SET007 Axioms: SET007+64.ax


%------------------------------------------------------------------------------
% File     : SET007+64 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Finite Sequences and Tuples of Elements of a Non-empty Sets
% 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    : finseq_2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  173 (  24 unit)
%            Number of atoms       : 1028 ( 170 equality)
%            Maximal formula depth :   27 (   8 average)
%            Number of connectives : 1012 ( 157 ~  ;   2  |; 314  &)
%                                         (   8 <=>; 531 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   19 (   1 propositional; 0-3 arity)
%            Number of functors    :   59 (  10 constant; 0-6 arity)
%            Number of variables   :  562 (   0 singleton; 538 !;  24 ?)
%            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(rc1_finseq_2,axiom,(
    ! [A] :
    ? [B] :
      ( m1_finseq_2(B,A)
      & ~ v1_xboole_0(B) ) )).

fof(fc1_finseq_2,axiom,(
    ! [A,B] :
      ( ( v4_ordinal2(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k4_finseq_2(A,B)) ) )).

fof(t1_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( m2_subset_1(k3_square_1(A,B),k1_numbers,k5_numbers)
            & m2_subset_1(k4_square_1(A,B),k1_numbers,k5_numbers) ) ) ) )).

fof(t2_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( A = k3_square_1(B,C)
               => k5_subset_1(k5_numbers,k2_finseq_1(B),k2_finseq_1(C)) = k2_finseq_1(A) ) ) ) ) )).

fof(t3_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_xreal_0(A,B)
           => k2_square_1(np__0,k6_xcmplx_0(A,B)) = np__0 ) ) ) )).

fof(t4_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_xreal_0(A,B)
           => k2_square_1(np__0,k6_xcmplx_0(B,A)) = k6_xcmplx_0(B,A) ) ) ) )).

fof(t5_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => m2_subset_1(k2_square_1(np__0,k6_xcmplx_0(A,B)),k1_numbers,k5_numbers) ) ) )).

fof(t6_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( k3_square_1(np__0,A) = np__0
        & k3_square_1(A,np__0) = np__0
        & k4_square_1(np__0,A) = A
        & k4_square_1(A,np__0) = A ) ) )).

fof(t7_finseq_2,axiom,(
    $true )).

fof(t8_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ~ ( r2_hidden(A,k2_finseq_1(k1_nat_1(B,np__1)))
              & ~ r2_hidden(A,k2_finseq_1(B))
              & A != k1_nat_1(B,np__1) ) ) ) )).

fof(t9_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( r2_hidden(A,k2_finseq_1(B))
               => r2_hidden(A,k2_finseq_1(k1_nat_1(B,C))) ) ) ) ) )).

fof(t10_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( ( k3_finseq_1(B) = A
                  & k3_finseq_1(C) = A
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( r2_hidden(D,k2_finseq_1(A))
                       => k1_funct_1(B,D) = k1_funct_1(C,D) ) ) )
               => B = C ) ) ) ) )).

fof(t11_finseq_2,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ~ ( r2_hidden(A,k2_relat_1(B))
          & ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ~ ( r2_hidden(C,k4_finseq_1(B))
                  & k1_funct_1(B,C) = A ) ) ) ) )).

fof(t12_finseq_2,axiom,(
    $true )).

fof(t13_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B,C] :
          ( m2_finseq_1(C,B)
         => ( r2_hidden(A,k4_finseq_1(C))
           => r2_hidden(k1_funct_1(C,A),B) ) ) ) )).

fof(t14_finseq_2,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( r2_hidden(C,k4_finseq_1(A))
               => r2_hidden(k1_funct_1(A,C),B) ) )
         => m2_finseq_1(A,B) ) ) )).

fof(t15_finseq_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => m2_finseq_1(k10_finseq_1(B,C),A) ) ) ) )).

fof(t16_finseq_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => m2_finseq_1(k11_finseq_1(B,C,D),A) ) ) ) ) )).

fof(t17_finseq_2,axiom,(
    $true )).

fof(t18_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( r2_hidden(A,k4_finseq_1(B))
               => r2_hidden(A,k4_finseq_1(k7_finseq_1(B,C))) ) ) ) ) )).

fof(t19_finseq_2,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => k3_finseq_1(k7_finseq_1(B,k9_finseq_1(A))) = k1_nat_1(k3_finseq_1(B),np__1) ) )).

fof(t20_finseq_2,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C)
        & v1_finseq_1(C) )
     => ! [D] :
          ( ( v1_relat_1(D)
            & v1_funct_1(D)
            & v1_finseq_1(D) )
         => ( k7_finseq_1(C,k9_finseq_1(A)) = k7_finseq_1(D,k9_finseq_1(B))
           => ( C = D
              & A = B ) ) ) ) )).

fof(t21_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ~ ( k3_finseq_1(B) = k1_nat_1(A,np__1)
              & ! [C] :
                  ( ( v1_relat_1(C)
                    & v1_funct_1(C)
                    & v1_finseq_1(C) )
                 => ! [D] : B != k7_finseq_1(C,k9_finseq_1(D)) ) ) ) ) )).

fof(t22_finseq_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => ~ ( k3_finseq_1(B) != np__0
              & ! [C] :
                  ( m2_finseq_1(C,A)
                 => ! [D] :
                      ( m1_subset_1(D,A)
                     => B != k8_finseq_1(A,C,k12_finseq_1(A,D)) ) ) ) ) ) )).

fof(t23_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( ( B = k7_relat_1(C,k2_finseq_1(A))
                  & r1_xreal_0(k3_finseq_1(C),A) )
               => C = B ) ) ) ) )).

fof(t24_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( B = k7_relat_1(C,k2_finseq_1(A))
               => k3_finseq_1(B) = k3_square_1(A,k3_finseq_1(C)) ) ) ) ) )).

fof(t25_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ~ ( k3_finseq_1(C) = k1_nat_1(A,B)
                  & ! [D] :
                      ( ( v1_relat_1(D)
                        & v1_funct_1(D)
                        & v1_finseq_1(D) )
                     => ! [E] :
                          ( ( v1_relat_1(E)
                            & v1_funct_1(E)
                            & v1_finseq_1(E) )
                         => ~ ( k3_finseq_1(D) = A
                              & k3_finseq_1(E) = B
                              & C = k7_finseq_1(D,E) ) ) ) ) ) ) ) )).

fof(t26_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m2_finseq_1(D,C)
                 => ~ ( k3_finseq_1(D) = k1_nat_1(A,B)
                      & ! [E] :
                          ( m2_finseq_1(E,C)
                         => ! [F] :
                              ( m2_finseq_1(F,C)
                             => ~ ( k3_finseq_1(E) = A
                                  & k3_finseq_1(F) = B
                                  & D = k8_finseq_1(C,E,F) ) ) ) ) ) ) ) ) )).

fof(t27_finseq_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(A)) )
         => ! [C] :
              ( m2_finseq_1(C,B)
             => m2_finseq_1(C,A) ) ) ) )).

fof(t28_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_finseq_1(A),B)
                & m2_relset_1(C,k2_finseq_1(A),B) )
             => m2_finseq_1(C,B) ) ) ) )).

fof(t29_finseq_2,axiom,(
    $true )).

fof(t30_finseq_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => ( v1_funct_1(B)
            & v1_funct_2(B,k4_finseq_1(B),A)
            & m2_relset_1(B,k4_finseq_1(B),A) ) ) ) )).

fof(t31_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,B)
                & m2_relset_1(C,k5_numbers,B) )
             => m2_finseq_1(k2_partfun1(k5_numbers,B,C,k2_finseq_1(A)),B) ) ) ) )).

fof(t32_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k5_numbers,B)
                    & m2_relset_1(D,k5_numbers,B) )
                 => ( C = k2_partfun1(k5_numbers,B,D,k2_finseq_1(A))
                   => k3_finseq_1(C) = A ) ) ) ) ) )).

fof(t33_finseq_2,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( ( r1_tarski(k2_relat_1(A),k1_relat_1(C))
                  & B = k5_relat_1(A,C) )
               => k3_finseq_1(B) = k3_finseq_1(A) ) ) ) ) )).

fof(t34_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ( B = k2_finseq_1(A)
           => ! [C] :
                ( ( v1_relat_1(C)
                  & v1_funct_1(C)
                  & v1_finseq_1(C) )
               => ! [D] :
                    ( m2_finseq_1(D,B)
                   => ( r1_xreal_0(A,k3_finseq_1(C))
                     => ( v1_relat_1(k5_relat_1(D,C))
                        & v1_funct_1(k5_relat_1(D,C))
                        & v1_finseq_1(k5_relat_1(D,C)) ) ) ) ) ) ) ) )).

fof(t35_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ( B = k2_finseq_1(A)
               => ! [D] :
                    ( m2_finseq_1(D,C)
                   => ! [E] :
                        ( m2_finseq_1(E,B)
                       => ( r1_xreal_0(A,k3_finseq_1(D))
                         => m2_finseq_1(k1_partfun1(k5_numbers,B,k5_numbers,C,E,D),C) ) ) ) ) ) ) ) )).

fof(t36_finseq_2,axiom,(
    ! [A,B,C] :
      ( m2_finseq_1(C,A)
     => ! [D] :
          ( ( v1_funct_1(D)
            & v1_funct_2(D,A,B)
            & m2_relset_1(D,A,B) )
         => m2_finseq_1(k1_partfun1(k5_numbers,A,A,B,C,D),B) ) ) )).

fof(t37_finseq_2,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ( v1_relat_1(C)
            & v1_funct_1(C)
            & v1_finseq_1(C) )
         => ! [D] :
              ( m2_finseq_1(D,A)
             => ! [E] :
                  ( ( v1_funct_1(E)
                    & v1_funct_2(E,A,B)
                    & m2_relset_1(E,A,B) )
                 => ( C = k1_partfun1(k5_numbers,A,A,B,D,E)
                   => k3_finseq_1(C) = k3_finseq_1(D) ) ) ) ) ) )).

fof(t38_finseq_2,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,B)
            & m2_relset_1(C,A,B) )
         => k1_partfun1(k5_numbers,A,A,B,k6_finseq_1(A),C) = k6_finseq_1(B) ) ) )).

fof(t39_finseq_2,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ~ v1_xboole_0(C)
         => ! [D] :
              ( m2_finseq_1(D,B)
             => ! [E] :
                  ( ( v1_funct_1(E)
                    & v1_funct_2(E,B,C)
                    & m2_relset_1(E,B,C) )
                 => ( D = k9_finseq_1(A)
                   => k1_partfun1(k5_numbers,B,B,C,D,E) = k9_finseq_1(k1_funct_1(E,A)) ) ) ) ) ) )).

fof(t40_finseq_2,axiom,(
    ! [A,B,C] :
      ( ~ v1_xboole_0(C)
     => ! [D] :
          ( ~ v1_xboole_0(D)
         => ! [E] :
              ( m2_finseq_1(E,C)
             => ! [F] :
                  ( ( v1_funct_1(F)
                    & v1_funct_2(F,C,D)
                    & m2_relset_1(F,C,D) )
                 => ( E = k10_finseq_1(A,B)
                   => k1_partfun1(k5_numbers,C,C,D,E,F) = k10_finseq_1(k1_funct_1(F,A),k1_funct_1(F,B)) ) ) ) ) ) )).

fof(t41_finseq_2,axiom,(
    ! [A,B,C,D] :
      ( ~ v1_xboole_0(D)
     => ! [E] :
          ( ~ v1_xboole_0(E)
         => ! [F] :
              ( m2_finseq_1(F,D)
             => ! [G] :
                  ( ( v1_funct_1(G)
                    & v1_funct_2(G,D,E)
                    & m2_relset_1(G,D,E) )
                 => ( F = k11_finseq_1(A,B,C)
                   => k1_partfun1(k5_numbers,D,D,E,F,G) = k11_finseq_1(k1_funct_1(G,A),k1_funct_1(G,B),k1_funct_1(G,C)) ) ) ) ) ) )).

fof(t42_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(B))
                    & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(B)) )
                 => ( r1_xreal_0(B,k3_finseq_1(C))
                   => ( ( B = np__0
                        & A != np__0 )
                      | ( v1_relat_1(k5_relat_1(D,C))
                        & v1_funct_1(k5_relat_1(D,C))
                        & v1_finseq_1(k5_relat_1(D,C)) ) ) ) ) ) ) ) )).

fof(t43_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_finseq_1(A),k2_finseq_1(A))
                & m2_relset_1(C,k2_finseq_1(A),k2_finseq_1(A)) )
             => ( r1_xreal_0(A,k3_finseq_1(B))
               => ( v1_relat_1(k5_relat_1(C,B))
                  & v1_funct_1(k5_relat_1(C,B))
                  & v1_finseq_1(k5_relat_1(C,B)) ) ) ) ) ) )).

fof(t44_finseq_2,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k4_finseq_1(A),k4_finseq_1(A))
            & m2_relset_1(B,k4_finseq_1(A),k4_finseq_1(A)) )
         => ( v1_relat_1(k5_relat_1(B,A))
            & v1_funct_1(k5_relat_1(B,A))
            & v1_finseq_1(k5_relat_1(B,A)) ) ) ) )).

fof(t45_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(A))
                    & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) )
                 => ( ( k2_relat_1(D) = k2_finseq_1(A)
                      & r1_xreal_0(A,k3_finseq_1(B))
                      & C = k5_relat_1(D,B) )
                   => k3_finseq_1(C) = A ) ) ) ) ) )).

fof(t46_finseq_2,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k4_finseq_1(A),k4_finseq_1(A))
                & m2_relset_1(C,k4_finseq_1(A),k4_finseq_1(A)) )
             => ( ( k2_relat_1(C) = k4_finseq_1(A)
                  & B = k5_relat_1(C,A) )
               => k3_finseq_1(B) = k3_finseq_1(A) ) ) ) ) )).

fof(t47_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(A))
                    & v3_funct_2(D,k2_finseq_1(A),k2_finseq_1(A))
                    & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) )
                 => ( ( r1_xreal_0(A,k3_finseq_1(B))
                      & C = k5_relat_1(D,B) )
                   => k3_finseq_1(C) = A ) ) ) ) ) )).

fof(t48_finseq_2,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k4_finseq_1(A),k4_finseq_1(A))
                & v3_funct_2(C,k4_finseq_1(A),k4_finseq_1(A))
                & m2_relset_1(C,k4_finseq_1(A),k4_finseq_1(A)) )
             => ( B = k5_relat_1(C,A)
               => k3_finseq_1(B) = k3_finseq_1(A) ) ) ) ) )).

fof(t49_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m2_finseq_1(D,C)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_finseq_1(A),k2_finseq_1(B))
                        & m2_relset_1(E,k2_finseq_1(A),k2_finseq_1(B)) )
                     => ( r1_xreal_0(B,k3_finseq_1(D))
                       => ( ( B = np__0
                            & A != np__0 )
                          | m2_finseq_1(k1_partfun1(k2_finseq_1(A),k2_finseq_1(B),k5_numbers,C,E,D),C) ) ) ) ) ) ) ) )).

fof(t50_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_finseq_1(C,B)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(A))
                    & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) )
                 => ( r1_xreal_0(A,k3_finseq_1(C))
                   => m2_finseq_1(k1_partfun1(k2_finseq_1(A),k2_finseq_1(A),k5_numbers,B,D,C),B) ) ) ) ) ) )).

fof(t51_finseq_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k4_finseq_1(B),k4_finseq_1(B))
                & m2_relset_1(C,k4_finseq_1(B),k4_finseq_1(B)) )
             => m2_finseq_1(k1_partfun1(k4_finseq_1(B),k4_finseq_1(B),k5_numbers,A,C,B),A) ) ) ) )).

fof(t52_finseq_2,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => m2_finseq_1(k6_partfun1(k2_finseq_1(A)),k5_numbers) ) )).

fof(d1_finseq_2,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => k1_finseq_2(A) = k6_partfun1(k2_finseq_1(A)) ) )).

fof(t53_finseq_2,axiom,(
    $true )).

fof(t54_finseq_2,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => k4_finseq_1(k1_finseq_2(A)) = k2_finseq_1(A) ) )).

fof(t55_finseq_2,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => k3_finseq_1(k1_finseq_2(A)) = A ) )).

fof(t56_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r2_hidden(A,k2_finseq_1(B))
           => k1_funct_1(k1_finseq_2(B),A) = A ) ) ) )).

fof(t57_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( A != np__0
       => ! [B] :
            ( m1_subset_1(B,k2_finseq_1(A))
           => k1_funct_1(k1_finseq_2(A),B) = B ) ) ) )).

fof(t58_finseq_2,axiom,(
    k1_finseq_2(np__0) = k1_xboole_0 )).

fof(t59_finseq_2,axiom,(
    k1_finseq_2(np__1) = k12_finseq_1(k5_numbers,np__1) )).

fof(t60_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k1_finseq_2(k1_nat_1(A,np__1)) = k7_finseq_1(k1_finseq_2(A),k12_finseq_1(k5_numbers,k1_nat_1(A,np__1))) ) )).

fof(t61_finseq_2,axiom,(
    k1_finseq_2(np__2) = k10_finseq_1(np__1,np__2) )).

fof(t62_finseq_2,axiom,(
    k1_finseq_2(np__3) = k11_finseq_1(np__1,np__2,np__3) )).

fof(t63_finseq_2,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => k5_relat_1(k1_finseq_2(A),B) = k7_relat_1(B,k2_finseq_1(A)) ) ) )).

fof(t64_finseq_2,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( r1_xreal_0(k3_finseq_1(B),A)
           => k5_relat_1(k1_finseq_2(A),B) = B ) ) ) )).

fof(t65_finseq_2,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ( v1_funct_1(k1_finseq_2(A))
        & v1_funct_2(k1_finseq_2(A),k2_finseq_1(A),k2_finseq_1(A))
        & v3_funct_2(k1_finseq_2(A),k2_finseq_1(A),k2_finseq_1(A))
        & m2_relset_1(k1_finseq_2(A),k2_finseq_1(A),k2_finseq_1(A)) ) ) )).

fof(t66_finseq_2,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ! [B] :
          ( v1_relat_1(k2_funcop_1(k2_finseq_1(A),B))
          & v1_funct_1(k2_funcop_1(k2_finseq_1(A),B))
          & v1_finseq_1(k2_funcop_1(k2_finseq_1(A),B)) ) ) )).

fof(d2_finseq_2,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ! [B] : k2_finseq_2(A,B) = k2_funcop_1(k2_finseq_1(A),B) ) )).

fof(t67_finseq_2,axiom,(
    $true )).

fof(t68_finseq_2,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ! [B] : k4_finseq_1(k2_finseq_2(A,B)) = k2_finseq_1(A) ) )).

fof(t69_finseq_2,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ! [B] : k3_finseq_1(k2_finseq_2(A,B)) = A ) )).

fof(t70_finseq_2,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ! [B,C] :
          ( r2_hidden(B,k2_finseq_1(A))
         => k1_funct_1(k2_finseq_2(A,C),B) = C ) ) )).

fof(t71_finseq_2,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,B)
             => ( A != np__0
               => ! [D] :
                    ( m1_subset_1(D,k2_finseq_1(A))
                   => k1_funct_1(k2_finseq_2(A,C),D) = C ) ) ) ) ) )).

fof(t72_finseq_2,axiom,(
    ! [A] : k2_finseq_2(np__0,A) = k1_xboole_0 )).

fof(t73_finseq_2,axiom,(
    ! [A] : k2_finseq_2(np__1,A) = k9_finseq_1(A) )).

fof(t74_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : k2_finseq_2(k1_nat_1(A,np__1),B) = k7_finseq_1(k2_finseq_2(A,B),k9_finseq_1(B)) ) )).

fof(t75_finseq_2,axiom,(
    ! [A] : k2_finseq_2(np__2,A) = k10_finseq_1(A,A) )).

fof(t76_finseq_2,axiom,(
    ! [A] : k2_finseq_2(np__3,A) = k11_finseq_1(A,A,A) )).

fof(t77_finseq_2,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,B)
             => m2_finseq_1(k2_finseq_2(A,C),B) ) ) ) )).

fof(t78_finseq_2,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( r1_tarski(k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B)),k1_relat_1(C))
               => ( v1_relat_1(k3_funcop_1(C,A,B))
                  & v1_funct_1(k3_funcop_1(C,A,B))
                  & v1_finseq_1(k3_funcop_1(C,A,B)) ) ) ) ) ) )).

fof(t79_finseq_2,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ( ( r1_tarski(k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B)),k1_relat_1(D))
                      & C = k3_funcop_1(D,A,B) )
                   => k3_finseq_1(C) = k3_square_1(k3_finseq_1(A),k3_finseq_1(B)) ) ) ) ) ) )).

fof(t80_finseq_2,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ! [C] :
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r1_tarski(k2_zfmisc_1(k1_tarski(A),k2_relat_1(B)),k1_relat_1(C))
           => ( v1_relat_1(k5_funcop_1(C,A,B))
              & v1_funct_1(k5_funcop_1(C,A,B))
              & v1_finseq_1(k5_funcop_1(C,A,B)) ) ) ) ) )).

fof(t81_finseq_2,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ! [C] :
          ( ( v1_relat_1(C)
            & v1_funct_1(C)
            & v1_finseq_1(C) )
         => ! [D] :
              ( ( v1_relat_1(D)
                & v1_funct_1(D) )
             => ( ( r1_tarski(k2_zfmisc_1(k1_tarski(A),k2_relat_1(B)),k1_relat_1(D))
                  & C = k5_funcop_1(D,A,B) )
               => k3_finseq_1(C) = k3_finseq_1(B) ) ) ) ) )).

fof(t82_finseq_2,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ! [C] :
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r1_tarski(k2_zfmisc_1(k2_relat_1(B),k1_tarski(A)),k1_relat_1(C))
           => ( v1_relat_1(k4_funcop_1(C,B,A))
              & v1_funct_1(k4_funcop_1(C,B,A))
              & v1_finseq_1(k4_funcop_1(C,B,A)) ) ) ) ) )).

fof(t83_finseq_2,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ! [C] :
          ( ( v1_relat_1(C)
            & v1_funct_1(C)
            & v1_finseq_1(C) )
         => ! [D] :
              ( ( v1_relat_1(D)
                & v1_funct_1(D) )
             => ( ( r1_tarski(k2_zfmisc_1(k2_relat_1(B),k1_tarski(A)),k1_relat_1(D))
                  & C = k4_funcop_1(D,B,A) )
               => k3_finseq_1(C) = k3_finseq_1(B) ) ) ) ) )).

fof(t84_finseq_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(A,B),C)
                    & m2_relset_1(D,k2_zfmisc_1(A,B),C) )
                 => ! [E] :
                      ( m2_finseq_1(E,A)
                     => ! [F] :
                          ( m2_finseq_1(F,B)
                         => m2_finseq_1(k3_funcop_1(D,E,F),C) ) ) ) ) ) ) )).

fof(t85_finseq_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D)
                    & v1_finseq_1(D) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(A,B),C)
                        & m2_relset_1(E,k2_zfmisc_1(A,B),C) )
                     => ! [F] :
                          ( m2_finseq_1(F,A)
                         => ! [G] :
                              ( m2_finseq_1(G,B)
                             => ( D = k3_funcop_1(E,F,G)
                               => k3_finseq_1(D) = k3_square_1(k3_finseq_1(F),k3_finseq_1(G)) ) ) ) ) ) ) ) ) )).

fof(t86_finseq_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D)
                    & v1_finseq_1(D) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(A,B),C)
                        & m2_relset_1(E,k2_zfmisc_1(A,B),C) )
                     => ! [F] :
                          ( m2_finseq_1(F,A)
                         => ! [G] :
                              ( m2_finseq_1(G,B)
                             => ( ( k3_finseq_1(F) = k3_finseq_1(G)
                                  & D = k3_funcop_1(E,F,G) )
                               => ( k3_finseq_1(D) = k3_finseq_1(F)
                                  & k3_finseq_1(D) = k3_finseq_1(G) ) ) ) ) ) ) ) ) ) )).

fof(t87_finseq_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(A,B),C)
                    & m2_relset_1(D,k2_zfmisc_1(A,B),C) )
                 => ! [E] :
                      ( m2_finseq_1(E,A)
                     => ! [F] :
                          ( m2_finseq_1(F,B)
                         => ( k3_funcop_1(D,k6_finseq_1(A),F) = k6_finseq_1(C)
                            & k3_funcop_1(D,E,k6_finseq_1(B)) = k6_finseq_1(C) ) ) ) ) ) ) ) )).

fof(t88_finseq_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( m1_subset_1(E,B)
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(A,B),C)
                            & m2_relset_1(F,k2_zfmisc_1(A,B),C) )
                         => ! [G] :
                              ( m2_finseq_1(G,A)
                             => ! [H] :
                                  ( m2_finseq_1(H,B)
                                 => ( ( G = k12_finseq_1(A,D)
                                      & H = k12_finseq_1(B,E) )
                                   => k3_funcop_1(F,G,H) = k12_finseq_1(C,k2_binop_1(A,B,C,F,D,E)) ) ) ) ) ) ) ) ) ) )).

fof(t89_finseq_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( m1_subset_1(E,A)
                     => ! [F] :
                          ( m1_subset_1(F,B)
                         => ! [G] :
                              ( m1_subset_1(G,B)
                             => ! [H] :
                                  ( ( v1_funct_1(H)
                                    & v1_funct_2(H,k2_zfmisc_1(A,B),C)
                                    & m2_relset_1(H,k2_zfmisc_1(A,B),C) )
                                 => ! [I] :
                                      ( m2_finseq_1(I,A)
                                     => ! [J] :
                                          ( m2_finseq_1(J,B)
                                         => ( ( I = k10_finseq_1(D,E)
                                              & J = k10_finseq_1(F,G) )
                                           => k3_funcop_1(H,I,J) = k10_finseq_1(k2_binop_1(A,B,C,H,D,F),k2_binop_1(A,B,C,H,E,G)) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t90_finseq_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( m1_subset_1(E,A)
                     => ! [F] :
                          ( m1_subset_1(F,A)
                         => ! [G] :
                              ( m1_subset_1(G,B)
                             => ! [H] :
                                  ( m1_subset_1(H,B)
                                 => ! [I] :
                                      ( m1_subset_1(I,B)
                                     => ! [J] :
                                          ( ( v1_funct_1(J)
                                            & v1_funct_2(J,k2_zfmisc_1(A,B),C)
                                            & m2_relset_1(J,k2_zfmisc_1(A,B),C) )
                                         => ! [K] :
                                              ( m2_finseq_1(K,A)
                                             => ! [L] :
                                                  ( m2_finseq_1(L,B)
                                                 => ( ( K = k11_finseq_1(D,E,F)
                                                      & L = k11_finseq_1(G,H,I) )
                                                   => k3_funcop_1(J,K,L) = k11_finseq_1(k2_binop_1(A,B,C,J,D,G),k2_binop_1(A,B,C,J,E,H),k2_binop_1(A,B,C,J,F,I)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t91_finseq_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(A,B),C)
                        & m2_relset_1(E,k2_zfmisc_1(A,B),C) )
                     => ! [F] :
                          ( m2_finseq_1(F,B)
                         => m2_finseq_1(k5_funcop_1(E,D,F),C) ) ) ) ) ) ) )).

fof(t92_finseq_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( ( v1_relat_1(E)
                        & v1_funct_1(E)
                        & v1_finseq_1(E) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(A,B),C)
                            & m2_relset_1(F,k2_zfmisc_1(A,B),C) )
                         => ! [G] :
                              ( m2_finseq_1(G,B)
                             => ( E = k5_funcop_1(F,D,G)
                               => k3_finseq_1(E) = k3_finseq_1(G) ) ) ) ) ) ) ) ) )).

fof(t93_finseq_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(A,B),C)
                        & m2_relset_1(E,k2_zfmisc_1(A,B),C) )
                     => k5_funcop_1(E,D,k6_finseq_1(B)) = k6_finseq_1(C) ) ) ) ) ) )).

fof(t94_finseq_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( m1_subset_1(E,B)
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(A,B),C)
                            & m2_relset_1(F,k2_zfmisc_1(A,B),C) )
                         => ! [G] :
                              ( m2_finseq_1(G,B)
                             => ( G = k12_finseq_1(B,E)
                               => k5_funcop_1(F,D,G) = k12_finseq_1(C,k2_binop_1(A,B,C,F,D,E)) ) ) ) ) ) ) ) ) )).

fof(t95_finseq_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( m1_subset_1(E,B)
                     => ! [F] :
                          ( m1_subset_1(F,B)
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,k2_zfmisc_1(A,B),C)
                                & m2_relset_1(G,k2_zfmisc_1(A,B),C) )
                             => ! [H] :
                                  ( m2_finseq_1(H,B)
                                 => ( H = k10_finseq_1(E,F)
                                   => k5_funcop_1(G,D,H) = k10_finseq_1(k2_binop_1(A,B,C,G,D,E),k2_binop_1(A,B,C,G,D,F)) ) ) ) ) ) ) ) ) ) )).

fof(t96_finseq_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( m1_subset_1(E,B)
                     => ! [F] :
                          ( m1_subset_1(F,B)
                         => ! [G] :
                              ( m1_subset_1(G,B)
                             => ! [H] :
                                  ( ( v1_funct_1(H)
                                    & v1_funct_2(H,k2_zfmisc_1(A,B),C)
                                    & m2_relset_1(H,k2_zfmisc_1(A,B),C) )
                                 => ! [I] :
                                      ( m2_finseq_1(I,B)
                                     => ( I = k11_finseq_1(E,F,G)
                                       => k5_funcop_1(H,D,I) = k11_finseq_1(k2_binop_1(A,B,C,H,D,E),k2_binop_1(A,B,C,H,D,F),k2_binop_1(A,B,C,H,D,G)) ) ) ) ) ) ) ) ) ) ) )).

fof(t97_finseq_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,B)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(A,B),C)
                        & m2_relset_1(E,k2_zfmisc_1(A,B),C) )
                     => ! [F] :
                          ( m2_finseq_1(F,A)
                         => m2_finseq_1(k4_funcop_1(E,F,D),C) ) ) ) ) ) ) )).

fof(t98_finseq_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,B)
                 => ! [E] :
                      ( ( v1_relat_1(E)
                        & v1_funct_1(E)
                        & v1_finseq_1(E) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(A,B),C)
                            & m2_relset_1(F,k2_zfmisc_1(A,B),C) )
                         => ! [G] :
                              ( m2_finseq_1(G,A)
                             => ( E = k4_funcop_1(F,G,D)
                               => k3_finseq_1(E) = k3_finseq_1(G) ) ) ) ) ) ) ) ) )).

fof(t99_finseq_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,B)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(A,B),C)
                        & m2_relset_1(E,k2_zfmisc_1(A,B),C) )
                     => k4_funcop_1(E,k6_finseq_1(A),D) = k6_finseq_1(C) ) ) ) ) ) )).

fof(t100_finseq_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( m1_subset_1(E,B)
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(A,B),C)
                            & m2_relset_1(F,k2_zfmisc_1(A,B),C) )
                         => ! [G] :
                              ( m2_finseq_1(G,A)
                             => ( G = k12_finseq_1(A,D)
                               => k4_funcop_1(F,G,E) = k12_finseq_1(C,k2_binop_1(A,B,C,F,D,E)) ) ) ) ) ) ) ) ) )).

fof(t101_finseq_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( m1_subset_1(E,A)
                     => ! [F] :
                          ( m1_subset_1(F,B)
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,k2_zfmisc_1(A,B),C)
                                & m2_relset_1(G,k2_zfmisc_1(A,B),C) )
                             => ! [H] :
                                  ( m2_finseq_1(H,A)
                                 => ( H = k10_finseq_1(D,E)
                                   => k4_funcop_1(G,H,F) = k10_finseq_1(k2_binop_1(A,B,C,G,D,F),k2_binop_1(A,B,C,G,E,F)) ) ) ) ) ) ) ) ) ) )).

fof(t102_finseq_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( m1_subset_1(E,A)
                     => ! [F] :
                          ( m1_subset_1(F,A)
                         => ! [G] :
                              ( m1_subset_1(G,B)
                             => ! [H] :
                                  ( ( v1_funct_1(H)
                                    & v1_funct_2(H,k2_zfmisc_1(A,B),C)
                                    & m2_relset_1(H,k2_zfmisc_1(A,B),C) )
                                 => ! [I] :
                                      ( m2_finseq_1(I,A)
                                     => ( I = k11_finseq_1(D,E,F)
                                       => k4_funcop_1(H,I,G) = k11_finseq_1(k2_binop_1(A,B,C,H,D,G),k2_binop_1(A,B,C,H,E,G),k2_binop_1(A,B,C,H,F,G)) ) ) ) ) ) ) ) ) ) ) )).

fof(d3_finseq_2,axiom,(
    ! [A,B] :
      ( m1_finseq_2(B,A)
    <=> ! [C] :
          ( r2_hidden(C,B)
         => m2_finseq_1(C,A) ) ) )).

fof(t103_finseq_2,axiom,(
    $true )).

fof(t104_finseq_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(k13_finseq_1(A))
      & m1_finseq_2(k13_finseq_1(A),A) ) )).

fof(t105_finseq_2,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & m1_finseq_2(B,A) )
     => r1_tarski(B,k3_finseq_2(A)) ) )).

fof(t106_finseq_2,axiom,(
    $true )).

fof(t107_finseq_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(A)) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_finseq_2(C,B) )
             => ( ~ v1_xboole_0(C)
                & m1_finseq_2(C,A) ) ) ) ) )).

fof(t108_finseq_2,axiom,(
    $true )).

fof(t109_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_finseq_2(C,B,k4_finseq_2(A,B))
             => k3_finseq_1(C) = A ) ) ) )).

fof(t110_finseq_2,axiom,(
    ! [A,B] :
      ( m2_finseq_1(B,A)
     => m1_subset_1(B,k4_finseq_2(k3_finseq_1(B),A)) ) )).

fof(t111_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => k4_finseq_2(A,B) = k1_funct_2(k2_finseq_1(A),B) ) ) )).

fof(t112_finseq_2,axiom,(
    ! [A] : k4_finseq_2(np__0,A) = k6_domain_1(k1_zfmisc_1(k2_zfmisc_1(k5_numbers,A)),k6_finseq_1(A)) )).

fof(t113_finseq_2,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k4_finseq_2(np__0,A))
     => B = k6_finseq_1(A) ) )).

fof(t114_finseq_2,axiom,(
    ! [A] : m1_subset_1(k6_finseq_1(A),k4_finseq_2(np__0,A)) )).

fof(t115_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_finseq_2(C,B,k4_finseq_2(np__0,B))
             => ! [D] :
                  ( m2_finseq_2(D,B,k4_finseq_2(A,B))
                 => ( k8_finseq_1(B,C,D) = D
                    & k8_finseq_1(B,D,C) = D ) ) ) ) ) )).

fof(t117_finseq_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_2(B,A,k4_finseq_2(np__1,A))
         => ? [C] :
              ( m1_subset_1(C,A)
              & B = k12_finseq_1(A,C) ) ) ) )).

fof(t118_finseq_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => m2_finseq_2(k12_finseq_1(A,B),A,k4_finseq_2(np__1,A)) ) ) )).

fof(t120_finseq_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_2(B,A,k4_finseq_2(np__2,A))
         => ? [C] :
              ( m1_subset_1(C,A)
              & ? [D] :
                  ( m1_subset_1(D,A)
                  & B = k10_finseq_1(C,D) ) ) ) ) )).

fof(t121_finseq_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => m2_finseq_2(k10_finseq_1(B,C),A,k4_finseq_2(np__2,A)) ) ) ) )).

fof(t123_finseq_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_2(B,A,k4_finseq_2(np__3,A))
         => ? [C] :
              ( m1_subset_1(C,A)
              & ? [D] :
                  ( m1_subset_1(D,A)
                  & ? [E] :
                      ( m1_subset_1(E,A)
                      & B = k11_finseq_1(C,D,E) ) ) ) ) ) )).

fof(t124_finseq_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => m2_finseq_2(k11_finseq_1(B,C,D),A,k4_finseq_2(np__3,A)) ) ) ) ) )).

fof(t126_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m2_finseq_2(D,C,k4_finseq_2(k1_nat_1(A,B),C))
                 => ? [E] :
                      ( m2_finseq_2(E,C,k4_finseq_2(A,C))
                      & ? [F] :
                          ( m2_finseq_2(F,C,k4_finseq_2(B,C))
                          & D = k8_finseq_1(C,E,F) ) ) ) ) ) ) )).

fof(t127_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m2_finseq_2(D,C,k4_finseq_2(A,C))
                 => ! [E] :
                      ( m2_finseq_2(E,C,k4_finseq_2(B,C))
                     => m2_finseq_2(k8_finseq_1(C,D,E),C,k4_finseq_2(k1_nat_1(A,B),C)) ) ) ) ) ) )).

fof(t129_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(B)) )
             => ! [D] :
                  ( m2_finseq_2(D,C,k4_finseq_2(A,C))
                 => m2_finseq_2(D,B,k4_finseq_2(A,B)) ) ) ) ) )).

fof(t130_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ( k4_finseq_2(A,C) = k4_finseq_2(B,C)
               => A = B ) ) ) ) )).

fof(t131_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => m2_finseq_2(k1_finseq_2(A),k5_numbers,k4_finseq_2(A,k5_numbers)) ) )).

fof(t132_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,B)
             => m2_finseq_2(k2_finseq_2(A,C),B,k4_finseq_2(A,B)) ) ) ) )).

fof(t133_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m2_finseq_2(D,B,k4_finseq_2(A,B))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,B,C)
                        & m2_relset_1(E,B,C) )
                     => m2_finseq_2(k1_partfun1(k5_numbers,B,B,C,D,E),C,k4_finseq_2(A,C)) ) ) ) ) ) )).

fof(t134_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_finseq_2(C,B,k4_finseq_2(A,B))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(A))
                    & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) )
                 => ( k2_relat_1(D) = k2_finseq_1(A)
                   => m2_finseq_2(k1_partfun1(k2_finseq_1(A),k2_finseq_1(A),k5_numbers,B,D,C),B,k4_finseq_2(A,B)) ) ) ) ) ) )).

fof(t135_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_finseq_2(C,B,k4_finseq_2(A,B))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(A))
                    & v3_funct_2(D,k2_finseq_1(A),k2_finseq_1(A))
                    & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) )
                 => m2_finseq_2(k1_partfun1(k2_finseq_1(A),k2_finseq_1(A),k5_numbers,B,D,C),B,k4_finseq_2(A,B)) ) ) ) ) )).

fof(t136_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_finseq_2(C,B,k4_finseq_2(A,B))
             => ! [D] :
                  ( m1_subset_1(D,B)
                 => k1_funct_1(k8_finseq_1(B,C,k12_finseq_1(B,D)),k1_nat_1(A,np__1)) = D ) ) ) ) )).

fof(t137_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_finseq_2(C,B,k4_finseq_2(k1_nat_1(A,np__1),B))
             => ? [D] :
                  ( m2_finseq_2(D,B,k4_finseq_2(A,B))
                  & ? [E] :
                      ( m1_subset_1(E,B)
                      & C = k8_finseq_1(B,D,k12_finseq_1(B,E)) ) ) ) ) ) )).

fof(t138_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_finseq_2(C,B,k4_finseq_2(A,B))
             => k5_relat_1(k1_finseq_2(A),C) = C ) ) ) )).

fof(t139_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_finseq_2(C,B,k4_finseq_2(A,B))
             => ! [D] :
                  ( m2_finseq_2(D,B,k4_finseq_2(A,B))
                 => ( ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => ( r2_hidden(E,k2_finseq_1(A))
                         => k1_funct_1(C,E) = k1_funct_1(D,E) ) )
                   => C = D ) ) ) ) ) )).

fof(t140_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ~ v1_xboole_0(D)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(B,C),D)
                        & m2_relset_1(E,k2_zfmisc_1(B,C),D) )
                     => ! [F] :
                          ( m2_finseq_2(F,B,k4_finseq_2(A,B))
                         => ! [G] :
                              ( m2_finseq_2(G,C,k4_finseq_2(A,C))
                             => m2_finseq_2(k3_funcop_1(E,F,G),D,k4_finseq_2(A,D)) ) ) ) ) ) ) ) )).

fof(t141_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ~ v1_xboole_0(D)
                 => ! [E] :
                      ( m1_subset_1(E,B)
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(B,C),D)
                            & m2_relset_1(F,k2_zfmisc_1(B,C),D) )
                         => ! [G] :
                              ( m2_finseq_2(G,C,k4_finseq_2(A,C))
                             => m2_finseq_2(k5_funcop_1(F,E,G),D,k4_finseq_2(A,D)) ) ) ) ) ) ) ) )).

fof(t142_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ~ v1_xboole_0(D)
                 => ! [E] :
                      ( m1_subset_1(E,C)
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(B,C),D)
                            & m2_relset_1(F,k2_zfmisc_1(B,C),D) )
                         => ! [G] :
                              ( m2_finseq_2(G,B,k4_finseq_2(A,B))
                             => m2_finseq_2(k4_funcop_1(F,G,E),D,k4_finseq_2(A,D)) ) ) ) ) ) ) ) )).

fof(t143_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : k2_finseq_2(k1_nat_1(A,B),C) = k7_finseq_1(k2_finseq_2(A,C),k2_finseq_2(B,C)) ) ) )).

fof(t144_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_finseq_2(C,B,k4_finseq_2(A,B))
             => k4_finseq_1(C) = k2_finseq_1(A) ) ) ) )).

fof(t145_finseq_2,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] :
          ( ( r2_hidden(B,k1_relat_1(A))
            & r2_hidden(C,k1_relat_1(A)) )
         => k5_relat_1(k10_finseq_1(B,C),A) = k10_finseq_1(k1_funct_1(A,B),k1_funct_1(A,C)) ) ) )).

fof(t146_finseq_2,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C,D] :
          ( ( r2_hidden(B,k1_relat_1(A))
            & r2_hidden(C,k1_relat_1(A))
            & r2_hidden(D,k1_relat_1(A)) )
         => k5_relat_1(k11_finseq_1(B,C,D),A) = k11_finseq_1(k1_funct_1(A,B),k1_funct_1(A,C),k1_funct_1(A,D)) ) ) )).

fof(t147_finseq_2,axiom,(
    ! [A,B] : k2_relat_1(k10_finseq_1(A,B)) = k2_tarski(A,B) )).

fof(t148_finseq_2,axiom,(
    ! [A,B,C] : k2_relat_1(k11_finseq_1(A,B,C)) = k1_enumset1(A,B,C) )).

fof(t149_finseq_2,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( ( r1_tarski(A,C)
                  & r1_tarski(B,C)
                  & k3_finseq_1(A) = k3_finseq_1(B) )
               => A = B ) ) ) ) )).

fof(s1_finseq_2,axiom,(
    ? [A] :
      ( m2_finseq_1(A,f2_s1_finseq_2)
      & k3_finseq_1(A) = f1_s1_finseq_2
      & ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r2_hidden(B,k2_finseq_1(f1_s1_finseq_2))
           => k1_funct_1(A,B) = f3_s1_finseq_2(B) ) ) ) )).

fof(s2_finseq_2,axiom,
    ( ( p1_s2_finseq_2(k6_finseq_1(f1_s2_finseq_2))
      & ! [A] :
          ( m2_finseq_1(A,f1_s2_finseq_2)
         => ! [B] :
              ( m1_subset_1(B,f1_s2_finseq_2)
             => ( p1_s2_finseq_2(A)
               => p1_s2_finseq_2(k8_finseq_1(f1_s2_finseq_2,A,k12_finseq_1(f1_s2_finseq_2,B))) ) ) ) )
   => ! [A] :
        ( m2_finseq_1(A,f1_s2_finseq_2)
       => p1_s2_finseq_2(A) ) )).

fof(dt_m1_finseq_2,axiom,(
    $true )).

fof(existence_m1_finseq_2,axiom,(
    ! [A] :
    ? [B] : m1_finseq_2(B,A) )).

fof(dt_m2_finseq_2,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & m1_finseq_2(B,A) )
     => ! [C] :
          ( m2_finseq_2(C,A,B)
         => m2_finseq_1(C,A) ) ) )).

fof(existence_m2_finseq_2,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & m1_finseq_2(B,A) )
     => ? [C] : m2_finseq_2(C,A,B) ) )).

fof(redefinition_m2_finseq_2,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & m1_finseq_2(B,A) )
     => ! [C] :
          ( m2_finseq_2(C,A,B)
        <=> m1_subset_1(C,B) ) ) )).

fof(dt_k1_finseq_2,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ( v1_relat_1(k1_finseq_2(A))
        & v1_funct_1(k1_finseq_2(A))
        & v1_finseq_1(k1_finseq_2(A)) ) ) )).

fof(dt_k2_finseq_2,axiom,(
    ! [A,B] :
      ( v4_ordinal2(A)
     => ( v1_relat_1(k2_finseq_2(A,B))
        & v1_funct_1(k2_finseq_2(A,B))
        & v1_finseq_1(k2_finseq_2(A,B)) ) ) )).

fof(dt_k3_finseq_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(k3_finseq_2(A))
      & m1_finseq_2(k3_finseq_2(A),A) ) )).

fof(redefinition_k3_finseq_2,axiom,(
    ! [A] : k3_finseq_2(A) = k13_finseq_1(A) )).

fof(dt_k4_finseq_2,axiom,(
    ! [A,B] :
      ( v4_ordinal2(A)
     => m1_finseq_2(k4_finseq_2(A,B),B) ) )).

fof(d4_finseq_2,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ! [B] : k4_finseq_2(A,B) = a_2_0_finseq_2(A,B) ) )).

fof(t116_finseq_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => k4_finseq_2(np__1,A) = a_1_0_finseq_2(A) ) )).

fof(t119_finseq_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => k4_finseq_2(np__2,A) = a_1_1_finseq_2(A) ) )).

fof(t122_finseq_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => k4_finseq_2(np__3,A) = a_1_2_finseq_2(A) ) )).

fof(t125_finseq_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => k4_finseq_2(k1_nat_1(A,B),C) = a_3_0_finseq_2(A,B,C) ) ) ) )).

fof(t128_finseq_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => k3_finseq_2(A) = k3_tarski(a_1_3_finseq_2(A)) ) )).

fof(fraenkel_a_2_0_finseq_2,axiom,(
    ! [A,B,C] :
      ( v4_ordinal2(B)
     => ( r2_hidden(A,a_2_0_finseq_2(B,C))
      <=> ? [D] :
            ( m2_finseq_2(D,C,k3_finseq_2(C))
            & A = D
            & k3_finseq_1(D) = B ) ) ) )).

fof(fraenkel_a_1_0_finseq_2,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ( r2_hidden(A,a_1_0_finseq_2(B))
      <=> ? [C] :
            ( m1_subset_1(C,B)
            & A = k12_finseq_1(B,C) ) ) ) )).

fof(fraenkel_a_1_1_finseq_2,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ( r2_hidden(A,a_1_1_finseq_2(B))
      <=> ? [C,D] :
            ( m1_subset_1(C,B)
            & m1_subset_1(D,B)
            & A = k10_finseq_1(C,D) ) ) ) )).

fof(fraenkel_a_1_2_finseq_2,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ( r2_hidden(A,a_1_2_finseq_2(B))
      <=> ? [C,D,E] :
            ( m1_subset_1(C,B)
            & m1_subset_1(D,B)
            & m1_subset_1(E,B)
            & A = k11_finseq_1(C,D,E) ) ) ) )).

fof(fraenkel_a_3_0_finseq_2,axiom,(
    ! [A,B,C,D] :
      ( ( m2_subset_1(B,k1_numbers,k5_numbers)
        & m2_subset_1(C,k1_numbers,k5_numbers)
        & ~ v1_xboole_0(D) )
     => ( r2_hidden(A,a_3_0_finseq_2(B,C,D))
      <=> ? [E,F] :
            ( m2_finseq_2(E,D,k4_finseq_2(B,D))
            & m2_finseq_2(F,D,k4_finseq_2(C,D))
            & A = k8_finseq_1(D,E,F) ) ) ) )).

fof(fraenkel_a_1_3_finseq_2,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ( r2_hidden(A,a_1_3_finseq_2(B))
      <=> ? [C] :
            ( m2_subset_1(C,k1_numbers,k5_numbers)
            & A = k4_finseq_2(C,B) ) ) ) )).
%------------------------------------------------------------------------------