (=> (= (@ tptp.size_size_list_nat Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_c Ws2)) (=> (@ (@ (@ (@ P Xs2) Ys5) Zs2) Ws2) (@ (@ (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) (@ (@ tptp.cons_int Y2) Ys5)) (@ (@ tptp.cons_d Z4) Zs2)) (@ (@ tptp.cons_c W3) Ws2))))))))) (@ (@ (@ (@ P Xs) Ys) Zs) Ws))))))))) (forall ((Xs tptp.list_nat) (Ys tptp.list_int) (Zs tptp.list_d) (Ws tptp.list_d) (P (-> tptp.list_nat tptp.list_int tptp.list_d tptp.list_d Bool))) (let ((_let_1 (@ tptp.size_size_list_d Zs))) (let ((_let_2 (@ tptp.size_size_list_int Ys))) (=> (= (@ tptp.size_size_list_nat Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_d Ws)) (=> (@ (@ (@ (@ P tptp.nil_nat) tptp.nil_int) tptp.nil_d) tptp.nil_d) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y2 tptp.int) (Ys5 tptp.list_int) (Z4 tptp.d) (Zs2 tptp.list_d) (W3 tptp.d) (Ws2 tptp.list_d)) (let ((_let_1 (@ tptp.size_size_list_d Zs2))) (let ((_let_2 (@ tptp.size_size_list_int Ys5))) (=> (= (@ tptp.size_size_list_nat Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_d Ws2)) (=> (@ (@ (@ (@ P Xs2) Ys5) Zs2) Ws2) (@ (@ (@ (@ P (@ (@ tptp.cons_nat X3) Xs2)) (@ (@ tptp.cons_int Y2) Ys5)) (@ (@ tptp.cons_d Z4) Zs2)) (@ (@ tptp.cons_d W3) Ws2))))))))) (@ (@ (@ (@ P Xs) Ys) Zs) Ws))))))))) (forall ((N tptp.nat) (K3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.ord_less_nat K3) (@ (@ tptp.power_power_nat N) K3)))) (forall ((K3 tptp.nat)) (let ((_let_1 (@ tptp.suc K3))) (= (@ tptp.set_or1210151606488870762an_nat _let_1) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_or1210151606488870762an_nat K3)) (@ (@ tptp.insert_nat2 _let_1) tptp.bot_bot_set_nat))))) (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B3)))) (forall ((P (-> tptp.int Bool)) (X tptp.nat) (Y tptp.nat)) (= (@ P (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat X) Y))) (and (=> (@ (@ tptp.ord_less_eq_nat Y) X) (@ P (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int X)) (@ tptp.semiri1314217659103216013at_int Y)))) (=> (@ (@ tptp.ord_less_nat X) Y) (@ P tptp.zero_zero_int))))) (forall ((X tptp.int) (X6 tptp.int) (P Bool) (P3 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ _let_1 X6))) (=> (= X X6) (=> (=> _let_2 (= P P3)) (= (=> (@ _let_1 X) P) (=> _let_2 P3))))))) (forall ((X tptp.int) (X6 tptp.int) (P Bool) (P3 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ _let_1 X6))) (=> (= X X6) (=> (=> _let_2 (= P P3)) (= (and (@ _let_1 X) P) (and _let_2 P3))))))) (forall ((D2 tptp.int) (P (-> tptp.int Bool)) (K3 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X3 tptp.int)) (=> (@ P X3) (@ P (@ (@ tptp.plus_plus_int X3) D2)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K3) (forall ((X7 tptp.int)) (=> (@ P X7) (@ P (@ (@ tptp.plus_plus_int X7) (@ (@ tptp.times_times_int K3) D2))))))))) (forall ((D2 tptp.int) (P (-> tptp.int Bool)) (K3 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X3 tptp.int)) (=> (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) D2)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K3) (forall ((X7 tptp.int)) (=> (@ P X7) (@ P (@ (@ tptp.minus_minus_int X7) (@ (@ tptp.times_times_int K3) D2))))))))) (forall ((D2 tptp.int) (P1 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P1 X3) (@ P1 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D2))))) (=> (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z3) (= (@ P X3) (@ P1 X3))))) (=> (exists ((X_12 tptp.int)) (@ P1 X_12)) (exists ((X_1 tptp.int)) (@ P X_1))))))) (forall ((D2 tptp.int) (P3 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P3 X3) (@ P3 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D2))))) (=> (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((X_12 tptp.int)) (@ P3 X_12)) (exists ((X_1 tptp.int)) (@ P X_1))))))) (forall ((K3 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K3) (not (forall ((N5 tptp.nat)) (=> (= K3 (@ tptp.semiri1314217659103216013at_int N5)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N5))))))) (forall ((K3 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K3) (exists ((N5 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N5) (= K3 (@ tptp.semiri1314217659103216013at_int N5)))))) (forall ((I tptp.int) (J tptp.int) (K3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int K3)))) (=> (@ (@ tptp.ord_less_int I) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (@ (@ tptp.ord_less_int (@ _let_1 I)) (@ _let_1 J)))))) (forall ((K3 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 K3) L) (@ (@ tptp.product_Pair_int_int Q6) R2)) (and (= K3 (@ (@ 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)))))))))) (forall ((N tptp.nat) (F4 (-> tptp.nat tptp.int)) (K3 tptp.int)) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) N) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F4 (@ (@ tptp.plus_plus_nat I5) tptp.one_one_nat))) (@ F4 I5)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F4 tptp.zero_zero_nat)) K3) (=> (@ (@ tptp.ord_less_eq_int K3) (@ F4 N)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I5) N) (= (@ F4 I5) K3))))))) (forall ((A2 tptp.int) (B2 tptp.int) (Q6 tptp.int) (R2 tptp.int) (Q7 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ (@ tptp.eucl_rel_int A2) B2))) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q6) R2)) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q7) R5)) (= R2 R5))))) (forall ((A2 tptp.int) (B2 tptp.int) (Q6 tptp.int) (R2 tptp.int) (Q7 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ (@ tptp.eucl_rel_int A2) B2))) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q6) R2)) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q7) R5)) (= Q6 Q7))))) (forall ((K3 tptp.int)) (@ (@ (@ tptp.eucl_rel_int K3) tptp.zero_zero_int) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K3))) (forall ((L tptp.int) (K3 tptp.int) (Q6 tptp.int)) (=> (not (= L tptp.zero_zero_int)) (=> (= K3 (@ (@ tptp.times_times_int Q6) L)) (@ (@ (@ tptp.eucl_rel_int K3) L) (@ (@ tptp.product_Pair_int_int Q6) tptp.zero_zero_int))))) (forall ((M2 tptp.nat) (N tptp.nat) (F4 (-> tptp.nat tptp.int)) (K3 tptp.int)) (=> (forall ((I5 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat M2) I5) (@ (@ tptp.ord_less_nat I5) N)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F4 (@ tptp.suc I5))) (@ F4 I5)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (=> (@ (@ tptp.ord_less_eq_int (@ F4 M2)) K3) (=> (@ (@ tptp.ord_less_eq_int K3) (@ F4 N)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M2) I5) (@ (@ tptp.ord_less_eq_nat I5) N) (= (@ F4 I5) K3)))))))) (forall ((D2 tptp.int) (Z tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (@ (@ tptp.ord_less_int Z) (@ (@ tptp.plus_plus_int X) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) Z))) tptp.one_one_int)) D2))))) (forall ((D2 tptp.int) (X tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int X))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (@ (@ tptp.ord_less_int (@ _let_1 (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ _let_1 Z))) tptp.one_one_int)) D2))) Z)))) (forall ((N tptp.nat) (F4 (-> tptp.nat tptp.int)) (K3 tptp.int)) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) N) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F4 (@ tptp.suc I5))) (@ F4 I5)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F4 tptp.zero_zero_nat)) K3) (=> (@ (@ tptp.ord_less_eq_int K3) (@ F4 N)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I5) N) (= (@ F4 I5) K3))))))) (= tptp.upto_aux (lambda ((I4 tptp.int) (J2 tptp.int) (Js tptp.list_int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_int J2) I4)) Js) (@ (@ (@ tptp.upto_aux I4) (@ (@ tptp.minus_minus_int J2) tptp.one_one_int)) (@ (@ tptp.cons_int J2) Js))))) _let_88 (forall ((A1 tptp.int) (A22 tptp.int) (A33 tptp.product_prod_int_int)) (=> (@ (@ (@ tptp.eucl_rel_int A1) A22) A33) (=> (=> (= A22 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 (= A22 tptp.zero_zero_int)) (not (= A1 (@ (@ tptp.times_times_int Q5) A22)))))) (not (forall ((R6 tptp.int) (Q5 tptp.int)) (=> (= A33 (@ (@ tptp.product_Pair_int_int Q5) R6)) (=> (= (@ tptp.sgn_sgn_int R6) (@ tptp.sgn_sgn_int A22)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R6)) (@ tptp.abs_abs_int A22)) (not (= A1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q5) A22)) R6)))))))))))) (forall ((R2 tptp.int) (L tptp.int) (K3 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)) (=> (= K3 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q6) L)) R2)) (@ (@ (@ tptp.eucl_rel_int K3) L) (@ (@ tptp.product_Pair_int_int Q6) R2)))))) (forall ((M2 tptp.nat) (K3 tptp.int)) (let ((_let_1 (@ tptp.power_power_int K3))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K3) (= (@ (@ tptp.divide_divide_int (@ _let_1 M2)) K3) (@ _let_1 (@ (@ tptp.minus_minus_nat M2) (@ tptp.suc tptp.zero_zero_nat)))))))) (= (@ (@ tptp.times_times_assn tptp.top_top_assn) tptp.top_top_assn) tptp.top_top_assn) (not (= tptp.top_top_assn tptp.one_one_assn)) (forall ((A tptp.assn)) (@ (@ tptp.entailst A) tptp.top_top_assn)) (not (= tptp.top_top_assn tptp.bot_bot_assn)) (forall ((A tptp.assn) (B tptp.assn)) (let ((_let_1 (@ tptp.entailst A))) (= (@ _let_1 (@ (@ tptp.times_times_assn B) tptp.top_top_assn)) (@ _let_1 B)))) (forall ((A tptp.assn) (B tptp.assn)) (= (@ (@ tptp.entailst (@ (@ tptp.times_times_assn A) tptp.top_top_assn)) B) (@ (@ tptp.entailst A) B))) (forall ((P tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn tptp.top_top_assn))) (let ((_let_2 (@ _let_1 P))) (= (@ _let_1 _let_2) _let_2)))) (forall ((P tptp.assn)) (@ (@ tptp.entails P) tptp.top_top_assn)) (forall ((X tptp.assn)) (= (@ (@ tptp.sup_sup_assn X) tptp.top_top_assn) tptp.top_top_assn)) (forall ((X tptp.assn)) (= (@ (@ tptp.sup_sup_assn tptp.top_top_assn) X) tptp.top_top_assn)) (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn X) tptp.top_top_assn) X)) (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn tptp.top_top_assn) X) X)) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M2)) (@ tptp.semiri1408675320244567234ct_nat N))))) (forall ((P tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P) H2) (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn P) tptp.top_top_assn)) H2))) (forall ((P tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn P) tptp.top_top_assn)) H2) (not (forall ((H5 tptp.produc3658429121746597890et_nat)) (not (@ (@ tptp.rep_assn P) H5)))))) (forall ((A tptp.assn) (A6 tptp.assn) (B tptp.assn) (B9 tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn A6))) (=> (@ (@ tptp.entails A) (@ _let_1 tptp.top_top_assn)) (=> (@ (@ tptp.entails B) (@ (@ tptp.times_times_assn B9) tptp.top_top_assn)) (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn A) B)) tptp.top_top_assn)) (@ (@ tptp.times_times_assn (@ _let_1 B9)) tptp.top_top_assn)))))) (forall ((A tptp.assn)) (@ (@ tptp.entails A) (@ (@ tptp.times_times_assn A) tptp.top_top_assn))) (forall ((P tptp.assn) (Q tptp.assn) (R tptp.assn)) (let ((_let_1 (@ (@ tptp.times_times_assn Q) tptp.top_top_assn))) (=> (@ (@ tptp.entails P) _let_1) (@ (@ tptp.entails (@ (@ tptp.times_times_assn P) R)) _let_1)))) (forall ((P tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 Q) (@ _let_1 (@ (@ tptp.times_times_assn Q) tptp.top_top_assn))))) (forall ((K3 tptp.int) (L tptp.int) (Q6 tptp.int) (R2 tptp.int)) (=> (@ (@ (@ tptp.eucl_rel_int K3) L) (@ (@ tptp.product_Pair_int_int Q6) R2)) (= (@ (@ tptp.divide_divide_int K3) L) Q6))) (forall ((H2 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.rep_assn tptp.top_top_assn) (@ (@ tptp.produc7507926704131184380et_nat H2) tptp.bot_bot_set_nat))) _let_87 (= tptp.entailst (lambda ((A5 tptp.assn) (B7 tptp.assn)) (@ (@ tptp.entails A5) (@ (@ tptp.times_times_assn B7) tptp.top_top_assn)))) (forall ((P tptp.assn) (Q tptp.assn)) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn P) tptp.top_top_assn)) (@ (@ tptp.times_times_assn Q) tptp.top_top_assn)) (@ (@ tptp.entailst P) Q))) (forall ((A tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.entails A) (@ (@ tptp.times_times_assn B) tptp.top_top_assn)) (@ (@ tptp.entailst A) B))) (forall ((A tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.entailst A) B) (@ (@ tptp.entails A) (@ (@ tptp.times_times_assn B) tptp.top_top_assn)))) (forall ((P tptp.assn) (Q tptp.assn)) (=> (@ (@ (@ tptp.fI_QUERY P) Q) tptp.top_top_assn) (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn Q) tptp.top_top_assn)))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (= (@ (@ tptp.divide_divide_nat M2) N) tptp.zero_zero_nat))) (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat M2) N)) N) M2))) (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N) M2)) N) M2))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.divide_divide_nat M2) N) tptp.zero_zero_nat) (or (@ (@ tptp.ord_less_nat M2) N) (= N tptp.zero_zero_nat)))) (forall ((M2 tptp.nat) (I tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.times_times_nat I) N)) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M2) N)) I))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.divide_divide_nat M2) N)) (and (@ (@ tptp.ord_less_eq_nat N) M2) (@ _let_1 N))))) (forall ((M2 tptp.nat) (N tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat K3))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M2)))))) (forall ((Q6 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q6) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M2) Q6)) N) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.times_times_nat N) Q6))))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (= (= (@ (@ tptp.divide_divide_nat M2) N) M2) (= N tptp.one_one_nat)))) (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M2) N)) M2)))) (= tptp.divide_divide_nat (lambda ((M tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (or (@ (@ tptp.ord_less_nat M) N2) (= N2 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M) N2)) N2))))) (forall ((Q6 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q6) (= (@ (@ tptp.ord_less_eq_nat M2) (@ (@ tptp.divide_divide_nat N) Q6)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M2) Q6)) N)))) (forall ((N tptp.nat) (Q6 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q6)) M2) (=> (@ (@ tptp.ord_less_nat M2) (@ _let_1 (@ tptp.suc Q6))) (= (@ (@ tptp.divide_divide_nat M2) N) Q6))))) (forall ((P (-> tptp.nat Bool)) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (= N tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.divide_divide_nat M2) N)) (and (=> _let_1 (@ P tptp.zero_zero_nat)) (=> (not _let_1) (forall ((I4 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J2) N) (=> (= M2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) I4)) J2)) (@ P I4))))))))) (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M2) N)) N))))) (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat N) (@ (@ tptp.divide_divide_nat M2) N)))))) (forall ((K3 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K3))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (= (@ (@ tptp.divide_divide_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.divide_divide_nat M2) N))))) (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ (@ tptp.divide_divide_nat M2) N) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M2) N)) N)))))) (forall ((P (-> tptp.nat Bool)) (M2 tptp.nat) (N tptp.nat)) (= (@ P (@ (@ tptp.divide_divide_nat M2) N)) (or (and (= N tptp.zero_zero_nat) (@ P tptp.zero_zero_nat)) (exists ((Q8 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q8)) M2) (@ (@ tptp.ord_less_nat M2) (@ _let_1 (@ tptp.suc Q8))) (@ P Q8))))))) (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (@ (@ tptp.ord_less_nat M2) N)) (= (@ (@ tptp.divide_divide_nat M2) N) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M2) N)) N)))))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (= (@ (@ tptp.modulo_modulo_nat M2) N) M2))) (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat M2) N)) N))) (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ (@ tptp.modulo_modulo_nat A) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.modulo_modulo_nat B) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat A) N)) (@ (@ tptp.divide_divide_nat B) N))))))) (forall ((P (-> tptp.nat Bool)) (N tptp.nat) (P6 tptp.nat) (M2 tptp.nat)) (=> (@ P N) (=> (@ (@ tptp.ord_less_nat N) P6) (=> (@ (@ tptp.ord_less_nat M2) P6) (=> (forall ((N5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N5) P6) (=> (@ P N5) (@ P (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N5)) P6))))) (@ P M2)))))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M2) N)) (= (@ (@ tptp.modulo_modulo_nat M2) N) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M2) N)) N)))) (= tptp.modulo_modulo_nat (lambda ((M tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat M) N2)) M) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M) N2)) N2)))) (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M2) N)) N))) (forall ((P (-> tptp.nat Bool)) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (= N tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.modulo_modulo_nat M2) N)) (and (=> _let_1 (@ P M2)) (=> (not _let_1) (forall ((I4 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J2) N) (=> (= M2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) I4)) J2)) (@ P J2))))))))) (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) N)) (@ (@ (@ tptp.if_nat (= (@ (@ tptp.modulo_modulo_nat B) N) tptp.zero_zero_nat)) tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.divide_divide_nat B) N))))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M2) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat M2) N))) M2) tptp.one_one_nat))) (forall ((P (-> tptp.nat tptp.nat Bool)) (M2 tptp.nat) (N tptp.nat)) (=> (forall ((M6 tptp.nat)) (@ (@ P M6) tptp.zero_zero_nat)) (=> (forall ((M6 tptp.nat) (N5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N5) (=> (@ (@ P N5) (@ (@ tptp.modulo_modulo_nat M6) N5)) (@ (@ P M6) N5)))) (@ (@ P M2) N)))) (forall ((K3 tptp.int) (L tptp.int) (Q6 tptp.int) (R2 tptp.int)) (=> (@ (@ (@ tptp.eucl_rel_int K3) L) (@ (@ tptp.product_Pair_int_int Q6) R2)) (= (@ (@ tptp.modulo_modulo_int K3) L) R2))) (forall ((K3 tptp.int) (L tptp.int)) (@ (@ (@ tptp.eucl_rel_int K3) L) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int K3) L)) (@ (@ tptp.modulo_modulo_int K3) L)))) (forall ((X tptp.nat)) (= (@ (@ tptp.bezw X) tptp.zero_zero_nat) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) _let_86 (forall ((M2 tptp.int)) (=> (forall ((N5 tptp.nat)) (not (= M2 (@ tptp.semiri1314217659103216013at_int N5)))) (not (forall ((N5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N5) (not (= M2 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N5))))))))) (forall ((K3 tptp.int)) (=> (not (= K3 tptp.zero_zero_int)) (=> (forall ((N5 tptp.nat)) (=> (= K3 (@ tptp.semiri1314217659103216013at_int N5)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N5)))) (not (forall ((N5 tptp.nat)) (=> (= K3 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N5))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N5)))))))) (forall ((K3 tptp.int)) (=> (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int) (not (forall ((N5 tptp.nat)) (=> (= K3 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N5))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N5))))))) (forall ((A2 tptp.int) (B2 tptp.int) (Q6 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.if_int (= R2 tptp.zero_zero_int)))) (let ((_let_2 (@ tptp.uminus_uminus_int Q6))) (=> (@ (@ (@ tptp.eucl_rel_int A2) B2) (@ (@ tptp.product_Pair_int_int Q6) R2)) (=> (not (= B2 tptp.zero_zero_int)) (@ (@ (@ tptp.eucl_rel_int (@ tptp.uminus_uminus_int A2)) B2) (@ (@ tptp.product_Pair_int_int (@ (@ _let_1 _let_2) (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int))) (@ (@ _let_1 tptp.zero_zero_int) (@ (@ tptp.minus_minus_int B2) R2))))))))) (forall ((M5 tptp.list_P8527749157015355191n_assn) (P tptp.assn)) (@ (@ (@ (@ tptp.fI_RESULT M5) P) tptp.one_one_assn) tptp.top_top_assn)) (forall ((M5 tptp.list_P8527749157015355191n_assn) (F tptp.assn)) (@ (@ (@ (@ tptp.fI_RESULT M5) F) tptp.one_one_assn) F)) (forall ((M5 tptp.list_P8527749157015355191n_assn)) (@ (@ (@ (@ tptp.fI_RESULT M5) tptp.one_one_assn) tptp.one_one_assn) tptp.one_one_assn)) _let_85 (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))) (let ((_let_2 (@ tptp.numeral_numeral_int M2))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))) (forall ((J tptp.int) (I tptp.int)) (=> (@ (@ tptp.ord_less_int J) I) (= (@ (@ tptp.upto I) J) tptp.nil_int))) (forall ((I tptp.int) (J tptp.int)) (= (= tptp.nil_int (@ (@ tptp.upto I) J)) (@ (@ tptp.ord_less_int J) I))) (forall ((I tptp.int) (J tptp.int)) (= (= (@ (@ tptp.upto I) J) tptp.nil_int) (@ (@ tptp.ord_less_int J) I))) (forall ((I tptp.int)) (= (@ (@ tptp.upto I) I) (@ (@ tptp.cons_int I) tptp.nil_int))) (forall ((I tptp.int) (K3 tptp.nat) (J tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int I) (@ tptp.semiri1314217659103216013at_int K3)))) (=> (@ (@ tptp.ord_less_eq_int _let_1) J) (= (@ (@ tptp.nth_int (@ (@ tptp.upto I) J)) K3) _let_1)))) (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M2))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))) (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2)))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))) (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2)))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))) (forall ((I tptp.int) (J tptp.int)) (@ tptp.distinct_int (@ (@ tptp.upto I) J))) (forall ((M2 tptp.int) (N tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) (@ (@ tptp.upto M2) N))) (forall ((I tptp.int) (J tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_int) (@ (@ tptp.upto I) J))) _let_83 (= tptp.upto (lambda ((I4 tptp.int) (J2 tptp.int)) (@ (@ (@ tptp.upto_aux I4) J2) tptp.nil_int))) (forall ((I tptp.int) (J tptp.int) (K3 tptp.int)) (let ((_let_1 (@ tptp.upto I))) (=> (@ (@ tptp.ord_less_eq_int I) J) (=> (@ (@ tptp.ord_less_eq_int J) K3) (= (@ _let_1 K3) (@ (@ tptp.append_int (@ _let_1 J)) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int J) tptp.one_one_int)) K3))))))) (forall ((I tptp.int) (J tptp.int) (K3 tptp.int)) (let ((_let_1 (@ tptp.upto I))) (=> (@ (@ tptp.ord_less_eq_int I) J) (=> (@ (@ tptp.ord_less_eq_int J) K3) (= (@ _let_1 K3) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.upto J) K3))))))) (forall ((I tptp.int) (J tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I) J) (= (@ (@ tptp.upto I) J) (@ (@ tptp.cons_int I) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I) tptp.one_one_int)) J))))) (= tptp.upto (lambda ((I4 tptp.int) (J2 tptp.int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_eq_int I4) J2)) (@ (@ tptp.cons_int I4) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) J2))) tptp.nil_int))) (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)))))) (forall ((I tptp.int) (J tptp.int)) (let ((_let_1 (@ tptp.upto I))) (=> (@ (@ tptp.ord_less_eq_int I) J) (= (@ _let_1 J) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.cons_int J) tptp.nil_int)))))) (forall ((I tptp.int) (J tptp.int) (K3 tptp.int)) (let ((_let_1 (@ tptp.upto I))) (=> (@ (@ tptp.ord_less_eq_int I) J) (=> (@ (@ tptp.ord_less_eq_int J) K3) (= (@ _let_1 K3) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.cons_int J) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int J) tptp.one_one_int)) K3)))))))) (forall ((X tptp.num) (N tptp.nat) (A2 tptp.int)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)) (@ tptp.nat2 A2)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) A2))) (forall ((A2 tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 A2)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)) (@ (@ tptp.ord_less_int A2) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))) (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z)) (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_int W) Z)))) (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))) (forall ((I tptp.int) (J tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.upto I) J)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int J) I)) tptp.one_one_int)))) (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z))) (forall ((Z tptp.int) (W tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int W) Z)))) (forall ((M2 tptp.nat) (Z tptp.int)) (= (@ (@ tptp.ord_less_nat M2) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M2)) Z))) (forall ((W tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int W) Z)))) (forall ((W tptp.int) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) M2) (@ (@ tptp.ord_less_int W) (@ tptp.semiri1314217659103216013at_int M2))))) (forall ((B2 tptp.int) (A2 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 B2) tptp.zero_zero_int) (=> (@ (@ (@ tptp.eucl_rel_int (@ (@ tptp.plus_plus_int A2) tptp.one_one_int)) B2) (@ _let_2 R2)) (@ (@ (@ tptp.eucl_rel_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 A2))) (@ _let_1 B2)) (@ _let_2 (@ (@ tptp.minus_minus_int (@ _let_1 R2)) tptp.one_one_int)))))))) (forall ((B2 tptp.int) (A2 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) B2) (=> (@ (@ (@ tptp.eucl_rel_int A2) B2) (@ _let_3 R2)) (@ (@ (@ tptp.eucl_rel_int (@ _let_2 (@ _let_1 A2))) (@ _let_1 B2)) (@ _let_3 (@ _let_2 (@ _let_1 R2)))))))))) (forall ((M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat M2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (= _let_1 tptp.one_one_nat)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (or (= N tptp.zero_zero_nat) (= N (@ tptp.suc tptp.zero_zero_nat))))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (or (= N tptp.zero_zero_nat) (= N (@ tptp.suc tptp.zero_zero_nat))))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (forall ((B2 tptp.nat) (K3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B2) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) K3) (exists ((N5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N5)) K3) (@ (@ tptp.ord_less_nat K3) (@ _let_1 (@ (@ tptp.plus_plus_nat N5) tptp.one_one_nat))))))))) (forall ((B2 tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ _let_1 B2) (=> (@ _let_1 K3) (exists ((N5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (and (@ (@ tptp.ord_less_nat (@ _let_1 N5)) K3) (@ (@ tptp.ord_less_eq_nat K3) (@ _let_1 (@ (@ tptp.plus_plus_nat N5) tptp.one_one_nat)))))))))) (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N5 tptp.nat)) (=> (@ P N5) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N5) (@ P (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N5))))) (=> (forall ((N5 tptp.nat)) (=> (@ P N5) (@ P (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N5))))) (@ P N))))) (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))) (= 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))) (= tptp.dvd_dvd_int (lambda ((D5 tptp.int) (T2 tptp.int)) (@ (@ tptp.dvd_dvd_int D5) (@ tptp.uminus_uminus_int T2)))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_nat M2) N) (not (@ (@ tptp.dvd_dvd_nat N) M2))))) (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (=> (@ (@ tptp.dvd_dvd_nat M2) N) (@ _let_1 M2))))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M2))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2)) (or (@ (@ tptp.ord_less_nat N) M2) (@ _let_1 N))))) (forall ((K3 tptp.int) (M2 tptp.int) (T tptp.int)) (let ((_let_1 (@ tptp.times_times_int K3))) (=> (not (= K3 tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int M2) T) (@ (@ tptp.dvd_dvd_int (@ _let_1 M2)) (@ _let_1 T)))))) (forall ((K3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat K3) N) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat K3) N)))) (forall ((K3 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K3))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.dvd_dvd_nat M2) N))))) (forall ((K3 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K3))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (@ (@ tptp.dvd_dvd_nat M2) N))))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.modulo_modulo_nat M2) N)) (not (@ (@ tptp.dvd_dvd_nat N) M2)))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat N) M2)) M2) (= N tptp.one_one_nat)))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat M2) N)) M2) (= N tptp.one_one_nat)))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)))) (= (@ _let_2 N) (@ _let_2 (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1)))))))) (forall ((R2 tptp.nat) (N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat R2) N) (=> (@ (@ tptp.ord_less_eq_nat R2) M2) (=> (@ (@ tptp.dvd_dvd_nat N) (@ (@ tptp.minus_minus_nat M2) R2)) (= (@ (@ tptp.modulo_modulo_nat M2) N) R2))))) (forall ((I tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) I) (@ (@ tptp.ord_less_eq_nat M2) N))))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) M2) M2))) (forall ((N tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M2)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (forall ((N tptp.nat) (M2 tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N) M2) M2) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M2)) M2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) M2))) (forall ((N tptp.nat) (K3 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int _let_1) K3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int N) K3)) (@ (@ tptp.minus_minus_int K3) _let_1)))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.suc tptp.zero_zero_nat))) (=> (= (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))) _let_3) (@ (@ tptp.dvd_dvd_nat _let_2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) _let_3)) _let_2))))))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)) (or (@ (@ tptp.ord_less_nat M2) N) (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)))))) (forall ((N tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (forall ((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)))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (=> (= (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (not (@ (@ tptp.dvd_dvd_nat _let_2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) _let_2))))))) (forall ((X tptp.product_prod_num_num)) (=> (not (= X (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one))) (=> (forall ((N5 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit0 N5))))) (=> (forall ((N5 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit1 N5))))) (=> (forall ((M6 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M6)) tptp.one)))) (=> (forall ((M6 tptp.num) (N5 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M6)) (@ tptp.bit0 N5))))) (=> (forall ((M6 tptp.num) (N5 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M6)) (@ tptp.bit1 N5))))) (=> (forall ((M6 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M6)) tptp.one)))) (=> (forall ((M6 tptp.num) (N5 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M6)) (@ tptp.bit0 N5))))) (not (forall ((M6 tptp.num) (N5 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M6)) (@ tptp.bit1 N5))))))))))))))) _let_82 _let_81 (forall ((M2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bitM M2)) (@ tptp.bit0 tptp.one)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M2)) tptp.one_one_int)) tptp.one_one_int))) (forall ((K3 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat K3)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat (@ tptp.pred_numeral K3)) N))) (forall ((N tptp.nat) (K3 tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K3)) (@ (@ tptp.ord_less_nat N) (@ tptp.pred_numeral K3)))) _let_80 (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.bit_se2002935070580805687sk_nat N)) (@ _let_1 N)))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.ord_less_nat N) (@ tptp.bit_se2002935070580805687sk_nat N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat (@ tptp.bit_se2002935070580805687sk_nat N)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (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_int2 tptp.zero_zero_int) (@ (@ tptp.insert_int2 (@ 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)))))))))))) (forall ((K3 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 K3)) (not (@ _let_2 L)))))) (let ((_let_4 (@ (@ tptp.bit_se725231765392027082nd_int K3) L))) (let ((_let_5 (@ (@ tptp.insert_int2 tptp.zero_zero_int) (@ (@ tptp.insert_int2 (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_6 (and (@ (@ tptp.member_int K3) _let_5) (@ (@ tptp.member_int L) _let_5)))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int K3) 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 K3) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1))))))))))))))) (forall ((N tptp.nat) (M2 tptp.nat) (K3 tptp.int)) (=> (@ (@ tptp.ord_less_nat N) M2) (=> (@ (@ tptp.bit_se1146084159140164899it_int K3) N) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int M2) K3))))) (forall ((K3 tptp.int)) (not (forall ((N5 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K3))) (=> (forall ((M3 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K3))) (=> (@ (@ tptp.ord_less_eq_nat N5) M3) (= (@ _let_1 M3) (@ _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)))))))))) (forall ((A0 tptp.int) (A1 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int A0) A1)) (=> (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.insert_int2 tptp.zero_zero_int) (@ (@ tptp.insert_int2 (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int K) L2)) (=> (=> (not (and (@ (@ tptp.member_int K) _let_2) (@ (@ tptp.member_int L2) _let_2))) (@ (@ P (@ (@ tptp.divide_divide_int K) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))) (@ (@ P K) L2)))))) (@ (@ P A0) A1)))) (forall ((I tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.upto I) J))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int I) J))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I) J)) (and (=> _let_2 (= _let_1 (@ (@ tptp.cons_int I) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I) tptp.one_one_int)) J)))) (=> (not _let_2) (= _let_1 tptp.nil_int))))))) (forall ((X tptp.int) (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)))))))) (forall ((A0 tptp.int) (A1 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int A0) A1)) (=> (forall ((I5 tptp.int) (J3 tptp.int)) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I5) J3)) (=> (=> (@ (@ tptp.ord_less_eq_int I5) J3) (@ (@ P (@ (@ tptp.plus_plus_int I5) tptp.one_one_int)) J3)) (@ (@ P I5) J3)))) (@ (@ P A0) A1)))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.num_of_nat (@ tptp.suc N)))) (let ((_let_2 (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (and (=> _let_2 (= _let_1 (@ tptp.inc (@ tptp.num_of_nat N)))) (=> (not _let_2) (= _let_1 tptp.one)))))) (= tptp.binomial (lambda ((N2 tptp.nat) (K4 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) K4))) (let ((_let_2 (@ tptp.ord_less_nat N2))) (@ (@ (@ tptp.if_nat (@ _let_2 K4)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_2 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K4))) (@ (@ tptp.binomial N2) _let_1)) (@ (@ tptp.divide_divide_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) N2) tptp.one_one_nat)) (@ tptp.semiri1408675320244567234ct_nat K4)))))))) (forall ((N tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.nat_set_decode Z))) (=> (not (@ (@ tptp.member_nat N) _let_1)) (= (@ tptp.nat_set_decode (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) Z)) (@ (@ tptp.insert_nat2 N) _let_1))))) (forall ((N tptp.nat) (K3 tptp.nat)) (= (= (@ (@ tptp.binomial N) K3) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat N) K3))) (= (@ tptp.nat_set_decode tptp.zero_zero_nat) tptp.bot_bot_set_nat) (forall ((N tptp.nat) (K3 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.binomial N) K3)) (@ (@ tptp.ord_less_eq_nat K3) N))) (forall ((N tptp.nat) (K3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K3) (= (@ (@ tptp.binomial N) K3) tptp.zero_zero_nat))) (forall ((K3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.binomial N) K3)))) (forall ((X tptp.product_prod_nat_nat)) (not (forall ((K tptp.nat) (M6 tptp.nat)) (not (= X (@ (@ tptp.product_Pair_nat_nat K) M6)))))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.numeral_numeral_nat (@ tptp.num_of_nat N)) N))) (forall ((N tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_2 N) (=> (@ _let_2 K3) (= (@ (@ tptp.binomial N) K3) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))) (@ _let_1 K3)))))))) (forall ((K3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (= (@ (@ tptp.times_times_nat K3) (@ (@ tptp.binomial N) K3)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat)))))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat N) N)) (@ tptp.bit0 (@ tptp.num_of_nat N))))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (= (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.plus_plus_num (@ tptp.num_of_nat M2)) (@ tptp.num_of_nat N))))))) (forall ((N tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) (let ((_let_2 (@ tptp.suc K3))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.binomial N) _let_2) (@ (@ tptp.plus_plus_nat (@ _let_1 _let_2)) (@ _let_1 K3))))))) (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))))))))) (= tptp.nat_prod_decode_aux (lambda ((K4 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc K4))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat M) K4)) (@ (@ tptp.product_Pair_nat_nat M) (@ (@ tptp.minus_minus_nat K4) M))) (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat M) _let_1)))))) (forall ((D tptp.int) (P (-> tptp.int Bool)) (P3 (-> tptp.int Bool)) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X3) (= (@ P X3) (@ P3 X3))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ P X3) (@ P (@ (@ tptp.plus_plus_int X3) D))))) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P3 X3) (@ P3 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D))))) (= (exists ((X8 tptp.int)) (@ P X8)) (or (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (@ P3 X2))) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (exists ((Y5 tptp.int)) (and (@ (@ tptp.member_int Y5) A) (@ P (@ (@ tptp.minus_minus_int Y5) X2))))))))))))) _let_79 (forall ((D tptp.int) (B tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) D))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ Q X3) (@ Q (@ (@ tptp.minus_minus_int X3) D))))) (forall ((X7 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X7) D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B) (not (= X7 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (and (@ P X7) (@ Q X7)) (and (@ P _let_1) (@ Q _let_1))))))))) (forall ((D tptp.int) (B tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) D))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ Q X3) (@ Q (@ (@ tptp.minus_minus_int X3) D))))) (forall ((X7 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X7) D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B) (not (= X7 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (or (@ P X7) (@ Q X7)) (or (@ P _let_1) (@ Q _let_1))))))))) (forall ((D tptp.int) (A tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ P X3) (@ P (@ (@ tptp.plus_plus_int X3) D))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ Q X3) (@ Q (@ (@ tptp.plus_plus_int X3) D))))) (forall ((X7 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int X7) D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A) (not (= X7 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (and (@ P X7) (@ Q X7)) (and (@ P _let_1) (@ Q _let_1))))))))) (forall ((D tptp.int) (A tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ P X3) (@ P (@ (@ tptp.plus_plus_int X3) D))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ Q X3) (@ Q (@ (@ tptp.plus_plus_int X3) D))))) (forall ((X7 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int X7) D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A) (not (= X7 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (or (@ P X7) (@ Q X7)) (or (@ P _let_1) (@ Q _let_1))))))))) (forall ((D2 tptp.int) (D tptp.int) (A tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D) (forall ((X7 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X7))) (let ((_let_2 (@ tptp.dvd_dvd_int D2))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A) (not (= X7 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (not (@ _let_2 (@ _let_1 T))) (not (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 D)) T)))))))))) (forall ((D2 tptp.int) (D tptp.int) (A tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D) (forall ((X7 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X7))) (let ((_let_2 (@ tptp.dvd_dvd_int D2))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A) (not (= X7 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ _let_2 (@ _let_1 T)) (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 D)) T))))))))) (forall ((D2 tptp.int) (D tptp.int) (B tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D) (forall ((X7 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D2))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B) (not (= X7 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (not (@ _let_1 (@ (@ tptp.plus_plus_int X7) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X7) D)) T))))))))) (forall ((D2 tptp.int) (D tptp.int) (B tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D) (forall ((X7 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D2))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B) (not (= X7 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ _let_1 (@ (@ tptp.plus_plus_int X7) T)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X7) D)) T)))))))) (forall ((D2 tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D2))))) (= (exists ((X8 tptp.int)) (@ P X8)) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D2)) (@ P X2))))))) (forall ((D tptp.int) (A tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (forall ((X7 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A) (not (= X7 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ _let_1 X7) (@ _let_1 (@ (@ tptp.plus_plus_int X7) D)))))))) (forall ((D tptp.int) (T tptp.int) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (@ (@ tptp.member_int T) A) (forall ((X7 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A) (not (= X7 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_int X7) T) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X7) D)) T))))))) (forall ((D tptp.int) (T tptp.int) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (@ (@ tptp.member_int T) A) (forall ((X7 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A) (not (= X7 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (not (= X7 T)) (not (= (@ (@ tptp.plus_plus_int X7) D) T)))))))) (forall ((D tptp.int) (T tptp.int) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T) tptp.one_one_int)) A) (forall ((X7 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A) (not (= X7 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (= X7 T) (= (@ (@ tptp.plus_plus_int X7) D) T))))))) (forall ((D tptp.int) (T tptp.int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (@ (@ tptp.member_int T) B) (forall ((X7 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B) (not (= X7 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ _let_1 X7) (@ _let_1 (@ (@ tptp.minus_minus_int X7) D))))))))) (forall ((D tptp.int) (B tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (forall ((X7 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B) (not (= X7 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_int X7) T) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int X7) D)) T)))))) (forall ((D tptp.int) (T tptp.int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (@ (@ tptp.member_int T) B) (forall ((X7 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B) (not (= X7 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (not (= X7 T)) (not (= (@ (@ tptp.minus_minus_int X7) D) T)))))))) (forall ((D tptp.int) (T tptp.int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T) tptp.one_one_int)) B) (forall ((X7 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B) (not (= X7 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (= X7 T) (= (@ (@ tptp.minus_minus_int X7) D) T))))))) (= tptp.set_or1266510415728281911st_int (lambda ((I4 tptp.int) (J2 tptp.int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_int J2) I4)) tptp.bot_bot_set_int) (@ (@ tptp.insert_int2 I4) (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) J2))))) (forall ((D tptp.int) (B tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (forall ((X7 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B) (not (= X7 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X7) T) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int X7) D)) T)))))) (forall ((D tptp.int) (T tptp.int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T) tptp.one_one_int)) B) (forall ((X7 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B) (not (= X7 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ _let_1 X7) (@ _let_1 (@ (@ tptp.minus_minus_int X7) D))))))))) (forall ((D tptp.int) (T tptp.int) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T) tptp.one_one_int)) A) (forall ((X7 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A) (not (= X7 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X7) T) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int X7) D)) T))))))) (forall ((D tptp.int) (A tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (forall ((X7 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A) (not (= X7 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ _let_1 X7) (@ _let_1 (@ (@ tptp.plus_plus_int X7) D)))))))) (forall ((D tptp.int) (P (-> tptp.int Bool)) (P3 (-> tptp.int Bool)) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z3) (= (@ P X3) (@ P3 X3))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) D))))) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P3 X3) (@ P3 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D))))) (= (exists ((X8 tptp.int)) (@ P X8)) (or (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (@ P3 X2))) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (exists ((Y5 tptp.int)) (and (@ (@ tptp.member_int Y5) B) (@ P (@ (@ tptp.plus_plus_int Y5) X2))))))))))))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat M2) N)) (@ tptp.transi6264000038957366511cl_nat tptp.pred_nat)) (@ (@ tptp.ord_less_nat M2) N))) (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ P M))) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P X2))))) (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ P M))) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P X2))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.suc N))) (= (@ _let_1 _let_2) (@ (@ tptp.insert_nat2 _let_2) (@ _let_1 N)))))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.insert_nat2 M2) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N)) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_nat2 _let_2) (@ _let_1 N))))))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.set_or1269000886237332187st_nat M2) N) (@ (@ tptp.insert_nat2 M2) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N))))) _let_78 (forall ((N tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.insert_nat2 tptp.zero_zero_nat) tptp.bot_bot_set_nat)))) (= (@ tptp.set_ord_atMost_nat tptp.zero_zero_nat) (@ (@ tptp.insert_nat2 tptp.zero_zero_nat) tptp.bot_bot_set_nat)) (forall ((K3 tptp.nat)) (let ((_let_1 (@ tptp.suc K3))) (= (@ tptp.set_ord_atMost_nat _let_1) (@ (@ tptp.insert_nat2 _let_1) (@ tptp.set_ord_atMost_nat K3))))) (forall ((K3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat K3))) (= (@ tptp.set_ord_atMost_nat _let_1) (@ (@ tptp.insert_nat2 _let_1) (@ tptp.set_ord_atMost_nat (@ tptp.pred_numeral K3)))))) (forall ((N tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.minus_minus_nat J) (@ tptp.suc I))) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I) J))) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) N))))) (forall ((K3 tptp.nat)) (let ((_let_1 (@ tptp.suc K3))) (= (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.append_nat (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_atMost_nat K3))) (@ (@ tptp.cons_nat _let_1) tptp.nil_nat))))) (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.suc I))) (=> (@ (@ tptp.ord_less_nat _let_1) J) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I) J)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat _let_1) J))))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.insert_nat2 tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ _let_1 N)))))) (forall ((N tptp.nat)) (= (@ tptp.set_ord_atMost_nat (@ tptp.suc N)) (@ (@ tptp.insert_nat2 tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_atMost_nat N))))) (forall ((N tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.minus_minus_nat J) I)) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I) J))) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) N))))) _let_77 (forall ((N7 tptp.set_nat) (N tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) N7) (@ (@ tptp.ord_less_nat X3) N))) (@ tptp.finite_finite_nat N7))) (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.suc I))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) J) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I) J)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat _let_1) J))))))) (forall ((M5 tptp.set_nat)) (=> (@ tptp.finite_finite_nat M5) (= (@ tptp.gcd_Gcd_nat M5) (@ tptp.gcd_Gcd_nat (@ (@ tptp.minus_minus_set_nat M5) (@ (@ tptp.insert_nat2 tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))) (forall ((A tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (@ (@ tptp.member_nat N) A)) (= (@ tptp.nat_set_encode (@ (@ tptp.insert_nat2 N) A)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.nat_set_encode A)))))) (= (@ tptp.nat_set_encode tptp.bot_bot_set_nat) tptp.zero_zero_nat) _let_76 (forall ((K3 tptp.nat) (S tptp.set_nat)) (=> (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K3) M6) (exists ((N9 tptp.nat)) (and (@ (@ tptp.ord_less_nat M6) N9) (@ (@ tptp.member_nat N9) S))))) (not (@ tptp.finite_finite_nat S)))) (forall ((S tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S)) (forall ((M tptp.nat)) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.member_nat N2) S)))))) (forall ((K3 tptp.nat)) (= (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_lessThan_nat (@ tptp.suc K3))) (@ (@ tptp.append_nat (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_lessThan_nat K3))) (@ (@ tptp.cons_nat K3) tptp.nil_nat)))) (= (@ tptp.set_ord_lessThan_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat) (forall ((M2 tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M2) (@ tptp.suc M2)) (@ (@ tptp.insert_nat2 M2) tptp.bot_bot_set_nat))) (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M tptp.nat)) (and (@ (@ tptp.ord_less_nat M) N) (@ P M))) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P X2))))) (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ P M))) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P X2))))) (forall ((N tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat N) tptp.bot_bot_set_nat) (= N tptp.zero_zero_nat))) (forall ((K3 tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K3)) (@ (@ tptp.insert_nat2 K3) (@ tptp.set_ord_lessThan_nat K3)))) (forall ((M2 tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M2) tptp.zero_zero_nat) tptp.bot_bot_set_nat)) (forall ((N tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.insert_nat2 tptp.zero_zero_nat) tptp.bot_bot_set_nat)))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.insert_nat2 N) (@ _let_1 N))))) (forall ((K3 tptp.num)) (let ((_let_1 (@ tptp.pred_numeral K3))) (= (@ tptp.set_ord_lessThan_nat (@ tptp.numeral_numeral_nat K3)) (@ (@ tptp.insert_nat2 _let_1) (@ tptp.set_ord_lessThan_nat _let_1))))) (forall ((N tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc N)) (@ (@ tptp.insert_nat2 tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_lessThan_nat N))))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M2))) (let ((_let_2 (@ _let_1 (@ tptp.suc N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat M2) N))) (and (=> _let_3 (= _let_2 (@ (@ tptp.insert_nat2 N) (@ _let_1 N)))) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_nat))))))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.insert_nat2 tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ _let_1 N)))))) (forall ((M2 tptp.nat) (K3 tptp.num)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M2))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat K3)))) (let ((_let_3 (@ tptp.pred_numeral K3))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat M2) _let_3))) (and (=> _let_4 (= _let_2 (@ (@ tptp.insert_nat2 _let_3) (@ _let_1 _let_3)))) (=> (not _let_4) (= _let_2 tptp.bot_bot_set_nat)))))))) _let_75 (forall ((K3 tptp.nat)) (= (@ tptp.set_ord_atLeast_nat (@ tptp.suc K3)) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_atLeast_nat K3)) (@ (@ tptp.insert_nat2 K3) tptp.bot_bot_set_nat)))) (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.ord_less_nat I4) N)))) N)) (forall ((K3 tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat N2) K3))))) (forall ((M5 tptp.set_nat) (I tptp.nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M5)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K4 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K4)) M5) (@ (@ tptp.ord_less_nat K4) I))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K4 tptp.nat)) (and (@ (@ tptp.member_nat K4) M5) (@ (@ tptp.ord_less_nat K4) (@ tptp.suc I))))))))) (forall ((M5 tptp.set_nat) (I tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M5) (= (@ tptp.suc (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K4 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K4)) M5) (@ (@ tptp.ord_less_nat K4) I)))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K4 tptp.nat)) (and (@ (@ tptp.member_nat K4) M5) (@ (@ tptp.ord_less_nat K4) (@ tptp.suc I))))))))) (forall ((M5 tptp.set_nat) (I tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M5) (not (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K4 tptp.nat)) (and (@ (@ tptp.member_nat K4) M5) (@ (@ tptp.ord_less_nat K4) (@ tptp.suc I)))))) tptp.zero_zero_nat)))) (forall ((P (-> tptp.nat Bool)) (I tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((K4 tptp.nat)) (and (@ P K4) (@ (@ tptp.ord_less_nat K4) I)))))) (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B3)))) (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((D5 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D5) M2)))))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.image_nat_nat (lambda ((M tptp.nat)) (@ (@ tptp.modulo_modulo_nat M) N))) tptp.top_top_set_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)))) (forall ((C tptp.nat) (Y tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat X) Y))) (let ((_let_2 (@ (@ tptp.ord_less_nat X) Y))) (let ((_let_3 (@ (@ tptp.ord_less_nat C) Y))) (and (=> _let_3 (= (@ (@ tptp.image_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat I4) C))) _let_1) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.minus_minus_nat X) C)) (@ (@ tptp.minus_minus_nat Y) C)))) (=> (not _let_3) (and (=> _let_2 (= (@ (@ tptp.image_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat I4) C))) _let_1) (@ (@ tptp.insert_nat2 tptp.zero_zero_nat) tptp.bot_bot_set_nat))) (=> (not _let_2) (= (@ (@ tptp.image_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat I4) C))) _let_1) tptp.bot_bot_set_nat))))))))) (= tptp.complete_Sup_Sup_nat (lambda ((X8 tptp.set_nat)) (@ (@ (@ tptp.if_nat (= X8 tptp.bot_bot_set_nat)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat X8)))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 N)) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ tptp.collect_nat (lambda ((Q8 tptp.nat)) (@ (@ tptp.ord_less_nat Q8) N))))))) (= tptp.divmod_nat (lambda ((M tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (or (= N2 tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat M) N2))) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) M)) (@ (@ 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 M) N2)) N2))))) _let_74 _let_73 (@ tptp.wf_nat _let_71) (forall ((N tptp.nat)) (@ tptp.bNF_We3818239936649020644el_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_nat X2) N) (@ (@ tptp.ord_less_nat Y5) N) (@ (@ tptp.ord_less_eq_nat X2) Y5))))))) (forall ((N tptp.nat)) (= (@ tptp.field_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_nat X2) N) (@ (@ tptp.ord_less_nat Y5) N) (@ (@ tptp.ord_less_eq_nat X2) Y5)))))) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_nat X2) N))))) _let_72 (forall ((I tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.upto I) J))) (= (@ (@ tptp.linord1735203802627413978nt_int (lambda ((X2 tptp.int)) X2)) _let_1) _let_1))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.upt M2) N))) (= (@ tptp.remdups_nat _let_1) _let_1))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.upt M2) N))) (= (@ (@ tptp.linord738340561235409698at_nat (lambda ((X2 tptp.nat)) X2)) _let_1) _let_1))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.tl_nat (@ (@ tptp.upt M2) N)) (@ (@ tptp.upt (@ tptp.suc M2)) N))) (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (= (@ tptp.hd_nat (@ (@ tptp.upt I) J)) I))) (forall ((M2 tptp.nat) (I tptp.nat) (J tptp.nat)) (= (@ (@ tptp.drop_nat M2) (@ (@ tptp.upt I) J)) (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat I) M2)) J))) (forall ((I tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I) M2))) (let ((_let_2 (@ tptp.upt I))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) N) (= (@ (@ tptp.take_nat M2) (@ _let_2 N)) (@ _let_2 _let_1)))))) (forall ((J tptp.nat)) (= (= (@ (@ tptp.upt tptp.zero_zero_nat) J) tptp.nil_nat) (= J tptp.zero_zero_nat))) (forall ((J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.upt I) J) tptp.nil_nat))) (forall ((I tptp.nat) (J tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ tptp.upt I))) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat J) K3)) (= (@ (@ tptp.append_nat (@ _let_1 J)) (@ (@ tptp.upt J) K3)) (@ _let_1 K3))))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or4665077453230672383an_nat M2) N)) (@ (@ tptp.upt M2) N))) (forall ((I tptp.nat) (J tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.upt I) J)) (@ (@ tptp.minus_minus_nat J) I))) (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (= (@ tptp.last_nat (@ (@ tptp.upt I) J)) (@ (@ tptp.minus_minus_nat J) tptp.one_one_nat)))) (forall ((I tptp.nat) (J tptp.nat)) (= (= (@ (@ tptp.upt I) J) tptp.nil_nat) (or (= J tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat J) I)))) (forall ((I tptp.nat) (K3 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I) K3))) (=> (@ (@ tptp.ord_less_nat _let_1) J) (= (@ (@ tptp.nth_nat (@ (@ tptp.upt I) J)) K3) _let_1)))) (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (let ((_let_2 (@ tptp.numeral_numeral_nat M2))) (let ((_let_3 (@ (@ tptp.upt _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_nat _let_2) (@ (@ tptp.upt (@ tptp.suc _let_2)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_nat)))))))) _let_70 (forall ((I tptp.nat) (J tptp.nat)) (@ tptp.distinct_nat (@ (@ tptp.upt I) J))) (forall ((Ofs tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat I4) Ofs))) (@ (@ tptp.upt A2) B2)) (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat A2) Ofs)) (@ (@ tptp.plus_plus_nat B2) Ofs)))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.map_nat_nat tptp.suc) (@ (@ tptp.upt M2) N)) (@ (@ tptp.upt (@ tptp.suc M2)) (@ tptp.suc N)))) _let_69 (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.upt M2))) (= (@ tptp.butlast_nat (@ _let_1 N)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))) _let_68 (forall ((M2 tptp.nat) (N tptp.nat) (Ns tptp.list_nat) (Q6 tptp.nat)) (let ((_let_1 (@ (@ tptp.cons_nat N) Ns))) (= (= (@ (@ tptp.cons_nat M2) _let_1) (@ (@ tptp.upt M2) Q6)) (= _let_1 (@ (@ tptp.upt (@ tptp.suc M2)) Q6))))) (forall ((I tptp.nat)) (= (@ (@ tptp.upt I) tptp.zero_zero_nat) tptp.nil_nat)) (forall ((M2 tptp.nat) (N tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) (@ (@ tptp.upt M2) N))) (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat I4) N))) (@ (@ tptp.upt tptp.zero_zero_nat) M2)) (@ (@ tptp.upt N) (@ (@ tptp.plus_plus_nat M2) N)))) (forall ((M2 tptp.nat) (N tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) (@ (@ tptp.upt M2) N))) _let_67 (forall ((I tptp.nat) (J tptp.nat) (Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (= (@ (@ tptp.upt I) J) (@ (@ tptp.append_nat Xs) Ys)) (exists ((K4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I) K4) (@ (@ tptp.ord_less_eq_nat K4) J) (= (@ (@ tptp.upt I) K4) Xs) (= (@ (@ tptp.upt K4) J) Ys)))))) _let_66 _let_65 (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (= (@ (@ tptp.upt I) J) (@ (@ tptp.cons_nat I) (@ (@ tptp.upt (@ tptp.suc I)) J))))) (forall ((U tptp.nat) (U3 tptp.nat) (P (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.upt tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.filter_nat2 P))) (=> (@ (@ tptp.ord_less_eq_nat U) U3) (=> (forall ((I5 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat U) I5) (@ (@ tptp.ord_less_nat I5) U3)) (not (@ P I5)))) (= (@ _let_2 (@ _let_1 U)) (@ _let_2 (@ _let_1 U3)))))))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))) (@ (@ tptp.upt (@ tptp.suc M2)) (@ tptp.suc N))) (@ (@ tptp.upt M2) N))) (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.upt tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat I) J) (= (@ (@ tptp.append_nat (@ _let_1 I)) (@ (@ tptp.upt I) J)) (@ _let_1 J))))) (forall ((I tptp.nat) (J tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J) K3))) (let ((_let_2 (@ tptp.upt I))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ _let_2 _let_1) (@ (@ tptp.append_nat (@ _let_2 J)) (@ (@ tptp.upt J) _let_1))))))) (forall ((I tptp.nat) (J tptp.nat) (X tptp.nat) (Xs tptp.list_nat)) (= (= (@ (@ tptp.upt I) J) (@ (@ tptp.cons_nat X) Xs)) (and (@ (@ tptp.ord_less_nat I) J) (= I X) (= (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat I) tptp.one_one_nat)) J) Xs)))) (= tptp.upt (lambda ((I4 tptp.nat) (J2 tptp.nat)) (@ (@ (@ tptp.if_list_nat (@ (@ tptp.ord_less_nat I4) J2)) (@ (@ tptp.cons_nat I4) (@ (@ tptp.upt (@ tptp.suc I4)) J2))) tptp.nil_nat))) (forall ((L tptp.nat) (H2 tptp.nat) (Is1 tptp.list_nat) (I tptp.nat) (Is2 tptp.list_nat)) (let ((_let_1 (@ tptp.upt L))) (= (= (@ _let_1 H2) (@ (@ tptp.append_nat Is1) (@ (@ tptp.cons_nat I) Is2))) (and (= Is1 (@ _let_1 I)) (= Is2 (@ (@ tptp.upt (@ tptp.suc I)) H2)) (@ (@ tptp.ord_less_eq_nat L) I) (@ (@ tptp.ord_less_nat I) H2))))) (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.upt I))) (let ((_let_2 (@ _let_1 (@ tptp.suc J)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat I) J))) (and (=> _let_3 (= _let_2 (@ (@ tptp.append_nat (@ _let_1 J)) (@ (@ tptp.cons_nat J) tptp.nil_nat)))) (=> (not _let_3) (= _let_2 tptp.nil_nat))))))) (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.upt I))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ _let_1 (@ tptp.suc J)) (@ (@ tptp.append_nat (@ _let_1 J)) (@ (@ tptp.cons_nat J) tptp.nil_nat)))))) _let_64 (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))) (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))) (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))) (forall ((L tptp.code_integer) (U tptp.code_integer)) (= (@ (@ tptp.image_4470545334726330049nteger (lambda ((X2 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger X2) L))) (@ (@ tptp.set_or8404916559141939852nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.minus_8373710615458151222nteger U) L))) (@ (@ tptp.set_or8404916559141939852nteger L) U))) _let_63 (forall ((S tptp.set_nat)) (=> (@ tptp.finite_finite_nat S) (exists ((R6 (-> tptp.nat tptp.nat))) (and (@ (@ tptp.strict1292158309912662752at_nat R6) (@ tptp.set_ord_lessThan_nat (@ tptp.finite_card_nat S))) (forall ((N9 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N9) (@ tptp.finite_card_nat S)) (@ (@ tptp.member_nat (@ R6 N9)) S))))))) (forall ((L tptp.code_integer) (U tptp.code_integer)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.set_or8404916559141939852nteger L) U))) (forall ((L tptp.code_integer) (U tptp.code_integer)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.set_or189985376899183464nteger L) U))) (forall ((L tptp.code_integer) (U tptp.code_integer)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.set_or4266950643985792945nteger L) U))) (forall ((L tptp.code_integer) (U tptp.code_integer)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.set_or2715278749043346189nteger L) U))) (forall ((U tptp.code_integer)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.set_or8404916559141939852nteger tptp.zero_z3403309356797280102nteger) U))) _let_62 _let_61 (= tptp.code_bit_cut_integer (lambda ((K4 tptp.code_integer)) (@ (@ (@ tptp.if_Pro5737122678794959658eger_o (= K4 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc6677183202524767010eger_o tptp.zero_z3403309356797280102nteger) false)) (@ (@ tptp.produc9125791028180074456eger_o (lambda ((R4 tptp.code_integer) (S6 tptp.code_integer)) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) K4)) R4) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger R4)) S6))) (= S6 tptp.one_one_Code_integer)))) (@ (@ tptp.code_divmod_abs K4) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))) (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)))))) (forall ((J tptp.code_integer)) (= (@ (@ tptp.code_divmod_abs tptp.zero_z3403309356797280102nteger) J) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))) (forall ((J tptp.code_integer)) (= (@ (@ tptp.code_divmod_abs J) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer J)))) (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)))))) _let_60 (= tptp.code_divmod_integer (lambda ((K4 tptp.code_integer) (L4 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.code_divmod_abs K4) L4))) (let ((_let_2 (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_3 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= K4 tptp.zero_z3403309356797280102nteger)) (@ _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ _let_3 L4)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ _let_3 K4)) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R4 tptp.code_integer) (S6 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R4))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S6 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger L4) S6)))))) _let_1))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= L4 tptp.zero_z3403309356797280102nteger)) (@ _let_2 K4)) (@ (@ tptp.produc6499014454317279255nteger tptp.uminus1351360451143612070nteger) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le6747313008572928689nteger K4) tptp.zero_z3403309356797280102nteger)) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R4 tptp.code_integer) (S6 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R4))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S6 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger L4)) S6)))))) _let_1))))))))))) (forall ((M5 tptp.set_nat)) (=> (@ tptp.finite_finite_nat M5) (=> (not (= M5 tptp.bot_bot_set_nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M5)) (= (@ tptp.gcd_Gcd_nat M5) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_nat_set_nat (lambda ((M tptp.nat)) (@ tptp.collect_nat (lambda ((D5 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D5) M))))) M5)))))))) (= (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_nat_set_nat tptp.set_or1210151606488870762an_nat) tptp.top_top_set_nat)) tptp.bot_bot_set_nat) (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 ((X2 tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y5))) (let ((_let_2 (@ tptp.times_times_nat X2))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U4)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U4))))))) __flatten_var_0))) Xa) X)))) (forall ((K5 tptp.set_nat)) (=> (not (= K5 tptp.bot_bot_set_nat)) (@ (@ tptp.member_nat (@ tptp.complete_Inf_Inf_nat K5)) K5))) (forall ((Z tptp.int)) (not (forall ((X3 tptp.nat) (Y2 tptp.nat)) (not (= Z (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat X3) Y2))))))) (= tptp.zero_zero_int (@ tptp.abs_Integ _let_46)) _let_59 (forall ((X tptp.product_prod_nat_nat)) (= (@ tptp.uminus_uminus_int (@ tptp.abs_Integ X)) (@ tptp.abs_Integ (@ (@ tptp.produc2626176000494625587at_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y5) X2))) X)))) _let_58 (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 ((X2 tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat U4) Y5)))) __flatten_var_0))) Xa) X))) (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 ((X2 tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) U4)) (@ (@ tptp.plus_plus_nat Y5) V4)))) __flatten_var_0))) Xa) X)))) (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 ((X2 tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat Y5) U4)))) __flatten_var_0))) Xa) X)))) (= tptp.code_divmod_integer (lambda ((K4 tptp.code_integer) (L4 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.code_divmod_abs K4) L4))) (let ((_let_2 (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= K4 tptp.zero_z3403309356797280102nteger)) (@ _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= L4 tptp.zero_z3403309356797280102nteger)) (@ _let_2 K4)) (@ (@ (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_C8797469213163452608nteger tptp.produc6499014454317279255nteger) tptp.times_3573771949741848930nteger)) tptp.sgn_sgn_Code_integer) L4) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= (@ tptp.sgn_sgn_Code_integer K4) (@ tptp.sgn_sgn_Code_integer L4))) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R4 tptp.code_integer) (S6 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R4))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S6 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer L4)) S6)))))) _let_1))))))))) (= tptp.ord_less_int (lambda ((X2 tptp.int) (Xa4 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y5 tptp.nat) (Z5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat Y5) V4)) (@ (@ tptp.plus_plus_nat U4) Z5)))) __flatten_var_0))) (@ tptp.rep_Integ X2)) (@ tptp.rep_Integ Xa4)))) (forall ((X tptp.assn) (Y tptp.assn) (A2 tptp.assn) (B2 tptp.assn)) (=> (@ (@ tptp.syntax7398250324933576852n_assn (@ (@ tptp.times_times_assn X) Y)) A2) (= (@ (@ tptp.times_times_assn A2) B2) (@ (@ tptp.times_times_assn B2) A2)))) _let_57 _let_56 _let_55 _let_54 (@ (@ (@ (@ tptp.semila1623282765462674594er_nat tptp.ord_max_nat) tptp.zero_zero_nat) (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y5) X2))) (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.ord_less_nat Y5) X2))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ tptp.order_mono_nat_nat (@ tptp.times_times_nat N)))) (= 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 ((X2 tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat U4) Y5)))) __flatten_var_0))))) (forall ((X tptp.nat) (Xa tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.bezw Xa) (@ (@ tptp.modulo_modulo_nat X) Xa)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (let ((_let_3 (= Xa tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X) Xa) Y) (and (=> _let_3 (= Y (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_3) (= Y (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Xa))))))))))))) (= tptp.bezw (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y5) (@ (@ tptp.modulo_modulo_nat X2) Y5)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= Y5 tptp.zero_zero_nat)) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X2) Y5)))))))))) (forall ((Y tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y) (@ (@ tptp.modulo_modulo_nat X) Y)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Y) (= (@ (@ tptp.bezw X) Y) (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Y)))))))))) (forall ((X tptp.nat) (Xa tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.bezw_rel) (@ (@ tptp.product_Pair_nat_nat X) Xa)))) (let ((_let_2 (@ (@ tptp.bezw Xa) (@ (@ tptp.modulo_modulo_nat X) Xa)))) (let ((_let_3 (@ tptp.product_snd_int_int _let_2))) (let ((_let_4 (= Xa tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X) Xa) Y) (=> _let_1 (not (=> (and (=> _let_4 (= Y (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_4) (= Y (@ (@ tptp.product_Pair_int_int _let_3) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_2)) (@ (@ tptp.times_times_int _let_3) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Xa)))))))) (not _let_1)))))))))) (forall ((B2 Bool) (H2 tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn (@ tptp.pure_assn B2)) H2) (and (= (@ tptp.produc8586169260539613262et_nat H2) tptp.bot_bot_set_nat) B2))) (forall ((H2 tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn tptp.one_one_assn) H2) (= (@ tptp.produc8586169260539613262et_nat H2) tptp.bot_bot_set_nat))) (forall ((M2 tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ tptp.foldr_assn_assn tptp.times_times_assn))) (=> (forall ((X3 tptp.produc6575502325842934193n_assn)) (=> (@ (@ tptp.member7957490590177025114n_assn X3) (@ tptp.set_Pr1139785259514867910n_assn M2)) (@ (@ tptp.produc7274209992780475162assn_o tptp.entails) X3))) (@ (@ tptp.entails (@ (@ _let_1 (@ (@ tptp.map_Pr8991440229025900053n_assn tptp.produc9167289414957590229n_assn) M2)) tptp.one_one_assn)) (@ (@ _let_1 (@ (@ tptp.map_Pr8991440229025900053n_assn tptp.produc2051961928117032727n_assn) M2)) tptp.one_one_assn))))) (forall ((P tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn P) tptp.top_top_assn)) H2) (not (forall ((H5 tptp.produc3658429121746597890et_nat)) (=> (= (@ tptp.produc1824681642469235216et_nat H5) (@ tptp.produc1824681642469235216et_nat H2)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.produc8586169260539613262et_nat H5)) (@ tptp.produc8586169260539613262et_nat H2)) (not (@ (@ tptp.rep_assn P) H5)))))))) _let_51 (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))))))))) _let_50 (forall ((M2 tptp.list_P8527749157015355191n_assn) (Ps2 tptp.assn) (Qs tptp.assn) (Q6 tptp.assn) (P6 tptp.assn) (Up2 tptp.assn) (Uq2 tptp.assn) (F4 tptp.assn)) (let ((_let_1 (@ (@ tptp.times_times_assn Qs) Q6))) (let ((_let_2 (@ tptp.fi M2))) (=> (@ (@ (@ (@ (@ _let_2 Ps2) _let_1) (@ (@ tptp.times_times_assn P6) Up2)) Uq2) F4) (@ (@ (@ (@ (@ _let_2 (@ (@ tptp.times_times_assn Ps2) P6)) _let_1) Up2) Uq2) F4))))) (forall ((M2 tptp.list_P8527749157015355191n_assn) (P6 tptp.assn) (Up2 tptp.assn) (Q6 tptp.assn) (Uq2 tptp.assn) (F4 tptp.assn)) (=> (@ (@ (@ (@ tptp.fI_RESULT M2) (@ (@ tptp.times_times_assn P6) Up2)) (@ (@ tptp.times_times_assn Q6) Uq2)) F4) (@ (@ (@ (@ (@ (@ tptp.fi M2) P6) Q6) Up2) Uq2) F4))) (forall ((P tptp.assn) (Q tptp.assn) (F tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn tptp.sln))) (=> (@ (@ (@ (@ (@ (@ tptp.fi tptp.nil_Pr5671120429643327159n_assn) (@ _let_1 P)) (@ _let_1 Q)) tptp.sln) tptp.sln) F) (@ (@ (@ tptp.fI_QUERY P) Q) F)))) (forall ((P tptp.assn)) (= (@ (@ tptp.times_times_assn P) tptp.sln) P)) (forall ((P tptp.assn)) (= (@ (@ tptp.times_times_assn tptp.sln) P) P)) _let_49 (forall ((M2 tptp.list_P8527749157015355191n_assn) (Up2 tptp.assn) (Qs tptp.assn) (Q6 tptp.assn) (Uq2 tptp.assn) (F4 tptp.assn)) (let ((_let_1 (@ tptp.fi M2))) (=> (@ (@ (@ (@ (@ _let_1 (@ (@ tptp.times_times_assn tptp.sln) Up2)) Qs) tptp.sln) (@ (@ tptp.times_times_assn Q6) Uq2)) F4) (@ (@ (@ (@ (@ _let_1 tptp.sln) (@ (@ tptp.times_times_assn Qs) Q6)) Up2) Uq2) F4)))) (forall ((P6 tptp.assn) (Q6 tptp.assn) (M2 tptp.list_P8527749157015355191n_assn) (Ps2 tptp.assn) (Up2 tptp.assn) (Qs tptp.assn) (Uq2 tptp.assn) (F4 tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn Qs))) (let ((_let_2 (@ tptp.times_times_assn Ps2))) (=> (@ (@ tptp.entails P6) Q6) (=> (@ (@ (@ (@ (@ (@ tptp.fi (@ (@ tptp.cons_P2971678138204555879n_assn (@ (@ tptp.produc118845697133431529n_assn P6) Q6)) M2)) (@ _let_2 Up2)) (@ _let_1 Uq2)) tptp.sln) tptp.sln) F4) (@ (@ (@ (@ (@ (@ tptp.fi M2) (@ _let_2 P6)) (@ _let_1 Q6)) Up2) Uq2) F4)))))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat M2) N)) (@ tptp.transi2905341329935302413cl_nat tptp.pred_nat)) (@ (@ tptp.ord_less_eq_nat M2) N))) (forall ((N tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.vimage_nat_nat tptp.suc))) (= (@ _let_1 (@ (@ tptp.insert_nat2 (@ tptp.suc N)) A)) (@ (@ tptp.insert_nat2 N) (@ _let_1 A))))) (forall ((A tptp.set_nat)) (let ((_let_1 (@ tptp.vimage_nat_nat tptp.suc))) (= (@ _let_1 (@ (@ tptp.insert_nat2 tptp.zero_zero_nat) A)) (@ _let_1 A)))) (forall ((S tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat S) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.finite_card_nat S)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.infini8530281810654367211te_nat S) N))))) (@ (@ (@ (@ tptp.bNF_re578469030762574527_nat_o (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2))) (@ (@ tptp.bNF_re4705727531993890431at_o_o (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2))) (lambda ((Y4 Bool) (Z2 Bool)) (= Y4 Z2)))) tptp.ord_less_nat) tptp.ord_less_nat) (@ (@ _let_48 (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y5))) (let ((_let_2 (@ tptp.times_times_nat X2))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U4)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U4))))))) __flatten_var_0)))) tptp.times_times_int) (@ (@ tptp.pcr_int _let_46) tptp.zero_zero_int) (@ (@ (@ (@ tptp.bNF_re6830278522597306478at_int (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2))) tptp.pcr_int) (lambda ((N2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat N2) tptp.zero_zero_nat))) tptp.semiri1314217659103216013at_int) (@ (@ _let_47 (@ tptp.produc2626176000494625587at_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y5) X2)))) tptp.uminus_uminus_int) (@ (@ tptp.pcr_int _let_44) tptp.one_one_int) (@ (@ (@ (@ tptp.bNF_re717283939379294677_int_o tptp.pcr_int) (@ (@ tptp.bNF_re6644619430987730960nt_o_o tptp.pcr_int) (lambda ((Y4 Bool) (Z2 Bool)) (= Y4 Z2)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat U4) Y5)))) __flatten_var_0)))) tptp.ord_less_int) (@ (@ _let_48 (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) U4)) (@ (@ tptp.plus_plus_nat Y5) V4)))) __flatten_var_0)))) tptp.plus_plus_int) (@ (@ _let_48 (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat Y5) U4)))) __flatten_var_0)))) tptp.minus_minus_int) (@ (@ _let_43 (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y5))) (let ((_let_2 (@ tptp.times_times_nat X2))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U4)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U4))))))) __flatten_var_0)))) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y5))) (let ((_let_2 (@ tptp.times_times_nat X2))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U4)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U4))))))) __flatten_var_0)))) (forall ((X tptp.nat) (Y tptp.nat) (U tptp.nat) (V2 tptp.nat)) (= (@ (@ tptp.intrel (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ (@ tptp.product_Pair_nat_nat U) V2)) (= (@ (@ tptp.plus_plus_nat X) V2) (@ (@ tptp.plus_plus_nat U) Y)))) (@ (@ (@ tptp.filterlim_nat_nat tptp.suc) tptp.at_top_nat) tptp.at_top_nat) (@ (@ tptp.intrel _let_46) _let_46) (@ (@ (@ tptp.filter3212408913953519116et_nat tptp.set_ord_atMost_nat) _let_45) tptp.at_top_nat) (@ (@ (@ tptp.filter3212408913953519116et_nat tptp.set_ord_lessThan_nat) _let_45) tptp.at_top_nat) (@ (@ _let_42 (@ tptp.produc2626176000494625587at_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y5) X2)))) (@ tptp.produc2626176000494625587at_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y5) X2)))) (@ (@ tptp.intrel _let_44) _let_44) (@ (@ (@ (@ tptp.bNF_re4202695980764964119_nat_o tptp.intrel) (@ (@ tptp.bNF_re3666534408544137501at_o_o tptp.intrel) (lambda ((Y4 Bool) (Z2 Bool)) (= Y4 Z2)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat U4) Y5)))) __flatten_var_0)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat U4) Y5)))) __flatten_var_0)))) (@ (@ _let_43 (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat Y5) U4)))) __flatten_var_0)))) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat Y5) U4)))) __flatten_var_0)))) (@ (@ _let_43 (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) U4)) (@ (@ tptp.plus_plus_nat Y5) V4)))) __flatten_var_0)))) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) U4)) (@ (@ tptp.plus_plus_nat Y5) V4)))) __flatten_var_0)))) (not (= tptp.at_top_nat tptp.bot_bot_filter_nat)) (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat (lambda ((I4 tptp.nat)) (@ P (@ tptp.suc I4)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))) (forall ((P (-> tptp.nat Bool)) (K3 tptp.nat)) (= (@ (@ tptp.eventually_nat (lambda ((N2 tptp.nat)) (@ P (@ (@ tptp.plus_plus_nat N2) K3)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))) (not (@ (@ tptp.eventually_nat (lambda ((N2 tptp.nat)) false)) tptp.at_top_nat)) (forall ((C tptp.nat) (P (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) X3) (@ P X3))) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))) (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (exists ((N8 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N2) (@ P N2)))))) (forall ((F tptp.filter_nat)) (= (@ (@ tptp.ord_le2510731241096832064er_nat F) tptp.at_top_nat) (forall ((N8 tptp.nat)) (@ (@ tptp.eventually_nat (@ tptp.ord_less_eq_nat N8)) F)))) (forall ((M2 tptp.nat) (K3 tptp.int) (L tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ (@ tptp.bit_concat_bit M2) K3) L)) N) (or (and (@ (@ tptp.ord_less_nat N) M2) (@ (@ tptp.bit_se1146084159140164899it_int K3) N)) (and (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.bit_se1146084159140164899it_int L) (@ (@ tptp.minus_minus_nat N) M2)))))) (@ (@ (@ tptp.ordering_top_nat (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y5) X2))) (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.ord_less_nat Y5) X2))) tptp.zero_zero_nat) (forall ((A2 tptp.nat) (B2 tptp.nat) (S3 tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_nat S3) T) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A2) S3)) (@ (@ tptp.product_Pair_nat_nat B2) T))) tptp.fun_pair_less)))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.product_Pair_nat_nat X))) (= (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ _let_1 Y)) (@ _let_1 Z))) tptp.fun_pair_less) (@ (@ tptp.ord_less_nat Y) Z)))) (forall ((A2 tptp.nat) (B2 tptp.nat) (S3 tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A2) S3)) (@ (@ tptp.product_Pair_nat_nat B2) T))) tptp.fun_pair_less))) (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)))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (S3 tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat S3) T) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A2) S3)) (@ (@ tptp.product_Pair_nat_nat B2) T))) tptp.fun_pair_leq)))) (forall ((X4 tptp.set_Pr1261947904930325089at_nat)) (=> (not (= X4 tptp.bot_bo2099793752762293965at_nat)) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X4) tptp.bot_bo2099793752762293965at_nat)) tptp.fun_min_strict))) (forall ((A2 tptp.nat) (B2 tptp.nat) (S3 tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A2) S3)) (@ (@ tptp.product_Pair_nat_nat B2) T))) tptp.fun_pair_leq))) (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))))) (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)))))) (forall ((X4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat X4) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat tptp.bot_bo2099793752762293965at_nat) X4)) tptp.fun_max_weak))) (forall ((X4 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X4) tptp.bot_bo2099793752762293965at_nat)) tptp.fun_min_weak)) (@ tptp.fun_re2478310338295953701at_nat (@ (@ tptp.produc9060074326276436823at_nat tptp.fun_min_strict) tptp.fun_min_weak)) _let_41 _let_40 (forall ((Y tptp.product_prod_nat_nat) (Y6 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (X4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat Y) Y6) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X) Y)) tptp.fun_pair_less) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X4) Y6)) tptp.fun_max_strict) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ (@ tptp.insert8211810215607154385at_nat X) X4)) Y6)) tptp.fun_max_strict))))) (@ tptp.fun_re2478310338295953701at_nat (@ (@ tptp.produc9060074326276436823at_nat tptp.fun_max_strict) tptp.fun_max_weak)) (forall ((Y6 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat Y6) (=> (not (= Y6 tptp.bot_bo2099793752762293965at_nat)) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat tptp.bot_bo2099793752762293965at_nat) Y6)) tptp.fun_max_strict)))) (forall ((A tptp.multis2468970476368604999at_nat) (B tptp.multis2468970476368604999at_nat) (Z6 tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.plus_p7104986032573967614at_nat Z6))) (=> (or (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ tptp.set_ms8126754132646256062at_nat A)) (@ tptp.set_ms8126754132646256062at_nat B))) tptp.fun_max_strict) (and (= A tptp.zero_z1048942125864253310at_nat) (= B tptp.zero_z1048942125864253310at_nat))) (@ (@ tptp.member6689249552917799696at_nat (@ (@ tptp.produc4348348721325984599at_nat (@ _let_1 A)) (@ _let_1 B))) tptp.ms_weak)))) (forall ((A tptp.multis2468970476368604999at_nat) (B tptp.multis2468970476368604999at_nat) (Z6 tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.plus_p7104986032573967614at_nat Z6))) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ tptp.set_ms8126754132646256062at_nat A)) (@ tptp.set_ms8126754132646256062at_nat B))) tptp.fun_max_strict) (@ (@ tptp.member6689249552917799696at_nat (@ (@ tptp.produc4348348721325984599at_nat (@ _let_1 A)) (@ _let_1 B))) tptp.ms_strict)))) (@ tptp.fun_re7357418987779152907at_nat (@ (@ tptp.produc5245064249948416855at_nat tptp.ms_strict) tptp.ms_weak)) (forall ((Z6 tptp.multis2468970476368604999at_nat) (Z7 tptp.multis2468970476368604999at_nat) (A tptp.multis2468970476368604999at_nat) (B tptp.multis2468970476368604999at_nat)) (=> (@ (@ tptp.pw_leq Z6) Z7) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ tptp.set_ms8126754132646256062at_nat A)) (@ tptp.set_ms8126754132646256062at_nat B))) tptp.fun_max_strict) (@ (@ tptp.member6689249552917799696at_nat (@ (@ tptp.produc4348348721325984599at_nat (@ (@ tptp.plus_p7104986032573967614at_nat Z6) A)) (@ (@ tptp.plus_p7104986032573967614at_nat Z7) B))) tptp.ms_weak)))) (forall ((Z6 tptp.multis2468970476368604999at_nat) (Z7 tptp.multis2468970476368604999at_nat) (A tptp.multis2468970476368604999at_nat) (B tptp.multis2468970476368604999at_nat)) (=> (@ (@ tptp.pw_leq Z6) Z7) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ tptp.set_ms8126754132646256062at_nat A)) (@ tptp.set_ms8126754132646256062at_nat B))) tptp.fun_max_strict) (@ (@ tptp.member6689249552917799696at_nat (@ (@ tptp.produc4348348721325984599at_nat (@ (@ tptp.plus_p7104986032573967614at_nat Z6) A)) (@ (@ tptp.plus_p7104986032573967614at_nat Z7) B))) tptp.ms_strict)))) (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X) Y)) tptp.fun_pair_leq) (@ (@ tptp.pw_leq (@ (@ tptp.add_ms2612439473150266591at_nat X) tptp.zero_z1048942125864253310at_nat)) (@ (@ tptp.add_ms2612439473150266591at_nat Y) tptp.zero_z1048942125864253310at_nat)))) (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat) (X4 tptp.multis2468970476368604999at_nat) (Y6 tptp.multis2468970476368604999at_nat)) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X) Y)) tptp.fun_pair_leq) (=> (@ (@ tptp.pw_leq X4) Y6) (@ (@ tptp.pw_leq (@ (@ tptp.plus_p7104986032573967614at_nat (@ (@ tptp.add_ms2612439473150266591at_nat X) tptp.zero_z1048942125864253310at_nat)) X4)) (@ (@ tptp.plus_p7104986032573967614at_nat (@ (@ tptp.add_ms2612439473150266591at_nat Y) tptp.zero_z1048942125864253310at_nat)) Y6))))) (= tptp.pw_leq (lambda ((A12 tptp.multis2468970476368604999at_nat) (A23 tptp.multis2468970476368604999at_nat)) (or (and (= A12 tptp.zero_z1048942125864253310at_nat) (= A23 tptp.zero_z1048942125864253310at_nat)) (exists ((X2 tptp.product_prod_nat_nat) (Y5 tptp.product_prod_nat_nat) (X8 tptp.multis2468970476368604999at_nat) (Y7 tptp.multis2468970476368604999at_nat)) (and (= A12 (@ (@ tptp.plus_p7104986032573967614at_nat (@ (@ tptp.add_ms2612439473150266591at_nat X2) tptp.zero_z1048942125864253310at_nat)) X8)) (= A23 (@ (@ tptp.plus_p7104986032573967614at_nat (@ (@ tptp.add_ms2612439473150266591at_nat Y5) tptp.zero_z1048942125864253310at_nat)) Y7)) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X2) Y5)) tptp.fun_pair_leq) (@ (@ tptp.pw_leq X8) Y7)))))) (forall ((A1 tptp.multis2468970476368604999at_nat) (A22 tptp.multis2468970476368604999at_nat)) (=> (@ (@ tptp.pw_leq A1) A22) (=> (=> (= A1 tptp.zero_z1048942125864253310at_nat) (not (= A22 tptp.zero_z1048942125864253310at_nat))) (not (forall ((X3 tptp.product_prod_nat_nat) (Y2 tptp.product_prod_nat_nat) (X9 tptp.multis2468970476368604999at_nat)) (=> (= A1 (@ (@ tptp.plus_p7104986032573967614at_nat (@ (@ tptp.add_ms2612439473150266591at_nat X3) tptp.zero_z1048942125864253310at_nat)) X9)) (forall ((Y8 tptp.multis2468970476368604999at_nat)) (=> (= A22 (@ (@ tptp.plus_p7104986032573967614at_nat (@ (@ tptp.add_ms2612439473150266591at_nat Y2) tptp.zero_z1048942125864253310at_nat)) Y8)) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X3) Y2)) tptp.fun_pair_leq) (not (@ (@ tptp.pw_leq X9) Y8))))))))))) (forall ((Z6 tptp.multis2468970476368604999at_nat) (Z7 tptp.multis2468970476368604999at_nat)) (=> (@ (@ tptp.pw_leq Z6) Z7) (@ (@ tptp.member6689249552917799696at_nat (@ (@ tptp.produc4348348721325984599at_nat (@ (@ tptp.plus_p7104986032573967614at_nat Z6) tptp.zero_z1048942125864253310at_nat)) (@ (@ tptp.plus_p7104986032573967614at_nat Z7) tptp.zero_z1048942125864253310at_nat))) tptp.ms_weak))) (forall ((X4 tptp.multis2468970476368604999at_nat) (Y6 tptp.multis2468970476368604999at_nat)) (=> (@ (@ tptp.pw_leq X4) Y6) (exists ((A9 tptp.multis2468970476368604999at_nat) (B5 tptp.multis2468970476368604999at_nat) (Z8 tptp.multis2468970476368604999at_nat)) (and (= X4 (@ (@ tptp.plus_p7104986032573967614at_nat A9) Z8)) (= Y6 (@ (@ tptp.plus_p7104986032573967614at_nat B5) Z8)) (or (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ tptp.set_ms8126754132646256062at_nat A9)) (@ tptp.set_ms8126754132646256062at_nat B5))) tptp.fun_max_strict) (and (= B5 tptp.zero_z1048942125864253310at_nat) (= A9 tptp.zero_z1048942125864253310at_nat))))))) (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) tptp.less_than) (@ (@ tptp.ord_less_nat X) Y))) (forall ((N tptp.nat)) (@ (@ tptp.order_2888998067076097458on_nat (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_nat X2) N)))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_nat X2) N) (@ (@ tptp.ord_less_nat Y5) N) (@ (@ tptp.ord_less_eq_nat X2) Y5))))))) (forall ((N tptp.nat)) (@ (@ tptp.order_2888998067076097458on_nat (@ tptp.field_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_nat X2) N) (@ (@ tptp.ord_less_nat Y5) N) (@ (@ tptp.ord_less_eq_nat X2) Y5))))))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_nat X2) N) (@ (@ tptp.ord_less_nat Y5) N) (@ (@ tptp.ord_less_eq_nat X2) Y5))))))) (forall ((P (-> tptp.product_prod_nat_nat Bool))) (= (@ (@ tptp.eventu1038000079068216329at_nat P) (@ (@ tptp.prod_filter_nat_nat tptp.at_top_nat) tptp.at_top_nat)) (exists ((N8 tptp.nat)) (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) M) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N2) (@ P (@ (@ tptp.product_Pair_nat_nat N2) M))))))))) _let_38 (and (not (@ (@ tptp.member444158400953824016od_o_o (@ (@ tptp.produc763777882069021527od_o_o tptp.bNF_Cardinal_ctwo) tptp.bNF_Cardinal_czero_o)) tptp.bNF_We2654380646378065620so_o_o)) (@ (@ tptp.bNF_Ca8331644756375544342r_on_o (@ tptp.field_o tptp.bNF_Cardinal_ctwo)) tptp.bNF_Cardinal_ctwo)) (@ (@ tptp.member4095101504841534314at_nat (@ (@ tptp.produc8517790099723286449at_nat tptp.bNF_Cardinal_ctwo) tptp.bNF_Ca8665028551170535155natLeq)) tptp.bNF_We8182288985678559134_o_nat) (forall ((N tptp.nat)) (= (@ (@ tptp.order_underS_nat tptp.bNF_Ca8665028551170535155natLeq) N) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_nat X2) N))))) (forall ((N tptp.nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bNF_Ca8665028551170535155natLeq) (@ (@ tptp.produc457027306803732586at_nat (@ (@ tptp.order_underS_nat tptp.bNF_Ca8665028551170535155natLeq) N)) (lambda ((Uu2 tptp.nat)) (@ (@ tptp.order_underS_nat tptp.bNF_Ca8665028551170535155natLeq) N)))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_nat X2) N) (@ (@ tptp.ord_less_nat Y5) N) (@ (@ tptp.ord_less_eq_nat X2) Y5))))))) (forall ((N tptp.nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bNF_Ca8665028551170535155natLeq) (@ (@ tptp.produc457027306803732586at_nat (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_nat X2) N)))) (lambda ((Uu2 tptp.nat)) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_nat X2) N)))))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_nat X2) N) (@ (@ tptp.ord_less_nat Y5) N) (@ (@ tptp.ord_less_eq_nat X2) Y5))))))) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ tptp.bNF_Ca3793111618940312692of_nat tptp.top_top_set_nat)) tptp.bNF_Ca8665028551170535155natLeq)) tptp.bNF_We5258908940166488438at_nat) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ tptp.bNF_Ca3793111618940312692of_nat (@ tptp.field_nat tptp.bNF_Ca8665028551170535155natLeq))) tptp.bNF_Ca8665028551170535155natLeq)) tptp.bNF_We5258908940166488438at_nat) (@ (@ _let_37 (lambda ((X2 tptp.product_prod_int_int) (Y5 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Y5))) (let ((_let_2 (@ tptp.product_snd_int_int X2))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) _let_1)) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y5)) _let_2))) (@ (@ tptp.times_times_int _let_2) _let_1)))))) tptp.plus_plus_rat) (@ (@ tptp.pcr_rat _let_30) tptp.one_one_rat) (@ (@ tptp.pcr_rat _let_29) tptp.zero_zero_rat) (@ (@ _let_37 (lambda ((X2 tptp.product_prod_int_int) (Y5 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) (@ tptp.product_fst_int_int Y5))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int X2)) (@ tptp.product_snd_int_int Y5))))) tptp.times_times_rat) (@ (@ _let_36 (lambda ((X2 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int (@ tptp.product_fst_int_int X2))) (@ tptp.product_snd_int_int X2)))) tptp.uminus_uminus_rat) (forall ((Q6 tptp.int) (P6 tptp.int)) (=> (@ (@ tptp.ord_less_int Q6) tptp.zero_zero_int) (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P6) Q6)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int P6)) (@ tptp.uminus_uminus_int Q6)))))) (@ (@ _let_36 (lambda ((X2 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_fst_int_int X2))) (@ (@ (@ 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 X2)) _let_1))))) tptp.inverse_inverse_rat) (forall ((P6 tptp.int)) (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P6) tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))) (forall ((R2 tptp.product_prod_int_int) (P6 tptp.int) (Q6 tptp.int)) (=> (= (@ tptp.normalize R2) (@ (@ tptp.product_Pair_int_int P6) Q6)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q6))) (forall ((Q6 tptp.int) (S3 tptp.int) (P6 tptp.int) (R2 tptp.int)) (=> (not (= Q6 tptp.zero_zero_int)) (=> (not (= S3 tptp.zero_zero_int)) (=> (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P6) Q6)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int R2) S3))) (= (@ (@ tptp.times_times_int P6) S3) (@ (@ tptp.times_times_int R2) Q6)))))) (forall ((P6 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.inverse_inverse_rat P6)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= A3 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A3)) B3)) (@ tptp.abs_abs_int A3))))) (@ tptp.quotient_of P6)))) _let_35 (forall ((K3 tptp.num)) (= (@ tptp.quotient_of (@ tptp.numeral_numeral_rat K3)) (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int K3)) tptp.one_one_int))) (= (@ tptp.quotient_of tptp.one_one_rat) _let_30) (= (@ tptp.quotient_of tptp.zero_zero_rat) _let_29) (forall ((K3 tptp.num)) (= (@ tptp.quotient_of (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat K3))) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K3))) tptp.one_one_int))) (= (@ tptp.quotient_of (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int)) (forall ((Xs tptp.list_int)) (= (@ tptp.gcd_Gcd_int (@ tptp.set_int2 Xs)) (@ (@ (@ tptp.fold_int_int tptp.gcd_gcd_int) Xs) tptp.zero_zero_int))) (forall ((R2 tptp.rat) (N tptp.int) (D2 tptp.int)) (=> (= (@ tptp.quotient_of R2) (@ (@ tptp.product_Pair_int_int N) D2)) (= R2 (@ (@ tptp.divide_divide_rat (@ tptp.ring_1_of_int_rat N)) (@ tptp.ring_1_of_int_rat D2))))) (forall ((R2 tptp.rat) (P6 tptp.int) (Q6 tptp.int)) (=> (= (@ tptp.quotient_of R2) (@ (@ tptp.product_Pair_int_int P6) Q6)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q6))) (forall ((P6 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.abs_abs_rat P6)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.product_Pair_int_int (@ tptp.abs_abs_int A3)) __flatten_var_0))) (@ tptp.quotient_of P6)))) (forall ((P6 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.sgn_sgn_rat P6)) (@ (@ tptp.product_Pair_int_int (@ tptp.sgn_sgn_int (@ tptp.product_fst_int_int (@ tptp.quotient_of P6)))) tptp.one_one_int))) (forall ((P6 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.uminus_uminus_rat P6)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int A3)) __flatten_var_0))) (@ tptp.quotient_of P6)))) (forall ((P6 tptp.rat) (Q6 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.divide_divide_rat P6) Q6)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (C5 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B3 tptp.int) (D5 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int A3) D5)) (@ (@ tptp.times_times_int C5) B3))))) (@ tptp.quotient_of Q6)))) (@ tptp.quotient_of P6)))) (forall ((P6 tptp.rat) (Q6 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.minus_minus_rat P6) Q6)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (C5 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B3 tptp.int) (D5 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A3) D5)) (@ (@ tptp.times_times_int B3) C5))) (@ (@ tptp.times_times_int C5) D5))))) (@ tptp.quotient_of Q6)))) (@ tptp.quotient_of P6)))) (forall ((P6 tptp.rat) (Q6 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.times_times_rat P6) Q6)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (C5 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B3 tptp.int) (D5 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int A3) B3)) (@ (@ tptp.times_times_int C5) D5))))) (@ tptp.quotient_of Q6)))) (@ tptp.quotient_of P6)))) (forall ((P6 tptp.rat) (Q6 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.plus_plus_rat P6) Q6)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (C5 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B3 tptp.int) (D5 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A3) D5)) (@ (@ tptp.times_times_int B3) C5))) (@ (@ tptp.times_times_int C5) D5))))) (@ tptp.quotient_of Q6)))) (@ tptp.quotient_of P6)))) (forall ((A2 tptp.int)) (= (@ tptp.quotient_of (@ tptp.of_int A2)) (@ (@ tptp.product_Pair_int_int A2) tptp.one_one_int))) (forall ((K3 tptp.num)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int tptp.one_one_int) (@ tptp.numeral_numeral_int K3))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat K3)))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.gcd_gcd_nat M2) N)) (or (not (= M2 tptp.zero_zero_nat)) (not (= N tptp.zero_zero_nat))))) (forall ((A tptp.set_nat)) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (@ (@ tptp.member_nat A4) A) (=> (@ (@ tptp.member_nat B4) A) (@ (@ tptp.member_nat (@ (@ tptp.gcd_gcd_nat A4) B4)) A)))) (=> (not (= A tptp.bot_bot_set_nat)) (@ (@ tptp.member_nat (@ tptp.gcd_Gcd_nat A)) A)))) (forall ((Xs tptp.list_nat)) (= (@ tptp.gcd_Gcd_nat (@ tptp.set_nat2 Xs)) (@ (@ (@ tptp.fold_nat_nat tptp.gcd_gcd_nat) Xs) tptp.zero_zero_nat))) (forall ((K3 tptp.num) (L tptp.num)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int K3)) (@ tptp.numeral_numeral_int L))) (@ (@ tptp.divide_divide_rat (@ tptp.numeral_numeral_rat K3)) (@ tptp.numeral_numeral_rat L)))) (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.gcd_gcd_nat M2) N) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((D5 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D5))) (and (@ _let_1 M2) (@ _let_1 N))))))))) (forall ((K3 tptp.num)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int K3)) tptp.one_one_int)) (@ tptp.numeral_numeral_rat K3))) (forall ((A2 tptp.int)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int A2) tptp.zero_zero_int)) tptp.zero_zero_rat)) (forall ((A2 tptp.int)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) A2)) tptp.zero_zero_rat)) _let_34 (forall ((A2 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.product_Pair_int_int A2))) (= (@ tptp.frct (@ _let_1 (@ tptp.uminus_uminus_int B2))) (@ tptp.uminus_uminus_rat (@ tptp.frct (@ _let_1 B2)))))) (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int A2)) B2)) (@ tptp.uminus_uminus_rat (@ tptp.frct (@ (@ tptp.product_Pair_int_int A2) B2))))) (forall ((X tptp.nat) (Xa tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.gcd_nat_rel) (@ (@ tptp.product_Pair_nat_nat X) Xa)))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= (@ (@ tptp.gcd_gcd_nat X) Xa) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y X)) (=> (not _let_2) (= Y (@ (@ tptp.gcd_gcd_nat Xa) (@ (@ tptp.modulo_modulo_nat X) Xa))))) (not _let_1)))))))) (@ (@ _let_32 (lambda ((X2 tptp.product_prod_int_int) (Y5 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Y5))) (let ((_let_2 (@ tptp.product_snd_int_int X2))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) _let_1)) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y5)) _let_2))) (@ (@ tptp.times_times_int _let_2) _let_1)))))) (lambda ((X2 tptp.product_prod_int_int) (Y5 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Y5))) (let ((_let_2 (@ tptp.product_snd_int_int X2))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) _let_1)) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y5)) _let_2))) (@ (@ tptp.times_times_int _let_2) _let_1)))))) (@ (@ tptp.ratrel _let_30) _let_30) (@ (@ tptp.ratrel _let_29) _let_29) (@ (@ (@ (@ tptp.bNF_re157797125943740599nt_int (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2))) (@ (@ tptp.bNF_re6250860962936578807nt_int (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2))) tptp.ratrel)) (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= B3 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int A3) B3)))) (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= B3 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int A3) B3)))) (@ (@ _let_32 (lambda ((X2 tptp.product_prod_int_int) (Y5 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) (@ tptp.product_fst_int_int Y5))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int X2)) (@ tptp.product_snd_int_int Y5))))) (lambda ((X2 tptp.product_prod_int_int) (Y5 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) (@ tptp.product_fst_int_int Y5))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int X2)) (@ tptp.product_snd_int_int Y5))))) (@ (@ _let_31 (lambda ((X2 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int (@ tptp.product_fst_int_int X2))) (@ tptp.product_snd_int_int X2)))) (lambda ((X2 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int (@ tptp.product_fst_int_int X2))) (@ tptp.product_snd_int_int X2)))) (@ (@ _let_31 (lambda ((X2 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_fst_int_int X2))) (@ (@ (@ 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 X2)) _let_1))))) (lambda ((X2 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_fst_int_int X2))) (@ (@ (@ 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 X2)) _let_1))))) (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))))))))) (forall ((X tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_fst_int_int X))) (=> (@ (@ tptp.ratrel X) X) (= (@ tptp.inverse_inverse_rat (@ tptp.abs_Rat X)) (@ tptp.abs_Rat (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= _let_1 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ tptp.product_snd_int_int X)) _let_1))))))) (= tptp.one_one_rat (@ tptp.abs_Rat _let_30)) (= tptp.zero_zero_rat (@ tptp.abs_Rat _let_29)) (forall ((X tptp.product_prod_int_int)) (=> (@ (@ tptp.ratrel X) X) (= (@ tptp.uminus_uminus_rat (@ tptp.abs_Rat X)) (@ tptp.abs_Rat (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int (@ tptp.product_fst_int_int X))) (@ tptp.product_snd_int_int X)))))) (forall ((Xa tptp.product_prod_int_int) (X tptp.product_prod_int_int)) (=> (@ (@ tptp.ratrel Xa) Xa) (=> (@ (@ tptp.ratrel X) X) (= (@ (@ tptp.times_times_rat (@ tptp.abs_Rat Xa)) (@ tptp.abs_Rat X)) (@ tptp.abs_Rat (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Xa)) (@ tptp.product_fst_int_int X))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int Xa)) (@ tptp.product_snd_int_int X)))))))) _let_28 _let_27 _let_26 _let_25 (forall ((X tptp.assn)) (= (@ tptp.abs_assn (@ tptp.rep_assn X)) X)) (forall ((P (-> tptp.produc3658429121746597890et_nat Bool)) (Pr tptp.assn)) (=> (forall ((H tptp.produc3658429121746597890et_nat)) (= (@ P H) (@ (@ tptp.rep_assn Pr) H))) (= Pr (@ tptp.abs_assn P)))) (forall ((P (-> tptp.produc3658429121746597890et_nat Bool)) (Pr tptp.assn)) (=> (forall ((H tptp.produc3658429121746597890et_nat)) (= (@ P H) (@ (@ tptp.rep_assn Pr) H))) (= (@ tptp.abs_assn P) Pr))) _let_22 (= tptp.bot_bot_assn (@ tptp.abs_assn (lambda ((Uu2 tptp.produc3658429121746597890et_nat)) false))) (= tptp.one_one_assn (@ tptp.abs_assn tptp.one_assn_raw)) _let_21 _let_20 _let_19 _let_18 _let_17 (forall ((H2 tptp.heap_e7401611519738050253t_unit)) (@ tptp.in_range (@ (@ tptp.produc7507926704131184380et_nat H2) tptp.bot_bot_set_nat))) (forall ((H2 tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn tptp.top_top_assn) H2) (@ tptp.in_range H2))) (forall ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat) (As3 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H2))) (= (@ tptp.in_range (@ _let_1 (@ (@ tptp.sup_sup_set_nat As2) As3))) (and (@ tptp.in_range (@ _let_1 As2)) (@ tptp.in_range (@ _let_1 As3)))))) (forall ((P tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn (@ tptp.uminus_uminus_assn P)) H2) (and (@ tptp.in_range H2) (not (@ (@ tptp.rep_assn P) H2))))) (forall ((As2 tptp.set_nat) (As3 tptp.set_nat) (H2 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H2))) (=> (@ (@ tptp.ord_less_eq_set_nat As2) As3) (=> (@ tptp.in_range (@ _let_1 As3)) (@ tptp.in_range (@ _let_1 As2)))))) (forall ((P tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P) H2) (@ tptp.in_range H2))) _let_16 (forall ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat) (Q tptp.assn) (R tptp.assn)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) As2))) (=> (@ tptp.in_range _let_1) (=> (forall ((H5 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H5))) (=> (= (@ (@ tptp.inf_inf_set_nat As2) As4) tptp.bot_bot_set_nat) (=> (@ (@ (@ tptp.relH As2) H2) H5) (=> (@ tptp.in_range (@ _let_1 As2)) (=> (@ (@ tptp.rep_assn Q) (@ _let_1 As4)) (@ (@ tptp.rep_assn R) (@ _let_1 (@ (@ tptp.sup_sup_set_nat As2) As4))))))))) (@ (@ tptp.rep_assn (@ (@ tptp.wand_assn Q) R)) _let_1))))) (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat)) (=> (not (@ (@ (@ tptp.wand_raw X) Xa) Xb)) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As))) (=> (= Xb _let_1) (and (@ tptp.in_range _let_1) (forall ((H5 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H5))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As) As4) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As) H) H5) (@ tptp.in_range (@ _let_1 As)) (@ X (@ _let_1 As4))) (@ Xa (@ _let_1 (@ (@ tptp.sup_sup_set_nat As) As4))))))))))))) (forall ((As2 tptp.set_nat) (As3 tptp.set_nat) (H2 tptp.heap_e7401611519738050253t_unit) (H4 tptp.heap_e7401611519738050253t_unit)) (= (@ (@ (@ tptp.relH (@ (@ tptp.sup_sup_set_nat As2) As3)) H2) H4) (and (@ (@ (@ tptp.relH As2) H2) H4) (@ (@ (@ tptp.relH As3) H2) H4)))) (forall ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (=> (@ tptp.in_range (@ (@ tptp.produc7507926704131184380et_nat H2) As2)) (@ (@ (@ tptp.relH As2) H2) H2))) (forall ((As2 tptp.set_nat) (H2 tptp.heap_e7401611519738050253t_unit) (H4 tptp.heap_e7401611519738050253t_unit)) (=> (@ (@ (@ tptp.relH As2) H2) H4) (@ tptp.in_range (@ (@ tptp.produc7507926704131184380et_nat H2) As2)))) (forall ((As2 tptp.set_nat) (H2 tptp.heap_e7401611519738050253t_unit) (H4 tptp.heap_e7401611519738050253t_unit)) (=> (@ (@ (@ tptp.relH As2) H2) H4) (@ tptp.in_range (@ (@ tptp.produc7507926704131184380et_nat H4) As2)))) (forall ((As2 tptp.set_nat) (H2 tptp.heap_e7401611519738050253t_unit) (H4 tptp.heap_e7401611519738050253t_unit) (P tptp.assn)) (let ((_let_1 (@ tptp.rep_assn P))) (=> (@ (@ (@ tptp.relH As2) H2) H4) (= (@ _let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) As2)) (@ _let_1 (@ (@ tptp.produc7507926704131184380et_nat H4) As2)))))) (forall ((As2 tptp.set_nat) (H12 tptp.heap_e7401611519738050253t_unit) (H23 tptp.heap_e7401611519738050253t_unit) (H32 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ tptp.relH As2))) (let ((_let_2 (@ _let_1 H12))) (=> (@ _let_2 H23) (=> (@ (@ _let_1 H23) H32) (@ _let_2 H32)))))) (forall ((As2 tptp.set_nat) (H2 tptp.heap_e7401611519738050253t_unit) (H4 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ tptp.relH As2))) (=> (@ (@ _let_1 H2) H4) (@ (@ _let_1 H4) H2)))) (forall ((Bs tptp.set_nat) (H2 tptp.heap_e7401611519738050253t_unit) (H4 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (=> (@ (@ (@ tptp.relH Bs) H2) H4) (=> (@ (@ tptp.ord_less_eq_set_nat As2) Bs) (@ (@ (@ tptp.relH As2) H2) H4)))) (forall ((P (-> tptp.produc3658429121746597890et_nat Bool)) (Q (-> tptp.produc3658429121746597890et_nat Bool)) (H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) As2))) (= (@ (@ (@ tptp.wand_raw P) Q) _let_1) (and (@ tptp.in_range _let_1) (forall ((H6 tptp.heap_e7401611519738050253t_unit) (As5 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H6))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As2) As5) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As2) H2) H6) (@ tptp.in_range (@ _let_1 As2)) (@ P (@ _let_1 As5))) (@ Q (@ _let_1 (@ (@ tptp.sup_sup_set_nat As2) As5)))))))))) (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 ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As))) (=> (= Xb _let_1) (= Y (not (and (@ tptp.in_range _let_1) (forall ((H6 tptp.heap_e7401611519738050253t_unit) (As5 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H6))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As) As5) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As) H) H6) (@ tptp.in_range (@ _let_1 As)) (@ X (@ _let_1 As5))) (@ Xa (@ _let_1 (@ (@ tptp.sup_sup_set_nat As) As5))))))))))))))) (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat)) (=> (@ (@ (@ tptp.wand_raw X) Xa) Xb) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As))) (=> (= Xb _let_1) (not (and (@ tptp.in_range _let_1) (forall ((H7 tptp.heap_e7401611519738050253t_unit) (As6 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H7))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As) As6) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As) H) H7) (@ tptp.in_range (@ _let_1 As)) (@ X (@ _let_1 As6))) (@ Xa (@ _let_1 (@ (@ tptp.sup_sup_set_nat As) As6)))))))))))))) (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 ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As))) (=> (= Xb _let_1) (=> (@ (@ tptp.accp_P1862375125659990705et_nat tptp.wand_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) _let_1))) (and (@ tptp.in_range _let_1) (forall ((H5 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H5))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As) As4) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As) H) H5) (@ tptp.in_range (@ _let_1 As)) (@ X (@ _let_1 As4))) (@ Xa (@ _let_1 (@ (@ tptp.sup_sup_set_nat As) As4))))))))))))))) (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 ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As))) (=> (= 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 ((H7 tptp.heap_e7401611519738050253t_unit) (As6 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H7))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As) As6) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As) H) H7) (@ tptp.in_range (@ _let_1 As)) (@ X (@ _let_1 As6))) (@ Xa (@ _let_1 (@ (@ tptp.sup_sup_set_nat As) As6)))))))))))))))) (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 ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As))) (=> (= Xb _let_1) (=> (= Y (and (@ tptp.in_range _let_1) (forall ((H6 tptp.heap_e7401611519738050253t_unit) (As5 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H6))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As) As5) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As) H) H6) (@ tptp.in_range (@ _let_1 As)) (@ X (@ _let_1 As5))) (@ Xa (@ _let_1 (@ (@ tptp.sup_sup_set_nat As) As5)))))))) (not (@ (@ tptp.accp_P1862375125659990705et_nat tptp.wand_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) _let_1)))))))))))) (forall ((Q6 tptp.int) (P6 tptp.int)) (let ((_let_1 (@ (@ tptp.product_Pair_int_int P6) Q6))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q6) (=> (@ (@ tptp.algebr932160517623751201me_int P6) Q6) (= (@ tptp.normalize _let_1) _let_1))))) (forall ((R2 tptp.product_prod_int_int) (P6 tptp.int) (Q6 tptp.int)) (=> (= (@ tptp.normalize R2) (@ (@ tptp.product_Pair_int_int P6) Q6)) (@ (@ tptp.algebr932160517623751201me_int P6) Q6))) (forall ((R2 tptp.rat) (P6 tptp.int) (Q6 tptp.int)) (=> (= (@ tptp.quotient_of R2) (@ (@ tptp.product_Pair_int_int P6) Q6)) (@ (@ tptp.algebr932160517623751201me_int P6) Q6))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.algebr934650988132801477me_nat N) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.algebr934650988132801477me_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) N))) (@ (@ (@ (@ tptp.bNF_re3461391660133120880nt_rat (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2))) (@ (@ tptp.bNF_re2214769303045360666nt_rat (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2))) tptp.pcr_rat)) (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= B3 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int A3) B3)))) tptp.fract) (forall ((A2 tptp.int) (B2 tptp.int) (P6 tptp.int) (Q6 tptp.int)) (let ((_let_1 (@ (@ tptp.fract A2) B2))) (=> (= (@ tptp.quotient_of _let_1) (@ (@ tptp.product_Pair_int_int P6) Q6)) (= (@ (@ tptp.fract P6) Q6) _let_1)))) (forall ((A2 tptp.int) (B2 tptp.int) (P6 tptp.int) (Q6 tptp.int)) (=> (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int A2) B2)) (@ (@ tptp.product_Pair_int_int P6) Q6)) (= (@ (@ tptp.fract P6) Q6) (@ (@ tptp.fract A2) B2)))) (forall ((A2 tptp.int) (B2 tptp.int)) (= (@ tptp.quotient_of (@ (@ tptp.fract A2) B2)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int A2) B2)))) _let_15 (forall ((X tptp.produc8763457246119570046nteger)) (not (forall ((F5 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (D3 tptp.code_integer) (I5 tptp.code_integer)) (not (= X (@ (@ tptp.produc6137756002093451184nteger F5) (@ (@ tptp.produc1086072967326762835nteger D3) I5))))))) (forall ((X tptp.produc7773217078559923341nt_int)) (not (forall ((F5 (-> tptp.int tptp.option6357759511663192854e_term)) (D3 tptp.int) (I5 tptp.int)) (not (= X (@ (@ tptp.produc4305682042979456191nt_int F5) (@ (@ tptp.product_Pair_int_int D3) I5))))))) (forall ((X tptp.produc2285326912895808259nt_int)) (not (forall ((F5 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (D3 tptp.int) (I5 tptp.int)) (not (= X (@ (@ tptp.produc5700946648718959541nt_int F5) (@ (@ tptp.product_Pair_int_int D3) I5))))))) (forall ((X tptp.produc1908205239877642774nteger)) (not (forall ((F5 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (D3 tptp.code_integer) (I5 tptp.code_integer)) (not (= X (@ (@ tptp.produc8603105652947943368nteger F5) (@ (@ tptp.produc1086072967326762835nteger D3) I5))))))) (forall ((X tptp.list_nat) (Y tptp.nat)) (=> (= (@ tptp.nat_list_encode X) Y) (=> (=> (= X tptp.nil_nat) (not (= Y tptp.zero_zero_nat))) (not (forall ((X3 tptp.nat) (Xs2 tptp.list_nat)) (=> (= X (@ (@ tptp.cons_nat X3) Xs2)) (not (= Y (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X3) (@ tptp.nat_list_encode Xs2)))))))))))) (forall ((X tptp.nat) (Xs tptp.list_nat)) (= (@ tptp.nat_list_encode (@ (@ tptp.cons_nat X) Xs)) (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X) (@ tptp.nat_list_encode Xs)))))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat A2) (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat A2) B2)))) (forall ((B2 tptp.nat) (A2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat B2) (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat A2) B2)))) (forall ((X tptp.list_nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.accp_list_nat tptp.nat_list_encode_rel))) (=> (= (@ tptp.nat_list_encode X) Y) (=> (@ _let_1 X) (=> (=> (= X tptp.nil_nat) (=> (= Y tptp.zero_zero_nat) (not (@ _let_1 tptp.nil_nat)))) (not (forall ((X3 tptp.nat) (Xs2 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat X3) Xs2))) (=> (= X _let_1) (=> (= Y (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X3) (@ tptp.nat_list_encode Xs2))))) (not (@ (@ tptp.accp_list_nat tptp.nat_list_encode_rel) _let_1)))))))))))) (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.frequently_nat P) tptp.cofinite_nat) (forall ((M tptp.nat)) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M) N2) (@ P N2)))))) (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (@ P tptp.zero_zero_nat) (=> (forall ((I5 tptp.nat)) (=> (@ P I5) (exists ((J4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) J4) (@ P J4) (@ Q J4))))) (@ (@ tptp.frequently_nat Q) tptp.cofinite_nat)))) (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat P) tptp.cofinite_nat) (exists ((M tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ P N2)))))) _let_14 (forall ((P (-> tptp.int Bool)) (I tptp.int) (J tptp.int)) (= (@ (@ tptp.list_ex_int P) (@ (@ tptp.upto I) J)) (not (@ (@ (@ tptp.all_interval_int (@ (@ tptp.comp_o_o_int (lambda ((_lvar_0 Bool)) (not _lvar_0))) P)) I) J)))) _let_13 (forall ((P (-> tptp.int Bool)) (I tptp.int) (J tptp.int)) (= (@ (@ tptp.list_all_int P) (@ (@ tptp.upto I) J)) (@ (@ (@ tptp.all_interval_int P) I) J))) (forall ((P Bool)) (@ tptp.is_pure_assn (@ tptp.pure_assn P))) (forall ((A2 tptp.assn) (B2 tptp.assn)) (=> (@ tptp.is_pure_assn A2) (=> (@ tptp.is_pure_assn B2) (@ tptp.is_pure_assn (@ (@ tptp.times_times_assn A2) B2))))) _let_12 (@ tptp.is_pure_assn tptp.one_one_assn) _let_10 (forall ((A2 tptp.assn)) (=> (@ tptp.is_pure_assn A2) (not (forall ((P5 Bool)) (not (= A2 (@ tptp.pure_assn P5))))))) (@ tptp.is_pure_assn tptp.bot_bot_assn) (forall ((M5 tptp.set_nat)) (=> (@ tptp.finite_finite_nat M5) (=> (not (= M5 tptp.bot_bot_set_nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M5)) (=> (forall ((M6 tptp.nat) (N5 tptp.nat)) (=> (@ (@ tptp.member_nat M6) M5) (=> (@ (@ tptp.member_nat N5) M5) (@ (@ tptp.member_nat (@ (@ tptp.gcd_lcm_nat M6) N5)) M5)))) (= (@ tptp.gcd_Lcm_nat M5) (@ tptp.lattic8265883725875713057ax_nat M5))))))) (forall ((N tptp.nat) (M5 tptp.set_nat)) (= (@ tptp.gcd_Lcm_nat (@ (@ tptp.insert_nat2 N) M5)) (@ (@ tptp.gcd_lcm_nat N) (@ tptp.gcd_Lcm_nat M5)))) (forall ((M5 tptp.set_nat)) (=> (@ tptp.finite_finite_nat M5) (=> (not (= M5 tptp.bot_bot_set_nat)) (=> (forall ((M6 tptp.nat) (N5 tptp.nat)) (=> (@ (@ tptp.member_nat M6) M5) (=> (@ (@ tptp.member_nat N5) M5) (@ (@ tptp.member_nat (@ (@ tptp.gcd_lcm_nat M6) N5)) M5)))) (@ (@ tptp.member_nat (@ tptp.gcd_Lcm_nat M5)) M5))))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.gcd_lcm_nat M2) N)))))) (forall ((Xs tptp.list_nat)) (= (@ tptp.gcd_Lcm_nat (@ tptp.set_nat2 Xs)) (@ (@ (@ tptp.fold_nat_nat tptp.gcd_lcm_nat) Xs) tptp.one_one_nat))) (forall ((Xs tptp.list_int)) (= (@ tptp.gcd_Lcm_int (@ tptp.set_int2 Xs)) (@ (@ (@ tptp.fold_int_int tptp.gcd_lcm_int) Xs) tptp.one_one_int))) (forall ((P (-> tptp.produc3658429121746597890et_nat Bool))) (=> (forall ((As tptp.set_nat) (H tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As))) (=> (@ P _let_1) (@ tptp.in_range _let_1)))) (=> (forall ((As tptp.set_nat) (H tptp.heap_e7401611519738050253t_unit) (H5 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H5) As))) (=> (@ P (@ (@ tptp.produc7507926704131184380et_nat H) As)) (=> (@ (@ (@ tptp.relH As) H) H5) (=> (@ tptp.in_range _let_1) (@ P _let_1)))))) (@ tptp.proper P)))) (forall ((P (-> tptp.produc3658429121746597890et_nat Bool)) (H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat) (H4 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H4) As2))) (=> (@ tptp.proper P) (=> (@ P (@ (@ tptp.produc7507926704131184380et_nat H2) As2)) (=> (@ (@ (@ tptp.relH As2) H2) H4) (=> (@ tptp.in_range _let_1) (@ P _let_1))))))) (forall ((P (-> tptp.produc3658429121746597890et_nat Bool)) (Q (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.proper P) (=> (@ tptp.proper Q) (@ tptp.proper (lambda ((H3 tptp.produc3658429121746597890et_nat)) (and (@ P H3) (@ Q H3))))))) (forall ((P (-> tptp.produc3658429121746597890et_nat Bool)) (Q (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.proper P) (=> (@ tptp.proper Q) (@ tptp.proper (lambda ((H3 tptp.produc3658429121746597890et_nat)) (or (@ P H3) (@ Q H3))))))) (@ tptp.proper (lambda ((Uu2 tptp.produc3658429121746597890et_nat)) false)) (@ tptp.proper tptp.in_range) (@ tptp.proper tptp.one_assn_raw) (forall ((P (-> tptp.produc3658429121746597890et_nat Bool)) (Q (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.proper P) (=> (@ tptp.proper Q) (@ tptp.proper (@ (@ tptp.times_assn_raw P) Q))))) (forall ((P (-> tptp.produc3658429121746597890et_nat Bool)) (Q (-> tptp.produc3658429121746597890et_nat Bool))) (@ tptp.proper (@ (@ tptp.wand_raw P) Q))) (forall ((P (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.proper P) (@ tptp.proper (lambda ((H3 tptp.produc3658429121746597890et_nat)) (and (@ tptp.in_range H3) (not (@ P H3))))))) (forall ((B2 Bool)) (@ tptp.proper (@ tptp.pure_a825153325127701367it_nat B2))) (forall ((Y (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o Y) (@ tptp.collec939566748876313656_nat_o tptp.proper)) (= (@ tptp.rep_assn (@ tptp.abs_assn Y)) Y))) (forall ((X tptp.assn)) (not (forall ((Y2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (= X (@ tptp.abs_assn Y2)) (not (@ (@ tptp.member6576561426505652726_nat_o Y2) (@ tptp.collec939566748876313656_nat_o tptp.proper))))))) (forall ((P (-> tptp.assn Bool)) (X tptp.assn)) (=> (forall ((Y2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o Y2) (@ tptp.collec939566748876313656_nat_o tptp.proper)) (@ P (@ tptp.abs_assn Y2)))) (@ P X))) (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Y (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.collec939566748876313656_nat_o tptp.proper))) (=> (@ (@ tptp.member6576561426505652726_nat_o X) _let_1) (=> (@ (@ tptp.member6576561426505652726_nat_o Y) _let_1) (= (= (@ tptp.abs_assn X) (@ tptp.abs_assn Y)) (= X Y)))))) (forall ((Y (-> tptp.produc3658429121746597890et_nat Bool)) (P (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o Y) (@ tptp.collec939566748876313656_nat_o tptp.proper)) (=> (forall ((X3 tptp.assn)) (@ P (@ tptp.rep_assn X3))) (@ P Y)))) (forall ((Y (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o Y) (@ tptp.collec939566748876313656_nat_o tptp.proper)) (not (forall ((X3 tptp.assn)) (not (= Y (@ tptp.rep_assn X3))))))) (forall ((X tptp.assn)) (@ (@ tptp.member6576561426505652726_nat_o (@ tptp.rep_assn X)) (@ tptp.collec939566748876313656_nat_o tptp.proper))) (forall ((P (-> tptp.produc3658429121746597890et_nat Bool)) (H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) As2))) (=> (@ tptp.proper P) (=> (@ P _let_1) (@ tptp.in_range _let_1))))) (forall ((P (-> tptp.produc3658429121746597890et_nat Bool)) (As2 tptp.set_nat) (H2 tptp.heap_e7401611519738050253t_unit) (H4 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H4) As2))) (=> (@ tptp.proper P) (=> (@ (@ (@ tptp.relH As2) H2) H4) (=> (@ tptp.in_range _let_1) (= (@ P (@ (@ tptp.produc7507926704131184380et_nat H2) As2)) (@ P _let_1))))))) _let_9 (forall ((P (-> tptp.nat Bool)) (I tptp.nat) (J tptp.nat)) (= (@ (@ tptp.list_ex_nat P) (@ (@ tptp.upt I) J)) (not (@ (@ (@ tptp.all_interval_nat (@ (@ tptp.comp_o_o_nat (lambda ((_lvar_0 Bool)) (not _lvar_0))) P)) I) J)))) (forall ((P (-> tptp.nat Bool)) (I tptp.nat) (J tptp.nat)) (= (@ (@ tptp.list_all_nat P) (@ (@ tptp.upt I) J)) (@ (@ (@ tptp.all_interval_nat P) I) J))) _let_8 (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.nat_of_num (@ tptp.num_of_nat N)) N))) (forall ((X tptp.num)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.nat_of_num X))) (= tptp.ord_less_num (lambda ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_nat (@ tptp.nat_of_num M)) (@ tptp.nat_of_num N2)))) (forall ((N tptp.code_natural)) (let ((_let_1 (@ tptp.code_nat_of_natural N))) (=> (not (= N tptp.zero_z2226904508553997617atural)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat _let_1) (@ tptp.suc tptp.zero_zero_nat))) _let_1)))) _let_7 (forall ((V2 tptp.code_natural) (W 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 W) _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 W) _let_4)) (@ tptp.numera5444537566228673987atural (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 _let_2)))))))))))))) (let ((_let_9 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 _let_3)))))))))))))))) (let ((_let_10 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 _let_7))))))))) (let ((_let_11 (@ (@ (@ tptp.minus_shift (@ tptp.numera5444537566228673987atural (@ tptp.bit1 _let_10))) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.modulo8411746178871703098atural V2) _let_9)) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 _let_6))))))))))))) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural V2) _let_9)) (@ tptp.numera5444537566228673987atural (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 _let_5))))))))))))))))) (= (@ tptp.next (@ (@ tptp.produc3574140220909816553atural V2) W)) (@ (@ 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))))))))))))))) (forall ((X tptp.produc989692990947075319atural)) (not (forall ((F5 (-> tptp.produc4972180933644002618e_term tptp.option6357759511663192854e_term)) (D3 tptp.code_natural) (I5 tptp.code_natural)) (not (= X (@ (@ tptp.produc3831813291587773865atural F5) (@ (@ tptp.produc3574140220909816553atural D3) I5))))))) (forall ((X tptp.produc8731074985263844745atural)) (not (forall ((F5 (-> tptp.code_natural tptp.option6357759511663192854e_term)) (D3 tptp.code_natural) (I5 tptp.code_natural)) (not (= X (@ (@ tptp.produc2252593628808123835atural F5) (@ (@ tptp.produc3574140220909816553atural D3) I5))))))) (forall ((X tptp.produc7822875418678951345atural)) (not (forall ((B4 tptp.code_natural) (I5 tptp.code_natural)) (not (= X (@ (@ tptp.produc3574140220909816553atural B4) I5)))))) _let_6 (forall ((X tptp.product_prod_int_int)) (not (forall ((D3 tptp.int) (I5 tptp.int)) (not (= X (@ (@ tptp.product_Pair_int_int D3) I5)))))) _let_5 (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))) (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))))))))) (forall ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (= (@ tptp.in_range (@ (@ tptp.produc7507926704131184380et_nat H2) As2)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) As2) (@ (@ tptp.ord_less_nat X2) (@ tptp.lim_Product_unit H2)))))) (forall ((X tptp.produc3658429121746597890et_nat)) (=> (not (@ tptp.in_range X)) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (= X (@ (@ tptp.produc7507926704131184380et_nat H) As)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) As) (@ (@ tptp.ord_less_nat X3) (@ tptp.lim_Product_unit H))))))))) (forall ((X tptp.produc3658429121746597890et_nat)) (=> (@ tptp.in_range X) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (= X (@ (@ tptp.produc7507926704131184380et_nat H) As)) (not (forall ((X7 tptp.nat)) (=> (@ (@ tptp.member_nat X7) As) (@ (@ tptp.ord_less_nat X7) (@ tptp.lim_Product_unit H)))))))))) (forall ((X tptp.produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ tptp.in_range X) Y) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (= X (@ (@ tptp.produc7507926704131184380et_nat H) As)) (= Y (not (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) As) (@ (@ tptp.ord_less_nat X2) (@ tptp.lim_Product_unit H))))))))))) _let_4 (forall ((P Bool) (H2 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ (@ tptp.heap_T875086893843062177t_unit (@ tptp.refine_Imp_assert P)) H2))) (and (=> P (= _let_1 (@ tptp.some_P1914260805536162275it_nat (@ (@ tptp.produc7133225469290080770it_nat tptp.product_Unity) (@ (@ tptp.produc584006145561248582it_nat H2) tptp.zero_zero_nat))))) (=> (not P) (= _let_1 tptp.none_P9117596204409417319it_nat))))) (forall ((P tptp.assn) (Phi Bool)) (=> (forall ((H tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P) H) Phi)) (@ (@ (@ tptp.hoare_8945653483474564448t_unit P) (@ tptp.refine_Imp_assert Phi)) (lambda ((Uu2 tptp.product_unit)) P)))) _let_3 (= tptp.ord_less_nat (@ tptp.transi2163837189807498211lp_nat (lambda ((M tptp.nat) (N2 tptp.nat)) (= N2 (@ tptp.suc M))))) (@ (@ (@ tptp.type_d3909072315231072503_nat_o tptp.rep_assn) tptp.abs_assn) (@ tptp.collec939566748876313656_nat_o tptp.proper)) (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int false) X) Y) Y)) (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int true) X) Y) X)) (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat false) X) Y) Y)) (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat true) X) Y) X)) (forall ((X tptp.assn) (Y tptp.assn)) (= (@ (@ (@ tptp.if_assn false) X) Y) Y)) (forall ((X tptp.assn) (Y tptp.assn)) (= (@ (@ (@ tptp.if_assn true) X) Y) X)) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer false) X) Y) Y)) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer true) X) Y) X)) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ (@ tptp.if_set_int false) X) Y) Y)) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ (@ tptp.if_set_int true) X) Y) X)) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ (@ tptp.if_set_nat false) X) Y) Y)) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ (@ tptp.if_set_nat true) X) Y) X)) (forall ((X tptp.list_int) (Y tptp.list_int)) (= (@ (@ (@ tptp.if_list_int false) X) Y) Y)) (forall ((X tptp.list_int) (Y tptp.list_int)) (= (@ (@ (@ tptp.if_list_int true) X) Y) X)) (forall ((X tptp.list_nat) (Y tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat false) X) Y) Y)) (forall ((X tptp.list_nat) (Y tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat true) X) Y) X)) (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (= (@ (@ (@ tptp.if_filter_nat false) X) Y) Y)) (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (= (@ (@ (@ tptp.if_filter_nat true) X) Y) X)) (forall ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int false) X) Y) Y)) (forall ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int true) X) Y) X)) (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat false) X) Y) Y)) (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat true) X) Y) X)) (forall ((X tptp.produc6271795597528267376eger_o) (Y tptp.produc6271795597528267376eger_o)) (= (@ (@ (@ tptp.if_Pro5737122678794959658eger_o false) X) Y) Y)) (forall ((X tptp.produc6271795597528267376eger_o) (Y tptp.produc6271795597528267376eger_o)) (= (@ (@ (@ tptp.if_Pro5737122678794959658eger_o true) X) Y) X)) (forall ((X tptp.list_P6011104703257516679at_nat) (Y tptp.list_P6011104703257516679at_nat)) (= (@ (@ (@ tptp.if_lis9186351972506106189at_nat false) X) Y) Y)) (forall ((X tptp.list_P6011104703257516679at_nat) (Y tptp.list_P6011104703257516679at_nat)) (= (@ (@ (@ tptp.if_lis9186351972506106189at_nat true) X) Y) X)) (forall ((X tptp.produc8923325533196201883nteger) (Y tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger false) X) Y) Y)) (forall ((X tptp.produc8923325533196201883nteger) (Y tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger true) X) Y) X)) (forall ((X tptp.list_P8527749157015355191n_assn) (Y tptp.list_P8527749157015355191n_assn)) (= (@ (@ (@ tptp.if_lis7173127979115136509n_assn false) X) Y) Y)) (forall ((X tptp.list_P8527749157015355191n_assn) (Y tptp.list_P8527749157015355191n_assn)) (= (@ (@ (@ tptp.if_lis7173127979115136509n_assn true) X) Y) X)) (forall ((X tptp.list_P7985473006766602707_nat_o) (Y tptp.list_P7985473006766602707_nat_o)) (= (@ (@ (@ tptp.if_lis2904118647880296857_nat_o false) X) Y) Y)) (forall ((X tptp.list_P7985473006766602707_nat_o) (Y tptp.list_P7985473006766602707_nat_o)) (= (@ (@ (@ tptp.if_lis2904118647880296857_nat_o true) X) Y) X)) (forall ((P Bool)) (or (= P true) (= P false))) (forall ((X tptp.list_P5464809261938338413at_nat) (Y tptp.list_P5464809261938338413at_nat)) (= (@ (@ (@ tptp.if_lis7508161100780771379at_nat false) X) Y) Y)) (forall ((X tptp.list_P5464809261938338413at_nat) (Y tptp.list_P5464809261938338413at_nat)) (= (@ (@ (@ tptp.if_lis7508161100780771379at_nat true) X) Y) X)) _let_2 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 11.88/12.16 )
% 11.88/12.16 % SZS output end Proof for ITP219^3
% 11.88/12.16 % cvc5---1.0.5 exiting
% 11.88/12.17 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------