SET007 Axioms: SET007+608.ax


%------------------------------------------------------------------------------
% File     : SET007+608 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Computation of Two Consecutive 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_5 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   86 (   1 unit)
%            Number of atoms       :  598 (  50 equality)
%            Maximal formula depth :   15 (   8 average)
%            Number of connectives :  526 (  14 ~  ;   3  |; 334  &)
%                                         (   6 <=>; 169 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   33 (   1 propositional; 0-3 arity)
%            Number of functors    :   69 (  10 constant; 0-4 arity)
%            Number of variables   :  208 (   0 singleton; 206 !;   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(rc1_scmpds_5,axiom,(
    ? [A] :
      ( m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
      & v4_scmpds_4(A)
      & v1_scmpds_5(A)
      & v2_scmpds_5(A) ) )).

fof(fc1_scmpds_5,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => v1_scmpds_5(k5_scmpds_2(A)) ) )).

fof(fc2_scmpds_5,axiom,(
    ! [A,B] :
      ( ( m1_scmpds_2(A)
        & v1_int_1(B) )
     => ( v4_scmpds_4(k6_scmpds_2(A,B))
        & v1_scmpds_5(k6_scmpds_2(A,B)) ) ) )).

fof(fc3_scmpds_5,axiom,(
    ! [A,B] :
      ( ( m1_scmpds_2(A)
        & v1_int_1(B) )
     => v1_scmpds_5(k7_scmpds_2(A,B)) ) )).

fof(fc4_scmpds_5,axiom,(
    ! [A,B,C] :
      ( ( m1_scmpds_2(A)
        & v1_int_1(B)
        & v1_int_1(C) )
     => v1_scmpds_5(k8_scmpds_2(A,B,C)) ) )).

fof(fc5_scmpds_5,axiom,(
    ! [A,B,C] :
      ( ( m1_scmpds_2(A)
        & v1_int_1(B)
        & v1_int_1(C) )
     => v1_scmpds_5(k9_scmpds_2(A,B,C)) ) )).

fof(fc6_scmpds_5,axiom,(
    ! [A,B,C] :
      ( ( m1_scmpds_2(A)
        & v1_int_1(B)
        & v1_int_1(C) )
     => v1_scmpds_5(k10_scmpds_2(A,B,C)) ) )).

fof(fc7_scmpds_5,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))
        & v1_scmpds_5(k11_scmpds_2(A,B,C)) ) ) )).

fof(fc8_scmpds_5,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))
        & v1_scmpds_5(k12_scmpds_2(A,B,C)) ) ) )).

fof(fc9_scmpds_5,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))
        & v1_scmpds_5(k13_scmpds_2(A,B,C,D)) ) ) )).

fof(fc10_scmpds_5,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))
        & v1_scmpds_5(k14_scmpds_2(A,B,C,D)) ) ) )).

fof(fc11_scmpds_5,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))
        & v1_scmpds_5(k15_scmpds_2(A,B,C,D)) ) ) )).

fof(fc12_scmpds_5,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))
        & v1_scmpds_5(k16_scmpds_2(A,B,C,D)) ) ) )).

fof(fc13_scmpds_5,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))
        & v1_scmpds_5(k17_scmpds_2(A,B,C,D)) ) ) )).

fof(fc14_scmpds_5,axiom,
    ( v3_ami_1(k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k1_tarski(k4_numbers),k1_scmpds_2)
    & v2_scmpds_5(k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) )).

fof(fc15_scmpds_5,axiom,(
    ! [A] :
      ( ( v2_scmpds_5(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))
        & v1_scmpds_4(k1_scmpds_4(A))
        & v2_scmpds_4(k1_scmpds_4(A)) ) ) )).

fof(fc16_scmpds_5,axiom,(
    ! [A,B] :
      ( ( m1_scmpds_2(A)
        & v1_int_1(B) )
     => ( v4_scmpds_4(k6_scmpds_2(A,B))
        & v1_scmpds_5(k6_scmpds_2(A,B))
        & v2_scmpds_5(k6_scmpds_2(A,B)) ) ) )).

fof(fc17_scmpds_5,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))
        & v1_scmpds_5(k11_scmpds_2(A,B,C))
        & v2_scmpds_5(k11_scmpds_2(A,B,C)) ) ) )).

fof(fc18_scmpds_5,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))
        & v1_scmpds_5(k12_scmpds_2(A,B,C))
        & v2_scmpds_5(k12_scmpds_2(A,B,C)) ) ) )).

fof(fc19_scmpds_5,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))
        & v1_scmpds_5(k13_scmpds_2(A,B,C,D))
        & v2_scmpds_5(k13_scmpds_2(A,B,C,D)) ) ) )).

fof(fc20_scmpds_5,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))
        & v1_scmpds_5(k14_scmpds_2(A,B,C,D))
        & v2_scmpds_5(k14_scmpds_2(A,B,C,D)) ) ) )).

fof(fc21_scmpds_5,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))
        & v1_scmpds_5(k15_scmpds_2(A,B,C,D))
        & v2_scmpds_5(k15_scmpds_2(A,B,C,D)) ) ) )).

fof(fc22_scmpds_5,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))
        & v1_scmpds_5(k16_scmpds_2(A,B,C,D))
        & v2_scmpds_5(k16_scmpds_2(A,B,C,D)) ) ) )).

fof(fc23_scmpds_5,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))
        & v1_scmpds_5(k17_scmpds_2(A,B,C,D))
        & v2_scmpds_5(k17_scmpds_2(A,B,C,D)) ) ) )).

fof(rc2_scmpds_5,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)
      & v3_scmpds_5(A) ) )).

fof(fc24_scmpds_5,axiom,(
    ! [A,B] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & v3_scmpds_5(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_5(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_5(k3_scmpds_4(A,B)) ) ) )).

fof(fc25_scmpds_5,axiom,(
    ! [A] :
      ( ( v1_scmpds_5(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_5(k1_scmpds_4(A)) ) ) )).

fof(fc26_scmpds_5,axiom,(
    ! [A,B] :
      ( ( v1_scmpds_5(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_5(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_5(k4_scmpds_4(A,B)) ) ) )).

fof(fc27_scmpds_5,axiom,(
    ! [A,B] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & v3_scmpds_5(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_5(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_5(k5_scmpds_4(A,B)) ) ) )).

fof(fc28_scmpds_5,axiom,(
    ! [A,B] :
      ( ( v1_scmpds_5(A)
        & m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
        & v1_scmpds_5(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_5(k6_scmpds_4(A,B)) ) ) )).

fof(fc29_scmpds_5,axiom,(
    ! [A,B] :
      ( ( 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_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(B)
        & v2_scmpds_4(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))
        & v1_scmpds_4(k3_scmpds_4(A,B))
        & v2_scmpds_4(k3_scmpds_4(A,B)) ) ) )).

fof(fc30_scmpds_5,axiom,(
    ! [A,B] :
      ( ( v2_scmpds_5(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)
        & v2_scmpds_4(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))
        & v1_scmpds_4(k4_scmpds_4(A,B))
        & v2_scmpds_4(k4_scmpds_4(A,B)) ) ) )).

fof(fc31_scmpds_5,axiom,(
    ! [A,B] :
      ( ( 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)
        & v4_scmpds_4(B)
        & v2_scmpds_5(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))
        & v1_scmpds_4(k5_scmpds_4(A,B))
        & v2_scmpds_4(k5_scmpds_4(A,B)) ) ) )).

fof(fc32_scmpds_5,axiom,(
    ! [A,B] :
      ( ( v2_scmpds_5(A)
        & m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
        & v4_scmpds_4(B)
        & v2_scmpds_5(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))
        & v1_scmpds_4(k6_scmpds_4(A,B))
        & v2_scmpds_4(k6_scmpds_4(A,B)) ) ) )).

fof(t1_scmpds_5,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)))
             => ( C = k9_ami_1(A,B,C)
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => k11_ami_1(A,B,k10_ami_1(A,B,C),D) = C ) ) ) ) ) )).

fof(t2_scmpds_5,axiom,(
    ! [A,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))
     => ( r2_hidden(A,k1_relat_1(k1_scmpds_4(B)))
      <=> A = k2_scmpds_3(np__0) ) ) )).

fof(t3_scmpds_5,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_scmpds_2,u2_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) )
         => ( r2_hidden(A,k1_relat_1(k8_scmpds_4(B)))
           => ( k1_funct_1(k8_scmpds_4(B),A) = k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)
              | r2_hidden(A,k1_relat_1(B)) ) ) ) ) )).

fof(t4_scmpds_5,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_relat_1(k1_scmpds_4(A)) = k1_struct_0(k1_scmpds_2,k2_scmpds_3(np__0))
        & k1_funct_1(k1_scmpds_4(A),k2_scmpds_3(np__0)) = A ) ) )).

fof(t5_scmpds_5,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))
     => r2_hidden(k2_scmpds_3(np__0),k1_relat_1(k1_scmpds_4(A))) ) )).

fof(t6_scmpds_5,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))
     => k4_card_1(k1_scmpds_4(A)) = np__1 ) )).

fof(t7_scmpds_5,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) )
     => k4_card_1(k8_scmpds_4(A)) = k1_nat_1(k4_card_1(A),np__1) ) )).

fof(t8_scmpds_5,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))
     => k4_card_1(k8_scmpds_4(k1_scmpds_4(A))) = np__2 ) )).

fof(t9_scmpds_5,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))
     => ( r2_hidden(k2_scmpds_3(np__0),k1_relat_1(k8_scmpds_4(k1_scmpds_4(A))))
        & r2_hidden(k2_scmpds_3(np__1),k1_relat_1(k8_scmpds_4(k1_scmpds_4(A)))) ) ) )).

fof(t10_scmpds_5,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_funct_1(k8_scmpds_4(k1_scmpds_4(A)),k2_scmpds_3(np__0)) = A
        & k1_funct_1(k8_scmpds_4(k1_scmpds_4(A)),k2_scmpds_3(np__1)) = k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) ) ) )).

fof(t11_scmpds_5,axiom,(
    ! [A,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))
     => ( r2_hidden(A,k1_relat_1(k8_scmpds_4(k1_scmpds_4(B))))
      <=> ( A = k2_scmpds_3(np__0)
          | A = k2_scmpds_3(np__1) ) ) ) )).

fof(t12_scmpds_5,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_relat_1(k8_scmpds_4(k1_scmpds_4(A))) = k2_struct_0(k1_scmpds_2,k2_scmpds_3(np__0),k2_scmpds_3(np__1)) ) )).

fof(t13_scmpds_5,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))
     => ( r2_hidden(k2_scmpds_3(np__0),k1_relat_1(k2_scmpds_4(k8_scmpds_4(k1_scmpds_4(A)))))
        & r2_hidden(k2_scmpds_3(np__1),k1_relat_1(k2_scmpds_4(k8_scmpds_4(k1_scmpds_4(A)))))
        & k1_funct_1(k2_scmpds_4(k8_scmpds_4(k1_scmpds_4(A))),k2_scmpds_3(np__0)) = A
        & k1_funct_1(k2_scmpds_4(k8_scmpds_4(k1_scmpds_4(A))),k2_scmpds_3(np__1)) = k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) ) ) )).

fof(t14_scmpds_5,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) )
         => k2_scmpds_4(k8_scmpds_4(k3_scmpds_4(A,B))) = k17_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k3_scmpds_4(A,k3_scmpds_4(B,k5_scmpds_3)),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(np__0))) ) ) )).

fof(t15_scmpds_5,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(k2_scmpds_4(A),k2_scmpds_4(k8_scmpds_4(k3_scmpds_4(A,B)))) ) ) )).

fof(t16_scmpds_5,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(k8_scmpds_4(A)),k1_relat_1(k8_scmpds_4(k3_scmpds_4(A,B)))) ) ) )).

fof(t17_scmpds_5,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(k8_scmpds_4(A)),k2_scmpds_4(k8_scmpds_4(k3_scmpds_4(A,B)))) = k2_scmpds_4(k8_scmpds_4(k3_scmpds_4(A,B))) ) ) )).

fof(t18_scmpds_5,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)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ( r1_tarski(k2_scmpds_4(B),A)
           => k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A) = k2_scmpds_3(np__0) ) ) ) )).

fof(t19_scmpds_5,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] :
              ( ( 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) )
             => k2_scmpds_2(k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,B,k2_scmpds_4(C)),A) = k2_scmpds_2(B,A) ) ) ) )).

fof(t20_scmpds_5,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)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ( ( r1_tarski(k2_scmpds_4(k8_scmpds_4(C)),A)
                  & r1_tarski(k2_scmpds_4(k8_scmpds_4(C)),B)
                  & r1_funct_7(A,B,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) )
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( r1_funct_7(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),D),k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
                      & 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),D)) = 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),D)) ) ) ) ) ) ) )).

fof(t21_scmpds_5,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)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ( ( r1_tarski(k2_scmpds_4(k8_scmpds_4(C)),A)
                  & r1_tarski(k2_scmpds_4(k8_scmpds_4(C)),B)
                  & r1_funct_7(A,B,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) )
               => ( k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,A) = k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,B)
                  & r1_funct_7(k12_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),k12_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) ) ) ) )).

fof(t22_scmpds_5,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)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(B,A)) = k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k12_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(B))))) ) ) )).

fof(t23_scmpds_5,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) )
         => ! [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) )
             => ( r1_tarski(k2_scmpds_4(k8_scmpds_4(B)),A)
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( r1_xreal_0(D,k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,A))
                     => r1_funct_7(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),D),k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k3_scmpds_4(B,C))),D),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) ) ) ) ) )).

fof(t24_scmpds_5,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) )
         => ! [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) )
             => ( r1_tarski(k2_scmpds_4(k8_scmpds_4(B)),A)
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( r1_xreal_0(D,k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,A))
                     => r1_funct_7(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),D),k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(k3_scmpds_4(B,C))))),D),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) ) ) ) ) )).

fof(d1_scmpds_5,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))
     => ( v1_scmpds_5(A)
      <=> A != k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) ) ) )).

fof(d2_scmpds_5,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))
     => ( v2_scmpds_5(A)
      <=> v2_scmpds_4(k1_scmpds_4(A)) ) ) )).

fof(t25_scmpds_5,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ( A != np__0
       => v1_scmpds_5(k4_scmpds_2(A)) ) ) )).

fof(t26_scmpds_5,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_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A) = np__1
          & v2_scmpds_5(A) ) ) )).

fof(d3_scmpds_5,axiom,(
    ! [A] :
      ( m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
     => ( v3_scmpds_5(A)
      <=> ! [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))
                & k1_funct_1(A,B) = k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) ) )).

fof(t27_scmpds_5,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)
            & v3_scmpds_5(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ( r1_tarski(k2_scmpds_4(k8_scmpds_4(B)),A)
           => 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),k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(B)))))) = k2_scmpds_3(k4_card_1(B)) ) ) ) )).

fof(t28_scmpds_5,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) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ~ r1_xreal_0(k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(B)))),C)
               => 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,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(B)))),C)),k1_relat_1(B)) ) ) ) ) )).

fof(t29_scmpds_5,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) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( r1_tarski(k2_scmpds_4(B),A)
                  & r1_xreal_0(C,k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(B))))) )
               => r1_funct_7(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),C),k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(B)))),C),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) ) ) )).

fof(t30_scmpds_5,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)
            & v3_scmpds_5(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ( r1_tarski(k2_scmpds_4(B),A)
           => 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),k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(B)))))) = k2_scmpds_3(k4_card_1(B)) ) ) ) )).

fof(t31_scmpds_5,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(B),A)
              & 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),k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(B)))))) != k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)
              & 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),k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(B)))))) != k2_scmpds_3(k4_card_1(B)) ) ) ) )).

fof(t32_scmpds_5,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)
            & v3_scmpds_5(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ~ ( r1_tarski(k2_scmpds_4(B),A)
                  & ~ r1_xreal_0(k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(B)))),C)
                  & 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),C)) = k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) ) )).

fof(t33_scmpds_5,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) )
         => ! [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) )
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( r1_xreal_0(D,k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(B)))))
                   => r1_funct_7(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(B)))),D),k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k17_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k3_scmpds_4(B,C),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(np__0))))),D),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) ) ) ) )).

fof(t34_scmpds_5,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) )
         => ! [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) )
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( r1_xreal_0(D,k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(B)))))
                   => r1_funct_7(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(B)))),D),k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(k3_scmpds_4(B,C))))),D),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) ) ) ) )).

fof(t35_scmpds_5,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_scmpds_2)))
             => ! [D] :
                  ( m1_subset_1(D,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
                 => ! [E] :
                      ( ( v1_ami_3(E,k1_tarski(k4_numbers),k1_scmpds_2)
                        & v1_scmpds_3(E)
                        & v2_scmpds_4(E)
                        & v3_scmpds_4(E)
                        & m1_ami_1(E,k1_tarski(k4_numbers),k1_scmpds_2) )
                     => ( C = k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,D,k2_scmpds_4(k8_scmpds_4(E)))),A)
                       => k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,C,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k3_scmpds_3(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),B)))) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k9_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k3_scmpds_3(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C)),B))) ) ) ) ) ) ) )).

fof(t36_scmpds_5,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)
            & v3_scmpds_5(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)
                & v2_scmpds_4(C)
                & v3_scmpds_4(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( r1_tarski(k2_scmpds_4(k8_scmpds_4(k3_scmpds_4(B,C))),A)
                   => r1_funct_7(k8_ami_5(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,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k12_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(B)))),k2_scmpds_4(k8_scmpds_4(C)))),D),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,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,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k12_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(B)))),k2_scmpds_4(k8_scmpds_4(C)))),D)),k4_card_1(B)))),k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(k3_scmpds_4(B,C))))),k1_nat_1(k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(B)))),D)),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) ) ) ) )).

fof(t37_scmpds_5,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)
            & v3_scmpds_5(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)
                & v2_scmpds_4(C)
                & v3_scmpds_4(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(k3_scmpds_4(B,C))))) = k1_nat_1(k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(B)))),k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k12_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(B)))),k2_scmpds_4(k8_scmpds_4(C))))) ) ) ) )).

fof(t38_scmpds_5,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)
            & v3_scmpds_5(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)
                & v2_scmpds_4(C)
                & v3_scmpds_4(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => k9_scmpds_4(k3_scmpds_4(B,C),A) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(C,k9_scmpds_4(B,A)),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k3_scmpds_3(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(C,k9_scmpds_4(B,A))),k4_card_1(B)))) ) ) ) )).

fof(t39_scmpds_5,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] :
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & v2_scmpds_4(C)
                & v3_scmpds_5(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ! [D] :
                  ( ( v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
                    & v1_scmpds_3(D)
                    & v2_scmpds_4(D)
                    & v3_scmpds_4(D)
                    & m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
                 => k2_scmpds_2(k9_scmpds_4(k3_scmpds_4(C,D),B),A) = k2_scmpds_2(k9_scmpds_4(D,k9_scmpds_4(C,B)),A) ) ) ) ) )).

fof(d4_scmpds_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => k1_scmpds_5(A) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(np__0))) ) )).

fof(t40_scmpds_5,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_struct_0(C,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
             => ( k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k1_scmpds_5(B)) = k2_scmpds_3(np__0)
                & k2_scmpds_2(k1_scmpds_5(B),A) = k2_scmpds_2(B,A)
                & k13_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k1_scmpds_5(B),C) = k13_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B,C) ) ) ) ) )).

fof(t41_scmpds_5,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_xboole_0(k2_ami_2,k1_struct_0(k1_scmpds_2,k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))) = k7_relat_1(B,k2_xboole_0(k2_ami_2,k1_struct_0(k1_scmpds_2,k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))) ) ) ) )).

fof(t42_scmpds_5,axiom,(
    $true )).

fof(t43_scmpds_5,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)))
             => ( k7_relat_1(B,k2_ami_2) = k7_relat_1(C,k2_ami_2)
               => ( k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A) = np__3
                  | k7_relat_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,B),k2_ami_2) = k7_relat_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,C),k2_ami_2) ) ) ) ) ) )).

fof(t44_scmpds_5,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] :
              ( ( v4_scmpds_4(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)) )
             => ( k7_relat_1(A,k2_ami_2) = k7_relat_1(B,k2_ami_2)
               => k7_relat_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C,A),k2_ami_2) = k7_relat_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C,B),k2_ami_2) ) ) ) ) )).

fof(t45_scmpds_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( ( v2_scmpds_5(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)) )
         => k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B,k1_scmpds_5(A)) = k9_scmpds_4(k1_scmpds_4(B),A) ) ) )).

fof(t46_scmpds_5,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] :
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & v2_scmpds_4(C)
                & v3_scmpds_5(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ! [D] :
                  ( ( v4_scmpds_4(D)
                    & v2_scmpds_5(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)) )
                 => k2_scmpds_2(k9_scmpds_4(k5_scmpds_4(C,D),B),A) = k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,D,k9_scmpds_4(C,B)),A) ) ) ) ) )).

fof(t47_scmpds_5,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] :
              ( ( v1_scmpds_5(C)
                & v2_scmpds_5(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)) )
             => ! [D] :
                  ( ( v4_scmpds_4(D)
                    & v2_scmpds_5(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)) )
                 => k2_scmpds_2(k9_scmpds_4(k6_scmpds_4(C,D),B),A) = k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,D,k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C,k1_scmpds_5(B))),A) ) ) ) ) )).

fof(dt_k1_scmpds_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => m1_subset_1(k1_scmpds_5(A),k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) ) )).
%------------------------------------------------------------------------------