SET007 Axioms: SET007+607.ax


%------------------------------------------------------------------------------
% File     : SET007+607 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : The Construction and Shiftability of Program Blocks for SCMPDS
% 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    : scmpds_4 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  136 (   5 unit)
%            Number of atoms       :  819 (  90 equality)
%            Maximal formula depth :   19 (   7 average)
%            Number of connectives :  723 (  40 ~  ;   3  |; 389  &)
%                                         (   8 <=>; 283 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   26 (   1 propositional; 0-3 arity)
%            Number of functors    :   85 (  14 constant; 0-5 arity)
%            Number of variables   :  308 (   0 singleton; 303 !;   5 ?)
%            Maximal term depth    :    6 (   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_scmpds_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ( ~ v1_xboole_0(k1_scmpds_4(A))
        & v1_relat_1(k1_scmpds_4(A))
        & v1_funct_1(k1_scmpds_4(A))
        & v1_finset_1(k1_scmpds_4(A))
        & v1_ami_3(k1_scmpds_4(A),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k1_scmpds_4(A)) ) ) )).

fof(fc2_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ( v1_relat_1(k6_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A))
        & v1_funct_1(k6_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A))
        & v1_finset_1(k6_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A))
        & v1_ami_3(k6_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k6_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A)) ) ) )).

fof(rc1_scmpds_4,axiom,(
    ? [A] :
      ( m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
      & v1_scmpds_3(A)
      & v2_scmpds_4(A) ) )).

fof(fc3_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & v2_scmpds_4(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ( v1_relat_1(k2_scmpds_4(k8_scmpds_4(A)))
        & v1_funct_1(k2_scmpds_4(k8_scmpds_4(A)))
        & v1_finset_1(k2_scmpds_4(k8_scmpds_4(A)))
        & v12_ami_1(k2_scmpds_4(k8_scmpds_4(A)),k1_tarski(k4_numbers),k1_scmpds_2) ) ) )).

fof(cc1_scmpds_4,axiom,(
    ! [A] :
      ( m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
     => ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
          & v1_scmpds_3(A)
          & v2_scmpds_4(A) )
       => ( v1_relat_1(A)
          & v1_funct_1(A)
          & v1_finset_1(A)
          & v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
          & v1_scmpds_3(A)
          & v1_scmpds_4(A) ) ) ) )).

fof(rc2_scmpds_4,axiom,(
    ? [A] :
      ( m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
      & v1_scmpds_3(A)
      & v1_scmpds_4(A)
      & v2_scmpds_4(A)
      & v3_scmpds_4(A) ) )).

fof(rc3_scmpds_4,axiom,(
    ? [A] :
      ( m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
      & v4_scmpds_4(A) ) )).

fof(fc4_scmpds_4,axiom,(
    ! [A,B] :
      ( ( m1_scmpds_2(A)
        & v1_int_1(B) )
     => v4_scmpds_4(k6_scmpds_2(A,B)) ) )).

fof(fc5_scmpds_4,axiom,(
    ! [A,B,C] :
      ( ( m1_scmpds_2(A)
        & v1_int_1(B)
        & v1_int_1(C) )
     => v4_scmpds_4(k11_scmpds_2(A,B,C)) ) )).

fof(fc6_scmpds_4,axiom,(
    ! [A,B,C] :
      ( ( m1_scmpds_2(A)
        & v1_int_1(B)
        & v1_int_1(C) )
     => v4_scmpds_4(k12_scmpds_2(A,B,C)) ) )).

fof(fc7_scmpds_4,axiom,(
    ! [A,B,C,D] :
      ( ( m1_scmpds_2(A)
        & m1_scmpds_2(B)
        & v1_int_1(C)
        & v1_int_1(D) )
     => v4_scmpds_4(k13_scmpds_2(A,B,C,D)) ) )).

fof(fc8_scmpds_4,axiom,(
    ! [A,B,C,D] :
      ( ( m1_scmpds_2(A)
        & m1_scmpds_2(B)
        & v1_int_1(C)
        & v1_int_1(D) )
     => v4_scmpds_4(k14_scmpds_2(A,B,C,D)) ) )).

fof(fc9_scmpds_4,axiom,(
    ! [A,B,C,D] :
      ( ( m1_scmpds_2(A)
        & m1_scmpds_2(B)
        & v1_int_1(C)
        & v1_int_1(D) )
     => v4_scmpds_4(k15_scmpds_2(A,B,C,D)) ) )).

fof(fc10_scmpds_4,axiom,(
    ! [A,B,C,D] :
      ( ( m1_scmpds_2(A)
        & m1_scmpds_2(B)
        & v1_int_1(C)
        & v1_int_1(D) )
     => v4_scmpds_4(k16_scmpds_2(A,B,C,D)) ) )).

fof(fc11_scmpds_4,axiom,(
    ! [A,B,C,D] :
      ( ( m1_scmpds_2(A)
        & m1_scmpds_2(B)
        & v1_int_1(C)
        & v1_int_1(D) )
     => v4_scmpds_4(k17_scmpds_2(A,B,C,D)) ) )).

fof(fc12_scmpds_4,axiom,(
    ! [A,B] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & v3_scmpds_4(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(B)
        & v3_scmpds_4(B)
        & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ( v1_relat_1(k3_scmpds_4(A,B))
        & v1_funct_1(k3_scmpds_4(A,B))
        & v1_finset_1(k3_scmpds_4(A,B))
        & v1_ami_3(k3_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k3_scmpds_4(A,B))
        & v3_scmpds_4(k3_scmpds_4(A,B)) ) ) )).

fof(fc13_scmpds_4,axiom,(
    ! [A] :
      ( ( v4_scmpds_4(A)
        & m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) )
     => ( ~ v1_xboole_0(k1_scmpds_4(A))
        & v1_relat_1(k1_scmpds_4(A))
        & v1_funct_1(k1_scmpds_4(A))
        & v1_finset_1(k1_scmpds_4(A))
        & v1_ami_3(k1_scmpds_4(A),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k1_scmpds_4(A))
        & v3_scmpds_4(k1_scmpds_4(A)) ) ) )).

fof(fc14_scmpds_4,axiom,(
    ! [A,B] :
      ( ( v4_scmpds_4(A)
        & m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
        & v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(B)
        & v3_scmpds_4(B)
        & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ( v1_relat_1(k4_scmpds_4(A,B))
        & v1_funct_1(k4_scmpds_4(A,B))
        & v1_finset_1(k4_scmpds_4(A,B))
        & v1_ami_3(k4_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k4_scmpds_4(A,B))
        & v3_scmpds_4(k4_scmpds_4(A,B)) ) ) )).

fof(fc15_scmpds_4,axiom,(
    ! [A,B] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & v3_scmpds_4(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v4_scmpds_4(B)
        & m1_subset_1(B,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) )
     => ( v1_relat_1(k5_scmpds_4(A,B))
        & v1_funct_1(k5_scmpds_4(A,B))
        & v1_finset_1(k5_scmpds_4(A,B))
        & v1_ami_3(k5_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k5_scmpds_4(A,B))
        & v3_scmpds_4(k5_scmpds_4(A,B)) ) ) )).

fof(fc16_scmpds_4,axiom,(
    ! [A,B] :
      ( ( v4_scmpds_4(A)
        & m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
        & v4_scmpds_4(B)
        & m1_subset_1(B,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) )
     => ( v1_relat_1(k6_scmpds_4(A,B))
        & v1_funct_1(k6_scmpds_4(A,B))
        & v1_finset_1(k6_scmpds_4(A,B))
        & v1_ami_3(k6_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k6_scmpds_4(A,B))
        & v3_scmpds_4(k6_scmpds_4(A,B)) ) ) )).

fof(fc17_scmpds_4,axiom,
    ( ~ v1_xboole_0(k5_scmpds_3)
    & v1_relat_1(k5_scmpds_3)
    & v1_funct_1(k5_scmpds_3)
    & v1_finset_1(k5_scmpds_3)
    & v1_ami_3(k5_scmpds_3,k1_tarski(k4_numbers),k1_scmpds_2)
    & v1_scmpds_3(k5_scmpds_3)
    & v1_scmpds_4(k5_scmpds_3)
    & v2_scmpds_4(k5_scmpds_3)
    & v3_scmpds_4(k5_scmpds_3) )).

fof(fc18_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & v3_scmpds_4(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ( v1_relat_1(k8_scmpds_4(A))
        & v1_funct_1(k8_scmpds_4(A))
        & v1_finset_1(k8_scmpds_4(A))
        & v1_ami_3(k8_scmpds_4(A),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k8_scmpds_4(A))
        & v3_scmpds_4(k8_scmpds_4(A)) ) ) )).

fof(fc19_scmpds_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => ( ~ v1_xboole_0(k1_scmpds_4(k4_scmpds_2(A)))
        & v1_relat_1(k1_scmpds_4(k4_scmpds_2(A)))
        & v1_funct_1(k1_scmpds_4(k4_scmpds_2(A)))
        & v1_finset_1(k1_scmpds_4(k4_scmpds_2(A)))
        & v1_ami_3(k1_scmpds_4(k4_scmpds_2(A)),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k1_scmpds_4(k4_scmpds_2(A)))
        & v3_scmpds_4(k1_scmpds_4(k4_scmpds_2(A))) ) ) )).

fof(fc20_scmpds_4,axiom,(
    ! [A,B,C] :
      ( ( v1_int_1(A)
        & m1_scmpds_2(B)
        & m1_subset_1(C,k5_numbers) )
     => ( ~ v1_xboole_0(k1_scmpds_4(k8_scmpds_2(B,A,C)))
        & v1_relat_1(k1_scmpds_4(k8_scmpds_2(B,A,C)))
        & v1_funct_1(k1_scmpds_4(k8_scmpds_2(B,A,C)))
        & v1_finset_1(k1_scmpds_4(k8_scmpds_2(B,A,C)))
        & v1_ami_3(k1_scmpds_4(k8_scmpds_2(B,A,C)),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k1_scmpds_4(k8_scmpds_2(B,A,C)))
        & v3_scmpds_4(k1_scmpds_4(k8_scmpds_2(B,A,C))) ) ) )).

fof(fc21_scmpds_4,axiom,(
    ! [A,B,C] :
      ( ( v1_int_1(A)
        & m1_scmpds_2(B)
        & m1_subset_1(C,k5_numbers) )
     => ( ~ v1_xboole_0(k1_scmpds_4(k9_scmpds_2(B,A,C)))
        & v1_relat_1(k1_scmpds_4(k9_scmpds_2(B,A,C)))
        & v1_funct_1(k1_scmpds_4(k9_scmpds_2(B,A,C)))
        & v1_finset_1(k1_scmpds_4(k9_scmpds_2(B,A,C)))
        & v1_ami_3(k1_scmpds_4(k9_scmpds_2(B,A,C)),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k1_scmpds_4(k9_scmpds_2(B,A,C)))
        & v3_scmpds_4(k1_scmpds_4(k9_scmpds_2(B,A,C))) ) ) )).

fof(fc22_scmpds_4,axiom,(
    ! [A,B,C] :
      ( ( v1_int_1(A)
        & m1_scmpds_2(B)
        & m1_subset_1(C,k5_numbers) )
     => ( ~ v1_xboole_0(k1_scmpds_4(k10_scmpds_2(B,A,C)))
        & v1_relat_1(k1_scmpds_4(k10_scmpds_2(B,A,C)))
        & v1_funct_1(k1_scmpds_4(k10_scmpds_2(B,A,C)))
        & v1_finset_1(k1_scmpds_4(k10_scmpds_2(B,A,C)))
        & v1_ami_3(k1_scmpds_4(k10_scmpds_2(B,A,C)),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k1_scmpds_4(k10_scmpds_2(B,A,C)))
        & v3_scmpds_4(k1_scmpds_4(k10_scmpds_2(B,A,C))) ) ) )).

fof(d1_scmpds_4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => k1_scmpds_4(A) = k14_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(np__0),A) ) )).

fof(t1_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ~ r1_xreal_0(k4_card_1(A),B)
          <=> r2_hidden(k2_scmpds_3(B),k1_relat_1(A)) ) ) ) )).

fof(t2_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => r1_xboole_0(k1_relat_1(A),k1_relat_1(k6_scmpds_3(B,k4_card_1(A)))) ) ) )).

fof(t3_scmpds_4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => k4_card_1(k6_scmpds_3(B,A)) = k4_card_1(B) ) ) )).

fof(t4_scmpds_4,axiom,(
    ! [A] :
      ( m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
     => ! [B] :
          ( m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2)
         => k6_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k17_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,B)) = k1_scmfsa_4(k1_tarski(k4_numbers),k1_scmpds_2,k6_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A),k6_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,B)) ) ) )).

fof(t5_scmpds_4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2)
         => ! [C] :
              ( m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2)
             => k6_scmpds_3(k6_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k17_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B,C)),A) = k1_scmfsa_4(k1_tarski(k4_numbers),k1_scmpds_2,k6_scmpds_3(k6_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,B),A),k6_scmpds_3(k6_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,C),A)) ) ) ) )).

fof(d2_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => k2_scmpds_4(A) = k17_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(np__0))) ) )).

fof(t6_scmpds_4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
         => ( r2_hidden(k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A),k3_enumset1(np__0,np__1,np__4,np__5,np__6))
            | k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,B),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B)) ) ) ) )).

fof(t7_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => r2_hidden(k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k1_relat_1(k2_scmpds_4(A))) ) )).

fof(t8_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => k13_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_4(A)) = k2_scmpds_3(np__0) ) )).

fof(t9_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => r1_tarski(A,k2_scmpds_4(A)) ) )).

fof(t10_scmpds_4,axiom,(
    $true )).

fof(t11_scmpds_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
         => ( ( k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A) = k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B)
              & ! [C] :
                  ( m1_scmpds_2(C)
                 => k2_scmpds_2(A,C) = k2_scmpds_2(B,C) ) )
           => r1_funct_7(A,B,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) ) )).

fof(t12_scmpds_4,axiom,(
    $true )).

fof(t13_scmpds_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
         => ( r1_funct_7(A,B,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
           => ! [C] :
                ( m1_scmpds_2(C)
               => k2_scmpds_2(A,C) = k2_scmpds_2(B,C) ) ) ) ) )).

fof(t14_scmpds_4,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
             => ! [D] :
                  ( v1_int_1(D)
                 => ( r1_funct_7(B,C,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
                   => k2_scmpds_2(B,k3_scmpds_2(k2_scmpds_2(B,A),D)) = k2_scmpds_2(C,k3_scmpds_2(k2_scmpds_2(C,A),D)) ) ) ) ) ) )).

fof(t15_scmpds_4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
             => ( r1_funct_7(B,C,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
               => r1_funct_7(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,B),k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,C),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) ) ) )).

fof(t16_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => k7_relat_1(k2_scmpds_4(A),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = A ) )).

fof(t17_scmpds_4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ~ ( A != B
              & k3_scmpds_2(A,np__0) = k3_scmpds_2(B,np__0) ) ) ) )).

fof(t18_scmpds_4,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ? [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
          & A = k3_scmpds_2(B,np__0) ) ) )).

fof(t19_scmpds_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => k1_relat_1(A) = k2_xboole_0(k2_xboole_0(k1_struct_0(k1_scmpds_2,k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)),k2_ami_2),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) )).

fof(t20_scmpds_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ~ ( r2_hidden(B,k1_relat_1(A))
            & ~ m1_scmpds_2(B)
            & B != k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)
            & ~ m1_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) )).

fof(t21_scmpds_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
         => ( ! [C] :
                ( m1_struct_0(C,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
               => k13_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,C) = k13_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B,C) )
          <=> k7_relat_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k7_relat_1(B,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) ) )).

fof(t22_scmpds_4,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ~ r2_hidden(A,k2_ami_2) ) )).

fof(t23_scmpds_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
         => ( ! [C] :
                ( m1_scmpds_2(C)
               => k2_scmpds_2(A,C) = k2_scmpds_2(B,C) )
          <=> k7_relat_1(A,k2_ami_2) = k7_relat_1(B,k2_ami_2) ) ) ) )).

fof(t24_scmpds_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
         => ( r1_funct_7(A,B,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
           => k7_relat_1(A,k2_ami_2) = k7_relat_1(B,k2_ami_2) ) ) ) )).

fof(t25_scmpds_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
         => ! [C] : k7_relat_1(k1_funct_4(B,k7_relat_1(A,C)),C) = k7_relat_1(A,C) ) ) )).

fof(t26_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => r1_funct_7(A,B,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) )).

fof(t27_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => k1_relat_1(k2_scmpds_4(A)) = k2_xboole_0(k1_relat_1(A),k1_struct_0(k1_scmpds_2,k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) ) )).

fof(t28_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ~ ( r2_hidden(B,k1_relat_1(k2_scmpds_4(A)))
            & ~ r2_hidden(B,k1_relat_1(A))
            & B != k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) ) ) )).

fof(t29_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => k1_funct_1(k2_scmpds_4(A),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k2_scmpds_3(np__0) ) )).

fof(t30_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ~ r2_hidden(k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k1_relat_1(A)) ) )).

fof(t31_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( m1_scmpds_2(B)
         => ~ r2_hidden(B,k1_relat_1(k2_scmpds_4(A))) ) ) )).

fof(t32_scmpds_4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( r2_hidden(C,k1_relat_1(B))
             => k1_funct_1(B,C) = k1_funct_1(k17_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(A))),C) ) ) ) )).

fof(t33_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( r2_hidden(B,k1_relat_1(A))
         => k1_funct_1(A,B) = k1_funct_1(k2_scmpds_4(A),B) ) ) )).

fof(t34_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
             => ( r1_tarski(k2_scmpds_4(B),C)
               => k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,C,k2_scmpds_4(A)) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,C,A) ) ) ) ) )).

fof(t35_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
             => ( r1_tarski(k2_scmpds_4(B),C)
               => r1_tarski(k2_scmpds_4(A),k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,C,A)) ) ) ) ) )).

fof(t36_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
             => r1_funct_7(k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,C,k2_scmpds_4(A)),k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,C,k2_scmpds_4(B)),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) ) )).

fof(d3_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => k3_scmpds_4(A,B) = k1_scmfsa_4(k1_tarski(k4_numbers),k1_scmpds_2,A,k6_scmpds_3(B,k4_card_1(A))) ) ) )).

fof(t37_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_struct_0(C,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
             => ( r2_hidden(C,k1_relat_1(A))
               => k1_funct_1(k3_scmpds_4(A,B),C) = k1_funct_1(A,C) ) ) ) ) )).

fof(t38_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_struct_0(C,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
             => ( r2_hidden(C,k1_relat_1(B))
               => k1_funct_1(k3_scmpds_4(A,B),k3_scmpds_3(C,k4_card_1(A))) = k1_funct_1(B,C) ) ) ) ) )).

fof(t39_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => r1_tarski(k1_relat_1(A),k1_relat_1(k3_scmpds_4(A,B))) ) ) )).

fof(t40_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => r1_tarski(A,k3_scmpds_4(A,B)) ) ) )).

fof(t41_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => k1_scmfsa_4(k1_tarski(k4_numbers),k1_scmpds_2,A,k3_scmpds_4(A,B)) = k3_scmpds_4(A,B) ) ) )).

fof(t42_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => k17_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_4(A),k3_scmpds_4(A,B)) = k2_scmpds_4(k3_scmpds_4(A,B)) ) ) )).

fof(d4_scmpds_4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => k4_scmpds_4(A,B) = k3_scmpds_4(k1_scmpds_4(A),B) ) ) )).

fof(d5_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
         => k5_scmpds_4(A,B) = k3_scmpds_4(A,k1_scmpds_4(B)) ) ) )).

fof(d6_scmpds_4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ! [B] :
          ( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
         => k6_scmpds_4(A,B) = k3_scmpds_4(k1_scmpds_4(A),k1_scmpds_4(B)) ) ) )).

fof(t43_scmpds_4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ! [B] :
          ( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
         => k6_scmpds_4(A,B) = k5_scmpds_4(k1_scmpds_4(A),B) ) ) )).

fof(t44_scmpds_4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ! [B] :
          ( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
         => k6_scmpds_4(A,B) = k4_scmpds_4(A,k1_scmpds_4(B)) ) ) )).

fof(t45_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => k4_card_1(k3_scmpds_4(A,B)) = k1_nat_1(k4_card_1(A),k4_card_1(B)) ) ) )).

fof(t46_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => k3_scmpds_4(k3_scmpds_4(A,B),C) = k3_scmpds_4(A,k3_scmpds_4(B,C)) ) ) ) )).

fof(t47_scmpds_4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => k5_scmpds_4(k3_scmpds_4(B,C),A) = k3_scmpds_4(B,k5_scmpds_4(C,A)) ) ) ) )).

fof(t48_scmpds_4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => k3_scmpds_4(k5_scmpds_4(B,A),C) = k3_scmpds_4(B,k4_scmpds_4(A,C)) ) ) ) )).

fof(t49_scmpds_4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ! [B] :
          ( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
         => ! [C] :
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => k5_scmpds_4(k5_scmpds_4(C,A),B) = k3_scmpds_4(C,k6_scmpds_4(A,B)) ) ) ) )).

fof(t50_scmpds_4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => k3_scmpds_4(k4_scmpds_4(A,B),C) = k4_scmpds_4(A,k3_scmpds_4(B,C)) ) ) ) )).

fof(t51_scmpds_4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ! [B] :
          ( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
         => ! [C] :
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => k5_scmpds_4(k4_scmpds_4(A,C),B) = k4_scmpds_4(A,k5_scmpds_4(C,B)) ) ) ) )).

fof(t52_scmpds_4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ! [B] :
          ( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
         => ! [C] :
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => k3_scmpds_4(k6_scmpds_4(A,B),C) = k4_scmpds_4(A,k4_scmpds_4(B,C)) ) ) ) )).

fof(t53_scmpds_4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ! [B] :
          ( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
         => ! [C] :
              ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
             => k5_scmpds_4(k6_scmpds_4(A,B),C) = k4_scmpds_4(A,k6_scmpds_4(B,C)) ) ) ) )).

fof(t54_scmpds_4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => r1_xboole_0(k1_relat_1(B),k1_relat_1(k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(A)))) ) ) )).

fof(t55_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => r1_tarski(k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(np__0)),k2_scmpds_4(A)) ) )).

fof(t56_scmpds_4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
             => ( r1_tarski(k17_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(A))),C)
               => r1_tarski(B,C) ) ) ) ) )).

fof(t57_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
         => ( r1_tarski(k2_scmpds_4(A),B)
           => r1_tarski(A,B) ) ) ) )).

fof(t58_scmpds_4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => k7_relat_1(k17_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(A))),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = B ) ) )).

fof(t59_scmpds_4,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( m1_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
         => ~ r2_hidden(A,k1_relat_1(k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,B))) ) ) )).

fof(t60_scmpds_4,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ! [B] :
          ( m1_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
         => ~ r2_hidden(A,k1_relat_1(k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,B))) ) ) )).

fof(t61_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( m1_scmpds_2(B)
         => ! [C] :
              ( m1_struct_0(C,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
             => ~ r2_hidden(B,k1_relat_1(k17_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,C)))) ) ) ) )).

fof(t62_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
         => k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,B,A),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(np__0))) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,B,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(np__0))),A) ) ) )).

fof(d7_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => k8_scmpds_4(A) = k3_scmpds_4(A,k5_scmpds_3) ) )).

fof(d8_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
         => k9_scmpds_4(A,B) = k1_funct_4(k12_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,B,k2_scmpds_4(k8_scmpds_4(A)))),k7_relat_1(B,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) ) ) )).

fof(d9_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ( v1_scmpds_4(A)
      <=> ! [B] :
            ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ( r1_tarski(k2_scmpds_4(k8_scmpds_4(A)),B)
                 => r2_hidden(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),C)),k1_relat_1(k8_scmpds_4(A))) ) ) ) ) ) )).

fof(d10_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ( v2_scmpds_4(A)
      <=> v12_ami_1(k2_scmpds_4(k8_scmpds_4(A)),k1_tarski(k4_numbers),k1_scmpds_2) ) ) )).

fof(t63_scmpds_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & v2_scmpds_4(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ( r1_tarski(k2_scmpds_4(k8_scmpds_4(B)),A)
           => v9_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) )).

fof(t64_scmpds_4,axiom,(
    $true )).

fof(t65_scmpds_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A) != k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A)) ) )).

fof(t66_scmpds_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ~ v9_ami_1(k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k10_scmpds_4(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A)),k4_scmpds_2(np__1),k4_scmpds_2(k4_xcmplx_0(np__1)))),k1_tarski(k4_numbers),k1_scmpds_2) ) )).

fof(t67_scmpds_4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
             => ! [D] :
                  ( m1_subset_1(D,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
                 => ( ( r1_funct_7(C,D,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
                      & r1_tarski(B,C)
                      & r1_tarski(B,D)
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ( ~ r1_xreal_0(A,E)
                           => r2_hidden(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,D),E)),k1_relat_1(B)) ) ) )
                   => ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => ( r1_xreal_0(E,A)
                         => r1_funct_7(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),E),k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,D),E),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) ) ) ) ) ) )).

fof(t68_scmpds_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( m1_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
         => r2_hidden(B,k1_relat_1(A)) ) ) )).

fof(t69_scmpds_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( m1_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
         => ! [C] :
              ( m1_struct_0(C,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
             => ! [D] :
                  ( m2_subset_1(D,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
                 => ! [E] :
                      ( m2_subset_1(E,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
                     => k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k10_scmpds_4(B,C,D,E)) = k2_funct_7(k2_funct_7(A,B,D),C,E) ) ) ) ) ) )).

fof(t70_scmpds_4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k18_scmpds_2(k2_scmpds_3(A)) = k2_scmpds_3(k1_nat_1(A,np__1)) ) )).

fof(t71_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
         => ~ ( ~ r2_hidden(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),k1_relat_1(A))
              & r2_hidden(k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B)),k1_relat_1(A)) ) ) ) )).

fof(t72_scmpds_4,axiom,(
    k1_relat_1(k5_scmpds_3) = k1_struct_0(k1_scmpds_2,k2_scmpds_3(np__0)) )).

fof(t73_scmpds_4,axiom,
    ( r2_hidden(k2_scmpds_3(np__0),k1_relat_1(k5_scmpds_3))
    & k1_funct_1(k5_scmpds_3,k2_scmpds_3(np__0)) = k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) )).

fof(t74_scmpds_4,axiom,(
    k4_card_1(k5_scmpds_3) = np__1 )).

fof(t75_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => r2_hidden(k2_scmpds_3(np__0),k1_relat_1(k8_scmpds_4(A))) ) )).

fof(t76_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m1_struct_0(C,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
             => ( r2_hidden(C,k1_relat_1(A))
               => r2_hidden(k3_scmpds_3(C,B),k1_relat_1(k6_scmpds_3(A,B))) ) ) ) ) )).

fof(d11_scmpds_4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_scmpds_4(A,B)
          <=> ( ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A) = np__0
                  & ! [C] :
                      ( v1_int_1(C)
                     => ~ ( A = k4_scmpds_2(C)
                          & r1_xreal_0(np__0,k2_xcmplx_0(B,C)) ) ) )
              & ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A) = np__4
                  & ! [C] :
                      ( m1_scmpds_2(C)
                     => ! [D] :
                          ( v1_int_1(D)
                         => ! [E] :
                              ( v1_int_1(E)
                             => ~ ( A = k8_scmpds_2(C,D,E)
                                  & r1_xreal_0(np__0,k2_xcmplx_0(B,E)) ) ) ) ) )
              & ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A) = np__5
                  & ! [C] :
                      ( m1_scmpds_2(C)
                     => ! [D] :
                          ( v1_int_1(D)
                         => ! [E] :
                              ( v1_int_1(E)
                             => ~ ( A = k9_scmpds_2(C,D,E)
                                  & r1_xreal_0(np__0,k2_xcmplx_0(B,E)) ) ) ) ) )
              & ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A) = np__6
                  & ! [C] :
                      ( m1_scmpds_2(C)
                     => ! [D] :
                          ( v1_int_1(D)
                         => ! [E] :
                              ( v1_int_1(E)
                             => ~ ( A = k10_scmpds_2(C,D,E)
                                  & r1_xreal_0(np__0,k2_xcmplx_0(B,E)) ) ) ) ) ) ) ) ) ) )).

fof(t77_scmpds_4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( r1_scmpds_4(A,B)
                  & r1_xreal_0(B,C) )
               => r1_scmpds_4(A,C) ) ) ) ) )).

fof(d12_scmpds_4,axiom,(
    ! [A] :
      ( m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
     => ( v3_scmpds_4(A)
      <=> ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ! [C] :
                ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
               => ( ( r2_hidden(k2_scmpds_3(B),k1_relat_1(A))
                    & C = k1_funct_1(A,k2_scmpds_3(B)) )
                 => ( k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,C) != np__1
                    & k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,C) != np__3
                    & r1_scmpds_4(C,B) ) ) ) ) ) ) )).

fof(d13_scmpds_4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ( v4_scmpds_4(A)
      <=> ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A) != np__2
            & r1_xreal_0(k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A),np__6) ) ) ) )).

fof(t78_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & v3_scmpds_4(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( v1_int_1(B)
         => ( r1_xreal_0(np__0,k2_xcmplx_0(k4_card_1(A),B))
           => v3_scmpds_4(k5_scmpds_4(A,k4_scmpds_2(B))) ) ) ) )).

fof(t79_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & v3_scmpds_4(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( v1_int_1(C)
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ( r1_xreal_0(np__0,k2_xcmplx_0(k4_card_1(A),C))
                   => v3_scmpds_4(k5_scmpds_4(A,k8_scmpds_2(D,B,C))) ) ) ) ) ) )).

fof(t80_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & v3_scmpds_4(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( v1_int_1(C)
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ( r1_xreal_0(np__0,k2_xcmplx_0(k4_card_1(A),C))
                   => v3_scmpds_4(k5_scmpds_4(A,k9_scmpds_2(D,B,C))) ) ) ) ) ) )).

fof(t81_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & v3_scmpds_4(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( v1_int_1(C)
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ( r1_xreal_0(np__0,k2_xcmplx_0(k4_card_1(A),C))
                   => v3_scmpds_4(k5_scmpds_4(A,k10_scmpds_2(D,B,C))) ) ) ) ) ) )).

fof(t82_scmpds_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( v1_int_1(E)
                     => ( ( k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A) = k2_scmpds_3(D)
                          & r1_xreal_0(np__0,k2_xcmplx_0(D,E))
                          & k3_scmpds_3(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),C) = k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B) )
                       => k3_scmpds_3(k19_scmpds_2(A,E),C) = k19_scmpds_2(B,E) ) ) ) ) ) ) )).

fof(t83_scmpds_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
                     => ( ( k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A) = k2_scmpds_3(D)
                          & r1_scmpds_4(E,D)
                          & k3_scmpds_3(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),C) = k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B)
                          & k7_relat_1(A,k2_ami_2) = k7_relat_1(B,k2_ami_2) )
                       => ( k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,E) = np__1
                          | k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,E) = np__3
                          | ( k3_scmpds_3(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,E,A)),C) = k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,E,B))
                            & k7_relat_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,E,A),k2_ami_2) = k7_relat_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,E,B),k2_ami_2) ) ) ) ) ) ) ) ) )).

fof(t84_scmpds_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
         => ! [C] :
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & v2_scmpds_4(C)
                & v3_scmpds_4(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ( r1_tarski(k2_scmpds_4(k8_scmpds_4(C)),A)
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( ( r1_tarski(k6_scmpds_3(k8_scmpds_4(C),D),B)
                        & k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B) = k2_scmpds_3(D)
                        & k7_relat_1(A,k2_ami_2) = k7_relat_1(B,k2_ami_2) )
                     => ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ( k3_scmpds_3(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),E)),D) = k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),E))
                            & k8_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),E)) = k8_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),E))
                            & k7_relat_1(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),E),k2_ami_2) = k7_relat_1(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),E),k2_ami_2) ) ) ) ) ) ) ) ) )).

fof(s1_scmpds_4,axiom,(
    ? [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
      & k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A) = f3_s1_scmpds_4
      & ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( k13_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_3(B)) = f1_s1_scmpds_4(B)
            & k2_scmpds_2(A,k3_scmpds_2(B,np__0)) = f2_s1_scmpds_4(B) ) ) ) )).

fof(dt_k1_scmpds_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ( v1_ami_3(k1_scmpds_4(A),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k1_scmpds_4(A))
        & m1_ami_1(k1_scmpds_4(A),k1_tarski(k4_numbers),k1_scmpds_2) ) ) )).

fof(dt_k2_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => m1_ami_1(k2_scmpds_4(A),k1_tarski(k4_numbers),k1_scmpds_2) ) )).

fof(dt_k3_scmpds_4,axiom,(
    ! [A,B] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(B)
        & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ( v1_ami_3(k3_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k3_scmpds_4(A,B))
        & m1_ami_1(k3_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2) ) ) )).

fof(dt_k4_scmpds_4,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
        & v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(B)
        & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ( v1_ami_3(k4_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k4_scmpds_4(A,B))
        & m1_ami_1(k4_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2) ) ) )).

fof(dt_k5_scmpds_4,axiom,(
    ! [A,B] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & m1_subset_1(B,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) )
     => ( v1_ami_3(k5_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k5_scmpds_4(A,B))
        & m1_ami_1(k5_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2) ) ) )).

fof(dt_k6_scmpds_4,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
        & m1_subset_1(B,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) )
     => ( v1_ami_3(k6_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k6_scmpds_4(A,B))
        & m1_ami_1(k6_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2) ) ) )).

fof(dt_k7_scmpds_4,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
        & m1_scmpds_2(B)
        & v1_int_1(C) )
     => m1_subset_1(k7_scmpds_4(A,B,C),k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) ) )).

fof(redefinition_k7_scmpds_4,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
        & m1_scmpds_2(B)
        & v1_int_1(C) )
     => k7_scmpds_4(A,B,C) = k2_funct_7(A,B,C) ) )).

fof(dt_k8_scmpds_4,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ( v1_ami_3(k8_scmpds_4(A),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k8_scmpds_4(A))
        & m1_ami_1(k8_scmpds_4(A),k1_tarski(k4_numbers),k1_scmpds_2) ) ) )).

fof(dt_k9_scmpds_4,axiom,(
    ! [A,B] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) )
     => m1_subset_1(k9_scmpds_4(A,B),k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) ) )).

fof(dt_k10_scmpds_4,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
        & m1_subset_1(B,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
        & m1_subset_1(C,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
        & m1_subset_1(D,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) )
     => m1_ami_1(k10_scmpds_4(A,B,C,D),k1_tarski(k4_numbers),k1_scmpds_2) ) )).

fof(redefinition_k10_scmpds_4,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
        & m1_subset_1(B,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
        & m1_subset_1(C,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
        & m1_subset_1(D,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) )
     => k10_scmpds_4(A,B,C,D) = k4_funct_4(A,B,C,D) ) )).
%------------------------------------------------------------------------------