SET007 Axioms: SET007+465.ax


%------------------------------------------------------------------------------
% File     : SET007+465 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Multi Instructions Defined by Sequence of Instructions of SCMFSA
% 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    : scmfsa_7 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   54 (  13 unit)
%            Number of atoms       :  253 (  71 equality)
%            Maximal formula depth :   23 (   6 average)
%            Number of connectives :  220 (  21 ~  ;   3  |;  66  &)
%                                         (  11 <=>; 119 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   21 (   1 propositional; 0-3 arity)
%            Number of functors    :   60 (  11 constant; 0-4 arity)
%            Number of variables   :  113 (   0 singleton; 106 !;   7 ?)
%            Maximal term depth    :    9 (   2 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_scmfsa_7,axiom,(
    ! [A] :
      ( m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) ) ) )).

fof(fc1_scmfsa_7,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(k2_funct_7(A,B,C))
        & v1_funct_1(k2_funct_7(A,B,C))
        & v1_finset_1(k2_funct_7(A,B,C))
        & v1_finseq_1(k2_funct_7(A,B,C)) ) ) )).

fof(t1_scmfsa_7,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => k1_int_2(A) = A ) )).

fof(t2_scmfsa_7,axiom,(
    $true )).

fof(t3_scmfsa_7,axiom,(
    $true )).

fof(t4_scmfsa_7,axiom,(
    $true )).

fof(t5_scmfsa_7,axiom,(
    $true )).

fof(t6_scmfsa_7,axiom,(
    $true )).

fof(t7_scmfsa_7,axiom,(
    $true )).

fof(t8_scmfsa_7,axiom,(
    $true )).

fof(t9_scmfsa_7,axiom,(
    $true )).

fof(t10_scmfsa_7,axiom,(
    $true )).

fof(t11_scmfsa_7,axiom,(
    $true )).

fof(t12_scmfsa_7,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( A != k1_xboole_0
       => r2_hidden(k3_finseq_1(A),k5_finsop_1(A)) ) ) )).

fof(t13_scmfsa_7,axiom,(
    ! [A] : k15_dtconstr(A,k6_finseq_1(k13_finseq_1(A))) = k6_finseq_1(A) )).

fof(t14_scmfsa_7,axiom,(
    ! [A,B] :
      ( m2_finseq_1(B,k13_finseq_1(A))
     => ! [C] :
          ( m2_finseq_1(C,k13_finseq_1(A))
         => k15_dtconstr(A,k8_finseq_1(k13_finseq_1(A),B,C)) = k8_finseq_1(A,k15_dtconstr(A,B),k15_dtconstr(A,C)) ) ) )).

fof(t15_scmfsa_7,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k13_finseq_1(A))
     => ! [C] :
          ( m1_subset_1(C,k13_finseq_1(A))
         => k15_dtconstr(A,k2_finseq_4(k13_finseq_1(A),B,C)) = k7_finseq_1(B,C) ) ) )).

fof(t16_scmfsa_7,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k13_finseq_1(A))
     => ! [C] :
          ( m1_subset_1(C,k13_finseq_1(A))
         => ! [D] :
              ( m1_subset_1(D,k13_finseq_1(A))
             => k15_dtconstr(A,k3_finseq_4(k13_finseq_1(A),B,C,D)) = k7_finseq_1(k7_finseq_1(B,C),D) ) ) ) )).

fof(t17_scmfsa_7,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => ! [C] :
              ( m2_finseq_1(C,A)
             => ~ ( r1_tarski(B,C)
                  & ! [D] :
                      ( m2_finseq_1(D,A)
                     => k8_finseq_1(A,B,D) != C ) ) ) ) ) )).

fof(t18_scmfsa_7,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => ! [C] :
              ( m2_finseq_1(C,A)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( ( r1_tarski(B,C)
                      & r1_xreal_0(np__1,D)
                      & r1_xreal_0(D,k3_finseq_1(B)) )
                   => k1_funct_1(C,D) = k1_funct_1(B,D) ) ) ) ) ) )).

fof(t19_scmfsa_7,axiom,(
    ! [A,B] :
      ( m2_finseq_1(B,k13_finseq_1(A))
     => ! [C] :
          ( m2_finseq_1(C,k13_finseq_1(A))
         => ( r1_tarski(B,C)
           => r1_tarski(k15_dtconstr(A,B),k15_dtconstr(A,C)) ) ) ) )).

fof(t20_scmfsa_7,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => k7_relat_1(A,k2_finseq_1(np__0)) = k1_xboole_0 ) )).

fof(t21_scmfsa_7,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) )
         => k7_relat_1(A,k2_finseq_1(np__0)) = k7_relat_1(B,k2_finseq_1(np__0)) ) ) )).

fof(t22_scmfsa_7,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => m2_finseq_1(k12_finseq_1(A,B),A) ) ) )).

fof(t23_scmfsa_7,axiom,(
    ! [A,B] :
      ( m2_finseq_1(B,A)
     => ! [C] :
          ( m2_finseq_1(C,A)
         => m2_finseq_1(k8_finseq_1(A,B,C),A) ) ) )).

fof(t24_scmfsa_7,axiom,(
    $true )).

fof(t25_scmfsa_7,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
     => k4_card_1(k1_scmfsa_7(A)) = k3_finseq_1(A) ) )).

fof(t26_scmfsa_7,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r2_hidden(k5_scmfsa_2(B),k1_relat_1(k1_scmfsa_7(A)))
          <=> r2_hidden(k1_nat_1(B,np__1),k5_finsop_1(A)) ) ) ) )).

fof(t27_scmfsa_7,axiom,(
    $true )).

fof(t28_scmfsa_7,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ~ r1_xreal_0(B,A)
          <=> ( r1_xreal_0(np__1,k1_nat_1(A,np__1))
              & r1_xreal_0(k1_nat_1(A,np__1),B) ) ) ) ) )).

fof(t29_scmfsa_7,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r2_hidden(k5_scmfsa_2(B),k1_relat_1(k1_scmfsa_7(A)))
          <=> ~ r1_xreal_0(k3_finseq_1(A),B) ) ) ) )).

fof(t30_scmfsa_7,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m2_finseq_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) )
     => ( r2_hidden(np__1,k5_finsop_1(A))
        & r2_hidden(k5_scmfsa_2(np__0),k1_relat_1(k1_scmfsa_7(A))) ) ) )).

fof(t31_scmfsa_7,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
     => ! [B] :
          ( m2_finseq_1(B,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
         => r1_tarski(k1_scmfsa_7(A),k1_scmfsa_7(k8_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),A,B))) ) ) )).

fof(t32_scmfsa_7,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
     => ! [B] :
          ( m2_finseq_1(B,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
         => ( r1_tarski(A,B)
           => r1_tarski(k1_scmfsa_7(A),k1_scmfsa_7(B)) ) ) ) )).

fof(d2_scmfsa_7,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
             => ( ( ~ r1_xreal_0(B,np__0)
                 => ( C = k2_scmfsa_7(A,B)
                  <=> ? [D] :
                        ( m2_subset_1(D,k1_numbers,k5_numbers)
                        & k1_nat_1(D,np__1) = B
                        & C = k1_scmfsa_7(k8_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k8_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k12_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k8_scmfsa_2(A,k4_scmfsa_2(np__0))),k1_finsop_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),D,k9_scmfsa_2(A,k4_scmfsa_2(np__0)))),k12_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))) ) ) )
                & ( r1_xreal_0(B,np__0)
                 => ( C = k2_scmfsa_7(A,B)
                  <=> ? [D] :
                        ( m2_subset_1(D,k1_numbers,k5_numbers)
                        & k2_xcmplx_0(D,B) = np__1
                        & C = k1_scmfsa_7(k8_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k8_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k12_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k8_scmfsa_2(A,k4_scmfsa_2(np__0))),k1_finsop_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),D,k10_scmfsa_2(A,k4_scmfsa_2(np__0)))),k12_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))) ) ) ) ) ) ) ) )).

fof(d3_scmfsa_7,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m2_finseq_1(C,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
             => ( ( ~ r1_xreal_0(B,np__0)
                 => ( C = k3_scmfsa_7(A,B)
                  <=> ? [D] :
                        ( m2_subset_1(D,k1_numbers,k5_numbers)
                        & k1_nat_1(D,np__1) = B
                        & C = k8_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k12_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k8_scmfsa_2(A,k4_scmfsa_2(np__0))),k1_finsop_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),D,k9_scmfsa_2(A,k4_scmfsa_2(np__0)))) ) ) )
                & ( r1_xreal_0(B,np__0)
                 => ( C = k3_scmfsa_7(A,B)
                  <=> ? [D] :
                        ( m2_subset_1(D,k1_numbers,k5_numbers)
                        & k2_xcmplx_0(D,B) = np__1
                        & C = k8_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k12_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k8_scmfsa_2(A,k4_scmfsa_2(np__0))),k1_finsop_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),D,k10_scmfsa_2(A,k4_scmfsa_2(np__0)))) ) ) ) ) ) ) ) )).

fof(t33_scmfsa_7,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => k2_scmfsa_7(A,B) = k1_scmfsa_7(k8_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k3_scmfsa_7(A,B),k12_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))) ) ) )).

fof(d4_scmfsa_7,axiom,(
    ! [A] :
      ( m2_scmfsa_2(A)
     => ! [B] :
          ( m2_finseq_1(B,k4_numbers)
         => ! [C] :
              ( m2_finseq_1(C,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
             => ( C = k4_scmfsa_7(A,B)
              <=> ? [D] :
                    ( m2_finseq_1(D,k13_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
                    & k3_finseq_1(D) = k3_finseq_1(B)
                    & ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => ~ ( r1_xreal_0(np__1,E)
                            & r1_xreal_0(E,k3_finseq_1(B))
                            & ! [F] :
                                ( v1_int_1(F)
                               => ~ ( F = k1_funct_1(B,E)
                                    & k1_funct_1(D,E) = k8_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k8_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k3_scmfsa_7(k4_scmfsa_2(np__1),E),k3_scmfsa_7(k4_scmfsa_2(np__2),F)),k12_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k17_scmfsa_2(k4_scmfsa_2(np__2),k4_scmfsa_2(np__1),A))) ) ) ) )
                    & C = k15_dtconstr(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),D) ) ) ) ) ) )).

fof(d5_scmfsa_7,axiom,(
    ! [A] :
      ( m2_scmfsa_2(A)
     => ! [B] :
          ( m2_finseq_1(B,k4_numbers)
         => k5_scmfsa_7(A,B) = k1_scmfsa_7(k8_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k8_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k8_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k3_scmfsa_7(k4_scmfsa_2(np__1),k3_finseq_1(B)),k12_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k19_scmfsa_2(k4_scmfsa_2(np__1),A))),k4_scmfsa_7(A,B)),k12_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))) ) ) )).

fof(t34_scmfsa_7,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => k2_scmfsa_7(A,np__1) = k1_scmfsa_7(k8_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k12_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k8_scmfsa_2(A,k4_scmfsa_2(np__0))),k12_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))) ) )).

fof(t35_scmfsa_7,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => k2_scmfsa_7(A,np__0) = k1_scmfsa_7(k8_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k8_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k12_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k8_scmfsa_2(A,k4_scmfsa_2(np__0))),k12_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k10_scmfsa_2(A,k4_scmfsa_2(np__0)))),k12_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))) ) )).

fof(t36_scmfsa_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
       => ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ( k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) = k5_scmfsa_2(B)
             => ! [C] :
                  ( m1_scmfsa_2(C)
                 => ! [D] :
                      ( v1_int_1(D)
                     => ( ! [E] :
                            ( m2_subset_1(E,k1_numbers,k5_numbers)
                           => ( r2_hidden(E,k5_finsop_1(k3_scmfsa_7(C,D)))
                             => k1_funct_1(k3_scmfsa_7(C,D),E) = k13_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k5_scmfsa_2(k5_binarith(k1_nat_1(B,E),np__1))) ) )
                       => ( C = k4_scmfsa_2(np__0)
                          | ( ! [E] :
                                ( m2_subset_1(E,k1_numbers,k5_numbers)
                               => ( r1_xreal_0(E,k3_finseq_1(k3_scmfsa_7(C,D)))
                                 => ( k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A),E)) = k5_scmfsa_2(k1_nat_1(B,E))
                                    & ! [F] :
                                        ( m1_scmfsa_2(F)
                                       => ( F != C
                                         => k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A),E),F) = k20_scmfsa_2(A,F) ) )
                                    & ! [F] :
                                        ( m2_scmfsa_2(F)
                                       => k21_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A),E),F) = k21_scmfsa_2(A,F) ) ) ) )
                            & k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A),k3_finseq_1(k3_scmfsa_7(C,D))),C) = D ) ) ) ) ) ) ) ) ) )).

fof(t37_scmfsa_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ( ( k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) = k5_scmfsa_2(np__0)
          & k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1 )
       => ! [B] :
            ( m1_scmfsa_2(B)
           => ! [C] :
                ( v1_int_1(C)
               => ( r1_tarski(k1_scmfsa_7(k3_scmfsa_7(B,C)),A)
                 => ( B = k4_scmfsa_2(np__0)
                    | ( ! [D] :
                          ( m2_subset_1(D,k1_numbers,k5_numbers)
                         => ( r1_xreal_0(D,k3_finseq_1(k3_scmfsa_7(B,C)))
                           => ( k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A),D)) = k5_scmfsa_2(D)
                              & ! [E] :
                                  ( m1_scmfsa_2(E)
                                 => ( E != B
                                   => k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A),D),E) = k20_scmfsa_2(A,E) ) )
                              & ! [E] :
                                  ( m2_scmfsa_2(E)
                                 => k21_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A),D),E) = k21_scmfsa_2(A,E) ) ) ) )
                      & k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A),k3_finseq_1(k3_scmfsa_7(B,C))),B) = C ) ) ) ) ) ) ) )).

fof(t38_scmfsa_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ( ( k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) = k5_scmfsa_2(np__0)
          & k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1 )
       => ! [B] :
            ( m1_scmfsa_2(B)
           => ! [C] :
                ( v1_int_1(C)
               => ( r1_tarski(k2_scmfsa_7(B,C),A)
                 => ( B = k4_scmfsa_2(np__0)
                    | ( v9_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                      & k20_scmfsa_2(k12_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A),B) = C
                      & ! [D] :
                          ( m1_scmfsa_2(D)
                         => ( D != B
                           => k20_scmfsa_2(k12_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A),D) = k20_scmfsa_2(A,D) ) )
                      & ! [D] :
                          ( m2_scmfsa_2(D)
                         => k21_scmfsa_2(k12_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A),D) = k21_scmfsa_2(A,D) ) ) ) ) ) ) ) ) )).

fof(t39_scmfsa_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ( ( k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) = k5_scmfsa_2(np__0)
          & k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1 )
       => ! [B] :
            ( m2_scmfsa_2(B)
           => ! [C] :
                ( m2_finseq_1(C,k4_numbers)
               => ( r1_tarski(k5_scmfsa_7(B,C),A)
                 => ( v9_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                    & k21_scmfsa_2(k12_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A),B) = C
                    & ! [D] :
                        ( m1_scmfsa_2(D)
                       => ~ ( D != k4_scmfsa_2(np__1)
                            & D != k4_scmfsa_2(np__2)
                            & k20_scmfsa_2(k12_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A),D) != k20_scmfsa_2(A,D) ) )
                    & ! [D] :
                        ( m2_scmfsa_2(D)
                       => ( D != B
                         => k21_scmfsa_2(k12_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A),D) = k21_scmfsa_2(A,D) ) ) ) ) ) ) ) ) )).

fof(dt_k1_scmfsa_7,axiom,(
    ! [A] :
      ( m1_finseq_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
     => m1_ami_1(k1_scmfsa_7(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) )).

fof(dt_k2_scmfsa_7,axiom,(
    ! [A,B] :
      ( ( m1_scmfsa_2(A)
        & v1_int_1(B) )
     => m1_ami_1(k2_scmfsa_7(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) )).

fof(dt_k3_scmfsa_7,axiom,(
    ! [A,B] :
      ( ( m1_scmfsa_2(A)
        & v1_int_1(B) )
     => m2_finseq_1(k3_scmfsa_7(A,B),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ) )).

fof(dt_k4_scmfsa_7,axiom,(
    ! [A,B] :
      ( ( m2_scmfsa_2(A)
        & m1_finseq_1(B,k4_numbers) )
     => m2_finseq_1(k4_scmfsa_7(A,B),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ) )).

fof(dt_k5_scmfsa_7,axiom,(
    ! [A,B] :
      ( ( m2_scmfsa_2(A)
        & m1_finseq_1(B,k4_numbers) )
     => m1_ami_1(k5_scmfsa_7(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) )).

fof(d1_scmfsa_7,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
     => ! [B] :
          ( m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
         => ( B = k1_scmfsa_7(A)
          <=> ( k1_relat_1(B) = a_1_0_scmfsa_7(A)
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( r2_hidden(k5_scmfsa_2(C),k1_relat_1(B))
                   => k1_funct_1(B,k5_scmfsa_2(C)) = k4_finseq_4(k5_numbers,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),A,k1_nat_1(C,np__1)) ) ) ) ) ) ) )).

fof(s1_scmfsa_7,axiom,
    ( ( r1_tarski(f1_s1_scmfsa_7,f2_s1_scmfsa_7)
      & ! [A] :
          ( m1_subset_1(A,f2_s1_scmfsa_7)
         => ! [B] :
              ( m1_subset_1(B,f2_s1_scmfsa_7)
             => ( ( r2_hidden(A,f1_s1_scmfsa_7)
                  & r2_hidden(B,f1_s1_scmfsa_7)
                  & f3_s1_scmfsa_7(A) = f3_s1_scmfsa_7(B) )
               => A = B ) ) ) )
   => r2_tarski(f1_s1_scmfsa_7,a_0_0_scmfsa_7) )).

fof(fraenkel_a_1_0_scmfsa_7,axiom,(
    ! [A,B] :
      ( m2_finseq_1(B,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
     => ( r2_hidden(A,a_1_0_scmfsa_7(B))
      <=> ? [C] :
            ( m2_subset_1(C,k1_numbers,k5_numbers)
            & A = k5_scmfsa_2(k5_binarith(C,np__1))
            & r2_hidden(C,k5_finsop_1(B)) ) ) ) )).

fof(fraenkel_a_0_0_scmfsa_7,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_0_scmfsa_7)
    <=> ? [B] :
          ( m1_subset_1(B,f2_s1_scmfsa_7)
          & A = f3_s1_scmfsa_7(B)
          & r2_hidden(B,f1_s1_scmfsa_7) ) ) )).
%------------------------------------------------------------------------------