DT2H2X---1.9.5.THM-Ref.s

%------------------------------------------------------------------------------
% File     : DT2H2X---1.9.5
% Problem  : ITP193^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300

% Computer : n027.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 : Wed Feb 25 08:56:18 AM UTC 2026

% Result   : Theorem 10.33s 3.09s
% Output   : Refutation 10.33s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : ITP193^2 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.12  % Command  : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.32  % Computer : n027.cluster.edu
% 0.14/0.32  % Model    : x86_64 x86_64
% 0.14/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32  % Memory   : 8042.1875MB
% 0.14/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32  % CPULimit : 300
% 0.14/0.32  % WCLimit  : 300
% 0.14/0.32  % DateTime : Tue Feb 24 08:29:52 EST 2026
% 0.14/0.33  % CPUTime  : 
% 0.14/0.33  Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.44  ---- Original DTF file ---
% 0.19/0.44  thf(spec,logic,$$dhol).
% 0.19/0.44  %------------------------------------------------------------------------------
% 0.19/0.44  % File     : ITP193^2 : TPTP v9.2.1. Released v7.5.0.
% 0.19/0.44  % Domain   : Interactive Theorem Proving
% 0.19/0.44  % Problem  : Sledgehammer Sturm_Tarski problem prob_1192__5884460_1
% 0.19/0.44  % Version  : Especial.
% 0.19/0.44  % English  :
% 0.19/0.44  
% 0.19/0.44  % Refs     : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.19/0.44  %          : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.19/0.44  % Source   : [Des21]
% 0.19/0.44  % Names    : Sturm_Tarski/prob_1192__5884460_1 [Des21]
% 0.19/0.44  
% 0.19/0.44  % Status   : Theorem
% 0.19/0.44  % Rating   : 0.00 v8.1.0, 0.25 v7.5.0
% 0.19/0.44  % Syntax   : Number of formulae    :  407 ( 108 unt;  55 typ;   0 def)
% 0.19/0.44  %            Number of atoms       : 1123 ( 221 equ;   0 cnn)
% 0.19/0.44  %            Maximal formula atoms :   13 (   3 avg)
% 0.19/0.44  %            Number of connectives : 3733 ( 103   ~;  27   |;  90   &;2937   @)
% 0.19/0.44  %                                         (   0 <=>; 576  =>;   0  <=;   0 <~>)
% 0.19/0.44  %            Maximal formula depth :   22 (   7 avg)
% 0.19/0.44  %            Number of types       :    4 (   3 usr)
% 0.19/0.44  %            Number of type conns  :  154 ( 154   >;   0   *;   0   +;   0  <<)
% 0.19/0.44  %            Number of symbols     :   55 (  52 usr;   7 con; 0-4 aty)
% 0.19/0.44  %            Number of variables   : 1086 (  94   ^; 900   !;  49   ?;1086   :)
% 0.19/0.44  %                                         (  43  !>;   0  ?*;   0  @-;   0  @+)
% 0.19/0.44  % SPC      : TH1_THM_EQU_NAR
% 0.19/0.44  
% 0.19/0.44  % Comments : This file was generated by Sledgehammer 2021-02-23 16:29:27.553
% 0.19/0.44  %------------------------------------------------------------------------------
% 0.19/0.44  % Could-be-implicit typings (5)
% 0.19/0.44  thf(ty_t_Polynomial_Opoly,type,
% 0.19/0.44      poly: $tType > $tType ).
% 0.19/0.44  
% 0.19/0.44  thf(ty_t_Real_Oreal,type,
% 0.19/0.44      real: $tType ).
% 0.19/0.44  
% 0.19/0.44  thf(ty_t_Set_Oset,type,
% 0.19/0.44      set: $tType > $tType ).
% 0.19/0.44  
% 0.19/0.44  thf(ty_t_Nat_Onat,type,
% 0.19/0.44      nat: $tType ).
% 0.19/0.44  
% 0.19/0.44  thf(ty_t_Int_Oint,type,
% 0.19/0.44      int: $tType ).
% 0.19/0.44  
% 0.19/0.44  % Explicit typings (50)
% 0.19/0.44  thf(sy_cl_Rings_Oidom,type,
% 0.19/0.44      idom: 
% 0.19/0.44        !>[A: $tType] : $o ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_cl_HOL_Otype,type,
% 0.19/0.44      type: 
% 0.19/0.44        !>[A: $tType] : $o ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_cl_Groups_Oone,type,
% 0.19/0.44      one: 
% 0.19/0.44        !>[A: $tType] : $o ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_cl_Groups_Ozero,type,
% 0.19/0.44      zero: 
% 0.19/0.44        !>[A: $tType] : $o ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_cl_Orderings_Oord,type,
% 0.19/0.44      ord: 
% 0.19/0.44        !>[A: $tType] : $o ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_cl_Nat_Oring__char__0,type,
% 0.19/0.44      ring_char_0: 
% 0.19/0.44        !>[A: $tType] : $o ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_cl_Orderings_Oorder,type,
% 0.19/0.44      order: 
% 0.19/0.44        !>[A: $tType] : $o ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_cl_Orderings_Ono__bot,type,
% 0.19/0.44      no_bot: 
% 0.19/0.44        !>[A: $tType] : $o ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_cl_Orderings_Ono__top,type,
% 0.19/0.44      no_top: 
% 0.19/0.44        !>[A: $tType] : $o ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_cl_Finite__Set_Ofinite,type,
% 0.19/0.44      finite_finite: 
% 0.19/0.44        !>[A: $tType] : $o ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_cl_Rings_Ocomm__ring__1,type,
% 0.19/0.44      comm_ring_1: 
% 0.19/0.44        !>[A: $tType] : $o ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_cl_Orderings_Olinorder,type,
% 0.19/0.44      linorder: 
% 0.19/0.44        !>[A: $tType] : $o ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_cl_Orderings_Opreorder,type,
% 0.19/0.44      preorder: 
% 0.19/0.44        !>[A: $tType] : $o ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_cl_Orderings_Owellorder,type,
% 0.19/0.44      wellorder: 
% 0.19/0.44        !>[A: $tType] : $o ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_cl_Rings_Ozero__less__one,type,
% 0.19/0.44      zero_less_one: 
% 0.19/0.44        !>[A: $tType] : $o ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_cl_Orderings_Odense__order,type,
% 0.19/0.44      dense_order: 
% 0.19/0.44        !>[A: $tType] : $o ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_cl_Rings_Ocomm__semiring__0,type,
% 0.19/0.44      comm_semiring_0: 
% 0.19/0.44        !>[A: $tType] : $o ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_cl_Rings_Ocomm__semiring__1,type,
% 0.19/0.44      comm_semiring_1: 
% 0.19/0.44        !>[A: $tType] : $o ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_cl_Rings_Olinordered__idom,type,
% 0.19/0.44      linordered_idom: 
% 0.19/0.44        !>[A: $tType] : $o ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_cl_Groups_Ocomm__monoid__add,type,
% 0.19/0.44      comm_monoid_add: 
% 0.19/0.44        !>[A: $tType] : $o ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_cl_Fields_Olinordered__field,type,
% 0.19/0.44      linordered_field: 
% 0.19/0.44        !>[A: $tType] : $o ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_cl_Orderings_Odense__linorder,type,
% 0.19/0.44      dense_linorder: 
% 0.19/0.44        !>[A: $tType] : $o ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_cl_Rings_Oring__no__zero__divisors,type,
% 0.19/0.44      ring_n68954251visors: 
% 0.19/0.44        !>[A: $tType] : $o ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_cl_Groups_Oordered__comm__monoid__add,type,
% 0.19/0.44      ordere216010020id_add: 
% 0.19/0.44        !>[A: $tType] : $o ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_cl_Rings_Olinordered__nonzero__semiring,type,
% 0.19/0.44      linord1659791738miring: 
% 0.19/0.44        !>[A: $tType] : $o ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 0.19/0.44      canoni770627133id_add: 
% 0.19/0.44        !>[A: $tType] : $o ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_cl_Groups_Oordered__cancel__comm__monoid__add,type,
% 0.19/0.44      ordere1818651114id_add: 
% 0.19/0.44        !>[A: $tType] : $o ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_cl_Conditionally__Complete__Lattices_Olinear__continuum,type,
% 0.19/0.44      condit1656338222tinuum: 
% 0.19/0.44        !>[A: $tType] : $o ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_cl_Conditionally__Complete__Lattices_Oconditionally__complete__linorder,type,
% 0.19/0.44      condit1037483654norder: 
% 0.19/0.44        !>[A: $tType] : $o ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_c_Finite__Set_Ofinite,type,
% 0.19/0.44      finite_finite2: 
% 0.19/0.44        !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_c_Groups_Oone__class_Oone,type,
% 0.19/0.44      one_one: 
% 0.19/0.44        !>[A: $tType] : A ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_c_Groups_Ozero__class_Ozero,type,
% 0.19/0.44      zero_zero: 
% 0.19/0.44        !>[A: $tType] : A ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum,type,
% 0.19/0.44      groups1340683514dd_sum: 
% 0.19/0.44        !>[B: $tType,A: $tType] : ( ( B > A ) > ( set @ B ) > A ) ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_c_If,type,
% 0.19/0.44      if: 
% 0.19/0.44        !>[A: $tType] : ( $o > A > A > A ) ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.19/0.44      ord_less: 
% 0.19/0.44        !>[A: $tType] : ( A > A > $o ) ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.19/0.44      ord_less_eq: 
% 0.19/0.44        !>[A: $tType] : ( A > A > $o ) ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_c_Polynomial_Ois__zero,type,
% 0.19/0.44      is_zero: 
% 0.19/0.44        !>[A: $tType] : ( ( poly @ A ) > $o ) ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_c_Polynomial_Opoly,type,
% 0.19/0.44      poly2: 
% 0.19/0.44        !>[A: $tType] : ( ( poly @ A ) > A > A ) ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_c_Polynomial_Opoly__cutoff,type,
% 0.19/0.44      poly_cutoff: 
% 0.19/0.44        !>[A: $tType] : ( nat > ( poly @ A ) > ( poly @ A ) ) ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_c_Polynomial_Oreflect__poly,type,
% 0.19/0.44      reflect_poly: 
% 0.19/0.44        !>[A: $tType] : ( ( poly @ A ) > ( poly @ A ) ) ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_c_Set_OCollect,type,
% 0.19/0.44      collect: 
% 0.19/0.44        !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_c_Sturm__Tarski__Mirabelle__osyjafhhev_Ocindex__poly,type,
% 0.19/0.44      sturm_1539314049x_poly: real > real > ( poly @ real ) > ( poly @ real ) > int ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_c_Sturm__Tarski__Mirabelle__osyjafhhev_Ocross,type,
% 0.19/0.44      sturm_424270202_cross: ( poly @ real ) > real > real > int ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_c_Sturm__Tarski__Mirabelle__osyjafhhev_Ojump__poly,type,
% 0.19/0.44      sturm_652470720p_poly: ( poly @ real ) > ( poly @ real ) > real > int ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_c_member,type,
% 0.19/0.44      member: 
% 0.19/0.44        !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_v_a,type,
% 0.19/0.44      a: real ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_v_a_H,type,
% 0.19/0.44      a2: real ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_v_b,type,
% 0.19/0.44      b: real ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_v_b_H,type,
% 0.19/0.44      b2: real ).
% 0.19/0.44  
% 0.19/0.44  thf(sy_v_p,type,
% 0.19/0.44      p: poly @ real ).
% 0.19/0.44  
% 0.19/0.44  % Relevant facts (254)
% 0.19/0.44  thf(fact_0__092_060open_062finite_A_123x_O_Apoly_Ap_Ax_A_061_A0_125_092_060close_062,axiom,
% 0.19/0.44      ( finite_finite2 @ real
% 0.19/0.44      @ ( collect @ real
% 0.19/0.44        @ ^ [X: real] :
% 0.19/0.44            ( ( poly2 @ real @ p @ X )
% 0.19/0.44            = ( zero_zero @ real ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % \<open>finite {x. poly p x = 0}\<close>
% 0.19/0.44  thf(fact_1_assms_I2_J,axiom,
% 0.19/0.44      ord_less @ real @ a2 @ b2 ).
% 0.19/0.44  
% 0.19/0.44  % assms(2)
% 0.19/0.44  thf(fact_2_assms_I3_J,axiom,
% 0.19/0.44      ord_less @ real @ b2 @ b ).
% 0.19/0.44  
% 0.19/0.44  % assms(3)
% 0.19/0.44  thf(fact_3_assms_I1_J,axiom,
% 0.19/0.44      ord_less @ real @ a @ a2 ).
% 0.19/0.44  
% 0.19/0.44  % assms(1)
% 0.19/0.44  thf(fact_4_False,axiom,
% 0.19/0.44      ( p
% 0.19/0.44     != ( zero_zero @ ( poly @ real ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % False
% 0.19/0.44  thf(fact_5_poly__0,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( comm_semiring_0 @ A )
% 0.19/0.44       => ! [X2: A] :
% 0.19/0.44            ( ( poly2 @ A @ ( zero_zero @ ( poly @ A ) ) @ X2 )
% 0.19/0.44            = ( zero_zero @ A ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % poly_0
% 0.19/0.44  thf(fact_6_not__gr__zero,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( canoni770627133id_add @ A )
% 0.19/0.44       => ! [N: A] :
% 0.19/0.44            ( ( ~ ( ord_less @ A @ ( zero_zero @ A ) @ N ) )
% 0.19/0.44            = ( N
% 0.19/0.44              = ( zero_zero @ A ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % not_gr_zero
% 0.19/0.44  thf(fact_7_assms_I4_J,axiom,
% 0.19/0.44      ! [X3: real] :
% 0.19/0.44        ( ( ( ( ord_less @ real @ a @ X3 )
% 0.19/0.44            & ( ord_less_eq @ real @ X3 @ a2 ) )
% 0.19/0.44          | ( ( ord_less_eq @ real @ b2 @ X3 )
% 0.19/0.44            & ( ord_less @ real @ X3 @ b ) ) )
% 0.19/0.44       => ( ( poly2 @ real @ p @ X3 )
% 0.19/0.44         != ( zero_zero @ real ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % assms(4)
% 0.19/0.44  thf(fact_8_finite__Collect__conjI,axiom,
% 0.19/0.44      ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.19/0.44        ( ( ( finite_finite2 @ A @ ( collect @ A @ P ) )
% 0.19/0.44          | ( finite_finite2 @ A @ ( collect @ A @ Q ) ) )
% 0.19/0.44       => ( finite_finite2 @ A
% 0.19/0.44          @ ( collect @ A
% 0.19/0.44            @ ^ [X: A] :
% 0.19/0.44                ( ( P @ X )
% 0.19/0.44                & ( Q @ X ) ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % finite_Collect_conjI
% 0.19/0.44  thf(fact_9_finite__Collect__disjI,axiom,
% 0.19/0.44      ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.19/0.44        ( ( finite_finite2 @ A
% 0.19/0.44          @ ( collect @ A
% 0.19/0.44            @ ^ [X: A] :
% 0.19/0.44                ( ( P @ X )
% 0.19/0.44                | ( Q @ X ) ) ) )
% 0.19/0.44        = ( ( finite_finite2 @ A @ ( collect @ A @ P ) )
% 0.19/0.44          & ( finite_finite2 @ A @ ( collect @ A @ Q ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % finite_Collect_disjI
% 0.19/0.44  thf(fact_10_poly__roots__finite,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( ( comm_ring_1 @ A )
% 0.19/0.44          & ( ring_n68954251visors @ A ) )
% 0.19/0.44       => ! [P2: poly @ A] :
% 0.19/0.44            ( ( P2
% 0.19/0.44             != ( zero_zero @ ( poly @ A ) ) )
% 0.19/0.44           => ( finite_finite2 @ A
% 0.19/0.44              @ ( collect @ A
% 0.19/0.44                @ ^ [X: A] :
% 0.19/0.44                    ( ( poly2 @ A @ P2 @ X )
% 0.19/0.44                    = ( zero_zero @ A ) ) ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % poly_roots_finite
% 0.19/0.44  thf(fact_11_poly__IVT__neg,axiom,
% 0.19/0.44      ! [A2: real,B2: real,P2: poly @ real] :
% 0.19/0.44        ( ( ord_less @ real @ A2 @ B2 )
% 0.19/0.44       => ( ( ord_less @ real @ ( zero_zero @ real ) @ ( poly2 @ real @ P2 @ A2 ) )
% 0.19/0.44         => ( ( ord_less @ real @ ( poly2 @ real @ P2 @ B2 ) @ ( zero_zero @ real ) )
% 0.19/0.44           => ? [X4: real] :
% 0.19/0.44                ( ( ord_less @ real @ A2 @ X4 )
% 0.19/0.44                & ( ord_less @ real @ X4 @ B2 )
% 0.19/0.44                & ( ( poly2 @ real @ P2 @ X4 )
% 0.19/0.44                  = ( zero_zero @ real ) ) ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % poly_IVT_neg
% 0.19/0.44  thf(fact_12_poly__IVT__pos,axiom,
% 0.19/0.44      ! [A2: real,B2: real,P2: poly @ real] :
% 0.19/0.44        ( ( ord_less @ real @ A2 @ B2 )
% 0.19/0.44       => ( ( ord_less @ real @ ( poly2 @ real @ P2 @ A2 ) @ ( zero_zero @ real ) )
% 0.19/0.44         => ( ( ord_less @ real @ ( zero_zero @ real ) @ ( poly2 @ real @ P2 @ B2 ) )
% 0.19/0.44           => ? [X4: real] :
% 0.19/0.44                ( ( ord_less @ real @ A2 @ X4 )
% 0.19/0.44                & ( ord_less @ real @ X4 @ B2 )
% 0.19/0.44                & ( ( poly2 @ real @ P2 @ X4 )
% 0.19/0.44                  = ( zero_zero @ real ) ) ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % poly_IVT_pos
% 0.19/0.44  thf(fact_13_finite__code,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( finite_finite @ A )
% 0.19/0.44       => ( ( finite_finite2 @ A )
% 0.19/0.44          = ( ^ [A3: set @ A] : $true ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % finite_code
% 0.19/0.44  thf(fact_14_poly__all__0__iff__0,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( ( ring_char_0 @ A )
% 0.19/0.44          & ( comm_ring_1 @ A )
% 0.19/0.44          & ( ring_n68954251visors @ A ) )
% 0.19/0.44       => ! [P2: poly @ A] :
% 0.19/0.44            ( ( ! [X: A] :
% 0.19/0.44                  ( ( poly2 @ A @ P2 @ X )
% 0.19/0.44                  = ( zero_zero @ A ) ) )
% 0.19/0.44            = ( P2
% 0.19/0.44              = ( zero_zero @ ( poly @ A ) ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % poly_all_0_iff_0
% 0.19/0.44  thf(fact_15_less__numeral__extra_I3_J,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( linord1659791738miring @ A )
% 0.19/0.44       => ~ ( ord_less @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % less_numeral_extra(3)
% 0.19/0.44  thf(fact_16_le__zero__eq,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( canoni770627133id_add @ A )
% 0.19/0.44       => ! [N: A] :
% 0.19/0.44            ( ( ord_less_eq @ A @ N @ ( zero_zero @ A ) )
% 0.19/0.44            = ( N
% 0.19/0.44              = ( zero_zero @ A ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % le_zero_eq
% 0.19/0.44  thf(fact_17_zero__le,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( canoni770627133id_add @ A )
% 0.19/0.44       => ! [X2: A] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ X2 ) ) ).
% 0.19/0.44  
% 0.19/0.44  % zero_le
% 0.19/0.44  thf(fact_18_le__numeral__extra_I3_J,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( linord1659791738miring @ A )
% 0.19/0.44       => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % le_numeral_extra(3)
% 0.19/0.44  thf(fact_19_finite__psubset__induct,axiom,
% 0.19/0.44      ! [A: $tType,A4: set @ A,P: ( set @ A ) > $o] :
% 0.19/0.44        ( ( finite_finite2 @ A @ A4 )
% 0.19/0.44       => ( ! [A5: set @ A] :
% 0.19/0.44              ( ( finite_finite2 @ A @ A5 )
% 0.19/0.44             => ( ! [B3: set @ A] :
% 0.19/0.44                    ( ( ord_less @ ( set @ A ) @ B3 @ A5 )
% 0.19/0.44                   => ( P @ B3 ) )
% 0.19/0.44               => ( P @ A5 ) ) )
% 0.19/0.44         => ( P @ A4 ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % finite_psubset_induct
% 0.19/0.44  thf(fact_20_finite__has__minimal2,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( order @ A )
% 0.19/0.44       => ! [A4: set @ A,A2: A] :
% 0.19/0.44            ( ( finite_finite2 @ A @ A4 )
% 0.19/0.44           => ( ( member @ A @ A2 @ A4 )
% 0.19/0.44             => ? [X4: A] :
% 0.19/0.44                  ( ( member @ A @ X4 @ A4 )
% 0.19/0.44                  & ( ord_less_eq @ A @ X4 @ A2 )
% 0.19/0.44                  & ! [Xa: A] :
% 0.19/0.44                      ( ( member @ A @ Xa @ A4 )
% 0.19/0.44                     => ( ( ord_less_eq @ A @ Xa @ X4 )
% 0.19/0.44                       => ( X4 = Xa ) ) ) ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % finite_has_minimal2
% 0.19/0.44  thf(fact_21_finite__has__maximal2,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( order @ A )
% 0.19/0.44       => ! [A4: set @ A,A2: A] :
% 0.19/0.44            ( ( finite_finite2 @ A @ A4 )
% 0.19/0.44           => ( ( member @ A @ A2 @ A4 )
% 0.19/0.44             => ? [X4: A] :
% 0.19/0.44                  ( ( member @ A @ X4 @ A4 )
% 0.19/0.44                  & ( ord_less_eq @ A @ A2 @ X4 )
% 0.19/0.44                  & ! [Xa: A] :
% 0.19/0.44                      ( ( member @ A @ Xa @ A4 )
% 0.19/0.44                     => ( ( ord_less_eq @ A @ X4 @ Xa )
% 0.19/0.44                       => ( X4 = Xa ) ) ) ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % finite_has_maximal2
% 0.19/0.44  thf(fact_22_next__non__root__interval,axiom,
% 0.19/0.44      ! [P2: poly @ real,Lb: real] :
% 0.19/0.44        ( ( P2
% 0.19/0.44         != ( zero_zero @ ( poly @ real ) ) )
% 0.19/0.44       => ~ ! [Ub: real] :
% 0.19/0.44              ( ( ord_less @ real @ Lb @ Ub )
% 0.19/0.44             => ~ ! [Z: real] :
% 0.19/0.44                    ( ( ( ord_less @ real @ Lb @ Z )
% 0.19/0.44                      & ( ord_less_eq @ real @ Z @ Ub ) )
% 0.19/0.44                   => ( ( poly2 @ real @ P2 @ Z )
% 0.19/0.44                     != ( zero_zero @ real ) ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % next_non_root_interval
% 0.19/0.44  thf(fact_23_last__non__root__interval,axiom,
% 0.19/0.44      ! [P2: poly @ real,Ub2: real] :
% 0.19/0.44        ( ( P2
% 0.19/0.44         != ( zero_zero @ ( poly @ real ) ) )
% 0.19/0.44       => ~ ! [Lb2: real] :
% 0.19/0.44              ( ( ord_less @ real @ Lb2 @ Ub2 )
% 0.19/0.44             => ~ ! [Z: real] :
% 0.19/0.44                    ( ( ( ord_less_eq @ real @ Lb2 @ Z )
% 0.19/0.44                      & ( ord_less @ real @ Z @ Ub2 ) )
% 0.19/0.44                   => ( ( poly2 @ real @ P2 @ Z )
% 0.19/0.44                     != ( zero_zero @ real ) ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % last_non_root_interval
% 0.19/0.44  thf(fact_24_zero__reorient,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( zero @ A )
% 0.19/0.44       => ! [X2: A] :
% 0.19/0.44            ( ( ( zero_zero @ A )
% 0.19/0.44              = X2 )
% 0.19/0.44            = ( X2
% 0.19/0.44              = ( zero_zero @ A ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % zero_reorient
% 0.19/0.44  thf(fact_25_finite,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( finite_finite @ A )
% 0.19/0.44       => ! [A4: set @ A] : ( finite_finite2 @ A @ A4 ) ) ).
% 0.19/0.44  
% 0.19/0.44  % finite
% 0.19/0.44  thf(fact_26_finite__set__choice,axiom,
% 0.19/0.44      ! [B: $tType,A: $tType,A4: set @ A,P: A > B > $o] :
% 0.19/0.44        ( ( finite_finite2 @ A @ A4 )
% 0.19/0.44       => ( ! [X4: A] :
% 0.19/0.44              ( ( member @ A @ X4 @ A4 )
% 0.19/0.44             => ? [X_1: B] : ( P @ X4 @ X_1 ) )
% 0.19/0.44         => ? [F: A > B] :
% 0.19/0.44            ! [X3: A] :
% 0.19/0.44              ( ( member @ A @ X3 @ A4 )
% 0.19/0.44             => ( P @ X3 @ ( F @ X3 ) ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % finite_set_choice
% 0.19/0.44  thf(fact_27_not__eq__pos__or__neg__iff__2,axiom,
% 0.19/0.44      ! [Lb: real,Ub2: real,P2: poly @ real] :
% 0.19/0.44        ( ( ! [Z2: real] :
% 0.19/0.44              ( ( ( ord_less_eq @ real @ Lb @ Z2 )
% 0.19/0.44                & ( ord_less @ real @ Z2 @ Ub2 ) )
% 0.19/0.44             => ( ( poly2 @ real @ P2 @ Z2 )
% 0.19/0.44               != ( zero_zero @ real ) ) ) )
% 0.19/0.44        = ( ! [Z2: real] :
% 0.19/0.44              ( ( ( ord_less_eq @ real @ Lb @ Z2 )
% 0.19/0.44                & ( ord_less @ real @ Z2 @ Ub2 ) )
% 0.19/0.44             => ( ord_less @ real @ ( zero_zero @ real ) @ ( poly2 @ real @ P2 @ Z2 ) ) )
% 0.19/0.44          | ! [Z2: real] :
% 0.19/0.44              ( ( ( ord_less_eq @ real @ Lb @ Z2 )
% 0.19/0.44                & ( ord_less @ real @ Z2 @ Ub2 ) )
% 0.19/0.44             => ( ord_less @ real @ ( poly2 @ real @ P2 @ Z2 ) @ ( zero_zero @ real ) ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % not_eq_pos_or_neg_iff_2
% 0.19/0.44  thf(fact_28_not__eq__pos__or__neg__iff__1,axiom,
% 0.19/0.44      ! [Lb: real,Ub2: real,P2: poly @ real] :
% 0.19/0.44        ( ( ! [Z2: real] :
% 0.19/0.44              ( ( ( ord_less @ real @ Lb @ Z2 )
% 0.19/0.44                & ( ord_less_eq @ real @ Z2 @ Ub2 ) )
% 0.19/0.44             => ( ( poly2 @ real @ P2 @ Z2 )
% 0.19/0.44               != ( zero_zero @ real ) ) ) )
% 0.19/0.44        = ( ! [Z2: real] :
% 0.19/0.44              ( ( ( ord_less @ real @ Lb @ Z2 )
% 0.19/0.44                & ( ord_less_eq @ real @ Z2 @ Ub2 ) )
% 0.19/0.44             => ( ord_less @ real @ ( zero_zero @ real ) @ ( poly2 @ real @ P2 @ Z2 ) ) )
% 0.19/0.44          | ! [Z2: real] :
% 0.19/0.44              ( ( ( ord_less @ real @ Lb @ Z2 )
% 0.19/0.44                & ( ord_less_eq @ real @ Z2 @ Ub2 ) )
% 0.19/0.44             => ( ord_less @ real @ ( poly2 @ real @ P2 @ Z2 ) @ ( zero_zero @ real ) ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % not_eq_pos_or_neg_iff_1
% 0.19/0.44  thf(fact_29_poly__eq__poly__eq__iff,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( ( ring_char_0 @ A )
% 0.19/0.44          & ( comm_ring_1 @ A )
% 0.19/0.44          & ( ring_n68954251visors @ A ) )
% 0.19/0.44       => ! [P2: poly @ A,Q2: poly @ A] :
% 0.19/0.44            ( ( ( poly2 @ A @ P2 )
% 0.19/0.44              = ( poly2 @ A @ Q2 ) )
% 0.19/0.44            = ( P2 = Q2 ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % poly_eq_poly_eq_iff
% 0.19/0.44  thf(fact_30_pigeonhole__infinite__rel,axiom,
% 0.19/0.44      ! [B: $tType,A: $tType,A4: set @ A,B4: set @ B,R: A > B > $o] :
% 0.19/0.44        ( ~ ( finite_finite2 @ A @ A4 )
% 0.19/0.44       => ( ( finite_finite2 @ B @ B4 )
% 0.19/0.44         => ( ! [X4: A] :
% 0.19/0.44                ( ( member @ A @ X4 @ A4 )
% 0.19/0.44               => ? [Xa: B] :
% 0.19/0.44                    ( ( member @ B @ Xa @ B4 )
% 0.19/0.44                    & ( R @ X4 @ Xa ) ) )
% 0.19/0.44           => ? [X4: B] :
% 0.19/0.44                ( ( member @ B @ X4 @ B4 )
% 0.19/0.44                & ~ ( finite_finite2 @ A
% 0.19/0.44                    @ ( collect @ A
% 0.19/0.44                      @ ^ [A6: A] :
% 0.19/0.44                          ( ( member @ A @ A6 @ A4 )
% 0.19/0.44                          & ( R @ A6 @ X4 ) ) ) ) ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % pigeonhole_infinite_rel
% 0.19/0.44  thf(fact_31_not__finite__existsD,axiom,
% 0.19/0.44      ! [A: $tType,P: A > $o] :
% 0.19/0.44        ( ~ ( finite_finite2 @ A @ ( collect @ A @ P ) )
% 0.19/0.44       => ? [X_12: A] : ( P @ X_12 ) ) ).
% 0.19/0.44  
% 0.19/0.44  % not_finite_existsD
% 0.19/0.44  thf(fact_32_zero__less__iff__neq__zero,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( canoni770627133id_add @ A )
% 0.19/0.44       => ! [N: A] :
% 0.19/0.44            ( ( ord_less @ A @ ( zero_zero @ A ) @ N )
% 0.19/0.44            = ( N
% 0.19/0.44             != ( zero_zero @ A ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % zero_less_iff_neq_zero
% 0.19/0.44  thf(fact_33_gr__implies__not__zero,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( canoni770627133id_add @ A )
% 0.19/0.44       => ! [M: A,N: A] :
% 0.19/0.44            ( ( ord_less @ A @ M @ N )
% 0.19/0.44           => ( N
% 0.19/0.44             != ( zero_zero @ A ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % gr_implies_not_zero
% 0.19/0.44  thf(fact_34_not__less__zero,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( canoni770627133id_add @ A )
% 0.19/0.44       => ! [N: A] :
% 0.19/0.44            ~ ( ord_less @ A @ N @ ( zero_zero @ A ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % not_less_zero
% 0.19/0.44  thf(fact_35_gr__zeroI,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( canoni770627133id_add @ A )
% 0.19/0.44       => ! [N: A] :
% 0.19/0.44            ( ( N
% 0.19/0.44             != ( zero_zero @ A ) )
% 0.19/0.44           => ( ord_less @ A @ ( zero_zero @ A ) @ N ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % gr_zeroI
% 0.19/0.44  thf(fact_36_order__refl,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( preorder @ A )
% 0.19/0.44       => ! [X2: A] : ( ord_less_eq @ A @ X2 @ X2 ) ) ).
% 0.19/0.44  
% 0.19/0.44  % order_refl
% 0.19/0.44  thf(fact_37_cross__no__root,axiom,
% 0.19/0.44      ! [A2: real,B2: real,P2: poly @ real] :
% 0.19/0.44        ( ( ord_less @ real @ A2 @ B2 )
% 0.19/0.44       => ( ! [X4: real] :
% 0.19/0.44              ( ( ( ord_less @ real @ A2 @ X4 )
% 0.19/0.44                & ( ord_less @ real @ X4 @ B2 ) )
% 0.19/0.44             => ( ( poly2 @ real @ P2 @ X4 )
% 0.19/0.44               != ( zero_zero @ real ) ) )
% 0.19/0.44         => ( ( sturm_424270202_cross @ P2 @ A2 @ B2 )
% 0.19/0.44            = ( zero_zero @ int ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % cross_no_root
% 0.19/0.44  thf(fact_38_less__eq__real__def,axiom,
% 0.19/0.44      ( ( ord_less_eq @ real )
% 0.19/0.44      = ( ^ [X: real,Y: real] :
% 0.19/0.44            ( ( ord_less @ real @ X @ Y )
% 0.19/0.44            | ( X = Y ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % less_eq_real_def
% 0.19/0.44  thf(fact_39_complete__interval,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( condit1037483654norder @ A )
% 0.19/0.44       => ! [A2: A,B2: A,P: A > $o] :
% 0.19/0.44            ( ( ord_less @ A @ A2 @ B2 )
% 0.19/0.44           => ( ( P @ A2 )
% 0.19/0.44             => ( ~ ( P @ B2 )
% 0.19/0.44               => ? [C: A] :
% 0.19/0.44                    ( ( ord_less_eq @ A @ A2 @ C )
% 0.19/0.44                    & ( ord_less_eq @ A @ C @ B2 )
% 0.19/0.44                    & ! [X3: A] :
% 0.19/0.44                        ( ( ( ord_less_eq @ A @ A2 @ X3 )
% 0.19/0.44                          & ( ord_less @ A @ X3 @ C ) )
% 0.19/0.44                       => ( P @ X3 ) )
% 0.19/0.44                    & ! [D: A] :
% 0.19/0.44                        ( ! [X4: A] :
% 0.19/0.44                            ( ( ( ord_less_eq @ A @ A2 @ X4 )
% 0.19/0.44                              & ( ord_less @ A @ X4 @ D ) )
% 0.19/0.44                           => ( P @ X4 ) )
% 0.19/0.44                       => ( ord_less_eq @ A @ D @ C ) ) ) ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % complete_interval
% 0.19/0.44  thf(fact_40_order_Onot__eq__order__implies__strict,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( order @ A )
% 0.19/0.44       => ! [A2: A,B2: A] :
% 0.19/0.44            ( ( A2 != B2 )
% 0.19/0.44           => ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.19/0.44             => ( ord_less @ A @ A2 @ B2 ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % order.not_eq_order_implies_strict
% 0.19/0.44  thf(fact_41_dual__order_Ostrict__implies__order,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( order @ A )
% 0.19/0.44       => ! [B2: A,A2: A] :
% 0.19/0.44            ( ( ord_less @ A @ B2 @ A2 )
% 0.19/0.44           => ( ord_less_eq @ A @ B2 @ A2 ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % dual_order.strict_implies_order
% 0.19/0.44  thf(fact_42_dual__order_Ostrict__iff__order,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( order @ A )
% 0.19/0.44       => ( ( ord_less @ A )
% 0.19/0.44          = ( ^ [B5: A,A6: A] :
% 0.19/0.44                ( ( ord_less_eq @ A @ B5 @ A6 )
% 0.19/0.44                & ( A6 != B5 ) ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % dual_order.strict_iff_order
% 0.19/0.44  thf(fact_43_dual__order_Oorder__iff__strict,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( order @ A )
% 0.19/0.44       => ( ( ord_less_eq @ A )
% 0.19/0.44          = ( ^ [B5: A,A6: A] :
% 0.19/0.44                ( ( ord_less @ A @ B5 @ A6 )
% 0.19/0.44                | ( A6 = B5 ) ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % dual_order.order_iff_strict
% 0.19/0.44  thf(fact_44_mem__Collect__eq,axiom,
% 0.19/0.44      ! [A: $tType,A2: A,P: A > $o] :
% 0.19/0.44        ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.19/0.44        = ( P @ A2 ) ) ).
% 0.19/0.44  
% 0.19/0.44  % mem_Collect_eq
% 0.19/0.44  thf(fact_45_Collect__mem__eq,axiom,
% 0.19/0.44      ! [A: $tType,A4: set @ A] :
% 0.19/0.44        ( ( collect @ A
% 0.19/0.44          @ ^ [X: A] : ( member @ A @ X @ A4 ) )
% 0.19/0.44        = A4 ) ).
% 0.19/0.44  
% 0.19/0.44  % Collect_mem_eq
% 0.19/0.44  thf(fact_46_Collect__cong,axiom,
% 0.19/0.44      ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.19/0.44        ( ! [X4: A] :
% 0.19/0.44            ( ( P @ X4 )
% 0.19/0.44            = ( Q @ X4 ) )
% 0.19/0.44       => ( ( collect @ A @ P )
% 0.19/0.44          = ( collect @ A @ Q ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % Collect_cong
% 0.19/0.44  thf(fact_47_ext,axiom,
% 0.19/0.44      ! [B: $tType,A: $tType,F2: A > B,G: A > B] :
% 0.19/0.44        ( ! [X4: A] :
% 0.19/0.44            ( ( F2 @ X4 )
% 0.19/0.44            = ( G @ X4 ) )
% 0.19/0.44       => ( F2 = G ) ) ).
% 0.19/0.44  
% 0.19/0.44  % ext
% 0.19/0.44  thf(fact_48_order_Ostrict__implies__order,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( order @ A )
% 0.19/0.44       => ! [A2: A,B2: A] :
% 0.19/0.44            ( ( ord_less @ A @ A2 @ B2 )
% 0.19/0.44           => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % order.strict_implies_order
% 0.19/0.44  thf(fact_49_dense__le__bounded,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( dense_linorder @ A )
% 0.19/0.44       => ! [X2: A,Y2: A,Z3: A] :
% 0.19/0.44            ( ( ord_less @ A @ X2 @ Y2 )
% 0.19/0.44           => ( ! [W: A] :
% 0.19/0.44                  ( ( ord_less @ A @ X2 @ W )
% 0.19/0.44                 => ( ( ord_less @ A @ W @ Y2 )
% 0.19/0.44                   => ( ord_less_eq @ A @ W @ Z3 ) ) )
% 0.19/0.44             => ( ord_less_eq @ A @ Y2 @ Z3 ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % dense_le_bounded
% 0.19/0.44  thf(fact_50_finite__Collect__subsets,axiom,
% 0.19/0.44      ! [A: $tType,A4: set @ A] :
% 0.19/0.44        ( ( finite_finite2 @ A @ A4 )
% 0.19/0.44       => ( finite_finite2 @ ( set @ A )
% 0.19/0.44          @ ( collect @ ( set @ A )
% 0.19/0.44            @ ^ [B6: set @ A] : ( ord_less_eq @ ( set @ A ) @ B6 @ A4 ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % finite_Collect_subsets
% 0.19/0.44  thf(fact_51_cross__0,axiom,
% 0.19/0.44      ! [A2: real,B2: real] :
% 0.19/0.44        ( ( sturm_424270202_cross @ ( zero_zero @ ( poly @ real ) ) @ A2 @ B2 )
% 0.19/0.44        = ( zero_zero @ int ) ) ).
% 0.19/0.44  
% 0.19/0.44  % cross_0
% 0.19/0.44  thf(fact_52_finite__subset,axiom,
% 0.19/0.44      ! [A: $tType,A4: set @ A,B4: set @ A] :
% 0.19/0.44        ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 0.19/0.44       => ( ( finite_finite2 @ A @ B4 )
% 0.19/0.44         => ( finite_finite2 @ A @ A4 ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % finite_subset
% 0.19/0.44  thf(fact_53_infinite__super,axiom,
% 0.19/0.44      ! [A: $tType,S: set @ A,T: set @ A] :
% 0.19/0.44        ( ( ord_less_eq @ ( set @ A ) @ S @ T )
% 0.19/0.44       => ( ~ ( finite_finite2 @ A @ S )
% 0.19/0.44         => ~ ( finite_finite2 @ A @ T ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % infinite_super
% 0.19/0.44  thf(fact_54_rev__finite__subset,axiom,
% 0.19/0.44      ! [A: $tType,B4: set @ A,A4: set @ A] :
% 0.19/0.44        ( ( finite_finite2 @ A @ B4 )
% 0.19/0.44       => ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 0.19/0.44         => ( finite_finite2 @ A @ A4 ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % rev_finite_subset
% 0.19/0.44  thf(fact_55_dual__order_Oantisym,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( order @ A )
% 0.19/0.44       => ! [B2: A,A2: A] :
% 0.19/0.44            ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.19/0.44           => ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.19/0.44             => ( A2 = B2 ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % dual_order.antisym
% 0.19/0.44  thf(fact_56_dual__order_Oeq__iff,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( order @ A )
% 0.19/0.44       => ( ( ^ [Y3: A,Z4: A] : ( Y3 = Z4 ) )
% 0.19/0.44          = ( ^ [A6: A,B5: A] :
% 0.19/0.44                ( ( ord_less_eq @ A @ B5 @ A6 )
% 0.19/0.44                & ( ord_less_eq @ A @ A6 @ B5 ) ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % dual_order.eq_iff
% 0.19/0.44  thf(fact_57_dual__order_Otrans,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( order @ A )
% 0.19/0.44       => ! [B2: A,A2: A,C2: A] :
% 0.19/0.44            ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.19/0.44           => ( ( ord_less_eq @ A @ C2 @ B2 )
% 0.19/0.44             => ( ord_less_eq @ A @ C2 @ A2 ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % dual_order.trans
% 0.19/0.44  thf(fact_58_linorder__wlog,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( linorder @ A )
% 0.19/0.44       => ! [P: A > A > $o,A2: A,B2: A] :
% 0.19/0.44            ( ! [A7: A,B7: A] :
% 0.19/0.44                ( ( ord_less_eq @ A @ A7 @ B7 )
% 0.19/0.44               => ( P @ A7 @ B7 ) )
% 0.19/0.44           => ( ! [A7: A,B7: A] :
% 0.19/0.44                  ( ( P @ B7 @ A7 )
% 0.19/0.44                 => ( P @ A7 @ B7 ) )
% 0.19/0.44             => ( P @ A2 @ B2 ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % linorder_wlog
% 0.19/0.44  thf(fact_59_dual__order_Orefl,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( order @ A )
% 0.19/0.44       => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 0.19/0.44  
% 0.19/0.44  % dual_order.refl
% 0.19/0.44  thf(fact_60_order__trans,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( preorder @ A )
% 0.19/0.44       => ! [X2: A,Y2: A,Z3: A] :
% 0.19/0.44            ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.19/0.44           => ( ( ord_less_eq @ A @ Y2 @ Z3 )
% 0.19/0.44             => ( ord_less_eq @ A @ X2 @ Z3 ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % order_trans
% 0.19/0.44  thf(fact_61_order__class_Oorder_Oantisym,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( order @ A )
% 0.19/0.44       => ! [A2: A,B2: A] :
% 0.19/0.44            ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.19/0.44           => ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.19/0.44             => ( A2 = B2 ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % order_class.order.antisym
% 0.19/0.44  thf(fact_62_ord__le__eq__trans,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( ord @ A )
% 0.19/0.44       => ! [A2: A,B2: A,C2: A] :
% 0.19/0.44            ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.19/0.44           => ( ( B2 = C2 )
% 0.19/0.44             => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % ord_le_eq_trans
% 0.19/0.44  thf(fact_63_ord__eq__le__trans,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( ord @ A )
% 0.19/0.44       => ! [A2: A,B2: A,C2: A] :
% 0.19/0.44            ( ( A2 = B2 )
% 0.19/0.44           => ( ( ord_less_eq @ A @ B2 @ C2 )
% 0.19/0.44             => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % ord_eq_le_trans
% 0.19/0.44  thf(fact_64_order__class_Oorder_Oeq__iff,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( order @ A )
% 0.19/0.44       => ( ( ^ [Y3: A,Z4: A] : ( Y3 = Z4 ) )
% 0.19/0.44          = ( ^ [A6: A,B5: A] :
% 0.19/0.44                ( ( ord_less_eq @ A @ A6 @ B5 )
% 0.19/0.44                & ( ord_less_eq @ A @ B5 @ A6 ) ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % order_class.order.eq_iff
% 0.19/0.44  thf(fact_65_antisym__conv,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( order @ A )
% 0.19/0.44       => ! [Y2: A,X2: A] :
% 0.19/0.44            ( ( ord_less_eq @ A @ Y2 @ X2 )
% 0.19/0.44           => ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.19/0.44              = ( X2 = Y2 ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % antisym_conv
% 0.19/0.44  thf(fact_66_le__cases3,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( linorder @ A )
% 0.19/0.44       => ! [X2: A,Y2: A,Z3: A] :
% 0.19/0.44            ( ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.19/0.44             => ~ ( ord_less_eq @ A @ Y2 @ Z3 ) )
% 0.19/0.44           => ( ( ( ord_less_eq @ A @ Y2 @ X2 )
% 0.19/0.44               => ~ ( ord_less_eq @ A @ X2 @ Z3 ) )
% 0.19/0.44             => ( ( ( ord_less_eq @ A @ X2 @ Z3 )
% 0.19/0.44                 => ~ ( ord_less_eq @ A @ Z3 @ Y2 ) )
% 0.19/0.44               => ( ( ( ord_less_eq @ A @ Z3 @ Y2 )
% 0.19/0.44                   => ~ ( ord_less_eq @ A @ Y2 @ X2 ) )
% 0.19/0.44                 => ( ( ( ord_less_eq @ A @ Y2 @ Z3 )
% 0.19/0.44                     => ~ ( ord_less_eq @ A @ Z3 @ X2 ) )
% 0.19/0.44                   => ~ ( ( ord_less_eq @ A @ Z3 @ X2 )
% 0.19/0.44                       => ~ ( ord_less_eq @ A @ X2 @ Y2 ) ) ) ) ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % le_cases3
% 0.19/0.44  thf(fact_67_order_Otrans,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( order @ A )
% 0.19/0.44       => ! [A2: A,B2: A,C2: A] :
% 0.19/0.44            ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.19/0.44           => ( ( ord_less_eq @ A @ B2 @ C2 )
% 0.19/0.44             => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % order.trans
% 0.19/0.44  thf(fact_68_le__cases,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( linorder @ A )
% 0.19/0.44       => ! [X2: A,Y2: A] :
% 0.19/0.44            ( ~ ( ord_less_eq @ A @ X2 @ Y2 )
% 0.19/0.44           => ( ord_less_eq @ A @ Y2 @ X2 ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % le_cases
% 0.19/0.44  thf(fact_69_eq__refl,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( preorder @ A )
% 0.19/0.44       => ! [X2: A,Y2: A] :
% 0.19/0.44            ( ( X2 = Y2 )
% 0.19/0.44           => ( ord_less_eq @ A @ X2 @ Y2 ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % eq_refl
% 0.19/0.44  thf(fact_70_linear,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( linorder @ A )
% 0.19/0.44       => ! [X2: A,Y2: A] :
% 0.19/0.44            ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.19/0.44            | ( ord_less_eq @ A @ Y2 @ X2 ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % linear
% 0.19/0.44  thf(fact_71_antisym,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( order @ A )
% 0.19/0.44       => ! [X2: A,Y2: A] :
% 0.19/0.44            ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.19/0.44           => ( ( ord_less_eq @ A @ Y2 @ X2 )
% 0.19/0.44             => ( X2 = Y2 ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % antisym
% 0.19/0.44  thf(fact_72_eq__iff,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( order @ A )
% 0.19/0.44       => ( ( ^ [Y3: A,Z4: A] : ( Y3 = Z4 ) )
% 0.19/0.44          = ( ^ [X: A,Y: A] :
% 0.19/0.44                ( ( ord_less_eq @ A @ X @ Y )
% 0.19/0.44                & ( ord_less_eq @ A @ Y @ X ) ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % eq_iff
% 0.19/0.44  thf(fact_73_ord__le__eq__subst,axiom,
% 0.19/0.44      ! [A: $tType,B: $tType] :
% 0.19/0.44        ( ( ( ord @ B )
% 0.19/0.44          & ( ord @ A ) )
% 0.19/0.44       => ! [A2: A,B2: A,F2: A > B,C2: B] :
% 0.19/0.44            ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.19/0.44           => ( ( ( F2 @ B2 )
% 0.19/0.44                = C2 )
% 0.19/0.44             => ( ! [X4: A,Y4: A] :
% 0.19/0.44                    ( ( ord_less_eq @ A @ X4 @ Y4 )
% 0.19/0.44                   => ( ord_less_eq @ B @ ( F2 @ X4 ) @ ( F2 @ Y4 ) ) )
% 0.19/0.44               => ( ord_less_eq @ B @ ( F2 @ A2 ) @ C2 ) ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % ord_le_eq_subst
% 0.19/0.44  thf(fact_74_ord__eq__le__subst,axiom,
% 0.19/0.44      ! [A: $tType,B: $tType] :
% 0.19/0.44        ( ( ( ord @ B )
% 0.19/0.44          & ( ord @ A ) )
% 0.19/0.44       => ! [A2: A,F2: B > A,B2: B,C2: B] :
% 0.19/0.44            ( ( A2
% 0.19/0.44              = ( F2 @ B2 ) )
% 0.19/0.44           => ( ( ord_less_eq @ B @ B2 @ C2 )
% 0.19/0.44             => ( ! [X4: B,Y4: B] :
% 0.19/0.44                    ( ( ord_less_eq @ B @ X4 @ Y4 )
% 0.19/0.44                   => ( ord_less_eq @ A @ ( F2 @ X4 ) @ ( F2 @ Y4 ) ) )
% 0.19/0.44               => ( ord_less_eq @ A @ A2 @ ( F2 @ C2 ) ) ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % ord_eq_le_subst
% 0.19/0.44  thf(fact_75_order__subst2,axiom,
% 0.19/0.44      ! [A: $tType,C3: $tType] :
% 0.19/0.44        ( ( ( order @ C3 )
% 0.19/0.44          & ( order @ A ) )
% 0.19/0.44       => ! [A2: A,B2: A,F2: A > C3,C2: C3] :
% 0.19/0.44            ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.19/0.44           => ( ( ord_less_eq @ C3 @ ( F2 @ B2 ) @ C2 )
% 0.19/0.44             => ( ! [X4: A,Y4: A] :
% 0.19/0.44                    ( ( ord_less_eq @ A @ X4 @ Y4 )
% 0.19/0.44                   => ( ord_less_eq @ C3 @ ( F2 @ X4 ) @ ( F2 @ Y4 ) ) )
% 0.19/0.44               => ( ord_less_eq @ C3 @ ( F2 @ A2 ) @ C2 ) ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % order_subst2
% 0.19/0.44  thf(fact_76_order__subst1,axiom,
% 0.19/0.44      ! [A: $tType,B: $tType] :
% 0.19/0.44        ( ( ( order @ B )
% 0.19/0.44          & ( order @ A ) )
% 0.19/0.44       => ! [A2: A,F2: B > A,B2: B,C2: B] :
% 0.19/0.44            ( ( ord_less_eq @ A @ A2 @ ( F2 @ B2 ) )
% 0.19/0.44           => ( ( ord_less_eq @ B @ B2 @ C2 )
% 0.19/0.44             => ( ! [X4: B,Y4: B] :
% 0.19/0.44                    ( ( ord_less_eq @ B @ X4 @ Y4 )
% 0.19/0.44                   => ( ord_less_eq @ A @ ( F2 @ X4 ) @ ( F2 @ Y4 ) ) )
% 0.19/0.44               => ( ord_less_eq @ A @ A2 @ ( F2 @ C2 ) ) ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % order_subst1
% 0.19/0.44  thf(fact_77_le__fun__def,axiom,
% 0.19/0.44      ! [B: $tType,A: $tType] :
% 0.19/0.44        ( ( ord @ B )
% 0.19/0.44       => ( ( ord_less_eq @ ( A > B ) )
% 0.19/0.44          = ( ^ [F3: A > B,G2: A > B] :
% 0.19/0.44              ! [X: A] : ( ord_less_eq @ B @ ( F3 @ X ) @ ( G2 @ X ) ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % le_fun_def
% 0.19/0.44  thf(fact_78_le__funI,axiom,
% 0.19/0.44      ! [B: $tType,A: $tType] :
% 0.19/0.44        ( ( ord @ B )
% 0.19/0.44       => ! [F2: A > B,G: A > B] :
% 0.19/0.44            ( ! [X4: A] : ( ord_less_eq @ B @ ( F2 @ X4 ) @ ( G @ X4 ) )
% 0.19/0.44           => ( ord_less_eq @ ( A > B ) @ F2 @ G ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % le_funI
% 0.19/0.44  thf(fact_79_le__funE,axiom,
% 0.19/0.44      ! [B: $tType,A: $tType] :
% 0.19/0.44        ( ( ord @ B )
% 0.19/0.44       => ! [F2: A > B,G: A > B,X2: A] :
% 0.19/0.44            ( ( ord_less_eq @ ( A > B ) @ F2 @ G )
% 0.19/0.44           => ( ord_less_eq @ B @ ( F2 @ X2 ) @ ( G @ X2 ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % le_funE
% 0.19/0.44  thf(fact_80_le__funD,axiom,
% 0.19/0.44      ! [B: $tType,A: $tType] :
% 0.19/0.44        ( ( ord @ B )
% 0.19/0.44       => ! [F2: A > B,G: A > B,X2: A] :
% 0.19/0.44            ( ( ord_less_eq @ ( A > B ) @ F2 @ G )
% 0.19/0.44           => ( ord_less_eq @ B @ ( F2 @ X2 ) @ ( G @ X2 ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % le_funD
% 0.19/0.44  thf(fact_81_ord__eq__less__subst,axiom,
% 0.19/0.44      ! [A: $tType,B: $tType] :
% 0.19/0.44        ( ( ( ord @ B )
% 0.19/0.44          & ( ord @ A ) )
% 0.19/0.44       => ! [A2: A,F2: B > A,B2: B,C2: B] :
% 0.19/0.44            ( ( A2
% 0.19/0.44              = ( F2 @ B2 ) )
% 0.19/0.44           => ( ( ord_less @ B @ B2 @ C2 )
% 0.19/0.44             => ( ! [X4: B,Y4: B] :
% 0.19/0.44                    ( ( ord_less @ B @ X4 @ Y4 )
% 0.19/0.44                   => ( ord_less @ A @ ( F2 @ X4 ) @ ( F2 @ Y4 ) ) )
% 0.19/0.44               => ( ord_less @ A @ A2 @ ( F2 @ C2 ) ) ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % ord_eq_less_subst
% 0.19/0.44  thf(fact_82_ord__less__eq__subst,axiom,
% 0.19/0.44      ! [A: $tType,B: $tType] :
% 0.19/0.44        ( ( ( ord @ B )
% 0.19/0.44          & ( ord @ A ) )
% 0.19/0.44       => ! [A2: A,B2: A,F2: A > B,C2: B] :
% 0.19/0.44            ( ( ord_less @ A @ A2 @ B2 )
% 0.19/0.44           => ( ( ( F2 @ B2 )
% 0.19/0.44                = C2 )
% 0.19/0.44             => ( ! [X4: A,Y4: A] :
% 0.19/0.44                    ( ( ord_less @ A @ X4 @ Y4 )
% 0.19/0.44                   => ( ord_less @ B @ ( F2 @ X4 ) @ ( F2 @ Y4 ) ) )
% 0.19/0.44               => ( ord_less @ B @ ( F2 @ A2 ) @ C2 ) ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % ord_less_eq_subst
% 0.19/0.44  thf(fact_83_order__less__subst1,axiom,
% 0.19/0.44      ! [A: $tType,B: $tType] :
% 0.19/0.44        ( ( ( order @ B )
% 0.19/0.44          & ( order @ A ) )
% 0.19/0.44       => ! [A2: A,F2: B > A,B2: B,C2: B] :
% 0.19/0.44            ( ( ord_less @ A @ A2 @ ( F2 @ B2 ) )
% 0.19/0.44           => ( ( ord_less @ B @ B2 @ C2 )
% 0.19/0.44             => ( ! [X4: B,Y4: B] :
% 0.19/0.44                    ( ( ord_less @ B @ X4 @ Y4 )
% 0.19/0.44                   => ( ord_less @ A @ ( F2 @ X4 ) @ ( F2 @ Y4 ) ) )
% 0.19/0.44               => ( ord_less @ A @ A2 @ ( F2 @ C2 ) ) ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % order_less_subst1
% 0.19/0.44  thf(fact_84_order__less__subst2,axiom,
% 0.19/0.44      ! [A: $tType,C3: $tType] :
% 0.19/0.44        ( ( ( order @ C3 )
% 0.19/0.44          & ( order @ A ) )
% 0.19/0.44       => ! [A2: A,B2: A,F2: A > C3,C2: C3] :
% 0.19/0.44            ( ( ord_less @ A @ A2 @ B2 )
% 0.19/0.44           => ( ( ord_less @ C3 @ ( F2 @ B2 ) @ C2 )
% 0.19/0.44             => ( ! [X4: A,Y4: A] :
% 0.19/0.44                    ( ( ord_less @ A @ X4 @ Y4 )
% 0.19/0.44                   => ( ord_less @ C3 @ ( F2 @ X4 ) @ ( F2 @ Y4 ) ) )
% 0.19/0.44               => ( ord_less @ C3 @ ( F2 @ A2 ) @ C2 ) ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % order_less_subst2
% 0.19/0.44  thf(fact_85_lt__ex,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( no_bot @ A )
% 0.19/0.44       => ! [X2: A] :
% 0.19/0.44          ? [Y4: A] : ( ord_less @ A @ Y4 @ X2 ) ) ).
% 0.19/0.44  
% 0.19/0.44  % lt_ex
% 0.19/0.44  thf(fact_86_gt__ex,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( no_top @ A )
% 0.19/0.44       => ! [X2: A] :
% 0.19/0.44          ? [X_12: A] : ( ord_less @ A @ X2 @ X_12 ) ) ).
% 0.19/0.44  
% 0.19/0.44  % gt_ex
% 0.19/0.44  thf(fact_87_neqE,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( linorder @ A )
% 0.19/0.44       => ! [X2: A,Y2: A] :
% 0.19/0.44            ( ( X2 != Y2 )
% 0.19/0.44           => ( ~ ( ord_less @ A @ X2 @ Y2 )
% 0.19/0.44             => ( ord_less @ A @ Y2 @ X2 ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % neqE
% 0.19/0.44  thf(fact_88_neq__iff,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( linorder @ A )
% 0.19/0.44       => ! [X2: A,Y2: A] :
% 0.19/0.44            ( ( X2 != Y2 )
% 0.19/0.44            = ( ( ord_less @ A @ X2 @ Y2 )
% 0.19/0.44              | ( ord_less @ A @ Y2 @ X2 ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % neq_iff
% 0.19/0.44  thf(fact_89_order_Oasym,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( order @ A )
% 0.19/0.44       => ! [A2: A,B2: A] :
% 0.19/0.44            ( ( ord_less @ A @ A2 @ B2 )
% 0.19/0.44           => ~ ( ord_less @ A @ B2 @ A2 ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % order.asym
% 0.19/0.44  thf(fact_90_dense,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( dense_order @ A )
% 0.19/0.44       => ! [X2: A,Y2: A] :
% 0.19/0.44            ( ( ord_less @ A @ X2 @ Y2 )
% 0.19/0.44           => ? [Z5: A] :
% 0.19/0.44                ( ( ord_less @ A @ X2 @ Z5 )
% 0.19/0.44                & ( ord_less @ A @ Z5 @ Y2 ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % dense
% 0.19/0.44  thf(fact_91_less__imp__neq,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( order @ A )
% 0.19/0.44       => ! [X2: A,Y2: A] :
% 0.19/0.44            ( ( ord_less @ A @ X2 @ Y2 )
% 0.19/0.44           => ( X2 != Y2 ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % less_imp_neq
% 0.19/0.44  thf(fact_92_less__asym,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( preorder @ A )
% 0.19/0.44       => ! [X2: A,Y2: A] :
% 0.19/0.44            ( ( ord_less @ A @ X2 @ Y2 )
% 0.19/0.44           => ~ ( ord_less @ A @ Y2 @ X2 ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % less_asym
% 0.19/0.44  thf(fact_93_less__asym_H,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( preorder @ A )
% 0.19/0.44       => ! [A2: A,B2: A] :
% 0.19/0.44            ( ( ord_less @ A @ A2 @ B2 )
% 0.19/0.44           => ~ ( ord_less @ A @ B2 @ A2 ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % less_asym'
% 0.19/0.44  thf(fact_94_less__trans,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( preorder @ A )
% 0.19/0.44       => ! [X2: A,Y2: A,Z3: A] :
% 0.19/0.44            ( ( ord_less @ A @ X2 @ Y2 )
% 0.19/0.44           => ( ( ord_less @ A @ Y2 @ Z3 )
% 0.19/0.44             => ( ord_less @ A @ X2 @ Z3 ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % less_trans
% 0.19/0.44  thf(fact_95_less__linear,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( linorder @ A )
% 0.19/0.44       => ! [X2: A,Y2: A] :
% 0.19/0.44            ( ( ord_less @ A @ X2 @ Y2 )
% 0.19/0.44            | ( X2 = Y2 )
% 0.19/0.44            | ( ord_less @ A @ Y2 @ X2 ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % less_linear
% 0.19/0.44  thf(fact_96_less__irrefl,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( preorder @ A )
% 0.19/0.44       => ! [X2: A] :
% 0.19/0.44            ~ ( ord_less @ A @ X2 @ X2 ) ) ).
% 0.19/0.44  
% 0.19/0.44  % less_irrefl
% 0.19/0.44  thf(fact_97_ord__eq__less__trans,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( ord @ A )
% 0.19/0.44       => ! [A2: A,B2: A,C2: A] :
% 0.19/0.44            ( ( A2 = B2 )
% 0.19/0.44           => ( ( ord_less @ A @ B2 @ C2 )
% 0.19/0.44             => ( ord_less @ A @ A2 @ C2 ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % ord_eq_less_trans
% 0.19/0.44  thf(fact_98_ord__less__eq__trans,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( ord @ A )
% 0.19/0.44       => ! [A2: A,B2: A,C2: A] :
% 0.19/0.44            ( ( ord_less @ A @ A2 @ B2 )
% 0.19/0.44           => ( ( B2 = C2 )
% 0.19/0.44             => ( ord_less @ A @ A2 @ C2 ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % ord_less_eq_trans
% 0.19/0.44  thf(fact_99_dual__order_Oasym,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( order @ A )
% 0.19/0.44       => ! [B2: A,A2: A] :
% 0.19/0.44            ( ( ord_less @ A @ B2 @ A2 )
% 0.19/0.44           => ~ ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % dual_order.asym
% 0.19/0.44  thf(fact_100_less__imp__not__eq,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( order @ A )
% 0.19/0.44       => ! [X2: A,Y2: A] :
% 0.19/0.44            ( ( ord_less @ A @ X2 @ Y2 )
% 0.19/0.44           => ( X2 != Y2 ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % less_imp_not_eq
% 0.19/0.44  thf(fact_101_less__not__sym,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( preorder @ A )
% 0.19/0.44       => ! [X2: A,Y2: A] :
% 0.19/0.44            ( ( ord_less @ A @ X2 @ Y2 )
% 0.19/0.44           => ~ ( ord_less @ A @ Y2 @ X2 ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % less_not_sym
% 0.19/0.44  thf(fact_102_less__induct,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( wellorder @ A )
% 0.19/0.44       => ! [P: A > $o,A2: A] :
% 0.19/0.44            ( ! [X4: A] :
% 0.19/0.44                ( ! [Y5: A] :
% 0.19/0.44                    ( ( ord_less @ A @ Y5 @ X4 )
% 0.19/0.44                   => ( P @ Y5 ) )
% 0.19/0.44               => ( P @ X4 ) )
% 0.19/0.44           => ( P @ A2 ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % less_induct
% 0.19/0.44  thf(fact_103_antisym__conv3,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( linorder @ A )
% 0.19/0.44       => ! [Y2: A,X2: A] :
% 0.19/0.44            ( ~ ( ord_less @ A @ Y2 @ X2 )
% 0.19/0.44           => ( ( ~ ( ord_less @ A @ X2 @ Y2 ) )
% 0.19/0.44              = ( X2 = Y2 ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % antisym_conv3
% 0.19/0.44  thf(fact_104_less__imp__not__eq2,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( order @ A )
% 0.19/0.44       => ! [X2: A,Y2: A] :
% 0.19/0.44            ( ( ord_less @ A @ X2 @ Y2 )
% 0.19/0.44           => ( Y2 != X2 ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % less_imp_not_eq2
% 0.19/0.44  thf(fact_105_less__imp__triv,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( preorder @ A )
% 0.19/0.44       => ! [X2: A,Y2: A,P: $o] :
% 0.19/0.44            ( ( ord_less @ A @ X2 @ Y2 )
% 0.19/0.44           => ( ( ord_less @ A @ Y2 @ X2 )
% 0.19/0.44             => P ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % less_imp_triv
% 0.19/0.44  thf(fact_106_linorder__cases,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( linorder @ A )
% 0.19/0.44       => ! [X2: A,Y2: A] :
% 0.19/0.44            ( ~ ( ord_less @ A @ X2 @ Y2 )
% 0.19/0.44           => ( ( X2 != Y2 )
% 0.19/0.44             => ( ord_less @ A @ Y2 @ X2 ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % linorder_cases
% 0.19/0.44  thf(fact_107_dual__order_Oirrefl,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( order @ A )
% 0.19/0.44       => ! [A2: A] :
% 0.19/0.44            ~ ( ord_less @ A @ A2 @ A2 ) ) ).
% 0.19/0.44  
% 0.19/0.44  % dual_order.irrefl
% 0.19/0.44  thf(fact_108_order_Ostrict__trans,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( order @ A )
% 0.19/0.44       => ! [A2: A,B2: A,C2: A] :
% 0.19/0.44            ( ( ord_less @ A @ A2 @ B2 )
% 0.19/0.44           => ( ( ord_less @ A @ B2 @ C2 )
% 0.19/0.44             => ( ord_less @ A @ A2 @ C2 ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % order.strict_trans
% 0.19/0.44  thf(fact_109_less__imp__not__less,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( preorder @ A )
% 0.19/0.44       => ! [X2: A,Y2: A] :
% 0.19/0.44            ( ( ord_less @ A @ X2 @ Y2 )
% 0.19/0.44           => ~ ( ord_less @ A @ Y2 @ X2 ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % less_imp_not_less
% 0.19/0.44  thf(fact_110_exists__least__iff,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( wellorder @ A )
% 0.19/0.44       => ( ( ^ [P3: A > $o] :
% 0.19/0.44              ? [X5: A] : ( P3 @ X5 ) )
% 0.19/0.44          = ( ^ [P4: A > $o] :
% 0.19/0.44              ? [N2: A] :
% 0.19/0.44                ( ( P4 @ N2 )
% 0.19/0.44                & ! [M2: A] :
% 0.19/0.44                    ( ( ord_less @ A @ M2 @ N2 )
% 0.19/0.44                   => ~ ( P4 @ M2 ) ) ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % exists_least_iff
% 0.19/0.44  thf(fact_111_linorder__less__wlog,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( linorder @ A )
% 0.19/0.44       => ! [P: A > A > $o,A2: A,B2: A] :
% 0.19/0.44            ( ! [A7: A,B7: A] :
% 0.19/0.44                ( ( ord_less @ A @ A7 @ B7 )
% 0.19/0.44               => ( P @ A7 @ B7 ) )
% 0.19/0.44           => ( ! [A7: A] : ( P @ A7 @ A7 )
% 0.19/0.44             => ( ! [A7: A,B7: A] :
% 0.19/0.44                    ( ( P @ B7 @ A7 )
% 0.19/0.44                   => ( P @ A7 @ B7 ) )
% 0.19/0.44               => ( P @ A2 @ B2 ) ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % linorder_less_wlog
% 0.19/0.44  thf(fact_112_dual__order_Ostrict__trans,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( order @ A )
% 0.19/0.44       => ! [B2: A,A2: A,C2: A] :
% 0.19/0.44            ( ( ord_less @ A @ B2 @ A2 )
% 0.19/0.44           => ( ( ord_less @ A @ C2 @ B2 )
% 0.19/0.44             => ( ord_less @ A @ C2 @ A2 ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % dual_order.strict_trans
% 0.19/0.44  thf(fact_113_not__less__iff__gr__or__eq,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.44        ( ( linorder @ A )
% 0.19/0.44       => ! [X2: A,Y2: A] :
% 0.19/0.44            ( ( ~ ( ord_less @ A @ X2 @ Y2 ) )
% 0.19/0.44            = ( ( ord_less @ A @ Y2 @ X2 )
% 0.19/0.44              | ( X2 = Y2 ) ) ) ) ).
% 0.19/0.44  
% 0.19/0.44  % not_less_iff_gr_or_eq
% 0.19/0.44  thf(fact_114_order_Ostrict__implies__not__eq,axiom,
% 0.19/0.44      ! [A: $tType] :
% 0.19/0.45        ( ( order @ A )
% 0.19/0.45       => ! [A2: A,B2: A] :
% 0.19/0.45            ( ( ord_less @ A @ A2 @ B2 )
% 0.19/0.45           => ( A2 != B2 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % order.strict_implies_not_eq
% 0.19/0.45  thf(fact_115_dual__order_Ostrict__implies__not__eq,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( order @ A )
% 0.19/0.45       => ! [B2: A,A2: A] :
% 0.19/0.45            ( ( ord_less @ A @ B2 @ A2 )
% 0.19/0.45           => ( A2 != B2 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % dual_order.strict_implies_not_eq
% 0.19/0.45  thf(fact_116_ex__gt__or__lt,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( condit1656338222tinuum @ A )
% 0.19/0.45       => ! [A2: A] :
% 0.19/0.45          ? [B7: A] :
% 0.19/0.45            ( ( ord_less @ A @ A2 @ B7 )
% 0.19/0.45            | ( ord_less @ A @ B7 @ A2 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % ex_gt_or_lt
% 0.19/0.45  thf(fact_117_complete__real,axiom,
% 0.19/0.45      ! [S: set @ real] :
% 0.19/0.45        ( ? [X3: real] : ( member @ real @ X3 @ S )
% 0.19/0.45       => ( ? [Z: real] :
% 0.19/0.45            ! [X4: real] :
% 0.19/0.45              ( ( member @ real @ X4 @ S )
% 0.19/0.45             => ( ord_less_eq @ real @ X4 @ Z ) )
% 0.19/0.45         => ? [Y4: real] :
% 0.19/0.45              ( ! [X3: real] :
% 0.19/0.45                  ( ( member @ real @ X3 @ S )
% 0.19/0.45                 => ( ord_less_eq @ real @ X3 @ Y4 ) )
% 0.19/0.45              & ! [Z: real] :
% 0.19/0.45                  ( ! [X4: real] :
% 0.19/0.45                      ( ( member @ real @ X4 @ S )
% 0.19/0.45                     => ( ord_less_eq @ real @ X4 @ Z ) )
% 0.19/0.45                 => ( ord_less_eq @ real @ Y4 @ Z ) ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % complete_real
% 0.19/0.45  thf(fact_118_field__lbound__gt__zero,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( linordered_field @ A )
% 0.19/0.45       => ! [D1: A,D2: A] :
% 0.19/0.45            ( ( ord_less @ A @ ( zero_zero @ A ) @ D1 )
% 0.19/0.45           => ( ( ord_less @ A @ ( zero_zero @ A ) @ D2 )
% 0.19/0.45             => ? [E: A] :
% 0.19/0.45                  ( ( ord_less @ A @ ( zero_zero @ A ) @ E )
% 0.19/0.45                  & ( ord_less @ A @ E @ D1 )
% 0.19/0.45                  & ( ord_less @ A @ E @ D2 ) ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % field_lbound_gt_zero
% 0.19/0.45  thf(fact_119_leD,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( order @ A )
% 0.19/0.45       => ! [Y2: A,X2: A] :
% 0.19/0.45            ( ( ord_less_eq @ A @ Y2 @ X2 )
% 0.19/0.45           => ~ ( ord_less @ A @ X2 @ Y2 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % leD
% 0.19/0.45  thf(fact_120_leI,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( linorder @ A )
% 0.19/0.45       => ! [X2: A,Y2: A] :
% 0.19/0.45            ( ~ ( ord_less @ A @ X2 @ Y2 )
% 0.19/0.45           => ( ord_less_eq @ A @ Y2 @ X2 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % leI
% 0.19/0.45  thf(fact_121_le__less,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( order @ A )
% 0.19/0.45       => ( ( ord_less_eq @ A )
% 0.19/0.45          = ( ^ [X: A,Y: A] :
% 0.19/0.45                ( ( ord_less @ A @ X @ Y )
% 0.19/0.45                | ( X = Y ) ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % le_less
% 0.19/0.45  thf(fact_122_less__le,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( order @ A )
% 0.19/0.45       => ( ( ord_less @ A )
% 0.19/0.45          = ( ^ [X: A,Y: A] :
% 0.19/0.45                ( ( ord_less_eq @ A @ X @ Y )
% 0.19/0.45                & ( X != Y ) ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % less_le
% 0.19/0.45  thf(fact_123_order__le__less__subst1,axiom,
% 0.19/0.45      ! [A: $tType,B: $tType] :
% 0.19/0.45        ( ( ( order @ B )
% 0.19/0.45          & ( order @ A ) )
% 0.19/0.45       => ! [A2: A,F2: B > A,B2: B,C2: B] :
% 0.19/0.45            ( ( ord_less_eq @ A @ A2 @ ( F2 @ B2 ) )
% 0.19/0.45           => ( ( ord_less @ B @ B2 @ C2 )
% 0.19/0.45             => ( ! [X4: B,Y4: B] :
% 0.19/0.45                    ( ( ord_less @ B @ X4 @ Y4 )
% 0.19/0.45                   => ( ord_less @ A @ ( F2 @ X4 ) @ ( F2 @ Y4 ) ) )
% 0.19/0.45               => ( ord_less @ A @ A2 @ ( F2 @ C2 ) ) ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % order_le_less_subst1
% 0.19/0.45  thf(fact_124_order__le__less__subst2,axiom,
% 0.19/0.45      ! [A: $tType,C3: $tType] :
% 0.19/0.45        ( ( ( order @ C3 )
% 0.19/0.45          & ( order @ A ) )
% 0.19/0.45       => ! [A2: A,B2: A,F2: A > C3,C2: C3] :
% 0.19/0.45            ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.19/0.45           => ( ( ord_less @ C3 @ ( F2 @ B2 ) @ C2 )
% 0.19/0.45             => ( ! [X4: A,Y4: A] :
% 0.19/0.45                    ( ( ord_less_eq @ A @ X4 @ Y4 )
% 0.19/0.45                   => ( ord_less_eq @ C3 @ ( F2 @ X4 ) @ ( F2 @ Y4 ) ) )
% 0.19/0.45               => ( ord_less @ C3 @ ( F2 @ A2 ) @ C2 ) ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % order_le_less_subst2
% 0.19/0.45  thf(fact_125_order__less__le__subst1,axiom,
% 0.19/0.45      ! [A: $tType,B: $tType] :
% 0.19/0.45        ( ( ( order @ B )
% 0.19/0.45          & ( order @ A ) )
% 0.19/0.45       => ! [A2: A,F2: B > A,B2: B,C2: B] :
% 0.19/0.45            ( ( ord_less @ A @ A2 @ ( F2 @ B2 ) )
% 0.19/0.45           => ( ( ord_less_eq @ B @ B2 @ C2 )
% 0.19/0.45             => ( ! [X4: B,Y4: B] :
% 0.19/0.45                    ( ( ord_less_eq @ B @ X4 @ Y4 )
% 0.19/0.45                   => ( ord_less_eq @ A @ ( F2 @ X4 ) @ ( F2 @ Y4 ) ) )
% 0.19/0.45               => ( ord_less @ A @ A2 @ ( F2 @ C2 ) ) ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % order_less_le_subst1
% 0.19/0.45  thf(fact_126_order__less__le__subst2,axiom,
% 0.19/0.45      ! [A: $tType,C3: $tType] :
% 0.19/0.45        ( ( ( order @ C3 )
% 0.19/0.45          & ( order @ A ) )
% 0.19/0.45       => ! [A2: A,B2: A,F2: A > C3,C2: C3] :
% 0.19/0.45            ( ( ord_less @ A @ A2 @ B2 )
% 0.19/0.45           => ( ( ord_less_eq @ C3 @ ( F2 @ B2 ) @ C2 )
% 0.19/0.45             => ( ! [X4: A,Y4: A] :
% 0.19/0.45                    ( ( ord_less @ A @ X4 @ Y4 )
% 0.19/0.45                   => ( ord_less @ C3 @ ( F2 @ X4 ) @ ( F2 @ Y4 ) ) )
% 0.19/0.45               => ( ord_less @ C3 @ ( F2 @ A2 ) @ C2 ) ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % order_less_le_subst2
% 0.19/0.45  thf(fact_127_not__le,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( linorder @ A )
% 0.19/0.45       => ! [X2: A,Y2: A] :
% 0.19/0.45            ( ( ~ ( ord_less_eq @ A @ X2 @ Y2 ) )
% 0.19/0.45            = ( ord_less @ A @ Y2 @ X2 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % not_le
% 0.19/0.45  thf(fact_128_not__less,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( linorder @ A )
% 0.19/0.45       => ! [X2: A,Y2: A] :
% 0.19/0.45            ( ( ~ ( ord_less @ A @ X2 @ Y2 ) )
% 0.19/0.45            = ( ord_less_eq @ A @ Y2 @ X2 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % not_less
% 0.19/0.45  thf(fact_129_le__neq__trans,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( order @ A )
% 0.19/0.45       => ! [A2: A,B2: A] :
% 0.19/0.45            ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.19/0.45           => ( ( A2 != B2 )
% 0.19/0.45             => ( ord_less @ A @ A2 @ B2 ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % le_neq_trans
% 0.19/0.45  thf(fact_130_antisym__conv1,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( order @ A )
% 0.19/0.45       => ! [X2: A,Y2: A] :
% 0.19/0.45            ( ~ ( ord_less @ A @ X2 @ Y2 )
% 0.19/0.45           => ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.19/0.45              = ( X2 = Y2 ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % antisym_conv1
% 0.19/0.45  thf(fact_131_antisym__conv2,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( order @ A )
% 0.19/0.45       => ! [X2: A,Y2: A] :
% 0.19/0.45            ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.19/0.45           => ( ( ~ ( ord_less @ A @ X2 @ Y2 ) )
% 0.19/0.45              = ( X2 = Y2 ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % antisym_conv2
% 0.19/0.45  thf(fact_132_less__imp__le,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( preorder @ A )
% 0.19/0.45       => ! [X2: A,Y2: A] :
% 0.19/0.45            ( ( ord_less @ A @ X2 @ Y2 )
% 0.19/0.45           => ( ord_less_eq @ A @ X2 @ Y2 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % less_imp_le
% 0.19/0.45  thf(fact_133_le__less__trans,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( preorder @ A )
% 0.19/0.45       => ! [X2: A,Y2: A,Z3: A] :
% 0.19/0.45            ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.19/0.45           => ( ( ord_less @ A @ Y2 @ Z3 )
% 0.19/0.45             => ( ord_less @ A @ X2 @ Z3 ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % le_less_trans
% 0.19/0.45  thf(fact_134_less__le__trans,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( preorder @ A )
% 0.19/0.45       => ! [X2: A,Y2: A,Z3: A] :
% 0.19/0.45            ( ( ord_less @ A @ X2 @ Y2 )
% 0.19/0.45           => ( ( ord_less_eq @ A @ Y2 @ Z3 )
% 0.19/0.45             => ( ord_less @ A @ X2 @ Z3 ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % less_le_trans
% 0.19/0.45  thf(fact_135_dense__ge,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( dense_linorder @ A )
% 0.19/0.45       => ! [Z3: A,Y2: A] :
% 0.19/0.45            ( ! [X4: A] :
% 0.19/0.45                ( ( ord_less @ A @ Z3 @ X4 )
% 0.19/0.45               => ( ord_less_eq @ A @ Y2 @ X4 ) )
% 0.19/0.45           => ( ord_less_eq @ A @ Y2 @ Z3 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % dense_ge
% 0.19/0.45  thf(fact_136_dense__le,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( dense_linorder @ A )
% 0.19/0.45       => ! [Y2: A,Z3: A] :
% 0.19/0.45            ( ! [X4: A] :
% 0.19/0.45                ( ( ord_less @ A @ X4 @ Y2 )
% 0.19/0.45               => ( ord_less_eq @ A @ X4 @ Z3 ) )
% 0.19/0.45           => ( ord_less_eq @ A @ Y2 @ Z3 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % dense_le
% 0.19/0.45  thf(fact_137_le__less__linear,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( linorder @ A )
% 0.19/0.45       => ! [X2: A,Y2: A] :
% 0.19/0.45            ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.19/0.45            | ( ord_less @ A @ Y2 @ X2 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % le_less_linear
% 0.19/0.45  thf(fact_138_le__imp__less__or__eq,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( order @ A )
% 0.19/0.45       => ! [X2: A,Y2: A] :
% 0.19/0.45            ( ( ord_less_eq @ A @ X2 @ Y2 )
% 0.19/0.45           => ( ( ord_less @ A @ X2 @ Y2 )
% 0.19/0.45              | ( X2 = Y2 ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % le_imp_less_or_eq
% 0.19/0.45  thf(fact_139_less__le__not__le,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( preorder @ A )
% 0.19/0.45       => ( ( ord_less @ A )
% 0.19/0.45          = ( ^ [X: A,Y: A] :
% 0.19/0.45                ( ( ord_less_eq @ A @ X @ Y )
% 0.19/0.45                & ~ ( ord_less_eq @ A @ Y @ X ) ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % less_le_not_le
% 0.19/0.45  thf(fact_140_not__le__imp__less,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( linorder @ A )
% 0.19/0.45       => ! [Y2: A,X2: A] :
% 0.19/0.45            ( ~ ( ord_less_eq @ A @ Y2 @ X2 )
% 0.19/0.45           => ( ord_less @ A @ X2 @ Y2 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % not_le_imp_less
% 0.19/0.45  thf(fact_141_order_Ostrict__trans1,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( order @ A )
% 0.19/0.45       => ! [A2: A,B2: A,C2: A] :
% 0.19/0.45            ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.19/0.45           => ( ( ord_less @ A @ B2 @ C2 )
% 0.19/0.45             => ( ord_less @ A @ A2 @ C2 ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % order.strict_trans1
% 0.19/0.45  thf(fact_142_order_Ostrict__trans2,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( order @ A )
% 0.19/0.45       => ! [A2: A,B2: A,C2: A] :
% 0.19/0.45            ( ( ord_less @ A @ A2 @ B2 )
% 0.19/0.45           => ( ( ord_less_eq @ A @ B2 @ C2 )
% 0.19/0.45             => ( ord_less @ A @ A2 @ C2 ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % order.strict_trans2
% 0.19/0.45  thf(fact_143_order_Oorder__iff__strict,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( order @ A )
% 0.19/0.45       => ( ( ord_less_eq @ A )
% 0.19/0.45          = ( ^ [A6: A,B5: A] :
% 0.19/0.45                ( ( ord_less @ A @ A6 @ B5 )
% 0.19/0.45                | ( A6 = B5 ) ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % order.order_iff_strict
% 0.19/0.45  thf(fact_144_order_Ostrict__iff__order,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( order @ A )
% 0.19/0.45       => ( ( ord_less @ A )
% 0.19/0.45          = ( ^ [A6: A,B5: A] :
% 0.19/0.45                ( ( ord_less_eq @ A @ A6 @ B5 )
% 0.19/0.45                & ( A6 != B5 ) ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % order.strict_iff_order
% 0.19/0.45  thf(fact_145_dual__order_Ostrict__trans1,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( order @ A )
% 0.19/0.45       => ! [B2: A,A2: A,C2: A] :
% 0.19/0.45            ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.19/0.45           => ( ( ord_less @ A @ C2 @ B2 )
% 0.19/0.45             => ( ord_less @ A @ C2 @ A2 ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % dual_order.strict_trans1
% 0.19/0.45  thf(fact_146_dual__order_Ostrict__trans2,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( order @ A )
% 0.19/0.45       => ! [B2: A,A2: A,C2: A] :
% 0.19/0.45            ( ( ord_less @ A @ B2 @ A2 )
% 0.19/0.45           => ( ( ord_less_eq @ A @ C2 @ B2 )
% 0.19/0.45             => ( ord_less @ A @ C2 @ A2 ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % dual_order.strict_trans2
% 0.19/0.45  thf(fact_147_dense__ge__bounded,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( dense_linorder @ A )
% 0.19/0.45       => ! [Z3: A,X2: A,Y2: A] :
% 0.19/0.45            ( ( ord_less @ A @ Z3 @ X2 )
% 0.19/0.45           => ( ! [W: A] :
% 0.19/0.45                  ( ( ord_less @ A @ Z3 @ W )
% 0.19/0.45                 => ( ( ord_less @ A @ W @ X2 )
% 0.19/0.45                   => ( ord_less_eq @ A @ Y2 @ W ) ) )
% 0.19/0.45             => ( ord_less_eq @ A @ Y2 @ Z3 ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % dense_ge_bounded
% 0.19/0.45  thf(fact_148_psubsetI,axiom,
% 0.19/0.45      ! [A: $tType,A4: set @ A,B4: set @ A] :
% 0.19/0.45        ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 0.19/0.45       => ( ( A4 != B4 )
% 0.19/0.45         => ( ord_less @ ( set @ A ) @ A4 @ B4 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % psubsetI
% 0.19/0.45  thf(fact_149_minf_I8_J,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( linorder @ A )
% 0.19/0.45       => ! [T2: A] :
% 0.19/0.45          ? [Z5: A] :
% 0.19/0.45          ! [X3: A] :
% 0.19/0.45            ( ( ord_less @ A @ X3 @ Z5 )
% 0.19/0.45           => ~ ( ord_less_eq @ A @ T2 @ X3 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % minf(8)
% 0.19/0.45  thf(fact_150_minf_I6_J,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( linorder @ A )
% 0.19/0.45       => ! [T2: A] :
% 0.19/0.45          ? [Z5: A] :
% 0.19/0.45          ! [X3: A] :
% 0.19/0.45            ( ( ord_less @ A @ X3 @ Z5 )
% 0.19/0.45           => ( ord_less_eq @ A @ X3 @ T2 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % minf(6)
% 0.19/0.45  thf(fact_151_pinf_I8_J,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( linorder @ A )
% 0.19/0.45       => ! [T2: A] :
% 0.19/0.45          ? [Z5: A] :
% 0.19/0.45          ! [X3: A] :
% 0.19/0.45            ( ( ord_less @ A @ Z5 @ X3 )
% 0.19/0.45           => ( ord_less_eq @ A @ T2 @ X3 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % pinf(8)
% 0.19/0.45  thf(fact_152_pinf_I6_J,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( linorder @ A )
% 0.19/0.45       => ! [T2: A] :
% 0.19/0.45          ? [Z5: A] :
% 0.19/0.45          ! [X3: A] :
% 0.19/0.45            ( ( ord_less @ A @ Z5 @ X3 )
% 0.19/0.45           => ~ ( ord_less_eq @ A @ X3 @ T2 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % pinf(6)
% 0.19/0.45  thf(fact_153_verit__comp__simplify1_I3_J,axiom,
% 0.19/0.45      ! [B: $tType] :
% 0.19/0.45        ( ( linorder @ B )
% 0.19/0.45       => ! [B8: B,A8: B] :
% 0.19/0.45            ( ( ~ ( ord_less_eq @ B @ B8 @ A8 ) )
% 0.19/0.45            = ( ord_less @ B @ A8 @ B8 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % verit_comp_simplify1(3)
% 0.19/0.45  thf(fact_154_is__zero__null,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( zero @ A )
% 0.19/0.45       => ( ( is_zero @ A )
% 0.19/0.45          = ( ^ [P5: poly @ A] :
% 0.19/0.45                ( P5
% 0.19/0.45                = ( zero_zero @ ( poly @ A ) ) ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % is_zero_null
% 0.19/0.45  thf(fact_155_poly__cutoff__0,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( zero @ A )
% 0.19/0.45       => ! [N: nat] :
% 0.19/0.45            ( ( poly_cutoff @ A @ N @ ( zero_zero @ ( poly @ A ) ) )
% 0.19/0.45            = ( zero_zero @ ( poly @ A ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % poly_cutoff_0
% 0.19/0.45  thf(fact_156_subsetI,axiom,
% 0.19/0.45      ! [A: $tType,A4: set @ A,B4: set @ A] :
% 0.19/0.45        ( ! [X4: A] :
% 0.19/0.45            ( ( member @ A @ X4 @ A4 )
% 0.19/0.45           => ( member @ A @ X4 @ B4 ) )
% 0.19/0.45       => ( ord_less_eq @ ( set @ A ) @ A4 @ B4 ) ) ).
% 0.19/0.45  
% 0.19/0.45  % subsetI
% 0.19/0.45  thf(fact_157_subset__antisym,axiom,
% 0.19/0.45      ! [A: $tType,A4: set @ A,B4: set @ A] :
% 0.19/0.45        ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 0.19/0.45       => ( ( ord_less_eq @ ( set @ A ) @ B4 @ A4 )
% 0.19/0.45         => ( A4 = B4 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % subset_antisym
% 0.19/0.45  thf(fact_158_in__mono,axiom,
% 0.19/0.45      ! [A: $tType,A4: set @ A,B4: set @ A,X2: A] :
% 0.19/0.45        ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 0.19/0.45       => ( ( member @ A @ X2 @ A4 )
% 0.19/0.45         => ( member @ A @ X2 @ B4 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % in_mono
% 0.19/0.45  thf(fact_159_subsetD,axiom,
% 0.19/0.45      ! [A: $tType,A4: set @ A,B4: set @ A,C2: A] :
% 0.19/0.45        ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 0.19/0.45       => ( ( member @ A @ C2 @ A4 )
% 0.19/0.45         => ( member @ A @ C2 @ B4 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % subsetD
% 0.19/0.45  thf(fact_160_equalityE,axiom,
% 0.19/0.45      ! [A: $tType,A4: set @ A,B4: set @ A] :
% 0.19/0.45        ( ( A4 = B4 )
% 0.19/0.45       => ~ ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 0.19/0.45           => ~ ( ord_less_eq @ ( set @ A ) @ B4 @ A4 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % equalityE
% 0.19/0.45  thf(fact_161_subset__eq,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( ord_less_eq @ ( set @ A ) )
% 0.19/0.45        = ( ^ [A3: set @ A,B6: set @ A] :
% 0.19/0.45            ! [X: A] :
% 0.19/0.45              ( ( member @ A @ X @ A3 )
% 0.19/0.45             => ( member @ A @ X @ B6 ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % subset_eq
% 0.19/0.45  thf(fact_162_equalityD1,axiom,
% 0.19/0.45      ! [A: $tType,A4: set @ A,B4: set @ A] :
% 0.19/0.45        ( ( A4 = B4 )
% 0.19/0.45       => ( ord_less_eq @ ( set @ A ) @ A4 @ B4 ) ) ).
% 0.19/0.45  
% 0.19/0.45  % equalityD1
% 0.19/0.45  thf(fact_163_equalityD2,axiom,
% 0.19/0.45      ! [A: $tType,A4: set @ A,B4: set @ A] :
% 0.19/0.45        ( ( A4 = B4 )
% 0.19/0.45       => ( ord_less_eq @ ( set @ A ) @ B4 @ A4 ) ) ).
% 0.19/0.45  
% 0.19/0.45  % equalityD2
% 0.19/0.45  thf(fact_164_subset__iff,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( ord_less_eq @ ( set @ A ) )
% 0.19/0.45        = ( ^ [A3: set @ A,B6: set @ A] :
% 0.19/0.45            ! [T3: A] :
% 0.19/0.45              ( ( member @ A @ T3 @ A3 )
% 0.19/0.45             => ( member @ A @ T3 @ B6 ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % subset_iff
% 0.19/0.45  thf(fact_165_subset__refl,axiom,
% 0.19/0.45      ! [A: $tType,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ A4 @ A4 ) ).
% 0.19/0.45  
% 0.19/0.45  % subset_refl
% 0.19/0.45  thf(fact_166_Collect__mono,axiom,
% 0.19/0.45      ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.19/0.45        ( ! [X4: A] :
% 0.19/0.45            ( ( P @ X4 )
% 0.19/0.45           => ( Q @ X4 ) )
% 0.19/0.45       => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % Collect_mono
% 0.19/0.45  thf(fact_167_subset__trans,axiom,
% 0.19/0.45      ! [A: $tType,A4: set @ A,B4: set @ A,C4: set @ A] :
% 0.19/0.45        ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 0.19/0.45       => ( ( ord_less_eq @ ( set @ A ) @ B4 @ C4 )
% 0.19/0.45         => ( ord_less_eq @ ( set @ A ) @ A4 @ C4 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % subset_trans
% 0.19/0.45  thf(fact_168_set__eq__subset,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( ^ [Y3: set @ A,Z4: set @ A] : ( Y3 = Z4 ) )
% 0.19/0.45        = ( ^ [A3: set @ A,B6: set @ A] :
% 0.19/0.45              ( ( ord_less_eq @ ( set @ A ) @ A3 @ B6 )
% 0.19/0.45              & ( ord_less_eq @ ( set @ A ) @ B6 @ A3 ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % set_eq_subset
% 0.19/0.45  thf(fact_169_Collect__subset,axiom,
% 0.19/0.45      ! [A: $tType,A4: set @ A,P: A > $o] :
% 0.19/0.45        ( ord_less_eq @ ( set @ A )
% 0.19/0.45        @ ( collect @ A
% 0.19/0.45          @ ^ [X: A] :
% 0.19/0.45              ( ( member @ A @ X @ A4 )
% 0.19/0.45              & ( P @ X ) ) )
% 0.19/0.45        @ A4 ) ).
% 0.19/0.45  
% 0.19/0.45  % Collect_subset
% 0.19/0.45  thf(fact_170_less__eq__set__def,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( ord_less_eq @ ( set @ A ) )
% 0.19/0.45        = ( ^ [A3: set @ A,B6: set @ A] :
% 0.19/0.45              ( ord_less_eq @ ( A > $o )
% 0.19/0.45              @ ^ [X: A] : ( member @ A @ X @ A3 )
% 0.19/0.45              @ ^ [X: A] : ( member @ A @ X @ B6 ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % less_eq_set_def
% 0.19/0.45  thf(fact_171_Collect__mono__iff,axiom,
% 0.19/0.45      ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.19/0.45        ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 0.19/0.45        = ( ! [X: A] :
% 0.19/0.45              ( ( P @ X )
% 0.19/0.45             => ( Q @ X ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % Collect_mono_iff
% 0.19/0.45  thf(fact_172_less__fun__def,axiom,
% 0.19/0.45      ! [B: $tType,A: $tType] :
% 0.19/0.45        ( ( ord @ B )
% 0.19/0.45       => ( ( ord_less @ ( A > B ) )
% 0.19/0.45          = ( ^ [F3: A > B,G2: A > B] :
% 0.19/0.45                ( ( ord_less_eq @ ( A > B ) @ F3 @ G2 )
% 0.19/0.45                & ~ ( ord_less_eq @ ( A > B ) @ G2 @ F3 ) ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % less_fun_def
% 0.19/0.45  thf(fact_173_verit__la__disequality,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( linorder @ A )
% 0.19/0.45       => ! [A2: A,B2: A] :
% 0.19/0.45            ( ( A2 = B2 )
% 0.19/0.45            | ~ ( ord_less_eq @ A @ A2 @ B2 )
% 0.19/0.45            | ~ ( ord_less_eq @ A @ B2 @ A2 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % verit_la_disequality
% 0.19/0.45  thf(fact_174_verit__comp__simplify1_I1_J,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( order @ A )
% 0.19/0.45       => ! [A2: A] :
% 0.19/0.45            ~ ( ord_less @ A @ A2 @ A2 ) ) ).
% 0.19/0.45  
% 0.19/0.45  % verit_comp_simplify1(1)
% 0.19/0.45  thf(fact_175_pinf_I1_J,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( linorder @ A )
% 0.19/0.45       => ! [P: A > $o,P6: A > $o,Q: A > $o,Q3: A > $o] :
% 0.19/0.45            ( ? [Z: A] :
% 0.19/0.45              ! [X4: A] :
% 0.19/0.45                ( ( ord_less @ A @ Z @ X4 )
% 0.19/0.45               => ( ( P @ X4 )
% 0.19/0.45                  = ( P6 @ X4 ) ) )
% 0.19/0.45           => ( ? [Z: A] :
% 0.19/0.45                ! [X4: A] :
% 0.19/0.45                  ( ( ord_less @ A @ Z @ X4 )
% 0.19/0.45                 => ( ( Q @ X4 )
% 0.19/0.45                    = ( Q3 @ X4 ) ) )
% 0.19/0.45             => ? [Z5: A] :
% 0.19/0.45                ! [X3: A] :
% 0.19/0.45                  ( ( ord_less @ A @ Z5 @ X3 )
% 0.19/0.45                 => ( ( ( P @ X3 )
% 0.19/0.45                      & ( Q @ X3 ) )
% 0.19/0.45                    = ( ( P6 @ X3 )
% 0.19/0.45                      & ( Q3 @ X3 ) ) ) ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % pinf(1)
% 0.19/0.45  thf(fact_176_pinf_I2_J,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( linorder @ A )
% 0.19/0.45       => ! [P: A > $o,P6: A > $o,Q: A > $o,Q3: A > $o] :
% 0.19/0.45            ( ? [Z: A] :
% 0.19/0.45              ! [X4: A] :
% 0.19/0.45                ( ( ord_less @ A @ Z @ X4 )
% 0.19/0.45               => ( ( P @ X4 )
% 0.19/0.45                  = ( P6 @ X4 ) ) )
% 0.19/0.45           => ( ? [Z: A] :
% 0.19/0.45                ! [X4: A] :
% 0.19/0.45                  ( ( ord_less @ A @ Z @ X4 )
% 0.19/0.45                 => ( ( Q @ X4 )
% 0.19/0.45                    = ( Q3 @ X4 ) ) )
% 0.19/0.45             => ? [Z5: A] :
% 0.19/0.45                ! [X3: A] :
% 0.19/0.45                  ( ( ord_less @ A @ Z5 @ X3 )
% 0.19/0.45                 => ( ( ( P @ X3 )
% 0.19/0.45                      | ( Q @ X3 ) )
% 0.19/0.45                    = ( ( P6 @ X3 )
% 0.19/0.45                      | ( Q3 @ X3 ) ) ) ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % pinf(2)
% 0.19/0.45  thf(fact_177_pinf_I3_J,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( linorder @ A )
% 0.19/0.45       => ! [T2: A] :
% 0.19/0.45          ? [Z5: A] :
% 0.19/0.45          ! [X3: A] :
% 0.19/0.45            ( ( ord_less @ A @ Z5 @ X3 )
% 0.19/0.45           => ( X3 != T2 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % pinf(3)
% 0.19/0.45  thf(fact_178_pinf_I4_J,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( linorder @ A )
% 0.19/0.45       => ! [T2: A] :
% 0.19/0.45          ? [Z5: A] :
% 0.19/0.45          ! [X3: A] :
% 0.19/0.45            ( ( ord_less @ A @ Z5 @ X3 )
% 0.19/0.45           => ( X3 != T2 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % pinf(4)
% 0.19/0.45  thf(fact_179_pinf_I5_J,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( linorder @ A )
% 0.19/0.45       => ! [T2: A] :
% 0.19/0.45          ? [Z5: A] :
% 0.19/0.45          ! [X3: A] :
% 0.19/0.45            ( ( ord_less @ A @ Z5 @ X3 )
% 0.19/0.45           => ~ ( ord_less @ A @ X3 @ T2 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % pinf(5)
% 0.19/0.45  thf(fact_180_pinf_I7_J,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( linorder @ A )
% 0.19/0.45       => ! [T2: A] :
% 0.19/0.45          ? [Z5: A] :
% 0.19/0.45          ! [X3: A] :
% 0.19/0.45            ( ( ord_less @ A @ Z5 @ X3 )
% 0.19/0.45           => ( ord_less @ A @ T2 @ X3 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % pinf(7)
% 0.19/0.45  thf(fact_181_pinf_I11_J,axiom,
% 0.19/0.45      ! [C3: $tType,D3: $tType] :
% 0.19/0.45        ( ( ord @ C3 )
% 0.19/0.45       => ! [F4: D3] :
% 0.19/0.45          ? [Z5: C3] :
% 0.19/0.45          ! [X3: C3] :
% 0.19/0.45            ( ( ord_less @ C3 @ Z5 @ X3 )
% 0.19/0.45           => ( F4 = F4 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % pinf(11)
% 0.19/0.45  thf(fact_182_minf_I1_J,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( linorder @ A )
% 0.19/0.45       => ! [P: A > $o,P6: A > $o,Q: A > $o,Q3: A > $o] :
% 0.19/0.45            ( ? [Z: A] :
% 0.19/0.45              ! [X4: A] :
% 0.19/0.45                ( ( ord_less @ A @ X4 @ Z )
% 0.19/0.45               => ( ( P @ X4 )
% 0.19/0.45                  = ( P6 @ X4 ) ) )
% 0.19/0.45           => ( ? [Z: A] :
% 0.19/0.45                ! [X4: A] :
% 0.19/0.45                  ( ( ord_less @ A @ X4 @ Z )
% 0.19/0.45                 => ( ( Q @ X4 )
% 0.19/0.45                    = ( Q3 @ X4 ) ) )
% 0.19/0.45             => ? [Z5: A] :
% 0.19/0.45                ! [X3: A] :
% 0.19/0.45                  ( ( ord_less @ A @ X3 @ Z5 )
% 0.19/0.45                 => ( ( ( P @ X3 )
% 0.19/0.45                      & ( Q @ X3 ) )
% 0.19/0.45                    = ( ( P6 @ X3 )
% 0.19/0.45                      & ( Q3 @ X3 ) ) ) ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % minf(1)
% 0.19/0.45  thf(fact_183_minf_I2_J,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( linorder @ A )
% 0.19/0.45       => ! [P: A > $o,P6: A > $o,Q: A > $o,Q3: A > $o] :
% 0.19/0.45            ( ? [Z: A] :
% 0.19/0.45              ! [X4: A] :
% 0.19/0.45                ( ( ord_less @ A @ X4 @ Z )
% 0.19/0.45               => ( ( P @ X4 )
% 0.19/0.45                  = ( P6 @ X4 ) ) )
% 0.19/0.45           => ( ? [Z: A] :
% 0.19/0.45                ! [X4: A] :
% 0.19/0.45                  ( ( ord_less @ A @ X4 @ Z )
% 0.19/0.45                 => ( ( Q @ X4 )
% 0.19/0.45                    = ( Q3 @ X4 ) ) )
% 0.19/0.45             => ? [Z5: A] :
% 0.19/0.45                ! [X3: A] :
% 0.19/0.45                  ( ( ord_less @ A @ X3 @ Z5 )
% 0.19/0.45                 => ( ( ( P @ X3 )
% 0.19/0.45                      | ( Q @ X3 ) )
% 0.19/0.45                    = ( ( P6 @ X3 )
% 0.19/0.45                      | ( Q3 @ X3 ) ) ) ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % minf(2)
% 0.19/0.45  thf(fact_184_minf_I3_J,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( linorder @ A )
% 0.19/0.45       => ! [T2: A] :
% 0.19/0.45          ? [Z5: A] :
% 0.19/0.45          ! [X3: A] :
% 0.19/0.45            ( ( ord_less @ A @ X3 @ Z5 )
% 0.19/0.45           => ( X3 != T2 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % minf(3)
% 0.19/0.45  thf(fact_185_minf_I4_J,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( linorder @ A )
% 0.19/0.45       => ! [T2: A] :
% 0.19/0.45          ? [Z5: A] :
% 0.19/0.45          ! [X3: A] :
% 0.19/0.45            ( ( ord_less @ A @ X3 @ Z5 )
% 0.19/0.45           => ( X3 != T2 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % minf(4)
% 0.19/0.45  thf(fact_186_minf_I5_J,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( linorder @ A )
% 0.19/0.45       => ! [T2: A] :
% 0.19/0.45          ? [Z5: A] :
% 0.19/0.45          ! [X3: A] :
% 0.19/0.45            ( ( ord_less @ A @ X3 @ Z5 )
% 0.19/0.45           => ( ord_less @ A @ X3 @ T2 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % minf(5)
% 0.19/0.45  thf(fact_187_minf_I7_J,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( linorder @ A )
% 0.19/0.45       => ! [T2: A] :
% 0.19/0.45          ? [Z5: A] :
% 0.19/0.45          ! [X3: A] :
% 0.19/0.45            ( ( ord_less @ A @ X3 @ Z5 )
% 0.19/0.45           => ~ ( ord_less @ A @ T2 @ X3 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % minf(7)
% 0.19/0.45  thf(fact_188_minf_I11_J,axiom,
% 0.19/0.45      ! [C3: $tType,D3: $tType] :
% 0.19/0.45        ( ( ord @ C3 )
% 0.19/0.45       => ! [F4: D3] :
% 0.19/0.45          ? [Z5: C3] :
% 0.19/0.45          ! [X3: C3] :
% 0.19/0.45            ( ( ord_less @ C3 @ X3 @ Z5 )
% 0.19/0.45           => ( F4 = F4 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % minf(11)
% 0.19/0.45  thf(fact_189_conj__le__cong,axiom,
% 0.19/0.45      ! [X2: int,X6: int,P: $o,P6: $o] :
% 0.19/0.45        ( ( X2 = X6 )
% 0.19/0.45       => ( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ X6 )
% 0.19/0.45           => ( P = P6 ) )
% 0.19/0.45         => ( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ X2 )
% 0.19/0.45              & P )
% 0.19/0.45            = ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ X6 )
% 0.19/0.45              & P6 ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % conj_le_cong
% 0.19/0.45  thf(fact_190_imp__le__cong,axiom,
% 0.19/0.45      ! [X2: int,X6: int,P: $o,P6: $o] :
% 0.19/0.45        ( ( X2 = X6 )
% 0.19/0.45       => ( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ X6 )
% 0.19/0.45           => ( P = P6 ) )
% 0.19/0.45         => ( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ X2 )
% 0.19/0.45             => P )
% 0.19/0.45            = ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ X6 )
% 0.19/0.45             => P6 ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % imp_le_cong
% 0.19/0.45  thf(fact_191_subset__iff__psubset__eq,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( ord_less_eq @ ( set @ A ) )
% 0.19/0.45        = ( ^ [A3: set @ A,B6: set @ A] :
% 0.19/0.45              ( ( ord_less @ ( set @ A ) @ A3 @ B6 )
% 0.19/0.45              | ( A3 = B6 ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % subset_iff_psubset_eq
% 0.19/0.45  thf(fact_192_subset__psubset__trans,axiom,
% 0.19/0.45      ! [A: $tType,A4: set @ A,B4: set @ A,C4: set @ A] :
% 0.19/0.45        ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 0.19/0.45       => ( ( ord_less @ ( set @ A ) @ B4 @ C4 )
% 0.19/0.45         => ( ord_less @ ( set @ A ) @ A4 @ C4 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % subset_psubset_trans
% 0.19/0.45  thf(fact_193_subset__not__subset__eq,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( ord_less @ ( set @ A ) )
% 0.19/0.45        = ( ^ [A3: set @ A,B6: set @ A] :
% 0.19/0.45              ( ( ord_less_eq @ ( set @ A ) @ A3 @ B6 )
% 0.19/0.45              & ~ ( ord_less_eq @ ( set @ A ) @ B6 @ A3 ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % subset_not_subset_eq
% 0.19/0.45  thf(fact_194_psubset__subset__trans,axiom,
% 0.19/0.45      ! [A: $tType,A4: set @ A,B4: set @ A,C4: set @ A] :
% 0.19/0.45        ( ( ord_less @ ( set @ A ) @ A4 @ B4 )
% 0.19/0.45       => ( ( ord_less_eq @ ( set @ A ) @ B4 @ C4 )
% 0.19/0.45         => ( ord_less @ ( set @ A ) @ A4 @ C4 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % psubset_subset_trans
% 0.19/0.45  thf(fact_195_psubset__imp__subset,axiom,
% 0.19/0.45      ! [A: $tType,A4: set @ A,B4: set @ A] :
% 0.19/0.45        ( ( ord_less @ ( set @ A ) @ A4 @ B4 )
% 0.19/0.45       => ( ord_less_eq @ ( set @ A ) @ A4 @ B4 ) ) ).
% 0.19/0.45  
% 0.19/0.45  % psubset_imp_subset
% 0.19/0.45  thf(fact_196_psubset__trans,axiom,
% 0.19/0.45      ! [A: $tType,A4: set @ A,B4: set @ A,C4: set @ A] :
% 0.19/0.45        ( ( ord_less @ ( set @ A ) @ A4 @ B4 )
% 0.19/0.45       => ( ( ord_less @ ( set @ A ) @ B4 @ C4 )
% 0.19/0.45         => ( ord_less @ ( set @ A ) @ A4 @ C4 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % psubset_trans
% 0.19/0.45  thf(fact_197_psubset__eq,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( ord_less @ ( set @ A ) )
% 0.19/0.45        = ( ^ [A3: set @ A,B6: set @ A] :
% 0.19/0.45              ( ( ord_less_eq @ ( set @ A ) @ A3 @ B6 )
% 0.19/0.45              & ( A3 != B6 ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % psubset_eq
% 0.19/0.45  thf(fact_198_psubsetE,axiom,
% 0.19/0.45      ! [A: $tType,A4: set @ A,B4: set @ A] :
% 0.19/0.45        ( ( ord_less @ ( set @ A ) @ A4 @ B4 )
% 0.19/0.45       => ~ ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 0.19/0.45           => ( ord_less_eq @ ( set @ A ) @ B4 @ A4 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % psubsetE
% 0.19/0.45  thf(fact_199_psubsetD,axiom,
% 0.19/0.45      ! [A: $tType,A4: set @ A,B4: set @ A,C2: A] :
% 0.19/0.45        ( ( ord_less @ ( set @ A ) @ A4 @ B4 )
% 0.19/0.45       => ( ( member @ A @ C2 @ A4 )
% 0.19/0.45         => ( member @ A @ C2 @ B4 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % psubsetD
% 0.19/0.45  thf(fact_200_less__set__def,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( ord_less @ ( set @ A ) )
% 0.19/0.45        = ( ^ [A3: set @ A,B6: set @ A] :
% 0.19/0.45              ( ord_less @ ( A > $o )
% 0.19/0.45              @ ^ [X: A] : ( member @ A @ X @ A3 )
% 0.19/0.45              @ ^ [X: A] : ( member @ A @ X @ B6 ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % less_set_def
% 0.19/0.45  thf(fact_201_reflect__poly__at__0__eq__0__iff,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( comm_semiring_0 @ A )
% 0.19/0.45       => ! [P2: poly @ A] :
% 0.19/0.45            ( ( ( poly2 @ A @ ( reflect_poly @ A @ P2 ) @ ( zero_zero @ A ) )
% 0.19/0.45              = ( zero_zero @ A ) )
% 0.19/0.45            = ( P2
% 0.19/0.45              = ( zero_zero @ ( poly @ A ) ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % reflect_poly_at_0_eq_0_iff
% 0.19/0.45  thf(fact_202_jump__poly__not__root,axiom,
% 0.19/0.45      ! [P2: poly @ real,X2: real,Q2: poly @ real] :
% 0.19/0.45        ( ( ( poly2 @ real @ P2 @ X2 )
% 0.19/0.45         != ( zero_zero @ real ) )
% 0.19/0.45       => ( ( sturm_652470720p_poly @ Q2 @ P2 @ X2 )
% 0.19/0.45          = ( zero_zero @ int ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % jump_poly_not_root
% 0.19/0.45  thf(fact_203_jump__poly0_I2_J,axiom,
% 0.19/0.45      ! [Q2: poly @ real,X2: real] :
% 0.19/0.45        ( ( sturm_652470720p_poly @ Q2 @ ( zero_zero @ ( poly @ real ) ) @ X2 )
% 0.19/0.45        = ( zero_zero @ int ) ) ).
% 0.19/0.45  
% 0.19/0.45  % jump_poly0(2)
% 0.19/0.45  thf(fact_204_predicate1I,axiom,
% 0.19/0.45      ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.19/0.45        ( ! [X4: A] :
% 0.19/0.45            ( ( P @ X4 )
% 0.19/0.45           => ( Q @ X4 ) )
% 0.19/0.45       => ( ord_less_eq @ ( A > $o ) @ P @ Q ) ) ).
% 0.19/0.45  
% 0.19/0.45  % predicate1I
% 0.19/0.45  thf(fact_205_reflect__poly__0,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( zero @ A )
% 0.19/0.45       => ( ( reflect_poly @ A @ ( zero_zero @ ( poly @ A ) ) )
% 0.19/0.45          = ( zero_zero @ ( poly @ A ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % reflect_poly_0
% 0.19/0.45  thf(fact_206_jump__poly0_I1_J,axiom,
% 0.19/0.45      ! [P2: poly @ real,X2: real] :
% 0.19/0.45        ( ( sturm_652470720p_poly @ ( zero_zero @ ( poly @ real ) ) @ P2 @ X2 )
% 0.19/0.45        = ( zero_zero @ int ) ) ).
% 0.19/0.45  
% 0.19/0.45  % jump_poly0(1)
% 0.19/0.45  thf(fact_207_verit__la__generic,axiom,
% 0.19/0.45      ! [A2: int,X2: int] :
% 0.19/0.45        ( ( ord_less_eq @ int @ A2 @ X2 )
% 0.19/0.45        | ( A2 = X2 )
% 0.19/0.45        | ( ord_less_eq @ int @ X2 @ A2 ) ) ).
% 0.19/0.45  
% 0.19/0.45  % verit_la_generic
% 0.19/0.45  thf(fact_208_predicate1D,axiom,
% 0.19/0.45      ! [A: $tType,P: A > $o,Q: A > $o,X2: A] :
% 0.19/0.45        ( ( ord_less_eq @ ( A > $o ) @ P @ Q )
% 0.19/0.45       => ( ( P @ X2 )
% 0.19/0.45         => ( Q @ X2 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % predicate1D
% 0.19/0.45  thf(fact_209_rev__predicate1D,axiom,
% 0.19/0.45      ! [A: $tType,P: A > $o,X2: A,Q: A > $o] :
% 0.19/0.45        ( ( P @ X2 )
% 0.19/0.45       => ( ( ord_less_eq @ ( A > $o ) @ P @ Q )
% 0.19/0.45         => ( Q @ X2 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % rev_predicate1D
% 0.19/0.45  thf(fact_210_finite__interval__int1,axiom,
% 0.19/0.45      ! [A2: int,B2: int] :
% 0.19/0.45        ( finite_finite2 @ int
% 0.19/0.45        @ ( collect @ int
% 0.19/0.45          @ ^ [I: int] :
% 0.19/0.45              ( ( ord_less_eq @ int @ A2 @ I )
% 0.19/0.45              & ( ord_less_eq @ int @ I @ B2 ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % finite_interval_int1
% 0.19/0.45  thf(fact_211_finite__interval__int2,axiom,
% 0.19/0.45      ! [A2: int,B2: int] :
% 0.19/0.45        ( finite_finite2 @ int
% 0.19/0.45        @ ( collect @ int
% 0.19/0.45          @ ^ [I: int] :
% 0.19/0.45              ( ( ord_less_eq @ int @ A2 @ I )
% 0.19/0.45              & ( ord_less @ int @ I @ B2 ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % finite_interval_int2
% 0.19/0.45  thf(fact_212_finite__interval__int4,axiom,
% 0.19/0.45      ! [A2: int,B2: int] :
% 0.19/0.45        ( finite_finite2 @ int
% 0.19/0.45        @ ( collect @ int
% 0.19/0.45          @ ^ [I: int] :
% 0.19/0.45              ( ( ord_less @ int @ A2 @ I )
% 0.19/0.45              & ( ord_less @ int @ I @ B2 ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % finite_interval_int4
% 0.19/0.45  thf(fact_213_finite__interval__int3,axiom,
% 0.19/0.45      ! [A2: int,B2: int] :
% 0.19/0.45        ( finite_finite2 @ int
% 0.19/0.45        @ ( collect @ int
% 0.19/0.45          @ ^ [I: int] :
% 0.19/0.45              ( ( ord_less @ int @ A2 @ I )
% 0.19/0.45              & ( ord_less_eq @ int @ I @ B2 ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % finite_interval_int3
% 0.19/0.45  thf(fact_214_less__int__code_I1_J,axiom,
% 0.19/0.45      ~ ( ord_less @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ) ) ).
% 0.19/0.45  
% 0.19/0.45  % less_int_code(1)
% 0.19/0.45  thf(fact_215_less__eq__int__code_I1_J,axiom,
% 0.19/0.45      ord_less_eq @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ) ).
% 0.19/0.45  
% 0.19/0.45  % less_eq_int_code(1)
% 0.19/0.45  thf(fact_216_pred__subset__eq,axiom,
% 0.19/0.45      ! [A: $tType,R: set @ A,S: set @ A] :
% 0.19/0.45        ( ( ord_less_eq @ ( A > $o )
% 0.19/0.45          @ ^ [X: A] : ( member @ A @ X @ R )
% 0.19/0.45          @ ^ [X: A] : ( member @ A @ X @ S ) )
% 0.19/0.45        = ( ord_less_eq @ ( set @ A ) @ R @ S ) ) ).
% 0.19/0.45  
% 0.19/0.45  % pred_subset_eq
% 0.19/0.45  thf(fact_217_cindex__poly__0_I2_J,axiom,
% 0.19/0.45      ! [A2: real,B2: real,Q2: poly @ real] :
% 0.19/0.45        ( ( sturm_1539314049x_poly @ A2 @ B2 @ Q2 @ ( zero_zero @ ( poly @ real ) ) )
% 0.19/0.45        = ( zero_zero @ int ) ) ).
% 0.19/0.45  
% 0.19/0.45  % cindex_poly_0(2)
% 0.19/0.45  thf(fact_218_cindex__poly__0_I1_J,axiom,
% 0.19/0.45      ! [A2: real,B2: real,P2: poly @ real] :
% 0.19/0.45        ( ( sturm_1539314049x_poly @ A2 @ B2 @ ( zero_zero @ ( poly @ real ) ) @ P2 )
% 0.19/0.45        = ( zero_zero @ int ) ) ).
% 0.19/0.45  
% 0.19/0.45  % cindex_poly_0(1)
% 0.19/0.45  thf(fact_219_cindex__poly__cross,axiom,
% 0.19/0.45      ! [A2: real,B2: real,P2: poly @ real] :
% 0.19/0.45        ( ( ord_less @ real @ A2 @ B2 )
% 0.19/0.45       => ( ( ( poly2 @ real @ P2 @ A2 )
% 0.19/0.45           != ( zero_zero @ real ) )
% 0.19/0.45         => ( ( ( poly2 @ real @ P2 @ B2 )
% 0.19/0.45             != ( zero_zero @ real ) )
% 0.19/0.45           => ( ( sturm_1539314049x_poly @ A2 @ B2 @ ( one_one @ ( poly @ real ) ) @ P2 )
% 0.19/0.45              = ( sturm_424270202_cross @ P2 @ A2 @ B2 ) ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % cindex_poly_cross
% 0.19/0.45  thf(fact_220_cindex__poly__def,axiom,
% 0.19/0.45      ( sturm_1539314049x_poly
% 0.19/0.45      = ( ^ [A6: real,B5: real,Q4: poly @ real,P5: poly @ real] :
% 0.19/0.45            ( groups1340683514dd_sum @ real @ int @ ( sturm_652470720p_poly @ Q4 @ P5 )
% 0.19/0.45            @ ( collect @ real
% 0.19/0.45              @ ^ [X: real] :
% 0.19/0.45                  ( ( ( poly2 @ real @ P5 @ X )
% 0.19/0.45                    = ( zero_zero @ real ) )
% 0.19/0.45                  & ( ord_less @ real @ A6 @ X )
% 0.19/0.45                  & ( ord_less @ real @ X @ B5 ) ) ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % cindex_poly_def
% 0.19/0.45  thf(fact_221_reflect__poly__1,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( comm_semiring_1 @ A )
% 0.19/0.45       => ( ( reflect_poly @ A @ ( one_one @ ( poly @ A ) ) )
% 0.19/0.45          = ( one_one @ ( poly @ A ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % reflect_poly_1
% 0.19/0.45  thf(fact_222_poly__1,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( comm_semiring_1 @ A )
% 0.19/0.45       => ! [X2: A] :
% 0.19/0.45            ( ( poly2 @ A @ ( one_one @ ( poly @ A ) ) @ X2 )
% 0.19/0.45            = ( one_one @ A ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % poly_1
% 0.19/0.45  thf(fact_223_poly__cutoff__1,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( comm_semiring_1 @ A )
% 0.19/0.45       => ! [N: nat] :
% 0.19/0.45            ( ( ( N
% 0.19/0.45                = ( zero_zero @ nat ) )
% 0.19/0.45             => ( ( poly_cutoff @ A @ N @ ( one_one @ ( poly @ A ) ) )
% 0.19/0.45                = ( zero_zero @ ( poly @ A ) ) ) )
% 0.19/0.45            & ( ( N
% 0.19/0.45               != ( zero_zero @ nat ) )
% 0.19/0.45             => ( ( poly_cutoff @ A @ N @ ( one_one @ ( poly @ A ) ) )
% 0.19/0.45                = ( one_one @ ( poly @ A ) ) ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % poly_cutoff_1
% 0.19/0.45  thf(fact_224_le__numeral__extra_I4_J,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( linord1659791738miring @ A )
% 0.19/0.45       => ( ord_less_eq @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % le_numeral_extra(4)
% 0.19/0.45  thf(fact_225_poly__sum,axiom,
% 0.19/0.45      ! [A: $tType,B: $tType] :
% 0.19/0.45        ( ( comm_semiring_0 @ A )
% 0.19/0.45       => ! [P2: B > ( poly @ A ),A4: set @ B,X2: A] :
% 0.19/0.45            ( ( poly2 @ A @ ( groups1340683514dd_sum @ B @ ( poly @ A ) @ P2 @ A4 ) @ X2 )
% 0.19/0.45            = ( groups1340683514dd_sum @ B @ A
% 0.19/0.45              @ ^ [K: B] : ( poly2 @ A @ ( P2 @ K ) @ X2 )
% 0.19/0.45              @ A4 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % poly_sum
% 0.19/0.45  thf(fact_226_one__reorient,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( one @ A )
% 0.19/0.45       => ! [X2: A] :
% 0.19/0.45            ( ( ( one_one @ A )
% 0.19/0.45              = X2 )
% 0.19/0.45            = ( X2
% 0.19/0.45              = ( one_one @ A ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % one_reorient
% 0.19/0.45  thf(fact_227_less__numeral__extra_I1_J,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( linord1659791738miring @ A )
% 0.19/0.45       => ( ord_less @ A @ ( zero_zero @ A ) @ ( one_one @ A ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % less_numeral_extra(1)
% 0.19/0.45  thf(fact_228_less__numeral__extra_I4_J,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( linord1659791738miring @ A )
% 0.19/0.45       => ~ ( ord_less @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % less_numeral_extra(4)
% 0.19/0.45  thf(fact_229_sum_Odelta_H,axiom,
% 0.19/0.45      ! [B: $tType,A: $tType] :
% 0.19/0.45        ( ( comm_monoid_add @ A )
% 0.19/0.45       => ! [S: set @ B,A2: B,B2: B > A] :
% 0.19/0.45            ( ( finite_finite2 @ B @ S )
% 0.19/0.45           => ( ( ( member @ B @ A2 @ S )
% 0.19/0.45               => ( ( groups1340683514dd_sum @ B @ A
% 0.19/0.45                    @ ^ [K: B] : ( if @ A @ ( A2 = K ) @ ( B2 @ K ) @ ( zero_zero @ A ) )
% 0.19/0.45                    @ S )
% 0.19/0.45                  = ( B2 @ A2 ) ) )
% 0.19/0.45              & ( ~ ( member @ B @ A2 @ S )
% 0.19/0.45               => ( ( groups1340683514dd_sum @ B @ A
% 0.19/0.45                    @ ^ [K: B] : ( if @ A @ ( A2 = K ) @ ( B2 @ K ) @ ( zero_zero @ A ) )
% 0.19/0.45                    @ S )
% 0.19/0.45                  = ( zero_zero @ A ) ) ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % sum.delta'
% 0.19/0.45  thf(fact_230_sum_Odelta,axiom,
% 0.19/0.45      ! [B: $tType,A: $tType] :
% 0.19/0.45        ( ( comm_monoid_add @ A )
% 0.19/0.45       => ! [S: set @ B,A2: B,B2: B > A] :
% 0.19/0.45            ( ( finite_finite2 @ B @ S )
% 0.19/0.45           => ( ( ( member @ B @ A2 @ S )
% 0.19/0.45               => ( ( groups1340683514dd_sum @ B @ A
% 0.19/0.45                    @ ^ [K: B] : ( if @ A @ ( K = A2 ) @ ( B2 @ K ) @ ( zero_zero @ A ) )
% 0.19/0.45                    @ S )
% 0.19/0.45                  = ( B2 @ A2 ) ) )
% 0.19/0.45              & ( ~ ( member @ B @ A2 @ S )
% 0.19/0.45               => ( ( groups1340683514dd_sum @ B @ A
% 0.19/0.45                    @ ^ [K: B] : ( if @ A @ ( K = A2 ) @ ( B2 @ K ) @ ( zero_zero @ A ) )
% 0.19/0.45                    @ S )
% 0.19/0.45                  = ( zero_zero @ A ) ) ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % sum.delta
% 0.19/0.45  thf(fact_231_sum_Oneutral__const,axiom,
% 0.19/0.45      ! [B: $tType,A: $tType] :
% 0.19/0.45        ( ( comm_monoid_add @ A )
% 0.19/0.45       => ! [A4: set @ B] :
% 0.19/0.45            ( ( groups1340683514dd_sum @ B @ A
% 0.19/0.45              @ ^ [Uu: B] : ( zero_zero @ A )
% 0.19/0.45              @ A4 )
% 0.19/0.45            = ( zero_zero @ A ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % sum.neutral_const
% 0.19/0.45  thf(fact_232_sum_Oinfinite,axiom,
% 0.19/0.45      ! [B: $tType,A: $tType] :
% 0.19/0.45        ( ( comm_monoid_add @ A )
% 0.19/0.45       => ! [A4: set @ B,G: B > A] :
% 0.19/0.45            ( ~ ( finite_finite2 @ B @ A4 )
% 0.19/0.45           => ( ( groups1340683514dd_sum @ B @ A @ G @ A4 )
% 0.19/0.45              = ( zero_zero @ A ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % sum.infinite
% 0.19/0.45  thf(fact_233_sum__eq__0__iff,axiom,
% 0.19/0.45      ! [A: $tType,B: $tType] :
% 0.19/0.45        ( ( canoni770627133id_add @ A )
% 0.19/0.45       => ! [F4: set @ B,F2: B > A] :
% 0.19/0.45            ( ( finite_finite2 @ B @ F4 )
% 0.19/0.45           => ( ( ( groups1340683514dd_sum @ B @ A @ F2 @ F4 )
% 0.19/0.45                = ( zero_zero @ A ) )
% 0.19/0.45              = ( ! [X: B] :
% 0.19/0.45                    ( ( member @ B @ X @ F4 )
% 0.19/0.45                   => ( ( F2 @ X )
% 0.19/0.45                      = ( zero_zero @ A ) ) ) ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % sum_eq_0_iff
% 0.19/0.45  thf(fact_234_sum__eq__1__iff,axiom,
% 0.19/0.45      ! [A: $tType,A4: set @ A,F2: A > nat] :
% 0.19/0.45        ( ( finite_finite2 @ A @ A4 )
% 0.19/0.45       => ( ( ( groups1340683514dd_sum @ A @ nat @ F2 @ A4 )
% 0.19/0.45            = ( one_one @ nat ) )
% 0.19/0.45          = ( ? [X: A] :
% 0.19/0.45                ( ( member @ A @ X @ A4 )
% 0.19/0.45                & ( ( F2 @ X )
% 0.19/0.45                  = ( one_one @ nat ) )
% 0.19/0.45                & ! [Y: A] :
% 0.19/0.45                    ( ( member @ A @ Y @ A4 )
% 0.19/0.45                   => ( ( X != Y )
% 0.19/0.45                     => ( ( F2 @ Y )
% 0.19/0.45                        = ( zero_zero @ nat ) ) ) ) ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % sum_eq_1_iff
% 0.19/0.45  thf(fact_235_int__one__le__iff__zero__less,axiom,
% 0.19/0.45      ! [Z3: int] :
% 0.19/0.45        ( ( ord_less_eq @ int @ ( one_one @ int ) @ Z3 )
% 0.19/0.45        = ( ord_less @ int @ ( zero_zero @ int ) @ Z3 ) ) ).
% 0.19/0.45  
% 0.19/0.45  % int_one_le_iff_zero_less
% 0.19/0.45  thf(fact_236_sum_Oswap,axiom,
% 0.19/0.45      ! [A: $tType,B: $tType,C3: $tType] :
% 0.19/0.45        ( ( comm_monoid_add @ A )
% 0.19/0.45       => ! [G: B > C3 > A,B4: set @ C3,A4: set @ B] :
% 0.19/0.45            ( ( groups1340683514dd_sum @ B @ A
% 0.19/0.45              @ ^ [I: B] : ( groups1340683514dd_sum @ C3 @ A @ ( G @ I ) @ B4 )
% 0.19/0.45              @ A4 )
% 0.19/0.45            = ( groups1340683514dd_sum @ C3 @ A
% 0.19/0.45              @ ^ [J: C3] :
% 0.19/0.45                  ( groups1340683514dd_sum @ B @ A
% 0.19/0.45                  @ ^ [I: B] : ( G @ I @ J )
% 0.19/0.45                  @ A4 )
% 0.19/0.45              @ B4 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % sum.swap
% 0.19/0.45  thf(fact_237_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.19/0.45      ! [B: $tType,A: $tType] :
% 0.19/0.45        ( ( comm_monoid_add @ A )
% 0.19/0.45       => ! [G: B > A,A4: set @ B] :
% 0.19/0.45            ( ( ( groups1340683514dd_sum @ B @ A @ G @ A4 )
% 0.19/0.45             != ( zero_zero @ A ) )
% 0.19/0.45           => ~ ! [A7: B] :
% 0.19/0.45                  ( ( member @ B @ A7 @ A4 )
% 0.19/0.45                 => ( ( G @ A7 )
% 0.19/0.45                    = ( zero_zero @ A ) ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % sum.not_neutral_contains_not_neutral
% 0.19/0.45  thf(fact_238_sum_Oneutral,axiom,
% 0.19/0.45      ! [B: $tType,A: $tType] :
% 0.19/0.45        ( ( comm_monoid_add @ A )
% 0.19/0.45       => ! [A4: set @ B,G: B > A] :
% 0.19/0.45            ( ! [X4: B] :
% 0.19/0.45                ( ( member @ B @ X4 @ A4 )
% 0.19/0.45               => ( ( G @ X4 )
% 0.19/0.45                  = ( zero_zero @ A ) ) )
% 0.19/0.45           => ( ( groups1340683514dd_sum @ B @ A @ G @ A4 )
% 0.19/0.45              = ( zero_zero @ A ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % sum.neutral
% 0.19/0.45  thf(fact_239_sum__mono,axiom,
% 0.19/0.45      ! [A: $tType,B: $tType] :
% 0.19/0.45        ( ( ordere216010020id_add @ A )
% 0.19/0.45       => ! [K2: set @ B,F2: B > A,G: B > A] :
% 0.19/0.45            ( ! [I2: B] :
% 0.19/0.45                ( ( member @ B @ I2 @ K2 )
% 0.19/0.45               => ( ord_less_eq @ A @ ( F2 @ I2 ) @ ( G @ I2 ) ) )
% 0.19/0.45           => ( ord_less_eq @ A @ ( groups1340683514dd_sum @ B @ A @ F2 @ K2 ) @ ( groups1340683514dd_sum @ B @ A @ G @ K2 ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % sum_mono
% 0.19/0.45  thf(fact_240_sum_Oswap__restrict,axiom,
% 0.19/0.45      ! [A: $tType,B: $tType,C3: $tType] :
% 0.19/0.45        ( ( comm_monoid_add @ A )
% 0.19/0.45       => ! [A4: set @ B,B4: set @ C3,G: B > C3 > A,R: B > C3 > $o] :
% 0.19/0.45            ( ( finite_finite2 @ B @ A4 )
% 0.19/0.45           => ( ( finite_finite2 @ C3 @ B4 )
% 0.19/0.45             => ( ( groups1340683514dd_sum @ B @ A
% 0.19/0.45                  @ ^ [X: B] :
% 0.19/0.45                      ( groups1340683514dd_sum @ C3 @ A @ ( G @ X )
% 0.19/0.45                      @ ( collect @ C3
% 0.19/0.45                        @ ^ [Y: C3] :
% 0.19/0.45                            ( ( member @ C3 @ Y @ B4 )
% 0.19/0.45                            & ( R @ X @ Y ) ) ) )
% 0.19/0.45                  @ A4 )
% 0.19/0.45                = ( groups1340683514dd_sum @ C3 @ A
% 0.19/0.45                  @ ^ [Y: C3] :
% 0.19/0.45                      ( groups1340683514dd_sum @ B @ A
% 0.19/0.45                      @ ^ [X: B] : ( G @ X @ Y )
% 0.19/0.45                      @ ( collect @ B
% 0.19/0.45                        @ ^ [X: B] :
% 0.19/0.45                            ( ( member @ B @ X @ A4 )
% 0.19/0.45                            & ( R @ X @ Y ) ) ) )
% 0.19/0.45                  @ B4 ) ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % sum.swap_restrict
% 0.19/0.45  thf(fact_241_sum__nonpos,axiom,
% 0.19/0.45      ! [B: $tType,A: $tType] :
% 0.19/0.45        ( ( ordere216010020id_add @ A )
% 0.19/0.45       => ! [A4: set @ B,F2: B > A] :
% 0.19/0.45            ( ! [X4: B] :
% 0.19/0.45                ( ( member @ B @ X4 @ A4 )
% 0.19/0.45               => ( ord_less_eq @ A @ ( F2 @ X4 ) @ ( zero_zero @ A ) ) )
% 0.19/0.45           => ( ord_less_eq @ A @ ( groups1340683514dd_sum @ B @ A @ F2 @ A4 ) @ ( zero_zero @ A ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % sum_nonpos
% 0.19/0.45  thf(fact_242_sum__nonneg,axiom,
% 0.19/0.45      ! [A: $tType,B: $tType] :
% 0.19/0.45        ( ( ordere216010020id_add @ A )
% 0.19/0.45       => ! [A4: set @ B,F2: B > A] :
% 0.19/0.45            ( ! [X4: B] :
% 0.19/0.45                ( ( member @ B @ X4 @ A4 )
% 0.19/0.45               => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( F2 @ X4 ) ) )
% 0.19/0.45           => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( groups1340683514dd_sum @ B @ A @ F2 @ A4 ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % sum_nonneg
% 0.19/0.45  thf(fact_243_sum__mono__inv,axiom,
% 0.19/0.45      ! [A: $tType,I3: $tType] :
% 0.19/0.45        ( ( ordere1818651114id_add @ A )
% 0.19/0.45       => ! [F2: I3 > A,I4: set @ I3,G: I3 > A,I5: I3] :
% 0.19/0.45            ( ( ( groups1340683514dd_sum @ I3 @ A @ F2 @ I4 )
% 0.19/0.45              = ( groups1340683514dd_sum @ I3 @ A @ G @ I4 ) )
% 0.19/0.45           => ( ! [I2: I3] :
% 0.19/0.45                  ( ( member @ I3 @ I2 @ I4 )
% 0.19/0.45                 => ( ord_less_eq @ A @ ( F2 @ I2 ) @ ( G @ I2 ) ) )
% 0.19/0.45             => ( ( member @ I3 @ I5 @ I4 )
% 0.19/0.45               => ( ( finite_finite2 @ I3 @ I4 )
% 0.19/0.45                 => ( ( F2 @ I5 )
% 0.19/0.45                    = ( G @ I5 ) ) ) ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % sum_mono_inv
% 0.19/0.45  thf(fact_244_sum_Ointer__filter,axiom,
% 0.19/0.45      ! [A: $tType,B: $tType] :
% 0.19/0.45        ( ( comm_monoid_add @ A )
% 0.19/0.45       => ! [A4: set @ B,G: B > A,P: B > $o] :
% 0.19/0.45            ( ( finite_finite2 @ B @ A4 )
% 0.19/0.45           => ( ( groups1340683514dd_sum @ B @ A @ G
% 0.19/0.45                @ ( collect @ B
% 0.19/0.45                  @ ^ [X: B] :
% 0.19/0.45                      ( ( member @ B @ X @ A4 )
% 0.19/0.45                      & ( P @ X ) ) ) )
% 0.19/0.45              = ( groups1340683514dd_sum @ B @ A
% 0.19/0.45                @ ^ [X: B] : ( if @ A @ ( P @ X ) @ ( G @ X ) @ ( zero_zero @ A ) )
% 0.19/0.45                @ A4 ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % sum.inter_filter
% 0.19/0.45  thf(fact_245_sum__le__included,axiom,
% 0.19/0.45      ! [B: $tType,A: $tType,C3: $tType] :
% 0.19/0.45        ( ( ordere216010020id_add @ A )
% 0.19/0.45       => ! [S2: set @ B,T2: set @ C3,G: C3 > A,I5: C3 > B,F2: B > A] :
% 0.19/0.45            ( ( finite_finite2 @ B @ S2 )
% 0.19/0.45           => ( ( finite_finite2 @ C3 @ T2 )
% 0.19/0.45             => ( ! [X4: C3] :
% 0.19/0.45                    ( ( member @ C3 @ X4 @ T2 )
% 0.19/0.45                   => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( G @ X4 ) ) )
% 0.19/0.45               => ( ! [X4: B] :
% 0.19/0.45                      ( ( member @ B @ X4 @ S2 )
% 0.19/0.45                     => ? [Xa: C3] :
% 0.19/0.45                          ( ( member @ C3 @ Xa @ T2 )
% 0.19/0.45                          & ( ( I5 @ Xa )
% 0.19/0.45                            = X4 )
% 0.19/0.45                          & ( ord_less_eq @ A @ ( F2 @ X4 ) @ ( G @ Xa ) ) ) )
% 0.19/0.45                 => ( ord_less_eq @ A @ ( groups1340683514dd_sum @ B @ A @ F2 @ S2 ) @ ( groups1340683514dd_sum @ C3 @ A @ G @ T2 ) ) ) ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % sum_le_included
% 0.19/0.45  thf(fact_246_sum__nonneg__eq__0__iff,axiom,
% 0.19/0.45      ! [A: $tType,B: $tType] :
% 0.19/0.45        ( ( ordere216010020id_add @ A )
% 0.19/0.45       => ! [A4: set @ B,F2: B > A] :
% 0.19/0.45            ( ( finite_finite2 @ B @ A4 )
% 0.19/0.45           => ( ! [X4: B] :
% 0.19/0.45                  ( ( member @ B @ X4 @ A4 )
% 0.19/0.45                 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( F2 @ X4 ) ) )
% 0.19/0.45             => ( ( ( groups1340683514dd_sum @ B @ A @ F2 @ A4 )
% 0.19/0.45                  = ( zero_zero @ A ) )
% 0.19/0.45                = ( ! [X: B] :
% 0.19/0.45                      ( ( member @ B @ X @ A4 )
% 0.19/0.45                     => ( ( F2 @ X )
% 0.19/0.45                        = ( zero_zero @ A ) ) ) ) ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % sum_nonneg_eq_0_iff
% 0.19/0.45  thf(fact_247_sum__strict__mono__ex1,axiom,
% 0.19/0.45      ! [A: $tType,I3: $tType] :
% 0.19/0.45        ( ( ordere1818651114id_add @ A )
% 0.19/0.45       => ! [A4: set @ I3,F2: I3 > A,G: I3 > A] :
% 0.19/0.45            ( ( finite_finite2 @ I3 @ A4 )
% 0.19/0.45           => ( ! [X4: I3] :
% 0.19/0.45                  ( ( member @ I3 @ X4 @ A4 )
% 0.19/0.45                 => ( ord_less_eq @ A @ ( F2 @ X4 ) @ ( G @ X4 ) ) )
% 0.19/0.45             => ( ? [X3: I3] :
% 0.19/0.45                    ( ( member @ I3 @ X3 @ A4 )
% 0.19/0.45                    & ( ord_less @ A @ ( F2 @ X3 ) @ ( G @ X3 ) ) )
% 0.19/0.45               => ( ord_less @ A @ ( groups1340683514dd_sum @ I3 @ A @ F2 @ A4 ) @ ( groups1340683514dd_sum @ I3 @ A @ G @ A4 ) ) ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % sum_strict_mono_ex1
% 0.19/0.45  thf(fact_248_sum__nonneg__0,axiom,
% 0.19/0.45      ! [B: $tType,A: $tType] :
% 0.19/0.45        ( ( ordere216010020id_add @ A )
% 0.19/0.45       => ! [S2: set @ B,F2: B > A,I5: B] :
% 0.19/0.45            ( ( finite_finite2 @ B @ S2 )
% 0.19/0.45           => ( ! [I2: B] :
% 0.19/0.45                  ( ( member @ B @ I2 @ S2 )
% 0.19/0.45                 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( F2 @ I2 ) ) )
% 0.19/0.45             => ( ( ( groups1340683514dd_sum @ B @ A @ F2 @ S2 )
% 0.19/0.45                  = ( zero_zero @ A ) )
% 0.19/0.45               => ( ( member @ B @ I5 @ S2 )
% 0.19/0.45                 => ( ( F2 @ I5 )
% 0.19/0.45                    = ( zero_zero @ A ) ) ) ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % sum_nonneg_0
% 0.19/0.45  thf(fact_249_sum__nonneg__leq__bound,axiom,
% 0.19/0.45      ! [B: $tType,A: $tType] :
% 0.19/0.45        ( ( ordere216010020id_add @ A )
% 0.19/0.45       => ! [S2: set @ B,F2: B > A,B4: A,I5: B] :
% 0.19/0.45            ( ( finite_finite2 @ B @ S2 )
% 0.19/0.45           => ( ! [I2: B] :
% 0.19/0.45                  ( ( member @ B @ I2 @ S2 )
% 0.19/0.45                 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( F2 @ I2 ) ) )
% 0.19/0.45             => ( ( ( groups1340683514dd_sum @ B @ A @ F2 @ S2 )
% 0.19/0.45                  = B4 )
% 0.19/0.45               => ( ( member @ B @ I5 @ S2 )
% 0.19/0.45                 => ( ord_less_eq @ A @ ( F2 @ I5 ) @ B4 ) ) ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % sum_nonneg_leq_bound
% 0.19/0.45  thf(fact_250_sum__pos2,axiom,
% 0.19/0.45      ! [A: $tType,B: $tType] :
% 0.19/0.45        ( ( ordere216010020id_add @ A )
% 0.19/0.45       => ! [I4: set @ B,I5: B,F2: B > A] :
% 0.19/0.45            ( ( finite_finite2 @ B @ I4 )
% 0.19/0.45           => ( ( member @ B @ I5 @ I4 )
% 0.19/0.45             => ( ( ord_less @ A @ ( zero_zero @ A ) @ ( F2 @ I5 ) )
% 0.19/0.45               => ( ! [I2: B] :
% 0.19/0.45                      ( ( member @ B @ I2 @ I4 )
% 0.19/0.45                     => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( F2 @ I2 ) ) )
% 0.19/0.45                 => ( ord_less @ A @ ( zero_zero @ A ) @ ( groups1340683514dd_sum @ B @ A @ F2 @ I4 ) ) ) ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % sum_pos2
% 0.19/0.45  thf(fact_251_not__one__less__zero,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( linord1659791738miring @ A )
% 0.19/0.45       => ~ ( ord_less @ A @ ( one_one @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % not_one_less_zero
% 0.19/0.45  thf(fact_252_zero__less__one,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( zero_less_one @ A )
% 0.19/0.45       => ( ord_less @ A @ ( zero_zero @ A ) @ ( one_one @ A ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % zero_less_one
% 0.19/0.45  thf(fact_253_linorder__neqE__linordered__idom,axiom,
% 0.19/0.45      ! [A: $tType] :
% 0.19/0.45        ( ( linordered_idom @ A )
% 0.19/0.45       => ! [X2: A,Y2: A] :
% 0.19/0.45            ( ( X2 != Y2 )
% 0.19/0.45           => ( ~ ( ord_less @ A @ X2 @ Y2 )
% 0.19/0.45             => ( ord_less @ A @ Y2 @ X2 ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % linorder_neqE_linordered_idom
% 0.19/0.45  
% 0.19/0.45  % Type constructors (94)
% 0.19/0.45  thf(tcon_Polynomial_Opoly___Rings_Oidom,axiom,
% 0.19/0.45      ! [A9: $tType] :
% 0.19/0.45        ( ( idom @ A9 )
% 0.19/0.45       => ( idom @ ( poly @ A9 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Real_Oreal___Rings_Oidom_1,axiom,
% 0.19/0.45      idom @ real ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Int_Oint___Rings_Oidom_2,axiom,
% 0.19/0.45      idom @ int ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.19/0.45      ! [A9: $tType,A10: $tType] :
% 0.19/0.45        ( ( preorder @ A10 )
% 0.19/0.45       => ( preorder @ ( A9 > A10 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_fun___Finite__Set_Ofinite,axiom,
% 0.19/0.45      ! [A9: $tType,A10: $tType] :
% 0.19/0.45        ( ( ( finite_finite @ A9 )
% 0.19/0.45          & ( finite_finite @ A10 ) )
% 0.19/0.45       => ( finite_finite @ ( A9 > A10 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_fun___Orderings_Oorder,axiom,
% 0.19/0.45      ! [A9: $tType,A10: $tType] :
% 0.19/0.45        ( ( order @ A10 )
% 0.19/0.45       => ( order @ ( A9 > A10 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_fun___Orderings_Oord,axiom,
% 0.19/0.45      ! [A9: $tType,A10: $tType] :
% 0.19/0.45        ( ( ord @ A10 )
% 0.19/0.45       => ( ord @ ( A9 > A10 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Int_Oint___Conditionally__Complete__Lattices_Oconditionally__complete__linorder,axiom,
% 0.19/0.45      condit1037483654norder @ int ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Int_Oint___Groups_Oordered__cancel__comm__monoid__add,axiom,
% 0.19/0.45      ordere1818651114id_add @ int ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Int_Oint___Rings_Olinordered__nonzero__semiring,axiom,
% 0.19/0.45      linord1659791738miring @ int ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Int_Oint___Groups_Oordered__comm__monoid__add,axiom,
% 0.19/0.45      ordere216010020id_add @ int ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Int_Oint___Rings_Oring__no__zero__divisors,axiom,
% 0.19/0.45      ring_n68954251visors @ int ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Int_Oint___Groups_Ocomm__monoid__add,axiom,
% 0.19/0.45      comm_monoid_add @ int ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Int_Oint___Rings_Olinordered__idom,axiom,
% 0.19/0.45      linordered_idom @ int ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Int_Oint___Rings_Ocomm__semiring__1,axiom,
% 0.19/0.45      comm_semiring_1 @ int ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Int_Oint___Rings_Ocomm__semiring__0,axiom,
% 0.19/0.45      comm_semiring_0 @ int ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Int_Oint___Rings_Ozero__less__one,axiom,
% 0.19/0.45      zero_less_one @ int ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Int_Oint___Orderings_Opreorder_3,axiom,
% 0.19/0.45      preorder @ int ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Int_Oint___Orderings_Olinorder,axiom,
% 0.19/0.45      linorder @ int ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Int_Oint___Rings_Ocomm__ring__1,axiom,
% 0.19/0.45      comm_ring_1 @ int ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Int_Oint___Orderings_Ono__top,axiom,
% 0.19/0.45      no_top @ int ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Int_Oint___Orderings_Ono__bot,axiom,
% 0.19/0.45      no_bot @ int ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Int_Oint___Orderings_Oorder_4,axiom,
% 0.19/0.45      order @ int ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Int_Oint___Nat_Oring__char__0,axiom,
% 0.19/0.45      ring_char_0 @ int ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Int_Oint___Orderings_Oord_5,axiom,
% 0.19/0.45      ord @ int ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Int_Oint___Groups_Ozero,axiom,
% 0.19/0.45      zero @ int ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Int_Oint___Groups_Oone,axiom,
% 0.19/0.45      one @ int ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Nat_Onat___Conditionally__Complete__Lattices_Oconditionally__complete__linorder_6,axiom,
% 0.19/0.45      condit1037483654norder @ nat ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Nat_Onat___Groups_Oordered__cancel__comm__monoid__add_7,axiom,
% 0.19/0.45      ordere1818651114id_add @ nat ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 0.19/0.45      canoni770627133id_add @ nat ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring_8,axiom,
% 0.19/0.45      linord1659791738miring @ nat ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Nat_Onat___Groups_Oordered__comm__monoid__add_9,axiom,
% 0.19/0.45      ordere216010020id_add @ nat ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Nat_Onat___Groups_Ocomm__monoid__add_10,axiom,
% 0.19/0.45      comm_monoid_add @ nat ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Nat_Onat___Rings_Ocomm__semiring__1_11,axiom,
% 0.19/0.45      comm_semiring_1 @ nat ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Nat_Onat___Rings_Ocomm__semiring__0_12,axiom,
% 0.19/0.45      comm_semiring_0 @ nat ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Nat_Onat___Rings_Ozero__less__one_13,axiom,
% 0.19/0.45      zero_less_one @ nat ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 0.19/0.45      wellorder @ nat ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Nat_Onat___Orderings_Opreorder_14,axiom,
% 0.19/0.45      preorder @ nat ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Nat_Onat___Orderings_Olinorder_15,axiom,
% 0.19/0.45      linorder @ nat ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Nat_Onat___Orderings_Ono__top_16,axiom,
% 0.19/0.45      no_top @ nat ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Nat_Onat___Orderings_Oorder_17,axiom,
% 0.19/0.45      order @ nat ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Nat_Onat___Orderings_Oord_18,axiom,
% 0.19/0.45      ord @ nat ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Nat_Onat___Groups_Ozero_19,axiom,
% 0.19/0.45      zero @ nat ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Nat_Onat___Groups_Oone_20,axiom,
% 0.19/0.45      one @ nat ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Set_Oset___Orderings_Opreorder_21,axiom,
% 0.19/0.45      ! [A9: $tType] : ( preorder @ ( set @ A9 ) ) ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Set_Oset___Finite__Set_Ofinite_22,axiom,
% 0.19/0.45      ! [A9: $tType] :
% 0.19/0.45        ( ( finite_finite @ A9 )
% 0.19/0.45       => ( finite_finite @ ( set @ A9 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Set_Oset___Orderings_Oorder_23,axiom,
% 0.19/0.45      ! [A9: $tType] : ( order @ ( set @ A9 ) ) ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Set_Oset___Orderings_Oord_24,axiom,
% 0.19/0.45      ! [A9: $tType] : ( ord @ ( set @ A9 ) ) ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_HOL_Obool___Orderings_Opreorder_25,axiom,
% 0.19/0.45      preorder @ $o ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_HOL_Obool___Orderings_Olinorder_26,axiom,
% 0.19/0.45      linorder @ $o ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_HOL_Obool___Finite__Set_Ofinite_27,axiom,
% 0.19/0.45      finite_finite @ $o ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_HOL_Obool___Orderings_Oorder_28,axiom,
% 0.19/0.45      order @ $o ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_HOL_Obool___Orderings_Oord_29,axiom,
% 0.19/0.45      ord @ $o ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Real_Oreal___Conditionally__Complete__Lattices_Oconditionally__complete__linorder_30,axiom,
% 0.19/0.45      condit1037483654norder @ real ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Real_Oreal___Conditionally__Complete__Lattices_Olinear__continuum,axiom,
% 0.19/0.45      condit1656338222tinuum @ real ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Real_Oreal___Groups_Oordered__cancel__comm__monoid__add_31,axiom,
% 0.19/0.45      ordere1818651114id_add @ real ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring_32,axiom,
% 0.19/0.45      linord1659791738miring @ real ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Real_Oreal___Groups_Oordered__comm__monoid__add_33,axiom,
% 0.19/0.45      ordere216010020id_add @ real ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Real_Oreal___Rings_Oring__no__zero__divisors_34,axiom,
% 0.19/0.45      ring_n68954251visors @ real ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Real_Oreal___Orderings_Odense__linorder,axiom,
% 0.19/0.45      dense_linorder @ real ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Real_Oreal___Fields_Olinordered__field,axiom,
% 0.19/0.45      linordered_field @ real ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Real_Oreal___Groups_Ocomm__monoid__add_35,axiom,
% 0.19/0.45      comm_monoid_add @ real ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Real_Oreal___Rings_Olinordered__idom_36,axiom,
% 0.19/0.45      linordered_idom @ real ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Real_Oreal___Rings_Ocomm__semiring__1_37,axiom,
% 0.19/0.45      comm_semiring_1 @ real ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Real_Oreal___Rings_Ocomm__semiring__0_38,axiom,
% 0.19/0.45      comm_semiring_0 @ real ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Real_Oreal___Orderings_Odense__order,axiom,
% 0.19/0.45      dense_order @ real ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Real_Oreal___Rings_Ozero__less__one_39,axiom,
% 0.19/0.45      zero_less_one @ real ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Real_Oreal___Orderings_Opreorder_40,axiom,
% 0.19/0.45      preorder @ real ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Real_Oreal___Orderings_Olinorder_41,axiom,
% 0.19/0.45      linorder @ real ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Real_Oreal___Rings_Ocomm__ring__1_42,axiom,
% 0.19/0.45      comm_ring_1 @ real ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Real_Oreal___Orderings_Ono__top_43,axiom,
% 0.19/0.45      no_top @ real ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Real_Oreal___Orderings_Ono__bot_44,axiom,
% 0.19/0.45      no_bot @ real ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Real_Oreal___Orderings_Oorder_45,axiom,
% 0.19/0.45      order @ real ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Real_Oreal___Nat_Oring__char__0_46,axiom,
% 0.19/0.45      ring_char_0 @ real ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Real_Oreal___Orderings_Oord_47,axiom,
% 0.19/0.45      ord @ real ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Real_Oreal___Groups_Ozero_48,axiom,
% 0.19/0.45      zero @ real ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Real_Oreal___Groups_Oone_49,axiom,
% 0.19/0.45      one @ real ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Polynomial_Opoly___Groups_Oordered__cancel__comm__monoid__add_50,axiom,
% 0.19/0.45      ! [A9: $tType] :
% 0.19/0.45        ( ( linordered_idom @ A9 )
% 0.19/0.45       => ( ordere1818651114id_add @ ( poly @ A9 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Polynomial_Opoly___Rings_Olinordered__nonzero__semiring_51,axiom,
% 0.19/0.45      ! [A9: $tType] :
% 0.19/0.45        ( ( linordered_idom @ A9 )
% 0.19/0.45       => ( linord1659791738miring @ ( poly @ A9 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Polynomial_Opoly___Groups_Oordered__comm__monoid__add_52,axiom,
% 0.19/0.45      ! [A9: $tType] :
% 0.19/0.45        ( ( linordered_idom @ A9 )
% 0.19/0.45       => ( ordere216010020id_add @ ( poly @ A9 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Polynomial_Opoly___Rings_Oring__no__zero__divisors_53,axiom,
% 0.19/0.45      ! [A9: $tType] :
% 0.19/0.45        ( ( idom @ A9 )
% 0.19/0.45       => ( ring_n68954251visors @ ( poly @ A9 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Polynomial_Opoly___Groups_Ocomm__monoid__add_54,axiom,
% 0.19/0.45      ! [A9: $tType] :
% 0.19/0.45        ( ( comm_monoid_add @ A9 )
% 0.19/0.45       => ( comm_monoid_add @ ( poly @ A9 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Polynomial_Opoly___Rings_Olinordered__idom_55,axiom,
% 0.19/0.45      ! [A9: $tType] :
% 0.19/0.45        ( ( linordered_idom @ A9 )
% 0.19/0.45       => ( linordered_idom @ ( poly @ A9 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Polynomial_Opoly___Rings_Ocomm__semiring__1_56,axiom,
% 0.19/0.45      ! [A9: $tType] :
% 0.19/0.45        ( ( comm_semiring_1 @ A9 )
% 0.19/0.45       => ( comm_semiring_1 @ ( poly @ A9 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Polynomial_Opoly___Rings_Ocomm__semiring__0_57,axiom,
% 0.19/0.45      ! [A9: $tType] :
% 0.19/0.45        ( ( comm_semiring_0 @ A9 )
% 0.19/0.45       => ( comm_semiring_0 @ ( poly @ A9 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Polynomial_Opoly___Rings_Ozero__less__one_58,axiom,
% 0.19/0.45      ! [A9: $tType] :
% 0.19/0.45        ( ( linordered_idom @ A9 )
% 0.19/0.45       => ( zero_less_one @ ( poly @ A9 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Polynomial_Opoly___Orderings_Opreorder_59,axiom,
% 0.19/0.45      ! [A9: $tType] :
% 0.19/0.45        ( ( linordered_idom @ A9 )
% 0.19/0.45       => ( preorder @ ( poly @ A9 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Polynomial_Opoly___Orderings_Olinorder_60,axiom,
% 0.19/0.45      ! [A9: $tType] :
% 0.19/0.45        ( ( linordered_idom @ A9 )
% 0.19/0.45       => ( linorder @ ( poly @ A9 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Polynomial_Opoly___Rings_Ocomm__ring__1_61,axiom,
% 0.19/0.45      ! [A9: $tType] :
% 0.19/0.45        ( ( comm_ring_1 @ A9 )
% 0.19/0.45       => ( comm_ring_1 @ ( poly @ A9 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Polynomial_Opoly___Orderings_Oorder_62,axiom,
% 0.19/0.45      ! [A9: $tType] :
% 0.19/0.45        ( ( linordered_idom @ A9 )
% 0.19/0.45       => ( order @ ( poly @ A9 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Polynomial_Opoly___Nat_Oring__char__0_63,axiom,
% 0.19/0.45      ! [A9: $tType] :
% 0.19/0.45        ( ( ( ring_char_0 @ A9 )
% 0.19/0.45          & ( comm_ring_1 @ A9 ) )
% 0.19/0.45       => ( ring_char_0 @ ( poly @ A9 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Polynomial_Opoly___Orderings_Oord_64,axiom,
% 0.19/0.45      ! [A9: $tType] :
% 0.19/0.45        ( ( linordered_idom @ A9 )
% 0.19/0.45       => ( ord @ ( poly @ A9 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Polynomial_Opoly___Groups_Ozero_65,axiom,
% 0.19/0.45      ! [A9: $tType] :
% 0.19/0.45        ( ( zero @ A9 )
% 0.19/0.45       => ( zero @ ( poly @ A9 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  thf(tcon_Polynomial_Opoly___Groups_Oone_66,axiom,
% 0.19/0.45      ! [A9: $tType] :
% 0.19/0.45        ( ( comm_semiring_1 @ A9 )
% 0.19/0.45       => ( one @ ( poly @ A9 ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  % Helper facts (3)
% 0.19/0.45  thf(help_If_3_1_T,axiom,
% 0.19/0.45      ! [P: $o] :
% 0.19/0.45        ( ( P = $true )
% 0.19/0.45        | ( P = $false ) ) ).
% 0.19/0.45  
% 0.19/0.45  thf(help_If_2_1_T,axiom,
% 0.19/0.45      ! [A: $tType,X2: A,Y2: A] :
% 0.19/0.45        ( ( if @ A @ $false @ X2 @ Y2 )
% 0.19/0.45        = Y2 ) ).
% 0.19/0.45  
% 0.19/0.45  thf(help_If_1_1_T,axiom,
% 0.19/0.45      ! [A: $tType,X2: A,Y2: A] :
% 0.19/0.45        ( ( if @ A @ $true @ X2 @ Y2 )
% 0.19/0.45        = X2 ) ).
% 0.19/0.45  
% 0.19/0.45  % Conjectures (1)
% 0.19/0.45  thf(conj_0,conjecture,
% 0.19/0.45      ( finite_finite2 @ real
% 0.19/0.45      @ ( collect @ real
% 0.19/0.45        @ ^ [X: real] :
% 0.19/0.45            ( ( ( poly2 @ real @ p @ X )
% 0.19/0.45              = ( zero_zero @ real ) )
% 0.19/0.45            & ( ord_less @ real @ a @ X )
% 0.19/0.45            & ( ord_less @ real @ X @ b ) ) ) ) ).
% 0.19/0.45  
% 0.19/0.45  %------------------------------------------------------------------------------
% 0.19/0.45  ------------------------
% 3.41/1.98  ---- Embedded in THF ---
% 3.41/1.98  %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.41/1.98  %%% Generated on Tue Feb 24 08:29:53 EST 2026
% 3.41/1.98  %%% using '$$dhol' embedding, version 1.3.0.
% 3.41/1.98  %%% Logic specification used:
% 3.41/1.98  %%% thf(spec, logic, $$dhol).
% 3.41/1.98  
% 3.41/1.98  % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.BBanjbptkj/DTF2DTF1969.p
% 3.41/1.98  thf(ty_t_Polynomial_Opoly, type, poly: ($tType > $tType)).
% 3.41/1.98  thf(ty_t_Real_Oreal, type, real: $tType).
% 3.41/1.98  thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 3.41/1.98  thf(ty_t_Nat_Onat, type, nat: $tType).
% 3.41/1.98  thf(ty_t_Int_Oint, type, int: $tType).
% 3.41/1.98  thf(sy_cl_Rings_Oidom, type, idom: (!> [A:$tType]: ($o))).
% 3.41/1.98  thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 3.41/1.98  thf(sy_cl_Groups_Oone, type, one: (!> [A:$tType]: ($o))).
% 3.41/1.98  thf(sy_cl_Groups_Ozero, type, zero: (!> [A:$tType]: ($o))).
% 3.41/1.98  thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 3.41/1.98  thf(sy_cl_Nat_Oring__char__0, type, ring_char_0: (!> [A:$tType]: ($o))).
% 3.41/1.98  thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 3.41/1.98  thf(sy_cl_Orderings_Ono__bot, type, no_bot: (!> [A:$tType]: ($o))).
% 3.41/1.98  thf(sy_cl_Orderings_Ono__top, type, no_top: (!> [A:$tType]: ($o))).
% 3.41/1.98  thf(sy_cl_Finite__Set_Ofinite, type, finite_finite: (!> [A:$tType]: ($o))).
% 3.41/1.98  thf(sy_cl_Rings_Ocomm__ring__1, type, comm_ring_1: (!> [A:$tType]: ($o))).
% 3.41/1.98  thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 3.41/1.98  thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: ($o))).
% 3.41/1.98  thf(sy_cl_Orderings_Owellorder, type, wellorder: (!> [A:$tType]: ($o))).
% 3.41/1.98  thf(sy_cl_Rings_Ozero__less__one, type, zero_less_one: (!> [A:$tType]: ($o))).
% 3.41/1.98  thf(sy_cl_Orderings_Odense__order, type, dense_order: (!> [A:$tType]: ($o))).
% 3.41/1.98  thf(sy_cl_Rings_Ocomm__semiring__0, type, comm_semiring_0: (!> [A:$tType]: ($o))).
% 3.41/1.98  thf(sy_cl_Rings_Ocomm__semiring__1, type, comm_semiring_1: (!> [A:$tType]: ($o))).
% 3.41/1.98  thf(sy_cl_Rings_Olinordered__idom, type, linordered_idom: (!> [A:$tType]: ($o))).
% 3.41/1.98  thf(sy_cl_Groups_Ocomm__monoid__add, type, comm_monoid_add: (!> [A:$tType]: ($o))).
% 3.41/1.98  thf(sy_cl_Fields_Olinordered__field, type, linordered_field: (!> [A:$tType]: ($o))).
% 3.41/1.98  thf(sy_cl_Orderings_Odense__linorder, type, dense_linorder: (!> [A:$tType]: ($o))).
% 3.41/1.98  thf(sy_cl_Rings_Oring__no__zero__divisors, type, ring_n68954251visors: (!> [A:$tType]: ($o))).
% 3.41/1.98  thf(sy_cl_Groups_Oordered__comm__monoid__add, type, ordere216010020id_add: (!> [A:$tType]: ($o))).
% 3.41/1.98  thf(sy_cl_Rings_Olinordered__nonzero__semiring, type, linord1659791738miring: (!> [A:$tType]: ($o))).
% 3.41/1.98  thf(sy_cl_Groups_Ocanonically__ordered__monoid__add, type, canoni770627133id_add: (!> [A:$tType]: ($o))).
% 3.41/1.98  thf(sy_cl_Groups_Oordered__cancel__comm__monoid__add, type, ordere1818651114id_add: (!> [A:$tType]: ($o))).
% 3.41/1.98  thf(sy_cl_Conditionally__Complete__Lattices_Olinear__continuum, type, condit1656338222tinuum: (!> [A:$tType]: ($o))).
% 3.41/1.98  thf(sy_cl_Conditionally__Complete__Lattices_Oconditionally__complete__linorder, type, condit1037483654norder: (!> [A:$tType]: ($o))).
% 3.41/1.98  thf(sy_c_Finite__Set_Ofinite, type, finite_finite2: (!> [A:$tType]: (((set @ A) > $o)))).
% 3.41/1.98  thf(sy_c_Groups_Oone__class_Oone, type, one_one: (!> [A:$tType]: (A))).
% 3.41/1.98  thf(sy_c_Groups_Ozero__class_Ozero, type, zero_zero: (!> [A:$tType]: (A))).
% 3.41/1.98  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum, type, groups1340683514dd_sum: (!> [B:$tType,A:$tType]: (((B > A) > ((set @ B) > A))))).
% 3.41/1.98  thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 3.41/1.98  thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 3.41/1.98  thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 3.41/1.98  thf(sy_c_Polynomial_Ois__zero, type, is_zero: (!> [A:$tType]: (((poly @ A) > $o)))).
% 3.41/1.98  thf(sy_c_Polynomial_Opoly, type, poly2: (!> [A:$tType]: (((poly @ A) > (A > A))))).
% 3.41/1.98  thf(sy_c_Polynomial_Opoly__cutoff, type, poly_cutoff: (!> [A:$tType]: ((nat > ((poly @ A) > (poly @ A)))))).
% 3.41/1.98  thf(sy_c_Polynomial_Oreflect__poly, type, reflect_poly: (!> [A:$tType]: (((poly @ A) > (poly @ A))))).
% 3.41/1.98  thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 3.41/1.98  thf(sy_c_Sturm__Tarski__Mirabelle__osyjafhhev_Ocindex__poly, type, sturm_1539314049x_poly: (real > (real > ((poly @ real) > ((poly @ real) > int))))).
% 3.41/1.98  thf(sy_c_Sturm__Tarski__Mirabelle__osyjafhhev_Ocross, type, sturm_424270202_cross: ((poly @ real) > (real > (real > int)))).
% 3.41/1.98  thf(sy_c_Sturm__Tarski__Mirabelle__osyjafhhev_Ojump__poly, type, sturm_652470720p_poly: ((poly @ real) > ((poly @ real) > (real > int)))).
% 3.41/1.98  thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 3.41/1.98  thf(sy_v_a, type, a: real).
% 3.41/1.98  thf(sy_v_a_H, type, a2: real).
% 3.41/1.98  thf(sy_v_b, type, b: real).
% 3.41/1.98  thf(sy_v_b_H, type, b2: real).
% 3.41/1.98  thf(sy_v_p, type, p: (poly @ real)).
% 3.41/1.98  thf(fact_0__092_060open_062finite_A_123x_O_Apoly_Ap_Ax_A_061_A0_125_092_060close_062, axiom, ((finite_finite2 @ real) @ ((collect @ real) @ (^ [X:real]: (((((poly2 @ real) @ p) @ X) = (zero_zero @ real))))))).
% 3.41/1.98  thf(fact_1_assms_I2_J, axiom, (((ord_less @ real) @ a2) @ b2)).
% 3.41/1.98  thf(fact_2_assms_I3_J, axiom, (((ord_less @ real) @ b2) @ b)).
% 3.41/1.98  thf(fact_3_assms_I1_J, axiom, (((ord_less @ real) @ a) @ a2)).
% 3.41/1.98  thf(fact_4_False, axiom, (p != (zero_zero @ (poly @ real)))).
% 3.41/1.98  thf(fact_5_poly__0, axiom, (! [A:$tType]: (((comm_semiring_0 @ A) => (! [X2:A]: (((((poly2 @ A) @ (zero_zero @ (poly @ A))) @ X2) = (zero_zero @ A)))))))).
% 3.41/1.98  thf(fact_6_not__gr__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((~ ((((ord_less @ A) @ (zero_zero @ A)) @ N))) = (N = (zero_zero @ A))))))))).
% 3.41/1.98  thf(fact_7_assms_I4_J, axiom, (! [X3:real]: (((((((ord_less @ real) @ a) @ X3) & (((ord_less_eq @ real) @ X3) @ a2)) | ((((ord_less_eq @ real) @ b2) @ X3) & (((ord_less @ real) @ X3) @ b))) => ((((poly2 @ real) @ p) @ X3) != (zero_zero @ real)))))).
% 3.41/1.98  thf(fact_8_finite__Collect__conjI, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((((finite_finite2 @ A) @ ((collect @ A) @ P)) | ((finite_finite2 @ A) @ ((collect @ A) @ Q))) => ((finite_finite2 @ A) @ ((collect @ A) @ (^ [X:A]: (((P @ X) & (Q @ X)))))))))).
% 3.41/1.98  thf(fact_9_finite__Collect__disjI, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: ((((finite_finite2 @ A) @ ((collect @ A) @ (^ [X:A]: (((P @ X) | (Q @ X)))))) = (((finite_finite2 @ A) @ ((collect @ A) @ P)) & ((finite_finite2 @ A) @ ((collect @ A) @ Q))))))).
% 3.41/1.98  thf(fact_10_poly__roots__finite, axiom, (! [A:$tType]: ((((comm_ring_1 @ A) & (ring_n68954251visors @ A)) => (! [P2:(poly @ A)]: (((P2 != (zero_zero @ (poly @ A))) => ((finite_finite2 @ A) @ ((collect @ A) @ (^ [X:A]: (((((poly2 @ A) @ P2) @ X) = (zero_zero @ A))))))))))))).
% 3.41/1.98  thf(fact_11_poly__IVT__neg, axiom, (! [A2:real,B2:real,P2:(poly @ real)]: (((((ord_less @ real) @ A2) @ B2) => ((((ord_less @ real) @ (zero_zero @ real)) @ (((poly2 @ real) @ P2) @ A2)) => ((((ord_less @ real) @ (((poly2 @ real) @ P2) @ B2)) @ (zero_zero @ real)) => (? [X4:real]: (((((ord_less @ real) @ A2) @ X4) & ((((ord_less @ real) @ X4) @ B2) & ((((poly2 @ real) @ P2) @ X4) = (zero_zero @ real)))))))))))).
% 3.41/1.98  thf(fact_12_poly__IVT__pos, axiom, (! [A2:real,B2:real,P2:(poly @ real)]: (((((ord_less @ real) @ A2) @ B2) => ((((ord_less @ real) @ (((poly2 @ real) @ P2) @ A2)) @ (zero_zero @ real)) => ((((ord_less @ real) @ (zero_zero @ real)) @ (((poly2 @ real) @ P2) @ B2)) => (? [X4:real]: (((((ord_less @ real) @ A2) @ X4) & ((((ord_less @ real) @ X4) @ B2) & ((((poly2 @ real) @ P2) @ X4) = (zero_zero @ real)))))))))))).
% 3.41/1.98  thf(fact_13_finite__code, axiom, (! [A:$tType]: (((finite_finite @ A) => ((finite_finite2 @ A) = (^ [A3:(set @ A)]: ($true))))))).
% 3.41/1.98  thf(fact_14_poly__all__0__iff__0, axiom, (! [A:$tType]: ((((ring_char_0 @ A) & ((comm_ring_1 @ A) & (ring_n68954251visors @ A))) => (! [P2:(poly @ A)]: (((! [X:A]: (((((poly2 @ A) @ P2) @ X) = (zero_zero @ A)))) = (P2 = (zero_zero @ (poly @ A)))))))))).
% 3.41/1.98  thf(fact_15_less__numeral__extra_I3_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (~ ((((ord_less @ A) @ (zero_zero @ A)) @ (zero_zero @ A)))))))).
% 3.41/1.98  thf(fact_16_le__zero__eq, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((((ord_less_eq @ A) @ N) @ (zero_zero @ A)) = (N = (zero_zero @ A))))))))).
% 3.41/1.98  thf(fact_17_zero__le, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [X2:A]: ((((ord_less_eq @ A) @ (zero_zero @ A)) @ X2))))))).
% 3.41/1.98  thf(fact_18_le__numeral__extra_I3_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (zero_zero @ A)))))).
% 3.41/1.98  thf(fact_19_finite__psubset__induct, axiom, (! [A:$tType,A4:(set @ A),P:((set @ A) > $o)]: ((((finite_finite2 @ A) @ A4) => ((! [A5:(set @ A)]: ((((finite_finite2 @ A) @ A5) => ((! [B3:(set @ A)]: (((((ord_less @ (set @ A)) @ B3) @ A5) => (P @ B3)))) => (P @ A5))))) => (P @ A4)))))).
% 3.41/1.98  thf(fact_20_finite__has__minimal2, axiom, (! [A:$tType]: (((order @ A) => (! [A4:(set @ A),A2:A]: ((((finite_finite2 @ A) @ A4) => ((((member @ A) @ A2) @ A4) => (? [X4:A]: (((((member @ A) @ X4) @ A4) & ((((ord_less_eq @ A) @ X4) @ A2) & (! [Xa:A]: (((((member @ A) @ Xa) @ A4) => ((((ord_less_eq @ A) @ Xa) @ X4) => (X4 = Xa))))))))))))))))).
% 3.41/1.98  thf(fact_21_finite__has__maximal2, axiom, (! [A:$tType]: (((order @ A) => (! [A4:(set @ A),A2:A]: ((((finite_finite2 @ A) @ A4) => ((((member @ A) @ A2) @ A4) => (? [X4:A]: (((((member @ A) @ X4) @ A4) & ((((ord_less_eq @ A) @ A2) @ X4) & (! [Xa:A]: (((((member @ A) @ Xa) @ A4) => ((((ord_less_eq @ A) @ X4) @ Xa) => (X4 = Xa))))))))))))))))).
% 3.41/1.98  thf(fact_22_next__non__root__interval, axiom, (! [P2:(poly @ real),Lb:real]: (((P2 != (zero_zero @ (poly @ real))) => (~ ((! [Ub:real]: (((((ord_less @ real) @ Lb) @ Ub) => (~ ((! [Z:real]: ((((((ord_less @ real) @ Lb) @ Z) & (((ord_less_eq @ real) @ Z) @ Ub)) => ((((poly2 @ real) @ P2) @ Z) != (zero_zero @ real)))))))))))))))).
% 3.41/1.98  thf(fact_23_last__non__root__interval, axiom, (! [P2:(poly @ real),Ub2:real]: (((P2 != (zero_zero @ (poly @ real))) => (~ ((! [Lb2:real]: (((((ord_less @ real) @ Lb2) @ Ub2) => (~ ((! [Z:real]: ((((((ord_less_eq @ real) @ Lb2) @ Z) & (((ord_less @ real) @ Z) @ Ub2)) => ((((poly2 @ real) @ P2) @ Z) != (zero_zero @ real)))))))))))))))).
% 3.41/1.98  thf(fact_24_zero__reorient, axiom, (! [A:$tType]: (((zero @ A) => (! [X2:A]: ((((zero_zero @ A) = X2) = (X2 = (zero_zero @ A))))))))).
% 3.41/1.98  thf(fact_25_finite, axiom, (! [A:$tType]: (((finite_finite @ A) => (! [A4:(set @ A)]: (((finite_finite2 @ A) @ A4))))))).
% 3.41/1.98  thf(fact_26_finite__set__choice, axiom, (! [B:$tType,A:$tType,A4:(set @ A),P:(A > (B > $o))]: ((((finite_finite2 @ A) @ A4) => ((! [X4:A]: (((((member @ A) @ X4) @ A4) => (? [X_1:B]: (((P @ X4) @ X_1)))))) => (? [F:(A > B)]: ((! [X3:A]: (((((member @ A) @ X3) @ A4) => ((P @ X3) @ (F @ X3)))))))))))).
% 3.41/1.98  thf(fact_27_not__eq__pos__or__neg__iff__2, axiom, (! [Lb:real,Ub2:real,P2:(poly @ real)]: (((! [Z2:real]: ((((((ord_less_eq @ real) @ Lb) @ Z2) & (((ord_less @ real) @ Z2) @ Ub2)) => ((((poly2 @ real) @ P2) @ Z2) != (zero_zero @ real))))) = ((! [Z2:real]: ((((((ord_less_eq @ real) @ Lb) @ Z2) & (((ord_less @ real) @ Z2) @ Ub2)) => (((ord_less @ real) @ (zero_zero @ real)) @ (((poly2 @ real) @ P2) @ Z2))))) | (! [Z2:real]: ((((((ord_less_eq @ real) @ Lb) @ Z2) & (((ord_less @ real) @ Z2) @ Ub2)) => (((ord_less @ real) @ (((poly2 @ real) @ P2) @ Z2)) @ (zero_zero @ real)))))))))).
% 3.41/1.98  thf(fact_28_not__eq__pos__or__neg__iff__1, axiom, (! [Lb:real,Ub2:real,P2:(poly @ real)]: (((! [Z2:real]: ((((((ord_less @ real) @ Lb) @ Z2) & (((ord_less_eq @ real) @ Z2) @ Ub2)) => ((((poly2 @ real) @ P2) @ Z2) != (zero_zero @ real))))) = ((! [Z2:real]: ((((((ord_less @ real) @ Lb) @ Z2) & (((ord_less_eq @ real) @ Z2) @ Ub2)) => (((ord_less @ real) @ (zero_zero @ real)) @ (((poly2 @ real) @ P2) @ Z2))))) | (! [Z2:real]: ((((((ord_less @ real) @ Lb) @ Z2) & (((ord_less_eq @ real) @ Z2) @ Ub2)) => (((ord_less @ real) @ (((poly2 @ real) @ P2) @ Z2)) @ (zero_zero @ real)))))))))).
% 3.41/1.98  thf(fact_29_poly__eq__poly__eq__iff, axiom, (! [A:$tType]: ((((ring_char_0 @ A) & ((comm_ring_1 @ A) & (ring_n68954251visors @ A))) => (! [P2:(poly @ A),Q2:(poly @ A)]: (((((poly2 @ A) @ P2) = ((poly2 @ A) @ Q2)) = (P2 = Q2)))))))).
% 3.41/1.98  thf(fact_30_pigeonhole__infinite__rel, axiom, (! [B:$tType,A:$tType,A4:(set @ A),B4:(set @ B),R:(A > (B > $o))]: (((~ (((finite_finite2 @ A) @ A4))) => (((finite_finite2 @ B) @ B4) => ((! [X4:A]: (((((member @ A) @ X4) @ A4) => (? [Xa:B]: (((((member @ B) @ Xa) @ B4) & ((R @ X4) @ Xa))))))) => (? [X4:B]: (((((member @ B) @ X4) @ B4) & (~ (((finite_finite2 @ A) @ ((collect @ A) @ (^ [A6:A]: (((((member @ A) @ A6) @ A4) & ((R @ A6) @ X4))))))))))))))))).
% 3.41/1.98  thf(fact_31_not__finite__existsD, axiom, (! [A:$tType,P:(A > $o)]: (((~ (((finite_finite2 @ A) @ ((collect @ A) @ P)))) => (? [X_12:A]: ((P @ X_12))))))).
% 3.41/1.98  thf(fact_32_zero__less__iff__neq__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ N) = (N != (zero_zero @ A))))))))).
% 3.41/1.98  thf(fact_33_gr__implies__not__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [M:A,N:A]: (((((ord_less @ A) @ M) @ N) => (N != (zero_zero @ A))))))))).
% 3.41/1.98  thf(fact_34_not__less__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: ((~ ((((ord_less @ A) @ N) @ (zero_zero @ A)))))))))).
% 3.41/1.98  thf(fact_35_gr__zeroI, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((N != (zero_zero @ A)) => (((ord_less @ A) @ (zero_zero @ A)) @ N)))))))).
% 3.41/1.98  thf(fact_36_order__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A]: ((((ord_less_eq @ A) @ X2) @ X2))))))).
% 3.41/1.98  thf(fact_37_cross__no__root, axiom, (! [A2:real,B2:real,P2:(poly @ real)]: (((((ord_less @ real) @ A2) @ B2) => ((! [X4:real]: ((((((ord_less @ real) @ A2) @ X4) & (((ord_less @ real) @ X4) @ B2)) => ((((poly2 @ real) @ P2) @ X4) != (zero_zero @ real))))) => ((((sturm_424270202_cross @ P2) @ A2) @ B2) = (zero_zero @ int))))))).
% 3.41/1.98  thf(fact_38_less__eq__real__def, axiom, ((ord_less_eq @ real) = (^ [X:real,Y:real]: (((((ord_less @ real) @ X) @ Y) | (X = Y)))))).
% 3.41/1.98  thf(fact_39_complete__interval, axiom, (! [A:$tType]: (((condit1037483654norder @ A) => (! [A2:A,B2:A,P:(A > $o)]: (((((ord_less @ A) @ A2) @ B2) => ((P @ A2) => ((~ ((P @ B2))) => (? [C:A]: (((((ord_less_eq @ A) @ A2) @ C) & ((((ord_less_eq @ A) @ C) @ B2) & ((! [X3:A]: ((((((ord_less_eq @ A) @ A2) @ X3) & (((ord_less @ A) @ X3) @ C)) => (P @ X3)))) & (! [D:A]: (((! [X4:A]: ((((((ord_less_eq @ A) @ A2) @ X4) & (((ord_less @ A) @ X4) @ D)) => (P @ X4)))) => (((ord_less_eq @ A) @ D) @ C)))))))))))))))))).
% 3.41/1.98  thf(fact_40_order_Onot__eq__order__implies__strict, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A]: (((A2 != B2) => ((((ord_less_eq @ A) @ A2) @ B2) => (((ord_less @ A) @ A2) @ B2))))))))).
% 3.41/1.98  thf(fact_41_dual__order_Ostrict__implies__order, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A]: (((((ord_less @ A) @ B2) @ A2) => (((ord_less_eq @ A) @ B2) @ A2)))))))).
% 3.41/1.98  thf(fact_42_dual__order_Ostrict__iff__order, axiom, (! [A:$tType]: (((order @ A) => ((ord_less @ A) = (^ [B5:A,A6:A]: (((((ord_less_eq @ A) @ B5) @ A6) & (A6 != B5))))))))).
% 3.41/1.98  thf(fact_43_dual__order_Oorder__iff__strict, axiom, (! [A:$tType]: (((order @ A) => ((ord_less_eq @ A) = (^ [B5:A,A6:A]: (((((ord_less @ A) @ B5) @ A6) | (A6 = B5))))))))).
% 3.41/1.98  thf(fact_44_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 3.41/1.98  thf(fact_45_Collect__mem__eq, axiom, (! [A:$tType,A4:(set @ A)]: ((((collect @ A) @ (^ [X:A]: ((((member @ A) @ X) @ A4)))) = A4)))).
% 3.41/1.98  thf(fact_46_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X4:A]: (((P @ X4) = (Q @ X4)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 3.41/1.98  thf(fact_47_ext, axiom, (! [B:$tType,A:$tType,F2:(A > B),G:(A > B)]: (((! [X4:A]: (((F2 @ X4) = (G @ X4)))) => (F2 = G))))).
% 3.41/1.98  thf(fact_48_order_Ostrict__implies__order, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ A2) @ B2) => (((ord_less_eq @ A) @ A2) @ B2)))))))).
% 3.41/1.98  thf(fact_49_dense__le__bounded, axiom, (! [A:$tType]: (((dense_linorder @ A) => (! [X2:A,Y2:A,Z3:A]: (((((ord_less @ A) @ X2) @ Y2) => ((! [W:A]: (((((ord_less @ A) @ X2) @ W) => ((((ord_less @ A) @ W) @ Y2) => (((ord_less_eq @ A) @ W) @ Z3))))) => (((ord_less_eq @ A) @ Y2) @ Z3))))))))).
% 3.41/1.98  thf(fact_50_finite__Collect__subsets, axiom, (! [A:$tType,A4:(set @ A)]: ((((finite_finite2 @ A) @ A4) => ((finite_finite2 @ (set @ A)) @ ((collect @ (set @ A)) @ (^ [B6:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ B6) @ A4))))))))).
% 3.41/1.98  thf(fact_51_cross__0, axiom, (! [A2:real,B2:real]: (((((sturm_424270202_cross @ (zero_zero @ (poly @ real))) @ A2) @ B2) = (zero_zero @ int))))).
% 3.41/1.98  thf(fact_52_finite__subset, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B4) => (((finite_finite2 @ A) @ B4) => ((finite_finite2 @ A) @ A4)))))).
% 3.41/1.98  thf(fact_53_infinite__super, axiom, (! [A:$tType,S:(set @ A),T:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ S) @ T) => ((~ (((finite_finite2 @ A) @ S))) => (~ (((finite_finite2 @ A) @ T)))))))).
% 3.41/1.98  thf(fact_54_rev__finite__subset, axiom, (! [A:$tType,B4:(set @ A),A4:(set @ A)]: ((((finite_finite2 @ A) @ B4) => ((((ord_less_eq @ (set @ A)) @ A4) @ B4) => ((finite_finite2 @ A) @ A4)))))).
% 3.41/1.98  thf(fact_55_dual__order_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ A2) @ B2) => (A2 = B2))))))))).
% 3.41/1.98  thf(fact_56_dual__order_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y3:A,Z4:A]: ((Y3 = Z4))) = (^ [A6:A,B5:A]: (((((ord_less_eq @ A) @ B5) @ A6) & (((ord_less_eq @ A) @ A6) @ B5))))))))).
% 3.41/1.98  thf(fact_57_dual__order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A,C2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ C2) @ B2) => (((ord_less_eq @ A) @ C2) @ A2))))))))).
% 3.41/1.98  thf(fact_58_linorder__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > (A > $o)),A2:A,B2:A]: (((! [A7:A,B7:A]: (((((ord_less_eq @ A) @ A7) @ B7) => ((P @ A7) @ B7)))) => ((! [A7:A,B7:A]: ((((P @ B7) @ A7) => ((P @ A7) @ B7)))) => ((P @ A2) @ B2))))))))).
% 3.41/1.98  thf(fact_59_dual__order_Orefl, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A]: ((((ord_less_eq @ A) @ A2) @ A2))))))).
% 3.41/1.98  thf(fact_60_order__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y2:A,Z3:A]: (((((ord_less_eq @ A) @ X2) @ Y2) => ((((ord_less_eq @ A) @ Y2) @ Z3) => (((ord_less_eq @ A) @ X2) @ Z3))))))))).
% 3.41/1.98  thf(fact_61_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ A2) => (A2 = B2))))))))).
% 3.41/1.98  thf(fact_62_ord__le__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((B2 = C2) => (((ord_less_eq @ A) @ A2) @ C2))))))))).
% 3.41/1.98  thf(fact_63_ord__eq__le__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C2:A]: (((A2 = B2) => ((((ord_less_eq @ A) @ B2) @ C2) => (((ord_less_eq @ A) @ A2) @ C2))))))))).
% 3.41/1.98  thf(fact_64_order__class_Oorder_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y3:A,Z4:A]: ((Y3 = Z4))) = (^ [A6:A,B5:A]: (((((ord_less_eq @ A) @ A6) @ B5) & (((ord_less_eq @ A) @ B5) @ A6))))))))).
% 3.41/1.98  thf(fact_65_antisym__conv, axiom, (! [A:$tType]: (((order @ A) => (! [Y2:A,X2:A]: (((((ord_less_eq @ A) @ Y2) @ X2) => ((((ord_less_eq @ A) @ X2) @ Y2) = (X2 = Y2))))))))).
% 3.41/1.98  thf(fact_66_le__cases3, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y2:A,Z3:A]: ((((((ord_less_eq @ A) @ X2) @ Y2) => (~ ((((ord_less_eq @ A) @ Y2) @ Z3)))) => (((((ord_less_eq @ A) @ Y2) @ X2) => (~ ((((ord_less_eq @ A) @ X2) @ Z3)))) => (((((ord_less_eq @ A) @ X2) @ Z3) => (~ ((((ord_less_eq @ A) @ Z3) @ Y2)))) => (((((ord_less_eq @ A) @ Z3) @ Y2) => (~ ((((ord_less_eq @ A) @ Y2) @ X2)))) => (((((ord_less_eq @ A) @ Y2) @ Z3) => (~ ((((ord_less_eq @ A) @ Z3) @ X2)))) => (~ (((((ord_less_eq @ A) @ Z3) @ X2) => (~ ((((ord_less_eq @ A) @ X2) @ Y2))))))))))))))))).
% 3.41/1.98  thf(fact_67_order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ C2) => (((ord_less_eq @ A) @ A2) @ C2))))))))).
% 3.41/1.98  thf(fact_68_le__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y2:A]: (((~ ((((ord_less_eq @ A) @ X2) @ Y2))) => (((ord_less_eq @ A) @ Y2) @ X2)))))))).
% 3.41/1.98  thf(fact_69_eq__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y2:A]: (((X2 = Y2) => (((ord_less_eq @ A) @ X2) @ Y2)))))))).
% 3.41/1.98  thf(fact_70_linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y2:A]: (((((ord_less_eq @ A) @ X2) @ Y2) | (((ord_less_eq @ A) @ Y2) @ X2)))))))).
% 3.41/1.98  thf(fact_71_antisym, axiom, (! [A:$tType]: (((order @ A) => (! [X2:A,Y2:A]: (((((ord_less_eq @ A) @ X2) @ Y2) => ((((ord_less_eq @ A) @ Y2) @ X2) => (X2 = Y2))))))))).
% 3.41/1.98  thf(fact_72_eq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y3:A,Z4:A]: ((Y3 = Z4))) = (^ [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) & (((ord_less_eq @ A) @ Y) @ X))))))))).
% 3.41/1.98  thf(fact_73_ord__le__eq__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,B2:A,F2:(A > B),C2:B]: (((((ord_less_eq @ A) @ A2) @ B2) => (((F2 @ B2) = C2) => ((! [X4:A,Y4:A]: (((((ord_less_eq @ A) @ X4) @ Y4) => (((ord_less_eq @ B) @ (F2 @ X4)) @ (F2 @ Y4))))) => (((ord_less_eq @ B) @ (F2 @ A2)) @ C2)))))))))).
% 3.41/1.98  thf(fact_74_ord__eq__le__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,F2:(B > A),B2:B,C2:B]: (((A2 = (F2 @ B2)) => ((((ord_less_eq @ B) @ B2) @ C2) => ((! [X4:B,Y4:B]: (((((ord_less_eq @ B) @ X4) @ Y4) => (((ord_less_eq @ A) @ (F2 @ X4)) @ (F2 @ Y4))))) => (((ord_less_eq @ A) @ A2) @ (F2 @ C2))))))))))).
% 3.41/1.98  thf(fact_75_order__subst2, axiom, (! [A:$tType,C3:$tType]: ((((order @ C3) & (order @ A)) => (! [A2:A,B2:A,F2:(A > C3),C2:C3]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ C3) @ (F2 @ B2)) @ C2) => ((! [X4:A,Y4:A]: (((((ord_less_eq @ A) @ X4) @ Y4) => (((ord_less_eq @ C3) @ (F2 @ X4)) @ (F2 @ Y4))))) => (((ord_less_eq @ C3) @ (F2 @ A2)) @ C2)))))))))).
% 3.41/1.98  thf(fact_76_order__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A2:A,F2:(B > A),B2:B,C2:B]: (((((ord_less_eq @ A) @ A2) @ (F2 @ B2)) => ((((ord_less_eq @ B) @ B2) @ C2) => ((! [X4:B,Y4:B]: (((((ord_less_eq @ B) @ X4) @ Y4) => (((ord_less_eq @ A) @ (F2 @ X4)) @ (F2 @ Y4))))) => (((ord_less_eq @ A) @ A2) @ (F2 @ C2))))))))))).
% 3.41/1.98  thf(fact_77_le__fun__def, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => ((ord_less_eq @ (A > B)) = (^ [F3:(A > B),G2:(A > B)]: ((! [X:A]: ((((ord_less_eq @ B) @ (F3 @ X)) @ (G2 @ X))))))))))).
% 3.41/1.98  thf(fact_78_le__funI, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F2:(A > B),G:(A > B)]: (((! [X4:A]: ((((ord_less_eq @ B) @ (F2 @ X4)) @ (G @ X4)))) => (((ord_less_eq @ (A > B)) @ F2) @ G)))))))).
% 3.41/1.98  thf(fact_79_le__funE, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F2:(A > B),G:(A > B),X2:A]: (((((ord_less_eq @ (A > B)) @ F2) @ G) => (((ord_less_eq @ B) @ (F2 @ X2)) @ (G @ X2))))))))).
% 3.41/1.98  thf(fact_80_le__funD, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F2:(A > B),G:(A > B),X2:A]: (((((ord_less_eq @ (A > B)) @ F2) @ G) => (((ord_less_eq @ B) @ (F2 @ X2)) @ (G @ X2))))))))).
% 3.41/1.98  thf(fact_81_ord__eq__less__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,F2:(B > A),B2:B,C2:B]: (((A2 = (F2 @ B2)) => ((((ord_less @ B) @ B2) @ C2) => ((! [X4:B,Y4:B]: (((((ord_less @ B) @ X4) @ Y4) => (((ord_less @ A) @ (F2 @ X4)) @ (F2 @ Y4))))) => (((ord_less @ A) @ A2) @ (F2 @ C2))))))))))).
% 3.41/1.98  thf(fact_82_ord__less__eq__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,B2:A,F2:(A > B),C2:B]: (((((ord_less @ A) @ A2) @ B2) => (((F2 @ B2) = C2) => ((! [X4:A,Y4:A]: (((((ord_less @ A) @ X4) @ Y4) => (((ord_less @ B) @ (F2 @ X4)) @ (F2 @ Y4))))) => (((ord_less @ B) @ (F2 @ A2)) @ C2)))))))))).
% 3.41/1.98  thf(fact_83_order__less__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A2:A,F2:(B > A),B2:B,C2:B]: (((((ord_less @ A) @ A2) @ (F2 @ B2)) => ((((ord_less @ B) @ B2) @ C2) => ((! [X4:B,Y4:B]: (((((ord_less @ B) @ X4) @ Y4) => (((ord_less @ A) @ (F2 @ X4)) @ (F2 @ Y4))))) => (((ord_less @ A) @ A2) @ (F2 @ C2))))))))))).
% 3.41/1.98  thf(fact_84_order__less__subst2, axiom, (! [A:$tType,C3:$tType]: ((((order @ C3) & (order @ A)) => (! [A2:A,B2:A,F2:(A > C3),C2:C3]: (((((ord_less @ A) @ A2) @ B2) => ((((ord_less @ C3) @ (F2 @ B2)) @ C2) => ((! [X4:A,Y4:A]: (((((ord_less @ A) @ X4) @ Y4) => (((ord_less @ C3) @ (F2 @ X4)) @ (F2 @ Y4))))) => (((ord_less @ C3) @ (F2 @ A2)) @ C2)))))))))).
% 3.41/1.98  thf(fact_85_lt__ex, axiom, (! [A:$tType]: (((no_bot @ A) => (! [X2:A]: ((? [Y4:A]: ((((ord_less @ A) @ Y4) @ X2))))))))).
% 3.41/1.98  thf(fact_86_gt__ex, axiom, (! [A:$tType]: (((no_top @ A) => (! [X2:A]: ((? [X_12:A]: ((((ord_less @ A) @ X2) @ X_12))))))))).
% 3.41/1.98  thf(fact_87_neqE, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y2:A]: (((X2 != Y2) => ((~ ((((ord_less @ A) @ X2) @ Y2))) => (((ord_less @ A) @ Y2) @ X2))))))))).
% 3.41/1.98  thf(fact_88_neq__iff, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y2:A]: (((X2 != Y2) = ((((ord_less @ A) @ X2) @ Y2) | (((ord_less @ A) @ Y2) @ X2))))))))).
% 3.41/1.98  thf(fact_89_order_Oasym, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ A2) @ B2) => (~ ((((ord_less @ A) @ B2) @ A2)))))))))).
% 3.41/1.98  thf(fact_90_dense, axiom, (! [A:$tType]: (((dense_order @ A) => (! [X2:A,Y2:A]: (((((ord_less @ A) @ X2) @ Y2) => (? [Z5:A]: (((((ord_less @ A) @ X2) @ Z5) & (((ord_less @ A) @ Z5) @ Y2))))))))))).
% 3.41/1.98  thf(fact_91_less__imp__neq, axiom, (! [A:$tType]: (((order @ A) => (! [X2:A,Y2:A]: (((((ord_less @ A) @ X2) @ Y2) => (X2 != Y2)))))))).
% 3.41/1.98  thf(fact_92_less__asym, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y2:A]: (((((ord_less @ A) @ X2) @ Y2) => (~ ((((ord_less @ A) @ Y2) @ X2)))))))))).
% 3.41/1.98  thf(fact_93_less__asym_H, axiom, (! [A:$tType]: (((preorder @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ A2) @ B2) => (~ ((((ord_less @ A) @ B2) @ A2)))))))))).
% 3.41/1.98  thf(fact_94_less__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y2:A,Z3:A]: (((((ord_less @ A) @ X2) @ Y2) => ((((ord_less @ A) @ Y2) @ Z3) => (((ord_less @ A) @ X2) @ Z3))))))))).
% 3.41/1.98  thf(fact_95_less__linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y2:A]: (((((ord_less @ A) @ X2) @ Y2) | ((X2 = Y2) | (((ord_less @ A) @ Y2) @ X2))))))))).
% 3.41/1.98  thf(fact_96_less__irrefl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A]: ((~ ((((ord_less @ A) @ X2) @ X2))))))))).
% 3.41/1.98  thf(fact_97_ord__eq__less__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C2:A]: (((A2 = B2) => ((((ord_less @ A) @ B2) @ C2) => (((ord_less @ A) @ A2) @ C2))))))))).
% 3.41/1.98  thf(fact_98_ord__less__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less @ A) @ A2) @ B2) => ((B2 = C2) => (((ord_less @ A) @ A2) @ C2))))))))).
% 3.41/1.98  thf(fact_99_dual__order_Oasym, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A]: (((((ord_less @ A) @ B2) @ A2) => (~ ((((ord_less @ A) @ A2) @ B2)))))))))).
% 3.41/1.98  thf(fact_100_less__imp__not__eq, axiom, (! [A:$tType]: (((order @ A) => (! [X2:A,Y2:A]: (((((ord_less @ A) @ X2) @ Y2) => (X2 != Y2)))))))).
% 3.41/1.98  thf(fact_101_less__not__sym, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y2:A]: (((((ord_less @ A) @ X2) @ Y2) => (~ ((((ord_less @ A) @ Y2) @ X2)))))))))).
% 3.41/1.98  thf(fact_102_less__induct, axiom, (! [A:$tType]: (((wellorder @ A) => (! [P:(A > $o),A2:A]: (((! [X4:A]: (((! [Y5:A]: (((((ord_less @ A) @ Y5) @ X4) => (P @ Y5)))) => (P @ X4)))) => (P @ A2)))))))).
% 3.41/1.98  thf(fact_103_antisym__conv3, axiom, (! [A:$tType]: (((linorder @ A) => (! [Y2:A,X2:A]: (((~ ((((ord_less @ A) @ Y2) @ X2))) => ((~ ((((ord_less @ A) @ X2) @ Y2))) = (X2 = Y2))))))))).
% 3.41/1.98  thf(fact_104_less__imp__not__eq2, axiom, (! [A:$tType]: (((order @ A) => (! [X2:A,Y2:A]: (((((ord_less @ A) @ X2) @ Y2) => (Y2 != X2)))))))).
% 3.41/1.98  thf(fact_105_less__imp__triv, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y2:A,P:$o]: (((((ord_less @ A) @ X2) @ Y2) => ((((ord_less @ A) @ Y2) @ X2) => P)))))))).
% 3.41/1.98  thf(fact_106_linorder__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y2:A]: (((~ ((((ord_less @ A) @ X2) @ Y2))) => ((X2 != Y2) => (((ord_less @ A) @ Y2) @ X2))))))))).
% 3.41/1.98  thf(fact_107_dual__order_Oirrefl, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A]: ((~ ((((ord_less @ A) @ A2) @ A2))))))))).
% 3.41/1.98  thf(fact_108_order_Ostrict__trans, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less @ A) @ A2) @ B2) => ((((ord_less @ A) @ B2) @ C2) => (((ord_less @ A) @ A2) @ C2))))))))).
% 3.41/1.98  thf(fact_109_less__imp__not__less, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y2:A]: (((((ord_less @ A) @ X2) @ Y2) => (~ ((((ord_less @ A) @ Y2) @ X2)))))))))).
% 3.41/1.98  thf(fact_110_exists__least__iff, axiom, (! [A:$tType]: (((wellorder @ A) => ((^ [P3:(A > $o)]: ((? [X5:A]: ((P3 @ X5))))) = (^ [P4:(A > $o)]: ((? [N2:A]: (((P4 @ N2) & (! [M2:A]: (((((ord_less @ A) @ M2) @ N2) => (~ ((P4 @ M2)))))))))))))))).
% 3.41/1.98  thf(fact_111_linorder__less__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > (A > $o)),A2:A,B2:A]: (((! [A7:A,B7:A]: (((((ord_less @ A) @ A7) @ B7) => ((P @ A7) @ B7)))) => ((! [A7:A]: (((P @ A7) @ A7))) => ((! [A7:A,B7:A]: ((((P @ B7) @ A7) => ((P @ A7) @ B7)))) => ((P @ A2) @ B2)))))))))).
% 3.41/1.98  thf(fact_112_dual__order_Ostrict__trans, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A,C2:A]: (((((ord_less @ A) @ B2) @ A2) => ((((ord_less @ A) @ C2) @ B2) => (((ord_less @ A) @ C2) @ A2))))))))).
% 3.41/1.98  thf(fact_113_not__less__iff__gr__or__eq, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y2:A]: (((~ ((((ord_less @ A) @ X2) @ Y2))) = ((((ord_less @ A) @ Y2) @ X2) | (X2 = Y2))))))))).
% 3.41/1.98  thf(fact_114_order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ A2) @ B2) => (A2 != B2)))))))).
% 3.41/1.98  thf(fact_115_dual__order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A]: (((((ord_less @ A) @ B2) @ A2) => (A2 != B2)))))))).
% 3.41/1.98  thf(fact_116_ex__gt__or__lt, axiom, (! [A:$tType]: (((condit1656338222tinuum @ A) => (! [A2:A]: ((? [B7:A]: (((((ord_less @ A) @ A2) @ B7) | (((ord_less @ A) @ B7) @ A2)))))))))).
% 3.41/1.98  thf(fact_117_complete__real, axiom, (! [S:(set @ real)]: (((? [X3:real]: ((((member @ real) @ X3) @ S))) => ((? [Z:real]: ((! [X4:real]: (((((member @ real) @ X4) @ S) => (((ord_less_eq @ real) @ X4) @ Z)))))) => (? [Y4:real]: (((! [X3:real]: (((((member @ real) @ X3) @ S) => (((ord_less_eq @ real) @ X3) @ Y4)))) & (! [Z:real]: (((! [X4:real]: (((((member @ real) @ X4) @ S) => (((ord_less_eq @ real) @ X4) @ Z)))) => (((ord_less_eq @ real) @ Y4) @ Z)))))))))))).
% 3.41/1.98  thf(fact_118_field__lbound__gt__zero, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [D1:A,D2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ D1) => ((((ord_less @ A) @ (zero_zero @ A)) @ D2) => (? [E:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ E) & ((((ord_less @ A) @ E) @ D1) & (((ord_less @ A) @ E) @ D2))))))))))))).
% 3.41/1.98  thf(fact_119_leD, axiom, (! [A:$tType]: (((order @ A) => (! [Y2:A,X2:A]: (((((ord_less_eq @ A) @ Y2) @ X2) => (~ ((((ord_less @ A) @ X2) @ Y2)))))))))).
% 3.41/1.98  thf(fact_120_leI, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y2:A]: (((~ ((((ord_less @ A) @ X2) @ Y2))) => (((ord_less_eq @ A) @ Y2) @ X2)))))))).
% 3.41/1.98  thf(fact_121_le__less, axiom, (! [A:$tType]: (((order @ A) => ((ord_less_eq @ A) = (^ [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) | (X = Y))))))))).
% 3.41/1.98  thf(fact_122_less__le, axiom, (! [A:$tType]: (((order @ A) => ((ord_less @ A) = (^ [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) & (X != Y))))))))).
% 3.41/1.98  thf(fact_123_order__le__less__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A2:A,F2:(B > A),B2:B,C2:B]: (((((ord_less_eq @ A) @ A2) @ (F2 @ B2)) => ((((ord_less @ B) @ B2) @ C2) => ((! [X4:B,Y4:B]: (((((ord_less @ B) @ X4) @ Y4) => (((ord_less @ A) @ (F2 @ X4)) @ (F2 @ Y4))))) => (((ord_less @ A) @ A2) @ (F2 @ C2))))))))))).
% 3.41/1.98  thf(fact_124_order__le__less__subst2, axiom, (! [A:$tType,C3:$tType]: ((((order @ C3) & (order @ A)) => (! [A2:A,B2:A,F2:(A > C3),C2:C3]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less @ C3) @ (F2 @ B2)) @ C2) => ((! [X4:A,Y4:A]: (((((ord_less_eq @ A) @ X4) @ Y4) => (((ord_less_eq @ C3) @ (F2 @ X4)) @ (F2 @ Y4))))) => (((ord_less @ C3) @ (F2 @ A2)) @ C2)))))))))).
% 3.41/1.98  thf(fact_125_order__less__le__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A2:A,F2:(B > A),B2:B,C2:B]: (((((ord_less @ A) @ A2) @ (F2 @ B2)) => ((((ord_less_eq @ B) @ B2) @ C2) => ((! [X4:B,Y4:B]: (((((ord_less_eq @ B) @ X4) @ Y4) => (((ord_less_eq @ A) @ (F2 @ X4)) @ (F2 @ Y4))))) => (((ord_less @ A) @ A2) @ (F2 @ C2))))))))))).
% 3.41/1.98  thf(fact_126_order__less__le__subst2, axiom, (! [A:$tType,C3:$tType]: ((((order @ C3) & (order @ A)) => (! [A2:A,B2:A,F2:(A > C3),C2:C3]: (((((ord_less @ A) @ A2) @ B2) => ((((ord_less_eq @ C3) @ (F2 @ B2)) @ C2) => ((! [X4:A,Y4:A]: (((((ord_less @ A) @ X4) @ Y4) => (((ord_less @ C3) @ (F2 @ X4)) @ (F2 @ Y4))))) => (((ord_less @ C3) @ (F2 @ A2)) @ C2)))))))))).
% 3.41/1.98  thf(fact_127_not__le, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y2:A]: (((~ ((((ord_less_eq @ A) @ X2) @ Y2))) = (((ord_less @ A) @ Y2) @ X2)))))))).
% 3.41/1.98  thf(fact_128_not__less, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y2:A]: (((~ ((((ord_less @ A) @ X2) @ Y2))) = (((ord_less_eq @ A) @ Y2) @ X2)))))))).
% 3.41/1.98  thf(fact_129_le__neq__trans, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((A2 != B2) => (((ord_less @ A) @ A2) @ B2))))))))).
% 3.41/1.98  thf(fact_130_antisym__conv1, axiom, (! [A:$tType]: (((order @ A) => (! [X2:A,Y2:A]: (((~ ((((ord_less @ A) @ X2) @ Y2))) => ((((ord_less_eq @ A) @ X2) @ Y2) = (X2 = Y2))))))))).
% 3.41/1.98  thf(fact_131_antisym__conv2, axiom, (! [A:$tType]: (((order @ A) => (! [X2:A,Y2:A]: (((((ord_less_eq @ A) @ X2) @ Y2) => ((~ ((((ord_less @ A) @ X2) @ Y2))) = (X2 = Y2))))))))).
% 3.41/1.98  thf(fact_132_less__imp__le, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y2:A]: (((((ord_less @ A) @ X2) @ Y2) => (((ord_less_eq @ A) @ X2) @ Y2)))))))).
% 3.41/1.98  thf(fact_133_le__less__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y2:A,Z3:A]: (((((ord_less_eq @ A) @ X2) @ Y2) => ((((ord_less @ A) @ Y2) @ Z3) => (((ord_less @ A) @ X2) @ Z3))))))))).
% 3.41/1.98  thf(fact_134_less__le__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y2:A,Z3:A]: (((((ord_less @ A) @ X2) @ Y2) => ((((ord_less_eq @ A) @ Y2) @ Z3) => (((ord_less @ A) @ X2) @ Z3))))))))).
% 3.41/1.98  thf(fact_135_dense__ge, axiom, (! [A:$tType]: (((dense_linorder @ A) => (! [Z3:A,Y2:A]: (((! [X4:A]: (((((ord_less @ A) @ Z3) @ X4) => (((ord_less_eq @ A) @ Y2) @ X4)))) => (((ord_less_eq @ A) @ Y2) @ Z3)))))))).
% 3.41/1.98  thf(fact_136_dense__le, axiom, (! [A:$tType]: (((dense_linorder @ A) => (! [Y2:A,Z3:A]: (((! [X4:A]: (((((ord_less @ A) @ X4) @ Y2) => (((ord_less_eq @ A) @ X4) @ Z3)))) => (((ord_less_eq @ A) @ Y2) @ Z3)))))))).
% 3.41/1.98  thf(fact_137_le__less__linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y2:A]: (((((ord_less_eq @ A) @ X2) @ Y2) | (((ord_less @ A) @ Y2) @ X2)))))))).
% 3.41/1.98  thf(fact_138_le__imp__less__or__eq, axiom, (! [A:$tType]: (((order @ A) => (! [X2:A,Y2:A]: (((((ord_less_eq @ A) @ X2) @ Y2) => ((((ord_less @ A) @ X2) @ Y2) | (X2 = Y2))))))))).
% 3.41/1.98  thf(fact_139_less__le__not__le, axiom, (! [A:$tType]: (((preorder @ A) => ((ord_less @ A) = (^ [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) & (~ ((((ord_less_eq @ A) @ Y) @ X))))))))))).
% 3.41/1.98  thf(fact_140_not__le__imp__less, axiom, (! [A:$tType]: (((linorder @ A) => (! [Y2:A,X2:A]: (((~ ((((ord_less_eq @ A) @ Y2) @ X2))) => (((ord_less @ A) @ X2) @ Y2)))))))).
% 3.41/1.98  thf(fact_141_order_Ostrict__trans1, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less @ A) @ B2) @ C2) => (((ord_less @ A) @ A2) @ C2))))))))).
% 3.41/1.98  thf(fact_142_order_Ostrict__trans2, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A,C2:A]: (((((ord_less @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ C2) => (((ord_less @ A) @ A2) @ C2))))))))).
% 3.41/1.98  thf(fact_143_order_Oorder__iff__strict, axiom, (! [A:$tType]: (((order @ A) => ((ord_less_eq @ A) = (^ [A6:A,B5:A]: (((((ord_less @ A) @ A6) @ B5) | (A6 = B5))))))))).
% 3.41/1.98  thf(fact_144_order_Ostrict__iff__order, axiom, (! [A:$tType]: (((order @ A) => ((ord_less @ A) = (^ [A6:A,B5:A]: (((((ord_less_eq @ A) @ A6) @ B5) & (A6 != B5))))))))).
% 3.41/1.98  thf(fact_145_dual__order_Ostrict__trans1, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A,C2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less @ A) @ C2) @ B2) => (((ord_less @ A) @ C2) @ A2))))))))).
% 3.41/1.98  thf(fact_146_dual__order_Ostrict__trans2, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A,C2:A]: (((((ord_less @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ C2) @ B2) => (((ord_less @ A) @ C2) @ A2))))))))).
% 3.41/1.98  thf(fact_147_dense__ge__bounded, axiom, (! [A:$tType]: (((dense_linorder @ A) => (! [Z3:A,X2:A,Y2:A]: (((((ord_less @ A) @ Z3) @ X2) => ((! [W:A]: (((((ord_less @ A) @ Z3) @ W) => ((((ord_less @ A) @ W) @ X2) => (((ord_less_eq @ A) @ Y2) @ W))))) => (((ord_less_eq @ A) @ Y2) @ Z3))))))))).
% 3.41/1.98  thf(fact_148_psubsetI, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B4) => ((A4 != B4) => (((ord_less @ (set @ A)) @ A4) @ B4)))))).
% 3.41/1.98  thf(fact_149_minf_I8_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T2:A]: ((? [Z5:A]: ((! [X3:A]: (((((ord_less @ A) @ X3) @ Z5) => (~ ((((ord_less_eq @ A) @ T2) @ X3)))))))))))))).
% 3.41/1.98  thf(fact_150_minf_I6_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T2:A]: ((? [Z5:A]: ((! [X3:A]: (((((ord_less @ A) @ X3) @ Z5) => (((ord_less_eq @ A) @ X3) @ T2)))))))))))).
% 3.41/1.98  thf(fact_151_pinf_I8_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T2:A]: ((? [Z5:A]: ((! [X3:A]: (((((ord_less @ A) @ Z5) @ X3) => (((ord_less_eq @ A) @ T2) @ X3)))))))))))).
% 3.41/1.98  thf(fact_152_pinf_I6_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T2:A]: ((? [Z5:A]: ((! [X3:A]: (((((ord_less @ A) @ Z5) @ X3) => (~ ((((ord_less_eq @ A) @ X3) @ T2)))))))))))))).
% 3.41/1.98  thf(fact_153_verit__comp__simplify1_I3_J, axiom, (! [B:$tType]: (((linorder @ B) => (! [B8:B,A8:B]: (((~ ((((ord_less_eq @ B) @ B8) @ A8))) = (((ord_less @ B) @ A8) @ B8)))))))).
% 3.41/1.98  thf(fact_154_is__zero__null, axiom, (! [A:$tType]: (((zero @ A) => ((is_zero @ A) = (^ [P5:(poly @ A)]: ((P5 = (zero_zero @ (poly @ A)))))))))).
% 3.41/1.98  thf(fact_155_poly__cutoff__0, axiom, (! [A:$tType]: (((zero @ A) => (! [N:nat]: (((((poly_cutoff @ A) @ N) @ (zero_zero @ (poly @ A))) = (zero_zero @ (poly @ A))))))))).
% 3.41/1.98  thf(fact_156_subsetI, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A)]: (((! [X4:A]: (((((member @ A) @ X4) @ A4) => (((member @ A) @ X4) @ B4)))) => (((ord_less_eq @ (set @ A)) @ A4) @ B4))))).
% 3.41/1.98  thf(fact_157_subset__antisym, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B4) => ((((ord_less_eq @ (set @ A)) @ B4) @ A4) => (A4 = B4)))))).
% 3.41/1.98  thf(fact_158_in__mono, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A),X2:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ B4) => ((((member @ A) @ X2) @ A4) => (((member @ A) @ X2) @ B4)))))).
% 3.41/1.98  thf(fact_159_subsetD, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A),C2:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ B4) => ((((member @ A) @ C2) @ A4) => (((member @ A) @ C2) @ B4)))))).
% 3.41/1.98  thf(fact_160_equalityE, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A)]: (((A4 = B4) => (~ (((((ord_less_eq @ (set @ A)) @ A4) @ B4) => (~ ((((ord_less_eq @ (set @ A)) @ B4) @ A4)))))))))).
% 3.41/1.98  thf(fact_161_subset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A3:(set @ A),B6:(set @ A)]: ((! [X:A]: (((((member @ A) @ X) @ A3) => (((member @ A) @ X) @ B6)))))))))).
% 3.41/1.98  thf(fact_162_equalityD1, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A)]: (((A4 = B4) => (((ord_less_eq @ (set @ A)) @ A4) @ B4))))).
% 3.41/1.98  thf(fact_163_equalityD2, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A)]: (((A4 = B4) => (((ord_less_eq @ (set @ A)) @ B4) @ A4))))).
% 3.41/1.98  thf(fact_164_subset__iff, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A3:(set @ A),B6:(set @ A)]: ((! [T3:A]: (((((member @ A) @ T3) @ A3) => (((member @ A) @ T3) @ B6)))))))))).
% 3.41/1.98  thf(fact_165_subset__refl, axiom, (! [A:$tType,A4:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A4) @ A4)))).
% 3.41/1.98  thf(fact_166_Collect__mono, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X4:A]: (((P @ X4) => (Q @ X4)))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)))))).
% 3.41/1.98  thf(fact_167_subset__trans, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A),C4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B4) => ((((ord_less_eq @ (set @ A)) @ B4) @ C4) => (((ord_less_eq @ (set @ A)) @ A4) @ C4)))))).
% 3.41/1.98  thf(fact_168_set__eq__subset, axiom, (! [A:$tType]: (((^ [Y3:(set @ A),Z4:(set @ A)]: ((Y3 = Z4))) = (^ [A3:(set @ A),B6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B6) & (((ord_less_eq @ (set @ A)) @ B6) @ A3)))))))).
% 3.41/1.98  thf(fact_169_Collect__subset, axiom, (! [A:$tType,A4:(set @ A),P:(A > $o)]: ((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ (^ [X:A]: (((((member @ A) @ X) @ A4) & (P @ X)))))) @ A4)))).
% 3.41/1.98  thf(fact_170_less__eq__set__def, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A3:(set @ A),B6:(set @ A)]: ((((ord_less_eq @ (A > $o)) @ (^ [X:A]: ((((member @ A) @ X) @ A3)))) @ (^ [X:A]: ((((member @ A) @ X) @ B6)))))))))).
% 3.41/1.98  thf(fact_171_Collect__mono__iff, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)) = (! [X:A]: (((P @ X) => (Q @ X)))))))).
% 3.41/1.98  thf(fact_172_less__fun__def, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => ((ord_less @ (A > B)) = (^ [F3:(A > B),G2:(A > B)]: (((((ord_less_eq @ (A > B)) @ F3) @ G2) & (~ ((((ord_less_eq @ (A > B)) @ G2) @ F3))))))))))).
% 3.41/1.98  thf(fact_173_verit__la__disequality, axiom, (! [A:$tType]: (((linorder @ A) => (! [A2:A,B2:A]: (((A2 = B2) | ((~ ((((ord_less_eq @ A) @ A2) @ B2))) | (~ ((((ord_less_eq @ A) @ B2) @ A2))))))))))).
% 3.41/1.98  thf(fact_174_verit__comp__simplify1_I1_J, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A]: ((~ ((((ord_less @ A) @ A2) @ A2))))))))).
% 3.41/1.98  thf(fact_175_pinf_I1_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > $o),P6:(A > $o),Q:(A > $o),Q3:(A > $o)]: (((? [Z:A]: ((! [X4:A]: (((((ord_less @ A) @ Z) @ X4) => ((P @ X4) = (P6 @ X4))))))) => ((? [Z:A]: ((! [X4:A]: (((((ord_less @ A) @ Z) @ X4) => ((Q @ X4) = (Q3 @ X4))))))) => (? [Z5:A]: ((! [X3:A]: (((((ord_less @ A) @ Z5) @ X3) => (((P @ X3) & (Q @ X3)) = ((P6 @ X3) & (Q3 @ X3)))))))))))))))).
% 3.41/1.98  thf(fact_176_pinf_I2_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > $o),P6:(A > $o),Q:(A > $o),Q3:(A > $o)]: (((? [Z:A]: ((! [X4:A]: (((((ord_less @ A) @ Z) @ X4) => ((P @ X4) = (P6 @ X4))))))) => ((? [Z:A]: ((! [X4:A]: (((((ord_less @ A) @ Z) @ X4) => ((Q @ X4) = (Q3 @ X4))))))) => (? [Z5:A]: ((! [X3:A]: (((((ord_less @ A) @ Z5) @ X3) => (((P @ X3) | (Q @ X3)) = ((P6 @ X3) | (Q3 @ X3)))))))))))))))).
% 3.41/1.98  thf(fact_177_pinf_I3_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T2:A]: ((? [Z5:A]: ((! [X3:A]: (((((ord_less @ A) @ Z5) @ X3) => (X3 != T2)))))))))))).
% 3.41/1.98  thf(fact_178_pinf_I4_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T2:A]: ((? [Z5:A]: ((! [X3:A]: (((((ord_less @ A) @ Z5) @ X3) => (X3 != T2)))))))))))).
% 3.41/1.98  thf(fact_179_pinf_I5_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T2:A]: ((? [Z5:A]: ((! [X3:A]: (((((ord_less @ A) @ Z5) @ X3) => (~ ((((ord_less @ A) @ X3) @ T2)))))))))))))).
% 3.41/1.98  thf(fact_180_pinf_I7_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T2:A]: ((? [Z5:A]: ((! [X3:A]: (((((ord_less @ A) @ Z5) @ X3) => (((ord_less @ A) @ T2) @ X3)))))))))))).
% 3.41/1.98  thf(fact_181_pinf_I11_J, axiom, (! [C3:$tType,D3:$tType]: (((ord @ C3) => (! [F4:D3]: ((? [Z5:C3]: ((! [X3:C3]: (((((ord_less @ C3) @ Z5) @ X3) => (F4 = F4)))))))))))).
% 3.41/1.98  thf(fact_182_minf_I1_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > $o),P6:(A > $o),Q:(A > $o),Q3:(A > $o)]: (((? [Z:A]: ((! [X4:A]: (((((ord_less @ A) @ X4) @ Z) => ((P @ X4) = (P6 @ X4))))))) => ((? [Z:A]: ((! [X4:A]: (((((ord_less @ A) @ X4) @ Z) => ((Q @ X4) = (Q3 @ X4))))))) => (? [Z5:A]: ((! [X3:A]: (((((ord_less @ A) @ X3) @ Z5) => (((P @ X3) & (Q @ X3)) = ((P6 @ X3) & (Q3 @ X3)))))))))))))))).
% 3.41/1.98  thf(fact_183_minf_I2_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > $o),P6:(A > $o),Q:(A > $o),Q3:(A > $o)]: (((? [Z:A]: ((! [X4:A]: (((((ord_less @ A) @ X4) @ Z) => ((P @ X4) = (P6 @ X4))))))) => ((? [Z:A]: ((! [X4:A]: (((((ord_less @ A) @ X4) @ Z) => ((Q @ X4) = (Q3 @ X4))))))) => (? [Z5:A]: ((! [X3:A]: (((((ord_less @ A) @ X3) @ Z5) => (((P @ X3) | (Q @ X3)) = ((P6 @ X3) | (Q3 @ X3)))))))))))))))).
% 3.41/1.98  thf(fact_184_minf_I3_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T2:A]: ((? [Z5:A]: ((! [X3:A]: (((((ord_less @ A) @ X3) @ Z5) => (X3 != T2)))))))))))).
% 3.41/1.98  thf(fact_185_minf_I4_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T2:A]: ((? [Z5:A]: ((! [X3:A]: (((((ord_less @ A) @ X3) @ Z5) => (X3 != T2)))))))))))).
% 3.41/1.98  thf(fact_186_minf_I5_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T2:A]: ((? [Z5:A]: ((! [X3:A]: (((((ord_less @ A) @ X3) @ Z5) => (((ord_less @ A) @ X3) @ T2)))))))))))).
% 3.41/1.98  thf(fact_187_minf_I7_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T2:A]: ((? [Z5:A]: ((! [X3:A]: (((((ord_less @ A) @ X3) @ Z5) => (~ ((((ord_less @ A) @ T2) @ X3)))))))))))))).
% 3.41/1.98  thf(fact_188_minf_I11_J, axiom, (! [C3:$tType,D3:$tType]: (((ord @ C3) => (! [F4:D3]: ((? [Z5:C3]: ((! [X3:C3]: (((((ord_less @ C3) @ X3) @ Z5) => (F4 = F4)))))))))))).
% 3.41/1.98  thf(fact_189_conj__le__cong, axiom, (! [X2:int,X6:int,P:$o,P6:$o]: (((X2 = X6) => (((((ord_less_eq @ int) @ (zero_zero @ int)) @ X6) => (P = P6)) => (((((ord_less_eq @ int) @ (zero_zero @ int)) @ X2) & P) = ((((ord_less_eq @ int) @ (zero_zero @ int)) @ X6) & P6))))))).
% 3.41/1.98  thf(fact_190_imp__le__cong, axiom, (! [X2:int,X6:int,P:$o,P6:$o]: (((X2 = X6) => (((((ord_less_eq @ int) @ (zero_zero @ int)) @ X6) => (P = P6)) => (((((ord_less_eq @ int) @ (zero_zero @ int)) @ X2) => P) = ((((ord_less_eq @ int) @ (zero_zero @ int)) @ X6) => P6))))))).
% 3.41/1.98  thf(fact_191_subset__iff__psubset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A3:(set @ A),B6:(set @ A)]: (((((ord_less @ (set @ A)) @ A3) @ B6) | (A3 = B6)))))))).
% 3.41/1.98  thf(fact_192_subset__psubset__trans, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A),C4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B4) => ((((ord_less @ (set @ A)) @ B4) @ C4) => (((ord_less @ (set @ A)) @ A4) @ C4)))))).
% 3.41/1.98  thf(fact_193_subset__not__subset__eq, axiom, (! [A:$tType]: (((ord_less @ (set @ A)) = (^ [A3:(set @ A),B6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B6) & (~ ((((ord_less_eq @ (set @ A)) @ B6) @ A3)))))))))).
% 3.41/1.98  thf(fact_194_psubset__subset__trans, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A),C4:(set @ A)]: (((((ord_less @ (set @ A)) @ A4) @ B4) => ((((ord_less_eq @ (set @ A)) @ B4) @ C4) => (((ord_less @ (set @ A)) @ A4) @ C4)))))).
% 3.41/1.98  thf(fact_195_psubset__imp__subset, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A)]: (((((ord_less @ (set @ A)) @ A4) @ B4) => (((ord_less_eq @ (set @ A)) @ A4) @ B4))))).
% 3.41/1.98  thf(fact_196_psubset__trans, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A),C4:(set @ A)]: (((((ord_less @ (set @ A)) @ A4) @ B4) => ((((ord_less @ (set @ A)) @ B4) @ C4) => (((ord_less @ (set @ A)) @ A4) @ C4)))))).
% 3.41/1.98  thf(fact_197_psubset__eq, axiom, (! [A:$tType]: (((ord_less @ (set @ A)) = (^ [A3:(set @ A),B6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B6) & (A3 != B6)))))))).
% 3.41/1.98  thf(fact_198_psubsetE, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A)]: (((((ord_less @ (set @ A)) @ A4) @ B4) => (~ (((((ord_less_eq @ (set @ A)) @ A4) @ B4) => (((ord_less_eq @ (set @ A)) @ B4) @ A4)))))))).
% 3.41/1.98  thf(fact_199_psubsetD, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A),C2:A]: (((((ord_less @ (set @ A)) @ A4) @ B4) => ((((member @ A) @ C2) @ A4) => (((member @ A) @ C2) @ B4)))))).
% 3.41/1.98  thf(fact_200_less__set__def, axiom, (! [A:$tType]: (((ord_less @ (set @ A)) = (^ [A3:(set @ A),B6:(set @ A)]: ((((ord_less @ (A > $o)) @ (^ [X:A]: ((((member @ A) @ X) @ A3)))) @ (^ [X:A]: ((((member @ A) @ X) @ B6)))))))))).
% 3.41/1.98  thf(fact_201_reflect__poly__at__0__eq__0__iff, axiom, (! [A:$tType]: (((comm_semiring_0 @ A) => (! [P2:(poly @ A)]: ((((((poly2 @ A) @ ((reflect_poly @ A) @ P2)) @ (zero_zero @ A)) = (zero_zero @ A)) = (P2 = (zero_zero @ (poly @ A)))))))))).
% 3.41/1.98  thf(fact_202_jump__poly__not__root, axiom, (! [P2:(poly @ real),X2:real,Q2:(poly @ real)]: ((((((poly2 @ real) @ P2) @ X2) != (zero_zero @ real)) => ((((sturm_652470720p_poly @ Q2) @ P2) @ X2) = (zero_zero @ int)))))).
% 3.41/1.98  thf(fact_203_jump__poly0_I2_J, axiom, (! [Q2:(poly @ real),X2:real]: (((((sturm_652470720p_poly @ Q2) @ (zero_zero @ (poly @ real))) @ X2) = (zero_zero @ int))))).
% 3.41/1.98  thf(fact_204_predicate1I, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X4:A]: (((P @ X4) => (Q @ X4)))) => (((ord_less_eq @ (A > $o)) @ P) @ Q))))).
% 3.41/1.98  thf(fact_205_reflect__poly__0, axiom, (! [A:$tType]: (((zero @ A) => (((reflect_poly @ A) @ (zero_zero @ (poly @ A))) = (zero_zero @ (poly @ A))))))).
% 3.41/1.98  thf(fact_206_jump__poly0_I1_J, axiom, (! [P2:(poly @ real),X2:real]: (((((sturm_652470720p_poly @ (zero_zero @ (poly @ real))) @ P2) @ X2) = (zero_zero @ int))))).
% 3.41/1.98  thf(fact_207_verit__la__generic, axiom, (! [A2:int,X2:int]: (((((ord_less_eq @ int) @ A2) @ X2) | ((A2 = X2) | (((ord_less_eq @ int) @ X2) @ A2)))))).
% 3.41/1.98  thf(fact_208_predicate1D, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o),X2:A]: (((((ord_less_eq @ (A > $o)) @ P) @ Q) => ((P @ X2) => (Q @ X2)))))).
% 3.41/1.98  thf(fact_209_rev__predicate1D, axiom, (! [A:$tType,P:(A > $o),X2:A,Q:(A > $o)]: (((P @ X2) => ((((ord_less_eq @ (A > $o)) @ P) @ Q) => (Q @ X2)))))).
% 3.41/1.98  thf(fact_210_finite__interval__int1, axiom, (! [A2:int,B2:int]: (((finite_finite2 @ int) @ ((collect @ int) @ (^ [I:int]: (((((ord_less_eq @ int) @ A2) @ I) & (((ord_less_eq @ int) @ I) @ B2))))))))).
% 3.41/1.98  thf(fact_211_finite__interval__int2, axiom, (! [A2:int,B2:int]: (((finite_finite2 @ int) @ ((collect @ int) @ (^ [I:int]: (((((ord_less_eq @ int) @ A2) @ I) & (((ord_less @ int) @ I) @ B2))))))))).
% 3.41/1.98  thf(fact_212_finite__interval__int4, axiom, (! [A2:int,B2:int]: (((finite_finite2 @ int) @ ((collect @ int) @ (^ [I:int]: (((((ord_less @ int) @ A2) @ I) & (((ord_less @ int) @ I) @ B2))))))))).
% 3.41/1.98  thf(fact_213_finite__interval__int3, axiom, (! [A2:int,B2:int]: (((finite_finite2 @ int) @ ((collect @ int) @ (^ [I:int]: (((((ord_less @ int) @ A2) @ I) & (((ord_less_eq @ int) @ I) @ B2))))))))).
% 3.41/1.98  thf(fact_214_less__int__code_I1_J, axiom, (~ ((((ord_less @ int) @ (zero_zero @ int)) @ (zero_zero @ int))))).
% 3.41/1.98  thf(fact_215_less__eq__int__code_I1_J, axiom, (((ord_less_eq @ int) @ (zero_zero @ int)) @ (zero_zero @ int))).
% 3.41/1.98  thf(fact_216_pred__subset__eq, axiom, (! [A:$tType,R:(set @ A),S:(set @ A)]: (((((ord_less_eq @ (A > $o)) @ (^ [X:A]: ((((member @ A) @ X) @ R)))) @ (^ [X:A]: ((((member @ A) @ X) @ S)))) = (((ord_less_eq @ (set @ A)) @ R) @ S))))).
% 3.41/1.98  thf(fact_217_cindex__poly__0_I2_J, axiom, (! [A2:real,B2:real,Q2:(poly @ real)]: ((((((sturm_1539314049x_poly @ A2) @ B2) @ Q2) @ (zero_zero @ (poly @ real))) = (zero_zero @ int))))).
% 3.41/1.98  thf(fact_218_cindex__poly__0_I1_J, axiom, (! [A2:real,B2:real,P2:(poly @ real)]: ((((((sturm_1539314049x_poly @ A2) @ B2) @ (zero_zero @ (poly @ real))) @ P2) = (zero_zero @ int))))).
% 3.41/1.98  thf(fact_219_cindex__poly__cross, axiom, (! [A2:real,B2:real,P2:(poly @ real)]: (((((ord_less @ real) @ A2) @ B2) => (((((poly2 @ real) @ P2) @ A2) != (zero_zero @ real)) => (((((poly2 @ real) @ P2) @ B2) != (zero_zero @ real)) => (((((sturm_1539314049x_poly @ A2) @ B2) @ (one_one @ (poly @ real))) @ P2) = (((sturm_424270202_cross @ P2) @ A2) @ B2)))))))).
% 3.41/1.98  thf(fact_220_cindex__poly__def, axiom, (sturm_1539314049x_poly = (^ [A6:real,B5:real,Q4:(poly @ real),P5:(poly @ real)]: (((((groups1340683514dd_sum @ real) @ int) @ ((sturm_652470720p_poly @ Q4) @ P5)) @ ((collect @ real) @ (^ [X:real]: ((((((poly2 @ real) @ P5) @ X) = (zero_zero @ real)) & ((((ord_less @ real) @ A6) @ X) & (((ord_less @ real) @ X) @ B5))))))))))).
% 3.41/1.98  thf(fact_221_reflect__poly__1, axiom, (! [A:$tType]: (((comm_semiring_1 @ A) => (((reflect_poly @ A) @ (one_one @ (poly @ A))) = (one_one @ (poly @ A))))))).
% 3.41/1.98  thf(fact_222_poly__1, axiom, (! [A:$tType]: (((comm_semiring_1 @ A) => (! [X2:A]: (((((poly2 @ A) @ (one_one @ (poly @ A))) @ X2) = (one_one @ A)))))))).
% 3.41/1.98  thf(fact_223_poly__cutoff__1, axiom, (! [A:$tType]: (((comm_semiring_1 @ A) => (! [N:nat]: ((((N = (zero_zero @ nat)) => ((((poly_cutoff @ A) @ N) @ (one_one @ (poly @ A))) = (zero_zero @ (poly @ A)))) & ((N != (zero_zero @ nat)) => ((((poly_cutoff @ A) @ N) @ (one_one @ (poly @ A))) = (one_one @ (poly @ A))))))))))).
% 3.41/1.98  thf(fact_224_le__numeral__extra_I4_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (((ord_less_eq @ A) @ (one_one @ A)) @ (one_one @ A)))))).
% 3.41/1.98  thf(fact_225_poly__sum, axiom, (! [A:$tType,B:$tType]: (((comm_semiring_0 @ A) => (! [P2:(B > (poly @ A)),A4:(set @ B),X2:A]: (((((poly2 @ A) @ ((((groups1340683514dd_sum @ B) @ (poly @ A)) @ P2) @ A4)) @ X2) = ((((groups1340683514dd_sum @ B) @ A) @ (^ [K:B]: ((((poly2 @ A) @ (P2 @ K)) @ X2)))) @ A4)))))))).
% 3.41/1.98  thf(fact_226_one__reorient, axiom, (! [A:$tType]: (((one @ A) => (! [X2:A]: ((((one_one @ A) = X2) = (X2 = (one_one @ A))))))))).
% 3.41/1.98  thf(fact_227_less__numeral__extra_I1_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (((ord_less @ A) @ (zero_zero @ A)) @ (one_one @ A)))))).
% 3.41/1.98  thf(fact_228_less__numeral__extra_I4_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (~ ((((ord_less @ A) @ (one_one @ A)) @ (one_one @ A)))))))).
% 3.41/1.98  thf(fact_229_sum_Odelta_H, axiom, (! [B:$tType,A:$tType]: (((comm_monoid_add @ A) => (! [S:(set @ B),A2:B,B2:(B > A)]: ((((finite_finite2 @ B) @ S) => (((((member @ B) @ A2) @ S) => (((((groups1340683514dd_sum @ B) @ A) @ (^ [K:B]: (((((if @ A) @ (A2 = K)) @ (B2 @ K)) @ (zero_zero @ A))))) @ S) = (B2 @ A2))) & ((~ ((((member @ B) @ A2) @ S))) => (((((groups1340683514dd_sum @ B) @ A) @ (^ [K:B]: (((((if @ A) @ (A2 = K)) @ (B2 @ K)) @ (zero_zero @ A))))) @ S) = (zero_zero @ A))))))))))).
% 3.41/1.98  thf(fact_230_sum_Odelta, axiom, (! [B:$tType,A:$tType]: (((comm_monoid_add @ A) => (! [S:(set @ B),A2:B,B2:(B > A)]: ((((finite_finite2 @ B) @ S) => (((((member @ B) @ A2) @ S) => (((((groups1340683514dd_sum @ B) @ A) @ (^ [K:B]: (((((if @ A) @ (K = A2)) @ (B2 @ K)) @ (zero_zero @ A))))) @ S) = (B2 @ A2))) & ((~ ((((member @ B) @ A2) @ S))) => (((((groups1340683514dd_sum @ B) @ A) @ (^ [K:B]: (((((if @ A) @ (K = A2)) @ (B2 @ K)) @ (zero_zero @ A))))) @ S) = (zero_zero @ A))))))))))).
% 3.41/1.98  thf(fact_231_sum_Oneutral__const, axiom, (! [B:$tType,A:$tType]: (((comm_monoid_add @ A) => (! [A4:(set @ B)]: ((((((groups1340683514dd_sum @ B) @ A) @ (^ [Uu:B]: ((zero_zero @ A)))) @ A4) = (zero_zero @ A)))))))).
% 3.41/1.98  thf(fact_232_sum_Oinfinite, axiom, (! [B:$tType,A:$tType]: (((comm_monoid_add @ A) => (! [A4:(set @ B),G:(B > A)]: (((~ (((finite_finite2 @ B) @ A4))) => (((((groups1340683514dd_sum @ B) @ A) @ G) @ A4) = (zero_zero @ A))))))))).
% 3.41/1.98  thf(fact_233_sum__eq__0__iff, axiom, (! [A:$tType,B:$tType]: (((canoni770627133id_add @ A) => (! [F4:(set @ B),F2:(B > A)]: ((((finite_finite2 @ B) @ F4) => ((((((groups1340683514dd_sum @ B) @ A) @ F2) @ F4) = (zero_zero @ A)) = (! [X:B]: (((((member @ B) @ X) @ F4) => ((F2 @ X) = (zero_zero @ A))))))))))))).
% 3.41/1.98  thf(fact_234_sum__eq__1__iff, axiom, (! [A:$tType,A4:(set @ A),F2:(A > nat)]: ((((finite_finite2 @ A) @ A4) => ((((((groups1340683514dd_sum @ A) @ nat) @ F2) @ A4) = (one_one @ nat)) = (? [X:A]: (((((member @ A) @ X) @ A4) & (((F2 @ X) = (one_one @ nat)) & (! [Y:A]: (((((member @ A) @ Y) @ A4) => ((X != Y) => ((F2 @ Y) = (zero_zero @ nat))))))))))))))).
% 3.41/1.98  thf(fact_235_int__one__le__iff__zero__less, axiom, (! [Z3:int]: (((((ord_less_eq @ int) @ (one_one @ int)) @ Z3) = (((ord_less @ int) @ (zero_zero @ int)) @ Z3))))).
% 3.41/1.98  thf(fact_236_sum_Oswap, axiom, (! [A:$tType,B:$tType,C3:$tType]: (((comm_monoid_add @ A) => (! [G:(B > (C3 > A)),B4:(set @ C3),A4:(set @ B)]: ((((((groups1340683514dd_sum @ B) @ A) @ (^ [I:B]: (((((groups1340683514dd_sum @ C3) @ A) @ (G @ I)) @ B4)))) @ A4) = ((((groups1340683514dd_sum @ C3) @ A) @ (^ [J:C3]: (((((groups1340683514dd_sum @ B) @ A) @ (^ [I:B]: (((G @ I) @ J)))) @ A4)))) @ B4)))))))).
% 3.41/1.98  thf(fact_237_sum_Onot__neutral__contains__not__neutral, axiom, (! [B:$tType,A:$tType]: (((comm_monoid_add @ A) => (! [G:(B > A),A4:(set @ B)]: (((((((groups1340683514dd_sum @ B) @ A) @ G) @ A4) != (zero_zero @ A)) => (~ ((! [A7:B]: (((((member @ B) @ A7) @ A4) => ((G @ A7) = (zero_zero @ A)))))))))))))).
% 3.41/1.98  thf(fact_238_sum_Oneutral, axiom, (! [B:$tType,A:$tType]: (((comm_monoid_add @ A) => (! [A4:(set @ B),G:(B > A)]: (((! [X4:B]: (((((member @ B) @ X4) @ A4) => ((G @ X4) = (zero_zero @ A))))) => (((((groups1340683514dd_sum @ B) @ A) @ G) @ A4) = (zero_zero @ A))))))))).
% 3.41/1.98  thf(fact_239_sum__mono, axiom, (! [A:$tType,B:$tType]: (((ordere216010020id_add @ A) => (! [K2:(set @ B),F2:(B > A),G:(B > A)]: (((! [I2:B]: (((((member @ B) @ I2) @ K2) => (((ord_less_eq @ A) @ (F2 @ I2)) @ (G @ I2))))) => (((ord_less_eq @ A) @ ((((groups1340683514dd_sum @ B) @ A) @ F2) @ K2)) @ ((((groups1340683514dd_sum @ B) @ A) @ G) @ K2))))))))).
% 3.41/1.98  thf(fact_240_sum_Oswap__restrict, axiom, (! [A:$tType,B:$tType,C3:$tType]: (((comm_monoid_add @ A) => (! [A4:(set @ B),B4:(set @ C3),G:(B > (C3 > A)),R:(B > (C3 > $o))]: ((((finite_finite2 @ B) @ A4) => (((finite_finite2 @ C3) @ B4) => (((((groups1340683514dd_sum @ B) @ A) @ (^ [X:B]: (((((groups1340683514dd_sum @ C3) @ A) @ (G @ X)) @ ((collect @ C3) @ (^ [Y:C3]: (((((member @ C3) @ Y) @ B4) & ((R @ X) @ Y))))))))) @ A4) = ((((groups1340683514dd_sum @ C3) @ A) @ (^ [Y:C3]: (((((groups1340683514dd_sum @ B) @ A) @ (^ [X:B]: (((G @ X) @ Y)))) @ ((collect @ B) @ (^ [X:B]: (((((member @ B) @ X) @ A4) & ((R @ X) @ Y))))))))) @ B4)))))))))).
% 3.41/1.98  thf(fact_241_sum__nonpos, axiom, (! [B:$tType,A:$tType]: (((ordere216010020id_add @ A) => (! [A4:(set @ B),F2:(B > A)]: (((! [X4:B]: (((((member @ B) @ X4) @ A4) => (((ord_less_eq @ A) @ (F2 @ X4)) @ (zero_zero @ A))))) => (((ord_less_eq @ A) @ ((((groups1340683514dd_sum @ B) @ A) @ F2) @ A4)) @ (zero_zero @ A))))))))).
% 3.41/1.98  thf(fact_242_sum__nonneg, axiom, (! [A:$tType,B:$tType]: (((ordere216010020id_add @ A) => (! [A4:(set @ B),F2:(B > A)]: (((! [X4:B]: (((((member @ B) @ X4) @ A4) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (F2 @ X4))))) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ ((((groups1340683514dd_sum @ B) @ A) @ F2) @ A4))))))))).
% 3.41/1.98  thf(fact_243_sum__mono__inv, axiom, (! [A:$tType,I3:$tType]: (((ordere1818651114id_add @ A) => (! [F2:(I3 > A),I4:(set @ I3),G:(I3 > A),I5:I3]: (((((((groups1340683514dd_sum @ I3) @ A) @ F2) @ I4) = ((((groups1340683514dd_sum @ I3) @ A) @ G) @ I4)) => ((! [I2:I3]: (((((member @ I3) @ I2) @ I4) => (((ord_less_eq @ A) @ (F2 @ I2)) @ (G @ I2))))) => ((((member @ I3) @ I5) @ I4) => (((finite_finite2 @ I3) @ I4) => ((F2 @ I5) = (G @ I5)))))))))))).
% 3.41/1.98  thf(fact_244_sum_Ointer__filter, axiom, (! [A:$tType,B:$tType]: (((comm_monoid_add @ A) => (! [A4:(set @ B),G:(B > A),P:(B > $o)]: ((((finite_finite2 @ B) @ A4) => (((((groups1340683514dd_sum @ B) @ A) @ G) @ ((collect @ B) @ (^ [X:B]: (((((member @ B) @ X) @ A4) & (P @ X)))))) = ((((groups1340683514dd_sum @ B) @ A) @ (^ [X:B]: (((((if @ A) @ (P @ X)) @ (G @ X)) @ (zero_zero @ A))))) @ A4))))))))).
% 3.41/1.98  thf(fact_245_sum__le__included, axiom, (! [B:$tType,A:$tType,C3:$tType]: (((ordere216010020id_add @ A) => (! [S2:(set @ B),T2:(set @ C3),G:(C3 > A),I5:(C3 > B),F2:(B > A)]: ((((finite_finite2 @ B) @ S2) => (((finite_finite2 @ C3) @ T2) => ((! [X4:C3]: (((((member @ C3) @ X4) @ T2) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (G @ X4))))) => ((! [X4:B]: (((((member @ B) @ X4) @ S2) => (? [Xa:C3]: (((((member @ C3) @ Xa) @ T2) & (((I5 @ Xa) = X4) & (((ord_less_eq @ A) @ (F2 @ X4)) @ (G @ Xa))))))))) => (((ord_less_eq @ A) @ ((((groups1340683514dd_sum @ B) @ A) @ F2) @ S2)) @ ((((groups1340683514dd_sum @ C3) @ A) @ G) @ T2)))))))))))).
% 3.41/1.98  thf(fact_246_sum__nonneg__eq__0__iff, axiom, (! [A:$tType,B:$tType]: (((ordere216010020id_add @ A) => (! [A4:(set @ B),F2:(B > A)]: ((((finite_finite2 @ B) @ A4) => ((! [X4:B]: (((((member @ B) @ X4) @ A4) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (F2 @ X4))))) => ((((((groups1340683514dd_sum @ B) @ A) @ F2) @ A4) = (zero_zero @ A)) = (! [X:B]: (((((member @ B) @ X) @ A4) => ((F2 @ X) = (zero_zero @ A)))))))))))))).
% 3.41/1.98  thf(fact_247_sum__strict__mono__ex1, axiom, (! [A:$tType,I3:$tType]: (((ordere1818651114id_add @ A) => (! [A4:(set @ I3),F2:(I3 > A),G:(I3 > A)]: ((((finite_finite2 @ I3) @ A4) => ((! [X4:I3]: (((((member @ I3) @ X4) @ A4) => (((ord_less_eq @ A) @ (F2 @ X4)) @ (G @ X4))))) => ((? [X3:I3]: (((((member @ I3) @ X3) @ A4) & (((ord_less @ A) @ (F2 @ X3)) @ (G @ X3))))) => (((ord_less @ A) @ ((((groups1340683514dd_sum @ I3) @ A) @ F2) @ A4)) @ ((((groups1340683514dd_sum @ I3) @ A) @ G) @ A4))))))))))).
% 3.41/1.98  thf(fact_248_sum__nonneg__0, axiom, (! [B:$tType,A:$tType]: (((ordere216010020id_add @ A) => (! [S2:(set @ B),F2:(B > A),I5:B]: ((((finite_finite2 @ B) @ S2) => ((! [I2:B]: (((((member @ B) @ I2) @ S2) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (F2 @ I2))))) => ((((((groups1340683514dd_sum @ B) @ A) @ F2) @ S2) = (zero_zero @ A)) => ((((member @ B) @ I5) @ S2) => ((F2 @ I5) = (zero_zero @ A)))))))))))).
% 3.41/1.98  thf(fact_249_sum__nonneg__leq__bound, axiom, (! [B:$tType,A:$tType]: (((ordere216010020id_add @ A) => (! [S2:(set @ B),F2:(B > A),B4:A,I5:B]: ((((finite_finite2 @ B) @ S2) => ((! [I2:B]: (((((member @ B) @ I2) @ S2) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (F2 @ I2))))) => ((((((groups1340683514dd_sum @ B) @ A) @ F2) @ S2) = B4) => ((((member @ B) @ I5) @ S2) => (((ord_less_eq @ A) @ (F2 @ I5)) @ B4))))))))))).
% 3.41/1.98  thf(fact_250_sum__pos2, axiom, (! [A:$tType,B:$tType]: (((ordere216010020id_add @ A) => (! [I4:(set @ B),I5:B,F2:(B > A)]: ((((finite_finite2 @ B) @ I4) => ((((member @ B) @ I5) @ I4) => ((((ord_less @ A) @ (zero_zero @ A)) @ (F2 @ I5)) => ((! [I2:B]: (((((member @ B) @ I2) @ I4) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (F2 @ I2))))) => (((ord_less @ A) @ (zero_zero @ A)) @ ((((groups1340683514dd_sum @ B) @ A) @ F2) @ I4)))))))))))).
% 3.41/1.98  thf(fact_251_not__one__less__zero, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (~ ((((ord_less @ A) @ (one_one @ A)) @ (zero_zero @ A)))))))).
% 3.41/1.98  thf(fact_252_zero__less__one, axiom, (! [A:$tType]: (((zero_less_one @ A) => (((ord_less @ A) @ (zero_zero @ A)) @ (one_one @ A)))))).
% 3.41/1.98  thf(fact_253_linorder__neqE__linordered__idom, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [X2:A,Y2:A]: (((X2 != Y2) => ((~ ((((ord_less @ A) @ X2) @ Y2))) => (((ord_less @ A) @ Y2) @ X2))))))))).
% 3.41/1.98  thf(tcon_Polynomial_Opoly___Rings_Oidom, axiom, (! [A9:$tType]: (((idom @ A9) => (idom @ (poly @ A9)))))).
% 3.41/1.98  thf(tcon_Real_Oreal___Rings_Oidom_1, axiom, (idom @ real)).
% 3.41/1.98  thf(tcon_Int_Oint___Rings_Oidom_2, axiom, (idom @ int)).
% 3.41/1.98  thf(tcon_fun___Orderings_Opreorder, axiom, (! [A9:$tType,A10:$tType]: (((preorder @ A10) => (preorder @ (A9 > A10)))))).
% 3.41/1.98  thf(tcon_fun___Finite__Set_Ofinite, axiom, (! [A9:$tType,A10:$tType]: ((((finite_finite @ A9) & (finite_finite @ A10)) => (finite_finite @ (A9 > A10)))))).
% 3.41/1.98  thf(tcon_fun___Orderings_Oorder, axiom, (! [A9:$tType,A10:$tType]: (((order @ A10) => (order @ (A9 > A10)))))).
% 3.41/1.98  thf(tcon_fun___Orderings_Oord, axiom, (! [A9:$tType,A10:$tType]: (((ord @ A10) => (ord @ (A9 > A10)))))).
% 3.41/1.98  thf(tcon_Int_Oint___Conditionally__Complete__Lattices_Oconditionally__complete__linorder, axiom, (condit1037483654norder @ int)).
% 3.41/1.98  thf(tcon_Int_Oint___Groups_Oordered__cancel__comm__monoid__add, axiom, (ordere1818651114id_add @ int)).
% 3.41/1.98  thf(tcon_Int_Oint___Rings_Olinordered__nonzero__semiring, axiom, (linord1659791738miring @ int)).
% 3.41/1.98  thf(tcon_Int_Oint___Groups_Oordered__comm__monoid__add, axiom, (ordere216010020id_add @ int)).
% 3.41/1.98  thf(tcon_Int_Oint___Rings_Oring__no__zero__divisors, axiom, (ring_n68954251visors @ int)).
% 3.41/1.98  thf(tcon_Int_Oint___Groups_Ocomm__monoid__add, axiom, (comm_monoid_add @ int)).
% 3.41/1.98  thf(tcon_Int_Oint___Rings_Olinordered__idom, axiom, (linordered_idom @ int)).
% 3.41/1.98  thf(tcon_Int_Oint___Rings_Ocomm__semiring__1, axiom, (comm_semiring_1 @ int)).
% 3.41/1.98  thf(tcon_Int_Oint___Rings_Ocomm__semiring__0, axiom, (comm_semiring_0 @ int)).
% 3.41/1.98  thf(tcon_Int_Oint___Rings_Ozero__less__one, axiom, (zero_less_one @ int)).
% 3.41/1.98  thf(tcon_Int_Oint___Orderings_Opreorder_3, axiom, (preorder @ int)).
% 3.41/1.98  thf(tcon_Int_Oint___Orderings_Olinorder, axiom, (linorder @ int)).
% 3.41/1.98  thf(tcon_Int_Oint___Rings_Ocomm__ring__1, axiom, (comm_ring_1 @ int)).
% 3.41/1.98  thf(tcon_Int_Oint___Orderings_Ono__top, axiom, (no_top @ int)).
% 3.41/1.98  thf(tcon_Int_Oint___Orderings_Ono__bot, axiom, (no_bot @ int)).
% 3.41/1.98  thf(tcon_Int_Oint___Orderings_Oorder_4, axiom, (order @ int)).
% 3.41/1.98  thf(tcon_Int_Oint___Nat_Oring__char__0, axiom, (ring_char_0 @ int)).
% 3.41/1.98  thf(tcon_Int_Oint___Orderings_Oord_5, axiom, (ord @ int)).
% 3.41/1.98  thf(tcon_Int_Oint___Groups_Ozero, axiom, (zero @ int)).
% 3.41/1.98  thf(tcon_Int_Oint___Groups_Oone, axiom, (one @ int)).
% 3.41/1.98  thf(tcon_Nat_Onat___Conditionally__Complete__Lattices_Oconditionally__complete__linorder_6, axiom, (condit1037483654norder @ nat)).
% 3.41/1.98  thf(tcon_Nat_Onat___Groups_Oordered__cancel__comm__monoid__add_7, axiom, (ordere1818651114id_add @ nat)).
% 3.41/1.98  thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, axiom, (canoni770627133id_add @ nat)).
% 3.41/1.98  thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring_8, axiom, (linord1659791738miring @ nat)).
% 3.41/1.98  thf(tcon_Nat_Onat___Groups_Oordered__comm__monoid__add_9, axiom, (ordere216010020id_add @ nat)).
% 3.41/1.98  thf(tcon_Nat_Onat___Groups_Ocomm__monoid__add_10, axiom, (comm_monoid_add @ nat)).
% 3.41/1.98  thf(tcon_Nat_Onat___Rings_Ocomm__semiring__1_11, axiom, (comm_semiring_1 @ nat)).
% 3.41/1.98  thf(tcon_Nat_Onat___Rings_Ocomm__semiring__0_12, axiom, (comm_semiring_0 @ nat)).
% 3.41/1.98  thf(tcon_Nat_Onat___Rings_Ozero__less__one_13, axiom, (zero_less_one @ nat)).
% 3.41/1.98  thf(tcon_Nat_Onat___Orderings_Owellorder, axiom, (wellorder @ nat)).
% 3.41/1.98  thf(tcon_Nat_Onat___Orderings_Opreorder_14, axiom, (preorder @ nat)).
% 3.41/1.98  thf(tcon_Nat_Onat___Orderings_Olinorder_15, axiom, (linorder @ nat)).
% 3.41/1.98  thf(tcon_Nat_Onat___Orderings_Ono__top_16, axiom, (no_top @ nat)).
% 3.41/1.98  thf(tcon_Nat_Onat___Orderings_Oorder_17, axiom, (order @ nat)).
% 3.41/1.98  thf(tcon_Nat_Onat___Orderings_Oord_18, axiom, (ord @ nat)).
% 3.41/1.98  thf(tcon_Nat_Onat___Groups_Ozero_19, axiom, (zero @ nat)).
% 3.41/1.98  thf(tcon_Nat_Onat___Groups_Oone_20, axiom, (one @ nat)).
% 3.41/1.98  thf(tcon_Set_Oset___Orderings_Opreorder_21, axiom, (! [A9:$tType]: ((preorder @ (set @ A9))))).
% 3.41/1.98  thf(tcon_Set_Oset___Finite__Set_Ofinite_22, axiom, (! [A9:$tType]: (((finite_finite @ A9) => (finite_finite @ (set @ A9)))))).
% 3.41/1.98  thf(tcon_Set_Oset___Orderings_Oorder_23, axiom, (! [A9:$tType]: ((order @ (set @ A9))))).
% 3.41/1.98  thf(tcon_Set_Oset___Orderings_Oord_24, axiom, (! [A9:$tType]: ((ord @ (set @ A9))))).
% 3.41/1.98  thf(tcon_HOL_Obool___Orderings_Opreorder_25, axiom, (preorder @ $o)).
% 3.41/1.98  thf(tcon_HOL_Obool___Orderings_Olinorder_26, axiom, (linorder @ $o)).
% 3.41/1.98  thf(tcon_HOL_Obool___Finite__Set_Ofinite_27, axiom, (finite_finite @ $o)).
% 3.41/1.98  thf(tcon_HOL_Obool___Orderings_Oorder_28, axiom, (order @ $o)).
% 3.41/1.98  thf(tcon_HOL_Obool___Orderings_Oord_29, axiom, (ord @ $o)).
% 3.41/1.98  thf(tcon_Real_Oreal___Conditionally__Complete__Lattices_Oconditionally__complete__linorder_30, axiom, (condit1037483654norder @ real)).
% 3.41/1.98  thf(tcon_Real_Oreal___Conditionally__Complete__Lattices_Olinear__continuum, axiom, (condit1656338222tinuum @ real)).
% 3.41/1.98  thf(tcon_Real_Oreal___Groups_Oordered__cancel__comm__monoid__add_31, axiom, (ordere1818651114id_add @ real)).
% 3.41/1.98  thf(tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring_32, axiom, (linord1659791738miring @ real)).
% 3.41/1.98  thf(tcon_Real_Oreal___Groups_Oordered__comm__monoid__add_33, axiom, (ordere216010020id_add @ real)).
% 3.41/1.98  thf(tcon_Real_Oreal___Rings_Oring__no__zero__divisors_34, axiom, (ring_n68954251visors @ real)).
% 3.41/1.98  thf(tcon_Real_Oreal___Orderings_Odense__linorder, axiom, (dense_linorder @ real)).
% 3.41/1.98  thf(tcon_Real_Oreal___Fields_Olinordered__field, axiom, (linordered_field @ real)).
% 3.41/1.98  thf(tcon_Real_Oreal___Groups_Ocomm__monoid__add_35, axiom, (comm_monoid_add @ real)).
% 3.41/1.98  thf(tcon_Real_Oreal___Rings_Olinordered__idom_36, axiom, (linordered_idom @ real)).
% 3.41/1.98  thf(tcon_Real_Oreal___Rings_Ocomm__semiring__1_37, axiom, (comm_semiring_1 @ real)).
% 3.41/1.98  thf(tcon_Real_Oreal___Rings_Ocomm__semiring__0_38, axiom, (comm_semiring_0 @ real)).
% 3.41/1.98  thf(tcon_Real_Oreal___Orderings_Odense__order, axiom, (dense_order @ real)).
% 3.41/1.98  thf(tcon_Real_Oreal___Rings_Ozero__less__one_39, axiom, (zero_less_one @ real)).
% 3.41/1.98  thf(tcon_Real_Oreal___Orderings_Opreorder_40, axiom, (preorder @ real)).
% 3.41/1.98  thf(tcon_Real_Oreal___Orderings_Olinorder_41, axiom, (linorder @ real)).
% 3.41/1.98  thf(tcon_Real_Oreal___Rings_Ocomm__ring__1_42, axiom, (comm_ring_1 @ real)).
% 3.41/1.98  thf(tcon_Real_Oreal___Orderings_Ono__top_43, axiom, (no_top @ real)).
% 3.41/1.98  thf(tcon_Real_Oreal___Orderings_Ono__bot_44, axiom, (no_bot @ real)).
% 3.41/1.98  thf(tcon_Real_Oreal___Orderings_Oorder_45, axiom, (order @ real)).
% 3.41/1.98  thf(tcon_Real_Oreal___Nat_Oring__char__0_46, axiom, (ring_char_0 @ real)).
% 3.41/1.98  thf(tcon_Real_Oreal___Orderings_Oord_47, axiom, (ord @ real)).
% 3.41/1.98  thf(tcon_Real_Oreal___Groups_Ozero_48, axiom, (zero @ real)).
% 3.41/1.98  thf(tcon_Real_Oreal___Groups_Oone_49, axiom, (one @ real)).
% 3.41/1.98  thf(tcon_Polynomial_Opoly___Groups_Oordered__cancel__comm__monoid__add_50, axiom, (! [A9:$tType]: (((linordered_idom @ A9) => (ordere1818651114id_add @ (poly @ A9)))))).
% 3.41/1.98  thf(tcon_Polynomial_Opoly___Rings_Olinordered__nonzero__semiring_51, axiom, (! [A9:$tType]: (((linordered_idom @ A9) => (linord1659791738miring @ (poly @ A9)))))).
% 3.41/1.98  thf(tcon_Polynomial_Opoly___Groups_Oordered__comm__monoid__add_52, axiom, (! [A9:$tType]: (((linordered_idom @ A9) => (ordere216010020id_add @ (poly @ A9)))))).
% 3.41/1.98  thf(tcon_Polynomial_Opoly___Rings_Oring__no__zero__divisors_53, axiom, (! [A9:$tType]: (((idom @ A9) => (ring_n68954251visors @ (poly @ A9)))))).
% 3.41/1.98  thf(tcon_Polynomial_Opoly___Groups_Ocomm__monoid__add_54, axiom, (! [A9:$tType]: (((comm_monoid_add @ A9) => (comm_monoid_add @ (poly @ A9)))))).
% 3.41/1.98  thf(tcon_Polynomial_Opoly___Rings_Olinordered__idom_55, axiom, (! [A9:$tType]: (((linordered_idom @ A9) => (linordered_idom @ (poly @ A9)))))).
% 3.41/1.98  thf(tcon_Polynomial_Opoly___Rings_Ocomm__semiring__1_56, axiom, (! [A9:$tType]: (((comm_semiring_1 @ A9) => (comm_semiring_1 @ (poly @ A9)))))).
% 3.41/1.98  thf(tcon_Polynomial_Opoly___Rings_Ocomm__semiring__0_57, axiom, (! [A9:$tType]: (((comm_semiring_0 @ A9) => (comm_semiring_0 @ (poly @ A9)))))).
% 3.41/1.98  thf(tcon_Polynomial_Opoly___Rings_Ozero__less__one_58, axiom, (! [A9:$tType]: (((linordered_idom @ A9) => (zero_less_one @ (poly @ A9)))))).
% 3.41/1.98  thf(tcon_Polynomial_Opoly___Orderings_Opreorder_59, axiom, (! [A9:$tType]: (((linordered_idom @ A9) => (preorder @ (poly @ A9)))))).
% 3.41/1.98  thf(tcon_Polynomial_Opoly___Orderings_Olinorder_60, axiom, (! [A9:$tType]: (((linordered_idom @ A9) => (linorder @ (poly @ A9)))))).
% 3.41/1.98  thf(tcon_Polynomial_Opoly___Rings_Ocomm__ring__1_61, axiom, (! [A9:$tType]: (((comm_ring_1 @ A9) => (comm_ring_1 @ (poly @ A9)))))).
% 3.41/1.98  thf(tcon_Polynomial_Opoly___Orderings_Oorder_62, axiom, (! [A9:$tType]: (((linordered_idom @ A9) => (order @ (poly @ A9)))))).
% 3.41/1.98  thf(tcon_Polynomial_Opoly___Nat_Oring__char__0_63, axiom, (! [A9:$tType]: ((((ring_char_0 @ A9) & (comm_ring_1 @ A9)) => (ring_char_0 @ (poly @ A9)))))).
% 3.41/1.98  thf(tcon_Polynomial_Opoly___Orderings_Oord_64, axiom, (! [A9:$tType]: (((linordered_idom @ A9) => (ord @ (poly @ A9)))))).
% 3.41/1.98  thf(tcon_Polynomial_Opoly___Groups_Ozero_65, axiom, (! [A9:$tType]: (((zero @ A9) => (zero @ (poly @ A9)))))).
% 3.41/1.98  thf(tcon_Polynomial_Opoly___Groups_Oone_66, axiom, (! [A9:$tType]: (((comm_semiring_1 @ A9) => (one @ (poly @ A9)))))).
% 3.41/1.98  thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 3.41/1.98  thf(help_If_2_1_T, axiom, (! [A:$tType,X2:A,Y2:A]: ((((((if @ A) @ $false) @ X2) @ Y2) = Y2)))).
% 3.41/1.98  thf(help_If_1_1_T, axiom, (! [A:$tType,X2:A,Y2:A]: ((((((if @ A) @ $true) @ X2) @ Y2) = X2)))).
% 3.41/1.98  thf(conj_0, conjecture, ((finite_finite2 @ real) @ ((collect @ real) @ (^ [X:real]: ((((((poly2 @ real) @ p) @ X) = (zero_zero @ real)) & ((((ord_less @ real) @ a) @ X) & (((ord_less @ real) @ X) @ b)))))))).
% 3.41/1.98  % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.BBanjbptkj/DTF2DTF1969.p
% 3.41/1.98  ------------------------
% 3.67/2.03  ---- Cleaned THF ---
% 3.67/2.03  thf(ty_t_Polynomial_Opoly,type,
% 3.67/2.03      poly: $tType > $tType ).
% 3.67/2.03  
% 3.67/2.03  thf(ty_t_Real_Oreal,type,
% 3.67/2.03      real: $tType ).
% 3.67/2.03  
% 3.67/2.03  thf(ty_t_Set_Oset,type,
% 3.67/2.03      set: $tType > $tType ).
% 3.67/2.03  
% 3.67/2.03  thf(ty_t_Nat_Onat,type,
% 3.67/2.03      nat: $tType ).
% 3.67/2.03  
% 3.67/2.03  thf(ty_t_Int_Oint,type,
% 3.67/2.03      int: $tType ).
% 3.67/2.03  
% 3.67/2.03  thf(sy_cl_Rings_Oidom,type,
% 3.67/2.03      idom: 
% 3.67/2.03        !>[A: $tType] : $o ).
% 3.67/2.03  
% 3.67/2.03  thf(sy_cl_HOL_Otype,type,
% 3.67/2.03      type: 
% 3.67/2.03        !>[A: $tType] : $o ).
% 3.67/2.03  
% 3.67/2.03  thf(sy_cl_Groups_Oone,type,
% 3.67/2.03      one: 
% 3.67/2.03        !>[A: $tType] : $o ).
% 3.67/2.03  
% 3.67/2.03  thf(sy_cl_Groups_Ozero,type,
% 3.67/2.03      zero: 
% 3.67/2.03        !>[A: $tType] : $o ).
% 3.67/2.03  
% 3.67/2.03  thf(sy_cl_Orderings_Oord,type,
% 3.67/2.03      ord: 
% 3.67/2.03        !>[A: $tType] : $o ).
% 3.67/2.03  
% 3.67/2.03  thf(sy_cl_Nat_Oring__char__0,type,
% 3.67/2.03      ring_char_0: 
% 3.67/2.03        !>[A: $tType] : $o ).
% 3.67/2.03  
% 3.67/2.03  thf(sy_cl_Orderings_Oorder,type,
% 3.67/2.03      order: 
% 3.67/2.03        !>[A: $tType] : $o ).
% 3.67/2.03  
% 3.67/2.03  thf(sy_cl_Orderings_Ono__bot,type,
% 3.67/2.03      no_bot: 
% 3.67/2.03        !>[A: $tType] : $o ).
% 3.67/2.03  
% 3.67/2.03  thf(sy_cl_Orderings_Ono__top,type,
% 3.67/2.03      no_top: 
% 3.67/2.03        !>[A: $tType] : $o ).
% 3.67/2.03  
% 3.67/2.03  thf(sy_cl_Finite__Set_Ofinite,type,
% 3.67/2.03      finite_finite: 
% 3.67/2.03        !>[A: $tType] : $o ).
% 3.67/2.03  
% 3.67/2.03  thf(sy_cl_Rings_Ocomm__ring__1,type,
% 3.67/2.03      comm_ring_1: 
% 3.67/2.03        !>[A: $tType] : $o ).
% 3.67/2.03  
% 3.67/2.03  thf(sy_cl_Orderings_Olinorder,type,
% 3.67/2.03      linorder: 
% 3.67/2.03        !>[A: $tType] : $o ).
% 3.67/2.03  
% 3.67/2.03  thf(sy_cl_Orderings_Opreorder,type,
% 3.67/2.03      preorder: 
% 3.67/2.03        !>[A: $tType] : $o ).
% 3.67/2.03  
% 3.67/2.03  thf(sy_cl_Orderings_Owellorder,type,
% 3.67/2.03      wellorder: 
% 3.67/2.03        !>[A: $tType] : $o ).
% 3.67/2.03  
% 3.67/2.03  thf(sy_cl_Rings_Ozero__less__one,type,
% 3.67/2.03      zero_less_one: 
% 3.67/2.03        !>[A: $tType] : $o ).
% 3.67/2.03  
% 3.67/2.03  thf(sy_cl_Orderings_Odense__order,type,
% 3.67/2.03      dense_order: 
% 3.67/2.03        !>[A: $tType] : $o ).
% 3.67/2.03  
% 3.67/2.03  thf(sy_cl_Rings_Ocomm__semiring__0,type,
% 3.67/2.03      comm_semiring_0: 
% 3.67/2.03        !>[A: $tType] : $o ).
% 3.67/2.03  
% 3.67/2.03  thf(sy_cl_Rings_Ocomm__semiring__1,type,
% 3.67/2.03      comm_semiring_1: 
% 3.67/2.03        !>[A: $tType] : $o ).
% 3.67/2.03  
% 3.67/2.03  thf(sy_cl_Rings_Olinordered__idom,type,
% 3.67/2.03      linordered_idom: 
% 3.67/2.03        !>[A: $tType] : $o ).
% 3.67/2.03  
% 3.67/2.03  thf(sy_cl_Groups_Ocomm__monoid__add,type,
% 3.67/2.03      comm_monoid_add: 
% 3.67/2.03        !>[A: $tType] : $o ).
% 3.67/2.03  
% 3.67/2.03  thf(sy_cl_Fields_Olinordered__field,type,
% 3.67/2.03      linordered_field: 
% 3.67/2.03        !>[A: $tType] : $o ).
% 3.67/2.03  
% 3.67/2.03  thf(sy_cl_Orderings_Odense__linorder,type,
% 3.67/2.03      dense_linorder: 
% 3.67/2.03        !>[A: $tType] : $o ).
% 3.67/2.03  
% 3.67/2.03  thf(sy_cl_Rings_Oring__no__zero__divisors,type,
% 3.67/2.04      ring_n68954251visors: 
% 3.67/2.04        !>[A: $tType] : $o ).
% 3.67/2.04  
% 3.67/2.04  thf(sy_cl_Groups_Oordered__comm__monoid__add,type,
% 3.67/2.04      ordere216010020id_add: 
% 3.67/2.04        !>[A: $tType] : $o ).
% 3.67/2.04  
% 3.67/2.04  thf(sy_cl_Rings_Olinordered__nonzero__semiring,type,
% 3.67/2.04      linord1659791738miring: 
% 3.67/2.04        !>[A: $tType] : $o ).
% 3.67/2.04  
% 3.67/2.04  thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 3.67/2.04      canoni770627133id_add: 
% 3.67/2.04        !>[A: $tType] : $o ).
% 3.67/2.04  
% 3.67/2.04  thf(sy_cl_Groups_Oordered__cancel__comm__monoid__add,type,
% 3.67/2.04      ordere1818651114id_add: 
% 3.67/2.04        !>[A: $tType] : $o ).
% 3.67/2.04  
% 3.67/2.04  thf(sy_cl_Conditionally__Complete__Lattices_Olinear__continuum,type,
% 3.67/2.04      condit1656338222tinuum: 
% 3.67/2.04        !>[A: $tType] : $o ).
% 3.67/2.04  
% 3.67/2.04  thf(sy_cl_Conditionally__Complete__Lattices_Oconditionally__complete__linorder,type,
% 3.67/2.04      condit1037483654norder: 
% 3.67/2.04        !>[A: $tType] : $o ).
% 3.67/2.04  
% 3.67/2.04  thf(sy_c_Finite__Set_Ofinite,type,
% 3.67/2.04      finite_finite2: 
% 3.67/2.04        !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 3.67/2.04  
% 3.67/2.04  thf(sy_c_Groups_Oone__class_Oone,type,
% 3.67/2.04      one_one: 
% 3.67/2.04        !>[A: $tType] : A ).
% 3.67/2.04  
% 3.67/2.04  thf(sy_c_Groups_Ozero__class_Ozero,type,
% 3.67/2.04      zero_zero: 
% 3.67/2.04        !>[A: $tType] : A ).
% 3.67/2.04  
% 3.67/2.04  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum,type,
% 3.67/2.04      groups1340683514dd_sum: 
% 3.67/2.04        !>[B: $tType,A: $tType] : ( ( B > A ) > ( set @ B ) > A ) ).
% 3.67/2.04  
% 3.67/2.04  thf(sy_c_If,type,
% 3.67/2.04      if: 
% 3.67/2.04        !>[A: $tType] : ( $o > A > A > A ) ).
% 3.67/2.04  
% 3.67/2.04  thf(sy_c_Orderings_Oord__class_Oless,type,
% 3.67/2.04      ord_less: 
% 3.67/2.04        !>[A: $tType] : ( A > A > $o ) ).
% 3.67/2.04  
% 3.67/2.04  thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 3.67/2.04      ord_less_eq: 
% 3.67/2.04        !>[A: $tType] : ( A > A > $o ) ).
% 3.67/2.04  
% 3.67/2.04  thf(sy_c_Polynomial_Ois__zero,type,
% 3.67/2.04      is_zero: 
% 3.67/2.04        !>[A: $tType] : ( ( poly @ A ) > $o ) ).
% 3.67/2.04  
% 3.67/2.04  thf(sy_c_Polynomial_Opoly,type,
% 3.67/2.04      poly2: 
% 3.67/2.04        !>[A: $tType] : ( ( poly @ A ) > A > A ) ).
% 3.67/2.04  
% 3.67/2.04  thf(sy_c_Polynomial_Opoly__cutoff,type,
% 3.67/2.04      poly_cutoff: 
% 3.67/2.04        !>[A: $tType] : ( nat > ( poly @ A ) > ( poly @ A ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(sy_c_Polynomial_Oreflect__poly,type,
% 3.67/2.04      reflect_poly: 
% 3.67/2.04        !>[A: $tType] : ( ( poly @ A ) > ( poly @ A ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(sy_c_Set_OCollect,type,
% 3.67/2.04      collect: 
% 3.67/2.04        !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(sy_c_Sturm__Tarski__Mirabelle__osyjafhhev_Ocindex__poly,type,
% 3.67/2.04      sturm_1539314049x_poly: real > real > ( poly @ real ) > ( poly @ real ) > int ).
% 3.67/2.04  
% 3.67/2.04  thf(sy_c_Sturm__Tarski__Mirabelle__osyjafhhev_Ocross,type,
% 3.67/2.04      sturm_424270202_cross: ( poly @ real ) > real > real > int ).
% 3.67/2.04  
% 3.67/2.04  thf(sy_c_Sturm__Tarski__Mirabelle__osyjafhhev_Ojump__poly,type,
% 3.67/2.04      sturm_652470720p_poly: ( poly @ real ) > ( poly @ real ) > real > int ).
% 3.67/2.04  
% 3.67/2.04  thf(sy_c_member,type,
% 3.67/2.04      member: 
% 3.67/2.04        !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 3.67/2.04  
% 3.67/2.04  thf(sy_v_a,type,
% 3.67/2.04      a: real ).
% 3.67/2.04  
% 3.67/2.04  thf(sy_v_a_H,type,
% 3.67/2.04      a2: real ).
% 3.67/2.04  
% 3.67/2.04  thf(sy_v_b,type,
% 3.67/2.04      b: real ).
% 3.67/2.04  
% 3.67/2.04  thf(sy_v_b_H,type,
% 3.67/2.04      b2: real ).
% 3.67/2.04  
% 3.67/2.04  thf(sy_v_p,type,
% 3.67/2.04      p: poly @ real ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_0__092_060open_062finite_A_123x_O_Apoly_Ap_Ax_A_061_A0_125_092_060close_062,axiom,
% 3.67/2.04      ( finite_finite2 @ real
% 3.67/2.04      @ ( collect @ real
% 3.67/2.04        @ ^ [X: real] :
% 3.67/2.04            ( ( poly2 @ real @ p @ X )
% 3.67/2.04            = ( zero_zero @ real ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_1_assms_I2_J,axiom,
% 3.67/2.04      ord_less @ real @ a2 @ b2 ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_2_assms_I3_J,axiom,
% 3.67/2.04      ord_less @ real @ b2 @ b ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_3_assms_I1_J,axiom,
% 3.67/2.04      ord_less @ real @ a @ a2 ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_4_False,axiom,
% 3.67/2.04      ( p
% 3.67/2.04     != ( zero_zero @ ( poly @ real ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_5_poly__0,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( comm_semiring_0 @ A )
% 3.67/2.04       => ! [X2: A] :
% 3.67/2.04            ( ( poly2 @ A @ ( zero_zero @ ( poly @ A ) ) @ X2 )
% 3.67/2.04            = ( zero_zero @ A ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_6_not__gr__zero,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( canoni770627133id_add @ A )
% 3.67/2.04       => ! [N: A] :
% 3.67/2.04            ( ( ~ ( ord_less @ A @ ( zero_zero @ A ) @ N ) )
% 3.67/2.04            = ( N
% 3.67/2.04              = ( zero_zero @ A ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_7_assms_I4_J,axiom,
% 3.67/2.04      ! [X3: real] :
% 3.67/2.04        ( ( ( ( ord_less @ real @ a @ X3 )
% 3.67/2.04            & ( ord_less_eq @ real @ X3 @ a2 ) )
% 3.67/2.04          | ( ( ord_less_eq @ real @ b2 @ X3 )
% 3.67/2.04            & ( ord_less @ real @ X3 @ b ) ) )
% 3.67/2.04       => ( ( poly2 @ real @ p @ X3 )
% 3.67/2.04         != ( zero_zero @ real ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_8_finite__Collect__conjI,axiom,
% 3.67/2.04      ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.67/2.04        ( ( ( finite_finite2 @ A @ ( collect @ A @ P ) )
% 3.67/2.04          | ( finite_finite2 @ A @ ( collect @ A @ Q ) ) )
% 3.67/2.04       => ( finite_finite2 @ A
% 3.67/2.04          @ ( collect @ A
% 3.67/2.04            @ ^ [X: A] :
% 3.67/2.04                ( ( P @ X )
% 3.67/2.04                & ( Q @ X ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_9_finite__Collect__disjI,axiom,
% 3.67/2.04      ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.67/2.04        ( ( finite_finite2 @ A
% 3.67/2.04          @ ( collect @ A
% 3.67/2.04            @ ^ [X: A] :
% 3.67/2.04                ( ( P @ X )
% 3.67/2.04                | ( Q @ X ) ) ) )
% 3.67/2.04        = ( ( finite_finite2 @ A @ ( collect @ A @ P ) )
% 3.67/2.04          & ( finite_finite2 @ A @ ( collect @ A @ Q ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_10_poly__roots__finite,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( ( comm_ring_1 @ A )
% 3.67/2.04          & ( ring_n68954251visors @ A ) )
% 3.67/2.04       => ! [P2: poly @ A] :
% 3.67/2.04            ( ( P2
% 3.67/2.04             != ( zero_zero @ ( poly @ A ) ) )
% 3.67/2.04           => ( finite_finite2 @ A
% 3.67/2.04              @ ( collect @ A
% 3.67/2.04                @ ^ [X: A] :
% 3.67/2.04                    ( ( poly2 @ A @ P2 @ X )
% 3.67/2.04                    = ( zero_zero @ A ) ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_11_poly__IVT__neg,axiom,
% 3.67/2.04      ! [A2: real,B2: real,P2: poly @ real] :
% 3.67/2.04        ( ( ord_less @ real @ A2 @ B2 )
% 3.67/2.04       => ( ( ord_less @ real @ ( zero_zero @ real ) @ ( poly2 @ real @ P2 @ A2 ) )
% 3.67/2.04         => ( ( ord_less @ real @ ( poly2 @ real @ P2 @ B2 ) @ ( zero_zero @ real ) )
% 3.67/2.04           => ? [X4: real] :
% 3.67/2.04                ( ( ord_less @ real @ A2 @ X4 )
% 3.67/2.04                & ( ord_less @ real @ X4 @ B2 )
% 3.67/2.04                & ( ( poly2 @ real @ P2 @ X4 )
% 3.67/2.04                  = ( zero_zero @ real ) ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_12_poly__IVT__pos,axiom,
% 3.67/2.04      ! [A2: real,B2: real,P2: poly @ real] :
% 3.67/2.04        ( ( ord_less @ real @ A2 @ B2 )
% 3.67/2.04       => ( ( ord_less @ real @ ( poly2 @ real @ P2 @ A2 ) @ ( zero_zero @ real ) )
% 3.67/2.04         => ( ( ord_less @ real @ ( zero_zero @ real ) @ ( poly2 @ real @ P2 @ B2 ) )
% 3.67/2.04           => ? [X4: real] :
% 3.67/2.04                ( ( ord_less @ real @ A2 @ X4 )
% 3.67/2.04                & ( ord_less @ real @ X4 @ B2 )
% 3.67/2.04                & ( ( poly2 @ real @ P2 @ X4 )
% 3.67/2.04                  = ( zero_zero @ real ) ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_13_finite__code,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( finite_finite @ A )
% 3.67/2.04       => ( ( finite_finite2 @ A )
% 3.67/2.04          = ( ^ [A3: set @ A] : $true ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_14_poly__all__0__iff__0,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( ( ring_char_0 @ A )
% 3.67/2.04          & ( comm_ring_1 @ A )
% 3.67/2.04          & ( ring_n68954251visors @ A ) )
% 3.67/2.04       => ! [P2: poly @ A] :
% 3.67/2.04            ( ( ! [X: A] :
% 3.67/2.04                  ( ( poly2 @ A @ P2 @ X )
% 3.67/2.04                  = ( zero_zero @ A ) ) )
% 3.67/2.04            = ( P2
% 3.67/2.04              = ( zero_zero @ ( poly @ A ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_15_less__numeral__extra_I3_J,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linord1659791738miring @ A )
% 3.67/2.04       => ~ ( ord_less @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_16_le__zero__eq,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( canoni770627133id_add @ A )
% 3.67/2.04       => ! [N: A] :
% 3.67/2.04            ( ( ord_less_eq @ A @ N @ ( zero_zero @ A ) )
% 3.67/2.04            = ( N
% 3.67/2.04              = ( zero_zero @ A ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_17_zero__le,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( canoni770627133id_add @ A )
% 3.67/2.04       => ! [X2: A] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ X2 ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_18_le__numeral__extra_I3_J,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linord1659791738miring @ A )
% 3.67/2.04       => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_19_finite__psubset__induct,axiom,
% 3.67/2.04      ! [A: $tType,A4: set @ A,P: ( set @ A ) > $o] :
% 3.67/2.04        ( ( finite_finite2 @ A @ A4 )
% 3.67/2.04       => ( ! [A5: set @ A] :
% 3.67/2.04              ( ( finite_finite2 @ A @ A5 )
% 3.67/2.04             => ( ! [B3: set @ A] :
% 3.67/2.04                    ( ( ord_less @ ( set @ A ) @ B3 @ A5 )
% 3.67/2.04                   => ( P @ B3 ) )
% 3.67/2.04               => ( P @ A5 ) ) )
% 3.67/2.04         => ( P @ A4 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_20_finite__has__minimal2,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ! [A4: set @ A,A2: A] :
% 3.67/2.04            ( ( finite_finite2 @ A @ A4 )
% 3.67/2.04           => ( ( member @ A @ A2 @ A4 )
% 3.67/2.04             => ? [X4: A] :
% 3.67/2.04                  ( ( member @ A @ X4 @ A4 )
% 3.67/2.04                  & ( ord_less_eq @ A @ X4 @ A2 )
% 3.67/2.04                  & ! [Xa: A] :
% 3.67/2.04                      ( ( member @ A @ Xa @ A4 )
% 3.67/2.04                     => ( ( ord_less_eq @ A @ Xa @ X4 )
% 3.67/2.04                       => ( X4 = Xa ) ) ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_21_finite__has__maximal2,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ! [A4: set @ A,A2: A] :
% 3.67/2.04            ( ( finite_finite2 @ A @ A4 )
% 3.67/2.04           => ( ( member @ A @ A2 @ A4 )
% 3.67/2.04             => ? [X4: A] :
% 3.67/2.04                  ( ( member @ A @ X4 @ A4 )
% 3.67/2.04                  & ( ord_less_eq @ A @ A2 @ X4 )
% 3.67/2.04                  & ! [Xa: A] :
% 3.67/2.04                      ( ( member @ A @ Xa @ A4 )
% 3.67/2.04                     => ( ( ord_less_eq @ A @ X4 @ Xa )
% 3.67/2.04                       => ( X4 = Xa ) ) ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_22_next__non__root__interval,axiom,
% 3.67/2.04      ! [P2: poly @ real,Lb: real] :
% 3.67/2.04        ( ( P2
% 3.67/2.04         != ( zero_zero @ ( poly @ real ) ) )
% 3.67/2.04       => ~ ! [Ub: real] :
% 3.67/2.04              ( ( ord_less @ real @ Lb @ Ub )
% 3.67/2.04             => ~ ! [Z: real] :
% 3.67/2.04                    ( ( ( ord_less @ real @ Lb @ Z )
% 3.67/2.04                      & ( ord_less_eq @ real @ Z @ Ub ) )
% 3.67/2.04                   => ( ( poly2 @ real @ P2 @ Z )
% 3.67/2.04                     != ( zero_zero @ real ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_23_last__non__root__interval,axiom,
% 3.67/2.04      ! [P2: poly @ real,Ub2: real] :
% 3.67/2.04        ( ( P2
% 3.67/2.04         != ( zero_zero @ ( poly @ real ) ) )
% 3.67/2.04       => ~ ! [Lb2: real] :
% 3.67/2.04              ( ( ord_less @ real @ Lb2 @ Ub2 )
% 3.67/2.04             => ~ ! [Z: real] :
% 3.67/2.04                    ( ( ( ord_less_eq @ real @ Lb2 @ Z )
% 3.67/2.04                      & ( ord_less @ real @ Z @ Ub2 ) )
% 3.67/2.04                   => ( ( poly2 @ real @ P2 @ Z )
% 3.67/2.04                     != ( zero_zero @ real ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_24_zero__reorient,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( zero @ A )
% 3.67/2.04       => ! [X2: A] :
% 3.67/2.04            ( ( ( zero_zero @ A )
% 3.67/2.04              = X2 )
% 3.67/2.04            = ( X2
% 3.67/2.04              = ( zero_zero @ A ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_25_finite,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( finite_finite @ A )
% 3.67/2.04       => ! [A4: set @ A] : ( finite_finite2 @ A @ A4 ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_26_finite__set__choice,axiom,
% 3.67/2.04      ! [B: $tType,A: $tType,A4: set @ A,P: A > B > $o] :
% 3.67/2.04        ( ( finite_finite2 @ A @ A4 )
% 3.67/2.04       => ( ! [X4: A] :
% 3.67/2.04              ( ( member @ A @ X4 @ A4 )
% 3.67/2.04             => ? [X_1: B] : ( P @ X4 @ X_1 ) )
% 3.67/2.04         => ? [F: A > B] :
% 3.67/2.04            ! [X3: A] :
% 3.67/2.04              ( ( member @ A @ X3 @ A4 )
% 3.67/2.04             => ( P @ X3 @ ( F @ X3 ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_27_not__eq__pos__or__neg__iff__2,axiom,
% 3.67/2.04      ! [Lb: real,Ub2: real,P2: poly @ real] :
% 3.67/2.04        ( ( ! [Z2: real] :
% 3.67/2.04              ( ( ( ord_less_eq @ real @ Lb @ Z2 )
% 3.67/2.04                & ( ord_less @ real @ Z2 @ Ub2 ) )
% 3.67/2.04             => ( ( poly2 @ real @ P2 @ Z2 )
% 3.67/2.04               != ( zero_zero @ real ) ) ) )
% 3.67/2.04        = ( ! [Z2: real] :
% 3.67/2.04              ( ( ( ord_less_eq @ real @ Lb @ Z2 )
% 3.67/2.04                & ( ord_less @ real @ Z2 @ Ub2 ) )
% 3.67/2.04             => ( ord_less @ real @ ( zero_zero @ real ) @ ( poly2 @ real @ P2 @ Z2 ) ) )
% 3.67/2.04          | ! [Z2: real] :
% 3.67/2.04              ( ( ( ord_less_eq @ real @ Lb @ Z2 )
% 3.67/2.04                & ( ord_less @ real @ Z2 @ Ub2 ) )
% 3.67/2.04             => ( ord_less @ real @ ( poly2 @ real @ P2 @ Z2 ) @ ( zero_zero @ real ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_28_not__eq__pos__or__neg__iff__1,axiom,
% 3.67/2.04      ! [Lb: real,Ub2: real,P2: poly @ real] :
% 3.67/2.04        ( ( ! [Z2: real] :
% 3.67/2.04              ( ( ( ord_less @ real @ Lb @ Z2 )
% 3.67/2.04                & ( ord_less_eq @ real @ Z2 @ Ub2 ) )
% 3.67/2.04             => ( ( poly2 @ real @ P2 @ Z2 )
% 3.67/2.04               != ( zero_zero @ real ) ) ) )
% 3.67/2.04        = ( ! [Z2: real] :
% 3.67/2.04              ( ( ( ord_less @ real @ Lb @ Z2 )
% 3.67/2.04                & ( ord_less_eq @ real @ Z2 @ Ub2 ) )
% 3.67/2.04             => ( ord_less @ real @ ( zero_zero @ real ) @ ( poly2 @ real @ P2 @ Z2 ) ) )
% 3.67/2.04          | ! [Z2: real] :
% 3.67/2.04              ( ( ( ord_less @ real @ Lb @ Z2 )
% 3.67/2.04                & ( ord_less_eq @ real @ Z2 @ Ub2 ) )
% 3.67/2.04             => ( ord_less @ real @ ( poly2 @ real @ P2 @ Z2 ) @ ( zero_zero @ real ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_29_poly__eq__poly__eq__iff,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( ( ring_char_0 @ A )
% 3.67/2.04          & ( comm_ring_1 @ A )
% 3.67/2.04          & ( ring_n68954251visors @ A ) )
% 3.67/2.04       => ! [P2: poly @ A,Q2: poly @ A] :
% 3.67/2.04            ( ( ( poly2 @ A @ P2 )
% 3.67/2.04              = ( poly2 @ A @ Q2 ) )
% 3.67/2.04            = ( P2 = Q2 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_30_pigeonhole__infinite__rel,axiom,
% 3.67/2.04      ! [B: $tType,A: $tType,A4: set @ A,B4: set @ B,R: A > B > $o] :
% 3.67/2.04        ( ~ ( finite_finite2 @ A @ A4 )
% 3.67/2.04       => ( ( finite_finite2 @ B @ B4 )
% 3.67/2.04         => ( ! [X4: A] :
% 3.67/2.04                ( ( member @ A @ X4 @ A4 )
% 3.67/2.04               => ? [Xa: B] :
% 3.67/2.04                    ( ( member @ B @ Xa @ B4 )
% 3.67/2.04                    & ( R @ X4 @ Xa ) ) )
% 3.67/2.04           => ? [X4: B] :
% 3.67/2.04                ( ( member @ B @ X4 @ B4 )
% 3.67/2.04                & ~ ( finite_finite2 @ A
% 3.67/2.04                    @ ( collect @ A
% 3.67/2.04                      @ ^ [A6: A] :
% 3.67/2.04                          ( ( member @ A @ A6 @ A4 )
% 3.67/2.04                          & ( R @ A6 @ X4 ) ) ) ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_31_not__finite__existsD,axiom,
% 3.67/2.04      ! [A: $tType,P: A > $o] :
% 3.67/2.04        ( ~ ( finite_finite2 @ A @ ( collect @ A @ P ) )
% 3.67/2.04       => ? [X_12: A] : ( P @ X_12 ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_32_zero__less__iff__neq__zero,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( canoni770627133id_add @ A )
% 3.67/2.04       => ! [N: A] :
% 3.67/2.04            ( ( ord_less @ A @ ( zero_zero @ A ) @ N )
% 3.67/2.04            = ( N
% 3.67/2.04             != ( zero_zero @ A ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_33_gr__implies__not__zero,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( canoni770627133id_add @ A )
% 3.67/2.04       => ! [M: A,N: A] :
% 3.67/2.04            ( ( ord_less @ A @ M @ N )
% 3.67/2.04           => ( N
% 3.67/2.04             != ( zero_zero @ A ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_34_not__less__zero,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( canoni770627133id_add @ A )
% 3.67/2.04       => ! [N: A] :
% 3.67/2.04            ~ ( ord_less @ A @ N @ ( zero_zero @ A ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_35_gr__zeroI,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( canoni770627133id_add @ A )
% 3.67/2.04       => ! [N: A] :
% 3.67/2.04            ( ( N
% 3.67/2.04             != ( zero_zero @ A ) )
% 3.67/2.04           => ( ord_less @ A @ ( zero_zero @ A ) @ N ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_36_order__refl,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( preorder @ A )
% 3.67/2.04       => ! [X2: A] : ( ord_less_eq @ A @ X2 @ X2 ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_37_cross__no__root,axiom,
% 3.67/2.04      ! [A2: real,B2: real,P2: poly @ real] :
% 3.67/2.04        ( ( ord_less @ real @ A2 @ B2 )
% 3.67/2.04       => ( ! [X4: real] :
% 3.67/2.04              ( ( ( ord_less @ real @ A2 @ X4 )
% 3.67/2.04                & ( ord_less @ real @ X4 @ B2 ) )
% 3.67/2.04             => ( ( poly2 @ real @ P2 @ X4 )
% 3.67/2.04               != ( zero_zero @ real ) ) )
% 3.67/2.04         => ( ( sturm_424270202_cross @ P2 @ A2 @ B2 )
% 3.67/2.04            = ( zero_zero @ int ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_38_less__eq__real__def,axiom,
% 3.67/2.04      ( ( ord_less_eq @ real )
% 3.67/2.04      = ( ^ [X: real,Y: real] :
% 3.67/2.04            ( ( ord_less @ real @ X @ Y )
% 3.67/2.04            | ( X = Y ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_39_complete__interval,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( condit1037483654norder @ A )
% 3.67/2.04       => ! [A2: A,B2: A,P: A > $o] :
% 3.67/2.04            ( ( ord_less @ A @ A2 @ B2 )
% 3.67/2.04           => ( ( P @ A2 )
% 3.67/2.04             => ( ~ ( P @ B2 )
% 3.67/2.04               => ? [C: A] :
% 3.67/2.04                    ( ( ord_less_eq @ A @ A2 @ C )
% 3.67/2.04                    & ( ord_less_eq @ A @ C @ B2 )
% 3.67/2.04                    & ! [X3: A] :
% 3.67/2.04                        ( ( ( ord_less_eq @ A @ A2 @ X3 )
% 3.67/2.04                          & ( ord_less @ A @ X3 @ C ) )
% 3.67/2.04                       => ( P @ X3 ) )
% 3.67/2.04                    & ! [D: A] :
% 3.67/2.04                        ( ! [X4: A] :
% 3.67/2.04                            ( ( ( ord_less_eq @ A @ A2 @ X4 )
% 3.67/2.04                              & ( ord_less @ A @ X4 @ D ) )
% 3.67/2.04                           => ( P @ X4 ) )
% 3.67/2.04                       => ( ord_less_eq @ A @ D @ C ) ) ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_40_order_Onot__eq__order__implies__strict,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ! [A2: A,B2: A] :
% 3.67/2.04            ( ( A2 != B2 )
% 3.67/2.04           => ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.67/2.04             => ( ord_less @ A @ A2 @ B2 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_41_dual__order_Ostrict__implies__order,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ! [B2: A,A2: A] :
% 3.67/2.04            ( ( ord_less @ A @ B2 @ A2 )
% 3.67/2.04           => ( ord_less_eq @ A @ B2 @ A2 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_42_dual__order_Ostrict__iff__order,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ( ( ord_less @ A )
% 3.67/2.04          = ( ^ [B5: A,A6: A] :
% 3.67/2.04                ( ( ord_less_eq @ A @ B5 @ A6 )
% 3.67/2.04                & ( A6 != B5 ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_43_dual__order_Oorder__iff__strict,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ( ( ord_less_eq @ A )
% 3.67/2.04          = ( ^ [B5: A,A6: A] :
% 3.67/2.04                ( ( ord_less @ A @ B5 @ A6 )
% 3.67/2.04                | ( A6 = B5 ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_44_mem__Collect__eq,axiom,
% 3.67/2.04      ! [A: $tType,A2: A,P: A > $o] :
% 3.67/2.04        ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 3.67/2.04        = ( P @ A2 ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_45_Collect__mem__eq,axiom,
% 3.67/2.04      ! [A: $tType,A4: set @ A] :
% 3.67/2.04        ( ( collect @ A
% 3.67/2.04          @ ^ [X: A] : ( member @ A @ X @ A4 ) )
% 3.67/2.04        = A4 ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_46_Collect__cong,axiom,
% 3.67/2.04      ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.67/2.04        ( ! [X4: A] :
% 3.67/2.04            ( ( P @ X4 )
% 3.67/2.04            = ( Q @ X4 ) )
% 3.67/2.04       => ( ( collect @ A @ P )
% 3.67/2.04          = ( collect @ A @ Q ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_47_ext,axiom,
% 3.67/2.04      ! [B: $tType,A: $tType,F2: A > B,G: A > B] :
% 3.67/2.04        ( ! [X4: A] :
% 3.67/2.04            ( ( F2 @ X4 )
% 3.67/2.04            = ( G @ X4 ) )
% 3.67/2.04       => ( F2 = G ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_48_order_Ostrict__implies__order,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ! [A2: A,B2: A] :
% 3.67/2.04            ( ( ord_less @ A @ A2 @ B2 )
% 3.67/2.04           => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_49_dense__le__bounded,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( dense_linorder @ A )
% 3.67/2.04       => ! [X2: A,Y2: A,Z3: A] :
% 3.67/2.04            ( ( ord_less @ A @ X2 @ Y2 )
% 3.67/2.04           => ( ! [W: A] :
% 3.67/2.04                  ( ( ord_less @ A @ X2 @ W )
% 3.67/2.04                 => ( ( ord_less @ A @ W @ Y2 )
% 3.67/2.04                   => ( ord_less_eq @ A @ W @ Z3 ) ) )
% 3.67/2.04             => ( ord_less_eq @ A @ Y2 @ Z3 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_50_finite__Collect__subsets,axiom,
% 3.67/2.04      ! [A: $tType,A4: set @ A] :
% 3.67/2.04        ( ( finite_finite2 @ A @ A4 )
% 3.67/2.04       => ( finite_finite2 @ ( set @ A )
% 3.67/2.04          @ ( collect @ ( set @ A )
% 3.67/2.04            @ ^ [B6: set @ A] : ( ord_less_eq @ ( set @ A ) @ B6 @ A4 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_51_cross__0,axiom,
% 3.67/2.04      ! [A2: real,B2: real] :
% 3.67/2.04        ( ( sturm_424270202_cross @ ( zero_zero @ ( poly @ real ) ) @ A2 @ B2 )
% 3.67/2.04        = ( zero_zero @ int ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_52_finite__subset,axiom,
% 3.67/2.04      ! [A: $tType,A4: set @ A,B4: set @ A] :
% 3.67/2.04        ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 3.67/2.04       => ( ( finite_finite2 @ A @ B4 )
% 3.67/2.04         => ( finite_finite2 @ A @ A4 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_53_infinite__super,axiom,
% 3.67/2.04      ! [A: $tType,S: set @ A,T: set @ A] :
% 3.67/2.04        ( ( ord_less_eq @ ( set @ A ) @ S @ T )
% 3.67/2.04       => ( ~ ( finite_finite2 @ A @ S )
% 3.67/2.04         => ~ ( finite_finite2 @ A @ T ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_54_rev__finite__subset,axiom,
% 3.67/2.04      ! [A: $tType,B4: set @ A,A4: set @ A] :
% 3.67/2.04        ( ( finite_finite2 @ A @ B4 )
% 3.67/2.04       => ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 3.67/2.04         => ( finite_finite2 @ A @ A4 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_55_dual__order_Oantisym,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ! [B2: A,A2: A] :
% 3.67/2.04            ( ( ord_less_eq @ A @ B2 @ A2 )
% 3.67/2.04           => ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.67/2.04             => ( A2 = B2 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_56_dual__order_Oeq__iff,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ( ( ^ [Y3: A,Z4: A] : ( Y3 = Z4 ) )
% 3.67/2.04          = ( ^ [A6: A,B5: A] :
% 3.67/2.04                ( ( ord_less_eq @ A @ B5 @ A6 )
% 3.67/2.04                & ( ord_less_eq @ A @ A6 @ B5 ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_57_dual__order_Otrans,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ! [B2: A,A2: A,C2: A] :
% 3.67/2.04            ( ( ord_less_eq @ A @ B2 @ A2 )
% 3.67/2.04           => ( ( ord_less_eq @ A @ C2 @ B2 )
% 3.67/2.04             => ( ord_less_eq @ A @ C2 @ A2 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_58_linorder__wlog,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linorder @ A )
% 3.67/2.04       => ! [P: A > A > $o,A2: A,B2: A] :
% 3.67/2.04            ( ! [A7: A,B7: A] :
% 3.67/2.04                ( ( ord_less_eq @ A @ A7 @ B7 )
% 3.67/2.04               => ( P @ A7 @ B7 ) )
% 3.67/2.04           => ( ! [A7: A,B7: A] :
% 3.67/2.04                  ( ( P @ B7 @ A7 )
% 3.67/2.04                 => ( P @ A7 @ B7 ) )
% 3.67/2.04             => ( P @ A2 @ B2 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_59_dual__order_Orefl,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_60_order__trans,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( preorder @ A )
% 3.67/2.04       => ! [X2: A,Y2: A,Z3: A] :
% 3.67/2.04            ( ( ord_less_eq @ A @ X2 @ Y2 )
% 3.67/2.04           => ( ( ord_less_eq @ A @ Y2 @ Z3 )
% 3.67/2.04             => ( ord_less_eq @ A @ X2 @ Z3 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_61_order__class_Oorder_Oantisym,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ! [A2: A,B2: A] :
% 3.67/2.04            ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.67/2.04           => ( ( ord_less_eq @ A @ B2 @ A2 )
% 3.67/2.04             => ( A2 = B2 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_62_ord__le__eq__trans,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( ord @ A )
% 3.67/2.04       => ! [A2: A,B2: A,C2: A] :
% 3.67/2.04            ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.67/2.04           => ( ( B2 = C2 )
% 3.67/2.04             => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_63_ord__eq__le__trans,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( ord @ A )
% 3.67/2.04       => ! [A2: A,B2: A,C2: A] :
% 3.67/2.04            ( ( A2 = B2 )
% 3.67/2.04           => ( ( ord_less_eq @ A @ B2 @ C2 )
% 3.67/2.04             => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_64_order__class_Oorder_Oeq__iff,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ( ( ^ [Y3: A,Z4: A] : ( Y3 = Z4 ) )
% 3.67/2.04          = ( ^ [A6: A,B5: A] :
% 3.67/2.04                ( ( ord_less_eq @ A @ A6 @ B5 )
% 3.67/2.04                & ( ord_less_eq @ A @ B5 @ A6 ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_65_antisym__conv,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ! [Y2: A,X2: A] :
% 3.67/2.04            ( ( ord_less_eq @ A @ Y2 @ X2 )
% 3.67/2.04           => ( ( ord_less_eq @ A @ X2 @ Y2 )
% 3.67/2.04              = ( X2 = Y2 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_66_le__cases3,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linorder @ A )
% 3.67/2.04       => ! [X2: A,Y2: A,Z3: A] :
% 3.67/2.04            ( ( ( ord_less_eq @ A @ X2 @ Y2 )
% 3.67/2.04             => ~ ( ord_less_eq @ A @ Y2 @ Z3 ) )
% 3.67/2.04           => ( ( ( ord_less_eq @ A @ Y2 @ X2 )
% 3.67/2.04               => ~ ( ord_less_eq @ A @ X2 @ Z3 ) )
% 3.67/2.04             => ( ( ( ord_less_eq @ A @ X2 @ Z3 )
% 3.67/2.04                 => ~ ( ord_less_eq @ A @ Z3 @ Y2 ) )
% 3.67/2.04               => ( ( ( ord_less_eq @ A @ Z3 @ Y2 )
% 3.67/2.04                   => ~ ( ord_less_eq @ A @ Y2 @ X2 ) )
% 3.67/2.04                 => ( ( ( ord_less_eq @ A @ Y2 @ Z3 )
% 3.67/2.04                     => ~ ( ord_less_eq @ A @ Z3 @ X2 ) )
% 3.67/2.04                   => ~ ( ( ord_less_eq @ A @ Z3 @ X2 )
% 3.67/2.04                       => ~ ( ord_less_eq @ A @ X2 @ Y2 ) ) ) ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_67_order_Otrans,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ! [A2: A,B2: A,C2: A] :
% 3.67/2.04            ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.67/2.04           => ( ( ord_less_eq @ A @ B2 @ C2 )
% 3.67/2.04             => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_68_le__cases,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linorder @ A )
% 3.67/2.04       => ! [X2: A,Y2: A] :
% 3.67/2.04            ( ~ ( ord_less_eq @ A @ X2 @ Y2 )
% 3.67/2.04           => ( ord_less_eq @ A @ Y2 @ X2 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_69_eq__refl,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( preorder @ A )
% 3.67/2.04       => ! [X2: A,Y2: A] :
% 3.67/2.04            ( ( X2 = Y2 )
% 3.67/2.04           => ( ord_less_eq @ A @ X2 @ Y2 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_70_linear,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linorder @ A )
% 3.67/2.04       => ! [X2: A,Y2: A] :
% 3.67/2.04            ( ( ord_less_eq @ A @ X2 @ Y2 )
% 3.67/2.04            | ( ord_less_eq @ A @ Y2 @ X2 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_71_antisym,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ! [X2: A,Y2: A] :
% 3.67/2.04            ( ( ord_less_eq @ A @ X2 @ Y2 )
% 3.67/2.04           => ( ( ord_less_eq @ A @ Y2 @ X2 )
% 3.67/2.04             => ( X2 = Y2 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_72_eq__iff,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ( ( ^ [Y3: A,Z4: A] : ( Y3 = Z4 ) )
% 3.67/2.04          = ( ^ [X: A,Y: A] :
% 3.67/2.04                ( ( ord_less_eq @ A @ X @ Y )
% 3.67/2.04                & ( ord_less_eq @ A @ Y @ X ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_73_ord__le__eq__subst,axiom,
% 3.67/2.04      ! [A: $tType,B: $tType] :
% 3.67/2.04        ( ( ( ord @ B )
% 3.67/2.04          & ( ord @ A ) )
% 3.67/2.04       => ! [A2: A,B2: A,F2: A > B,C2: B] :
% 3.67/2.04            ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.67/2.04           => ( ( ( F2 @ B2 )
% 3.67/2.04                = C2 )
% 3.67/2.04             => ( ! [X4: A,Y4: A] :
% 3.67/2.04                    ( ( ord_less_eq @ A @ X4 @ Y4 )
% 3.67/2.04                   => ( ord_less_eq @ B @ ( F2 @ X4 ) @ ( F2 @ Y4 ) ) )
% 3.67/2.04               => ( ord_less_eq @ B @ ( F2 @ A2 ) @ C2 ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_74_ord__eq__le__subst,axiom,
% 3.67/2.04      ! [A: $tType,B: $tType] :
% 3.67/2.04        ( ( ( ord @ B )
% 3.67/2.04          & ( ord @ A ) )
% 3.67/2.04       => ! [A2: A,F2: B > A,B2: B,C2: B] :
% 3.67/2.04            ( ( A2
% 3.67/2.04              = ( F2 @ B2 ) )
% 3.67/2.04           => ( ( ord_less_eq @ B @ B2 @ C2 )
% 3.67/2.04             => ( ! [X4: B,Y4: B] :
% 3.67/2.04                    ( ( ord_less_eq @ B @ X4 @ Y4 )
% 3.67/2.04                   => ( ord_less_eq @ A @ ( F2 @ X4 ) @ ( F2 @ Y4 ) ) )
% 3.67/2.04               => ( ord_less_eq @ A @ A2 @ ( F2 @ C2 ) ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_75_order__subst2,axiom,
% 3.67/2.04      ! [A: $tType,C3: $tType] :
% 3.67/2.04        ( ( ( order @ C3 )
% 3.67/2.04          & ( order @ A ) )
% 3.67/2.04       => ! [A2: A,B2: A,F2: A > C3,C2: C3] :
% 3.67/2.04            ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.67/2.04           => ( ( ord_less_eq @ C3 @ ( F2 @ B2 ) @ C2 )
% 3.67/2.04             => ( ! [X4: A,Y4: A] :
% 3.67/2.04                    ( ( ord_less_eq @ A @ X4 @ Y4 )
% 3.67/2.04                   => ( ord_less_eq @ C3 @ ( F2 @ X4 ) @ ( F2 @ Y4 ) ) )
% 3.67/2.04               => ( ord_less_eq @ C3 @ ( F2 @ A2 ) @ C2 ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_76_order__subst1,axiom,
% 3.67/2.04      ! [A: $tType,B: $tType] :
% 3.67/2.04        ( ( ( order @ B )
% 3.67/2.04          & ( order @ A ) )
% 3.67/2.04       => ! [A2: A,F2: B > A,B2: B,C2: B] :
% 3.67/2.04            ( ( ord_less_eq @ A @ A2 @ ( F2 @ B2 ) )
% 3.67/2.04           => ( ( ord_less_eq @ B @ B2 @ C2 )
% 3.67/2.04             => ( ! [X4: B,Y4: B] :
% 3.67/2.04                    ( ( ord_less_eq @ B @ X4 @ Y4 )
% 3.67/2.04                   => ( ord_less_eq @ A @ ( F2 @ X4 ) @ ( F2 @ Y4 ) ) )
% 3.67/2.04               => ( ord_less_eq @ A @ A2 @ ( F2 @ C2 ) ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_77_le__fun__def,axiom,
% 3.67/2.04      ! [B: $tType,A: $tType] :
% 3.67/2.04        ( ( ord @ B )
% 3.67/2.04       => ( ( ord_less_eq @ ( A > B ) )
% 3.67/2.04          = ( ^ [F3: A > B,G2: A > B] :
% 3.67/2.04              ! [X: A] : ( ord_less_eq @ B @ ( F3 @ X ) @ ( G2 @ X ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_78_le__funI,axiom,
% 3.67/2.04      ! [B: $tType,A: $tType] :
% 3.67/2.04        ( ( ord @ B )
% 3.67/2.04       => ! [F2: A > B,G: A > B] :
% 3.67/2.04            ( ! [X4: A] : ( ord_less_eq @ B @ ( F2 @ X4 ) @ ( G @ X4 ) )
% 3.67/2.04           => ( ord_less_eq @ ( A > B ) @ F2 @ G ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_79_le__funE,axiom,
% 3.67/2.04      ! [B: $tType,A: $tType] :
% 3.67/2.04        ( ( ord @ B )
% 3.67/2.04       => ! [F2: A > B,G: A > B,X2: A] :
% 3.67/2.04            ( ( ord_less_eq @ ( A > B ) @ F2 @ G )
% 3.67/2.04           => ( ord_less_eq @ B @ ( F2 @ X2 ) @ ( G @ X2 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_80_le__funD,axiom,
% 3.67/2.04      ! [B: $tType,A: $tType] :
% 3.67/2.04        ( ( ord @ B )
% 3.67/2.04       => ! [F2: A > B,G: A > B,X2: A] :
% 3.67/2.04            ( ( ord_less_eq @ ( A > B ) @ F2 @ G )
% 3.67/2.04           => ( ord_less_eq @ B @ ( F2 @ X2 ) @ ( G @ X2 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_81_ord__eq__less__subst,axiom,
% 3.67/2.04      ! [A: $tType,B: $tType] :
% 3.67/2.04        ( ( ( ord @ B )
% 3.67/2.04          & ( ord @ A ) )
% 3.67/2.04       => ! [A2: A,F2: B > A,B2: B,C2: B] :
% 3.67/2.04            ( ( A2
% 3.67/2.04              = ( F2 @ B2 ) )
% 3.67/2.04           => ( ( ord_less @ B @ B2 @ C2 )
% 3.67/2.04             => ( ! [X4: B,Y4: B] :
% 3.67/2.04                    ( ( ord_less @ B @ X4 @ Y4 )
% 3.67/2.04                   => ( ord_less @ A @ ( F2 @ X4 ) @ ( F2 @ Y4 ) ) )
% 3.67/2.04               => ( ord_less @ A @ A2 @ ( F2 @ C2 ) ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_82_ord__less__eq__subst,axiom,
% 3.67/2.04      ! [A: $tType,B: $tType] :
% 3.67/2.04        ( ( ( ord @ B )
% 3.67/2.04          & ( ord @ A ) )
% 3.67/2.04       => ! [A2: A,B2: A,F2: A > B,C2: B] :
% 3.67/2.04            ( ( ord_less @ A @ A2 @ B2 )
% 3.67/2.04           => ( ( ( F2 @ B2 )
% 3.67/2.04                = C2 )
% 3.67/2.04             => ( ! [X4: A,Y4: A] :
% 3.67/2.04                    ( ( ord_less @ A @ X4 @ Y4 )
% 3.67/2.04                   => ( ord_less @ B @ ( F2 @ X4 ) @ ( F2 @ Y4 ) ) )
% 3.67/2.04               => ( ord_less @ B @ ( F2 @ A2 ) @ C2 ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_83_order__less__subst1,axiom,
% 3.67/2.04      ! [A: $tType,B: $tType] :
% 3.67/2.04        ( ( ( order @ B )
% 3.67/2.04          & ( order @ A ) )
% 3.67/2.04       => ! [A2: A,F2: B > A,B2: B,C2: B] :
% 3.67/2.04            ( ( ord_less @ A @ A2 @ ( F2 @ B2 ) )
% 3.67/2.04           => ( ( ord_less @ B @ B2 @ C2 )
% 3.67/2.04             => ( ! [X4: B,Y4: B] :
% 3.67/2.04                    ( ( ord_less @ B @ X4 @ Y4 )
% 3.67/2.04                   => ( ord_less @ A @ ( F2 @ X4 ) @ ( F2 @ Y4 ) ) )
% 3.67/2.04               => ( ord_less @ A @ A2 @ ( F2 @ C2 ) ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_84_order__less__subst2,axiom,
% 3.67/2.04      ! [A: $tType,C3: $tType] :
% 3.67/2.04        ( ( ( order @ C3 )
% 3.67/2.04          & ( order @ A ) )
% 3.67/2.04       => ! [A2: A,B2: A,F2: A > C3,C2: C3] :
% 3.67/2.04            ( ( ord_less @ A @ A2 @ B2 )
% 3.67/2.04           => ( ( ord_less @ C3 @ ( F2 @ B2 ) @ C2 )
% 3.67/2.04             => ( ! [X4: A,Y4: A] :
% 3.67/2.04                    ( ( ord_less @ A @ X4 @ Y4 )
% 3.67/2.04                   => ( ord_less @ C3 @ ( F2 @ X4 ) @ ( F2 @ Y4 ) ) )
% 3.67/2.04               => ( ord_less @ C3 @ ( F2 @ A2 ) @ C2 ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_85_lt__ex,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( no_bot @ A )
% 3.67/2.04       => ! [X2: A] :
% 3.67/2.04          ? [Y4: A] : ( ord_less @ A @ Y4 @ X2 ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_86_gt__ex,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( no_top @ A )
% 3.67/2.04       => ! [X2: A] :
% 3.67/2.04          ? [X_12: A] : ( ord_less @ A @ X2 @ X_12 ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_87_neqE,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linorder @ A )
% 3.67/2.04       => ! [X2: A,Y2: A] :
% 3.67/2.04            ( ( X2 != Y2 )
% 3.67/2.04           => ( ~ ( ord_less @ A @ X2 @ Y2 )
% 3.67/2.04             => ( ord_less @ A @ Y2 @ X2 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_88_neq__iff,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linorder @ A )
% 3.67/2.04       => ! [X2: A,Y2: A] :
% 3.67/2.04            ( ( X2 != Y2 )
% 3.67/2.04            = ( ( ord_less @ A @ X2 @ Y2 )
% 3.67/2.04              | ( ord_less @ A @ Y2 @ X2 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_89_order_Oasym,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ! [A2: A,B2: A] :
% 3.67/2.04            ( ( ord_less @ A @ A2 @ B2 )
% 3.67/2.04           => ~ ( ord_less @ A @ B2 @ A2 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_90_dense,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( dense_order @ A )
% 3.67/2.04       => ! [X2: A,Y2: A] :
% 3.67/2.04            ( ( ord_less @ A @ X2 @ Y2 )
% 3.67/2.04           => ? [Z5: A] :
% 3.67/2.04                ( ( ord_less @ A @ X2 @ Z5 )
% 3.67/2.04                & ( ord_less @ A @ Z5 @ Y2 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_91_less__imp__neq,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ! [X2: A,Y2: A] :
% 3.67/2.04            ( ( ord_less @ A @ X2 @ Y2 )
% 3.67/2.04           => ( X2 != Y2 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_92_less__asym,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( preorder @ A )
% 3.67/2.04       => ! [X2: A,Y2: A] :
% 3.67/2.04            ( ( ord_less @ A @ X2 @ Y2 )
% 3.67/2.04           => ~ ( ord_less @ A @ Y2 @ X2 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_93_less__asym_H,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( preorder @ A )
% 3.67/2.04       => ! [A2: A,B2: A] :
% 3.67/2.04            ( ( ord_less @ A @ A2 @ B2 )
% 3.67/2.04           => ~ ( ord_less @ A @ B2 @ A2 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_94_less__trans,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( preorder @ A )
% 3.67/2.04       => ! [X2: A,Y2: A,Z3: A] :
% 3.67/2.04            ( ( ord_less @ A @ X2 @ Y2 )
% 3.67/2.04           => ( ( ord_less @ A @ Y2 @ Z3 )
% 3.67/2.04             => ( ord_less @ A @ X2 @ Z3 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_95_less__linear,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linorder @ A )
% 3.67/2.04       => ! [X2: A,Y2: A] :
% 3.67/2.04            ( ( ord_less @ A @ X2 @ Y2 )
% 3.67/2.04            | ( X2 = Y2 )
% 3.67/2.04            | ( ord_less @ A @ Y2 @ X2 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_96_less__irrefl,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( preorder @ A )
% 3.67/2.04       => ! [X2: A] :
% 3.67/2.04            ~ ( ord_less @ A @ X2 @ X2 ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_97_ord__eq__less__trans,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( ord @ A )
% 3.67/2.04       => ! [A2: A,B2: A,C2: A] :
% 3.67/2.04            ( ( A2 = B2 )
% 3.67/2.04           => ( ( ord_less @ A @ B2 @ C2 )
% 3.67/2.04             => ( ord_less @ A @ A2 @ C2 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_98_ord__less__eq__trans,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( ord @ A )
% 3.67/2.04       => ! [A2: A,B2: A,C2: A] :
% 3.67/2.04            ( ( ord_less @ A @ A2 @ B2 )
% 3.67/2.04           => ( ( B2 = C2 )
% 3.67/2.04             => ( ord_less @ A @ A2 @ C2 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_99_dual__order_Oasym,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ! [B2: A,A2: A] :
% 3.67/2.04            ( ( ord_less @ A @ B2 @ A2 )
% 3.67/2.04           => ~ ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_100_less__imp__not__eq,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ! [X2: A,Y2: A] :
% 3.67/2.04            ( ( ord_less @ A @ X2 @ Y2 )
% 3.67/2.04           => ( X2 != Y2 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_101_less__not__sym,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( preorder @ A )
% 3.67/2.04       => ! [X2: A,Y2: A] :
% 3.67/2.04            ( ( ord_less @ A @ X2 @ Y2 )
% 3.67/2.04           => ~ ( ord_less @ A @ Y2 @ X2 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_102_less__induct,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( wellorder @ A )
% 3.67/2.04       => ! [P: A > $o,A2: A] :
% 3.67/2.04            ( ! [X4: A] :
% 3.67/2.04                ( ! [Y5: A] :
% 3.67/2.04                    ( ( ord_less @ A @ Y5 @ X4 )
% 3.67/2.04                   => ( P @ Y5 ) )
% 3.67/2.04               => ( P @ X4 ) )
% 3.67/2.04           => ( P @ A2 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_103_antisym__conv3,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linorder @ A )
% 3.67/2.04       => ! [Y2: A,X2: A] :
% 3.67/2.04            ( ~ ( ord_less @ A @ Y2 @ X2 )
% 3.67/2.04           => ( ( ~ ( ord_less @ A @ X2 @ Y2 ) )
% 3.67/2.04              = ( X2 = Y2 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_104_less__imp__not__eq2,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ! [X2: A,Y2: A] :
% 3.67/2.04            ( ( ord_less @ A @ X2 @ Y2 )
% 3.67/2.04           => ( Y2 != X2 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_105_less__imp__triv,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( preorder @ A )
% 3.67/2.04       => ! [X2: A,Y2: A,P: $o] :
% 3.67/2.04            ( ( ord_less @ A @ X2 @ Y2 )
% 3.67/2.04           => ( ( ord_less @ A @ Y2 @ X2 )
% 3.67/2.04             => P ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_106_linorder__cases,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linorder @ A )
% 3.67/2.04       => ! [X2: A,Y2: A] :
% 3.67/2.04            ( ~ ( ord_less @ A @ X2 @ Y2 )
% 3.67/2.04           => ( ( X2 != Y2 )
% 3.67/2.04             => ( ord_less @ A @ Y2 @ X2 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_107_dual__order_Oirrefl,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ! [A2: A] :
% 3.67/2.04            ~ ( ord_less @ A @ A2 @ A2 ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_108_order_Ostrict__trans,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ! [A2: A,B2: A,C2: A] :
% 3.67/2.04            ( ( ord_less @ A @ A2 @ B2 )
% 3.67/2.04           => ( ( ord_less @ A @ B2 @ C2 )
% 3.67/2.04             => ( ord_less @ A @ A2 @ C2 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_109_less__imp__not__less,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( preorder @ A )
% 3.67/2.04       => ! [X2: A,Y2: A] :
% 3.67/2.04            ( ( ord_less @ A @ X2 @ Y2 )
% 3.67/2.04           => ~ ( ord_less @ A @ Y2 @ X2 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_110_exists__least__iff,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( wellorder @ A )
% 3.67/2.04       => ( ( ^ [P3: A > $o] :
% 3.67/2.04              ? [X5: A] : ( P3 @ X5 ) )
% 3.67/2.04          = ( ^ [P4: A > $o] :
% 3.67/2.04              ? [N2: A] :
% 3.67/2.04                ( ( P4 @ N2 )
% 3.67/2.04                & ! [M2: A] :
% 3.67/2.04                    ( ( ord_less @ A @ M2 @ N2 )
% 3.67/2.04                   => ~ ( P4 @ M2 ) ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_111_linorder__less__wlog,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linorder @ A )
% 3.67/2.04       => ! [P: A > A > $o,A2: A,B2: A] :
% 3.67/2.04            ( ! [A7: A,B7: A] :
% 3.67/2.04                ( ( ord_less @ A @ A7 @ B7 )
% 3.67/2.04               => ( P @ A7 @ B7 ) )
% 3.67/2.04           => ( ! [A7: A] : ( P @ A7 @ A7 )
% 3.67/2.04             => ( ! [A7: A,B7: A] :
% 3.67/2.04                    ( ( P @ B7 @ A7 )
% 3.67/2.04                   => ( P @ A7 @ B7 ) )
% 3.67/2.04               => ( P @ A2 @ B2 ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_112_dual__order_Ostrict__trans,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ! [B2: A,A2: A,C2: A] :
% 3.67/2.04            ( ( ord_less @ A @ B2 @ A2 )
% 3.67/2.04           => ( ( ord_less @ A @ C2 @ B2 )
% 3.67/2.04             => ( ord_less @ A @ C2 @ A2 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_113_not__less__iff__gr__or__eq,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linorder @ A )
% 3.67/2.04       => ! [X2: A,Y2: A] :
% 3.67/2.04            ( ( ~ ( ord_less @ A @ X2 @ Y2 ) )
% 3.67/2.04            = ( ( ord_less @ A @ Y2 @ X2 )
% 3.67/2.04              | ( X2 = Y2 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_114_order_Ostrict__implies__not__eq,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ! [A2: A,B2: A] :
% 3.67/2.04            ( ( ord_less @ A @ A2 @ B2 )
% 3.67/2.04           => ( A2 != B2 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_115_dual__order_Ostrict__implies__not__eq,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ! [B2: A,A2: A] :
% 3.67/2.04            ( ( ord_less @ A @ B2 @ A2 )
% 3.67/2.04           => ( A2 != B2 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_116_ex__gt__or__lt,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( condit1656338222tinuum @ A )
% 3.67/2.04       => ! [A2: A] :
% 3.67/2.04          ? [B7: A] :
% 3.67/2.04            ( ( ord_less @ A @ A2 @ B7 )
% 3.67/2.04            | ( ord_less @ A @ B7 @ A2 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_117_complete__real,axiom,
% 3.67/2.04      ! [S: set @ real] :
% 3.67/2.04        ( ? [X3: real] : ( member @ real @ X3 @ S )
% 3.67/2.04       => ( ? [Z: real] :
% 3.67/2.04            ! [X4: real] :
% 3.67/2.04              ( ( member @ real @ X4 @ S )
% 3.67/2.04             => ( ord_less_eq @ real @ X4 @ Z ) )
% 3.67/2.04         => ? [Y4: real] :
% 3.67/2.04              ( ! [X3: real] :
% 3.67/2.04                  ( ( member @ real @ X3 @ S )
% 3.67/2.04                 => ( ord_less_eq @ real @ X3 @ Y4 ) )
% 3.67/2.04              & ! [Z: real] :
% 3.67/2.04                  ( ! [X4: real] :
% 3.67/2.04                      ( ( member @ real @ X4 @ S )
% 3.67/2.04                     => ( ord_less_eq @ real @ X4 @ Z ) )
% 3.67/2.04                 => ( ord_less_eq @ real @ Y4 @ Z ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_118_field__lbound__gt__zero,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linordered_field @ A )
% 3.67/2.04       => ! [D1: A,D2: A] :
% 3.67/2.04            ( ( ord_less @ A @ ( zero_zero @ A ) @ D1 )
% 3.67/2.04           => ( ( ord_less @ A @ ( zero_zero @ A ) @ D2 )
% 3.67/2.04             => ? [E: A] :
% 3.67/2.04                  ( ( ord_less @ A @ ( zero_zero @ A ) @ E )
% 3.67/2.04                  & ( ord_less @ A @ E @ D1 )
% 3.67/2.04                  & ( ord_less @ A @ E @ D2 ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_119_leD,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ! [Y2: A,X2: A] :
% 3.67/2.04            ( ( ord_less_eq @ A @ Y2 @ X2 )
% 3.67/2.04           => ~ ( ord_less @ A @ X2 @ Y2 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_120_leI,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linorder @ A )
% 3.67/2.04       => ! [X2: A,Y2: A] :
% 3.67/2.04            ( ~ ( ord_less @ A @ X2 @ Y2 )
% 3.67/2.04           => ( ord_less_eq @ A @ Y2 @ X2 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_121_le__less,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ( ( ord_less_eq @ A )
% 3.67/2.04          = ( ^ [X: A,Y: A] :
% 3.67/2.04                ( ( ord_less @ A @ X @ Y )
% 3.67/2.04                | ( X = Y ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_122_less__le,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ( ( ord_less @ A )
% 3.67/2.04          = ( ^ [X: A,Y: A] :
% 3.67/2.04                ( ( ord_less_eq @ A @ X @ Y )
% 3.67/2.04                & ( X != Y ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_123_order__le__less__subst1,axiom,
% 3.67/2.04      ! [A: $tType,B: $tType] :
% 3.67/2.04        ( ( ( order @ B )
% 3.67/2.04          & ( order @ A ) )
% 3.67/2.04       => ! [A2: A,F2: B > A,B2: B,C2: B] :
% 3.67/2.04            ( ( ord_less_eq @ A @ A2 @ ( F2 @ B2 ) )
% 3.67/2.04           => ( ( ord_less @ B @ B2 @ C2 )
% 3.67/2.04             => ( ! [X4: B,Y4: B] :
% 3.67/2.04                    ( ( ord_less @ B @ X4 @ Y4 )
% 3.67/2.04                   => ( ord_less @ A @ ( F2 @ X4 ) @ ( F2 @ Y4 ) ) )
% 3.67/2.04               => ( ord_less @ A @ A2 @ ( F2 @ C2 ) ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_124_order__le__less__subst2,axiom,
% 3.67/2.04      ! [A: $tType,C3: $tType] :
% 3.67/2.04        ( ( ( order @ C3 )
% 3.67/2.04          & ( order @ A ) )
% 3.67/2.04       => ! [A2: A,B2: A,F2: A > C3,C2: C3] :
% 3.67/2.04            ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.67/2.04           => ( ( ord_less @ C3 @ ( F2 @ B2 ) @ C2 )
% 3.67/2.04             => ( ! [X4: A,Y4: A] :
% 3.67/2.04                    ( ( ord_less_eq @ A @ X4 @ Y4 )
% 3.67/2.04                   => ( ord_less_eq @ C3 @ ( F2 @ X4 ) @ ( F2 @ Y4 ) ) )
% 3.67/2.04               => ( ord_less @ C3 @ ( F2 @ A2 ) @ C2 ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_125_order__less__le__subst1,axiom,
% 3.67/2.04      ! [A: $tType,B: $tType] :
% 3.67/2.04        ( ( ( order @ B )
% 3.67/2.04          & ( order @ A ) )
% 3.67/2.04       => ! [A2: A,F2: B > A,B2: B,C2: B] :
% 3.67/2.04            ( ( ord_less @ A @ A2 @ ( F2 @ B2 ) )
% 3.67/2.04           => ( ( ord_less_eq @ B @ B2 @ C2 )
% 3.67/2.04             => ( ! [X4: B,Y4: B] :
% 3.67/2.04                    ( ( ord_less_eq @ B @ X4 @ Y4 )
% 3.67/2.04                   => ( ord_less_eq @ A @ ( F2 @ X4 ) @ ( F2 @ Y4 ) ) )
% 3.67/2.04               => ( ord_less @ A @ A2 @ ( F2 @ C2 ) ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_126_order__less__le__subst2,axiom,
% 3.67/2.04      ! [A: $tType,C3: $tType] :
% 3.67/2.04        ( ( ( order @ C3 )
% 3.67/2.04          & ( order @ A ) )
% 3.67/2.04       => ! [A2: A,B2: A,F2: A > C3,C2: C3] :
% 3.67/2.04            ( ( ord_less @ A @ A2 @ B2 )
% 3.67/2.04           => ( ( ord_less_eq @ C3 @ ( F2 @ B2 ) @ C2 )
% 3.67/2.04             => ( ! [X4: A,Y4: A] :
% 3.67/2.04                    ( ( ord_less @ A @ X4 @ Y4 )
% 3.67/2.04                   => ( ord_less @ C3 @ ( F2 @ X4 ) @ ( F2 @ Y4 ) ) )
% 3.67/2.04               => ( ord_less @ C3 @ ( F2 @ A2 ) @ C2 ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_127_not__le,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linorder @ A )
% 3.67/2.04       => ! [X2: A,Y2: A] :
% 3.67/2.04            ( ( ~ ( ord_less_eq @ A @ X2 @ Y2 ) )
% 3.67/2.04            = ( ord_less @ A @ Y2 @ X2 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_128_not__less,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linorder @ A )
% 3.67/2.04       => ! [X2: A,Y2: A] :
% 3.67/2.04            ( ( ~ ( ord_less @ A @ X2 @ Y2 ) )
% 3.67/2.04            = ( ord_less_eq @ A @ Y2 @ X2 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_129_le__neq__trans,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ! [A2: A,B2: A] :
% 3.67/2.04            ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.67/2.04           => ( ( A2 != B2 )
% 3.67/2.04             => ( ord_less @ A @ A2 @ B2 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_130_antisym__conv1,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ! [X2: A,Y2: A] :
% 3.67/2.04            ( ~ ( ord_less @ A @ X2 @ Y2 )
% 3.67/2.04           => ( ( ord_less_eq @ A @ X2 @ Y2 )
% 3.67/2.04              = ( X2 = Y2 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_131_antisym__conv2,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ! [X2: A,Y2: A] :
% 3.67/2.04            ( ( ord_less_eq @ A @ X2 @ Y2 )
% 3.67/2.04           => ( ( ~ ( ord_less @ A @ X2 @ Y2 ) )
% 3.67/2.04              = ( X2 = Y2 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_132_less__imp__le,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( preorder @ A )
% 3.67/2.04       => ! [X2: A,Y2: A] :
% 3.67/2.04            ( ( ord_less @ A @ X2 @ Y2 )
% 3.67/2.04           => ( ord_less_eq @ A @ X2 @ Y2 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_133_le__less__trans,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( preorder @ A )
% 3.67/2.04       => ! [X2: A,Y2: A,Z3: A] :
% 3.67/2.04            ( ( ord_less_eq @ A @ X2 @ Y2 )
% 3.67/2.04           => ( ( ord_less @ A @ Y2 @ Z3 )
% 3.67/2.04             => ( ord_less @ A @ X2 @ Z3 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_134_less__le__trans,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( preorder @ A )
% 3.67/2.04       => ! [X2: A,Y2: A,Z3: A] :
% 3.67/2.04            ( ( ord_less @ A @ X2 @ Y2 )
% 3.67/2.04           => ( ( ord_less_eq @ A @ Y2 @ Z3 )
% 3.67/2.04             => ( ord_less @ A @ X2 @ Z3 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_135_dense__ge,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( dense_linorder @ A )
% 3.67/2.04       => ! [Z3: A,Y2: A] :
% 3.67/2.04            ( ! [X4: A] :
% 3.67/2.04                ( ( ord_less @ A @ Z3 @ X4 )
% 3.67/2.04               => ( ord_less_eq @ A @ Y2 @ X4 ) )
% 3.67/2.04           => ( ord_less_eq @ A @ Y2 @ Z3 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_136_dense__le,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( dense_linorder @ A )
% 3.67/2.04       => ! [Y2: A,Z3: A] :
% 3.67/2.04            ( ! [X4: A] :
% 3.67/2.04                ( ( ord_less @ A @ X4 @ Y2 )
% 3.67/2.04               => ( ord_less_eq @ A @ X4 @ Z3 ) )
% 3.67/2.04           => ( ord_less_eq @ A @ Y2 @ Z3 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_137_le__less__linear,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linorder @ A )
% 3.67/2.04       => ! [X2: A,Y2: A] :
% 3.67/2.04            ( ( ord_less_eq @ A @ X2 @ Y2 )
% 3.67/2.04            | ( ord_less @ A @ Y2 @ X2 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_138_le__imp__less__or__eq,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ! [X2: A,Y2: A] :
% 3.67/2.04            ( ( ord_less_eq @ A @ X2 @ Y2 )
% 3.67/2.04           => ( ( ord_less @ A @ X2 @ Y2 )
% 3.67/2.04              | ( X2 = Y2 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_139_less__le__not__le,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( preorder @ A )
% 3.67/2.04       => ( ( ord_less @ A )
% 3.67/2.04          = ( ^ [X: A,Y: A] :
% 3.67/2.04                ( ( ord_less_eq @ A @ X @ Y )
% 3.67/2.04                & ~ ( ord_less_eq @ A @ Y @ X ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_140_not__le__imp__less,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linorder @ A )
% 3.67/2.04       => ! [Y2: A,X2: A] :
% 3.67/2.04            ( ~ ( ord_less_eq @ A @ Y2 @ X2 )
% 3.67/2.04           => ( ord_less @ A @ X2 @ Y2 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_141_order_Ostrict__trans1,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ! [A2: A,B2: A,C2: A] :
% 3.67/2.04            ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.67/2.04           => ( ( ord_less @ A @ B2 @ C2 )
% 3.67/2.04             => ( ord_less @ A @ A2 @ C2 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_142_order_Ostrict__trans2,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ! [A2: A,B2: A,C2: A] :
% 3.67/2.04            ( ( ord_less @ A @ A2 @ B2 )
% 3.67/2.04           => ( ( ord_less_eq @ A @ B2 @ C2 )
% 3.67/2.04             => ( ord_less @ A @ A2 @ C2 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_143_order_Oorder__iff__strict,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ( ( ord_less_eq @ A )
% 3.67/2.04          = ( ^ [A6: A,B5: A] :
% 3.67/2.04                ( ( ord_less @ A @ A6 @ B5 )
% 3.67/2.04                | ( A6 = B5 ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_144_order_Ostrict__iff__order,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ( ( ord_less @ A )
% 3.67/2.04          = ( ^ [A6: A,B5: A] :
% 3.67/2.04                ( ( ord_less_eq @ A @ A6 @ B5 )
% 3.67/2.04                & ( A6 != B5 ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_145_dual__order_Ostrict__trans1,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ! [B2: A,A2: A,C2: A] :
% 3.67/2.04            ( ( ord_less_eq @ A @ B2 @ A2 )
% 3.67/2.04           => ( ( ord_less @ A @ C2 @ B2 )
% 3.67/2.04             => ( ord_less @ A @ C2 @ A2 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_146_dual__order_Ostrict__trans2,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ! [B2: A,A2: A,C2: A] :
% 3.67/2.04            ( ( ord_less @ A @ B2 @ A2 )
% 3.67/2.04           => ( ( ord_less_eq @ A @ C2 @ B2 )
% 3.67/2.04             => ( ord_less @ A @ C2 @ A2 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_147_dense__ge__bounded,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( dense_linorder @ A )
% 3.67/2.04       => ! [Z3: A,X2: A,Y2: A] :
% 3.67/2.04            ( ( ord_less @ A @ Z3 @ X2 )
% 3.67/2.04           => ( ! [W: A] :
% 3.67/2.04                  ( ( ord_less @ A @ Z3 @ W )
% 3.67/2.04                 => ( ( ord_less @ A @ W @ X2 )
% 3.67/2.04                   => ( ord_less_eq @ A @ Y2 @ W ) ) )
% 3.67/2.04             => ( ord_less_eq @ A @ Y2 @ Z3 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_148_psubsetI,axiom,
% 3.67/2.04      ! [A: $tType,A4: set @ A,B4: set @ A] :
% 3.67/2.04        ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 3.67/2.04       => ( ( A4 != B4 )
% 3.67/2.04         => ( ord_less @ ( set @ A ) @ A4 @ B4 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_149_minf_I8_J,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linorder @ A )
% 3.67/2.04       => ! [T2: A] :
% 3.67/2.04          ? [Z5: A] :
% 3.67/2.04          ! [X3: A] :
% 3.67/2.04            ( ( ord_less @ A @ X3 @ Z5 )
% 3.67/2.04           => ~ ( ord_less_eq @ A @ T2 @ X3 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_150_minf_I6_J,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linorder @ A )
% 3.67/2.04       => ! [T2: A] :
% 3.67/2.04          ? [Z5: A] :
% 3.67/2.04          ! [X3: A] :
% 3.67/2.04            ( ( ord_less @ A @ X3 @ Z5 )
% 3.67/2.04           => ( ord_less_eq @ A @ X3 @ T2 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_151_pinf_I8_J,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linorder @ A )
% 3.67/2.04       => ! [T2: A] :
% 3.67/2.04          ? [Z5: A] :
% 3.67/2.04          ! [X3: A] :
% 3.67/2.04            ( ( ord_less @ A @ Z5 @ X3 )
% 3.67/2.04           => ( ord_less_eq @ A @ T2 @ X3 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_152_pinf_I6_J,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linorder @ A )
% 3.67/2.04       => ! [T2: A] :
% 3.67/2.04          ? [Z5: A] :
% 3.67/2.04          ! [X3: A] :
% 3.67/2.04            ( ( ord_less @ A @ Z5 @ X3 )
% 3.67/2.04           => ~ ( ord_less_eq @ A @ X3 @ T2 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_153_verit__comp__simplify1_I3_J,axiom,
% 3.67/2.04      ! [B: $tType] :
% 3.67/2.04        ( ( linorder @ B )
% 3.67/2.04       => ! [B8: B,A8: B] :
% 3.67/2.04            ( ( ~ ( ord_less_eq @ B @ B8 @ A8 ) )
% 3.67/2.04            = ( ord_less @ B @ A8 @ B8 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_154_is__zero__null,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( zero @ A )
% 3.67/2.04       => ( ( is_zero @ A )
% 3.67/2.04          = ( ^ [P5: poly @ A] :
% 3.67/2.04                ( P5
% 3.67/2.04                = ( zero_zero @ ( poly @ A ) ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_155_poly__cutoff__0,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( zero @ A )
% 3.67/2.04       => ! [N: nat] :
% 3.67/2.04            ( ( poly_cutoff @ A @ N @ ( zero_zero @ ( poly @ A ) ) )
% 3.67/2.04            = ( zero_zero @ ( poly @ A ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_156_subsetI,axiom,
% 3.67/2.04      ! [A: $tType,A4: set @ A,B4: set @ A] :
% 3.67/2.04        ( ! [X4: A] :
% 3.67/2.04            ( ( member @ A @ X4 @ A4 )
% 3.67/2.04           => ( member @ A @ X4 @ B4 ) )
% 3.67/2.04       => ( ord_less_eq @ ( set @ A ) @ A4 @ B4 ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_157_subset__antisym,axiom,
% 3.67/2.04      ! [A: $tType,A4: set @ A,B4: set @ A] :
% 3.67/2.04        ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 3.67/2.04       => ( ( ord_less_eq @ ( set @ A ) @ B4 @ A4 )
% 3.67/2.04         => ( A4 = B4 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_158_in__mono,axiom,
% 3.67/2.04      ! [A: $tType,A4: set @ A,B4: set @ A,X2: A] :
% 3.67/2.04        ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 3.67/2.04       => ( ( member @ A @ X2 @ A4 )
% 3.67/2.04         => ( member @ A @ X2 @ B4 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_159_subsetD,axiom,
% 3.67/2.04      ! [A: $tType,A4: set @ A,B4: set @ A,C2: A] :
% 3.67/2.04        ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 3.67/2.04       => ( ( member @ A @ C2 @ A4 )
% 3.67/2.04         => ( member @ A @ C2 @ B4 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_160_equalityE,axiom,
% 3.67/2.04      ! [A: $tType,A4: set @ A,B4: set @ A] :
% 3.67/2.04        ( ( A4 = B4 )
% 3.67/2.04       => ~ ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 3.67/2.04           => ~ ( ord_less_eq @ ( set @ A ) @ B4 @ A4 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_161_subset__eq,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( ord_less_eq @ ( set @ A ) )
% 3.67/2.04        = ( ^ [A3: set @ A,B6: set @ A] :
% 3.67/2.04            ! [X: A] :
% 3.67/2.04              ( ( member @ A @ X @ A3 )
% 3.67/2.04             => ( member @ A @ X @ B6 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_162_equalityD1,axiom,
% 3.67/2.04      ! [A: $tType,A4: set @ A,B4: set @ A] :
% 3.67/2.04        ( ( A4 = B4 )
% 3.67/2.04       => ( ord_less_eq @ ( set @ A ) @ A4 @ B4 ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_163_equalityD2,axiom,
% 3.67/2.04      ! [A: $tType,A4: set @ A,B4: set @ A] :
% 3.67/2.04        ( ( A4 = B4 )
% 3.67/2.04       => ( ord_less_eq @ ( set @ A ) @ B4 @ A4 ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_164_subset__iff,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( ord_less_eq @ ( set @ A ) )
% 3.67/2.04        = ( ^ [A3: set @ A,B6: set @ A] :
% 3.67/2.04            ! [T3: A] :
% 3.67/2.04              ( ( member @ A @ T3 @ A3 )
% 3.67/2.04             => ( member @ A @ T3 @ B6 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_165_subset__refl,axiom,
% 3.67/2.04      ! [A: $tType,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ A4 @ A4 ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_166_Collect__mono,axiom,
% 3.67/2.04      ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.67/2.04        ( ! [X4: A] :
% 3.67/2.04            ( ( P @ X4 )
% 3.67/2.04           => ( Q @ X4 ) )
% 3.67/2.04       => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_167_subset__trans,axiom,
% 3.67/2.04      ! [A: $tType,A4: set @ A,B4: set @ A,C4: set @ A] :
% 3.67/2.04        ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 3.67/2.04       => ( ( ord_less_eq @ ( set @ A ) @ B4 @ C4 )
% 3.67/2.04         => ( ord_less_eq @ ( set @ A ) @ A4 @ C4 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_168_set__eq__subset,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( ^ [Y3: set @ A,Z4: set @ A] : ( Y3 = Z4 ) )
% 3.67/2.04        = ( ^ [A3: set @ A,B6: set @ A] :
% 3.67/2.04              ( ( ord_less_eq @ ( set @ A ) @ A3 @ B6 )
% 3.67/2.04              & ( ord_less_eq @ ( set @ A ) @ B6 @ A3 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_169_Collect__subset,axiom,
% 3.67/2.04      ! [A: $tType,A4: set @ A,P: A > $o] :
% 3.67/2.04        ( ord_less_eq @ ( set @ A )
% 3.67/2.04        @ ( collect @ A
% 3.67/2.04          @ ^ [X: A] :
% 3.67/2.04              ( ( member @ A @ X @ A4 )
% 3.67/2.04              & ( P @ X ) ) )
% 3.67/2.04        @ A4 ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_170_less__eq__set__def,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( ord_less_eq @ ( set @ A ) )
% 3.67/2.04        = ( ^ [A3: set @ A,B6: set @ A] :
% 3.67/2.04              ( ord_less_eq @ ( A > $o )
% 3.67/2.04              @ ^ [X: A] : ( member @ A @ X @ A3 )
% 3.67/2.04              @ ^ [X: A] : ( member @ A @ X @ B6 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_171_Collect__mono__iff,axiom,
% 3.67/2.04      ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.67/2.04        ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 3.67/2.04        = ( ! [X: A] :
% 3.67/2.04              ( ( P @ X )
% 3.67/2.04             => ( Q @ X ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_172_less__fun__def,axiom,
% 3.67/2.04      ! [B: $tType,A: $tType] :
% 3.67/2.04        ( ( ord @ B )
% 3.67/2.04       => ( ( ord_less @ ( A > B ) )
% 3.67/2.04          = ( ^ [F3: A > B,G2: A > B] :
% 3.67/2.04                ( ( ord_less_eq @ ( A > B ) @ F3 @ G2 )
% 3.67/2.04                & ~ ( ord_less_eq @ ( A > B ) @ G2 @ F3 ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_173_verit__la__disequality,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linorder @ A )
% 3.67/2.04       => ! [A2: A,B2: A] :
% 3.67/2.04            ( ( A2 = B2 )
% 3.67/2.04            | ~ ( ord_less_eq @ A @ A2 @ B2 )
% 3.67/2.04            | ~ ( ord_less_eq @ A @ B2 @ A2 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_174_verit__comp__simplify1_I1_J,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( order @ A )
% 3.67/2.04       => ! [A2: A] :
% 3.67/2.04            ~ ( ord_less @ A @ A2 @ A2 ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_175_pinf_I1_J,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linorder @ A )
% 3.67/2.04       => ! [P: A > $o,P6: A > $o,Q: A > $o,Q3: A > $o] :
% 3.67/2.04            ( ? [Z: A] :
% 3.67/2.04              ! [X4: A] :
% 3.67/2.04                ( ( ord_less @ A @ Z @ X4 )
% 3.67/2.04               => ( ( P @ X4 )
% 3.67/2.04                  = ( P6 @ X4 ) ) )
% 3.67/2.04           => ( ? [Z: A] :
% 3.67/2.04                ! [X4: A] :
% 3.67/2.04                  ( ( ord_less @ A @ Z @ X4 )
% 3.67/2.04                 => ( ( Q @ X4 )
% 3.67/2.04                    = ( Q3 @ X4 ) ) )
% 3.67/2.04             => ? [Z5: A] :
% 3.67/2.04                ! [X3: A] :
% 3.67/2.04                  ( ( ord_less @ A @ Z5 @ X3 )
% 3.67/2.04                 => ( ( ( P @ X3 )
% 3.67/2.04                      & ( Q @ X3 ) )
% 3.67/2.04                    = ( ( P6 @ X3 )
% 3.67/2.04                      & ( Q3 @ X3 ) ) ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_176_pinf_I2_J,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linorder @ A )
% 3.67/2.04       => ! [P: A > $o,P6: A > $o,Q: A > $o,Q3: A > $o] :
% 3.67/2.04            ( ? [Z: A] :
% 3.67/2.04              ! [X4: A] :
% 3.67/2.04                ( ( ord_less @ A @ Z @ X4 )
% 3.67/2.04               => ( ( P @ X4 )
% 3.67/2.04                  = ( P6 @ X4 ) ) )
% 3.67/2.04           => ( ? [Z: A] :
% 3.67/2.04                ! [X4: A] :
% 3.67/2.04                  ( ( ord_less @ A @ Z @ X4 )
% 3.67/2.04                 => ( ( Q @ X4 )
% 3.67/2.04                    = ( Q3 @ X4 ) ) )
% 3.67/2.04             => ? [Z5: A] :
% 3.67/2.04                ! [X3: A] :
% 3.67/2.04                  ( ( ord_less @ A @ Z5 @ X3 )
% 3.67/2.04                 => ( ( ( P @ X3 )
% 3.67/2.04                      | ( Q @ X3 ) )
% 3.67/2.04                    = ( ( P6 @ X3 )
% 3.67/2.04                      | ( Q3 @ X3 ) ) ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_177_pinf_I3_J,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linorder @ A )
% 3.67/2.04       => ! [T2: A] :
% 3.67/2.04          ? [Z5: A] :
% 3.67/2.04          ! [X3: A] :
% 3.67/2.04            ( ( ord_less @ A @ Z5 @ X3 )
% 3.67/2.04           => ( X3 != T2 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_178_pinf_I4_J,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linorder @ A )
% 3.67/2.04       => ! [T2: A] :
% 3.67/2.04          ? [Z5: A] :
% 3.67/2.04          ! [X3: A] :
% 3.67/2.04            ( ( ord_less @ A @ Z5 @ X3 )
% 3.67/2.04           => ( X3 != T2 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_179_pinf_I5_J,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linorder @ A )
% 3.67/2.04       => ! [T2: A] :
% 3.67/2.04          ? [Z5: A] :
% 3.67/2.04          ! [X3: A] :
% 3.67/2.04            ( ( ord_less @ A @ Z5 @ X3 )
% 3.67/2.04           => ~ ( ord_less @ A @ X3 @ T2 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_180_pinf_I7_J,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linorder @ A )
% 3.67/2.04       => ! [T2: A] :
% 3.67/2.04          ? [Z5: A] :
% 3.67/2.04          ! [X3: A] :
% 3.67/2.04            ( ( ord_less @ A @ Z5 @ X3 )
% 3.67/2.04           => ( ord_less @ A @ T2 @ X3 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_181_pinf_I11_J,axiom,
% 3.67/2.04      ! [C3: $tType,D3: $tType] :
% 3.67/2.04        ( ( ord @ C3 )
% 3.67/2.04       => ! [F4: D3] :
% 3.67/2.04          ? [Z5: C3] :
% 3.67/2.04          ! [X3: C3] :
% 3.67/2.04            ( ( ord_less @ C3 @ Z5 @ X3 )
% 3.67/2.04           => ( F4 = F4 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_182_minf_I1_J,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linorder @ A )
% 3.67/2.04       => ! [P: A > $o,P6: A > $o,Q: A > $o,Q3: A > $o] :
% 3.67/2.04            ( ? [Z: A] :
% 3.67/2.04              ! [X4: A] :
% 3.67/2.04                ( ( ord_less @ A @ X4 @ Z )
% 3.67/2.04               => ( ( P @ X4 )
% 3.67/2.04                  = ( P6 @ X4 ) ) )
% 3.67/2.04           => ( ? [Z: A] :
% 3.67/2.04                ! [X4: A] :
% 3.67/2.04                  ( ( ord_less @ A @ X4 @ Z )
% 3.67/2.04                 => ( ( Q @ X4 )
% 3.67/2.04                    = ( Q3 @ X4 ) ) )
% 3.67/2.04             => ? [Z5: A] :
% 3.67/2.04                ! [X3: A] :
% 3.67/2.04                  ( ( ord_less @ A @ X3 @ Z5 )
% 3.67/2.04                 => ( ( ( P @ X3 )
% 3.67/2.04                      & ( Q @ X3 ) )
% 3.67/2.04                    = ( ( P6 @ X3 )
% 3.67/2.04                      & ( Q3 @ X3 ) ) ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_183_minf_I2_J,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linorder @ A )
% 3.67/2.04       => ! [P: A > $o,P6: A > $o,Q: A > $o,Q3: A > $o] :
% 3.67/2.04            ( ? [Z: A] :
% 3.67/2.04              ! [X4: A] :
% 3.67/2.04                ( ( ord_less @ A @ X4 @ Z )
% 3.67/2.04               => ( ( P @ X4 )
% 3.67/2.04                  = ( P6 @ X4 ) ) )
% 3.67/2.04           => ( ? [Z: A] :
% 3.67/2.04                ! [X4: A] :
% 3.67/2.04                  ( ( ord_less @ A @ X4 @ Z )
% 3.67/2.04                 => ( ( Q @ X4 )
% 3.67/2.04                    = ( Q3 @ X4 ) ) )
% 3.67/2.04             => ? [Z5: A] :
% 3.67/2.04                ! [X3: A] :
% 3.67/2.04                  ( ( ord_less @ A @ X3 @ Z5 )
% 3.67/2.04                 => ( ( ( P @ X3 )
% 3.67/2.04                      | ( Q @ X3 ) )
% 3.67/2.04                    = ( ( P6 @ X3 )
% 3.67/2.04                      | ( Q3 @ X3 ) ) ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_184_minf_I3_J,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linorder @ A )
% 3.67/2.04       => ! [T2: A] :
% 3.67/2.04          ? [Z5: A] :
% 3.67/2.04          ! [X3: A] :
% 3.67/2.04            ( ( ord_less @ A @ X3 @ Z5 )
% 3.67/2.04           => ( X3 != T2 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_185_minf_I4_J,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linorder @ A )
% 3.67/2.04       => ! [T2: A] :
% 3.67/2.04          ? [Z5: A] :
% 3.67/2.04          ! [X3: A] :
% 3.67/2.04            ( ( ord_less @ A @ X3 @ Z5 )
% 3.67/2.04           => ( X3 != T2 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_186_minf_I5_J,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linorder @ A )
% 3.67/2.04       => ! [T2: A] :
% 3.67/2.04          ? [Z5: A] :
% 3.67/2.04          ! [X3: A] :
% 3.67/2.04            ( ( ord_less @ A @ X3 @ Z5 )
% 3.67/2.04           => ( ord_less @ A @ X3 @ T2 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_187_minf_I7_J,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linorder @ A )
% 3.67/2.04       => ! [T2: A] :
% 3.67/2.04          ? [Z5: A] :
% 3.67/2.04          ! [X3: A] :
% 3.67/2.04            ( ( ord_less @ A @ X3 @ Z5 )
% 3.67/2.04           => ~ ( ord_less @ A @ T2 @ X3 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_188_minf_I11_J,axiom,
% 3.67/2.04      ! [C3: $tType,D3: $tType] :
% 3.67/2.04        ( ( ord @ C3 )
% 3.67/2.04       => ! [F4: D3] :
% 3.67/2.04          ? [Z5: C3] :
% 3.67/2.04          ! [X3: C3] :
% 3.67/2.04            ( ( ord_less @ C3 @ X3 @ Z5 )
% 3.67/2.04           => ( F4 = F4 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_189_conj__le__cong,axiom,
% 3.67/2.04      ! [X2: int,X6: int,P: $o,P6: $o] :
% 3.67/2.04        ( ( X2 = X6 )
% 3.67/2.04       => ( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ X6 )
% 3.67/2.04           => ( P = P6 ) )
% 3.67/2.04         => ( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ X2 )
% 3.67/2.04              & P )
% 3.67/2.04            = ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ X6 )
% 3.67/2.04              & P6 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_190_imp__le__cong,axiom,
% 3.67/2.04      ! [X2: int,X6: int,P: $o,P6: $o] :
% 3.67/2.04        ( ( X2 = X6 )
% 3.67/2.04       => ( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ X6 )
% 3.67/2.04           => ( P = P6 ) )
% 3.67/2.04         => ( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ X2 )
% 3.67/2.04             => P )
% 3.67/2.04            = ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ X6 )
% 3.67/2.04             => P6 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_191_subset__iff__psubset__eq,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( ord_less_eq @ ( set @ A ) )
% 3.67/2.04        = ( ^ [A3: set @ A,B6: set @ A] :
% 3.67/2.04              ( ( ord_less @ ( set @ A ) @ A3 @ B6 )
% 3.67/2.04              | ( A3 = B6 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_192_subset__psubset__trans,axiom,
% 3.67/2.04      ! [A: $tType,A4: set @ A,B4: set @ A,C4: set @ A] :
% 3.67/2.04        ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 3.67/2.04       => ( ( ord_less @ ( set @ A ) @ B4 @ C4 )
% 3.67/2.04         => ( ord_less @ ( set @ A ) @ A4 @ C4 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_193_subset__not__subset__eq,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( ord_less @ ( set @ A ) )
% 3.67/2.04        = ( ^ [A3: set @ A,B6: set @ A] :
% 3.67/2.04              ( ( ord_less_eq @ ( set @ A ) @ A3 @ B6 )
% 3.67/2.04              & ~ ( ord_less_eq @ ( set @ A ) @ B6 @ A3 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_194_psubset__subset__trans,axiom,
% 3.67/2.04      ! [A: $tType,A4: set @ A,B4: set @ A,C4: set @ A] :
% 3.67/2.04        ( ( ord_less @ ( set @ A ) @ A4 @ B4 )
% 3.67/2.04       => ( ( ord_less_eq @ ( set @ A ) @ B4 @ C4 )
% 3.67/2.04         => ( ord_less @ ( set @ A ) @ A4 @ C4 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_195_psubset__imp__subset,axiom,
% 3.67/2.04      ! [A: $tType,A4: set @ A,B4: set @ A] :
% 3.67/2.04        ( ( ord_less @ ( set @ A ) @ A4 @ B4 )
% 3.67/2.04       => ( ord_less_eq @ ( set @ A ) @ A4 @ B4 ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_196_psubset__trans,axiom,
% 3.67/2.04      ! [A: $tType,A4: set @ A,B4: set @ A,C4: set @ A] :
% 3.67/2.04        ( ( ord_less @ ( set @ A ) @ A4 @ B4 )
% 3.67/2.04       => ( ( ord_less @ ( set @ A ) @ B4 @ C4 )
% 3.67/2.04         => ( ord_less @ ( set @ A ) @ A4 @ C4 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_197_psubset__eq,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( ord_less @ ( set @ A ) )
% 3.67/2.04        = ( ^ [A3: set @ A,B6: set @ A] :
% 3.67/2.04              ( ( ord_less_eq @ ( set @ A ) @ A3 @ B6 )
% 3.67/2.04              & ( A3 != B6 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_198_psubsetE,axiom,
% 3.67/2.04      ! [A: $tType,A4: set @ A,B4: set @ A] :
% 3.67/2.04        ( ( ord_less @ ( set @ A ) @ A4 @ B4 )
% 3.67/2.04       => ~ ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 3.67/2.04           => ( ord_less_eq @ ( set @ A ) @ B4 @ A4 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_199_psubsetD,axiom,
% 3.67/2.04      ! [A: $tType,A4: set @ A,B4: set @ A,C2: A] :
% 3.67/2.04        ( ( ord_less @ ( set @ A ) @ A4 @ B4 )
% 3.67/2.04       => ( ( member @ A @ C2 @ A4 )
% 3.67/2.04         => ( member @ A @ C2 @ B4 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_200_less__set__def,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( ord_less @ ( set @ A ) )
% 3.67/2.04        = ( ^ [A3: set @ A,B6: set @ A] :
% 3.67/2.04              ( ord_less @ ( A > $o )
% 3.67/2.04              @ ^ [X: A] : ( member @ A @ X @ A3 )
% 3.67/2.04              @ ^ [X: A] : ( member @ A @ X @ B6 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_201_reflect__poly__at__0__eq__0__iff,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( comm_semiring_0 @ A )
% 3.67/2.04       => ! [P2: poly @ A] :
% 3.67/2.04            ( ( ( poly2 @ A @ ( reflect_poly @ A @ P2 ) @ ( zero_zero @ A ) )
% 3.67/2.04              = ( zero_zero @ A ) )
% 3.67/2.04            = ( P2
% 3.67/2.04              = ( zero_zero @ ( poly @ A ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_202_jump__poly__not__root,axiom,
% 3.67/2.04      ! [P2: poly @ real,X2: real,Q2: poly @ real] :
% 3.67/2.04        ( ( ( poly2 @ real @ P2 @ X2 )
% 3.67/2.04         != ( zero_zero @ real ) )
% 3.67/2.04       => ( ( sturm_652470720p_poly @ Q2 @ P2 @ X2 )
% 3.67/2.04          = ( zero_zero @ int ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_203_jump__poly0_I2_J,axiom,
% 3.67/2.04      ! [Q2: poly @ real,X2: real] :
% 3.67/2.04        ( ( sturm_652470720p_poly @ Q2 @ ( zero_zero @ ( poly @ real ) ) @ X2 )
% 3.67/2.04        = ( zero_zero @ int ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_204_predicate1I,axiom,
% 3.67/2.04      ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.67/2.04        ( ! [X4: A] :
% 3.67/2.04            ( ( P @ X4 )
% 3.67/2.04           => ( Q @ X4 ) )
% 3.67/2.04       => ( ord_less_eq @ ( A > $o ) @ P @ Q ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_205_reflect__poly__0,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( zero @ A )
% 3.67/2.04       => ( ( reflect_poly @ A @ ( zero_zero @ ( poly @ A ) ) )
% 3.67/2.04          = ( zero_zero @ ( poly @ A ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_206_jump__poly0_I1_J,axiom,
% 3.67/2.04      ! [P2: poly @ real,X2: real] :
% 3.67/2.04        ( ( sturm_652470720p_poly @ ( zero_zero @ ( poly @ real ) ) @ P2 @ X2 )
% 3.67/2.04        = ( zero_zero @ int ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_207_verit__la__generic,axiom,
% 3.67/2.04      ! [A2: int,X2: int] :
% 3.67/2.04        ( ( ord_less_eq @ int @ A2 @ X2 )
% 3.67/2.04        | ( A2 = X2 )
% 3.67/2.04        | ( ord_less_eq @ int @ X2 @ A2 ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_208_predicate1D,axiom,
% 3.67/2.04      ! [A: $tType,P: A > $o,Q: A > $o,X2: A] :
% 3.67/2.04        ( ( ord_less_eq @ ( A > $o ) @ P @ Q )
% 3.67/2.04       => ( ( P @ X2 )
% 3.67/2.04         => ( Q @ X2 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_209_rev__predicate1D,axiom,
% 3.67/2.04      ! [A: $tType,P: A > $o,X2: A,Q: A > $o] :
% 3.67/2.04        ( ( P @ X2 )
% 3.67/2.04       => ( ( ord_less_eq @ ( A > $o ) @ P @ Q )
% 3.67/2.04         => ( Q @ X2 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_210_finite__interval__int1,axiom,
% 3.67/2.04      ! [A2: int,B2: int] :
% 3.67/2.04        ( finite_finite2 @ int
% 3.67/2.04        @ ( collect @ int
% 3.67/2.04          @ ^ [I: int] :
% 3.67/2.04              ( ( ord_less_eq @ int @ A2 @ I )
% 3.67/2.04              & ( ord_less_eq @ int @ I @ B2 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_211_finite__interval__int2,axiom,
% 3.67/2.04      ! [A2: int,B2: int] :
% 3.67/2.04        ( finite_finite2 @ int
% 3.67/2.04        @ ( collect @ int
% 3.67/2.04          @ ^ [I: int] :
% 3.67/2.04              ( ( ord_less_eq @ int @ A2 @ I )
% 3.67/2.04              & ( ord_less @ int @ I @ B2 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_212_finite__interval__int4,axiom,
% 3.67/2.04      ! [A2: int,B2: int] :
% 3.67/2.04        ( finite_finite2 @ int
% 3.67/2.04        @ ( collect @ int
% 3.67/2.04          @ ^ [I: int] :
% 3.67/2.04              ( ( ord_less @ int @ A2 @ I )
% 3.67/2.04              & ( ord_less @ int @ I @ B2 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_213_finite__interval__int3,axiom,
% 3.67/2.04      ! [A2: int,B2: int] :
% 3.67/2.04        ( finite_finite2 @ int
% 3.67/2.04        @ ( collect @ int
% 3.67/2.04          @ ^ [I: int] :
% 3.67/2.04              ( ( ord_less @ int @ A2 @ I )
% 3.67/2.04              & ( ord_less_eq @ int @ I @ B2 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_214_less__int__code_I1_J,axiom,
% 3.67/2.04      ~ ( ord_less @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_215_less__eq__int__code_I1_J,axiom,
% 3.67/2.04      ord_less_eq @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_216_pred__subset__eq,axiom,
% 3.67/2.04      ! [A: $tType,R: set @ A,S: set @ A] :
% 3.67/2.04        ( ( ord_less_eq @ ( A > $o )
% 3.67/2.04          @ ^ [X: A] : ( member @ A @ X @ R )
% 3.67/2.04          @ ^ [X: A] : ( member @ A @ X @ S ) )
% 3.67/2.04        = ( ord_less_eq @ ( set @ A ) @ R @ S ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_217_cindex__poly__0_I2_J,axiom,
% 3.67/2.04      ! [A2: real,B2: real,Q2: poly @ real] :
% 3.67/2.04        ( ( sturm_1539314049x_poly @ A2 @ B2 @ Q2 @ ( zero_zero @ ( poly @ real ) ) )
% 3.67/2.04        = ( zero_zero @ int ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_218_cindex__poly__0_I1_J,axiom,
% 3.67/2.04      ! [A2: real,B2: real,P2: poly @ real] :
% 3.67/2.04        ( ( sturm_1539314049x_poly @ A2 @ B2 @ ( zero_zero @ ( poly @ real ) ) @ P2 )
% 3.67/2.04        = ( zero_zero @ int ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_219_cindex__poly__cross,axiom,
% 3.67/2.04      ! [A2: real,B2: real,P2: poly @ real] :
% 3.67/2.04        ( ( ord_less @ real @ A2 @ B2 )
% 3.67/2.04       => ( ( ( poly2 @ real @ P2 @ A2 )
% 3.67/2.04           != ( zero_zero @ real ) )
% 3.67/2.04         => ( ( ( poly2 @ real @ P2 @ B2 )
% 3.67/2.04             != ( zero_zero @ real ) )
% 3.67/2.04           => ( ( sturm_1539314049x_poly @ A2 @ B2 @ ( one_one @ ( poly @ real ) ) @ P2 )
% 3.67/2.04              = ( sturm_424270202_cross @ P2 @ A2 @ B2 ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_220_cindex__poly__def,axiom,
% 3.67/2.04      ( sturm_1539314049x_poly
% 3.67/2.04      = ( ^ [A6: real,B5: real,Q4: poly @ real,P5: poly @ real] :
% 3.67/2.04            ( groups1340683514dd_sum @ real @ int @ ( sturm_652470720p_poly @ Q4 @ P5 )
% 3.67/2.04            @ ( collect @ real
% 3.67/2.04              @ ^ [X: real] :
% 3.67/2.04                  ( ( ( poly2 @ real @ P5 @ X )
% 3.67/2.04                    = ( zero_zero @ real ) )
% 3.67/2.04                  & ( ord_less @ real @ A6 @ X )
% 3.67/2.04                  & ( ord_less @ real @ X @ B5 ) ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_221_reflect__poly__1,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( comm_semiring_1 @ A )
% 3.67/2.04       => ( ( reflect_poly @ A @ ( one_one @ ( poly @ A ) ) )
% 3.67/2.04          = ( one_one @ ( poly @ A ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_222_poly__1,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( comm_semiring_1 @ A )
% 3.67/2.04       => ! [X2: A] :
% 3.67/2.04            ( ( poly2 @ A @ ( one_one @ ( poly @ A ) ) @ X2 )
% 3.67/2.04            = ( one_one @ A ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_223_poly__cutoff__1,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( comm_semiring_1 @ A )
% 3.67/2.04       => ! [N: nat] :
% 3.67/2.04            ( ( ( N
% 3.67/2.04                = ( zero_zero @ nat ) )
% 3.67/2.04             => ( ( poly_cutoff @ A @ N @ ( one_one @ ( poly @ A ) ) )
% 3.67/2.04                = ( zero_zero @ ( poly @ A ) ) ) )
% 3.67/2.04            & ( ( N
% 3.67/2.04               != ( zero_zero @ nat ) )
% 3.67/2.04             => ( ( poly_cutoff @ A @ N @ ( one_one @ ( poly @ A ) ) )
% 3.67/2.04                = ( one_one @ ( poly @ A ) ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_224_le__numeral__extra_I4_J,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linord1659791738miring @ A )
% 3.67/2.04       => ( ord_less_eq @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_225_poly__sum,axiom,
% 3.67/2.04      ! [A: $tType,B: $tType] :
% 3.67/2.04        ( ( comm_semiring_0 @ A )
% 3.67/2.04       => ! [P2: B > ( poly @ A ),A4: set @ B,X2: A] :
% 3.67/2.04            ( ( poly2 @ A @ ( groups1340683514dd_sum @ B @ ( poly @ A ) @ P2 @ A4 ) @ X2 )
% 3.67/2.04            = ( groups1340683514dd_sum @ B @ A
% 3.67/2.04              @ ^ [K: B] : ( poly2 @ A @ ( P2 @ K ) @ X2 )
% 3.67/2.04              @ A4 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_226_one__reorient,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( one @ A )
% 3.67/2.04       => ! [X2: A] :
% 3.67/2.04            ( ( ( one_one @ A )
% 3.67/2.04              = X2 )
% 3.67/2.04            = ( X2
% 3.67/2.04              = ( one_one @ A ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_227_less__numeral__extra_I1_J,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linord1659791738miring @ A )
% 3.67/2.04       => ( ord_less @ A @ ( zero_zero @ A ) @ ( one_one @ A ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_228_less__numeral__extra_I4_J,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linord1659791738miring @ A )
% 3.67/2.04       => ~ ( ord_less @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_229_sum_Odelta_H,axiom,
% 3.67/2.04      ! [B: $tType,A: $tType] :
% 3.67/2.04        ( ( comm_monoid_add @ A )
% 3.67/2.04       => ! [S: set @ B,A2: B,B2: B > A] :
% 3.67/2.04            ( ( finite_finite2 @ B @ S )
% 3.67/2.04           => ( ( ( member @ B @ A2 @ S )
% 3.67/2.04               => ( ( groups1340683514dd_sum @ B @ A
% 3.67/2.04                    @ ^ [K: B] : ( if @ A @ ( A2 = K ) @ ( B2 @ K ) @ ( zero_zero @ A ) )
% 3.67/2.04                    @ S )
% 3.67/2.04                  = ( B2 @ A2 ) ) )
% 3.67/2.04              & ( ~ ( member @ B @ A2 @ S )
% 3.67/2.04               => ( ( groups1340683514dd_sum @ B @ A
% 3.67/2.04                    @ ^ [K: B] : ( if @ A @ ( A2 = K ) @ ( B2 @ K ) @ ( zero_zero @ A ) )
% 3.67/2.04                    @ S )
% 3.67/2.04                  = ( zero_zero @ A ) ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_230_sum_Odelta,axiom,
% 3.67/2.04      ! [B: $tType,A: $tType] :
% 3.67/2.04        ( ( comm_monoid_add @ A )
% 3.67/2.04       => ! [S: set @ B,A2: B,B2: B > A] :
% 3.67/2.04            ( ( finite_finite2 @ B @ S )
% 3.67/2.04           => ( ( ( member @ B @ A2 @ S )
% 3.67/2.04               => ( ( groups1340683514dd_sum @ B @ A
% 3.67/2.04                    @ ^ [K: B] : ( if @ A @ ( K = A2 ) @ ( B2 @ K ) @ ( zero_zero @ A ) )
% 3.67/2.04                    @ S )
% 3.67/2.04                  = ( B2 @ A2 ) ) )
% 3.67/2.04              & ( ~ ( member @ B @ A2 @ S )
% 3.67/2.04               => ( ( groups1340683514dd_sum @ B @ A
% 3.67/2.04                    @ ^ [K: B] : ( if @ A @ ( K = A2 ) @ ( B2 @ K ) @ ( zero_zero @ A ) )
% 3.67/2.04                    @ S )
% 3.67/2.04                  = ( zero_zero @ A ) ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_231_sum_Oneutral__const,axiom,
% 3.67/2.04      ! [B: $tType,A: $tType] :
% 3.67/2.04        ( ( comm_monoid_add @ A )
% 3.67/2.04       => ! [A4: set @ B] :
% 3.67/2.04            ( ( groups1340683514dd_sum @ B @ A
% 3.67/2.04              @ ^ [Uu: B] : ( zero_zero @ A )
% 3.67/2.04              @ A4 )
% 3.67/2.04            = ( zero_zero @ A ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_232_sum_Oinfinite,axiom,
% 3.67/2.04      ! [B: $tType,A: $tType] :
% 3.67/2.04        ( ( comm_monoid_add @ A )
% 3.67/2.04       => ! [A4: set @ B,G: B > A] :
% 3.67/2.04            ( ~ ( finite_finite2 @ B @ A4 )
% 3.67/2.04           => ( ( groups1340683514dd_sum @ B @ A @ G @ A4 )
% 3.67/2.04              = ( zero_zero @ A ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_233_sum__eq__0__iff,axiom,
% 3.67/2.04      ! [A: $tType,B: $tType] :
% 3.67/2.04        ( ( canoni770627133id_add @ A )
% 3.67/2.04       => ! [F4: set @ B,F2: B > A] :
% 3.67/2.04            ( ( finite_finite2 @ B @ F4 )
% 3.67/2.04           => ( ( ( groups1340683514dd_sum @ B @ A @ F2 @ F4 )
% 3.67/2.04                = ( zero_zero @ A ) )
% 3.67/2.04              = ( ! [X: B] :
% 3.67/2.04                    ( ( member @ B @ X @ F4 )
% 3.67/2.04                   => ( ( F2 @ X )
% 3.67/2.04                      = ( zero_zero @ A ) ) ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_234_sum__eq__1__iff,axiom,
% 3.67/2.04      ! [A: $tType,A4: set @ A,F2: A > nat] :
% 3.67/2.04        ( ( finite_finite2 @ A @ A4 )
% 3.67/2.04       => ( ( ( groups1340683514dd_sum @ A @ nat @ F2 @ A4 )
% 3.67/2.04            = ( one_one @ nat ) )
% 3.67/2.04          = ( ? [X: A] :
% 3.67/2.04                ( ( member @ A @ X @ A4 )
% 3.67/2.04                & ( ( F2 @ X )
% 3.67/2.04                  = ( one_one @ nat ) )
% 3.67/2.04                & ! [Y: A] :
% 3.67/2.04                    ( ( member @ A @ Y @ A4 )
% 3.67/2.04                   => ( ( X != Y )
% 3.67/2.04                     => ( ( F2 @ Y )
% 3.67/2.04                        = ( zero_zero @ nat ) ) ) ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_235_int__one__le__iff__zero__less,axiom,
% 3.67/2.04      ! [Z3: int] :
% 3.67/2.04        ( ( ord_less_eq @ int @ ( one_one @ int ) @ Z3 )
% 3.67/2.04        = ( ord_less @ int @ ( zero_zero @ int ) @ Z3 ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_236_sum_Oswap,axiom,
% 3.67/2.04      ! [A: $tType,B: $tType,C3: $tType] :
% 3.67/2.04        ( ( comm_monoid_add @ A )
% 3.67/2.04       => ! [G: B > C3 > A,B4: set @ C3,A4: set @ B] :
% 3.67/2.04            ( ( groups1340683514dd_sum @ B @ A
% 3.67/2.04              @ ^ [I: B] : ( groups1340683514dd_sum @ C3 @ A @ ( G @ I ) @ B4 )
% 3.67/2.04              @ A4 )
% 3.67/2.04            = ( groups1340683514dd_sum @ C3 @ A
% 3.67/2.04              @ ^ [J: C3] :
% 3.67/2.04                  ( groups1340683514dd_sum @ B @ A
% 3.67/2.04                  @ ^ [I: B] : ( G @ I @ J )
% 3.67/2.04                  @ A4 )
% 3.67/2.04              @ B4 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_237_sum_Onot__neutral__contains__not__neutral,axiom,
% 3.67/2.04      ! [B: $tType,A: $tType] :
% 3.67/2.04        ( ( comm_monoid_add @ A )
% 3.67/2.04       => ! [G: B > A,A4: set @ B] :
% 3.67/2.04            ( ( ( groups1340683514dd_sum @ B @ A @ G @ A4 )
% 3.67/2.04             != ( zero_zero @ A ) )
% 3.67/2.04           => ~ ! [A7: B] :
% 3.67/2.04                  ( ( member @ B @ A7 @ A4 )
% 3.67/2.04                 => ( ( G @ A7 )
% 3.67/2.04                    = ( zero_zero @ A ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_238_sum_Oneutral,axiom,
% 3.67/2.04      ! [B: $tType,A: $tType] :
% 3.67/2.04        ( ( comm_monoid_add @ A )
% 3.67/2.04       => ! [A4: set @ B,G: B > A] :
% 3.67/2.04            ( ! [X4: B] :
% 3.67/2.04                ( ( member @ B @ X4 @ A4 )
% 3.67/2.04               => ( ( G @ X4 )
% 3.67/2.04                  = ( zero_zero @ A ) ) )
% 3.67/2.04           => ( ( groups1340683514dd_sum @ B @ A @ G @ A4 )
% 3.67/2.04              = ( zero_zero @ A ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_239_sum__mono,axiom,
% 3.67/2.04      ! [A: $tType,B: $tType] :
% 3.67/2.04        ( ( ordere216010020id_add @ A )
% 3.67/2.04       => ! [K2: set @ B,F2: B > A,G: B > A] :
% 3.67/2.04            ( ! [I2: B] :
% 3.67/2.04                ( ( member @ B @ I2 @ K2 )
% 3.67/2.04               => ( ord_less_eq @ A @ ( F2 @ I2 ) @ ( G @ I2 ) ) )
% 3.67/2.04           => ( ord_less_eq @ A @ ( groups1340683514dd_sum @ B @ A @ F2 @ K2 ) @ ( groups1340683514dd_sum @ B @ A @ G @ K2 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_240_sum_Oswap__restrict,axiom,
% 3.67/2.04      ! [A: $tType,B: $tType,C3: $tType] :
% 3.67/2.04        ( ( comm_monoid_add @ A )
% 3.67/2.04       => ! [A4: set @ B,B4: set @ C3,G: B > C3 > A,R: B > C3 > $o] :
% 3.67/2.04            ( ( finite_finite2 @ B @ A4 )
% 3.67/2.04           => ( ( finite_finite2 @ C3 @ B4 )
% 3.67/2.04             => ( ( groups1340683514dd_sum @ B @ A
% 3.67/2.04                  @ ^ [X: B] :
% 3.67/2.04                      ( groups1340683514dd_sum @ C3 @ A @ ( G @ X )
% 3.67/2.04                      @ ( collect @ C3
% 3.67/2.04                        @ ^ [Y: C3] :
% 3.67/2.04                            ( ( member @ C3 @ Y @ B4 )
% 3.67/2.04                            & ( R @ X @ Y ) ) ) )
% 3.67/2.04                  @ A4 )
% 3.67/2.04                = ( groups1340683514dd_sum @ C3 @ A
% 3.67/2.04                  @ ^ [Y: C3] :
% 3.67/2.04                      ( groups1340683514dd_sum @ B @ A
% 3.67/2.04                      @ ^ [X: B] : ( G @ X @ Y )
% 3.67/2.04                      @ ( collect @ B
% 3.67/2.04                        @ ^ [X: B] :
% 3.67/2.04                            ( ( member @ B @ X @ A4 )
% 3.67/2.04                            & ( R @ X @ Y ) ) ) )
% 3.67/2.04                  @ B4 ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_241_sum__nonpos,axiom,
% 3.67/2.04      ! [B: $tType,A: $tType] :
% 3.67/2.04        ( ( ordere216010020id_add @ A )
% 3.67/2.04       => ! [A4: set @ B,F2: B > A] :
% 3.67/2.04            ( ! [X4: B] :
% 3.67/2.04                ( ( member @ B @ X4 @ A4 )
% 3.67/2.04               => ( ord_less_eq @ A @ ( F2 @ X4 ) @ ( zero_zero @ A ) ) )
% 3.67/2.04           => ( ord_less_eq @ A @ ( groups1340683514dd_sum @ B @ A @ F2 @ A4 ) @ ( zero_zero @ A ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_242_sum__nonneg,axiom,
% 3.67/2.04      ! [A: $tType,B: $tType] :
% 3.67/2.04        ( ( ordere216010020id_add @ A )
% 3.67/2.04       => ! [A4: set @ B,F2: B > A] :
% 3.67/2.04            ( ! [X4: B] :
% 3.67/2.04                ( ( member @ B @ X4 @ A4 )
% 3.67/2.04               => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( F2 @ X4 ) ) )
% 3.67/2.04           => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( groups1340683514dd_sum @ B @ A @ F2 @ A4 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_243_sum__mono__inv,axiom,
% 3.67/2.04      ! [A: $tType,I3: $tType] :
% 3.67/2.04        ( ( ordere1818651114id_add @ A )
% 3.67/2.04       => ! [F2: I3 > A,I4: set @ I3,G: I3 > A,I5: I3] :
% 3.67/2.04            ( ( ( groups1340683514dd_sum @ I3 @ A @ F2 @ I4 )
% 3.67/2.04              = ( groups1340683514dd_sum @ I3 @ A @ G @ I4 ) )
% 3.67/2.04           => ( ! [I2: I3] :
% 3.67/2.04                  ( ( member @ I3 @ I2 @ I4 )
% 3.67/2.04                 => ( ord_less_eq @ A @ ( F2 @ I2 ) @ ( G @ I2 ) ) )
% 3.67/2.04             => ( ( member @ I3 @ I5 @ I4 )
% 3.67/2.04               => ( ( finite_finite2 @ I3 @ I4 )
% 3.67/2.04                 => ( ( F2 @ I5 )
% 3.67/2.04                    = ( G @ I5 ) ) ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_244_sum_Ointer__filter,axiom,
% 3.67/2.04      ! [A: $tType,B: $tType] :
% 3.67/2.04        ( ( comm_monoid_add @ A )
% 3.67/2.04       => ! [A4: set @ B,G: B > A,P: B > $o] :
% 3.67/2.04            ( ( finite_finite2 @ B @ A4 )
% 3.67/2.04           => ( ( groups1340683514dd_sum @ B @ A @ G
% 3.67/2.04                @ ( collect @ B
% 3.67/2.04                  @ ^ [X: B] :
% 3.67/2.04                      ( ( member @ B @ X @ A4 )
% 3.67/2.04                      & ( P @ X ) ) ) )
% 3.67/2.04              = ( groups1340683514dd_sum @ B @ A
% 3.67/2.04                @ ^ [X: B] : ( if @ A @ ( P @ X ) @ ( G @ X ) @ ( zero_zero @ A ) )
% 3.67/2.04                @ A4 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_245_sum__le__included,axiom,
% 3.67/2.04      ! [B: $tType,A: $tType,C3: $tType] :
% 3.67/2.04        ( ( ordere216010020id_add @ A )
% 3.67/2.04       => ! [S2: set @ B,T2: set @ C3,G: C3 > A,I5: C3 > B,F2: B > A] :
% 3.67/2.04            ( ( finite_finite2 @ B @ S2 )
% 3.67/2.04           => ( ( finite_finite2 @ C3 @ T2 )
% 3.67/2.04             => ( ! [X4: C3] :
% 3.67/2.04                    ( ( member @ C3 @ X4 @ T2 )
% 3.67/2.04                   => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( G @ X4 ) ) )
% 3.67/2.04               => ( ! [X4: B] :
% 3.67/2.04                      ( ( member @ B @ X4 @ S2 )
% 3.67/2.04                     => ? [Xa: C3] :
% 3.67/2.04                          ( ( member @ C3 @ Xa @ T2 )
% 3.67/2.04                          & ( ( I5 @ Xa )
% 3.67/2.04                            = X4 )
% 3.67/2.04                          & ( ord_less_eq @ A @ ( F2 @ X4 ) @ ( G @ Xa ) ) ) )
% 3.67/2.04                 => ( ord_less_eq @ A @ ( groups1340683514dd_sum @ B @ A @ F2 @ S2 ) @ ( groups1340683514dd_sum @ C3 @ A @ G @ T2 ) ) ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_246_sum__nonneg__eq__0__iff,axiom,
% 3.67/2.04      ! [A: $tType,B: $tType] :
% 3.67/2.04        ( ( ordere216010020id_add @ A )
% 3.67/2.04       => ! [A4: set @ B,F2: B > A] :
% 3.67/2.04            ( ( finite_finite2 @ B @ A4 )
% 3.67/2.04           => ( ! [X4: B] :
% 3.67/2.04                  ( ( member @ B @ X4 @ A4 )
% 3.67/2.04                 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( F2 @ X4 ) ) )
% 3.67/2.04             => ( ( ( groups1340683514dd_sum @ B @ A @ F2 @ A4 )
% 3.67/2.04                  = ( zero_zero @ A ) )
% 3.67/2.04                = ( ! [X: B] :
% 3.67/2.04                      ( ( member @ B @ X @ A4 )
% 3.67/2.04                     => ( ( F2 @ X )
% 3.67/2.04                        = ( zero_zero @ A ) ) ) ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_247_sum__strict__mono__ex1,axiom,
% 3.67/2.04      ! [A: $tType,I3: $tType] :
% 3.67/2.04        ( ( ordere1818651114id_add @ A )
% 3.67/2.04       => ! [A4: set @ I3,F2: I3 > A,G: I3 > A] :
% 3.67/2.04            ( ( finite_finite2 @ I3 @ A4 )
% 3.67/2.04           => ( ! [X4: I3] :
% 3.67/2.04                  ( ( member @ I3 @ X4 @ A4 )
% 3.67/2.04                 => ( ord_less_eq @ A @ ( F2 @ X4 ) @ ( G @ X4 ) ) )
% 3.67/2.04             => ( ? [X3: I3] :
% 3.67/2.04                    ( ( member @ I3 @ X3 @ A4 )
% 3.67/2.04                    & ( ord_less @ A @ ( F2 @ X3 ) @ ( G @ X3 ) ) )
% 3.67/2.04               => ( ord_less @ A @ ( groups1340683514dd_sum @ I3 @ A @ F2 @ A4 ) @ ( groups1340683514dd_sum @ I3 @ A @ G @ A4 ) ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_248_sum__nonneg__0,axiom,
% 3.67/2.04      ! [B: $tType,A: $tType] :
% 3.67/2.04        ( ( ordere216010020id_add @ A )
% 3.67/2.04       => ! [S2: set @ B,F2: B > A,I5: B] :
% 3.67/2.04            ( ( finite_finite2 @ B @ S2 )
% 3.67/2.04           => ( ! [I2: B] :
% 3.67/2.04                  ( ( member @ B @ I2 @ S2 )
% 3.67/2.04                 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( F2 @ I2 ) ) )
% 3.67/2.04             => ( ( ( groups1340683514dd_sum @ B @ A @ F2 @ S2 )
% 3.67/2.04                  = ( zero_zero @ A ) )
% 3.67/2.04               => ( ( member @ B @ I5 @ S2 )
% 3.67/2.04                 => ( ( F2 @ I5 )
% 3.67/2.04                    = ( zero_zero @ A ) ) ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_249_sum__nonneg__leq__bound,axiom,
% 3.67/2.04      ! [B: $tType,A: $tType] :
% 3.67/2.04        ( ( ordere216010020id_add @ A )
% 3.67/2.04       => ! [S2: set @ B,F2: B > A,B4: A,I5: B] :
% 3.67/2.04            ( ( finite_finite2 @ B @ S2 )
% 3.67/2.04           => ( ! [I2: B] :
% 3.67/2.04                  ( ( member @ B @ I2 @ S2 )
% 3.67/2.04                 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( F2 @ I2 ) ) )
% 3.67/2.04             => ( ( ( groups1340683514dd_sum @ B @ A @ F2 @ S2 )
% 3.67/2.04                  = B4 )
% 3.67/2.04               => ( ( member @ B @ I5 @ S2 )
% 3.67/2.04                 => ( ord_less_eq @ A @ ( F2 @ I5 ) @ B4 ) ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_250_sum__pos2,axiom,
% 3.67/2.04      ! [A: $tType,B: $tType] :
% 3.67/2.04        ( ( ordere216010020id_add @ A )
% 3.67/2.04       => ! [I4: set @ B,I5: B,F2: B > A] :
% 3.67/2.04            ( ( finite_finite2 @ B @ I4 )
% 3.67/2.04           => ( ( member @ B @ I5 @ I4 )
% 3.67/2.04             => ( ( ord_less @ A @ ( zero_zero @ A ) @ ( F2 @ I5 ) )
% 3.67/2.04               => ( ! [I2: B] :
% 3.67/2.04                      ( ( member @ B @ I2 @ I4 )
% 3.67/2.04                     => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( F2 @ I2 ) ) )
% 3.67/2.04                 => ( ord_less @ A @ ( zero_zero @ A ) @ ( groups1340683514dd_sum @ B @ A @ F2 @ I4 ) ) ) ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_251_not__one__less__zero,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linord1659791738miring @ A )
% 3.67/2.04       => ~ ( ord_less @ A @ ( one_one @ A ) @ ( zero_zero @ A ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_252_zero__less__one,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( zero_less_one @ A )
% 3.67/2.04       => ( ord_less @ A @ ( zero_zero @ A ) @ ( one_one @ A ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(fact_253_linorder__neqE__linordered__idom,axiom,
% 3.67/2.04      ! [A: $tType] :
% 3.67/2.04        ( ( linordered_idom @ A )
% 3.67/2.04       => ! [X2: A,Y2: A] :
% 3.67/2.04            ( ( X2 != Y2 )
% 3.67/2.04           => ( ~ ( ord_less @ A @ X2 @ Y2 )
% 3.67/2.04             => ( ord_less @ A @ Y2 @ X2 ) ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Polynomial_Opoly___Rings_Oidom,axiom,
% 3.67/2.04      ! [A9: $tType] :
% 3.67/2.04        ( ( idom @ A9 )
% 3.67/2.04       => ( idom @ ( poly @ A9 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Real_Oreal___Rings_Oidom_1,axiom,
% 3.67/2.04      idom @ real ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Int_Oint___Rings_Oidom_2,axiom,
% 3.67/2.04      idom @ int ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_fun___Orderings_Opreorder,axiom,
% 3.67/2.04      ! [A9: $tType,A10: $tType] :
% 3.67/2.04        ( ( preorder @ A10 )
% 3.67/2.04       => ( preorder @ ( A9 > A10 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_fun___Finite__Set_Ofinite,axiom,
% 3.67/2.04      ! [A9: $tType,A10: $tType] :
% 3.67/2.04        ( ( ( finite_finite @ A9 )
% 3.67/2.04          & ( finite_finite @ A10 ) )
% 3.67/2.04       => ( finite_finite @ ( A9 > A10 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_fun___Orderings_Oorder,axiom,
% 3.67/2.04      ! [A9: $tType,A10: $tType] :
% 3.67/2.04        ( ( order @ A10 )
% 3.67/2.04       => ( order @ ( A9 > A10 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_fun___Orderings_Oord,axiom,
% 3.67/2.04      ! [A9: $tType,A10: $tType] :
% 3.67/2.04        ( ( ord @ A10 )
% 3.67/2.04       => ( ord @ ( A9 > A10 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Int_Oint___Conditionally__Complete__Lattices_Oconditionally__complete__linorder,axiom,
% 3.67/2.04      condit1037483654norder @ int ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Int_Oint___Groups_Oordered__cancel__comm__monoid__add,axiom,
% 3.67/2.04      ordere1818651114id_add @ int ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Int_Oint___Rings_Olinordered__nonzero__semiring,axiom,
% 3.67/2.04      linord1659791738miring @ int ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Int_Oint___Groups_Oordered__comm__monoid__add,axiom,
% 3.67/2.04      ordere216010020id_add @ int ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Int_Oint___Rings_Oring__no__zero__divisors,axiom,
% 3.67/2.04      ring_n68954251visors @ int ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Int_Oint___Groups_Ocomm__monoid__add,axiom,
% 3.67/2.04      comm_monoid_add @ int ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Int_Oint___Rings_Olinordered__idom,axiom,
% 3.67/2.04      linordered_idom @ int ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Int_Oint___Rings_Ocomm__semiring__1,axiom,
% 3.67/2.04      comm_semiring_1 @ int ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Int_Oint___Rings_Ocomm__semiring__0,axiom,
% 3.67/2.04      comm_semiring_0 @ int ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Int_Oint___Rings_Ozero__less__one,axiom,
% 3.67/2.04      zero_less_one @ int ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Int_Oint___Orderings_Opreorder_3,axiom,
% 3.67/2.04      preorder @ int ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Int_Oint___Orderings_Olinorder,axiom,
% 3.67/2.04      linorder @ int ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Int_Oint___Rings_Ocomm__ring__1,axiom,
% 3.67/2.04      comm_ring_1 @ int ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Int_Oint___Orderings_Ono__top,axiom,
% 3.67/2.04      no_top @ int ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Int_Oint___Orderings_Ono__bot,axiom,
% 3.67/2.04      no_bot @ int ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Int_Oint___Orderings_Oorder_4,axiom,
% 3.67/2.04      order @ int ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Int_Oint___Nat_Oring__char__0,axiom,
% 3.67/2.04      ring_char_0 @ int ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Int_Oint___Orderings_Oord_5,axiom,
% 3.67/2.04      ord @ int ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Int_Oint___Groups_Ozero,axiom,
% 3.67/2.04      zero @ int ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Int_Oint___Groups_Oone,axiom,
% 3.67/2.04      one @ int ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Nat_Onat___Conditionally__Complete__Lattices_Oconditionally__complete__linorder_6,axiom,
% 3.67/2.04      condit1037483654norder @ nat ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Nat_Onat___Groups_Oordered__cancel__comm__monoid__add_7,axiom,
% 3.67/2.04      ordere1818651114id_add @ nat ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 3.67/2.04      canoni770627133id_add @ nat ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring_8,axiom,
% 3.67/2.04      linord1659791738miring @ nat ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Nat_Onat___Groups_Oordered__comm__monoid__add_9,axiom,
% 3.67/2.04      ordere216010020id_add @ nat ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Nat_Onat___Groups_Ocomm__monoid__add_10,axiom,
% 3.67/2.04      comm_monoid_add @ nat ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Nat_Onat___Rings_Ocomm__semiring__1_11,axiom,
% 3.67/2.04      comm_semiring_1 @ nat ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Nat_Onat___Rings_Ocomm__semiring__0_12,axiom,
% 3.67/2.04      comm_semiring_0 @ nat ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Nat_Onat___Rings_Ozero__less__one_13,axiom,
% 3.67/2.04      zero_less_one @ nat ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 3.67/2.04      wellorder @ nat ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Nat_Onat___Orderings_Opreorder_14,axiom,
% 3.67/2.04      preorder @ nat ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Nat_Onat___Orderings_Olinorder_15,axiom,
% 3.67/2.04      linorder @ nat ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Nat_Onat___Orderings_Ono__top_16,axiom,
% 3.67/2.04      no_top @ nat ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Nat_Onat___Orderings_Oorder_17,axiom,
% 3.67/2.04      order @ nat ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Nat_Onat___Orderings_Oord_18,axiom,
% 3.67/2.04      ord @ nat ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Nat_Onat___Groups_Ozero_19,axiom,
% 3.67/2.04      zero @ nat ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Nat_Onat___Groups_Oone_20,axiom,
% 3.67/2.04      one @ nat ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Set_Oset___Orderings_Opreorder_21,axiom,
% 3.67/2.04      ! [A9: $tType] : ( preorder @ ( set @ A9 ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Set_Oset___Finite__Set_Ofinite_22,axiom,
% 3.67/2.04      ! [A9: $tType] :
% 3.67/2.04        ( ( finite_finite @ A9 )
% 3.67/2.04       => ( finite_finite @ ( set @ A9 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Set_Oset___Orderings_Oorder_23,axiom,
% 3.67/2.04      ! [A9: $tType] : ( order @ ( set @ A9 ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Set_Oset___Orderings_Oord_24,axiom,
% 3.67/2.04      ! [A9: $tType] : ( ord @ ( set @ A9 ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_HOL_Obool___Orderings_Opreorder_25,axiom,
% 3.67/2.04      preorder @ $o ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_HOL_Obool___Orderings_Olinorder_26,axiom,
% 3.67/2.04      linorder @ $o ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_HOL_Obool___Finite__Set_Ofinite_27,axiom,
% 3.67/2.04      finite_finite @ $o ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_HOL_Obool___Orderings_Oorder_28,axiom,
% 3.67/2.04      order @ $o ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_HOL_Obool___Orderings_Oord_29,axiom,
% 3.67/2.04      ord @ $o ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Real_Oreal___Conditionally__Complete__Lattices_Oconditionally__complete__linorder_30,axiom,
% 3.67/2.04      condit1037483654norder @ real ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Real_Oreal___Conditionally__Complete__Lattices_Olinear__continuum,axiom,
% 3.67/2.04      condit1656338222tinuum @ real ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Real_Oreal___Groups_Oordered__cancel__comm__monoid__add_31,axiom,
% 3.67/2.04      ordere1818651114id_add @ real ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring_32,axiom,
% 3.67/2.04      linord1659791738miring @ real ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Real_Oreal___Groups_Oordered__comm__monoid__add_33,axiom,
% 3.67/2.04      ordere216010020id_add @ real ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Real_Oreal___Rings_Oring__no__zero__divisors_34,axiom,
% 3.67/2.04      ring_n68954251visors @ real ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Real_Oreal___Orderings_Odense__linorder,axiom,
% 3.67/2.04      dense_linorder @ real ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Real_Oreal___Fields_Olinordered__field,axiom,
% 3.67/2.04      linordered_field @ real ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Real_Oreal___Groups_Ocomm__monoid__add_35,axiom,
% 3.67/2.04      comm_monoid_add @ real ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Real_Oreal___Rings_Olinordered__idom_36,axiom,
% 3.67/2.04      linordered_idom @ real ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Real_Oreal___Rings_Ocomm__semiring__1_37,axiom,
% 3.67/2.04      comm_semiring_1 @ real ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Real_Oreal___Rings_Ocomm__semiring__0_38,axiom,
% 3.67/2.04      comm_semiring_0 @ real ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Real_Oreal___Orderings_Odense__order,axiom,
% 3.67/2.04      dense_order @ real ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Real_Oreal___Rings_Ozero__less__one_39,axiom,
% 3.67/2.04      zero_less_one @ real ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Real_Oreal___Orderings_Opreorder_40,axiom,
% 3.67/2.04      preorder @ real ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Real_Oreal___Orderings_Olinorder_41,axiom,
% 3.67/2.04      linorder @ real ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Real_Oreal___Rings_Ocomm__ring__1_42,axiom,
% 3.67/2.04      comm_ring_1 @ real ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Real_Oreal___Orderings_Ono__top_43,axiom,
% 3.67/2.04      no_top @ real ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Real_Oreal___Orderings_Ono__bot_44,axiom,
% 3.67/2.04      no_bot @ real ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Real_Oreal___Orderings_Oorder_45,axiom,
% 3.67/2.04      order @ real ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Real_Oreal___Nat_Oring__char__0_46,axiom,
% 3.67/2.04      ring_char_0 @ real ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Real_Oreal___Orderings_Oord_47,axiom,
% 3.67/2.04      ord @ real ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Real_Oreal___Groups_Ozero_48,axiom,
% 3.67/2.04      zero @ real ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Real_Oreal___Groups_Oone_49,axiom,
% 3.67/2.04      one @ real ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Polynomial_Opoly___Groups_Oordered__cancel__comm__monoid__add_50,axiom,
% 3.67/2.04      ! [A9: $tType] :
% 3.67/2.04        ( ( linordered_idom @ A9 )
% 3.67/2.04       => ( ordere1818651114id_add @ ( poly @ A9 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Polynomial_Opoly___Rings_Olinordered__nonzero__semiring_51,axiom,
% 3.67/2.04      ! [A9: $tType] :
% 3.67/2.04        ( ( linordered_idom @ A9 )
% 3.67/2.04       => ( linord1659791738miring @ ( poly @ A9 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Polynomial_Opoly___Groups_Oordered__comm__monoid__add_52,axiom,
% 3.67/2.04      ! [A9: $tType] :
% 3.67/2.04        ( ( linordered_idom @ A9 )
% 3.67/2.04       => ( ordere216010020id_add @ ( poly @ A9 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Polynomial_Opoly___Rings_Oring__no__zero__divisors_53,axiom,
% 3.67/2.04      ! [A9: $tType] :
% 3.67/2.04        ( ( idom @ A9 )
% 3.67/2.04       => ( ring_n68954251visors @ ( poly @ A9 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Polynomial_Opoly___Groups_Ocomm__monoid__add_54,axiom,
% 3.67/2.04      ! [A9: $tType] :
% 3.67/2.04        ( ( comm_monoid_add @ A9 )
% 3.67/2.04       => ( comm_monoid_add @ ( poly @ A9 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Polynomial_Opoly___Rings_Olinordered__idom_55,axiom,
% 3.67/2.04      ! [A9: $tType] :
% 3.67/2.04        ( ( linordered_idom @ A9 )
% 3.67/2.04       => ( linordered_idom @ ( poly @ A9 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Polynomial_Opoly___Rings_Ocomm__semiring__1_56,axiom,
% 3.67/2.04      ! [A9: $tType] :
% 3.67/2.04        ( ( comm_semiring_1 @ A9 )
% 3.67/2.04       => ( comm_semiring_1 @ ( poly @ A9 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Polynomial_Opoly___Rings_Ocomm__semiring__0_57,axiom,
% 3.67/2.04      ! [A9: $tType] :
% 3.67/2.04        ( ( comm_semiring_0 @ A9 )
% 3.67/2.04       => ( comm_semiring_0 @ ( poly @ A9 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Polynomial_Opoly___Rings_Ozero__less__one_58,axiom,
% 3.67/2.04      ! [A9: $tType] :
% 3.67/2.04        ( ( linordered_idom @ A9 )
% 3.67/2.04       => ( zero_less_one @ ( poly @ A9 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Polynomial_Opoly___Orderings_Opreorder_59,axiom,
% 3.67/2.04      ! [A9: $tType] :
% 3.67/2.04        ( ( linordered_idom @ A9 )
% 3.67/2.04       => ( preorder @ ( poly @ A9 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Polynomial_Opoly___Orderings_Olinorder_60,axiom,
% 3.67/2.04      ! [A9: $tType] :
% 3.67/2.04        ( ( linordered_idom @ A9 )
% 3.67/2.04       => ( linorder @ ( poly @ A9 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Polynomial_Opoly___Rings_Ocomm__ring__1_61,axiom,
% 3.67/2.04      ! [A9: $tType] :
% 3.67/2.04        ( ( comm_ring_1 @ A9 )
% 3.67/2.04       => ( comm_ring_1 @ ( poly @ A9 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Polynomial_Opoly___Orderings_Oorder_62,axiom,
% 3.67/2.04      ! [A9: $tType] :
% 3.67/2.04        ( ( linordered_idom @ A9 )
% 3.67/2.04       => ( order @ ( poly @ A9 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Polynomial_Opoly___Nat_Oring__char__0_63,axiom,
% 3.67/2.04      ! [A9: $tType] :
% 3.67/2.04        ( ( ( ring_char_0 @ A9 )
% 3.67/2.04          & ( comm_ring_1 @ A9 ) )
% 3.67/2.04       => ( ring_char_0 @ ( poly @ A9 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Polynomial_Opoly___Orderings_Oord_64,axiom,
% 3.67/2.04      ! [A9: $tType] :
% 3.67/2.04        ( ( linordered_idom @ A9 )
% 3.67/2.04       => ( ord @ ( poly @ A9 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Polynomial_Opoly___Groups_Ozero_65,axiom,
% 3.67/2.04      ! [A9: $tType] :
% 3.67/2.04        ( ( zero @ A9 )
% 3.67/2.04       => ( zero @ ( poly @ A9 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(tcon_Polynomial_Opoly___Groups_Oone_66,axiom,
% 3.67/2.04      ! [A9: $tType] :
% 3.67/2.04        ( ( comm_semiring_1 @ A9 )
% 3.67/2.04       => ( one @ ( poly @ A9 ) ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(help_If_3_1_T,axiom,
% 3.67/2.04      ! [P: $o] :
% 3.67/2.04        ( ( P = $true )
% 3.67/2.04        | ( P = $false ) ) ).
% 3.67/2.04  
% 3.67/2.04  thf(help_If_2_1_T,axiom,
% 3.67/2.04      ! [A: $tType,X2: A,Y2: A] :
% 3.67/2.04        ( ( if @ A @ $false @ X2 @ Y2 )
% 3.67/2.04        = Y2 ) ).
% 3.67/2.04  
% 3.67/2.04  thf(help_If_1_1_T,axiom,
% 3.67/2.04      ! [A: $tType,X2: A,Y2: A] :
% 3.67/2.04        ( ( if @ A @ $true @ X2 @ Y2 )
% 3.67/2.04        = X2 ) ).
% 3.67/2.04  
% 3.67/2.04  thf(conj_0,conjecture,
% 3.67/2.04      ( finite_finite2 @ real
% 3.67/2.04      @ ( collect @ real
% 3.67/2.04        @ ^ [X: real] :
% 3.67/2.04            ( ( ( poly2 @ real @ p @ X )
% 3.67/2.04              = ( zero_zero @ real ) )
% 3.67/2.04            & ( ord_less @ real @ a @ X )
% 3.67/2.04            & ( ord_less @ real @ X @ b ) ) ) ) ).
% 3.67/2.04  ------------------------
% 3.67/2.08  % (2074)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_1969 for (2999ds/2Mi)
% 3.67/2.08  % (2073)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1969 for (2999ds/2Mi)
% 3.67/2.08  % (2072)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_1969 for (2999ds/27Mi)
% 3.67/2.08  % (2075)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_1969 for (2999ds/275Mi)
% 3.67/2.08  % (2071)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_1969 for (2999ds/4Mi)
% 3.67/2.08  % (2070)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1969 for (2999ds/183Mi)
% 3.67/2.08  % (2076)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1969 for (2999ds/18Mi)
% 3.67/2.08  % (2073)Instruction limit reached!
% 3.67/2.08  % (2073)------------------------------
% 3.67/2.08  % (2073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.67/2.08  % (2073)Termination reason: Unknown
% 3.67/2.08  % (2073)Termination phase: shuffling
% 3.67/2.08  
% 3.67/2.08  % (2073)Memory used [KB]: 1407
% 3.67/2.08  % (2073)Time elapsed: 0.003 s
% 3.67/2.08  % (2073)Instructions burned: 2 (million)
% 3.67/2.08  % (2073)------------------------------
% 3.67/2.08  % (2073)------------------------------
% 3.67/2.09  % (2071)Instruction limit reached!
% 3.67/2.09  % (2071)------------------------------
% 3.67/2.09  % (2071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.67/2.09  % (2071)Termination reason: Unknown
% 3.67/2.09  % (2071)Termination phase: shuffling
% 3.67/2.09  
% 3.67/2.09  % (2071)Memory used [KB]: 1407
% 3.67/2.09  % (2071)Time elapsed: 0.004 s
% 3.67/2.09  % (2071)Instructions burned: 4 (million)
% 3.67/2.09  % (2071)------------------------------
% 3.67/2.09  % (2071)------------------------------
% 3.67/2.09  % (2074)Instruction limit reached!
% 3.67/2.09  % (2074)------------------------------
% 3.67/2.09  % (2074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.67/2.09  % (2074)Termination reason: Unknown
% 3.67/2.09  % (2074)Termination phase: shuffling
% 3.67/2.09  
% 3.67/2.09  % (2074)Memory used [KB]: 1407
% 3.67/2.09  % (2074)Time elapsed: 0.005 s
% 3.67/2.09  % (2074)Instructions burned: 2 (million)
% 3.67/2.09  % (2074)------------------------------
% 3.67/2.09  % (2074)------------------------------
% 3.67/2.09  % (2076)Instruction limit reached!
% 3.67/2.09  % (2076)------------------------------
% 3.67/2.09  % (2076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.67/2.09  % (2076)Termination reason: Unknown
% 3.67/2.09  % (2076)Termination phase: shuffling
% 3.67/2.09  
% 3.67/2.09  % (2076)Memory used [KB]: 1791
% 3.67/2.09  % (2076)Time elapsed: 0.013 s
% 3.67/2.09  % (2076)Instructions burned: 18 (million)
% 3.67/2.09  % (2076)------------------------------
% 3.67/2.09  % (2076)------------------------------
% 3.67/2.10  % (2072)Instruction limit reached!
% 3.67/2.10  % (2072)------------------------------
% 3.67/2.10  % (2072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.67/2.10  % (2072)Termination reason: Unknown
% 3.67/2.10  % (2072)Termination phase: Property scanning
% 3.67/2.10  
% 3.67/2.10  % (2072)Memory used [KB]: 2046
% 3.67/2.10  % (2072)Time elapsed: 0.017 s
% 3.67/2.10  % (2072)Instructions burned: 27 (million)
% 3.67/2.10  % (2072)------------------------------
% 3.67/2.10  % (2072)------------------------------
% 3.67/2.10  % (2078)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_1969 for (2999ds/37Mi)
% 3.67/2.10  % (2077)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_1969 for (2999ds/3Mi)
% 3.67/2.10  % (2079)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_1969 for (2999ds/15Mi)
% 3.67/2.11  % (2077)Instruction limit reached!
% 3.67/2.11  % (2077)------------------------------
% 3.67/2.11  % (2077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.67/2.11  % (2077)Termination reason: Unknown
% 3.67/2.11  % (2077)Termination phase: shuffling
% 3.67/2.11  
% 3.67/2.11  % (2077)Memory used [KB]: 1407
% 3.67/2.11  % (2077)Time elapsed: 0.004 s
% 3.67/2.11  % (2077)Instructions burned: 3 (million)
% 3.67/2.11  % (2077)------------------------------
% 3.67/2.11  % (2077)------------------------------
% 3.67/2.11  % (2079)Instruction limit reached!
% 3.67/2.11  % (2079)------------------------------
% 3.67/2.11  % (2079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.67/2.11  % (2079)Termination reason: Unknown
% 3.67/2.11  % (2079)Termination phase: shuffling
% 3.67/2.11  
% 3.67/2.11  % (2079)Memory used [KB]: 1791
% 3.67/2.11  % (2079)Time elapsed: 0.011 s
% 3.67/2.11  % (2079)Instructions burned: 15 (million)
% 3.67/2.11  % (2079)------------------------------
% 3.67/2.11  % (2079)------------------------------
% 3.67/2.11  % (2080)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_1969 for (2999ds/3Mi)
% 3.67/2.12  % (2080)Instruction limit reached!
% 3.67/2.12  % (2080)------------------------------
% 3.67/2.12  % (2080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.67/2.12  % (2080)Termination reason: Unknown
% 3.67/2.12  % (2080)Termination phase: shuffling
% 3.67/2.12  
% 3.67/2.12  % (2080)Memory used [KB]: 1407
% 3.67/2.12  % (2080)Time elapsed: 0.004 s
% 3.67/2.12  % (2080)Instructions burned: 3 (million)
% 3.67/2.12  % (2080)------------------------------
% 3.67/2.12  % (2080)------------------------------
% 3.67/2.12  % (2081)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_1969 for (2999ds/1041Mi)
% 3.67/2.12  % (2078)Instruction limit reached!
% 3.67/2.12  % (2078)------------------------------
% 3.67/2.12  % (2078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.67/2.12  % (2078)Termination reason: Unknown
% 3.67/2.12  % (2078)Termination phase: shuffling
% 3.67/2.12  
% 3.67/2.12  % (2078)Memory used [KB]: 2174
% 3.67/2.12  % (2078)Time elapsed: 0.021 s
% 3.67/2.12  % (2078)Instructions burned: 37 (million)
% 3.67/2.12  % (2078)------------------------------
% 3.67/2.12  % (2078)------------------------------
% 3.67/2.13  % (2082)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_1969 for (2999ds/7Mi)
% 3.70/2.13  % (2082)Instruction limit reached!
% 3.70/2.13  % (2082)------------------------------
% 3.70/2.13  % (2082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.13  % (2082)Termination reason: Unknown
% 3.70/2.13  % (2082)Termination phase: shuffling
% 3.70/2.13  
% 3.70/2.13  % (2082)Memory used [KB]: 1535
% 3.70/2.13  % (2082)Time elapsed: 0.007 s
% 3.70/2.13  % (2082)Instructions burned: 8 (million)
% 3.70/2.13  % (2082)------------------------------
% 3.70/2.13  % (2082)------------------------------
% 3.70/2.13  % (2083)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_1969 for (2999ds/16Mi)
% 3.70/2.14  % (2084)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_1969 for (2999ds/3Mi)
% 3.70/2.14  % (2084)Instruction limit reached!
% 3.70/2.14  % (2084)------------------------------
% 3.70/2.14  % (2084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.14  % (2084)Termination reason: Unknown
% 3.70/2.14  % (2084)Termination phase: shuffling
% 3.70/2.14  
% 3.70/2.14  % (2084)Memory used [KB]: 1407
% 3.70/2.14  % (2084)Time elapsed: 0.004 s
% 3.70/2.14  % (2084)Instructions burned: 4 (million)
% 3.70/2.14  % (2084)------------------------------
% 3.70/2.14  % (2084)------------------------------
% 3.70/2.14  % (2083)Instruction limit reached!
% 3.70/2.14  % (2083)------------------------------
% 3.70/2.14  % (2083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.14  % (2083)Termination reason: Unknown
% 3.70/2.14  % (2083)Termination phase: shuffling
% 3.70/2.14  
% 3.70/2.14  % (2083)Memory used [KB]: 1791
% 3.70/2.14  % (2083)Time elapsed: 0.012 s
% 3.70/2.14  % (2083)Instructions burned: 17 (million)
% 3.70/2.14  % (2083)------------------------------
% 3.70/2.14  % (2083)------------------------------
% 3.70/2.14  % (2085)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_1969 for (2999ds/3Mi)
% 3.70/2.15  % (2085)Instruction limit reached!
% 3.70/2.15  % (2085)------------------------------
% 3.70/2.15  % (2085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.15  % (2085)Termination reason: Unknown
% 3.70/2.15  % (2085)Termination phase: shuffling
% 3.70/2.15  
% 3.70/2.15  % (2085)Memory used [KB]: 1407
% 3.70/2.15  % (2085)Time elapsed: 0.004 s
% 3.70/2.15  % (2085)Instructions burned: 3 (million)
% 3.70/2.15  % (2085)------------------------------
% 3.70/2.15  % (2085)------------------------------
% 3.70/2.15  % (2086)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_1969 for (2999ds/7Mi)
% 3.70/2.15  % (2086)Instruction limit reached!
% 3.70/2.15  % (2086)------------------------------
% 3.70/2.15  % (2086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.15  % (2086)Termination reason: Unknown
% 3.70/2.15  % (2086)Termination phase: shuffling
% 3.70/2.15  
% 3.70/2.16  % (2086)Memory used [KB]: 1535
% 3.70/2.16  % (2086)Time elapsed: 0.006 s
% 3.70/2.16  % (2086)Instructions burned: 7 (million)
% 3.70/2.16  % (2086)------------------------------
% 3.70/2.16  % (2086)------------------------------
% 3.70/2.16  % (2087)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_1969 for (2999ds/3Mi)
% 3.70/2.16  % (2087)Instruction limit reached!
% 3.70/2.16  % (2087)------------------------------
% 3.70/2.16  % (2087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.16  % (2087)Termination reason: Unknown
% 3.70/2.16  % (2087)Termination phase: shuffling
% 3.70/2.16  
% 3.70/2.16  % (2087)Memory used [KB]: 1407
% 3.70/2.16  % (2087)Time elapsed: 0.004 s
% 3.70/2.16  % (2087)Instructions burned: 3 (million)
% 3.70/2.16  % (2087)------------------------------
% 3.70/2.16  % (2087)------------------------------
% 3.70/2.16  % (2088)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_1969 for (2999ds/4Mi)
% 3.70/2.17  % (2088)Instruction limit reached!
% 3.70/2.17  % (2088)------------------------------
% 3.70/2.17  % (2088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.17  % (2089)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_1969 for (2999ds/18Mi)
% 3.70/2.17  % (2088)Termination reason: Unknown
% 3.70/2.17  % (2088)Termination phase: shuffling
% 3.70/2.17  
% 3.70/2.17  % (2088)Memory used [KB]: 1535
% 3.70/2.17  % (2088)Time elapsed: 0.005 s
% 3.70/2.17  % (2088)Instructions burned: 5 (million)
% 3.70/2.17  % (2088)------------------------------
% 3.70/2.17  % (2088)------------------------------
% 3.70/2.17  % (2090)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_1969 for (2999ds/710Mi)
% 3.70/2.18  % (2089)Instruction limit reached!
% 3.70/2.18  % (2089)------------------------------
% 3.70/2.18  % (2089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.18  % (2089)Termination reason: Unknown
% 3.70/2.18  % (2089)Termination phase: shuffling
% 3.70/2.18  
% 3.70/2.18  % (2089)Memory used [KB]: 1918
% 3.70/2.18  % (2089)Time elapsed: 0.013 s
% 3.70/2.18  % (2089)Instructions burned: 19 (million)
% 3.70/2.18  % (2089)------------------------------
% 3.70/2.18  % (2089)------------------------------
% 3.70/2.18  % (2091)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_1969 for (2999ds/6Mi)
% 3.70/2.18  % (2091)Instruction limit reached!
% 3.70/2.18  % (2091)------------------------------
% 3.70/2.18  % (2091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.18  % (2091)Termination reason: Unknown
% 3.70/2.18  % (2091)Termination phase: shuffling
% 3.70/2.18  
% 3.70/2.18  % (2091)Memory used [KB]: 1535
% 3.70/2.18  % (2091)Time elapsed: 0.006 s
% 3.70/2.18  % (2091)Instructions burned: 7 (million)
% 3.70/2.18  % (2091)------------------------------
% 3.70/2.18  % (2091)------------------------------
% 3.70/2.19  % (2070)Instruction limit reached!
% 3.70/2.19  % (2070)------------------------------
% 3.70/2.19  % (2070)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.19  % (2070)Termination reason: Unknown
% 3.70/2.19  % (2070)Termination phase: Saturation
% 3.70/2.19  
% 3.70/2.19  % (2070)Memory used [KB]: 7419
% 3.70/2.19  % (2070)Time elapsed: 0.104 s
% 3.70/2.19  % (2070)Instructions burned: 183 (million)
% 3.70/2.19  % (2070)------------------------------
% 3.70/2.19  % (2070)------------------------------
% 3.70/2.19  % (2092)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_1969 for (2998ds/902Mi)
% 3.70/2.20  % (2093)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_1969 for (2998ds/21Mi)
% 3.70/2.20  % (2094)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_1969 for (2998ds/5Mi)
% 3.70/2.21  % (2095)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_1969 for (2998ds/6Mi)
% 3.70/2.21  % (2094)Instruction limit reached!
% 3.70/2.21  % (2094)------------------------------
% 3.70/2.21  % (2094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.21  % (2094)Termination reason: Unknown
% 3.70/2.21  % (2094)Termination phase: shuffling
% 3.70/2.21  
% 3.70/2.21  % (2094)Memory used [KB]: 1407
% 3.70/2.21  % (2094)Time elapsed: 0.005 s
% 3.70/2.21  % (2094)Instructions burned: 5 (million)
% 3.70/2.21  % (2094)------------------------------
% 3.70/2.21  % (2094)------------------------------
% 3.70/2.21  % (2095)Instruction limit reached!
% 3.70/2.21  % (2095)------------------------------
% 3.70/2.21  % (2095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.21  % (2095)Termination reason: Unknown
% 3.70/2.21  % (2095)Termination phase: shuffling
% 3.70/2.21  
% 3.70/2.21  % (2095)Memory used [KB]: 1407
% 3.70/2.21  % (2095)Time elapsed: 0.005 s
% 3.70/2.21  % (2095)Instructions burned: 6 (million)
% 3.70/2.21  % (2095)------------------------------
% 3.70/2.21  % (2095)------------------------------
% 3.70/2.21  % (2093)Instruction limit reached!
% 3.70/2.21  % (2093)------------------------------
% 3.70/2.21  % (2093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.21  % (2093)Termination reason: Unknown
% 3.70/2.21  % (2093)Termination phase: shuffling
% 3.70/2.21  
% 3.70/2.21  % (2093)Memory used [KB]: 1918
% 3.70/2.21  % (2093)Time elapsed: 0.015 s
% 3.70/2.21  % (2093)Instructions burned: 22 (million)
% 3.70/2.21  % (2093)------------------------------
% 3.70/2.21  % (2093)------------------------------
% 3.70/2.23  % (2098)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_1969 for (2998ds/19Mi)
% 3.70/2.23  % (2097)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_1969 for (2998ds/779Mi)
% 3.70/2.23  % (2096)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_1969 for (2998ds/377Mi)
% 3.70/2.24  % (2075)Instruction limit reached!
% 3.70/2.24  % (2075)------------------------------
% 3.70/2.24  % (2075)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.24  % (2075)Termination reason: Unknown
% 3.70/2.24  % (2075)Termination phase: Saturation
% 3.70/2.24  
% 3.70/2.24  % (2075)Memory used [KB]: 7036
% 3.70/2.24  % (2075)Time elapsed: 0.156 s
% 3.70/2.24  % (2075)Instructions burned: 275 (million)
% 3.70/2.24  % (2075)------------------------------
% 3.70/2.24  % (2075)------------------------------
% 3.70/2.24  % (2098)Instruction limit reached!
% 3.70/2.24  % (2098)------------------------------
% 3.70/2.24  % (2098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.24  % (2098)Termination reason: Unknown
% 3.70/2.24  % (2098)Termination phase: shuffling
% 3.70/2.24  
% 3.70/2.24  % (2098)Memory used [KB]: 1791
% 3.70/2.24  % (2098)Time elapsed: 0.013 s
% 3.70/2.24  % (2098)Instructions burned: 20 (million)
% 3.70/2.24  % (2098)------------------------------
% 3.70/2.24  % (2098)------------------------------
% 3.70/2.26  % (2099)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_1969 for (2998ds/879Mi)
% 3.70/2.26  % (2100)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_1969 for (2998ds/17Mi)
% 3.70/2.27  % (2100)Instruction limit reached!
% 3.70/2.27  % (2100)------------------------------
% 3.70/2.27  % (2100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.27  % (2100)Termination reason: Unknown
% 3.70/2.27  % (2100)Termination phase: shuffling
% 3.70/2.27  
% 3.70/2.27  % (2100)Memory used [KB]: 1791
% 3.70/2.27  % (2100)Time elapsed: 0.012 s
% 3.70/2.27  % (2100)Instructions burned: 18 (million)
% 3.70/2.27  % (2100)------------------------------
% 3.70/2.27  % (2100)------------------------------
% 3.70/2.29  % (2101)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_1969 for (2997ds/3Mi)
% 3.70/2.30  % (2101)Instruction limit reached!
% 3.70/2.30  % (2101)------------------------------
% 3.70/2.30  % (2101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.30  % (2101)Termination reason: Unknown
% 3.70/2.30  % (2101)Termination phase: shuffling
% 3.70/2.30  
% 3.70/2.30  % (2101)Memory used [KB]: 1407
% 3.70/2.30  % (2101)Time elapsed: 0.004 s
% 3.70/2.30  % (2101)Instructions burned: 3 (million)
% 3.70/2.30  % (2101)------------------------------
% 3.70/2.30  % (2101)------------------------------
% 3.70/2.32  % (2102)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_1969 for (2997ds/30Mi)
% 3.70/2.34  % (2102)Instruction limit reached!
% 3.70/2.34  % (2102)------------------------------
% 3.70/2.34  % (2102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.34  % (2102)Termination reason: Unknown
% 3.70/2.34  % (2102)Termination phase: Property scanning
% 3.70/2.34  
% 3.70/2.34  % (2102)Memory used [KB]: 2046
% 3.70/2.34  % (2102)Time elapsed: 0.020 s
% 3.70/2.34  % (2102)Instructions burned: 31 (million)
% 3.70/2.34  % (2102)------------------------------
% 3.70/2.34  % (2102)------------------------------
% 3.70/2.36  % (2103)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_1969 for (2997ds/127Mi)
% 3.70/2.43  % (2103)Instruction limit reached!
% 3.70/2.43  % (2103)------------------------------
% 3.70/2.43  % (2103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.43  % (2103)Termination reason: Unknown
% 3.70/2.43  % (2103)Termination phase: Saturation
% 3.70/2.43  
% 3.70/2.43  % (2103)Memory used [KB]: 7036
% 3.70/2.43  % (2103)Time elapsed: 0.075 s
% 3.70/2.43  % (2103)Instructions burned: 127 (million)
% 3.70/2.43  % (2103)------------------------------
% 3.70/2.43  % (2103)------------------------------
% 3.70/2.44  % (2096)Instruction limit reached!
% 3.70/2.44  % (2096)------------------------------
% 3.70/2.44  % (2096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.44  % (2096)Termination reason: Unknown
% 3.70/2.44  % (2096)Termination phase: Saturation
% 3.70/2.44  
% 3.70/2.44  % (2096)Memory used [KB]: 7931
% 3.70/2.44  % (2096)Time elapsed: 0.215 s
% 3.70/2.44  % (2096)Instructions burned: 378 (million)
% 3.70/2.44  % (2096)------------------------------
% 3.70/2.44  % (2096)------------------------------
% 3.70/2.45  % (2104)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_1969 for (2996ds/100Mi)
% 3.70/2.46  % (2105)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_1969 for (2996ds/3Mi)
% 3.70/2.47  % (2105)Instruction limit reached!
% 3.70/2.47  % (2105)------------------------------
% 3.70/2.47  % (2105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.47  % (2105)Termination reason: Unknown
% 3.70/2.47  % (2105)Termination phase: shuffling
% 3.70/2.47  
% 3.70/2.47  % (2105)Memory used [KB]: 1407
% 3.70/2.47  % (2105)Time elapsed: 0.004 s
% 3.70/2.47  % (2105)Instructions burned: 3 (million)
% 3.70/2.47  % (2105)------------------------------
% 3.70/2.47  % (2105)------------------------------
% 3.70/2.49  % (2106)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_1969 for (2995ds/20Mi)
% 3.70/2.50  % (2106)Instruction limit reached!
% 3.70/2.50  % (2106)------------------------------
% 3.70/2.50  % (2106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.50  % (2106)Termination reason: Unknown
% 3.70/2.50  % (2106)Termination phase: shuffling
% 3.70/2.50  
% 3.70/2.50  % (2106)Memory used [KB]: 1918
% 3.70/2.50  % (2106)Time elapsed: 0.014 s
% 3.70/2.50  % (2106)Instructions burned: 20 (million)
% 3.70/2.50  % (2106)------------------------------
% 3.70/2.50  % (2106)------------------------------
% 3.70/2.51  % (2104)Instruction limit reached!
% 3.70/2.51  % (2104)------------------------------
% 3.70/2.51  % (2104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.51  % (2104)Termination reason: Unknown
% 3.70/2.51  % (2104)Termination phase: Property scanning
% 3.70/2.51  
% 3.70/2.51  % (2104)Memory used [KB]: 2430
% 3.70/2.51  % (2104)Time elapsed: 0.055 s
% 3.70/2.51  % (2104)Instructions burned: 100 (million)
% 3.70/2.51  % (2104)------------------------------
% 3.70/2.51  % (2104)------------------------------
% 3.70/2.52  % (2107)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_1969 for (2995ds/86Mi)
% 3.70/2.53  % (2108)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_1969 for (2995ds/107Mi)
% 3.70/2.57  % (2107)Instruction limit reached!
% 3.70/2.57  % (2107)------------------------------
% 3.70/2.57  % (2107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.57  % (2107)Termination reason: Unknown
% 3.70/2.57  % (2107)Termination phase: Property scanning
% 3.70/2.57  
% 3.70/2.57  % (2107)Memory used [KB]: 2430
% 3.70/2.57  % (2107)Time elapsed: 0.051 s
% 3.70/2.57  % (2107)Instructions burned: 86 (million)
% 3.70/2.57  % (2107)------------------------------
% 3.70/2.57  % (2107)------------------------------
% 3.70/2.58  % (2090)Instruction limit reached!
% 3.70/2.58  % (2090)------------------------------
% 3.70/2.58  % (2090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.58  % (2090)Termination reason: Unknown
% 3.70/2.58  % (2090)Termination phase: Saturation
% 3.70/2.58  
% 3.70/2.58  % (2090)Memory used [KB]: 8059
% 3.70/2.58  % (2090)Time elapsed: 0.409 s
% 3.70/2.58  % (2090)Instructions burned: 710 (million)
% 3.70/2.58  % (2090)------------------------------
% 3.70/2.58  % (2090)------------------------------
% 3.70/2.59  % (2108)Instruction limit reached!
% 3.70/2.59  % (2108)------------------------------
% 3.70/2.59  % (2108)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.59  % (2108)Termination reason: Unknown
% 3.70/2.59  % (2108)Termination phase: Saturation
% 3.70/2.59  
% 3.70/2.59  % (2108)Memory used [KB]: 7036
% 3.70/2.59  % (2108)Time elapsed: 0.062 s
% 3.70/2.59  % (2108)Instructions burned: 107 (million)
% 3.70/2.59  % (2108)------------------------------
% 3.70/2.59  % (2108)------------------------------
% 3.70/2.59  % (2109)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_1969 for (2994ds/39Mi)
% 3.70/2.60  % (2110)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_1969 for (2994ds/448Mi)
% 3.70/2.61  % (2111)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_1969 for (2994ds/46Mi)
% 3.70/2.61  % (2109)Instruction limit reached!
% 3.70/2.61  % (2109)------------------------------
% 3.70/2.61  % (2109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.61  % (2109)Termination reason: Unknown
% 3.70/2.61  % (2109)Termination phase: Property scanning
% 3.70/2.61  
% 3.70/2.61  % (2109)Memory used [KB]: 2174
% 3.70/2.61  % (2109)Time elapsed: 0.024 s
% 3.70/2.61  % (2109)Instructions burned: 40 (million)
% 3.70/2.61  % (2109)------------------------------
% 3.70/2.61  % (2109)------------------------------
% 3.70/2.64  % (2112)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_1969 for (2994ds/98Mi)
% 3.70/2.64  % (2111)Instruction limit reached!
% 3.70/2.64  % (2111)------------------------------
% 3.70/2.64  % (2111)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.64  % (2111)Termination reason: Unknown
% 3.70/2.64  % (2111)Termination phase: Naming
% 3.70/2.64  
% 3.70/2.64  % (2111)Memory used [KB]: 2174
% 3.70/2.64  % (2111)Time elapsed: 0.029 s
% 3.70/2.64  % (2111)Instructions burned: 46 (million)
% 3.70/2.64  % (2111)------------------------------
% 3.70/2.64  % (2111)------------------------------
% 3.70/2.66  % (2113)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_1969 for (2994ds/507Mi)
% 3.70/2.67  % (2097)Instruction limit reached!
% 3.70/2.67  % (2097)------------------------------
% 3.70/2.67  % (2097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.67  % (2097)Termination reason: Unknown
% 3.70/2.67  % (2097)Termination phase: Saturation
% 3.70/2.67  
% 3.70/2.67  % (2097)Memory used [KB]: 8315
% 3.70/2.67  % (2097)Time elapsed: 0.467 s
% 3.70/2.67  % (2097)Instructions burned: 779 (million)
% 3.70/2.67  % (2097)------------------------------
% 3.70/2.67  % (2097)------------------------------
% 3.70/2.68  % (2092)Instruction limit reached!
% 3.70/2.68  % (2092)------------------------------
% 3.70/2.68  % (2092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.68  % (2092)Termination reason: Unknown
% 3.70/2.68  % (2092)Termination phase: Saturation
% 3.70/2.68  
% 3.70/2.68  % (2092)Memory used [KB]: 8571
% 3.70/2.68  % (2092)Time elapsed: 0.496 s
% 3.70/2.68  % (2092)Instructions burned: 903 (million)
% 3.70/2.68  % (2092)------------------------------
% 3.70/2.68  % (2092)------------------------------
% 3.70/2.69  % (2112)Instruction limit reached!
% 3.70/2.69  % (2112)------------------------------
% 3.70/2.69  % (2112)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.69  % (2112)Termination reason: Unknown
% 3.70/2.69  % (2112)Termination phase: Property scanning
% 3.70/2.69  
% 3.70/2.69  % (2112)Memory used [KB]: 2430
% 3.70/2.69  % (2112)Time elapsed: 0.054 s
% 3.70/2.69  % (2112)Instructions burned: 99 (million)
% 3.70/2.69  % (2112)------------------------------
% 3.70/2.69  % (2112)------------------------------
% 3.70/2.69  % (2114)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_1969 for (2993ds/149Mi)
% 3.70/2.70  % (2115)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_1969 for (2993ds/39Mi)
% 3.70/2.71  % (2116)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_1969 for (2993ds/6Mi)
% 3.70/2.71  % (2116)Instruction limit reached!
% 3.70/2.71  % (2116)------------------------------
% 3.70/2.71  % (2116)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.71  % (2116)Termination reason: Unknown
% 3.70/2.71  % (2116)Termination phase: shuffling
% 3.70/2.71  
% 3.70/2.71  % (2116)Memory used [KB]: 1407
% 3.70/2.71  % (2116)Time elapsed: 0.006 s
% 3.70/2.71  % (2116)Instructions burned: 6 (million)
% 3.70/2.71  % (2116)------------------------------
% 3.70/2.71  % (2116)------------------------------
% 3.70/2.72  % (2115)Instruction limit reached!
% 3.70/2.72  % (2115)------------------------------
% 3.70/2.72  % (2115)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.72  % (2115)Termination reason: Unknown
% 3.70/2.72  % (2115)Termination phase: Preprocessing 2
% 3.70/2.72  
% 3.70/2.72  % (2115)Memory used [KB]: 2174
% 3.70/2.72  % (2115)Time elapsed: 0.024 s
% 3.70/2.72  % (2115)Instructions burned: 39 (million)
% 3.70/2.72  % (2115)------------------------------
% 3.70/2.72  % (2115)------------------------------
% 3.70/2.73  % (2081)Instruction limit reached!
% 3.70/2.73  % (2081)------------------------------
% 3.70/2.73  % (2081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.73  % (2081)Termination reason: Unknown
% 3.70/2.73  % (2081)Termination phase: Saturation
% 3.70/2.73  
% 3.70/2.73  % (2081)Memory used [KB]: 9594
% 3.70/2.73  % (2081)Time elapsed: 0.616 s
% 3.70/2.73  % (2081)Instructions burned: 1042 (million)
% 3.70/2.73  % (2081)------------------------------
% 3.70/2.73  % (2081)------------------------------
% 3.70/2.74  % (2117)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_1969 for (2993ds/1087Mi)
% 3.70/2.75  % (2118)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_1969 for (2993ds/47Mi)
% 3.70/2.75  % (2099)Instruction limit reached!
% 3.70/2.75  % (2099)------------------------------
% 3.70/2.75  % (2099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.75  % (2099)Termination reason: Unknown
% 3.70/2.75  % (2099)Termination phase: Saturation
% 3.70/2.75  
% 3.70/2.75  % (2099)Memory used [KB]: 7803
% 3.70/2.75  % (2099)Time elapsed: 0.514 s
% 3.70/2.75  % (2099)Instructions burned: 879 (million)
% 3.70/2.75  % (2099)------------------------------
% 3.70/2.75  % (2099)------------------------------
% 3.70/2.75  % (2119)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_1969 for (2993ds/44Mi)
% 3.70/2.77  % (2120)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_1969 for (2993ds/432Mi)
% 3.70/2.77  % (2118)Instruction limit reached!
% 3.70/2.77  % (2118)------------------------------
% 3.70/2.77  % (2118)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.77  % (2118)Termination reason: Unknown
% 3.70/2.77  % (2118)Termination phase: Preprocessing 3
% 3.70/2.77  
% 3.70/2.77  % (2118)Memory used [KB]: 2302
% 3.70/2.77  % (2118)Time elapsed: 0.029 s
% 3.70/2.77  % (2118)Instructions burned: 47 (million)
% 3.70/2.77  % (2118)------------------------------
% 3.70/2.77  % (2118)------------------------------
% 3.70/2.78  % (2114)Instruction limit reached!
% 3.70/2.78  % (2114)------------------------------
% 3.70/2.78  % (2114)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.78  % (2114)Termination reason: Unknown
% 3.70/2.78  % (2114)Termination phase: Saturation
% 3.70/2.78  
% 3.70/2.78  % (2114)Memory used [KB]: 7164
% 3.70/2.78  % (2114)Time elapsed: 0.085 s
% 3.70/2.78  % (2114)Instructions burned: 150 (million)
% 3.70/2.78  % (2114)------------------------------
% 3.70/2.78  % (2114)------------------------------
% 3.70/2.78  % (2119)Instruction limit reached!
% 3.70/2.78  % (2119)------------------------------
% 3.70/2.78  % (2119)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.78  % (2119)Termination reason: Unknown
% 3.70/2.78  % (2119)Termination phase: Property scanning
% 3.70/2.78  
% 3.70/2.78  % (2119)Memory used [KB]: 2174
% 3.70/2.78  % (2119)Time elapsed: 0.026 s
% 3.70/2.78  % (2119)Instructions burned: 45 (million)
% 3.70/2.78  % (2119)------------------------------
% 3.70/2.78  % (2119)------------------------------
% 3.70/2.79  % (2121)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_1969 for (2992ds/62Mi)
% 3.70/2.80  % (2123)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_1969 for (2992ds/96Mi)
% 3.70/2.80  % (2122)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_1969 for (2992ds/31Mi)
% 3.70/2.81  % (2122)Instruction limit reached!
% 3.70/2.81  % (2122)------------------------------
% 3.70/2.81  % (2122)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.81  % (2122)Termination reason: Unknown
% 3.70/2.82  % (2122)Termination phase: Property scanning
% 3.70/2.82  
% 3.70/2.82  % (2122)Memory used [KB]: 1918
% 3.70/2.82  % (2122)Time elapsed: 0.020 s
% 3.70/2.82  % (2122)Instructions burned: 32 (million)
% 3.70/2.82  % (2122)------------------------------
% 3.70/2.82  % (2122)------------------------------
% 3.70/2.83  % (2121)Instruction limit reached!
% 3.70/2.83  % (2121)------------------------------
% 3.70/2.83  % (2121)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.83  % (2121)Termination reason: Unknown
% 3.70/2.83  % (2121)Termination phase: Property scanning
% 3.70/2.83  
% 3.70/2.83  % (2121)Memory used [KB]: 2174
% 3.70/2.83  % (2121)Time elapsed: 0.035 s
% 3.70/2.83  % (2121)Instructions burned: 62 (million)
% 3.70/2.83  % (2121)------------------------------
% 3.70/2.83  % (2121)------------------------------
% 3.70/2.84  % (2124)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_1969 for (2992ds/453Mi)
% 3.70/2.85  % (2125)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_1969 for (2992ds/71Mi)
% 3.70/2.85  % (2123)Instruction limit reached!
% 3.70/2.85  % (2123)------------------------------
% 3.70/2.85  % (2123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.85  % (2123)Termination reason: Unknown
% 3.70/2.85  % (2123)Termination phase: Saturation
% 3.70/2.85  
% 3.70/2.85  % (2123)Memory used [KB]: 7036
% 3.70/2.85  % (2123)Time elapsed: 0.055 s
% 3.70/2.85  % (2123)Instructions burned: 96 (million)
% 3.70/2.85  % (2123)------------------------------
% 3.70/2.85  % (2123)------------------------------
% 3.70/2.86  % (2110)Instruction limit reached!
% 3.70/2.86  % (2110)------------------------------
% 3.70/2.86  % (2110)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.86  % (2110)Termination reason: Unknown
% 3.70/2.86  % (2110)Termination phase: Saturation
% 3.70/2.86  
% 3.70/2.86  % (2110)Memory used [KB]: 8059
% 3.70/2.86  % (2110)Time elapsed: 0.256 s
% 3.70/2.86  % (2110)Instructions burned: 449 (million)
% 3.70/2.86  % (2110)------------------------------
% 3.70/2.86  % (2110)------------------------------
% 3.70/2.87  % (2127)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_1969 for (2992ds/83Mi)
% 3.70/2.88  % (2128)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_1969 for (2992ds/11Mi)
% 3.70/2.88  % (2128)Instruction limit reached!
% 3.70/2.88  % (2128)------------------------------
% 3.70/2.88  % (2128)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.88  % (2128)Termination reason: Unknown
% 3.70/2.88  % (2128)Termination phase: shuffling
% 3.70/2.89  
% 3.70/2.89  % (2128)Memory used [KB]: 1663
% 3.70/2.89  % (2128)Time elapsed: 0.008 s
% 3.70/2.89  % (2128)Instructions burned: 11 (million)
% 3.70/2.89  % (2128)------------------------------
% 3.70/2.89  % (2128)------------------------------
% 3.70/2.89  % (2125)Instruction limit reached!
% 3.70/2.89  % (2125)------------------------------
% 3.70/2.89  % (2125)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.89  % (2125)Termination reason: Unknown
% 3.70/2.89  % (2125)Termination phase: Property scanning
% 3.70/2.89  
% 3.70/2.89  % (2125)Memory used [KB]: 2430
% 3.70/2.89  % (2125)Time elapsed: 0.042 s
% 3.70/2.89  % (2125)Instructions burned: 72 (million)
% 3.70/2.89  % (2125)------------------------------
% 3.70/2.89  % (2125)------------------------------
% 3.70/2.91  % (2129)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_1969 for (2991ds/41Mi)
% 3.70/2.91  % (2130)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_1969 for (2991ds/6Mi)
% 3.70/2.91  % (2130)Instruction limit reached!
% 3.70/2.91  % (2130)------------------------------
% 3.70/2.91  % (2130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.91  % (2130)Termination reason: Unknown
% 3.70/2.91  % (2130)Termination phase: shuffling
% 3.70/2.91  
% 3.70/2.91  % (2130)Memory used [KB]: 1535
% 3.70/2.91  % (2130)Time elapsed: 0.006 s
% 3.70/2.91  % (2130)Instructions burned: 7 (million)
% 3.70/2.91  % (2130)------------------------------
% 3.70/2.91  % (2130)------------------------------
% 3.70/2.92  % (2127)Instruction limit reached!
% 3.70/2.92  % (2127)------------------------------
% 3.70/2.92  % (2127)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.92  % (2127)Termination reason: Unknown
% 3.70/2.92  % (2127)Termination phase: Saturation
% 3.70/2.92  
% 3.70/2.92  % (2127)Memory used [KB]: 6780
% 3.70/2.92  % (2127)Time elapsed: 0.050 s
% 3.70/2.92  % (2127)Instructions burned: 84 (million)
% 3.70/2.92  % (2127)------------------------------
% 3.70/2.92  % (2127)------------------------------
% 3.70/2.93  % (2129)Instruction limit reached!
% 3.70/2.93  % (2129)------------------------------
% 3.70/2.93  % (2129)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.93  % (2129)Termination reason: Unknown
% 3.70/2.93  % (2129)Termination phase: Property scanning
% 3.70/2.93  
% 3.70/2.93  % (2129)Memory used [KB]: 2174
% 3.70/2.93  % (2129)Time elapsed: 0.024 s
% 3.70/2.93  % (2129)Instructions burned: 41 (million)
% 3.70/2.93  % (2129)------------------------------
% 3.70/2.93  % (2129)------------------------------
% 3.70/2.94  % (2131)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_1969 for (2991ds/150Mi)
% 3.70/2.94  % (2132)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_1969 for (2991ds/343Mi)
% 3.70/2.94  % (2113)Instruction limit reached!
% 3.70/2.94  % (2113)------------------------------
% 3.70/2.94  % (2113)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/2.94  % (2113)Termination reason: Unknown
% 3.70/2.94  % (2113)Termination phase: Saturation
% 3.70/2.94  
% 3.70/2.94  % (2113)Memory used [KB]: 8059
% 3.70/2.94  % (2113)Time elapsed: 0.284 s
% 3.70/2.94  % (2113)Instructions burned: 507 (million)
% 3.70/2.94  % (2113)------------------------------
% 3.70/2.94  % (2113)------------------------------
% 3.70/2.95  % (2133)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_1969 for (2991ds/109Mi)
% 3.70/2.97  % (2134)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_1969 for (2991ds/253Mi)
% 3.70/3.01  % (2133)Instruction limit reached!
% 3.70/3.01  % (2133)------------------------------
% 3.70/3.01  % (2133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/3.01  % (2133)Termination reason: Unknown
% 3.70/3.01  % (2133)Termination phase: Saturation
% 3.70/3.01  
% 3.70/3.01  % (2133)Memory used [KB]: 7036
% 3.70/3.01  % (2133)Time elapsed: 0.063 s
% 3.70/3.01  % (2133)Instructions burned: 109 (million)
% 3.70/3.01  % (2133)------------------------------
% 3.70/3.01  % (2133)------------------------------
% 3.70/3.02  % (2120)Instruction limit reached!
% 3.70/3.02  % (2120)------------------------------
% 3.70/3.02  % (2120)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.70/3.02  % (2120)Termination reason: Unknown
% 3.70/3.02  % (2120)Termination phase: Saturation
% 3.70/3.02  
% 3.70/3.02  % (2120)Memory used [KB]: 4605
% 3.70/3.02  % (2120)Time elapsed: 0.249 s
% 3.70/3.02  % (2120)Instructions burned: 433 (million)
% 3.70/3.02  % (2120)------------------------------
% 3.70/3.02  % (2120)------------------------------
% 10.33/3.03  % (2135)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_1969 for (2990ds/140Mi)
% 10.33/3.03  % (2131)Instruction limit reached!
% 10.33/3.03  % (2131)------------------------------
% 10.33/3.03  % (2131)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.33/3.03  % (2131)Termination reason: Unknown
% 10.33/3.03  % (2131)Termination phase: Saturation
% 10.33/3.03  
% 10.33/3.03  % (2131)Memory used [KB]: 7164
% 10.33/3.03  % (2131)Time elapsed: 0.111 s
% 10.33/3.03  % (2131)Instructions burned: 150 (million)
% 10.33/3.03  % (2131)------------------------------
% 10.33/3.03  % (2131)------------------------------
% 10.33/3.04  % (2136)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_1969 for (2990ds/614Mi)
% 10.33/3.06  % (2138)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_1969 for (2990ds/202Mi)
% 10.33/3.09  % (2138)First to succeed.
% 10.33/3.09  % (2124)Instruction limit reached!
% 10.33/3.09  % (2124)------------------------------
% 10.33/3.09  % (2124)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.33/3.09  % (2124)Termination reason: Unknown
% 10.33/3.09  % (2124)Termination phase: Saturation
% 10.33/3.09  
% 10.33/3.09  % (2124)Memory used [KB]: 7931
% 10.33/3.09  % (2124)Time elapsed: 0.255 s
% 10.33/3.09  % (2124)Instructions burned: 453 (million)
% 10.33/3.09  % (2124)------------------------------
% 10.33/3.09  % (2124)------------------------------
% 10.33/3.09  % (2138)Refutation found. Thanks to Tanya!
% 10.33/3.09  % SZS status Theorem for DTF2THF_1969
% 10.33/3.09  % SZS output start Proof for DTF2THF_1969
% 10.33/3.09  thf(type_def_5, type, set: ($tType) > $tType).
% 10.33/3.09  thf(type_def_7, type, poly: ($tType) > $tType).
% 10.33/3.09  thf(type_def_8, type, nat: $tType).
% 10.33/3.09  thf(type_def_9, type, real: $tType).
% 10.33/3.09  thf(type_def_10, type, int: $tType).
% 10.33/3.09  thf(func_def_0, type, poly: ($tType) > $tType).
% 10.33/3.09  thf(func_def_1, type, real: $tType).
% 10.33/3.09  thf(func_def_2, type, set: ($tType) > $tType).
% 10.33/3.09  thf(func_def_3, type, nat: $tType).
% 10.33/3.09  thf(func_def_4, type, int: $tType).
% 10.33/3.09  thf(func_def_5, type, idom: !>[X0: $tType]:($o)).
% 10.33/3.09  thf(func_def_6, type, type: !>[X0: $tType]:($o)).
% 10.33/3.09  thf(func_def_7, type, one: !>[X0: $tType]:($o)).
% 10.33/3.09  thf(func_def_8, type, zero: !>[X0: $tType]:($o)).
% 10.33/3.09  thf(func_def_9, type, ord: !>[X0: $tType]:($o)).
% 10.33/3.09  thf(func_def_10, type, ring_char_0: !>[X0: $tType]:($o)).
% 10.33/3.09  thf(func_def_11, type, order: !>[X0: $tType]:($o)).
% 10.33/3.09  thf(func_def_12, type, no_bot: !>[X0: $tType]:($o)).
% 10.33/3.09  thf(func_def_13, type, no_top: !>[X0: $tType]:($o)).
% 10.33/3.09  thf(func_def_14, type, finite_finite: !>[X0: $tType]:($o)).
% 10.33/3.09  thf(func_def_15, type, comm_ring_1: !>[X0: $tType]:($o)).
% 10.33/3.09  thf(func_def_16, type, linorder: !>[X0: $tType]:($o)).
% 10.33/3.09  thf(func_def_17, type, preorder: !>[X0: $tType]:($o)).
% 10.33/3.09  thf(func_def_18, type, wellorder: !>[X0: $tType]:($o)).
% 10.33/3.09  thf(func_def_19, type, zero_less_one: !>[X0: $tType]:($o)).
% 10.33/3.09  thf(func_def_20, type, dense_order: !>[X0: $tType]:($o)).
% 10.33/3.09  thf(func_def_21, type, comm_semiring_0: !>[X0: $tType]:($o)).
% 10.33/3.09  thf(func_def_22, type, comm_semiring_1: !>[X0: $tType]:($o)).
% 10.33/3.09  thf(func_def_23, type, linordered_idom: !>[X0: $tType]:($o)).
% 10.33/3.09  thf(func_def_24, type, comm_monoid_add: !>[X0: $tType]:($o)).
% 10.33/3.09  thf(func_def_25, type, linordered_field: !>[X0: $tType]:($o)).
% 10.33/3.09  thf(func_def_26, type, dense_linorder: !>[X0: $tType]:($o)).
% 10.33/3.09  thf(func_def_27, type, ring_n68954251visors: !>[X0: $tType]:($o)).
% 10.33/3.09  thf(func_def_28, type, ordere216010020id_add: !>[X0: $tType]:($o)).
% 10.33/3.09  thf(func_def_29, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 10.33/3.09  thf(func_def_30, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 10.33/3.09  thf(func_def_31, type, ordere1818651114id_add: !>[X0: $tType]:($o)).
% 10.33/3.09  thf(func_def_32, type, condit1656338222tinuum: !>[X0: $tType]:($o)).
% 10.33/3.09  thf(func_def_33, type, condit1037483654norder: !>[X0: $tType]:($o)).
% 10.33/3.09  thf(func_def_34, type, finite_finite2: !>[X0: $tType]:(set @ X0 > $o)).
% 10.33/3.09  thf(func_def_35, type, one_one: !>[X0: $tType]:(X0)).
% 10.33/3.09  thf(func_def_36, type, zero_zero: !>[X0: $tType]:(X0)).
% 10.33/3.09  thf(func_def_37, type, groups1340683514dd_sum: !>[X0: $tType, X1: $tType]:((X0 > X1) > set @ X0 > X1)).
% 10.33/3.09  thf(func_def_38, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 10.33/3.09  thf(func_def_39, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 10.33/3.09  thf(func_def_40, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 10.33/3.09  thf(func_def_41, type, is_zero: !>[X0: $tType]:(poly @ X0 > $o)).
% 10.33/3.09  thf(func_def_42, type, poly2: !>[X0: $tType]:(poly @ X0 > X0 > X0)).
% 10.33/3.09  thf(func_def_43, type, poly_cutoff: !>[X0: $tType]:(nat > poly @ X0 > poly @ X0)).
% 10.33/3.09  thf(func_def_44, type, reflect_poly: !>[X0: $tType]:(poly @ X0 > poly @ X0)).
% 10.33/3.09  thf(func_def_45, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 10.33/3.09  thf(func_def_46, type, sturm_1539314049x_poly: real > real > poly @ real > poly @ real > int).
% 10.33/3.09  thf(func_def_47, type, sturm_424270202_cross: poly @ real > real > real > int).
% 10.33/3.09  thf(func_def_48, type, sturm_652470720p_poly: poly @ real > poly @ real > real > int).
% 10.33/3.09  thf(func_def_49, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 10.33/3.09  thf(func_def_50, type, a: real).
% 10.33/3.09  thf(func_def_51, type, a2: real).
% 10.33/3.09  thf(func_def_52, type, b: real).
% 10.33/3.09  thf(func_def_53, type, b2: real).
% 10.33/3.09  thf(func_def_54, type, p: poly @ real).
% 10.33/3.09  thf(func_def_71, type, diff: !>[X0: $tType, X1: $tType]:((X0 > X1) > (X0 > X1) > X0)).
% 10.33/3.09  thf(func_def_72, type, sK0: real > poly @ real > real).
% 10.33/3.09  thf(func_def_73, type, sK1: !>[X0: $tType]:((X0 > $o) > X0)).
% 10.33/3.09  thf(func_def_74, type, sK2: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > set @ X0 > set @ X1 > X0)).
% 10.33/3.09  thf(func_def_75, type, sK3: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > set @ X0 > set @ X1 > X1)).
% 10.33/3.09  thf(func_def_76, type, sK4: poly @ real > real > real > real).
% 10.33/3.09  thf(func_def_77, type, sK5: poly @ real > real > real > real).
% 10.33/3.09  thf(func_def_78, type, sK6: poly @ real > real > real > real).
% 10.33/3.09  thf(func_def_79, type, sK7: poly @ real > real > real > real).
% 10.33/3.09  thf(func_def_80, type, sK8: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 10.33/3.09  thf(func_def_81, type, sK9: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 10.33/3.09  thf(func_def_82, type, sK10: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > set @ X1 > X1)).
% 10.33/3.09  thf(func_def_83, type, sK11: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > set @ X1 > X1 > X0)).
% 10.33/3.09  thf(func_def_84, type, sK12: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 10.33/3.09  thf(func_def_85, type, sK13: poly @ real > real > real > real).
% 10.33/3.09  thf(func_def_86, type, sK14: !>[X0: $tType]:(X0 > set @ X0 > X0)).
% 10.33/3.09  thf(func_def_87, type, sK15: poly @ real > real > real > real).
% 10.33/3.09  thf(func_def_88, type, sK16: poly @ real > real > real > real).
% 10.33/3.09  thf(func_def_89, type, sK17: poly @ real > real > real > real).
% 10.33/3.09  thf(func_def_90, type, sK18: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 10.33/3.09  thf(func_def_91, type, sK19: real > poly @ real > real).
% 10.33/3.09  thf(func_def_92, type, sK20: !>[X0: $tType]:(X0 > set @ X0 > X0)).
% 10.33/3.09  thf(func_def_93, type, sK21: !>[X0: $tType]:((set @ X0 > $o) > set @ X0)).
% 10.33/3.09  thf(func_def_94, type, sK22: set @ real > real).
% 10.33/3.09  thf(func_def_95, type, sK23: real > set @ real > real).
% 10.33/3.09  thf(func_def_96, type, sK24: real > set @ real > real).
% 10.33/3.09  thf(func_def_97, type, sK25: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 10.33/3.09  thf(func_def_99, type, ph27: !>[X0: $tType]:(X0)).
% 10.33/3.09  thf(f1384,plain,(
% 10.33/3.09    $false),
% 10.33/3.09    inference(subsumption_resolution,[status(thm)],[f1365,f1176])).
% 10.33/3.09  thf(f1176,plain,(
% 10.33/3.09    ($true = (finite_finite2 @ real @ (collect @ real @ (^[Y0 : real]: (zero_zero @ real = (poly2 @ real @ p @ Y0))))))),
% 10.33/3.09    inference(cnf_transformation,[status(thm)],[f948])).
% 10.33/3.09  thf(f948,plain,(
% 10.33/3.09    ($true = (finite_finite2 @ real @ (collect @ real @ (^[Y0 : real]: (zero_zero @ real = (poly2 @ real @ p @ Y0))))))),
% 10.33/3.09    inference(fool_elimination,[status(thm)],[f947])).
% 10.33/3.09  thf(f947,plain,(
% 10.33/3.09    (finite_finite2 @ real @ (collect @ real @ (^[X0 : real] : ((zero_zero @ real = (poly2 @ real @ p @ X0))))))),
% 10.33/3.09    inference(rectify,[status(thm)],[f1])).
% 10.33/3.09  thf(f1,axiom,(
% 10.33/3.09    (finite_finite2 @ real @ (collect @ real @ (^[X2 : real] : (((poly2 @ real @ p @ X2) = zero_zero @ real)))))),
% 10.33/3.09    file('/export/starexec/sandbox/tmp/tmp.BBanjbptkj/DTF2THF_1969.p',fact_0__092_060open_062finite_A_123x_O_Apoly_Ap_Ax_A_061_A0_125_092_060close_062)).
% 10.33/3.09  thf(f1365,plain,(
% 10.33/3.09    ($true != (finite_finite2 @ real @ (collect @ real @ (^[Y0 : real]: (zero_zero @ real = (poly2 @ real @ p @ Y0))))))),
% 10.33/3.09    inference(trivial_inequality_removal,[status(thm)],[f1350])).
% 10.33/3.09  thf(f1350,plain,(
% 10.33/3.09    ($true != $true) | ($true != (finite_finite2 @ real @ (collect @ real @ (^[Y0 : real]: (zero_zero @ real = (poly2 @ real @ p @ Y0))))))),
% 10.33/3.09    inference(superposition,[status(thm)],[f1296,f1183])).
% 10.33/3.09  thf(f1183,plain,(
% 10.33/3.09    ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : (((finite_finite2 @ X0 @ (collect @ X0 @ (^[Y0 : X0]: ((X1 @ Y0) & (X2 @ Y0))))) = $true) | ((finite_finite2 @ X0 @ (collect @ X0 @ X2)) != $true)) )),
% 10.33/3.09    inference(cnf_transformation,[status(thm)],[f1071])).
% 10.33/3.09  thf(f1071,plain,(
% 10.33/3.09    ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((((finite_finite2 @ X0 @ (collect @ X0 @ X1)) != $true) & ((finite_finite2 @ X0 @ (collect @ X0 @ X2)) != $true)) | ((finite_finite2 @ X0 @ (collect @ X0 @ (^[Y0 : X0]: ((X1 @ Y0) & (X2 @ Y0))))) = $true))),
% 10.33/3.09    inference(ennf_transformation,[status(thm)],[f396])).
% 10.33/3.09  thf(f396,plain,(
% 10.33/3.09    ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((((finite_finite2 @ X0 @ (collect @ X0 @ X1)) = $true) | ((finite_finite2 @ X0 @ (collect @ X0 @ X2)) = $true)) => ((finite_finite2 @ X0 @ (collect @ X0 @ (^[Y0 : X0]: ((X1 @ Y0) & (X2 @ Y0))))) = $true))),
% 10.33/3.09    inference(fool_elimination,[status(thm)],[f395])).
% 10.33/3.09  thf(f395,plain,(
% 10.33/3.09    ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (((finite_finite2 @ X0 @ (collect @ X0 @ X1)) | (finite_finite2 @ X0 @ (collect @ X0 @ X2))) => (finite_finite2 @ X0 @ (collect @ X0 @ (^[X3 : X0] : ((X2 @ X3) & (X1 @ X3))))))),
% 10.33/3.09    inference(rectify,[status(thm)],[f9])).
% 10.33/3.09  thf(f9,axiom,(
% 10.33/3.09    ! [X0 : $tType,X6 : X0 > $o,X7 : X0 > $o] : (((finite_finite2 @ X0 @ (collect @ X0 @ X6)) | (finite_finite2 @ X0 @ (collect @ X0 @ X7))) => (finite_finite2 @ X0 @ (collect @ X0 @ (^[X2 : X0] : ((X7 @ X2) & (X6 @ X2))))))),
% 10.33/3.09    file('/export/starexec/sandbox/tmp/tmp.BBanjbptkj/DTF2THF_1969.p',fact_8_finite__Collect__conjI)).
% 10.33/3.09  thf(f1296,plain,(
% 10.33/3.09    ((finite_finite2 @ real @ (collect @ real @ (^[Y0 : real]: (((ord_less @ real @ Y0 @ b) & (ord_less @ real @ a @ Y0)) & (zero_zero @ real = (poly2 @ real @ p @ Y0)))))) != $true)),
% 10.33/3.09    inference(cnf_transformation,[status(thm)],[f1038])).
% 10.33/3.09  thf(f1038,plain,(
% 10.33/3.09    ((finite_finite2 @ real @ (collect @ real @ (^[Y0 : real]: (((ord_less @ real @ Y0 @ b) & (ord_less @ real @ a @ Y0)) & (zero_zero @ real = (poly2 @ real @ p @ Y0)))))) != $true)),
% 10.33/3.09    inference(flattening,[status(thm)],[f774])).
% 10.33/3.09  thf(f774,plain,(
% 10.33/3.09    ~((finite_finite2 @ real @ (collect @ real @ (^[Y0 : real]: (((ord_less @ real @ Y0 @ b) & (ord_less @ real @ a @ Y0)) & (zero_zero @ real = (poly2 @ real @ p @ Y0)))))) = $true)),
% 10.33/3.09    inference(fool_elimination,[status(thm)],[f773])).
% 10.33/3.09  thf(f773,plain,(
% 10.33/3.09    ~(finite_finite2 @ real @ (collect @ real @ (^[X0 : real] : ((zero_zero @ real = (poly2 @ real @ p @ X0)) & (ord_less @ real @ a @ X0) & (ord_less @ real @ X0 @ b)))))),
% 10.33/3.09    inference(rectify,[status(thm)],[f353])).
% 10.33/3.09  thf(f353,negated_conjecture,(
% 10.33/3.09    ~(finite_finite2 @ real @ (collect @ real @ (^[X2 : real] : (((poly2 @ real @ p @ X2) = zero_zero @ real) & (ord_less @ real @ a @ X2) & (ord_less @ real @ X2 @ b)))))),
% 10.33/3.09    inference(negated_conjecture,[status(cth)],[f352])).
% 10.33/3.09  thf(f352,conjecture,(
% 10.33/3.09    (finite_finite2 @ real @ (collect @ real @ (^[X2 : real] : (((poly2 @ real @ p @ X2) = zero_zero @ real) & (ord_less @ real @ a @ X2) & (ord_less @ real @ X2 @ b)))))),
% 10.33/3.09    file('/export/starexec/sandbox/tmp/tmp.BBanjbptkj/DTF2THF_1969.p',conj_0)).
% 10.33/3.09  % SZS output end Proof for DTF2THF_1969
% 10.33/3.09  % (2138)------------------------------
% 10.33/3.09  % (2138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.33/3.09  % (2138)Termination reason: Refutation
% 10.33/3.09  
% 10.33/3.09  % (2138)Memory used [KB]: 6908
% 10.33/3.09  % (2138)Time elapsed: 0.033 s
% 10.33/3.09  % (2138)Instructions burned: 81 (million)
% 10.33/3.09  % (2138)------------------------------
% 10.33/3.09  % (2138)------------------------------
% 10.33/3.09  % (2069)Success in time 1.039 s
%------------------------------------------------------------------------------