SET007 Axioms: SET007+85.ax


%------------------------------------------------------------------------------
% File     : SET007+85 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Monotone Real Sequences. Subsequences
% 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    : seqm_3 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  110 (  10 unit)
%            Number of atoms       :  829 (  27 equality)
%            Maximal formula depth :   13 (   7 average)
%            Number of connectives :  735 (  16 ~  ;   9  |; 415  &)
%                                         (  27 <=>; 268 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   26 (   1 propositional; 0-3 arity)
%            Number of functors    :   25 (   4 constant; 0-4 arity)
%            Number of variables   :  214 (   0 singleton; 209 !;   5 ?)
%            Maximal term depth    :    4 (   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(cc1_seqm_3,axiom,(
    ! [A] :
      ( m1_relset_1(A,k5_numbers,k1_numbers)
     => ( ( v1_funct_1(A)
          & v1_seqm_3(A) )
       => ( v1_funct_1(A)
          & v1_seq_1(A)
          & v3_seqm_3(A) ) ) ) )).

fof(cc2_seqm_3,axiom,(
    ! [A] :
      ( m1_relset_1(A,k5_numbers,k1_numbers)
     => ( ( v1_funct_1(A)
          & v2_seqm_3(A) )
       => ( v1_funct_1(A)
          & v1_seq_1(A)
          & v4_seqm_3(A) ) ) ) )).

fof(cc3_seqm_3,axiom,(
    ! [A] :
      ( m1_relset_1(A,k5_numbers,k1_numbers)
     => ( ( v1_funct_1(A)
          & v5_seqm_3(A) )
       => ( v1_funct_1(A)
          & v1_seq_1(A)
          & v3_seqm_3(A)
          & v4_seqm_3(A) ) ) ) )).

fof(cc4_seqm_3,axiom,(
    ! [A] :
      ( m1_relset_1(A,k5_numbers,k1_numbers)
     => ( ( v1_funct_1(A)
          & v3_seqm_3(A)
          & v4_seqm_3(A) )
       => ( v1_funct_1(A)
          & v1_seq_1(A)
          & v5_seqm_3(A) ) ) ) )).

fof(rc1_seqm_3,axiom,(
    ? [A] :
      ( m1_relset_1(A,k5_numbers,k1_numbers)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_funct_2(A,k5_numbers,k1_numbers)
      & v1_seq_1(A)
      & v1_seqm_3(A)
      & v3_seqm_3(A)
      & v7_seqm_3(A) ) )).

fof(fc1_seqm_3,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & v1_seqm_3(A)
        & v7_seqm_3(A)
        & m1_relset_1(A,k5_numbers,k1_numbers)
        & m1_subset_1(B,k5_numbers) )
     => ( v1_relat_1(k1_seqm_3(A,B))
        & v1_funct_1(k1_seqm_3(A,B))
        & v1_funct_2(k1_seqm_3(A,B),k5_numbers,k1_numbers)
        & v1_seq_1(k1_seqm_3(A,B))
        & v1_seqm_3(k1_seqm_3(A,B))
        & v3_seqm_3(k1_seqm_3(A,B))
        & v7_seqm_3(k1_seqm_3(A,B)) ) ) )).

fof(fc2_seqm_3,axiom,(
    ! [A,B] :
      ( v1_relat_1(k2_funcop_1(A,B))
      & v1_funct_1(k2_funcop_1(A,B))
      & v5_seqm_3(k2_funcop_1(A,B)) ) )).

fof(d1_seqm_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v1_seqm_3(A)
      <=> ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ~ ( r2_hidden(B,k1_relat_1(A))
                    & r2_hidden(C,k1_relat_1(A))
                    & ~ r1_xreal_0(C,B)
                    & r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,C),k2_seq_1(k5_numbers,k1_numbers,A,B)) ) ) ) ) ) )).

fof(d2_seqm_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v2_seqm_3(A)
      <=> ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ~ ( r2_hidden(B,k1_relat_1(A))
                    & r2_hidden(C,k1_relat_1(A))
                    & ~ r1_xreal_0(C,B)
                    & r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,B),k2_seq_1(k5_numbers,k1_numbers,A,C)) ) ) ) ) ) )).

fof(d3_seqm_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v3_seqm_3(A)
      <=> ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ( ( r2_hidden(B,k1_relat_1(A))
                    & r2_hidden(C,k1_relat_1(A))
                    & r1_xreal_0(B,C) )
                 => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,B),k2_seq_1(k5_numbers,k1_numbers,A,C)) ) ) ) ) ) )).

fof(d4_seqm_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v4_seqm_3(A)
      <=> ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ( ( r2_hidden(B,k1_relat_1(A))
                    & r2_hidden(C,k1_relat_1(A))
                    & r1_xreal_0(B,C) )
                 => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,C),k2_seq_1(k5_numbers,k1_numbers,A,B)) ) ) ) ) ) )).

fof(d5_seqm_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v5_seqm_3(A)
      <=> ! [B,C] :
            ( ( r2_hidden(B,k1_relat_1(A))
              & r2_hidden(C,k1_relat_1(A)) )
           => k1_funct_1(A,B) = k1_funct_1(A,C) ) ) ) )).

fof(d6_seqm_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v5_seqm_3(A)
      <=> ? [B] :
            ( v1_xreal_0(B)
            & ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => k2_seq_1(k5_numbers,k1_numbers,A,C) = B ) ) ) ) )).

fof(d7_seqm_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v6_seqm_3(A)
      <=> ( v3_seqm_3(A)
          | v4_seqm_3(A) ) ) ) )).

fof(t1_seqm_3,axiom,(
    $true )).

fof(t2_seqm_3,axiom,(
    $true )).

fof(t3_seqm_3,axiom,(
    $true )).

fof(t4_seqm_3,axiom,(
    $true )).

fof(t5_seqm_3,axiom,(
    $true )).

fof(t6_seqm_3,axiom,(
    $true )).

fof(t7_seqm_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v1_seqm_3(A)
      <=> ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ~ ( ~ r1_xreal_0(C,B)
                    & r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,C),k2_seq_1(k5_numbers,k1_numbers,A,B)) ) ) ) ) ) )).

fof(t8_seqm_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v1_seqm_3(A)
      <=> ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ~ r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(k1_nat_1(B,np__1),C)),k2_seq_1(k5_numbers,k1_numbers,A,B)) ) ) ) ) )).

fof(t9_seqm_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v2_seqm_3(A)
      <=> ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ~ r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,B),k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(k1_nat_1(B,np__1),C))) ) ) ) ) )).

fof(t10_seqm_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v2_seqm_3(A)
      <=> ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ~ ( ~ r1_xreal_0(C,B)
                    & r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,B),k2_seq_1(k5_numbers,k1_numbers,A,C)) ) ) ) ) ) )).

fof(t11_seqm_3,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] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,B),k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(B,C))) ) ) ) ) )).

fof(t12_seqm_3,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] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ( r1_xreal_0(B,C)
                 => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,B),k2_seq_1(k5_numbers,k1_numbers,A,C)) ) ) ) ) ) )).

fof(t13_seqm_3,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] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(B,C)),k2_seq_1(k5_numbers,k1_numbers,A,B)) ) ) ) ) )).

fof(t14_seqm_3,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] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ( r1_xreal_0(B,C)
                 => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,C),k2_seq_1(k5_numbers,k1_numbers,A,B)) ) ) ) ) ) )).

fof(t15_seqm_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v5_seqm_3(A)
      <=> ? [B] :
            ( v1_xreal_0(B)
            & k2_relat_1(A) = k1_tarski(B) ) ) ) )).

fof(t16_seqm_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v5_seqm_3(A)
      <=> ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => k2_seq_1(k5_numbers,k1_numbers,A,B) = k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(B,np__1)) ) ) ) )).

fof(t17_seqm_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v5_seqm_3(A)
      <=> ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => k2_seq_1(k5_numbers,k1_numbers,A,B) = k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(B,C)) ) ) ) ) )).

fof(t18_seqm_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v5_seqm_3(A)
      <=> ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => k2_seq_1(k5_numbers,k1_numbers,A,B) = k2_seq_1(k5_numbers,k1_numbers,A,C) ) ) ) ) )).

fof(t19_seqm_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v1_seqm_3(A)
       => ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ~ ( ~ r1_xreal_0(B,np__0)
                & r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,B),k2_seq_1(k5_numbers,k1_numbers,A,np__0)) ) ) ) ) )).

fof(t20_seqm_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v2_seqm_3(A)
       => ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ~ ( ~ r1_xreal_0(B,np__0)
                & r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,np__0),k2_seq_1(k5_numbers,k1_numbers,A,B)) ) ) ) ) )).

fof(t21_seqm_3,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)
           => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,np__0),k2_seq_1(k5_numbers,k1_numbers,A,B)) ) ) ) )).

fof(t22_seqm_3,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)
           => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,B),k2_seq_1(k5_numbers,k1_numbers,A,np__0)) ) ) ) )).

fof(t23_seqm_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v1_seqm_3(A)
       => v3_seqm_3(A) ) ) )).

fof(t24_seqm_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v2_seqm_3(A)
       => v4_seqm_3(A) ) ) )).

fof(t25_seqm_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v5_seqm_3(A)
       => v3_seqm_3(A) ) ) )).

fof(t26_seqm_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v5_seqm_3(A)
       => v4_seqm_3(A) ) ) )).

fof(t27_seqm_3,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)
          & v4_seqm_3(A) )
       => v5_seqm_3(A) ) ) )).

fof(d8_seqm_3,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ( v7_seqm_3(A)
      <=> r1_tarski(k2_relat_1(A),k5_numbers) ) ) )).

fof(d9_seqm_3,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)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_numbers)
                & m2_relset_1(C,k5_numbers,k1_numbers) )
             => ( C = k1_seqm_3(A,B)
              <=> ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => k2_seq_1(k5_numbers,k1_numbers,C,D) = k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(D,B)) ) ) ) ) ) )).

fof(t28_seqm_3,axiom,(
    $true )).

fof(t29_seqm_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( ( v1_funct_1(A)
          & v1_funct_2(A,k5_numbers,k1_numbers)
          & v1_seqm_3(A)
          & v7_seqm_3(A)
          & m2_relset_1(A,k5_numbers,k1_numbers) )
      <=> ( v1_seqm_3(A)
          & ! [B] :
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => m2_subset_1(k2_seq_1(k5_numbers,k1_numbers,A,B),k1_numbers,k5_numbers) ) ) ) ) )).

fof(t30_seqm_3,axiom,(
    $true )).

fof(t31_seqm_3,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)
            & v1_seqm_3(B)
            & v7_seqm_3(B)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => k1_funct_1(k5_relat_1(B,A),C) = k2_seq_1(k5_numbers,k1_numbers,A,k2_seq_1(k5_numbers,k1_numbers,B,C)) ) ) ) )).

fof(d10_seqm_3,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) )
         => ( m1_seqm_3(B,A)
          <=> ? [C] :
                ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_numbers)
                & v1_seqm_3(C)
                & v7_seqm_3(C)
                & m2_relset_1(C,k5_numbers,k1_numbers)
                & B = k3_seqm_3(C,A) ) ) ) ) )).

fof(d11_seqm_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v1_seqm_3(A)
      <=> ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ~ r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(B,np__1)),k2_seq_1(k5_numbers,k1_numbers,A,B)) ) ) ) )).

fof(d12_seqm_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v2_seqm_3(A)
      <=> ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ~ r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,B),k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(B,np__1))) ) ) ) )).

fof(d13_seqm_3,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)
           => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,B),k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(B,np__1))) ) ) ) )).

fof(d14_seqm_3,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)
           => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(B,np__1)),k2_seq_1(k5_numbers,k1_numbers,A,B)) ) ) ) )).

fof(t32_seqm_3,axiom,(
    $true )).

fof(t33_seqm_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & v1_seqm_3(A)
        & v7_seqm_3(A)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => r1_xreal_0(B,k2_seqm_3(A,B)) ) ) )).

fof(t34_seqm_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => k1_seqm_3(A,np__0) = A ) )).

fof(t35_seqm_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_numbers)
                & m2_relset_1(C,k5_numbers,k1_numbers) )
             => k1_seqm_3(k1_seqm_3(C,A),B) = k1_seqm_3(k1_seqm_3(C,B),A) ) ) ) )).

fof(t36_seqm_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_numbers)
                & m2_relset_1(C,k5_numbers,k1_numbers) )
             => k1_seqm_3(k1_seqm_3(C,A),B) = k1_seqm_3(C,k1_nat_1(A,B)) ) ) ) )).

fof(t37_seqm_3,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) )
             => k1_seqm_3(k9_seq_1(B,C),A) = k9_seq_1(k1_seqm_3(B,A),k1_seqm_3(C,A)) ) ) ) )).

fof(t38_seqm_3,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_seqm_3(k17_seq_1(B),A) = k17_seq_1(k1_seqm_3(B,A)) ) ) )).

fof(t39_seqm_3,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) )
             => k1_seqm_3(k10_seq_1(B,C),A) = k10_seq_1(k1_seqm_3(B,A),k1_seqm_3(C,A)) ) ) ) )).

fof(t40_seqm_3,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_relat_1(B)
           => v2_relat_1(k1_seqm_3(B,A)) ) ) ) )).

fof(t41_seqm_3,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_seqm_3(k18_seq_1(B),A) = k18_seq_1(k1_seqm_3(B,A)) ) ) )).

fof(t42_seqm_3,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) )
             => k1_seqm_3(k11_seq_1(B,C),A) = k11_seq_1(k1_seqm_3(B,A),k1_seqm_3(C,A)) ) ) ) )).

fof(t43_seqm_3,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) )
             => k1_seqm_3(k19_seq_1(B,C),A) = k19_seq_1(k1_seqm_3(B,A),k1_seqm_3(C,A)) ) ) ) )).

fof(t44_seqm_3,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) )
             => k1_seqm_3(k14_seq_1(C,B),A) = k14_seq_1(k1_seqm_3(C,A),B) ) ) ) )).

fof(t45_seqm_3,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)
                & v1_seqm_3(C)
                & v7_seqm_3(C)
                & m2_relset_1(C,k5_numbers,k1_numbers) )
             => k1_seqm_3(k3_seqm_3(C,B),A) = k3_seqm_3(k1_seqm_3(C,A),B) ) ) ) )).

fof(t46_seqm_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => m1_seqm_3(A,A) ) )).

fof(t47_seqm_3,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) )
         => m1_seqm_3(k1_seqm_3(B,A),B) ) ) )).

fof(t48_seqm_3,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] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_numbers)
                & m2_relset_1(C,k5_numbers,k1_numbers) )
             => ( ( m1_seqm_3(A,B)
                  & m1_seqm_3(B,C) )
               => m1_seqm_3(A,C) ) ) ) ) )).

fof(t49_seqm_3,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_seqm_3(A)
              & m1_seqm_3(B,A) )
           => v1_seqm_3(B) ) ) ) )).

fof(t50_seqm_3,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_seqm_3(A)
              & m1_seqm_3(B,A) )
           => v2_seqm_3(B) ) ) ) )).

fof(t51_seqm_3,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_seqm_3(A)
              & m1_seqm_3(B,A) )
           => v3_seqm_3(B) ) ) ) )).

fof(t52_seqm_3,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) )
         => ( ( v4_seqm_3(A)
              & m1_seqm_3(B,A) )
           => v4_seqm_3(B) ) ) ) )).

fof(t53_seqm_3,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) )
         => ( ( v6_seqm_3(A)
              & m1_seqm_3(B,A) )
           => v6_seqm_3(B) ) ) ) )).

fof(t54_seqm_3,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) )
         => ( ( v5_seqm_3(A)
              & m1_seqm_3(B,A) )
           => v5_seqm_3(B) ) ) ) )).

fof(t55_seqm_3,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) )
         => ( ( v5_seqm_3(A)
              & m1_seqm_3(B,A) )
           => A = B ) ) ) )).

fof(t56_seqm_3,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)
              & m1_seqm_3(B,A) )
           => v1_seq_2(B) ) ) ) )).

fof(t57_seqm_3,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)
              & m1_seqm_3(B,A) )
           => v2_seq_2(B) ) ) ) )).

fof(t58_seqm_3,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)
              & m1_seqm_3(B,A) )
           => v3_seq_2(B) ) ) ) )).

fof(t59_seqm_3,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_seqm_3(B)
             => ( r1_xreal_0(A,np__0)
                | v1_seqm_3(k14_seq_1(B,A)) ) )
            & ( np__0 = A
             => v5_seqm_3(k14_seq_1(B,A)) )
            & ( v1_seqm_3(B)
             => ( r1_xreal_0(np__0,A)
                | v2_seqm_3(k14_seq_1(B,A)) ) ) ) ) ) )).

fof(t60_seqm_3,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_seqm_3(B)
             => ( r1_xreal_0(A,np__0)
                | v2_seqm_3(k14_seq_1(B,A)) ) )
            & ( v2_seqm_3(B)
             => ( r1_xreal_0(np__0,A)
                | v1_seqm_3(k14_seq_1(B,A)) ) ) ) ) ) )).

fof(t61_seqm_3,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_seqm_3(B)
                & r1_xreal_0(np__0,A) )
             => v3_seqm_3(k14_seq_1(B,A)) )
            & ( ( v3_seqm_3(B)
                & r1_xreal_0(A,np__0) )
             => v4_seqm_3(k14_seq_1(B,A)) ) ) ) ) )).

fof(t62_seqm_3,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) )
         => ( ( ( v4_seqm_3(B)
                & r1_xreal_0(np__0,A) )
             => v4_seqm_3(k14_seq_1(B,A)) )
            & ( ( v4_seqm_3(B)
                & r1_xreal_0(A,np__0) )
             => v3_seqm_3(k14_seq_1(B,A)) ) ) ) ) )).

fof(t63_seqm_3,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_seqm_3(A)
                & v1_seqm_3(B) )
             => v1_seqm_3(k9_seq_1(A,B)) )
            & ( ( v2_seqm_3(A)
                & v2_seqm_3(B) )
             => v2_seqm_3(k9_seq_1(A,B)) )
            & ( ( v3_seqm_3(A)
                & v3_seqm_3(B) )
             => v3_seqm_3(k9_seq_1(A,B)) )
            & ( ( v4_seqm_3(A)
                & v4_seqm_3(B) )
             => v4_seqm_3(k9_seq_1(A,B)) ) ) ) ) )).

fof(t64_seqm_3,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_seqm_3(A)
                & v5_seqm_3(B) )
             => v1_seqm_3(k9_seq_1(A,B)) )
            & ( ( v2_seqm_3(A)
                & v5_seqm_3(B) )
             => v2_seqm_3(k9_seq_1(A,B)) )
            & ( ( v3_seqm_3(A)
                & v5_seqm_3(B) )
             => v3_seqm_3(k9_seq_1(A,B)) )
            & ( ( v4_seqm_3(A)
                & v5_seqm_3(B) )
             => v4_seqm_3(k9_seq_1(A,B)) ) ) ) ) )).

fof(t65_seqm_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v5_seqm_3(A)
       => ( ! [B] :
              ( v1_xreal_0(B)
             => v5_seqm_3(k14_seq_1(A,B)) )
          & v5_seqm_3(k17_seq_1(A))
          & v5_seqm_3(k22_seq_1(A)) ) ) ) )).

fof(t66_seqm_3,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) )
         => ( ( v5_seqm_3(A)
              & v5_seqm_3(B) )
           => ( v5_seqm_3(k11_seq_1(A,B))
              & v5_seqm_3(k9_seq_1(A,B)) ) ) ) ) )).

fof(t67_seqm_3,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) )
         => ( ( v5_seqm_3(A)
              & v5_seqm_3(B) )
           => v5_seqm_3(k10_seq_1(A,B)) ) ) ) )).

fof(t68_seqm_3,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)
             => ( r1_xreal_0(A,np__0)
                | v1_seq_2(k14_seq_1(B,A)) ) )
            & ( np__0 = A
             => v3_seq_2(k14_seq_1(B,A)) )
            & ( v1_seq_2(B)
             => ( r1_xreal_0(np__0,A)
                | v2_seq_2(k14_seq_1(B,A)) ) ) ) ) ) )).

fof(t69_seqm_3,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)
             => ( r1_xreal_0(A,np__0)
                | v2_seq_2(k14_seq_1(B,A)) ) )
            & ( v2_seq_2(B)
             => ( r1_xreal_0(np__0,A)
                | v1_seq_2(k14_seq_1(B,A)) ) ) ) ) ) )).

fof(t70_seqm_3,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] :
              ( v1_xreal_0(B)
             => v3_seq_2(k14_seq_1(A,B)) ) )
        & ( v3_seq_2(A)
         => v3_seq_2(k17_seq_1(A)) )
        & ( v3_seq_2(A)
         => v3_seq_2(k22_seq_1(A)) )
        & ( v3_seq_2(k22_seq_1(A))
         => v3_seq_2(A) ) ) ) )).

fof(t71_seqm_3,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) )
             => v1_seq_2(k9_seq_1(A,B)) )
            & ( ( v2_seq_2(A)
                & v2_seq_2(B) )
             => v2_seq_2(k9_seq_1(A,B)) )
            & ( ( v3_seq_2(A)
                & v3_seq_2(B) )
             => v3_seq_2(k9_seq_1(A,B)) ) ) ) ) )).

fof(t72_seqm_3,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) )
           => ( v3_seq_2(k11_seq_1(A,B))
              & v3_seq_2(k10_seq_1(A,B)) ) ) ) ) )).

fof(t73_seqm_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v5_seqm_3(A)
       => v3_seq_2(A) ) ) )).

fof(t74_seqm_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v5_seqm_3(A)
       => ( ! [B] :
              ( v1_xreal_0(B)
             => v3_seq_2(k14_seq_1(A,B)) )
          & v3_seq_2(k17_seq_1(A))
          & v3_seq_2(k22_seq_1(A)) ) ) ) )).

fof(t75_seqm_3,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)
                & v5_seqm_3(B) )
             => v1_seq_2(k9_seq_1(A,B)) )
            & ( ( v2_seq_2(A)
                & v5_seqm_3(B) )
             => v2_seq_2(k9_seq_1(A,B)) )
            & ( ( v3_seq_2(A)
                & v5_seqm_3(B) )
             => v3_seq_2(k9_seq_1(A,B)) ) ) ) ) )).

fof(t76_seqm_3,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)
                & v5_seqm_3(B) )
             => v1_seq_2(k10_seq_1(A,B)) )
            & ( ( v2_seq_2(A)
                & v5_seqm_3(B) )
             => v2_seq_2(k10_seq_1(A,B)) )
            & ( ( v3_seq_2(A)
                & v5_seqm_3(B) )
             => ( v3_seq_2(k10_seq_1(A,B))
                & v3_seq_2(k10_seq_1(B,A))
                & v3_seq_2(k11_seq_1(A,B)) ) ) ) ) ) )).

fof(t77_seqm_3,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_seqm_3(B) )
           => v1_seq_2(k9_seq_1(A,B)) ) ) ) )).

fof(t78_seqm_3,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)
              & v3_seqm_3(B) )
           => v2_seq_2(k9_seq_1(A,B)) ) ) ) )).

fof(t79_seqm_3,axiom,(
    ! [A,B] : v5_seqm_3(k2_funcop_1(A,B)) )).

fof(t80_seqm_3,axiom,
    ( v1_seqm_3(k6_funct_3(k1_numbers,k5_numbers))
    & v7_seqm_3(k6_funct_3(k1_numbers,k5_numbers)) )).

fof(dt_m1_seqm_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m1_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( m1_seqm_3(B,A)
         => ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) ) ) ) )).

fof(existence_m1_seqm_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m1_relset_1(A,k5_numbers,k1_numbers) )
     => ? [B] : m1_seqm_3(B,A) ) )).

fof(dt_k1_seqm_3,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m1_relset_1(A,k5_numbers,k1_numbers)
        & m1_subset_1(B,k5_numbers) )
     => ( v1_funct_1(k1_seqm_3(A,B))
        & v1_funct_2(k1_seqm_3(A,B),k5_numbers,k1_numbers)
        & m2_relset_1(k1_seqm_3(A,B),k5_numbers,k1_numbers) ) ) )).

fof(dt_k2_seqm_3,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & v1_seqm_3(A)
        & v7_seqm_3(A)
        & m1_relset_1(A,k5_numbers,k1_numbers)
        & m1_subset_1(B,k5_numbers) )
     => m2_subset_1(k2_seqm_3(A,B),k1_numbers,k5_numbers) ) )).

fof(redefinition_k2_seqm_3,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & v1_seqm_3(A)
        & v7_seqm_3(A)
        & m1_relset_1(A,k5_numbers,k1_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k2_seqm_3(A,B) = k1_funct_1(A,B) ) )).

fof(dt_k3_seqm_3,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & v1_seqm_3(A)
        & v7_seqm_3(A)
        & m1_relset_1(A,k5_numbers,k1_numbers)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_numbers)
        & m1_relset_1(B,k5_numbers,k1_numbers) )
     => ( v1_funct_1(k3_seqm_3(A,B))
        & v1_funct_2(k3_seqm_3(A,B),k5_numbers,k1_numbers)
        & m2_relset_1(k3_seqm_3(A,B),k5_numbers,k1_numbers) ) ) )).

fof(redefinition_k3_seqm_3,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & v1_seqm_3(A)
        & v7_seqm_3(A)
        & m1_relset_1(A,k5_numbers,k1_numbers)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_numbers)
        & m1_relset_1(B,k5_numbers,k1_numbers) )
     => k3_seqm_3(A,B) = k5_relat_1(A,B) ) )).

fof(dt_k4_seqm_3,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & v1_seqm_3(A)
        & v7_seqm_3(A)
        & m1_relset_1(A,k5_numbers,k1_numbers)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_numbers)
        & v1_seqm_3(B)
        & v7_seqm_3(B)
        & m1_relset_1(B,k5_numbers,k1_numbers) )
     => ( v1_funct_1(k4_seqm_3(A,B))
        & v1_funct_2(k4_seqm_3(A,B),k5_numbers,k1_numbers)
        & v1_seqm_3(k4_seqm_3(A,B))
        & v7_seqm_3(k4_seqm_3(A,B))
        & m2_relset_1(k4_seqm_3(A,B),k5_numbers,k1_numbers) ) ) )).

fof(redefinition_k4_seqm_3,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & v1_seqm_3(A)
        & v7_seqm_3(A)
        & m1_relset_1(A,k5_numbers,k1_numbers)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_numbers)
        & v1_seqm_3(B)
        & v7_seqm_3(B)
        & m1_relset_1(B,k5_numbers,k1_numbers) )
     => k4_seqm_3(A,B) = k5_relat_1(A,B) ) )).
%------------------------------------------------------------------------------