SET007 Axioms: SET007+380.ax


%------------------------------------------------------------------------------
% File     : SET007+380 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Development of Terminology for bf 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    : scm_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   46 (   2 unit)
%            Number of atoms       :  452 ( 203 equality)
%            Maximal formula depth :   45 (  14 average)
%            Number of connectives :  437 (  31 ~  ;   4  |; 182  &)
%                                         (   3 <=>; 217 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   23 (   1 propositional; 0-6 arity)
%            Number of functors    :   61 (  14 constant; 0-4 arity)
%            Number of variables   :  230 (   0 singleton; 228 !;   2 ?)
%            Maximal term depth    :   12 (   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(t1_scm_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
     => ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,A) = k1_funct_1(A,np__0)
        & k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,A) = k1_funct_1(A,k1_funct_1(A,np__0)) ) ) )).

fof(t2_scm_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,A),B)) = k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,A,k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,A),B)))
            & k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,A),B)) = k1_funct_1(A,k1_funct_1(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,A),B),np__0)) ) ) ) )).

fof(t3_scm_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
     => ( ? [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
            & k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,A,k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,A),B))) = k5_ami_1(k1_tarski(k4_numbers),k1_ami_3) )
       => v9_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) ) ) )).

fof(t4_scm_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,A,k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,A),B))) = k5_ami_1(k1_tarski(k4_numbers),k1_ami_3)
           => k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,A) = k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,A),B) ) ) ) )).

fof(t5_scm_1,axiom,(
    $true )).

fof(t6_scm_1,axiom,(
    $true )).

fof(t7_scm_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( k2_ami_1(k1_tarski(k4_numbers),k1_ami_3) != k16_ami_3(A)
            & k2_ami_1(k1_tarski(k4_numbers),k1_ami_3) != k15_ami_3(A)
            & k16_ami_3(A) != k15_ami_3(B) ) ) ) )).

fof(d1_scm_1,axiom,(
    ! [A] :
      ( m2_finseq_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => ! [B] :
          ( m2_finseq_1(B,k4_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( m1_subset_1(F,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
                         => ( m1_scm_1(F,A,B,C,D,E)
                          <=> ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,F) = k16_ami_3(C)
                              & ! [G] :
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ( ~ r1_xreal_0(k3_finseq_1(A),G)
                                   => k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,F,k16_ami_3(k1_nat_1(D,G))) = k1_funct_1(A,k1_nat_1(G,np__1)) ) )
                              & ! [G] :
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ( ~ r1_xreal_0(k3_finseq_1(B),G)
                                   => k2_ami_3(F,k15_ami_3(k1_nat_1(E,G))) = k1_funct_1(B,k1_nat_1(G,np__1)) ) ) ) ) ) ) ) ) ) ) )).

fof(t8_scm_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( v1_relat_1(E)
        & v1_funct_1(E)
        & v1_finseq_1(E) )
     => ( E = k7_finseq_1(k7_finseq_1(k7_finseq_1(k9_finseq_1(A),k9_finseq_1(B)),k9_finseq_1(C)),k9_finseq_1(D))
       => ( k3_finseq_1(E) = np__4
          & k1_funct_1(E,np__1) = A
          & k1_funct_1(E,np__2) = B
          & k1_funct_1(E,np__3) = C
          & k1_funct_1(E,np__4) = D ) ) ) )).

fof(t9_scm_1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( v1_relat_1(F)
        & v1_funct_1(F)
        & v1_finseq_1(F) )
     => ( F = k7_finseq_1(k7_finseq_1(k7_finseq_1(k7_finseq_1(k9_finseq_1(A),k9_finseq_1(B)),k9_finseq_1(C)),k9_finseq_1(D)),k9_finseq_1(E))
       => ( k3_finseq_1(F) = np__5
          & k1_funct_1(F,np__1) = A
          & k1_funct_1(F,np__2) = B
          & k1_funct_1(F,np__3) = C
          & k1_funct_1(F,np__4) = D
          & k1_funct_1(F,np__5) = E ) ) ) )).

fof(t10_scm_1,axiom,(
    ! [A,B,C,D,E,F,G] :
      ( ( v1_relat_1(G)
        & v1_funct_1(G)
        & v1_finseq_1(G) )
     => ( G = k7_finseq_1(k7_finseq_1(k7_finseq_1(k7_finseq_1(k7_finseq_1(k9_finseq_1(A),k9_finseq_1(B)),k9_finseq_1(C)),k9_finseq_1(D)),k9_finseq_1(E)),k9_finseq_1(F))
       => ( k3_finseq_1(G) = np__6
          & k1_funct_1(G,np__1) = A
          & k1_funct_1(G,np__2) = B
          & k1_funct_1(G,np__3) = C
          & k1_funct_1(G,np__4) = D
          & k1_funct_1(G,np__5) = E
          & k1_funct_1(G,np__6) = F ) ) ) )).

fof(t11_scm_1,axiom,(
    ! [A,B,C,D,E,F,G,H] :
      ( ( v1_relat_1(H)
        & v1_funct_1(H)
        & v1_finseq_1(H) )
     => ( H = k7_finseq_1(k7_finseq_1(k7_finseq_1(k7_finseq_1(k7_finseq_1(k7_finseq_1(k9_finseq_1(A),k9_finseq_1(B)),k9_finseq_1(C)),k9_finseq_1(D)),k9_finseq_1(E)),k9_finseq_1(F)),k9_finseq_1(G))
       => ( k3_finseq_1(H) = np__7
          & k1_funct_1(H,np__1) = A
          & k1_funct_1(H,np__2) = B
          & k1_funct_1(H,np__3) = C
          & k1_funct_1(H,np__4) = D
          & k1_funct_1(H,np__5) = E
          & k1_funct_1(H,np__6) = F
          & k1_funct_1(H,np__7) = G ) ) ) )).

fof(t12_scm_1,axiom,(
    ! [A,B,C,D,E,F,G,H,I] :
      ( ( v1_relat_1(I)
        & v1_funct_1(I)
        & v1_finseq_1(I) )
     => ( I = k7_finseq_1(k7_finseq_1(k7_finseq_1(k7_finseq_1(k7_finseq_1(k7_finseq_1(k7_finseq_1(k9_finseq_1(A),k9_finseq_1(B)),k9_finseq_1(C)),k9_finseq_1(D)),k9_finseq_1(E)),k9_finseq_1(F)),k9_finseq_1(G)),k9_finseq_1(H))
       => ( k3_finseq_1(I) = np__8
          & k1_funct_1(I,np__1) = A
          & k1_funct_1(I,np__2) = B
          & k1_funct_1(I,np__3) = C
          & k1_funct_1(I,np__4) = D
          & k1_funct_1(I,np__5) = E
          & k1_funct_1(I,np__6) = F
          & k1_funct_1(I,np__7) = G
          & k1_funct_1(I,np__8) = H ) ) ) )).

fof(t13_scm_1,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J] :
      ( ( v1_relat_1(J)
        & v1_funct_1(J)
        & v1_finseq_1(J) )
     => ( J = k7_finseq_1(k7_finseq_1(k7_finseq_1(k7_finseq_1(k7_finseq_1(k7_finseq_1(k7_finseq_1(k7_finseq_1(k9_finseq_1(A),k9_finseq_1(B)),k9_finseq_1(C)),k9_finseq_1(D)),k9_finseq_1(E)),k9_finseq_1(F)),k9_finseq_1(G)),k9_finseq_1(H)),k9_finseq_1(I))
       => ( k3_finseq_1(J) = np__9
          & k1_funct_1(J,np__1) = A
          & k1_funct_1(J,np__2) = B
          & k1_funct_1(J,np__3) = C
          & k1_funct_1(J,np__4) = D
          & k1_funct_1(J,np__5) = E
          & k1_funct_1(J,np__6) = F
          & k1_funct_1(J,np__7) = G
          & k1_funct_1(J,np__8) = H
          & k1_funct_1(J,np__9) = I ) ) ) )).

fof(t14_scm_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => ! [B] :
          ( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
         => ! [C] :
              ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
             => ! [D] :
                  ( m2_subset_1(D,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
                 => ! [E] :
                      ( m2_subset_1(E,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
                     => ! [F] :
                          ( m2_subset_1(F,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
                         => ! [G] :
                              ( m2_subset_1(G,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
                             => ! [H] :
                                  ( m2_subset_1(H,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
                                 => ! [I] :
                                      ( m2_subset_1(I,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
                                     => ! [J] :
                                          ( v1_int_1(J)
                                         => ! [K] :
                                              ( v1_int_1(K)
                                             => ! [L] :
                                                  ( v1_int_1(L)
                                                 => ! [M] :
                                                      ( v1_int_1(M)
                                                     => ! [N] :
                                                          ( m2_subset_1(N,k1_numbers,k5_numbers)
                                                         => ! [O] :
                                                              ( m1_scm_1(O,k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),A),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),B)),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),C)),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),D)),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),E)),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),F)),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),G)),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),H)),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),I)),k8_finseq_1(k4_numbers,k8_finseq_1(k4_numbers,k8_finseq_1(k4_numbers,k1_scm_1(J),k1_scm_1(K)),k1_scm_1(L)),k1_scm_1(M)),N,np__0,np__0)
                                                             => ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,O) = k16_ami_3(N)
                                                                & k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,O,k16_ami_3(np__0)) = A
                                                                & k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,O,k16_ami_3(np__1)) = B
                                                                & k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,O,k16_ami_3(np__2)) = C
                                                                & k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,O,k16_ami_3(np__3)) = D
                                                                & k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,O,k16_ami_3(np__4)) = E
                                                                & k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,O,k16_ami_3(np__5)) = F
                                                                & k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,O,k16_ami_3(np__6)) = G
                                                                & k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,O,k16_ami_3(np__7)) = H
                                                                & k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,O,k16_ami_3(np__8)) = I
                                                                & k2_ami_3(O,k15_ami_3(np__0)) = J
                                                                & k2_ami_3(O,k15_ami_3(np__1)) = K
                                                                & k2_ami_3(O,k15_ami_3(np__2)) = L
                                                                & k2_ami_3(O,k15_ami_3(np__3)) = M ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t15_scm_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => ! [B] :
          ( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
         => ! [C] :
              ( v1_int_1(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( m1_scm_1(F,k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),A),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),B)),k8_finseq_1(k4_numbers,k1_scm_1(C),k1_scm_1(D)),E,np__0,np__0)
                         => ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,F) = k16_ami_3(E)
                            & k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,F,k16_ami_3(np__0)) = A
                            & k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,F,k16_ami_3(np__1)) = B
                            & k2_ami_3(F,k15_ami_3(np__0)) = C
                            & k2_ami_3(F,k15_ami_3(np__1)) = D ) ) ) ) ) ) ) )).

fof(d2_scm_1,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
             => ( v9_ami_1(C,A,B)
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( D = k2_scm_1(A,B,C)
                    <=> ( k8_ami_1(A,B,k11_ami_1(A,B,k10_ami_1(A,B,C),D)) = k5_ami_1(A,B)
                        & ! [E] :
                            ( m2_subset_1(E,k1_numbers,k5_numbers)
                           => ( k8_ami_1(A,B,k11_ami_1(A,B,k10_ami_1(A,B,C),E)) = k5_ami_1(A,B)
                             => r1_xreal_0(D,E) ) ) ) ) ) ) ) ) ) )).

fof(t16_scm_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ( k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,A,k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,A),k1_nat_1(B,np__1)))) = k5_ami_1(k1_tarski(k4_numbers),k1_ami_3)
             => ( k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,A,k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,A),B))) = k5_ami_1(k1_tarski(k4_numbers),k1_ami_3)
                | ( k2_scm_1(k1_tarski(k4_numbers),k1_ami_3,A) = k1_nat_1(B,np__1)
                  & v9_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) ) ) )
            & ( ( k2_scm_1(k1_tarski(k4_numbers),k1_ami_3,A) = k1_nat_1(B,np__1)
                & v9_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) )
             => ( k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,A,k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,A),B))) != k5_ami_1(k1_tarski(k4_numbers),k1_ami_3)
                & k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,A,k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,A),k1_nat_1(B,np__1)))) = k5_ami_1(k1_tarski(k4_numbers),k1_ami_3) ) ) ) ) ) )).

fof(t17_scm_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,A,k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,A),k1_nat_1(B,np__1)))) = k5_ami_1(k1_tarski(k4_numbers),k1_ami_3)
           => ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,A),B)) = k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,A),k1_nat_1(B,np__1)))
              | k2_scm_1(k1_tarski(k4_numbers),k1_ami_3,A) = k1_nat_1(B,np__1) ) ) ) ) )).

fof(t18_scm_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
             => ! [D] :
                  ( m1_ami_3(D)
                 => ! [E] :
                      ( m1_ami_3(E)
                     => ( ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A)) = k16_ami_3(B)
                          & k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,C,k16_ami_3(B)) = k3_ami_3(D,E) )
                       => ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1))) = k16_ami_3(k1_nat_1(B,np__1))
                          & k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1)),D) = k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),E)
                          & ! [F] :
                              ( m1_ami_3(F)
                             => ( F != D
                               => k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1)),F) = k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),F) ) ) ) ) ) ) ) ) ) )).

fof(t19_scm_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
             => ! [D] :
                  ( m1_ami_3(D)
                 => ! [E] :
                      ( m1_ami_3(E)
                     => ( ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A)) = k16_ami_3(B)
                          & k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,C,k16_ami_3(B)) = k4_ami_3(D,E) )
                       => ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1))) = k16_ami_3(k1_nat_1(B,np__1))
                          & k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1)),D) = k2_xcmplx_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),D),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),E))
                          & ! [F] :
                              ( m1_ami_3(F)
                             => ( F != D
                               => k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1)),F) = k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),F) ) ) ) ) ) ) ) ) ) )).

fof(t20_scm_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
             => ! [D] :
                  ( m1_ami_3(D)
                 => ! [E] :
                      ( m1_ami_3(E)
                     => ( ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A)) = k16_ami_3(B)
                          & k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,C,k16_ami_3(B)) = k5_ami_3(D,E) )
                       => ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1))) = k16_ami_3(k1_nat_1(B,np__1))
                          & k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1)),D) = k6_xcmplx_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),D),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),E))
                          & ! [F] :
                              ( m1_ami_3(F)
                             => ( F != D
                               => k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1)),F) = k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),F) ) ) ) ) ) ) ) ) ) )).

fof(t21_scm_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
             => ! [D] :
                  ( m1_ami_3(D)
                 => ! [E] :
                      ( m1_ami_3(E)
                     => ( ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A)) = k16_ami_3(B)
                          & k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,C,k16_ami_3(B)) = k6_ami_3(D,E) )
                       => ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1))) = k16_ami_3(k1_nat_1(B,np__1))
                          & k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1)),D) = k3_xcmplx_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),D),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),E))
                          & ! [F] :
                              ( m1_ami_3(F)
                             => ( F != D
                               => k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1)),F) = k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),F) ) ) ) ) ) ) ) ) ) )).

fof(t22_scm_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
             => ! [D] :
                  ( m1_ami_3(D)
                 => ! [E] :
                      ( m1_ami_3(E)
                     => ( ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A)) = k16_ami_3(B)
                          & k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,C,k16_ami_3(B)) = k7_ami_3(D,E) )
                       => ( D = E
                          | ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1))) = k16_ami_3(k1_nat_1(B,np__1))
                            & k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1)),D) = k5_int_1(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),D),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),E))
                            & k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1)),E) = k6_int_1(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),D),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),E))
                            & ! [F] :
                                ( m1_ami_3(F)
                               => ~ ( F != D
                                    & F != E
                                    & k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1)),F) != k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),F) ) ) ) ) ) ) ) ) ) ) )).

fof(t23_scm_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
             => ! [D] :
                  ( m1_struct_0(D,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
                 => ( ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A)) = k16_ami_3(B)
                      & k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,C,k16_ami_3(B)) = k8_ami_3(D) )
                   => ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1))) = D
                      & ! [E] :
                          ( m1_ami_3(E)
                         => k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1)),E) = k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),E) ) ) ) ) ) ) ) )).

fof(t24_scm_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
             => ! [D] :
                  ( m1_ami_3(D)
                 => ! [E] :
                      ( m1_struct_0(E,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
                     => ( ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A)) = k16_ami_3(B)
                          & k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,C,k16_ami_3(B)) = k9_ami_3(E,D) )
                       => ( ( k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),D) = np__0
                           => k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1))) = E )
                          & ( k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),D) != np__0
                           => k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1))) = k16_ami_3(k1_nat_1(B,np__1)) )
                          & ! [F] :
                              ( m1_ami_3(F)
                             => k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1)),F) = k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),F) ) ) ) ) ) ) ) ) )).

fof(t25_scm_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
             => ! [D] :
                  ( m1_ami_3(D)
                 => ! [E] :
                      ( m1_struct_0(E,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
                     => ( ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A)) = k16_ami_3(B)
                          & k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,C,k16_ami_3(B)) = k10_ami_3(E,D) )
                       => ( ( ~ r1_xreal_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),D),np__0)
                           => k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1))) = E )
                          & ( r1_xreal_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),D),np__0)
                           => k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1))) = k16_ami_3(k1_nat_1(B,np__1)) )
                          & ! [F] :
                              ( m1_ami_3(F)
                             => k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,np__1)),F) = k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),F) ) ) ) ) ) ) ) ) )).

fof(t26_scm_1,axiom,
    ( k1_mcart_1(k5_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = np__0
    & ! [A] :
        ( m1_ami_3(A)
       => ! [B] :
            ( m1_ami_3(B)
           => k1_mcart_1(k3_ami_3(A,B)) = np__1 ) )
    & ! [A] :
        ( m1_ami_3(A)
       => ! [B] :
            ( m1_ami_3(B)
           => k1_mcart_1(k4_ami_3(A,B)) = np__2 ) )
    & ! [A] :
        ( m1_ami_3(A)
       => ! [B] :
            ( m1_ami_3(B)
           => k1_mcart_1(k5_ami_3(A,B)) = np__3 ) )
    & ! [A] :
        ( m1_ami_3(A)
       => ! [B] :
            ( m1_ami_3(B)
           => k1_mcart_1(k6_ami_3(A,B)) = np__4 ) )
    & ! [A] :
        ( m1_ami_3(A)
       => ! [B] :
            ( m1_ami_3(B)
           => k1_mcart_1(k7_ami_3(A,B)) = np__5 ) )
    & ! [A] :
        ( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
       => k1_mcart_1(k8_ami_3(A)) = np__6 )
    & ! [A] :
        ( m1_ami_3(A)
       => ! [B] :
            ( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
           => k1_mcart_1(k9_ami_3(B,A)) = np__7 ) )
    & ! [A] :
        ( m1_ami_3(A)
       => ! [B] :
            ( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
           => k1_mcart_1(k10_ami_3(B,A)) = np__8 ) ) )).

fof(t27_scm_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_setfam_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( v9_ami_1(C,A,B)
                  <=> v9_ami_1(k11_ami_1(A,B,k10_ami_1(A,B,C),D),A,B) ) ) ) ) ) )).

fof(t28_scm_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( ( B = k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,A),C)
                      & k2_scm_1(k1_tarski(k4_numbers),k1_ami_3,B) = D
                      & v9_ami_1(B,k1_tarski(k4_numbers),k1_ami_3) )
                   => ( r1_xreal_0(D,np__0)
                      | k2_scm_1(k1_tarski(k4_numbers),k1_ami_3,A) = k1_nat_1(C,D) ) ) ) ) ) ) )).

fof(t29_scm_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( B = k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,A),C)
                  & v9_ami_1(B,k1_tarski(k4_numbers),k1_ami_3) )
               => k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,B) = k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,A) ) ) ) ) )).

fof(t30_scm_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => ! [B] :
          ( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
         => ! [C] :
              ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
             => ! [D] :
                  ( m2_subset_1(D,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
                 => ! [E] :
                      ( m2_subset_1(E,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
                     => ! [F] :
                          ( m2_subset_1(F,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
                         => ! [G] :
                              ( m2_subset_1(G,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
                             => ! [H] :
                                  ( m2_subset_1(H,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
                                 => ! [I] :
                                      ( m2_subset_1(I,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
                                     => ! [J] :
                                          ( v1_int_1(J)
                                         => ! [K] :
                                              ( v1_int_1(K)
                                             => ! [L] :
                                                  ( v1_int_1(L)
                                                 => ! [M] :
                                                      ( v1_int_1(M)
                                                     => ! [N] :
                                                          ( m2_subset_1(N,k1_numbers,k5_numbers)
                                                         => ! [O] :
                                                              ( m1_subset_1(O,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
                                                             => ( ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,O) = k16_ami_3(N)
                                                                  & k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,O,k16_ami_3(np__0)) = A
                                                                  & k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,O,k16_ami_3(np__1)) = B
                                                                  & k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,O,k16_ami_3(np__2)) = C
                                                                  & k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,O,k16_ami_3(np__3)) = D
                                                                  & k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,O,k16_ami_3(np__4)) = E
                                                                  & k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,O,k16_ami_3(np__5)) = F
                                                                  & k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,O,k16_ami_3(np__6)) = G
                                                                  & k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,O,k16_ami_3(np__7)) = H
                                                                  & k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,O,k16_ami_3(np__8)) = I
                                                                  & k2_ami_3(O,k15_ami_3(np__0)) = J
                                                                  & k2_ami_3(O,k15_ami_3(np__1)) = K
                                                                  & k2_ami_3(O,k15_ami_3(np__2)) = L
                                                                  & k2_ami_3(O,k15_ami_3(np__3)) = M )
                                                               => m1_scm_1(O,k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),A),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),B)),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),C)),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),D)),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),E)),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),F)),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),G)),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),H)),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),I)),k8_finseq_1(k4_numbers,k8_finseq_1(k4_numbers,k8_finseq_1(k4_numbers,k1_scm_1(J),k1_scm_1(K)),k1_scm_1(L)),k1_scm_1(M)),N,np__0,np__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t31_scm_1,axiom,(
    ! [A] :
      ( m1_scm_1(A,k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k5_ami_1(k1_tarski(k4_numbers),k1_ami_3)),k6_finseq_1(k4_numbers),np__0,np__0,np__0)
     => ( v9_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
        & k2_scm_1(k1_tarski(k4_numbers),k1_ami_3,A) = np__0
        & k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,A) = A ) ) )).

fof(t32_scm_1,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m1_scm_1(C,k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k3_ami_3(k15_ami_3(np__0),k15_ami_3(np__1))),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k5_ami_1(k1_tarski(k4_numbers),k1_ami_3))),k8_finseq_1(k4_numbers,k1_scm_1(A),k1_scm_1(B)),np__0,np__0,np__0)
             => ( v9_ami_1(C,k1_tarski(k4_numbers),k1_ami_3)
                & k2_scm_1(k1_tarski(k4_numbers),k1_ami_3,C) = np__1
                & k2_ami_3(k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k15_ami_3(np__0)) = B
                & ! [D] :
                    ( m1_ami_3(D)
                   => ( D != k15_ami_3(np__0)
                     => k2_ami_3(k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D) = k2_ami_3(C,D) ) ) ) ) ) ) )).

fof(t33_scm_1,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m1_scm_1(C,k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k4_ami_3(k15_ami_3(np__0),k15_ami_3(np__1))),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k5_ami_1(k1_tarski(k4_numbers),k1_ami_3))),k8_finseq_1(k4_numbers,k1_scm_1(A),k1_scm_1(B)),np__0,np__0,np__0)
             => ( v9_ami_1(C,k1_tarski(k4_numbers),k1_ami_3)
                & k2_scm_1(k1_tarski(k4_numbers),k1_ami_3,C) = np__1
                & k2_ami_3(k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k15_ami_3(np__0)) = k2_xcmplx_0(A,B)
                & ! [D] :
                    ( m1_ami_3(D)
                   => ( D != k15_ami_3(np__0)
                     => k2_ami_3(k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D) = k2_ami_3(C,D) ) ) ) ) ) ) )).

fof(t34_scm_1,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m1_scm_1(C,k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k5_ami_3(k15_ami_3(np__0),k15_ami_3(np__1))),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k5_ami_1(k1_tarski(k4_numbers),k1_ami_3))),k8_finseq_1(k4_numbers,k1_scm_1(A),k1_scm_1(B)),np__0,np__0,np__0)
             => ( v9_ami_1(C,k1_tarski(k4_numbers),k1_ami_3)
                & k2_scm_1(k1_tarski(k4_numbers),k1_ami_3,C) = np__1
                & k2_ami_3(k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k15_ami_3(np__0)) = k6_xcmplx_0(A,B)
                & ! [D] :
                    ( m1_ami_3(D)
                   => ( D != k15_ami_3(np__0)
                     => k2_ami_3(k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D) = k2_ami_3(C,D) ) ) ) ) ) ) )).

fof(t35_scm_1,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m1_scm_1(C,k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k6_ami_3(k15_ami_3(np__0),k15_ami_3(np__1))),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k5_ami_1(k1_tarski(k4_numbers),k1_ami_3))),k8_finseq_1(k4_numbers,k1_scm_1(A),k1_scm_1(B)),np__0,np__0,np__0)
             => ( v9_ami_1(C,k1_tarski(k4_numbers),k1_ami_3)
                & k2_scm_1(k1_tarski(k4_numbers),k1_ami_3,C) = np__1
                & k2_ami_3(k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k15_ami_3(np__0)) = k3_xcmplx_0(A,B)
                & ! [D] :
                    ( m1_ami_3(D)
                   => ( D != k15_ami_3(np__0)
                     => k2_ami_3(k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D) = k2_ami_3(C,D) ) ) ) ) ) ) )).

fof(t36_scm_1,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m1_scm_1(C,k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k7_ami_3(k15_ami_3(np__0),k15_ami_3(np__1))),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k5_ami_1(k1_tarski(k4_numbers),k1_ami_3))),k8_finseq_1(k4_numbers,k1_scm_1(A),k1_scm_1(B)),np__0,np__0,np__0)
             => ( v9_ami_1(C,k1_tarski(k4_numbers),k1_ami_3)
                & k2_scm_1(k1_tarski(k4_numbers),k1_ami_3,C) = np__1
                & k2_ami_3(k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k15_ami_3(np__0)) = k5_int_1(A,B)
                & k2_ami_3(k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k15_ami_3(np__1)) = k6_int_1(A,B)
                & ! [D] :
                    ( m1_ami_3(D)
                   => ~ ( D != k15_ami_3(np__0)
                        & D != k15_ami_3(np__1)
                        & k2_ami_3(k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D) != k2_ami_3(C,D) ) ) ) ) ) ) )).

fof(t37_scm_1,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m1_scm_1(C,k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_ami_3(k16_ami_3(np__1))),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k5_ami_1(k1_tarski(k4_numbers),k1_ami_3))),k8_finseq_1(k4_numbers,k1_scm_1(A),k1_scm_1(B)),np__0,np__0,np__0)
             => ( v9_ami_1(C,k1_tarski(k4_numbers),k1_ami_3)
                & k2_scm_1(k1_tarski(k4_numbers),k1_ami_3,C) = np__1
                & ! [D] :
                    ( m1_ami_3(D)
                   => k2_ami_3(k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D) = k2_ami_3(C,D) ) ) ) ) ) )).

fof(t38_scm_1,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m1_scm_1(C,k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k9_ami_3(k16_ami_3(np__1),k15_ami_3(np__0))),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k5_ami_1(k1_tarski(k4_numbers),k1_ami_3))),k8_finseq_1(k4_numbers,k1_scm_1(A),k1_scm_1(B)),np__0,np__0,np__0)
             => ( v9_ami_1(C,k1_tarski(k4_numbers),k1_ami_3)
                & k2_scm_1(k1_tarski(k4_numbers),k1_ami_3,C) = np__1
                & ! [D] :
                    ( m1_ami_3(D)
                   => k2_ami_3(k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D) = k2_ami_3(C,D) ) ) ) ) ) )).

fof(t39_scm_1,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m1_scm_1(C,k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k10_ami_3(k16_ami_3(np__1),k15_ami_3(np__0))),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k5_ami_1(k1_tarski(k4_numbers),k1_ami_3))),k8_finseq_1(k4_numbers,k1_scm_1(A),k1_scm_1(B)),np__0,np__0,np__0)
             => ( v9_ami_1(C,k1_tarski(k4_numbers),k1_ami_3)
                & k2_scm_1(k1_tarski(k4_numbers),k1_ami_3,C) = np__1
                & ! [D] :
                    ( m1_ami_3(D)
                   => k2_ami_3(k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D) = k2_ami_3(C,D) ) ) ) ) ) )).

fof(dt_m1_scm_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( m1_finseq_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
        & m1_finseq_1(B,k4_numbers)
        & m1_subset_1(C,k5_numbers)
        & m1_subset_1(D,k5_numbers)
        & m1_subset_1(E,k5_numbers) )
     => ! [F] :
          ( m1_scm_1(F,A,B,C,D,E)
         => m1_subset_1(F,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) ) ) )).

fof(existence_m1_scm_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( m1_finseq_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
        & m1_finseq_1(B,k4_numbers)
        & m1_subset_1(C,k5_numbers)
        & m1_subset_1(D,k5_numbers)
        & m1_subset_1(E,k5_numbers) )
     => ? [F] : m1_scm_1(F,A,B,C,D,E) ) )).

fof(dt_k1_scm_1,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => m2_finseq_1(k1_scm_1(A),k4_numbers) ) )).

fof(redefinition_k1_scm_1,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => k1_scm_1(A) = k5_finseq_1(A) ) )).

fof(dt_k2_scm_1,axiom,(
    ! [A,B,C] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v4_ami_1(B,A)
        & v5_ami_1(B,A)
        & v8_ami_1(B,A)
        & l1_ami_1(B,A)
        & m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) )
     => m2_subset_1(k2_scm_1(A,B,C),k1_numbers,k5_numbers) ) )).
%------------------------------------------------------------------------------