SET007 Axioms: SET007+903.ax


%------------------------------------------------------------------------------
% File     : SET007+903 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Inferior Limit and Superior Limit of Sequences of Real Numbers
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : rinfsup1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  110 (   0 unit)
%            Number of atoms       :  819 (  63 equality)
%            Maximal formula depth :   16 (   8 average)
%            Number of connectives :  734 (  25 ~  ;   1  |; 346  &)
%                                         (  28 <=>; 334 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   21 (   0 propositional; 1-3 arity)
%            Number of functors    :   34 (   4 constant; 0-4 arity)
%            Number of variables   :  252 (   0 singleton; 244 !;   8 ?)
%            Maximal term depth    :    5 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(t1_rinfsup1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( ( ~ r1_xreal_0(C,k6_xcmplx_0(A,B))
                  & ~ r1_xreal_0(k2_xcmplx_0(A,B),C) )
              <=> ~ r1_xreal_0(B,k18_complex1(k6_xcmplx_0(C,A))) ) ) ) ) )).

fof(d1_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => k1_rinfsup1(A) = k3_pscomp_1(k1_pscomp_1(k5_numbers,k1_numbers,A)) ) )).

fof(d2_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => k2_rinfsup1(A) = k4_pscomp_1(k1_pscomp_1(k5_numbers,k1_numbers,A)) ) )).

fof(t2_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => k4_partfun3(k5_numbers,k3_partfun3(k5_numbers,A,B),B) = A ) ) )).

fof(t3_rinfsup1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( r2_hidden(A,k1_pscomp_1(k5_numbers,k1_numbers,B))
          <=> r2_hidden(k4_xcmplx_0(A),k1_pscomp_1(k5_numbers,k1_numbers,k6_partfun3(k5_numbers,B))) ) ) ) )).

fof(t4_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => k1_pscomp_1(k5_numbers,k1_numbers,k6_partfun3(k5_numbers,A)) = k5_pscomp_1(k1_pscomp_1(k5_numbers,k1_numbers,A)) ) )).

fof(t5_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v1_seq_2(A)
      <=> v1_seq_4(k1_pscomp_1(k5_numbers,k1_numbers,A)) ) ) )).

fof(t6_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v2_seq_2(A)
      <=> v2_seq_4(k1_pscomp_1(k5_numbers,k1_numbers,A)) ) ) )).

fof(t7_rinfsup1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( v1_seq_2(B)
           => ( A = k1_rinfsup1(B)
            <=> ( ! [C] :
                    ( m2_subset_1(C,k1_numbers,k5_numbers)
                   => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,B,C),A) )
                & ! [C] :
                    ( v1_xreal_0(C)
                   => ~ ( ~ r1_xreal_0(C,np__0)
                        & ! [D] :
                            ( m2_subset_1(D,k1_numbers,k5_numbers)
                           => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,B,D),k6_xcmplx_0(A,C)) ) ) ) ) ) ) ) ) )).

fof(t8_rinfsup1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( v2_seq_2(B)
           => ( A = k2_rinfsup1(B)
            <=> ( ! [C] :
                    ( m2_subset_1(C,k1_numbers,k5_numbers)
                   => r1_xreal_0(A,k2_seq_1(k5_numbers,k1_numbers,B,C)) )
                & ! [C] :
                    ( v1_xreal_0(C)
                   => ~ ( ~ r1_xreal_0(C,np__0)
                        & ! [D] :
                            ( m2_subset_1(D,k1_numbers,k5_numbers)
                           => r1_xreal_0(k2_xcmplx_0(A,C),k2_seq_1(k5_numbers,k1_numbers,B,D)) ) ) ) ) ) ) ) ) )).

fof(t9_rinfsup1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,B,C),A) )
          <=> ( v1_seq_2(B)
              & r1_xreal_0(k1_rinfsup1(B),A) ) ) ) ) )).

fof(t10_rinfsup1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => r1_xreal_0(A,k2_seq_1(k5_numbers,k1_numbers,B,C)) )
          <=> ( v2_seq_2(B)
              & r1_xreal_0(A,k2_rinfsup1(B)) ) ) ) ) )).

fof(t11_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v1_seq_2(A)
      <=> v2_seq_2(k6_partfun3(k5_numbers,A)) ) ) )).

fof(t12_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v2_seq_2(A)
      <=> v1_seq_2(k6_partfun3(k5_numbers,A)) ) ) )).

fof(t13_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v1_seq_2(A)
       => k1_rinfsup1(A) = k1_real_1(k2_rinfsup1(k6_partfun3(k5_numbers,A))) ) ) )).

fof(t14_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v2_seq_2(A)
       => k2_rinfsup1(A) = k1_real_1(k1_rinfsup1(k6_partfun3(k5_numbers,A))) ) ) )).

fof(t15_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( ( v2_seq_2(A)
              & v2_seq_2(B) )
           => r1_xreal_0(k3_real_1(k2_rinfsup1(A),k2_rinfsup1(B)),k2_rinfsup1(k3_partfun3(k5_numbers,A,B))) ) ) ) )).

fof(t16_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( ( v1_seq_2(A)
              & v1_seq_2(B) )
           => r1_xreal_0(k1_rinfsup1(k3_partfun3(k5_numbers,A,B)),k3_real_1(k1_rinfsup1(A),k1_rinfsup1(B))) ) ) ) )).

fof(d3_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v4_partfun3(A)
      <=> ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => r1_xreal_0(np__0,k2_seq_1(k5_numbers,k1_numbers,A,B)) ) ) ) )).

fof(t17_rinfsup1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( v4_partfun3(B)
           => v4_partfun3(k1_seqm_3(B,A)) ) ) ) )).

fof(t18_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( ( v2_seq_2(A)
          & v4_partfun3(A) )
       => r1_xreal_0(np__0,k2_rinfsup1(A)) ) ) )).

fof(t19_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( ( v1_seq_2(A)
          & v4_partfun3(A) )
       => r1_xreal_0(np__0,k1_rinfsup1(A)) ) ) )).

fof(t20_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( ( v2_seq_2(A)
              & v4_partfun3(A)
              & v2_seq_2(B)
              & v4_partfun3(B) )
           => ( v2_seq_2(k5_partfun3(k5_numbers,A,B))
              & r1_xreal_0(k4_real_1(k2_rinfsup1(A),k2_rinfsup1(B)),k2_rinfsup1(k5_partfun3(k5_numbers,A,B))) ) ) ) ) )).

fof(t21_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( ( v1_seq_2(A)
              & v4_partfun3(A)
              & v1_seq_2(B)
              & v4_partfun3(B) )
           => ( v1_seq_2(k5_partfun3(k5_numbers,A,B))
              & r1_xreal_0(k1_rinfsup1(k5_partfun3(k5_numbers,A,B)),k4_real_1(k1_rinfsup1(A),k1_rinfsup1(B))) ) ) ) ) )).

fof(t22_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( ( v3_seqm_3(A)
          & v1_seq_2(A) )
       => v3_seq_2(A) ) ) )).

fof(t23_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( ( v4_seqm_3(A)
          & v2_seq_2(A) )
       => v3_seq_2(A) ) ) )).

fof(t24_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( ( v3_seqm_3(A)
          & v1_seq_2(A) )
       => k2_seq_2(A) = k1_rinfsup1(A) ) ) )).

fof(t25_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( ( v4_seqm_3(A)
          & v2_seq_2(A) )
       => k2_seq_2(A) = k2_rinfsup1(A) ) ) )).

fof(t26_rinfsup1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( v1_seq_2(B)
           => v1_seq_2(k1_seqm_3(B,A)) ) ) ) )).

fof(t27_rinfsup1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( v2_seq_2(B)
           => v2_seq_2(k1_seqm_3(B,A)) ) ) ) )).

fof(t28_rinfsup1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( v3_seq_2(B)
           => v3_seq_2(k1_seqm_3(B,A)) ) ) ) )).

fof(t38_rinfsup1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(B),A) = k2_rinfsup1(k1_seqm_3(B,A)) ) ) )).

fof(t39_rinfsup1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(B),A) = k1_rinfsup1(k1_seqm_3(B,A)) ) ) )).

fof(t40_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v2_seq_2(A)
       => k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(A),np__0) = k2_rinfsup1(A) ) ) )).

fof(t41_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v1_seq_2(A)
       => k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(A),np__0) = k1_rinfsup1(A) ) ) )).

fof(t42_rinfsup1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_numbers)
                & m2_relset_1(C,k5_numbers,k1_numbers) )
             => ( v2_seq_2(C)
               => ( B = k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(C),A)
                <=> ( ! [D] :
                        ( m2_subset_1(D,k1_numbers,k5_numbers)
                       => r1_xreal_0(B,k2_seq_1(k5_numbers,k1_numbers,C,k1_nat_1(A,D))) )
                    & ! [D] :
                        ( v1_xreal_0(D)
                       => ~ ( ~ r1_xreal_0(D,np__0)
                            & ! [E] :
                                ( m2_subset_1(E,k1_numbers,k5_numbers)
                               => r1_xreal_0(k2_xcmplx_0(B,D),k2_seq_1(k5_numbers,k1_numbers,C,k1_nat_1(A,E))) ) ) ) ) ) ) ) ) ) )).

fof(t43_rinfsup1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_numbers)
                & m2_relset_1(C,k5_numbers,k1_numbers) )
             => ( v1_seq_2(C)
               => ( B = k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(C),A)
                <=> ( ! [D] :
                        ( m2_subset_1(D,k1_numbers,k5_numbers)
                       => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,C,k1_nat_1(A,D)),B) )
                    & ! [D] :
                        ( v1_xreal_0(D)
                       => ~ ( ~ r1_xreal_0(D,np__0)
                            & ! [E] :
                                ( m2_subset_1(E,k1_numbers,k5_numbers)
                               => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,C,k1_nat_1(A,E)),k6_xcmplx_0(B,D)) ) ) ) ) ) ) ) ) ) )).

fof(t44_rinfsup1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_numbers)
                & m2_relset_1(C,k5_numbers,k1_numbers) )
             => ( v2_seq_2(C)
               => ( ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => r1_xreal_0(B,k2_seq_1(k5_numbers,k1_numbers,C,k1_nat_1(A,D))) )
                <=> r1_xreal_0(B,k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(C),A)) ) ) ) ) ) )).

fof(t45_rinfsup1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_numbers)
                & m2_relset_1(C,k5_numbers,k1_numbers) )
             => ( v2_seq_2(C)
               => ( ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( r1_xreal_0(A,D)
                       => r1_xreal_0(B,k2_seq_1(k5_numbers,k1_numbers,C,D)) ) )
                <=> r1_xreal_0(B,k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(C),A)) ) ) ) ) ) )).

fof(t46_rinfsup1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_numbers)
                & m2_relset_1(C,k5_numbers,k1_numbers) )
             => ( v1_seq_2(C)
               => ( ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,C,k1_nat_1(A,D)),B) )
                <=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(C),A),B) ) ) ) ) ) )).

fof(t47_rinfsup1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_numbers)
                & m2_relset_1(C,k5_numbers,k1_numbers) )
             => ( v1_seq_2(C)
               => ( ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( r1_xreal_0(A,D)
                       => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,C,D),B) ) )
                <=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(C),A),B) ) ) ) ) ) )).

fof(t48_rinfsup1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( v2_seq_2(B)
           => k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(B),A) = k3_square_1(k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(B),k1_nat_1(A,np__1)),k2_seq_1(k5_numbers,k1_numbers,B,A)) ) ) ) )).

fof(t49_rinfsup1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( v1_seq_2(B)
           => k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(B),A) = k4_square_1(k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(B),k1_nat_1(A,np__1)),k2_seq_1(k5_numbers,k1_numbers,B,A)) ) ) ) )).

fof(t50_rinfsup1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( v2_seq_2(B)
           => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(B),A),k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(B),k1_nat_1(A,np__1))) ) ) ) )).

fof(t51_rinfsup1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( v1_seq_2(B)
           => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(B),k1_nat_1(A,np__1)),k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(B),A)) ) ) ) )).

fof(t52_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v2_seq_2(A)
       => v3_seqm_3(k3_rinfsup1(A)) ) ) )).

fof(t53_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v1_seq_2(A)
       => v4_seqm_3(k4_rinfsup1(A)) ) ) )).

fof(t54_rinfsup1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( v3_seq_2(B)
           => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(B),A),k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(B),A)) ) ) ) )).

fof(t55_rinfsup1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( v3_seq_2(B)
           => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(B),A),k2_rinfsup1(k4_rinfsup1(B))) ) ) ) )).

fof(t56_rinfsup1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( v3_seq_2(B)
           => r1_xreal_0(k1_rinfsup1(k3_rinfsup1(B)),k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(B),A)) ) ) ) )).

fof(t57_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v3_seq_2(A)
       => r1_xreal_0(k1_rinfsup1(k3_rinfsup1(A)),k2_rinfsup1(k4_rinfsup1(A))) ) ) )).

fof(t58_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v3_seq_2(A)
       => ( v3_seq_2(k4_rinfsup1(A))
          & v3_seq_2(k3_rinfsup1(A)) ) ) ) )).

fof(t59_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v3_seq_2(A)
       => ( v4_seq_2(k3_rinfsup1(A))
          & k2_seq_2(k3_rinfsup1(A)) = k1_rinfsup1(k3_rinfsup1(A)) ) ) ) )).

fof(t60_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v3_seq_2(A)
       => ( v4_seq_2(k4_rinfsup1(A))
          & k2_seq_2(k4_rinfsup1(A)) = k2_rinfsup1(k4_rinfsup1(A)) ) ) ) )).

fof(t61_rinfsup1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( v2_seq_2(B)
           => k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(B),A) = k1_real_1(k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(k6_partfun3(k5_numbers,B)),A)) ) ) ) )).

fof(t62_rinfsup1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( v1_seq_2(B)
           => k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(B),A) = k1_real_1(k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(k6_partfun3(k5_numbers,B)),A)) ) ) ) )).

fof(t63_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v2_seq_2(A)
       => k3_rinfsup1(A) = k6_partfun3(k5_numbers,k4_rinfsup1(k6_partfun3(k5_numbers,A))) ) ) )).

fof(t64_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v1_seq_2(A)
       => k4_rinfsup1(A) = k6_partfun3(k5_numbers,k3_rinfsup1(k6_partfun3(k5_numbers,A))) ) ) )).

fof(t65_rinfsup1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( v3_seqm_3(B)
           => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,B,A),k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(B),k1_nat_1(A,np__1))) ) ) ) )).

fof(t66_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v3_seqm_3(A)
       => k3_rinfsup1(A) = A ) ) )).

fof(t67_rinfsup1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( ( v3_seqm_3(B)
              & v1_seq_2(B) )
           => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,B,A),k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(B),k1_nat_1(A,np__1))) ) ) ) )).

fof(t68_rinfsup1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( ( v3_seqm_3(B)
              & v1_seq_2(B) )
           => k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(B),A) = k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(B),k1_nat_1(A,np__1)) ) ) ) )).

fof(t69_rinfsup1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( ( v3_seqm_3(B)
              & v1_seq_2(B) )
           => ( k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(B),A) = k1_rinfsup1(B)
              & v5_seqm_3(k4_rinfsup1(B)) ) ) ) ) )).

fof(t70_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( ( v3_seqm_3(A)
          & v1_seq_2(A) )
       => k2_rinfsup1(k4_rinfsup1(A)) = k1_rinfsup1(A) ) ) )).

fof(t71_rinfsup1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( v4_seqm_3(B)
           => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(B),k1_nat_1(A,np__1)),k2_seq_1(k5_numbers,k1_numbers,B,A)) ) ) ) )).

fof(t72_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v4_seqm_3(A)
       => k4_rinfsup1(A) = A ) ) )).

fof(t73_rinfsup1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( ( v4_seqm_3(B)
              & v2_seq_2(B) )
           => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(B),k1_nat_1(A,np__1)),k2_seq_1(k5_numbers,k1_numbers,B,A)) ) ) ) )).

fof(t74_rinfsup1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( ( v4_seqm_3(B)
              & v2_seq_2(B) )
           => k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(B),A) = k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(B),k1_nat_1(A,np__1)) ) ) ) )).

fof(t75_rinfsup1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( ( v4_seqm_3(B)
              & v2_seq_2(B) )
           => ( k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(B),A) = k2_rinfsup1(B)
              & v5_seqm_3(k3_rinfsup1(B)) ) ) ) ) )).

fof(t76_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( ( v4_seqm_3(A)
          & v2_seq_2(A) )
       => k1_rinfsup1(k3_rinfsup1(A)) = k2_rinfsup1(A) ) ) )).

fof(t77_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( ( v3_seq_2(A)
              & v3_seq_2(B)
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,C),k2_seq_1(k5_numbers,k1_numbers,B,C)) ) )
           => ( ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(A),C),k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(B),C)) )
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(A),C),k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(B),C)) ) ) ) ) ) )).

fof(t78_rinfsup1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_numbers)
                & m2_relset_1(C,k5_numbers,k1_numbers) )
             => ( ( v2_seq_2(B)
                  & v2_seq_2(C) )
               => r1_xreal_0(k3_real_1(k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(B),A),k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(C),A)),k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(k3_partfun3(k5_numbers,B,C)),A)) ) ) ) ) )).

fof(t79_rinfsup1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_numbers)
                & m2_relset_1(C,k5_numbers,k1_numbers) )
             => ( ( v1_seq_2(B)
                  & v1_seq_2(C) )
               => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(k3_partfun3(k5_numbers,B,C)),A),k3_real_1(k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(B),A),k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(C),A))) ) ) ) ) )).

fof(t80_rinfsup1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_numbers)
                & m2_relset_1(C,k5_numbers,k1_numbers) )
             => ( ( v2_seq_2(B)
                  & v4_partfun3(B)
                  & v2_seq_2(C)
                  & v4_partfun3(C) )
               => r1_xreal_0(k4_real_1(k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(B),A),k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(C),A)),k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(k5_partfun3(k5_numbers,B,C)),A)) ) ) ) ) )).

fof(t81_rinfsup1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_numbers)
                & m2_relset_1(C,k5_numbers,k1_numbers) )
             => ( ( v2_seq_2(B)
                  & v4_partfun3(B)
                  & v2_seq_2(C)
                  & v4_partfun3(C) )
               => r1_xreal_0(k4_real_1(k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(B),A),k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(C),A)),k2_seq_1(k5_numbers,k1_numbers,k3_rinfsup1(k5_partfun3(k5_numbers,B,C)),A)) ) ) ) ) )).

fof(t82_rinfsup1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_numbers)
                & m2_relset_1(C,k5_numbers,k1_numbers) )
             => ( ( v1_seq_2(B)
                  & v4_partfun3(B)
                  & v1_seq_2(C)
                  & v4_partfun3(C) )
               => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(k5_partfun3(k5_numbers,B,C)),A),k4_real_1(k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(B),A),k2_seq_1(k5_numbers,k1_numbers,k4_rinfsup1(C),A))) ) ) ) ) )).

fof(d6_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => k5_rinfsup1(A) = k2_rinfsup1(k4_rinfsup1(A)) ) )).

fof(d7_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => k6_rinfsup1(A) = k1_rinfsup1(k3_rinfsup1(A)) ) )).

fof(t83_rinfsup1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( v3_seq_2(B)
           => ( r1_xreal_0(k6_rinfsup1(B),A)
            <=> ! [C] :
                  ( v1_xreal_0(C)
                 => ( ~ r1_xreal_0(C,np__0)
                   => ! [D] :
                        ( m2_subset_1(D,k1_numbers,k5_numbers)
                       => ~ ! [E] :
                              ( m2_subset_1(E,k1_numbers,k5_numbers)
                             => r1_xreal_0(k2_xcmplx_0(A,C),k2_seq_1(k5_numbers,k1_numbers,B,k1_nat_1(D,E))) ) ) ) ) ) ) ) ) )).

fof(t84_rinfsup1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( v3_seq_2(B)
           => ( r1_xreal_0(A,k6_rinfsup1(B))
            <=> ! [C] :
                  ( v1_xreal_0(C)
                 => ~ ( ~ r1_xreal_0(C,np__0)
                      & ! [D] :
                          ( m2_subset_1(D,k1_numbers,k5_numbers)
                         => ? [E] :
                              ( m2_subset_1(E,k1_numbers,k5_numbers)
                              & r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,B,k1_nat_1(D,E)),k6_xcmplx_0(A,C)) ) ) ) ) ) ) ) ) )).

fof(t85_rinfsup1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( v3_seq_2(B)
           => ( A = k6_rinfsup1(B)
            <=> ! [C] :
                  ( v1_xreal_0(C)
                 => ( ~ r1_xreal_0(C,np__0)
                   => ( ! [D] :
                          ( m2_subset_1(D,k1_numbers,k5_numbers)
                         => ~ ! [E] :
                                ( m2_subset_1(E,k1_numbers,k5_numbers)
                               => r1_xreal_0(k2_xcmplx_0(A,C),k2_seq_1(k5_numbers,k1_numbers,B,k1_nat_1(D,E))) ) )
                      & ? [D] :
                          ( m2_subset_1(D,k1_numbers,k5_numbers)
                          & ! [E] :
                              ( m2_subset_1(E,k1_numbers,k5_numbers)
                             => ~ r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,B,k1_nat_1(D,E)),k6_xcmplx_0(A,C)) ) ) ) ) ) ) ) ) ) )).

fof(t86_rinfsup1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( v3_seq_2(B)
           => ( r1_xreal_0(A,k5_rinfsup1(B))
            <=> ! [C] :
                  ( v1_xreal_0(C)
                 => ( ~ r1_xreal_0(C,np__0)
                   => ! [D] :
                        ( m2_subset_1(D,k1_numbers,k5_numbers)
                       => ~ ! [E] :
                              ( m2_subset_1(E,k1_numbers,k5_numbers)
                             => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,B,k1_nat_1(D,E)),k6_xcmplx_0(A,C)) ) ) ) ) ) ) ) ) )).

fof(t87_rinfsup1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( v3_seq_2(B)
           => ( r1_xreal_0(k5_rinfsup1(B),A)
            <=> ! [C] :
                  ( v1_xreal_0(C)
                 => ~ ( ~ r1_xreal_0(C,np__0)
                      & ! [D] :
                          ( m2_subset_1(D,k1_numbers,k5_numbers)
                         => ? [E] :
                              ( m2_subset_1(E,k1_numbers,k5_numbers)
                              & r1_xreal_0(k2_xcmplx_0(A,C),k2_seq_1(k5_numbers,k1_numbers,B,k1_nat_1(D,E))) ) ) ) ) ) ) ) ) )).

fof(t88_rinfsup1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( v3_seq_2(B)
           => ( A = k5_rinfsup1(B)
            <=> ! [C] :
                  ( v1_xreal_0(C)
                 => ( ~ r1_xreal_0(C,np__0)
                   => ( ! [D] :
                          ( m2_subset_1(D,k1_numbers,k5_numbers)
                         => ~ ! [E] :
                                ( m2_subset_1(E,k1_numbers,k5_numbers)
                               => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,B,k1_nat_1(D,E)),k6_xcmplx_0(A,C)) ) )
                      & ? [D] :
                          ( m2_subset_1(D,k1_numbers,k5_numbers)
                          & ! [E] :
                              ( m2_subset_1(E,k1_numbers,k5_numbers)
                             => ~ r1_xreal_0(k2_xcmplx_0(A,C),k2_seq_1(k5_numbers,k1_numbers,B,k1_nat_1(D,E))) ) ) ) ) ) ) ) ) ) )).

fof(t89_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v3_seq_2(A)
       => r1_xreal_0(k6_rinfsup1(A),k5_rinfsup1(A)) ) ) )).

fof(t90_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( ( v3_seq_2(A)
          & k5_rinfsup1(A) = k6_rinfsup1(A) )
      <=> v4_seq_2(A) ) ) )).

fof(t91_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v4_seq_2(A)
       => ( k2_seq_2(A) = k5_rinfsup1(A)
          & k2_seq_2(A) = k6_rinfsup1(A) ) ) ) )).

fof(t92_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v3_seq_2(A)
       => ( k5_rinfsup1(k6_partfun3(k5_numbers,A)) = k1_real_1(k6_rinfsup1(A))
          & k6_rinfsup1(k6_partfun3(k5_numbers,A)) = k1_real_1(k5_rinfsup1(A)) ) ) ) )).

fof(t93_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( ( v3_seq_2(A)
              & v3_seq_2(B)
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,C),k2_seq_1(k5_numbers,k1_numbers,B,C)) ) )
           => ( r1_xreal_0(k5_rinfsup1(A),k5_rinfsup1(B))
              & r1_xreal_0(k6_rinfsup1(A),k6_rinfsup1(B)) ) ) ) ) )).

fof(t94_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( ( v3_seq_2(A)
              & v3_seq_2(B) )
           => ( r1_xreal_0(k3_real_1(k6_rinfsup1(A),k6_rinfsup1(B)),k6_rinfsup1(k3_partfun3(k5_numbers,A,B)))
              & r1_xreal_0(k6_rinfsup1(k3_partfun3(k5_numbers,A,B)),k3_real_1(k6_rinfsup1(A),k5_rinfsup1(B)))
              & r1_xreal_0(k6_rinfsup1(k3_partfun3(k5_numbers,A,B)),k3_real_1(k5_rinfsup1(A),k6_rinfsup1(B)))
              & r1_xreal_0(k3_real_1(k6_rinfsup1(A),k5_rinfsup1(B)),k5_rinfsup1(k3_partfun3(k5_numbers,A,B)))
              & r1_xreal_0(k3_real_1(k5_rinfsup1(A),k6_rinfsup1(B)),k5_rinfsup1(k3_partfun3(k5_numbers,A,B)))
              & r1_xreal_0(k5_rinfsup1(k3_partfun3(k5_numbers,A,B)),k3_real_1(k5_rinfsup1(A),k5_rinfsup1(B)))
              & ( ( v4_seq_2(A)
                  | v4_seq_2(B) )
               => ( k6_rinfsup1(k3_partfun3(k5_numbers,A,B)) = k3_real_1(k6_rinfsup1(A),k6_rinfsup1(B))
                  & k5_rinfsup1(k3_partfun3(k5_numbers,A,B)) = k3_real_1(k5_rinfsup1(A),k5_rinfsup1(B)) ) ) ) ) ) ) )).

fof(t95_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( ( v3_seq_2(A)
              & v4_partfun3(A)
              & v3_seq_2(B)
              & v4_partfun3(B) )
           => ( r1_xreal_0(k4_real_1(k6_rinfsup1(A),k6_rinfsup1(B)),k6_rinfsup1(k5_partfun3(k5_numbers,A,B)))
              & r1_xreal_0(k5_rinfsup1(k5_partfun3(k5_numbers,A,B)),k4_real_1(k5_rinfsup1(A),k5_rinfsup1(B))) ) ) ) ) )).

fof(dt_k1_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m1_relset_1(A,k5_numbers,k1_numbers) )
     => m1_subset_1(k1_rinfsup1(A),k1_numbers) ) )).

fof(dt_k2_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m1_relset_1(A,k5_numbers,k1_numbers) )
     => m1_subset_1(k2_rinfsup1(A),k1_numbers) ) )).

fof(dt_k3_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m1_relset_1(A,k5_numbers,k1_numbers) )
     => ( v1_funct_1(k3_rinfsup1(A))
        & v1_funct_2(k3_rinfsup1(A),k5_numbers,k1_numbers)
        & m2_relset_1(k3_rinfsup1(A),k5_numbers,k1_numbers) ) ) )).

fof(dt_k4_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m1_relset_1(A,k5_numbers,k1_numbers) )
     => ( v1_funct_1(k4_rinfsup1(A))
        & v1_funct_2(k4_rinfsup1(A),k5_numbers,k1_numbers)
        & m2_relset_1(k4_rinfsup1(A),k5_numbers,k1_numbers) ) ) )).

fof(dt_k5_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m1_relset_1(A,k5_numbers,k1_numbers) )
     => m1_subset_1(k5_rinfsup1(A),k1_numbers) ) )).

fof(dt_k6_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m1_relset_1(A,k5_numbers,k1_numbers) )
     => m1_subset_1(k6_rinfsup1(A),k1_numbers) ) )).

fof(t29_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => m1_subset_1(a_2_0_rinfsup1(A,B),k1_zfmisc_1(k1_numbers)) ) ) )).

fof(t30_rinfsup1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => k1_pscomp_1(k5_numbers,k1_numbers,k1_seqm_3(B,A)) = a_2_1_rinfsup1(A,B) ) ) )).

fof(t31_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v1_seq_2(A)
       => ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(k1_numbers))
               => ( C = a_2_0_rinfsup1(A,B)
                 => v1_seq_4(C) ) ) ) ) ) )).

fof(t32_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v2_seq_2(A)
       => ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(k1_numbers))
               => ( C = a_2_0_rinfsup1(A,B)
                 => v2_seq_4(C) ) ) ) ) ) )).

fof(t33_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v3_seq_2(A)
       => ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(k1_numbers))
               => ( C = a_2_0_rinfsup1(A,B)
                 => v3_seq_4(C) ) ) ) ) ) )).

fof(t34_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v3_seqm_3(A)
       => ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(k1_numbers))
               => ( C = a_2_0_rinfsup1(A,B)
                 => k4_pscomp_1(C) = k2_seq_1(k5_numbers,k1_numbers,A,B) ) ) ) ) ) )).

fof(t35_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v4_seqm_3(A)
       => ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(k1_numbers))
               => ( C = a_2_0_rinfsup1(A,B)
                 => k3_pscomp_1(C) = k2_seq_1(k5_numbers,k1_numbers,A,B) ) ) ) ) ) )).

fof(t36_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ? [B] :
          ( v1_funct_1(B)
          & v1_funct_2(B,k5_numbers,k1_numbers)
          & m2_relset_1(B,k5_numbers,k1_numbers)
          & ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(k1_numbers))
                 => ( D = a_2_0_rinfsup1(A,C)
                   => k2_seq_1(k5_numbers,k1_numbers,B,C) = k3_pscomp_1(D) ) ) ) ) ) )).

fof(t37_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ? [B] :
          ( v1_funct_1(B)
          & v1_funct_2(B,k5_numbers,k1_numbers)
          & m2_relset_1(B,k5_numbers,k1_numbers)
          & ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(k1_numbers))
                 => ( D = a_2_0_rinfsup1(A,C)
                   => k2_seq_1(k5_numbers,k1_numbers,B,C) = k4_pscomp_1(D) ) ) ) ) ) )).

fof(d4_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( B = k3_rinfsup1(A)
          <=> ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(k1_numbers))
                   => ( D = a_2_0_rinfsup1(A,C)
                     => k2_seq_1(k5_numbers,k1_numbers,B,C) = k4_pscomp_1(D) ) ) ) ) ) ) )).

fof(d5_rinfsup1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( B = k4_rinfsup1(A)
          <=> ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(k1_numbers))
                   => ( D = a_2_0_rinfsup1(A,C)
                     => k2_seq_1(k5_numbers,k1_numbers,B,C) = k3_pscomp_1(D) ) ) ) ) ) ) )).

fof(fraenkel_a_2_0_rinfsup1,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_numbers)
        & m2_relset_1(B,k5_numbers,k1_numbers)
        & m2_subset_1(C,k1_numbers,k5_numbers) )
     => ( r2_hidden(A,a_2_0_rinfsup1(B,C))
      <=> ? [D] :
            ( m2_subset_1(D,k1_numbers,k5_numbers)
            & A = k2_seq_1(k5_numbers,k1_numbers,B,D)
            & r1_xreal_0(C,D) ) ) ) )).

fof(fraenkel_a_2_1_rinfsup1,axiom,(
    ! [A,B,C] :
      ( ( m2_subset_1(B,k1_numbers,k5_numbers)
        & v1_funct_1(C)
        & v1_funct_2(C,k5_numbers,k1_numbers)
        & m2_relset_1(C,k5_numbers,k1_numbers) )
     => ( r2_hidden(A,a_2_1_rinfsup1(B,C))
      <=> ? [D] :
            ( m2_subset_1(D,k1_numbers,k5_numbers)
            & A = k2_seq_1(k5_numbers,k1_numbers,C,D)
            & r1_xreal_0(B,D) ) ) ) )).
%------------------------------------------------------------------------------