SET007 Axioms: SET007+477.ax


%------------------------------------------------------------------------------
% File     : SET007+477 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Constant Assignment Macro Instructions of SCMFSA. Part II
% 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    : scmfsa7b [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   50 (   1 unit)
%            Number of atoms       :  303 (  52 equality)
%            Maximal formula depth :   24 (   8 average)
%            Number of connectives :  303 (  50 ~  ;   0  |; 125  &)
%                                         (  11 <=>; 117 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   32 (   0 propositional; 1-3 arity)
%            Number of functors    :   62 (   8 constant; 0-4 arity)
%            Number of variables   :  112 (   0 singleton; 109 !;   3 ?)
%            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(fc1_scmfsa7b,axiom,(
    ! [A] :
      ( m1_finseq_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
     => ( v1_relat_1(k1_scmfsa_7(A))
        & v1_funct_1(k1_scmfsa_7(A))
        & v1_finset_1(k1_scmfsa_7(A))
        & v1_ami_3(k1_scmfsa_7(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(k1_scmfsa_7(A)) ) ) )).

fof(fc2_scmfsa7b,axiom,(
    ! [A,B] :
      ( ( m1_scmfsa_2(A)
        & v1_int_1(B) )
     => ( v1_relat_1(k2_scmfsa_7(A,B))
        & v1_funct_1(k2_scmfsa_7(A,B))
        & v1_finset_1(k2_scmfsa_7(A,B))
        & v1_ami_3(k2_scmfsa_7(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(k2_scmfsa_7(A,B)) ) ) )).

fof(fc3_scmfsa7b,axiom,(
    ! [A,B] :
      ( ( m1_scmfsa_2(A)
        & v1_int_1(B) )
     => ( v1_relat_1(k2_scmfsa_7(A,B))
        & v1_funct_1(k2_scmfsa_7(A,B))
        & ~ v1_xboole_0(k2_scmfsa_7(A,B))
        & v1_finset_1(k2_scmfsa_7(A,B))
        & v1_ami_3(k2_scmfsa_7(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(k2_scmfsa_7(A,B))
        & v1_scmfsa6b(k2_scmfsa_7(A,B))
        & v2_scmfsa6b(k2_scmfsa_7(A,B)) ) ) )).

fof(fc4_scmfsa7b,axiom,(
    ! [A,B] :
      ( ( m2_scmfsa_2(A)
        & m1_finseq_1(B,k4_numbers) )
     => ( v1_relat_1(k5_scmfsa_7(A,B))
        & v1_funct_1(k5_scmfsa_7(A,B))
        & v1_finset_1(k5_scmfsa_7(A,B))
        & v1_ami_3(k5_scmfsa_7(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(k5_scmfsa_7(A,B)) ) ) )).

fof(fc5_scmfsa7b,axiom,(
    ! [A,B] :
      ( ( m2_scmfsa_2(A)
        & m1_finseq_1(B,k4_numbers) )
     => ( v1_relat_1(k5_scmfsa_7(A,B))
        & v1_funct_1(k5_scmfsa_7(A,B))
        & ~ v1_xboole_0(k5_scmfsa_7(A,B))
        & v1_finset_1(k5_scmfsa_7(A,B))
        & v1_ami_3(k5_scmfsa_7(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(k5_scmfsa_7(A,B))
        & v1_scmfsa6b(k5_scmfsa_7(A,B))
        & v2_scmfsa6b(k5_scmfsa_7(A,B)) ) ) )).

fof(rc1_scmfsa7b,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)
      & v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
      & v1_scmfsa_4(A)
      & v1_scmfsa7b(A)
      & v2_scmfsa7b(A) ) )).

fof(rc2_scmfsa7b,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_xboole_0(A)
      & v1_finset_1(A)
      & v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
      & v1_scmfsa_4(A)
      & v1_scmfsa6b(A)
      & v2_scmfsa6b(A)
      & v1_scmfsa7b(A) ) )).

fof(fc6_scmfsa7b,axiom,
    ( v1_relat_1(k5_scmfsa_4)
    & v1_funct_1(k5_scmfsa_4)
    & ~ v1_xboole_0(k5_scmfsa_4)
    & v1_finset_1(k5_scmfsa_4)
    & v1_ami_3(k5_scmfsa_4,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
    & v1_scmfsa_4(k5_scmfsa_4)
    & v1_scmfsa6b(k5_scmfsa_4)
    & v2_scmfsa6b(k5_scmfsa_4)
    & v1_scmfsa7b(k5_scmfsa_4) )).

fof(cc1_scmfsa7b,axiom,(
    ! [A] :
      ( m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
     => ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
          & v1_scmfsa_4(A)
          & v1_scmfsa6b(A)
          & v1_scmfsa7b(A) )
       => ( v1_relat_1(A)
          & v1_funct_1(A)
          & v1_finset_1(A)
          & v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
          & v1_scmfsa_4(A)
          & v1_scmfsa6b(A)
          & v3_scmfsa6b(A) ) ) ) )).

fof(fc7_scmfsa7b,axiom,(
    ! [A,B] :
      ( ( ~ v1_sf_mastr(A)
        & m1_scmfsa_2(A)
        & v1_int_1(B) )
     => ( v1_relat_1(k2_scmfsa_7(A,B))
        & v1_funct_1(k2_scmfsa_7(A,B))
        & ~ v1_xboole_0(k2_scmfsa_7(A,B))
        & v1_finset_1(k2_scmfsa_7(A,B))
        & v1_ami_3(k2_scmfsa_7(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(k2_scmfsa_7(A,B))
        & v1_scmfsa6b(k2_scmfsa_7(A,B))
        & v2_scmfsa6b(k2_scmfsa_7(A,B))
        & v3_scmfsa6b(k2_scmfsa_7(A,B))
        & v1_scmfsa7b(k2_scmfsa_7(A,B)) ) ) )).

fof(fc8_scmfsa7b,axiom,(
    ! [A,B] :
      ( ( ~ v1_sf_mastr(A)
        & m1_scmfsa_2(A)
        & v1_int_1(B) )
     => ( v1_relat_1(k2_scmfsa_7(A,B))
        & v1_funct_1(k2_scmfsa_7(A,B))
        & ~ v1_xboole_0(k2_scmfsa_7(A,B))
        & v1_finset_1(k2_scmfsa_7(A,B))
        & v1_ami_3(k2_scmfsa_7(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(k2_scmfsa_7(A,B))
        & v1_scmfsa6b(k2_scmfsa_7(A,B))
        & v2_scmfsa6b(k2_scmfsa_7(A,B))
        & v3_scmfsa6b(k2_scmfsa_7(A,B))
        & v1_scmfsa7b(k2_scmfsa_7(A,B)) ) ) )).

fof(t2_scmfsa7b,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
     => k2_relat_1(k1_scmfsa_7(A)) = k2_relat_1(A) ) )).

fof(t3_scmfsa7b,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
     => k1_scmfsa_7(k13_binarith(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),A)) = k14_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0),A) ) )).

fof(t4_scmfsa7b,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
     => k1_relat_1(k2_scmfsa6a(A)) = k2_tarski(k5_scmfsa_2(np__0),k5_scmfsa_2(np__1)) ) )).

fof(t5_scmfsa7b,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
     => k2_scmfsa6a(A) = k1_scmfsa_7(k2_finseq_4(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),A,k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) ) )).

fof(t6_scmfsa7b,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
     => k4_card_1(k2_scmfsa6a(A)) = np__2 ) )).

fof(t7_scmfsa7b,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
     => ( ( A = k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
         => k1_funct_1(k1_scmfsa6a(k2_scmfsa6a(A)),k5_scmfsa_2(np__0)) = k13_scmfsa_2(k5_scmfsa_2(np__2)) )
        & ( A != k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
         => k1_funct_1(k1_scmfsa6a(k2_scmfsa6a(A)),k5_scmfsa_2(np__0)) = A ) ) ) )).

fof(t8_scmfsa7b,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
     => k1_funct_1(k1_scmfsa6a(k2_scmfsa6a(A)),k5_scmfsa_2(np__1)) = k13_scmfsa_2(k5_scmfsa_2(np__2)) ) )).

fof(t9_scmfsa7b,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( ~ v1_sf_mastr(B)
            & m1_scmfsa_2(B) )
         => ! [C] :
              ( v1_int_1(C)
             => ( k20_scmfsa_2(k3_scmfsa6b(k2_scmfsa_7(B,C),A),B) = C
                & ! [D] :
                    ( ( ~ v1_sf_mastr(D)
                      & m1_scmfsa_2(D) )
                   => ( D != B
                     => k20_scmfsa_2(k3_scmfsa6b(k2_scmfsa_7(B,C),A),D) = k20_scmfsa_2(A,D) ) )
                & ! [D] :
                    ( m2_scmfsa_2(D)
                   => k21_scmfsa_2(k3_scmfsa6b(k2_scmfsa_7(B,C),A),D) = k21_scmfsa_2(A,D) ) ) ) ) ) )).

fof(t10_scmfsa7b,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( m2_scmfsa_2(B)
         => ! [C] :
              ( m2_finseq_1(C,k4_numbers)
             => ( k21_scmfsa_2(k3_scmfsa6b(k5_scmfsa_7(B,C),A),B) = C
                & ! [D] :
                    ( ( ~ v1_sf_mastr(D)
                      & m1_scmfsa_2(D) )
                   => ~ ( D != k4_scmfsa_2(np__1)
                        & D != k4_scmfsa_2(np__2)
                        & k20_scmfsa_2(k3_scmfsa6b(k5_scmfsa_7(B,C),A),D) != k20_scmfsa_2(A,D) ) )
                & ! [D] :
                    ( m2_scmfsa_2(D)
                   => ( D != B
                     => k21_scmfsa_2(k3_scmfsa6b(k5_scmfsa_7(B,C),A),D) = k21_scmfsa_2(A,D) ) ) ) ) ) ) )).

fof(d1_scmfsa7b,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ( r1_scmfsa7b(A,B)
          <=> ! [C] :
                ( m1_scmfsa_2(C)
               => ! [D] :
                    ( m1_struct_0(D,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
                   => ! [E] :
                        ( m2_scmfsa_2(E)
                       => ( k8_scmfsa_2(C,B) != A
                          & k9_scmfsa_2(C,B) != A
                          & k10_scmfsa_2(C,B) != A
                          & k11_scmfsa_2(C,B) != A
                          & k12_scmfsa_2(C,B) != A
                          & k12_scmfsa_2(B,C) != A
                          & k14_scmfsa_2(D,B) != A
                          & k15_scmfsa_2(D,B) != A
                          & k16_scmfsa_2(C,B,E) != A
                          & k17_scmfsa_2(B,C,E) != A
                          & k17_scmfsa_2(C,B,E) != A
                          & k19_scmfsa_2(B,E) != A ) ) ) ) ) ) ) )).

fof(d2_scmfsa7b,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ( r2_scmfsa7b(A,B)
          <=> ! [C] :
                ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
               => ( r2_hidden(C,k2_relat_1(A))
                 => r1_scmfsa7b(C,B) ) ) ) ) ) )).

fof(d3_scmfsa7b,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ( r3_scmfsa7b(A,B)
          <=> ! [C] :
                ( m1_scmfsa_2(C)
               => ! [D] :
                    ( m2_scmfsa_2(D)
                   => ( k8_scmfsa_2(B,C) != A
                      & k9_scmfsa_2(B,C) != A
                      & k10_scmfsa_2(B,C) != A
                      & k11_scmfsa_2(B,C) != A
                      & k12_scmfsa_2(B,C) != A
                      & k12_scmfsa_2(C,B) != A
                      & k16_scmfsa_2(B,C,D) != A
                      & k18_scmfsa_2(B,D) != A ) ) ) ) ) ) )).

fof(d4_scmfsa7b,axiom,(
    ! [A] :
      ( m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ( r4_scmfsa7b(A,B)
          <=> ! [C] :
                ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
               => ( r2_hidden(C,k2_relat_1(A))
                 => r3_scmfsa7b(C,B) ) ) ) ) ) )).

fof(d5_scmfsa7b,axiom,(
    ! [A] :
      ( m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
     => ( v1_scmfsa7b(A)
      <=> r4_scmfsa7b(A,k4_scmfsa_2(np__0)) ) ) )).

fof(d6_scmfsa7b,axiom,(
    ! [A] :
      ( m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
     => ( v2_scmfsa7b(A)
      <=> ~ r2_hidden(k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k2_relat_1(A)) ) ) )).

fof(t11_scmfsa7b,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => r3_scmfsa7b(k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),A) ) )).

fof(t12_scmfsa7b,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m1_scmfsa_2(C)
             => ( A != B
               => r3_scmfsa7b(k8_scmfsa_2(B,C),A) ) ) ) ) )).

fof(t13_scmfsa7b,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m1_scmfsa_2(C)
             => ( A != B
               => r3_scmfsa7b(k9_scmfsa_2(B,C),A) ) ) ) ) )).

fof(t14_scmfsa7b,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m1_scmfsa_2(C)
             => ( A != B
               => r3_scmfsa7b(k10_scmfsa_2(B,C),A) ) ) ) ) )).

fof(t15_scmfsa7b,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m1_scmfsa_2(C)
             => ( A != B
               => r3_scmfsa7b(k11_scmfsa_2(B,C),A) ) ) ) ) )).

fof(t16_scmfsa7b,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m1_scmfsa_2(C)
             => ~ ( A != B
                  & A != C
                  & ~ r3_scmfsa7b(k12_scmfsa_2(B,C),A) ) ) ) ) )).

fof(t17_scmfsa7b,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_struct_0(B,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
         => r3_scmfsa7b(k13_scmfsa_2(B),A) ) ) )).

fof(t18_scmfsa7b,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m1_struct_0(C,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
             => r3_scmfsa7b(k14_scmfsa_2(C,B),A) ) ) ) )).

fof(t19_scmfsa7b,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m1_struct_0(C,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
             => r3_scmfsa7b(k15_scmfsa_2(C,B),A) ) ) ) )).

fof(t20_scmfsa7b,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m1_scmfsa_2(C)
             => ! [D] :
                  ( m2_scmfsa_2(D)
                 => ( A != B
                   => r3_scmfsa7b(k16_scmfsa_2(B,C,D),A) ) ) ) ) ) )).

fof(t21_scmfsa7b,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m1_scmfsa_2(C)
             => ! [D] :
                  ( m2_scmfsa_2(D)
                 => r3_scmfsa7b(k17_scmfsa_2(B,C,D),A) ) ) ) ) )).

fof(t22_scmfsa7b,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m2_scmfsa_2(C)
             => ( A != B
               => r3_scmfsa7b(k18_scmfsa_2(B,C),A) ) ) ) ) )).

fof(t23_scmfsa7b,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m2_scmfsa_2(C)
             => r3_scmfsa7b(k19_scmfsa_2(B,C),A) ) ) ) )).

fof(d7_scmfsa7b,axiom,(
    ! [A] :
      ( m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
         => ( r5_scmfsa7b(A,B)
          <=> ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => r2_hidden(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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),C)),k1_relat_1(A)) ) ) ) ) )).

fof(d8_scmfsa7b,axiom,(
    ! [A] :
      ( m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
         => ( r6_scmfsa7b(A,B)
          <=> v9_ami_1(k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0)))),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ) )).

fof(t24_scmfsa7b,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(A)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ( v1_scmfsa6b(A)
      <=> ! [B] :
            ( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
           => r5_scmfsa7b(A,B) ) ) ) )).

fof(t25_scmfsa7b,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(A)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ( v2_scmfsa6b(A)
      <=> ! [B] :
            ( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
           => r6_scmfsa7b(A,B) ) ) ) )).

fof(t26_scmfsa7b,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
             => ( r3_scmfsa7b(A,B)
               => k20_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,C),B) = k20_scmfsa_2(C,B) ) ) ) ) )).

fof(t27_scmfsa7b,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ! [C] :
              ( m1_scmfsa_2(C)
             => ( ( r4_scmfsa7b(B,C)
                  & r5_scmfsa7b(B,A) )
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => 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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),D),C) = k20_scmfsa_2(A,C) ) ) ) ) ) )).

fof(t28_scmfsa7b,axiom,(
    r4_scmfsa7b(k5_scmfsa_4,k4_scmfsa_2(np__0)) )).

fof(t29_scmfsa7b,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => r1_tarski(k2_relat_1(k3_scmfsa_7(A,B)),k1_enumset1(k8_scmfsa_2(A,k4_scmfsa_2(np__0)),k9_scmfsa_2(A,k4_scmfsa_2(np__0)),k10_scmfsa_2(A,k4_scmfsa_2(np__0)))) ) ) )).

fof(t30_scmfsa7b,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => r1_tarski(k2_relat_1(k2_scmfsa_7(A,B)),k2_enumset1(k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k8_scmfsa_2(A,k4_scmfsa_2(np__0)),k9_scmfsa_2(A,k4_scmfsa_2(np__0)),k10_scmfsa_2(A,k4_scmfsa_2(np__0)))) ) ) )).

fof(t1_scmfsa7b,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
     => k1_relat_1(k1_scmfsa_7(A)) = a_1_0_scmfsa7b(A) ) )).

fof(fraenkel_a_1_0_scmfsa7b,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_scmfsa7b(B))
      <=> ? [C] :
            ( m2_subset_1(C,k1_numbers,k5_numbers)
            & A = k5_scmfsa_2(C)
            & ~ r1_xreal_0(k3_finseq_1(B),C) ) ) ) )).
%------------------------------------------------------------------------------