SET007 Axioms: SET007+450.ax


%------------------------------------------------------------------------------
% File     : SET007+450 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : An Extension of SCM
% 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_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   78 (  18 unit)
%            Number of atoms       :  311 (  97 equality)
%            Maximal formula depth :   20 (   5 average)
%            Number of connectives :  251 (  18 ~  ;   0  |;  94  &)
%                                         (  15 <=>; 124 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   15 (   1 propositional; 0-3 arity)
%            Number of functors    :   69 (  23 constant; 0-6 arity)
%            Number of variables   :  166 (   0 singleton; 119 !;  47 ?)
%            Maximal term depth    :    8 (   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(fc1_scmfsa_1,axiom,(
    ~ v1_xboole_0(k2_scmfsa_1) )).

fof(fc2_scmfsa_1,axiom,(
    ~ v1_xboole_0(k1_scmfsa_1) )).

fof(fc3_scmfsa_1,axiom,(
    ~ v1_xboole_0(k3_scmfsa_1) )).

fof(fc4_scmfsa_1,axiom,
    ( ~ v1_xboole_0(k4_scmfsa_1)
    & v1_relat_1(k4_scmfsa_1) )).

fof(d1_scmfsa_1,axiom,(
    k1_scmfsa_1 = k2_ami_2 )).

fof(d2_scmfsa_1,axiom,(
    k2_scmfsa_1 = k4_xboole_0(k4_numbers,k5_numbers) )).

fof(d3_scmfsa_1,axiom,(
    k3_scmfsa_1 = k3_ami_2 )).

fof(t1_scmfsa_1,axiom,(
    $true )).

fof(t2_scmfsa_1,axiom,(
    r1_tarski(k4_ami_2,k4_scmfsa_1) )).

fof(d5_scmfsa_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(k1_gr_cy_1(np__13),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k13_finseq_1(k4_numbers))),k4_numbers))),k4_scmfsa_1)
     => k5_scmfsa_1(A) = k1_mcart_1(A) ) )).

fof(t3_scmfsa_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(k1_gr_cy_1(np__13),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k13_finseq_1(k4_numbers))),k4_numbers))),k4_scmfsa_1)
     => ( r1_xreal_0(k5_scmfsa_1(A),np__8)
       => r2_hidden(A,k4_ami_2) ) ) )).

fof(t4_scmfsa_1,axiom,(
    r2_hidden(k4_tarski(np__0,k1_xboole_0),k4_scmfsa_1) )).

fof(d6_scmfsa_1,axiom,(
    k6_scmfsa_1 = k1_funct_4(k1_funct_4(k10_pboole(k4_numbers,k13_finseq_1(k4_numbers)),k5_ami_2),k5_relat_1(k7_relat_1(k5_ami_2,k3_ami_2),k3_cqc_lang(k4_ami_2,k4_scmfsa_1))) )).

fof(t5_scmfsa_1,axiom,(
    $true )).

fof(t6_scmfsa_1,axiom,(
    ! [A,B] :
      ( m2_subset_1(B,k4_numbers,k1_scmfsa_1)
     => ! [C] :
          ( m2_subset_1(C,k4_numbers,k1_scmfsa_1)
         => ! [D] :
              ( m2_subset_1(D,k4_numbers,k2_scmfsa_1)
             => ( r2_hidden(A,k2_tarski(np__9,np__10))
               => r2_hidden(k4_tarski(A,k3_finseq_4(k4_numbers,B,D,C)),k4_scmfsa_1) ) ) ) ) )).

fof(t7_scmfsa_1,axiom,(
    ! [A,B] :
      ( m2_subset_1(B,k4_numbers,k1_scmfsa_1)
     => ! [C] :
          ( m2_subset_1(C,k4_numbers,k2_scmfsa_1)
         => ( r2_hidden(A,k2_tarski(np__11,np__12))
           => r2_hidden(k4_tarski(A,k2_finseq_4(k4_numbers,B,C)),k4_scmfsa_1) ) ) ) )).

fof(t8_scmfsa_1,axiom,(
    k4_numbers = k2_xboole_0(k2_xboole_0(k2_xboole_0(k1_tarski(np__0),k1_scmfsa_1),k2_scmfsa_1),k3_scmfsa_1) )).

fof(t9_scmfsa_1,axiom,(
    k1_funct_1(k6_scmfsa_1,np__0) = k3_scmfsa_1 )).

fof(t10_scmfsa_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k4_numbers,k1_scmfsa_1)
     => k8_funct_2(k4_numbers,k2_xboole_0(k2_tarski(k4_numbers,k13_finseq_1(k4_numbers)),k2_tarski(k4_scmfsa_1,k3_scmfsa_1)),k6_scmfsa_1,A) = k4_numbers ) )).

fof(t11_scmfsa_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k4_numbers,k3_scmfsa_1)
     => k8_funct_2(k4_numbers,k2_xboole_0(k2_tarski(k4_numbers,k13_finseq_1(k4_numbers)),k2_tarski(k4_scmfsa_1,k3_scmfsa_1)),k6_scmfsa_1,A) = k4_scmfsa_1 ) )).

fof(t12_scmfsa_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k4_numbers,k2_scmfsa_1)
     => k8_funct_2(k4_numbers,k2_xboole_0(k2_tarski(k4_numbers,k13_finseq_1(k4_numbers)),k2_tarski(k4_scmfsa_1,k3_scmfsa_1)),k6_scmfsa_1,A) = k13_finseq_1(k4_numbers) ) )).

fof(t13_scmfsa_1,axiom,
    ( k3_scmfsa_1 != k4_numbers
    & k4_scmfsa_1 != k4_numbers
    & k3_scmfsa_1 != k4_scmfsa_1
    & k3_scmfsa_1 != k13_finseq_1(k4_numbers)
    & k4_scmfsa_1 != k13_finseq_1(k4_numbers) )).

fof(t14_scmfsa_1,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ( k1_funct_1(k6_scmfsa_1,A) = k3_scmfsa_1
       => A = np__0 ) ) )).

fof(t15_scmfsa_1,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ( k1_funct_1(k6_scmfsa_1,A) = k4_numbers
       => r2_hidden(A,k1_scmfsa_1) ) ) )).

fof(t16_scmfsa_1,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ( k1_funct_1(k6_scmfsa_1,A) = k4_scmfsa_1
       => r2_hidden(A,k3_scmfsa_1) ) ) )).

fof(t17_scmfsa_1,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ( k1_funct_1(k6_scmfsa_1,A) = k13_finseq_1(k4_numbers)
       => r2_hidden(A,k2_scmfsa_1) ) ) )).

fof(t18_scmfsa_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
     => ! [B] :
          ( m2_subset_1(B,k2_zfmisc_1(k1_gr_cy_1(np__9),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),k5_numbers))),k4_ami_2)
         => m1_subset_1(k1_funct_4(k7_relat_1(A,k5_numbers),k3_finsop_1(k4_ami_2,k3_ami_2,B)),k4_card_3(k5_ami_2)) ) ) )).

fof(t19_scmfsa_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(k5_ami_2))
         => m1_subset_1(k1_funct_4(k1_funct_4(A,B),k7_relat_1(A,k3_scmfsa_1)),k4_card_3(k6_scmfsa_1)) ) ) )).

fof(d7_scmfsa_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
     => ! [B] :
          ( m2_subset_1(B,k4_numbers,k3_scmfsa_1)
         => k7_scmfsa_1(A,B) = k1_funct_4(A,k3_cqc_lang(np__0,B)) ) ) )).

fof(d8_scmfsa_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
     => ! [B] :
          ( m2_subset_1(B,k4_numbers,k1_scmfsa_1)
         => ! [C] :
              ( v1_int_1(C)
             => k8_scmfsa_1(A,B,C) = k1_funct_4(A,k3_cqc_lang(B,C)) ) ) ) )).

fof(d9_scmfsa_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
     => ! [B] :
          ( m2_subset_1(B,k4_numbers,k2_scmfsa_1)
         => ! [C] :
              ( m2_finseq_1(C,k4_numbers)
             => k9_scmfsa_1(A,B,C) = k1_funct_4(A,k3_cqc_lang(B,C)) ) ) ) )).

fof(d10_scmfsa_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(k1_gr_cy_1(np__13),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k13_finseq_1(k4_numbers))),k4_numbers))),k4_scmfsa_1)
     => ( ? [B] :
            ( m2_subset_1(B,k4_numbers,k1_scmfsa_1)
            & ? [C] :
                ( m2_subset_1(C,k4_numbers,k2_scmfsa_1)
                & ? [D] :
                    ( m2_subset_1(D,k4_numbers,k1_scmfsa_1)
                    & ? [E] :
                        ( m2_subset_1(E,k5_numbers,k1_gr_cy_1(np__13))
                        & A = k4_tarski(E,k3_finseq_4(k4_numbers,B,C,D)) ) ) ) )
       => ! [B] :
            ( m2_subset_1(B,k4_numbers,k1_scmfsa_1)
           => ( B = k12_scmfsa_1(A)
            <=> ? [C] :
                  ( m2_subset_1(C,k4_numbers,k1_scmfsa_1)
                  & ? [D] :
                      ( m2_subset_1(D,k4_numbers,k2_scmfsa_1)
                      & ? [E] :
                          ( m2_subset_1(E,k4_numbers,k1_scmfsa_1)
                          & k3_finseq_4(k4_numbers,C,D,E) = k2_mcart_1(A)
                          & B = C ) ) ) ) ) ) ) )).

fof(d11_scmfsa_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(k1_gr_cy_1(np__13),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k13_finseq_1(k4_numbers))),k4_numbers))),k4_scmfsa_1)
     => ( ? [B] :
            ( m2_subset_1(B,k4_numbers,k1_scmfsa_1)
            & ? [C] :
                ( m2_subset_1(C,k4_numbers,k2_scmfsa_1)
                & ? [D] :
                    ( m2_subset_1(D,k4_numbers,k1_scmfsa_1)
                    & ? [E] :
                        ( m2_subset_1(E,k5_numbers,k1_gr_cy_1(np__13))
                        & A = k4_tarski(E,k3_finseq_4(k4_numbers,B,C,D)) ) ) ) )
       => ! [B] :
            ( m2_subset_1(B,k4_numbers,k1_scmfsa_1)
           => ( B = k13_scmfsa_1(A)
            <=> ? [C] :
                  ( m2_subset_1(C,k4_numbers,k1_scmfsa_1)
                  & ? [D] :
                      ( m2_subset_1(D,k4_numbers,k2_scmfsa_1)
                      & ? [E] :
                          ( m2_subset_1(E,k4_numbers,k1_scmfsa_1)
                          & k3_finseq_4(k4_numbers,C,D,E) = k2_mcart_1(A)
                          & B = E ) ) ) ) ) ) ) )).

fof(d12_scmfsa_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(k1_gr_cy_1(np__13),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k13_finseq_1(k4_numbers))),k4_numbers))),k4_scmfsa_1)
     => ( ? [B] :
            ( m2_subset_1(B,k4_numbers,k1_scmfsa_1)
            & ? [C] :
                ( m2_subset_1(C,k4_numbers,k2_scmfsa_1)
                & ? [D] :
                    ( m2_subset_1(D,k4_numbers,k1_scmfsa_1)
                    & ? [E] :
                        ( m2_subset_1(E,k5_numbers,k1_gr_cy_1(np__13))
                        & A = k4_tarski(E,k3_finseq_4(k4_numbers,B,C,D)) ) ) ) )
       => ! [B] :
            ( m2_subset_1(B,k4_numbers,k2_scmfsa_1)
           => ( B = k14_scmfsa_1(A)
            <=> ? [C] :
                  ( m2_subset_1(C,k4_numbers,k1_scmfsa_1)
                  & ? [D] :
                      ( m2_subset_1(D,k4_numbers,k2_scmfsa_1)
                      & ? [E] :
                          ( m2_subset_1(E,k4_numbers,k1_scmfsa_1)
                          & k3_finseq_4(k4_numbers,C,D,E) = k2_mcart_1(A)
                          & B = D ) ) ) ) ) ) ) )).

fof(d13_scmfsa_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(k1_gr_cy_1(np__13),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k13_finseq_1(k4_numbers))),k4_numbers))),k4_scmfsa_1)
     => ( ? [B] :
            ( m2_subset_1(B,k4_numbers,k1_scmfsa_1)
            & ? [C] :
                ( m2_subset_1(C,k4_numbers,k2_scmfsa_1)
                & ? [D] :
                    ( m2_subset_1(D,k5_numbers,k1_gr_cy_1(np__13))
                    & A = k4_tarski(D,k2_finseq_4(k4_numbers,B,C)) ) ) )
       => ! [B] :
            ( m2_subset_1(B,k4_numbers,k1_scmfsa_1)
           => ( B = k15_scmfsa_1(A)
            <=> ? [C] :
                  ( m2_subset_1(C,k4_numbers,k1_scmfsa_1)
                  & ? [D] :
                      ( m2_subset_1(D,k4_numbers,k2_scmfsa_1)
                      & k2_finseq_4(k4_numbers,C,D) = k2_mcart_1(A)
                      & B = C ) ) ) ) ) ) )).

fof(d14_scmfsa_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(k1_gr_cy_1(np__13),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k13_finseq_1(k4_numbers))),k4_numbers))),k4_scmfsa_1)
     => ( ? [B] :
            ( m2_subset_1(B,k4_numbers,k1_scmfsa_1)
            & ? [C] :
                ( m2_subset_1(C,k4_numbers,k2_scmfsa_1)
                & ? [D] :
                    ( m2_subset_1(D,k5_numbers,k1_gr_cy_1(np__13))
                    & A = k4_tarski(D,k2_finseq_4(k4_numbers,B,C)) ) ) )
       => ! [B] :
            ( m2_subset_1(B,k4_numbers,k2_scmfsa_1)
           => ( B = k16_scmfsa_1(A)
            <=> ? [C] :
                  ( m2_subset_1(C,k4_numbers,k1_scmfsa_1)
                  & ? [D] :
                      ( m2_subset_1(D,k4_numbers,k2_scmfsa_1)
                      & k2_finseq_4(k4_numbers,C,D) = k2_mcart_1(A)
                      & B = D ) ) ) ) ) ) )).

fof(d15_scmfsa_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k4_numbers,k3_scmfsa_1)
     => ! [B] :
          ( m2_subset_1(B,k4_numbers,k3_scmfsa_1)
         => ( B = k17_scmfsa_1(A)
          <=> ? [C] :
                ( m2_subset_1(C,k5_numbers,k3_ami_2)
                & C = A
                & B = k15_ami_2(C) ) ) ) ) )).

fof(d16_scmfsa_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
     => k18_scmfsa_1(A) = k1_funct_1(A,np__0) ) )).

fof(d17_scmfsa_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(k1_gr_cy_1(np__13),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k13_finseq_1(k4_numbers))),k4_numbers))),k4_scmfsa_1)
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(k6_scmfsa_1))
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(k6_scmfsa_1))
             => ( ( r1_xreal_0(k5_scmfsa_1(A),np__8)
                 => ( C = k19_scmfsa_1(A,B)
                  <=> ? [D] :
                        ( m2_subset_1(D,k2_zfmisc_1(k1_gr_cy_1(np__9),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),k5_numbers))),k4_ami_2)
                        & ? [E] :
                            ( m1_subset_1(E,k4_card_3(k5_ami_2))
                            & A = D
                            & E = k1_funct_4(k7_relat_1(B,k5_numbers),k3_finsop_1(k4_ami_2,k3_ami_2,D))
                            & C = k1_funct_4(k1_funct_4(B,k16_ami_2(D,E)),k7_relat_1(B,k3_scmfsa_1)) ) ) ) )
                & ( k5_scmfsa_1(A) = np__9
                 => ( C = k19_scmfsa_1(A,B)
                  <=> ? [D] :
                        ( v1_int_1(D)
                        & ? [E] :
                            ( m2_subset_1(E,k1_numbers,k5_numbers)
                            & E = k1_int_2(k10_scmfsa_1(B,k13_scmfsa_1(A)))
                            & D = k4_finseq_4(k5_numbers,k4_numbers,k11_scmfsa_1(B,k14_scmfsa_1(A)),E)
                            & C = k7_scmfsa_1(k8_scmfsa_1(B,k12_scmfsa_1(A),D),k17_scmfsa_1(k18_scmfsa_1(B))) ) ) ) )
                & ( k5_scmfsa_1(A) = np__10
                 => ( C = k19_scmfsa_1(A,B)
                  <=> ? [D] :
                        ( m2_finseq_1(D,k4_numbers)
                        & ? [E] :
                            ( m2_subset_1(E,k1_numbers,k5_numbers)
                            & E = k1_int_2(k10_scmfsa_1(B,k13_scmfsa_1(A)))
                            & D = k2_funct_7(k11_scmfsa_1(B,k14_scmfsa_1(A)),E,k10_scmfsa_1(B,k12_scmfsa_1(A)))
                            & C = k7_scmfsa_1(k9_scmfsa_1(B,k14_scmfsa_1(A),D),k17_scmfsa_1(k18_scmfsa_1(B))) ) ) ) )
                & ( k5_scmfsa_1(A) = np__11
                 => ( C = k19_scmfsa_1(A,B)
                  <=> C = k7_scmfsa_1(k8_scmfsa_1(B,k15_scmfsa_1(A),k3_finseq_1(k11_scmfsa_1(B,k16_scmfsa_1(A)))),k17_scmfsa_1(k18_scmfsa_1(B))) ) )
                & ( k5_scmfsa_1(A) = np__12
                 => ( C = k19_scmfsa_1(A,B)
                  <=> ? [D] :
                        ( m2_finseq_1(D,k4_numbers)
                        & ? [E] :
                            ( m2_subset_1(E,k1_numbers,k5_numbers)
                            & E = k1_int_2(k10_scmfsa_1(B,k15_scmfsa_1(A)))
                            & D = k1_finsop_1(k5_numbers,E,np__0)
                            & C = k7_scmfsa_1(k9_scmfsa_1(B,k16_scmfsa_1(A),D),k17_scmfsa_1(k18_scmfsa_1(B))) ) ) ) )
                & ~ ( ~ r1_xreal_0(k5_scmfsa_1(A),np__8)
                    & k5_scmfsa_1(A) != np__9
                    & k5_scmfsa_1(A) != np__10
                    & k5_scmfsa_1(A) != np__11
                    & k5_scmfsa_1(A) != np__12
                    & ~ ( C = k19_scmfsa_1(A,B)
                      <=> C = B ) ) ) ) ) ) )).

fof(d18_scmfsa_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k4_scmfsa_1,k1_fraenkel(k4_card_3(k6_scmfsa_1),k4_card_3(k6_scmfsa_1)))
        & m2_relset_1(A,k4_scmfsa_1,k1_fraenkel(k4_card_3(k6_scmfsa_1),k4_card_3(k6_scmfsa_1))) )
     => ( A = k20_scmfsa_1
      <=> ! [B] :
            ( m2_subset_1(B,k2_zfmisc_1(k1_gr_cy_1(np__13),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k13_finseq_1(k4_numbers))),k4_numbers))),k4_scmfsa_1)
           => ! [C] :
                ( m1_subset_1(C,k4_card_3(k6_scmfsa_1))
               => k8_funct_2(k4_card_3(k6_scmfsa_1),k4_card_3(k6_scmfsa_1),k1_cat_2(k4_scmfsa_1,k4_card_3(k6_scmfsa_1),k4_card_3(k6_scmfsa_1),k1_fraenkel(k4_card_3(k6_scmfsa_1),k4_card_3(k6_scmfsa_1)),A,B),C) = k19_scmfsa_1(B,C) ) ) ) ) )).

fof(t20_scmfsa_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
     => ! [B] :
          ( m2_subset_1(B,k4_numbers,k3_scmfsa_1)
         => k1_funct_1(k7_scmfsa_1(A,B),np__0) = B ) ) )).

fof(t21_scmfsa_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
     => ! [B] :
          ( m2_subset_1(B,k4_numbers,k3_scmfsa_1)
         => ! [C] :
              ( m2_subset_1(C,k4_numbers,k1_scmfsa_1)
             => k10_scmfsa_1(k7_scmfsa_1(A,B),C) = k10_scmfsa_1(A,C) ) ) ) )).

fof(t22_scmfsa_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
     => ! [B] :
          ( m2_subset_1(B,k4_numbers,k3_scmfsa_1)
         => ! [C] :
              ( m2_subset_1(C,k4_numbers,k2_scmfsa_1)
             => k11_scmfsa_1(k7_scmfsa_1(A,B),C) = k11_scmfsa_1(A,C) ) ) ) )).

fof(t23_scmfsa_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
     => ! [B] :
          ( m2_subset_1(B,k4_numbers,k3_scmfsa_1)
         => ! [C] :
              ( m2_subset_1(C,k4_numbers,k3_scmfsa_1)
             => k1_funct_1(k7_scmfsa_1(A,B),C) = k1_funct_1(A,C) ) ) ) )).

fof(t24_scmfsa_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
     => ! [B] :
          ( m2_subset_1(B,k4_numbers,k1_scmfsa_1)
         => ! [C] :
              ( v1_int_1(C)
             => k1_funct_1(k8_scmfsa_1(A,B,C),np__0) = k1_funct_1(A,np__0) ) ) ) )).

fof(t25_scmfsa_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
     => ! [B] :
          ( m2_subset_1(B,k4_numbers,k1_scmfsa_1)
         => ! [C] :
              ( v1_int_1(C)
             => k10_scmfsa_1(k8_scmfsa_1(A,B,C),B) = C ) ) ) )).

fof(t26_scmfsa_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
     => ! [B] :
          ( m2_subset_1(B,k4_numbers,k1_scmfsa_1)
         => ! [C] :
              ( v1_int_1(C)
             => ! [D] :
                  ( m2_subset_1(D,k4_numbers,k1_scmfsa_1)
                 => ( D != B
                   => k10_scmfsa_1(k8_scmfsa_1(A,B,C),D) = k10_scmfsa_1(A,D) ) ) ) ) ) )).

fof(t27_scmfsa_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
     => ! [B] :
          ( m2_subset_1(B,k4_numbers,k1_scmfsa_1)
         => ! [C] :
              ( v1_int_1(C)
             => ! [D] :
                  ( m2_subset_1(D,k4_numbers,k2_scmfsa_1)
                 => k11_scmfsa_1(k8_scmfsa_1(A,B,C),D) = k11_scmfsa_1(A,D) ) ) ) ) )).

fof(t28_scmfsa_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
     => ! [B] :
          ( m2_subset_1(B,k4_numbers,k1_scmfsa_1)
         => ! [C] :
              ( v1_int_1(C)
             => ! [D] :
                  ( m2_subset_1(D,k4_numbers,k3_scmfsa_1)
                 => k1_funct_1(k8_scmfsa_1(A,B,C),D) = k1_funct_1(A,D) ) ) ) ) )).

fof(t29_scmfsa_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
     => ! [B] :
          ( m2_subset_1(B,k4_numbers,k2_scmfsa_1)
         => ! [C] :
              ( m2_finseq_1(C,k4_numbers)
             => k11_scmfsa_1(k9_scmfsa_1(A,B,C),B) = C ) ) ) )).

fof(t30_scmfsa_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
     => ! [B] :
          ( m2_subset_1(B,k4_numbers,k2_scmfsa_1)
         => ! [C] :
              ( m2_finseq_1(C,k4_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k4_numbers,k2_scmfsa_1)
                 => ( D != B
                   => k11_scmfsa_1(k9_scmfsa_1(A,B,C),D) = k11_scmfsa_1(A,D) ) ) ) ) ) )).

fof(t31_scmfsa_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
     => ! [B] :
          ( m2_subset_1(B,k4_numbers,k2_scmfsa_1)
         => ! [C] :
              ( m2_finseq_1(C,k4_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k4_numbers,k1_scmfsa_1)
                 => k10_scmfsa_1(k9_scmfsa_1(A,B,C),D) = k10_scmfsa_1(A,D) ) ) ) ) )).

fof(t32_scmfsa_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
     => ! [B] :
          ( m2_subset_1(B,k4_numbers,k2_scmfsa_1)
         => ! [C] :
              ( m2_finseq_1(C,k4_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k4_numbers,k3_scmfsa_1)
                 => k1_funct_1(k9_scmfsa_1(A,B,C),D) = k1_funct_1(A,D) ) ) ) ) )).

fof(dt_k1_scmfsa_1,axiom,(
    m1_subset_1(k1_scmfsa_1,k1_zfmisc_1(k4_numbers)) )).

fof(dt_k2_scmfsa_1,axiom,(
    m1_subset_1(k2_scmfsa_1,k1_zfmisc_1(k4_numbers)) )).

fof(dt_k3_scmfsa_1,axiom,(
    m1_subset_1(k3_scmfsa_1,k1_zfmisc_1(k4_numbers)) )).

fof(dt_k4_scmfsa_1,axiom,(
    m1_subset_1(k4_scmfsa_1,k1_zfmisc_1(k2_zfmisc_1(k1_gr_cy_1(np__13),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k13_finseq_1(k4_numbers))),k4_numbers))))) )).

fof(dt_k5_scmfsa_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_scmfsa_1)
     => m2_subset_1(k5_scmfsa_1(A),k1_numbers,k5_numbers) ) )).

fof(dt_k6_scmfsa_1,axiom,
    ( v1_funct_1(k6_scmfsa_1)
    & v1_funct_2(k6_scmfsa_1,k4_numbers,k2_xboole_0(k2_tarski(k4_numbers,k13_finseq_1(k4_numbers)),k2_tarski(k4_scmfsa_1,k3_scmfsa_1)))
    & m2_relset_1(k6_scmfsa_1,k4_numbers,k2_xboole_0(k2_tarski(k4_numbers,k13_finseq_1(k4_numbers)),k2_tarski(k4_scmfsa_1,k3_scmfsa_1))) )).

fof(dt_k7_scmfsa_1,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
        & m1_subset_1(B,k3_scmfsa_1) )
     => m1_subset_1(k7_scmfsa_1(A,B),k4_card_3(k6_scmfsa_1)) ) )).

fof(dt_k8_scmfsa_1,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
        & m1_subset_1(B,k1_scmfsa_1)
        & v1_int_1(C) )
     => m1_subset_1(k8_scmfsa_1(A,B,C),k4_card_3(k6_scmfsa_1)) ) )).

fof(dt_k9_scmfsa_1,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
        & m1_subset_1(B,k2_scmfsa_1)
        & m1_finseq_1(C,k4_numbers) )
     => m1_subset_1(k9_scmfsa_1(A,B,C),k4_card_3(k6_scmfsa_1)) ) )).

fof(dt_k10_scmfsa_1,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
        & m1_subset_1(B,k1_scmfsa_1) )
     => v1_int_1(k10_scmfsa_1(A,B)) ) )).

fof(redefinition_k10_scmfsa_1,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
        & m1_subset_1(B,k1_scmfsa_1) )
     => k10_scmfsa_1(A,B) = k1_funct_1(A,B) ) )).

fof(dt_k11_scmfsa_1,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
        & m1_subset_1(B,k2_scmfsa_1) )
     => m2_finseq_1(k11_scmfsa_1(A,B),k4_numbers) ) )).

fof(redefinition_k11_scmfsa_1,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
        & m1_subset_1(B,k2_scmfsa_1) )
     => k11_scmfsa_1(A,B) = k1_funct_1(A,B) ) )).

fof(dt_k12_scmfsa_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_scmfsa_1)
     => m2_subset_1(k12_scmfsa_1(A),k4_numbers,k1_scmfsa_1) ) )).

fof(dt_k13_scmfsa_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_scmfsa_1)
     => m2_subset_1(k13_scmfsa_1(A),k4_numbers,k1_scmfsa_1) ) )).

fof(dt_k14_scmfsa_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_scmfsa_1)
     => m2_subset_1(k14_scmfsa_1(A),k4_numbers,k2_scmfsa_1) ) )).

fof(dt_k15_scmfsa_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_scmfsa_1)
     => m2_subset_1(k15_scmfsa_1(A),k4_numbers,k1_scmfsa_1) ) )).

fof(dt_k16_scmfsa_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_scmfsa_1)
     => m2_subset_1(k16_scmfsa_1(A),k4_numbers,k2_scmfsa_1) ) )).

fof(dt_k17_scmfsa_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_scmfsa_1)
     => m2_subset_1(k17_scmfsa_1(A),k4_numbers,k3_scmfsa_1) ) )).

fof(dt_k18_scmfsa_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
     => m2_subset_1(k18_scmfsa_1(A),k4_numbers,k3_scmfsa_1) ) )).

fof(dt_k19_scmfsa_1,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k4_scmfsa_1)
        & m1_subset_1(B,k4_card_3(k6_scmfsa_1)) )
     => m1_subset_1(k19_scmfsa_1(A,B),k4_card_3(k6_scmfsa_1)) ) )).

fof(dt_k20_scmfsa_1,axiom,
    ( v1_funct_1(k20_scmfsa_1)
    & v1_funct_2(k20_scmfsa_1,k4_scmfsa_1,k1_fraenkel(k4_card_3(k6_scmfsa_1),k4_card_3(k6_scmfsa_1)))
    & m2_relset_1(k20_scmfsa_1,k4_scmfsa_1,k1_fraenkel(k4_card_3(k6_scmfsa_1),k4_card_3(k6_scmfsa_1))) )).

fof(d4_scmfsa_1,axiom,(
    k4_scmfsa_1 = k2_xboole_0(k2_xboole_0(k4_ami_2,a_0_0_scmfsa_1),a_0_1_scmfsa_1) )).

fof(fraenkel_a_0_0_scmfsa_1,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_0_scmfsa_1)
    <=> ? [B,C,D,E] :
          ( m2_subset_1(B,k5_numbers,k1_gr_cy_1(np__13))
          & m2_subset_1(C,k4_numbers,k1_scmfsa_1)
          & m2_subset_1(D,k4_numbers,k1_scmfsa_1)
          & m2_subset_1(E,k4_numbers,k2_scmfsa_1)
          & A = k4_tarski(B,k3_finseq_4(k4_numbers,C,E,D))
          & r2_hidden(B,k2_tarski(np__9,np__10)) ) ) )).

fof(fraenkel_a_0_1_scmfsa_1,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_1_scmfsa_1)
    <=> ? [B,C,D] :
          ( m2_subset_1(B,k5_numbers,k1_gr_cy_1(np__13))
          & m2_subset_1(C,k4_numbers,k1_scmfsa_1)
          & m2_subset_1(D,k4_numbers,k2_scmfsa_1)
          & A = k4_tarski(B,k2_finseq_4(k4_numbers,C,D))
          & r2_hidden(B,k2_tarski(np__11,np__12)) ) ) )).
%------------------------------------------------------------------------------