SET007 Axioms: SET007+609.ax


%------------------------------------------------------------------------------
% File     : SET007+609 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Construction and Computation of Conditional Statements 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_6 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  182 (   1 unit)
%            Number of atoms       : 1729 ( 137 equality)
%            Maximal formula depth :   17 (  10 average)
%            Number of connectives : 1567 (  20 ~  ;  14  |; 880  &)
%                                         (   6 <=>; 647 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   27 (   1 propositional; 0-3 arity)
%            Number of functors    :   64 (   8 constant; 0-4 arity)
%            Number of variables   :  634 (   0 singleton; 634 !;   0 ?)
%            Maximal term depth    :    8 (   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_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => v1_scmpds_5(k4_scmpds_2(k1_nat_1(A,np__1))) ) )).

fof(fc2_scmpds_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => v1_scmpds_5(k4_scmpds_2(k4_xcmplx_0(k1_nat_1(A,np__1)))) ) )).

fof(fc3_scmpds_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => ( v1_relat_1(k1_scmpds_6(k1_nat_1(A,np__1)))
        & v1_funct_1(k1_scmpds_6(k1_nat_1(A,np__1)))
        & v1_finset_1(k1_scmpds_6(k1_nat_1(A,np__1)))
        & v1_ami_3(k1_scmpds_6(k1_nat_1(A,np__1)),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k1_scmpds_6(k1_nat_1(A,np__1)))
        & v3_scmpds_5(k1_scmpds_6(k1_nat_1(A,np__1))) ) ) )).

fof(fc4_scmpds_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => ( v1_relat_1(k1_scmpds_6(k4_xcmplx_0(k1_nat_1(A,np__1))))
        & v1_funct_1(k1_scmpds_6(k4_xcmplx_0(k1_nat_1(A,np__1))))
        & v1_finset_1(k1_scmpds_6(k4_xcmplx_0(k1_nat_1(A,np__1))))
        & v1_ami_3(k1_scmpds_6(k4_xcmplx_0(k1_nat_1(A,np__1))),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k1_scmpds_6(k4_xcmplx_0(k1_nat_1(A,np__1))))
        & v3_scmpds_5(k1_scmpds_6(k4_xcmplx_0(k1_nat_1(A,np__1)))) ) ) )).

fof(fc5_scmpds_6,axiom,(
    ! [A,B,C,D] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & v2_scmpds_4(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)
        & v2_scmpds_4(B)
        & v3_scmpds_4(B)
        & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2)
        & m1_scmpds_2(C)
        & v1_int_1(D) )
     => ( v1_relat_1(k2_scmpds_6(C,D,A,B))
        & v1_funct_1(k2_scmpds_6(C,D,A,B))
        & v1_finset_1(k2_scmpds_6(C,D,A,B))
        & v1_ami_3(k2_scmpds_6(C,D,A,B),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k2_scmpds_6(C,D,A,B))
        & v1_scmpds_4(k2_scmpds_6(C,D,A,B))
        & v2_scmpds_4(k2_scmpds_6(C,D,A,B))
        & v3_scmpds_4(k2_scmpds_6(C,D,A,B)) ) ) )).

fof(fc6_scmpds_6,axiom,(
    ! [A,B,C,D] :
      ( ( 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)
        & m1_scmpds_2(C)
        & v1_int_1(D) )
     => ( v1_relat_1(k2_scmpds_6(C,D,A,B))
        & v1_funct_1(k2_scmpds_6(C,D,A,B))
        & v1_finset_1(k2_scmpds_6(C,D,A,B))
        & v1_ami_3(k2_scmpds_6(C,D,A,B),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k2_scmpds_6(C,D,A,B))
        & v3_scmpds_5(k2_scmpds_6(C,D,A,B)) ) ) )).

fof(fc7_scmpds_6,axiom,(
    ! [A,B,C] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & v2_scmpds_4(A)
        & v3_scmpds_4(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & m1_scmpds_2(B)
        & v1_int_1(C) )
     => ( v1_relat_1(k5_scmpds_6(B,C,A))
        & v1_funct_1(k5_scmpds_6(B,C,A))
        & v1_finset_1(k5_scmpds_6(B,C,A))
        & v1_ami_3(k5_scmpds_6(B,C,A),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k5_scmpds_6(B,C,A))
        & v1_scmpds_4(k5_scmpds_6(B,C,A))
        & v2_scmpds_4(k5_scmpds_6(B,C,A))
        & v3_scmpds_4(k5_scmpds_6(B,C,A)) ) ) )).

fof(fc8_scmpds_6,axiom,(
    ! [A,B,C] :
      ( ( 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)
        & m1_scmpds_2(B)
        & v1_int_1(C) )
     => ( v1_relat_1(k5_scmpds_6(B,C,A))
        & v1_funct_1(k5_scmpds_6(B,C,A))
        & v1_finset_1(k5_scmpds_6(B,C,A))
        & v1_ami_3(k5_scmpds_6(B,C,A),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k5_scmpds_6(B,C,A))
        & v3_scmpds_5(k5_scmpds_6(B,C,A)) ) ) )).

fof(fc9_scmpds_6,axiom,(
    ! [A,B,C] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & v2_scmpds_4(A)
        & v3_scmpds_4(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & m1_scmpds_2(B)
        & v1_int_1(C) )
     => ( v1_relat_1(k6_scmpds_6(B,C,A))
        & v1_funct_1(k6_scmpds_6(B,C,A))
        & v1_finset_1(k6_scmpds_6(B,C,A))
        & v1_ami_3(k6_scmpds_6(B,C,A),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k6_scmpds_6(B,C,A))
        & v1_scmpds_4(k6_scmpds_6(B,C,A))
        & v2_scmpds_4(k6_scmpds_6(B,C,A))
        & v3_scmpds_4(k6_scmpds_6(B,C,A)) ) ) )).

fof(fc10_scmpds_6,axiom,(
    ! [A,B,C] :
      ( ( 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)
        & m1_scmpds_2(B)
        & v1_int_1(C) )
     => ( v1_relat_1(k6_scmpds_6(B,C,A))
        & v1_funct_1(k6_scmpds_6(B,C,A))
        & v1_finset_1(k6_scmpds_6(B,C,A))
        & v1_ami_3(k6_scmpds_6(B,C,A),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k6_scmpds_6(B,C,A))
        & v3_scmpds_5(k6_scmpds_6(B,C,A)) ) ) )).

fof(fc11_scmpds_6,axiom,(
    ! [A,B,C,D] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & v2_scmpds_4(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)
        & v2_scmpds_4(B)
        & v3_scmpds_4(B)
        & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2)
        & m1_scmpds_2(C)
        & v1_int_1(D) )
     => ( v1_relat_1(k3_scmpds_6(C,D,A,B))
        & v1_funct_1(k3_scmpds_6(C,D,A,B))
        & v1_finset_1(k3_scmpds_6(C,D,A,B))
        & v1_ami_3(k3_scmpds_6(C,D,A,B),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k3_scmpds_6(C,D,A,B))
        & v1_scmpds_4(k3_scmpds_6(C,D,A,B))
        & v2_scmpds_4(k3_scmpds_6(C,D,A,B))
        & v3_scmpds_4(k3_scmpds_6(C,D,A,B)) ) ) )).

fof(fc12_scmpds_6,axiom,(
    ! [A,B,C,D] :
      ( ( 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)
        & m1_scmpds_2(C)
        & v1_int_1(D) )
     => ( v1_relat_1(k3_scmpds_6(C,D,A,B))
        & v1_funct_1(k3_scmpds_6(C,D,A,B))
        & v1_finset_1(k3_scmpds_6(C,D,A,B))
        & v1_ami_3(k3_scmpds_6(C,D,A,B),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k3_scmpds_6(C,D,A,B))
        & v3_scmpds_5(k3_scmpds_6(C,D,A,B)) ) ) )).

fof(fc13_scmpds_6,axiom,(
    ! [A,B,C] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & v2_scmpds_4(A)
        & v3_scmpds_4(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & m1_scmpds_2(B)
        & v1_int_1(C) )
     => ( v1_relat_1(k7_scmpds_6(B,C,A))
        & v1_funct_1(k7_scmpds_6(B,C,A))
        & v1_finset_1(k7_scmpds_6(B,C,A))
        & v1_ami_3(k7_scmpds_6(B,C,A),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k7_scmpds_6(B,C,A))
        & v1_scmpds_4(k7_scmpds_6(B,C,A))
        & v2_scmpds_4(k7_scmpds_6(B,C,A))
        & v3_scmpds_4(k7_scmpds_6(B,C,A)) ) ) )).

fof(fc14_scmpds_6,axiom,(
    ! [A,B,C] :
      ( ( 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)
        & m1_scmpds_2(B)
        & v1_int_1(C) )
     => ( v1_relat_1(k7_scmpds_6(B,C,A))
        & v1_funct_1(k7_scmpds_6(B,C,A))
        & v1_finset_1(k7_scmpds_6(B,C,A))
        & v1_ami_3(k7_scmpds_6(B,C,A),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k7_scmpds_6(B,C,A))
        & v3_scmpds_5(k7_scmpds_6(B,C,A)) ) ) )).

fof(fc15_scmpds_6,axiom,(
    ! [A,B,C] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & v2_scmpds_4(A)
        & v3_scmpds_4(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & m1_scmpds_2(B)
        & v1_int_1(C) )
     => ( v1_relat_1(k8_scmpds_6(B,C,A))
        & v1_funct_1(k8_scmpds_6(B,C,A))
        & v1_finset_1(k8_scmpds_6(B,C,A))
        & v1_ami_3(k8_scmpds_6(B,C,A),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k8_scmpds_6(B,C,A))
        & v1_scmpds_4(k8_scmpds_6(B,C,A))
        & v2_scmpds_4(k8_scmpds_6(B,C,A))
        & v3_scmpds_4(k8_scmpds_6(B,C,A)) ) ) )).

fof(fc16_scmpds_6,axiom,(
    ! [A,B,C] :
      ( ( 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)
        & m1_scmpds_2(B)
        & v1_int_1(C) )
     => ( v1_relat_1(k8_scmpds_6(B,C,A))
        & v1_funct_1(k8_scmpds_6(B,C,A))
        & v1_finset_1(k8_scmpds_6(B,C,A))
        & v1_ami_3(k8_scmpds_6(B,C,A),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k8_scmpds_6(B,C,A))
        & v3_scmpds_5(k8_scmpds_6(B,C,A)) ) ) )).

fof(fc17_scmpds_6,axiom,(
    ! [A,B,C,D] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & v2_scmpds_4(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)
        & v2_scmpds_4(B)
        & v3_scmpds_4(B)
        & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2)
        & m1_scmpds_2(C)
        & v1_int_1(D) )
     => ( v1_relat_1(k4_scmpds_6(C,D,A,B))
        & v1_funct_1(k4_scmpds_6(C,D,A,B))
        & v1_finset_1(k4_scmpds_6(C,D,A,B))
        & v1_ami_3(k4_scmpds_6(C,D,A,B),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k4_scmpds_6(C,D,A,B))
        & v1_scmpds_4(k4_scmpds_6(C,D,A,B))
        & v2_scmpds_4(k4_scmpds_6(C,D,A,B))
        & v3_scmpds_4(k4_scmpds_6(C,D,A,B)) ) ) )).

fof(fc18_scmpds_6,axiom,(
    ! [A,B,C,D] :
      ( ( 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)
        & m1_scmpds_2(C)
        & v1_int_1(D) )
     => ( v1_relat_1(k4_scmpds_6(C,D,A,B))
        & v1_funct_1(k4_scmpds_6(C,D,A,B))
        & v1_finset_1(k4_scmpds_6(C,D,A,B))
        & v1_ami_3(k4_scmpds_6(C,D,A,B),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k4_scmpds_6(C,D,A,B))
        & v3_scmpds_5(k4_scmpds_6(C,D,A,B)) ) ) )).

fof(fc19_scmpds_6,axiom,(
    ! [A,B,C] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & v2_scmpds_4(A)
        & v3_scmpds_4(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & m1_scmpds_2(B)
        & v1_int_1(C) )
     => ( v1_relat_1(k9_scmpds_6(B,C,A))
        & v1_funct_1(k9_scmpds_6(B,C,A))
        & v1_finset_1(k9_scmpds_6(B,C,A))
        & v1_ami_3(k9_scmpds_6(B,C,A),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k9_scmpds_6(B,C,A))
        & v1_scmpds_4(k9_scmpds_6(B,C,A))
        & v2_scmpds_4(k9_scmpds_6(B,C,A))
        & v3_scmpds_4(k9_scmpds_6(B,C,A)) ) ) )).

fof(fc20_scmpds_6,axiom,(
    ! [A,B,C] :
      ( ( 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)
        & m1_scmpds_2(B)
        & v1_int_1(C) )
     => ( v1_relat_1(k9_scmpds_6(B,C,A))
        & v1_funct_1(k9_scmpds_6(B,C,A))
        & v1_finset_1(k9_scmpds_6(B,C,A))
        & v1_ami_3(k9_scmpds_6(B,C,A),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k9_scmpds_6(B,C,A))
        & v3_scmpds_5(k9_scmpds_6(B,C,A)) ) ) )).

fof(fc21_scmpds_6,axiom,(
    ! [A,B,C] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & v2_scmpds_4(A)
        & v3_scmpds_4(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & m1_scmpds_2(B)
        & v1_int_1(C) )
     => ( v1_relat_1(k10_scmpds_6(B,C,A))
        & v1_funct_1(k10_scmpds_6(B,C,A))
        & v1_finset_1(k10_scmpds_6(B,C,A))
        & v1_ami_3(k10_scmpds_6(B,C,A),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k10_scmpds_6(B,C,A))
        & v1_scmpds_4(k10_scmpds_6(B,C,A))
        & v2_scmpds_4(k10_scmpds_6(B,C,A))
        & v3_scmpds_4(k10_scmpds_6(B,C,A)) ) ) )).

fof(fc22_scmpds_6,axiom,(
    ! [A,B,C] :
      ( ( 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)
        & m1_scmpds_2(B)
        & v1_int_1(C) )
     => ( v1_relat_1(k10_scmpds_6(B,C,A))
        & v1_funct_1(k10_scmpds_6(B,C,A))
        & v1_finset_1(k10_scmpds_6(B,C,A))
        & v1_ami_3(k10_scmpds_6(B,C,A),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k10_scmpds_6(B,C,A))
        & v3_scmpds_5(k10_scmpds_6(B,C,A)) ) ) )).

fof(t1_scmpds_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => k1_relat_1(k7_relat_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) = u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) ) )).

fof(t2_scmpds_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ( v9_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
       => ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ( r1_xreal_0(k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,A),B)
             => 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),B)) = k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) ) )).

fof(t3_scmpds_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ( v9_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
       => ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ( r1_xreal_0(k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,A),B)
             => 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),B)) = 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,A))) ) ) ) ) )).

fof(t4_scmpds_6,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))
          <=> ( k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A) = 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) ) ) ) ) )).

fof(t5_scmpds_6,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) )
         => k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k1_scmpds_5(A),k2_scmpds_4(B)) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(B)) ) ) )).

fof(t6_scmpds_6,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_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
         => r1_tarski(A,k17_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,B))) ) ) )).

fof(t7_scmpds_6,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))
         => k7_relat_1(A,k2_ami_2) = k7_relat_1(k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,B)),k2_ami_2) ) ) )).

fof(t8_scmpds_6,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) )
         => ! [C] :
              ( m1_struct_0(C,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
             => k7_relat_1(A,k2_ami_2) = k7_relat_1(k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k17_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,C))),k2_ami_2) ) ) ) )).

fof(t9_scmpds_6,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) )
         => k7_relat_1(A,k2_ami_2) = k7_relat_1(k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(B)),k2_ami_2) ) ) )).

fof(t10_scmpds_6,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))
         => r1_xboole_0(k1_relat_1(k7_relat_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))),k1_relat_1(k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,B))) ) ) )).

fof(t11_scmpds_6,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) )
         => ! [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] :
                  ( m1_struct_0(D,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
                 => r1_funct_7(k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k17_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,D))),k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k17_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,D))),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) ) ) )).

fof(t12_scmpds_6,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)
                & 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)
                    & m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
                 => ( k7_relat_1(A,k2_ami_2) = k7_relat_1(B,k2_ami_2)
                   => r1_funct_7(k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(C)),k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,B,k2_scmpds_4(D)),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) ) ) ) )).

fof(t13_scmpds_6,axiom,(
    $true )).

fof(t14_scmpds_6,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))
             => k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,B)),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,C)) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,C)) ) ) ) )).

fof(t15_scmpds_6,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_card_1(k4_scmpds_4(A,B)) = k1_nat_1(k4_card_1(B),np__1) ) ) )).

fof(t16_scmpds_6,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) )
         => k1_funct_1(k4_scmpds_4(A,B),k2_scmpds_3(np__0)) = A ) ) )).

fof(t17_scmpds_6,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(k8_scmpds_4(A))) ) )).

fof(t18_scmpds_6,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(B))
           => r2_hidden(A,k1_relat_1(k8_scmpds_4(B))) ) ) ) )).

fof(t19_scmpds_6,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(B))
           => k1_funct_1(k8_scmpds_4(B),A) = k1_funct_1(B,A) ) ) ) )).

fof(t20_scmpds_6,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(B))
           => k1_funct_1(k2_scmpds_4(k8_scmpds_4(B)),A) = k1_funct_1(B,A) ) ) ) )).

fof(t21_scmpds_6,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,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(B))) = k2_scmpds_3(np__0) ) ) )).

fof(t22_scmpds_6,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] :
              ( ( 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) )
             => k8_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(k4_scmpds_4(A,C))))) = A ) ) ) )).

fof(t23_scmpds_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_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)
             => ( k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A) = k2_scmpds_3(B)
               => k19_scmpds_2(A,C) = k2_scmpds_3(k1_nat_1(B,C)) ) ) ) ) )).

fof(t24_scmpds_6,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(k6_scmpds_3(k8_scmpds_4(B),k4_card_1(A)),k8_scmpds_4(k3_scmpds_4(A,B))) ) ) )).

fof(t25_scmpds_6,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(k4_card_1(A)),k1_relat_1(k8_scmpds_4(A)))
        & k1_funct_1(k8_scmpds_4(A),k2_scmpds_3(k4_card_1(A))) = k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) ) ) )).

fof(t26_scmpds_6,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) )
         => ! [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] :
                  ( m1_struct_0(D,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
                 => ! [E] :
                      ( m1_struct_0(E,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
                     => k13_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(B,A),D) = k13_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(C,A),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,E)),D) ) ) ) ) ) )).

fof(t27_scmpds_6,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) )
         => ! [C] :
              ( m1_struct_0(C,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
             => ! [D] :
                  ( m1_struct_0(D,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
                 => k13_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(B,A),C) = k13_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,D)),C) ) ) ) ) )).

fof(t28_scmpds_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( ( v1_scmpds_5(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)) )
         => ! [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] :
                  ( m1_scmpds_2(D)
                 => k2_scmpds_2(k9_scmpds_4(k4_scmpds_4(B,C),A),D) = k2_scmpds_2(k9_scmpds_4(C,k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B,k1_scmpds_5(A))),D) ) ) ) ) )).

fof(t29_scmpds_6,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( v1_int_1(C)
             => k8_scmpds_2(A,B,C) != k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) )).

fof(t30_scmpds_6,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( v1_int_1(C)
             => k9_scmpds_2(A,B,C) != k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) )).

fof(t31_scmpds_6,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( v1_int_1(C)
             => k10_scmpds_2(A,B,C) != k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) )).

fof(d1_scmpds_6,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => k1_scmpds_6(A) = k1_scmpds_4(k4_scmpds_2(A)) ) )).

fof(t32_scmpds_6,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => k4_card_1(k1_scmpds_6(A)) = np__1 ) )).

fof(t33_scmpds_6,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ( r2_hidden(k2_scmpds_3(np__0),k1_relat_1(k1_scmpds_6(A)))
        & k1_funct_1(k1_scmpds_6(A),k2_scmpds_3(np__0)) = k4_scmpds_2(A) ) ) )).

fof(d2_scmpds_6,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_scmpds_6(A,B)
          <=> ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => 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,B,k2_scmpds_4(k8_scmpds_4(A)))),C)),k1_relat_1(k8_scmpds_4(A))) ) ) ) ) )).

fof(d3_scmpds_6,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_scmpds_6(A,B)
          <=> v9_ami_1(k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,B,k2_scmpds_4(k8_scmpds_4(A))),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) )).

fof(t34_scmpds_6,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)))
           => r1_scmpds_6(A,B) ) ) ) )).

fof(t35_scmpds_6,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)
      <=> ! [B] :
            ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
           => r2_scmpds_6(A,B) ) ) ) )).

fof(t36_scmpds_6,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)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ( ( k7_relat_1(A,k2_ami_2) = k7_relat_1(B,k2_ami_2)
                  & r1_scmpds_6(C,A) )
               => r1_scmpds_6(C,B) ) ) ) ) )).

fof(t37_scmpds_6,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)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ( ( k7_relat_1(A,k2_ami_2) = k7_relat_1(B,k2_ami_2)
                  & r1_scmpds_6(C,A)
                  & r2_scmpds_6(C,A) )
               => ( r1_scmpds_6(C,B)
                  & r2_scmpds_6(C,B) ) ) ) ) ) )).

fof(t38_scmpds_6,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) )
         => ! [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_scmpds_6(B,A)
              <=> r1_scmpds_6(B,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(C))) ) ) ) ) )).

fof(t39_scmpds_6,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_scmpds_6(A,C)
                  & r2_scmpds_6(A,C) )
               => ( ! [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,C,k2_scmpds_4(k8_scmpds_4(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,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,C,k2_scmpds_4(k8_scmpds_4(A)))),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,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,C,k2_scmpds_4(k8_scmpds_4(k3_scmpds_4(A,B))))),D)) ) )
                  & k7_relat_1(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,C,k2_scmpds_4(k8_scmpds_4(A)))),k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,C,k2_scmpds_4(k8_scmpds_4(A))))),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,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,C,k2_scmpds_4(k8_scmpds_4(k3_scmpds_4(A,B))))),k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,C,k2_scmpds_4(k8_scmpds_4(A))))),k2_ami_2) ) ) ) ) ) )).

fof(t40_scmpds_6,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) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( r1_scmpds_6(B,A)
                  & r2_scmpds_6(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)
                  | 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(t41_scmpds_6,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)))
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( ( r1_scmpds_6(A,C)
                      & r2_scmpds_6(A,C) )
                   => ( r1_xreal_0(k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,C,k2_scmpds_4(k8_scmpds_4(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,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,C,k2_scmpds_4(k8_scmpds_4(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,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,C,k2_scmpds_4(k8_scmpds_4(k3_scmpds_4(A,B))))),D)) ) ) ) ) ) ) )).

fof(t42_scmpds_6,axiom,(
    ! [A] :
      ( ( 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) )
     => ! [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_scmpds_6(A,B)
                  & r2_scmpds_6(A,B)
                  & ~ r1_xreal_0(k2_scm_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)))),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,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,B,k2_scmpds_4(k8_scmpds_4(A)))),C)) = k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) ) )).

fof(t43_scmpds_6,axiom,(
    ! [A] :
      ( ( 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) )
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
         => ( ( r1_scmpds_6(A,B)
              & r2_scmpds_6(A,B) )
           => 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,B,k2_scmpds_4(k8_scmpds_4(A)))),k2_scm_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)))))) = k2_scmpds_3(k4_card_1(A)) ) ) ) )).

fof(t44_scmpds_6,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_scmpds_6(A,C)
                  & r2_scmpds_6(A,C) )
               => ( r2_scmpds_6(k3_scmpds_4(k3_scmpds_4(A,k1_scmpds_6(k1_nat_1(k4_card_1(B),np__1))),B),C)
                  & r1_scmpds_6(k3_scmpds_4(k3_scmpds_4(A,k1_scmpds_6(k1_nat_1(k4_card_1(B),np__1))),B),C) ) ) ) ) ) )).

fof(t45_scmpds_6,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)
                & 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)
                  & r1_scmpds_6(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(t46_scmpds_6,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)
            & 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)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ( ( r1_scmpds_6(B,A)
                  & r2_scmpds_6(B,A) )
               => k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(k3_scmpds_4(k3_scmpds_4(B,k1_scmpds_6(k1_nat_1(k4_card_1(C),np__1))),C),A)) = k2_scmpds_3(k1_nat_1(k1_nat_1(k4_card_1(B),k4_card_1(C)),np__1)) ) ) ) ) )).

fof(t47_scmpds_6,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)
            & 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)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ( ( r1_scmpds_6(B,A)
                  & r2_scmpds_6(B,A) )
               => k9_scmpds_4(k3_scmpds_4(k3_scmpds_4(B,k1_scmpds_6(k1_nat_1(k4_card_1(C),np__1))),C),A) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(B,A),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(k1_nat_1(k1_nat_1(k4_card_1(B),k4_card_1(C)),np__1)))) ) ) ) ) )).

fof(t48_scmpds_6,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)
            & v3_scmpds_5(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ( ( r1_scmpds_6(B,A)
              & r2_scmpds_6(B,A) )
           => k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(B,A)) = k2_scmpds_3(k4_card_1(B)) ) ) ) )).

fof(d4_scmpds_6,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [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] :
                  ( ( v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
                    & v1_scmpds_3(D)
                    & m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
                 => k2_scmpds_6(A,B,C,D) = k3_scmpds_4(k3_scmpds_4(k4_scmpds_4(k8_scmpds_2(A,B,k1_nat_1(k4_card_1(C),np__2)),C),k1_scmpds_6(k1_nat_1(k4_card_1(D),np__1))),D) ) ) ) ) )).

fof(d5_scmpds_6,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [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] :
                  ( ( v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
                    & v1_scmpds_3(D)
                    & m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
                 => k3_scmpds_6(A,B,C,D) = k3_scmpds_4(k3_scmpds_4(k4_scmpds_4(k9_scmpds_2(A,B,k1_nat_1(k4_card_1(C),np__2)),C),k1_scmpds_6(k1_nat_1(k4_card_1(D),np__1))),D) ) ) ) ) )).

fof(d6_scmpds_6,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [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] :
                  ( ( v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
                    & v1_scmpds_3(D)
                    & m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
                 => k4_scmpds_6(A,B,C,D) = k3_scmpds_4(k3_scmpds_4(k4_scmpds_4(k10_scmpds_2(A,B,k1_nat_1(k4_card_1(C),np__2)),C),k1_scmpds_6(k1_nat_1(k4_card_1(D),np__1))),D) ) ) ) ) )).

fof(d7_scmpds_6,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [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_6(A,B,C) = k4_scmpds_4(k8_scmpds_2(A,B,k1_nat_1(k4_card_1(C),np__1)),C) ) ) ) )).

fof(d8_scmpds_6,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [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) )
             => k6_scmpds_6(A,B,C) = k3_scmpds_4(k6_scmpds_4(k8_scmpds_2(A,B,np__2),k4_scmpds_2(k1_nat_1(k4_card_1(C),np__1))),C) ) ) ) )).

fof(d9_scmpds_6,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [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) )
             => k7_scmpds_6(A,B,C) = k4_scmpds_4(k9_scmpds_2(A,B,k1_nat_1(k4_card_1(C),np__1)),C) ) ) ) )).

fof(d10_scmpds_6,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [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) )
             => k8_scmpds_6(A,B,C) = k3_scmpds_4(k6_scmpds_4(k9_scmpds_2(A,B,np__2),k4_scmpds_2(k1_nat_1(k4_card_1(C),np__1))),C) ) ) ) )).

fof(d11_scmpds_6,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [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) )
             => k9_scmpds_6(A,B,C) = k4_scmpds_4(k10_scmpds_2(A,B,k1_nat_1(k4_card_1(C),np__1)),C) ) ) ) )).

fof(d12_scmpds_6,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [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) )
             => k10_scmpds_6(A,B,C) = k3_scmpds_4(k6_scmpds_4(k10_scmpds_2(A,B,np__2),k4_scmpds_2(k1_nat_1(k4_card_1(C),np__1))),C) ) ) ) )).

fof(t49_scmpds_6,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [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] :
                  ( ( v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
                    & v1_scmpds_3(D)
                    & m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
                 => k4_card_1(k2_scmpds_6(A,B,C,D)) = k1_nat_1(k1_nat_1(k4_card_1(C),k4_card_1(D)),np__2) ) ) ) ) )).

fof(t50_scmpds_6,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [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] :
                  ( ( v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
                    & v1_scmpds_3(D)
                    & m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
                 => ( r2_hidden(k2_scmpds_3(np__0),k1_relat_1(k2_scmpds_6(A,B,C,D)))
                    & r2_hidden(k2_scmpds_3(np__1),k1_relat_1(k2_scmpds_6(A,B,C,D))) ) ) ) ) ) )).

fof(t51_scmpds_6,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [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] :
                  ( ( v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
                    & v1_scmpds_3(D)
                    & m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
                 => k1_funct_1(k2_scmpds_6(A,B,C,D),k2_scmpds_3(np__0)) = k8_scmpds_2(A,B,k1_nat_1(k4_card_1(C),np__2)) ) ) ) ) )).

fof(t52_scmpds_6,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)
            & v3_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)
                & v3_scmpds_4(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( v1_int_1(E)
                     => ( ( k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),E)) = np__0
                          & r1_scmpds_6(B,A)
                          & r2_scmpds_6(B,A) )
                       => ( r1_scmpds_6(k2_scmpds_6(D,E,B,C),A)
                          & r2_scmpds_6(k2_scmpds_6(D,E,B,C),A) ) ) ) ) ) ) ) )).

fof(t53_scmpds_6,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) )
         => ! [C] :
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & v3_scmpds_4(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( v1_int_1(E)
                     => ( ( r1_scmpds_6(C,A)
                          & r2_scmpds_6(C,A) )
                       => ( k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),E)) = np__0
                          | ( r1_scmpds_6(k2_scmpds_6(D,E,B,C),A)
                            & r2_scmpds_6(k2_scmpds_6(D,E,B,C),A) ) ) ) ) ) ) ) ) )).

fof(t54_scmpds_6,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)
            & v3_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)
                & v3_scmpds_4(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( v1_int_1(E)
                     => ( ( k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),E)) = np__0
                          & r1_scmpds_6(B,A)
                          & r2_scmpds_6(B,A) )
                       => k9_scmpds_4(k2_scmpds_6(D,E,B,C),A) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(B,A),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(k1_nat_1(k1_nat_1(k4_card_1(B),k4_card_1(C)),np__2)))) ) ) ) ) ) ) )).

fof(t55_scmpds_6,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) )
         => ! [C] :
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & v3_scmpds_4(C)
                & v3_scmpds_5(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( v1_int_1(E)
                     => ( ( r1_scmpds_6(C,A)
                          & r2_scmpds_6(C,A) )
                       => ( k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),E)) = np__0
                          | k9_scmpds_4(k2_scmpds_6(D,E,B,C),A) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(C,A),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(k1_nat_1(k1_nat_1(k4_card_1(B),k4_card_1(C)),np__2)))) ) ) ) ) ) ) ) )).

fof(t56_scmpds_6,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_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)
                & v3_scmpds_5(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( v1_int_1(E)
                     => k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(k2_scmpds_6(D,E,B,C),A)) = k2_scmpds_3(k1_nat_1(k1_nat_1(k4_card_1(B),k4_card_1(C)),np__2)) ) ) ) ) ) )).

fof(t57_scmpds_6,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_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)
                & v3_scmpds_4(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( m1_scmpds_2(E)
                     => ! [F] :
                          ( v1_int_1(F)
                         => ( k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),F)) = np__0
                           => k2_scmpds_2(k9_scmpds_4(k2_scmpds_6(D,F,B,C),A),E) = k2_scmpds_2(k9_scmpds_4(B,A),E) ) ) ) ) ) ) ) )).

fof(t58_scmpds_6,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) )
         => ! [C] :
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & v2_scmpds_4(C)
                & v3_scmpds_4(C)
                & v3_scmpds_5(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( m1_scmpds_2(E)
                     => ! [F] :
                          ( v1_int_1(F)
                         => ( k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),F)) != np__0
                           => k2_scmpds_2(k9_scmpds_4(k2_scmpds_6(D,F,B,C),A),E) = k2_scmpds_2(k9_scmpds_4(C,A),E) ) ) ) ) ) ) ) )).

fof(t59_scmpds_6,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [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) )
             => k4_card_1(k5_scmpds_6(A,B,C)) = k1_nat_1(k4_card_1(C),np__1) ) ) ) )).

fof(t60_scmpds_6,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [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) )
             => r2_hidden(k2_scmpds_3(np__0),k1_relat_1(k5_scmpds_6(A,B,C))) ) ) ) )).

fof(t61_scmpds_6,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [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) )
             => k1_funct_1(k5_scmpds_6(A,B,C),k2_scmpds_3(np__0)) = k8_scmpds_2(A,B,k1_nat_1(k4_card_1(C),np__1)) ) ) ) )).

fof(t62_scmpds_6,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)
            & v3_scmpds_4(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => ( ( k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)) = np__0
                      & r1_scmpds_6(B,A)
                      & r2_scmpds_6(B,A) )
                   => ( r1_scmpds_6(k5_scmpds_6(C,D,B),A)
                      & r2_scmpds_6(k5_scmpds_6(C,D,B),A) ) ) ) ) ) ) )).

fof(t63_scmpds_6,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) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => ( k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)) != np__0
                   => ( r1_scmpds_6(k5_scmpds_6(C,D,B),A)
                      & r2_scmpds_6(k5_scmpds_6(C,D,B),A) ) ) ) ) ) ) )).

fof(t64_scmpds_6,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)
            & v3_scmpds_4(B)
            & v3_scmpds_5(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => ( ( k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)) = np__0
                      & r1_scmpds_6(B,A)
                      & r2_scmpds_6(B,A) )
                   => k9_scmpds_4(k5_scmpds_6(C,D,B),A) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(B,A),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(k1_nat_1(k4_card_1(B),np__1)))) ) ) ) ) ) )).

fof(t65_scmpds_6,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) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => ( k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)) != np__0
                   => k9_scmpds_4(k5_scmpds_6(C,D,B),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(k1_nat_1(k4_card_1(B),np__1)))) ) ) ) ) ) )).

fof(t66_scmpds_6,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_4(B)
            & v3_scmpds_5(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(k5_scmpds_6(C,D,B),A)) = k2_scmpds_3(k1_nat_1(k4_card_1(B),np__1)) ) ) ) ) )).

fof(t67_scmpds_6,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_4(B)
            & v3_scmpds_5(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( v1_int_1(E)
                     => ( k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),E)) = np__0
                       => k2_scmpds_2(k9_scmpds_4(k5_scmpds_6(C,E,B),A),D) = k2_scmpds_2(k9_scmpds_4(B,A),D) ) ) ) ) ) ) )).

fof(t68_scmpds_6,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) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( v1_int_1(E)
                     => ( k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),E)) != np__0
                       => k2_scmpds_2(k9_scmpds_4(k5_scmpds_6(C,E,B),A),D) = k2_scmpds_2(A,D) ) ) ) ) ) ) )).

fof(t69_scmpds_6,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [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) )
             => k4_card_1(k6_scmpds_6(A,B,C)) = k1_nat_1(k4_card_1(C),np__2) ) ) ) )).

fof(t70_scmpds_6,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [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) )
             => ( r2_hidden(k2_scmpds_3(np__0),k1_relat_1(k6_scmpds_6(A,B,C)))
                & r2_hidden(k2_scmpds_3(np__1),k1_relat_1(k6_scmpds_6(A,B,C))) ) ) ) ) )).

fof(t71_scmpds_6,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [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) )
             => ( k1_funct_1(k6_scmpds_6(A,B,C),k2_scmpds_3(np__0)) = k8_scmpds_2(A,B,np__2)
                & k1_funct_1(k6_scmpds_6(A,B,C),k2_scmpds_3(np__1)) = k4_scmpds_2(k1_nat_1(k4_card_1(C),np__1)) ) ) ) ) )).

fof(t72_scmpds_6,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)
            & v3_scmpds_4(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => ( ( r1_scmpds_6(B,A)
                      & r2_scmpds_6(B,A) )
                   => ( k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)) = np__0
                      | ( r1_scmpds_6(k6_scmpds_6(C,D,B),A)
                        & r2_scmpds_6(k6_scmpds_6(C,D,B),A) ) ) ) ) ) ) ) )).

fof(t73_scmpds_6,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) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => ( k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)) = np__0
                   => ( r1_scmpds_6(k6_scmpds_6(C,D,B),A)
                      & r2_scmpds_6(k6_scmpds_6(C,D,B),A) ) ) ) ) ) ) )).

fof(t74_scmpds_6,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)
            & v3_scmpds_4(B)
            & v3_scmpds_5(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => ( ( r1_scmpds_6(B,A)
                      & r2_scmpds_6(B,A) )
                   => ( k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)) = np__0
                      | k9_scmpds_4(k6_scmpds_6(C,D,B),A) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(B,A),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(k1_nat_1(k4_card_1(B),np__2)))) ) ) ) ) ) ) )).

fof(t75_scmpds_6,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) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => ( k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)) = np__0
                   => k9_scmpds_4(k6_scmpds_6(C,D,B),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(k1_nat_1(k4_card_1(B),np__2)))) ) ) ) ) ) )).

fof(t76_scmpds_6,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_4(B)
            & v3_scmpds_5(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(k6_scmpds_6(C,D,B),A)) = k2_scmpds_3(k1_nat_1(k4_card_1(B),np__2)) ) ) ) ) )).

fof(t77_scmpds_6,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_4(B)
            & v3_scmpds_5(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( v1_int_1(E)
                     => ( k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),E)) != np__0
                       => k2_scmpds_2(k9_scmpds_4(k6_scmpds_6(C,E,B),A),D) = k2_scmpds_2(k9_scmpds_4(B,A),D) ) ) ) ) ) ) )).

fof(t78_scmpds_6,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) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( v1_int_1(E)
                     => ( k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),E)) = np__0
                       => k2_scmpds_2(k9_scmpds_4(k6_scmpds_6(C,E,B),A),D) = k2_scmpds_2(A,D) ) ) ) ) ) ) )).

fof(t79_scmpds_6,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [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] :
                  ( ( v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
                    & v1_scmpds_3(D)
                    & m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
                 => k4_card_1(k3_scmpds_6(A,B,C,D)) = k1_nat_1(k1_nat_1(k4_card_1(C),k4_card_1(D)),np__2) ) ) ) ) )).

fof(t80_scmpds_6,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [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] :
                  ( ( v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
                    & v1_scmpds_3(D)
                    & m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
                 => ( r2_hidden(k2_scmpds_3(np__0),k1_relat_1(k3_scmpds_6(A,B,C,D)))
                    & r2_hidden(k2_scmpds_3(np__1),k1_relat_1(k3_scmpds_6(A,B,C,D))) ) ) ) ) ) )).

fof(t81_scmpds_6,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [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] :
                  ( ( v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
                    & v1_scmpds_3(D)
                    & m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
                 => k1_funct_1(k3_scmpds_6(A,B,C,D),k2_scmpds_3(np__0)) = k9_scmpds_2(A,B,k1_nat_1(k4_card_1(C),np__2)) ) ) ) ) )).

fof(t82_scmpds_6,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)
            & v3_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)
                & v3_scmpds_4(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( v1_int_1(E)
                     => ( ( r1_scmpds_6(B,A)
                          & r2_scmpds_6(B,A) )
                       => ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),E)),np__0)
                          | ( r1_scmpds_6(k3_scmpds_6(D,E,B,C),A)
                            & r2_scmpds_6(k3_scmpds_6(D,E,B,C),A) ) ) ) ) ) ) ) ) )).

fof(t83_scmpds_6,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) )
         => ! [C] :
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & v3_scmpds_4(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( v1_int_1(E)
                     => ( ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),E)),np__0)
                          & r1_scmpds_6(C,A)
                          & r2_scmpds_6(C,A) )
                       => ( r1_scmpds_6(k3_scmpds_6(D,E,B,C),A)
                          & r2_scmpds_6(k3_scmpds_6(D,E,B,C),A) ) ) ) ) ) ) ) )).

fof(t84_scmpds_6,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)
            & v3_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)
                & v3_scmpds_4(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( v1_int_1(E)
                     => ( ( r1_scmpds_6(B,A)
                          & r2_scmpds_6(B,A) )
                       => ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),E)),np__0)
                          | k9_scmpds_4(k3_scmpds_6(D,E,B,C),A) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(B,A),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(k1_nat_1(k1_nat_1(k4_card_1(B),k4_card_1(C)),np__2)))) ) ) ) ) ) ) ) )).

fof(t85_scmpds_6,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) )
         => ! [C] :
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & v3_scmpds_4(C)
                & v3_scmpds_5(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( v1_int_1(E)
                     => ( ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),E)),np__0)
                          & r1_scmpds_6(C,A)
                          & r2_scmpds_6(C,A) )
                       => k9_scmpds_4(k3_scmpds_6(D,E,B,C),A) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(C,A),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(k1_nat_1(k1_nat_1(k4_card_1(B),k4_card_1(C)),np__2)))) ) ) ) ) ) ) )).

fof(t86_scmpds_6,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_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)
                & v3_scmpds_5(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( v1_int_1(E)
                     => k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(k3_scmpds_6(D,E,B,C),A)) = k2_scmpds_3(k1_nat_1(k1_nat_1(k4_card_1(B),k4_card_1(C)),np__2)) ) ) ) ) ) )).

fof(t87_scmpds_6,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_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)
                & v3_scmpds_4(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( m1_scmpds_2(E)
                     => ! [F] :
                          ( v1_int_1(F)
                         => ( ~ r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),F)),np__0)
                           => k2_scmpds_2(k9_scmpds_4(k3_scmpds_6(D,F,B,C),A),E) = k2_scmpds_2(k9_scmpds_4(B,A),E) ) ) ) ) ) ) ) )).

fof(t88_scmpds_6,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) )
         => ! [C] :
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & v2_scmpds_4(C)
                & v3_scmpds_4(C)
                & v3_scmpds_5(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( m1_scmpds_2(E)
                     => ! [F] :
                          ( v1_int_1(F)
                         => ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),F)),np__0)
                           => k2_scmpds_2(k9_scmpds_4(k3_scmpds_6(D,F,B,C),A),E) = k2_scmpds_2(k9_scmpds_4(C,A),E) ) ) ) ) ) ) ) )).

fof(t89_scmpds_6,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [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) )
             => k4_card_1(k7_scmpds_6(A,B,C)) = k1_nat_1(k4_card_1(C),np__1) ) ) ) )).

fof(t90_scmpds_6,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [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) )
             => r2_hidden(k2_scmpds_3(np__0),k1_relat_1(k7_scmpds_6(A,B,C))) ) ) ) )).

fof(t91_scmpds_6,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [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) )
             => k1_funct_1(k7_scmpds_6(A,B,C),k2_scmpds_3(np__0)) = k9_scmpds_2(A,B,k1_nat_1(k4_card_1(C),np__1)) ) ) ) )).

fof(t92_scmpds_6,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)
            & v3_scmpds_4(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => ( ( r1_scmpds_6(B,A)
                      & r2_scmpds_6(B,A) )
                   => ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0)
                      | ( r1_scmpds_6(k7_scmpds_6(C,D,B),A)
                        & r2_scmpds_6(k7_scmpds_6(C,D,B),A) ) ) ) ) ) ) ) )).

fof(t93_scmpds_6,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) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0)
                   => ( r1_scmpds_6(k7_scmpds_6(C,D,B),A)
                      & r2_scmpds_6(k7_scmpds_6(C,D,B),A) ) ) ) ) ) ) )).

fof(t94_scmpds_6,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)
            & v3_scmpds_4(B)
            & v3_scmpds_5(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => ( ( r1_scmpds_6(B,A)
                      & r2_scmpds_6(B,A) )
                   => ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0)
                      | k9_scmpds_4(k7_scmpds_6(C,D,B),A) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(B,A),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(k1_nat_1(k4_card_1(B),np__1)))) ) ) ) ) ) ) )).

fof(t95_scmpds_6,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) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0)
                   => k9_scmpds_4(k7_scmpds_6(C,D,B),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(k1_nat_1(k4_card_1(B),np__1)))) ) ) ) ) ) )).

fof(t96_scmpds_6,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_4(B)
            & v3_scmpds_5(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(k7_scmpds_6(C,D,B),A)) = k2_scmpds_3(k1_nat_1(k4_card_1(B),np__1)) ) ) ) ) )).

fof(t97_scmpds_6,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_4(B)
            & v3_scmpds_5(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( v1_int_1(E)
                     => ( ~ r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),E)),np__0)
                       => k2_scmpds_2(k9_scmpds_4(k7_scmpds_6(C,E,B),A),D) = k2_scmpds_2(k9_scmpds_4(B,A),D) ) ) ) ) ) ) )).

fof(t98_scmpds_6,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) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( v1_int_1(E)
                     => ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),E)),np__0)
                       => k2_scmpds_2(k9_scmpds_4(k7_scmpds_6(C,E,B),A),D) = k2_scmpds_2(A,D) ) ) ) ) ) ) )).

fof(t99_scmpds_6,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [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) )
             => k4_card_1(k8_scmpds_6(A,B,C)) = k1_nat_1(k4_card_1(C),np__2) ) ) ) )).

fof(t100_scmpds_6,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [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) )
             => ( r2_hidden(k2_scmpds_3(np__0),k1_relat_1(k8_scmpds_6(A,B,C)))
                & r2_hidden(k2_scmpds_3(np__1),k1_relat_1(k8_scmpds_6(A,B,C))) ) ) ) ) )).

fof(t101_scmpds_6,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [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) )
             => ( k1_funct_1(k8_scmpds_6(A,B,C),k2_scmpds_3(np__0)) = k9_scmpds_2(A,B,np__2)
                & k1_funct_1(k8_scmpds_6(A,B,C),k2_scmpds_3(np__1)) = k4_scmpds_2(k1_nat_1(k4_card_1(C),np__1)) ) ) ) ) )).

fof(t102_scmpds_6,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)
            & v3_scmpds_4(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => ( ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0)
                      & r1_scmpds_6(B,A)
                      & r2_scmpds_6(B,A) )
                   => ( r1_scmpds_6(k8_scmpds_6(C,D,B),A)
                      & r2_scmpds_6(k8_scmpds_6(C,D,B),A) ) ) ) ) ) ) )).

fof(t103_scmpds_6,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) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => ( ~ r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0)
                   => ( r1_scmpds_6(k8_scmpds_6(C,D,B),A)
                      & r2_scmpds_6(k8_scmpds_6(C,D,B),A) ) ) ) ) ) ) )).

fof(t104_scmpds_6,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)
            & v3_scmpds_4(B)
            & v3_scmpds_5(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => ( ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0)
                      & r1_scmpds_6(B,A)
                      & r2_scmpds_6(B,A) )
                   => k9_scmpds_4(k8_scmpds_6(C,D,B),A) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(B,A),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(k1_nat_1(k4_card_1(B),np__2)))) ) ) ) ) ) )).

fof(t105_scmpds_6,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) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => ( ~ r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0)
                   => k9_scmpds_4(k8_scmpds_6(C,D,B),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(k1_nat_1(k4_card_1(B),np__2)))) ) ) ) ) ) )).

fof(t106_scmpds_6,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_4(B)
            & v3_scmpds_5(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(k8_scmpds_6(C,D,B),A)) = k2_scmpds_3(k1_nat_1(k4_card_1(B),np__2)) ) ) ) ) )).

fof(t107_scmpds_6,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_4(B)
            & v3_scmpds_5(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( v1_int_1(E)
                     => ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),E)),np__0)
                       => k2_scmpds_2(k9_scmpds_4(k8_scmpds_6(C,E,B),A),D) = k2_scmpds_2(k9_scmpds_4(B,A),D) ) ) ) ) ) ) )).

fof(t108_scmpds_6,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) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( v1_int_1(E)
                     => ( ~ r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),E)),np__0)
                       => k2_scmpds_2(k9_scmpds_4(k8_scmpds_6(C,E,B),A),D) = k2_scmpds_2(A,D) ) ) ) ) ) ) )).

fof(t109_scmpds_6,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [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] :
                  ( ( v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
                    & v1_scmpds_3(D)
                    & m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
                 => k4_card_1(k4_scmpds_6(A,B,C,D)) = k1_nat_1(k1_nat_1(k4_card_1(C),k4_card_1(D)),np__2) ) ) ) ) )).

fof(t110_scmpds_6,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [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] :
                  ( ( v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
                    & v1_scmpds_3(D)
                    & m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
                 => ( r2_hidden(k2_scmpds_3(np__0),k1_relat_1(k4_scmpds_6(A,B,C,D)))
                    & r2_hidden(k2_scmpds_3(np__1),k1_relat_1(k4_scmpds_6(A,B,C,D))) ) ) ) ) ) )).

fof(t111_scmpds_6,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [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] :
                  ( ( v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
                    & v1_scmpds_3(D)
                    & m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
                 => k1_funct_1(k4_scmpds_6(A,B,C,D),k2_scmpds_3(np__0)) = k10_scmpds_2(A,B,k1_nat_1(k4_card_1(C),np__2)) ) ) ) ) )).

fof(t112_scmpds_6,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)
            & v3_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)
                & v3_scmpds_4(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( v1_int_1(E)
                     => ( ( r1_scmpds_6(B,A)
                          & r2_scmpds_6(B,A) )
                       => ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),E)))
                          | ( r1_scmpds_6(k4_scmpds_6(D,E,B,C),A)
                            & r2_scmpds_6(k4_scmpds_6(D,E,B,C),A) ) ) ) ) ) ) ) ) )).

fof(t113_scmpds_6,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) )
         => ! [C] :
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & v3_scmpds_4(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( v1_int_1(E)
                     => ( ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),E)))
                          & r1_scmpds_6(C,A)
                          & r2_scmpds_6(C,A) )
                       => ( r1_scmpds_6(k4_scmpds_6(D,E,B,C),A)
                          & r2_scmpds_6(k4_scmpds_6(D,E,B,C),A) ) ) ) ) ) ) ) )).

fof(t114_scmpds_6,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)
            & v3_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)
                & v3_scmpds_4(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( v1_int_1(E)
                     => ( ( r1_scmpds_6(B,A)
                          & r2_scmpds_6(B,A) )
                       => ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),E)))
                          | k9_scmpds_4(k4_scmpds_6(D,E,B,C),A) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(B,A),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(k1_nat_1(k1_nat_1(k4_card_1(B),k4_card_1(C)),np__2)))) ) ) ) ) ) ) ) )).

fof(t115_scmpds_6,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) )
         => ! [C] :
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & v3_scmpds_4(C)
                & v3_scmpds_5(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( v1_int_1(E)
                     => ( ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),E)))
                          & r1_scmpds_6(C,A)
                          & r2_scmpds_6(C,A) )
                       => k9_scmpds_4(k4_scmpds_6(D,E,B,C),A) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(C,A),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(k1_nat_1(k1_nat_1(k4_card_1(B),k4_card_1(C)),np__2)))) ) ) ) ) ) ) )).

fof(t116_scmpds_6,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_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)
                & v3_scmpds_5(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( v1_int_1(E)
                     => k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(k4_scmpds_6(D,E,B,C),A)) = k2_scmpds_3(k1_nat_1(k1_nat_1(k4_card_1(B),k4_card_1(C)),np__2)) ) ) ) ) ) )).

fof(t117_scmpds_6,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_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)
                & v3_scmpds_4(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( m1_scmpds_2(E)
                     => ! [F] :
                          ( v1_int_1(F)
                         => ( ~ r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),F)))
                           => k2_scmpds_2(k9_scmpds_4(k4_scmpds_6(D,F,B,C),A),E) = k2_scmpds_2(k9_scmpds_4(B,A),E) ) ) ) ) ) ) ) )).

fof(t118_scmpds_6,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) )
         => ! [C] :
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & v2_scmpds_4(C)
                & v3_scmpds_4(C)
                & v3_scmpds_5(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( m1_scmpds_2(E)
                     => ! [F] :
                          ( v1_int_1(F)
                         => ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),F)))
                           => k2_scmpds_2(k9_scmpds_4(k4_scmpds_6(D,F,B,C),A),E) = k2_scmpds_2(k9_scmpds_4(C,A),E) ) ) ) ) ) ) ) )).

fof(t119_scmpds_6,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [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) )
             => k4_card_1(k9_scmpds_6(A,B,C)) = k1_nat_1(k4_card_1(C),np__1) ) ) ) )).

fof(t120_scmpds_6,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [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) )
             => r2_hidden(k2_scmpds_3(np__0),k1_relat_1(k9_scmpds_6(A,B,C))) ) ) ) )).

fof(t121_scmpds_6,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [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) )
             => k1_funct_1(k9_scmpds_6(A,B,C),k2_scmpds_3(np__0)) = k10_scmpds_2(A,B,k1_nat_1(k4_card_1(C),np__1)) ) ) ) )).

fof(t122_scmpds_6,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)
            & v3_scmpds_4(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => ( ( r1_scmpds_6(B,A)
                      & r2_scmpds_6(B,A) )
                   => ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)))
                      | ( r1_scmpds_6(k9_scmpds_6(C,D,B),A)
                        & r2_scmpds_6(k9_scmpds_6(C,D,B),A) ) ) ) ) ) ) ) )).

fof(t123_scmpds_6,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) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)))
                   => ( r1_scmpds_6(k9_scmpds_6(C,D,B),A)
                      & r2_scmpds_6(k9_scmpds_6(C,D,B),A) ) ) ) ) ) ) )).

fof(t124_scmpds_6,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)
            & v3_scmpds_4(B)
            & v3_scmpds_5(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => ( ( r1_scmpds_6(B,A)
                      & r2_scmpds_6(B,A) )
                   => ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)))
                      | k9_scmpds_4(k9_scmpds_6(C,D,B),A) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(B,A),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(k1_nat_1(k4_card_1(B),np__1)))) ) ) ) ) ) ) )).

fof(t125_scmpds_6,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) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)))
                   => k9_scmpds_4(k9_scmpds_6(C,D,B),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(k1_nat_1(k4_card_1(B),np__1)))) ) ) ) ) ) )).

fof(t126_scmpds_6,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_4(B)
            & v3_scmpds_5(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(k9_scmpds_6(C,D,B),A)) = k2_scmpds_3(k1_nat_1(k4_card_1(B),np__1)) ) ) ) ) )).

fof(t127_scmpds_6,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_4(B)
            & v3_scmpds_5(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( v1_int_1(E)
                     => ( ~ r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),E)))
                       => k2_scmpds_2(k9_scmpds_4(k9_scmpds_6(C,E,B),A),D) = k2_scmpds_2(k9_scmpds_4(B,A),D) ) ) ) ) ) ) )).

fof(t128_scmpds_6,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) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( v1_int_1(E)
                     => ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),E)))
                       => k2_scmpds_2(k9_scmpds_4(k9_scmpds_6(C,E,B),A),D) = k2_scmpds_2(A,D) ) ) ) ) ) ) )).

fof(t129_scmpds_6,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [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) )
             => k4_card_1(k10_scmpds_6(A,B,C)) = k1_nat_1(k4_card_1(C),np__2) ) ) ) )).

fof(t130_scmpds_6,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [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) )
             => ( r2_hidden(k2_scmpds_3(np__0),k1_relat_1(k10_scmpds_6(A,B,C)))
                & r2_hidden(k2_scmpds_3(np__1),k1_relat_1(k10_scmpds_6(A,B,C))) ) ) ) ) )).

fof(t131_scmpds_6,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [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) )
             => ( k1_funct_1(k10_scmpds_6(A,B,C),k2_scmpds_3(np__0)) = k10_scmpds_2(A,B,np__2)
                & k1_funct_1(k10_scmpds_6(A,B,C),k2_scmpds_3(np__1)) = k4_scmpds_2(k1_nat_1(k4_card_1(C),np__1)) ) ) ) ) )).

fof(t132_scmpds_6,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)
            & v3_scmpds_4(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => ( ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)))
                      & r1_scmpds_6(B,A)
                      & r2_scmpds_6(B,A) )
                   => ( r1_scmpds_6(k10_scmpds_6(C,D,B),A)
                      & r2_scmpds_6(k10_scmpds_6(C,D,B),A) ) ) ) ) ) ) )).

fof(t133_scmpds_6,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) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => ( ~ r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)))
                   => ( r1_scmpds_6(k10_scmpds_6(C,D,B),A)
                      & r2_scmpds_6(k10_scmpds_6(C,D,B),A) ) ) ) ) ) ) )).

fof(t134_scmpds_6,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)
            & v3_scmpds_4(B)
            & v3_scmpds_5(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => ( ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)))
                      & r1_scmpds_6(B,A)
                      & r2_scmpds_6(B,A) )
                   => k9_scmpds_4(k10_scmpds_6(C,D,B),A) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(B,A),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(k1_nat_1(k4_card_1(B),np__2)))) ) ) ) ) ) )).

fof(t135_scmpds_6,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) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => ( ~ r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)))
                   => k9_scmpds_4(k10_scmpds_6(C,D,B),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(k1_nat_1(k4_card_1(B),np__2)))) ) ) ) ) ) )).

fof(t136_scmpds_6,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_4(B)
            & v3_scmpds_5(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(k10_scmpds_6(C,D,B),A)) = k2_scmpds_3(k1_nat_1(k4_card_1(B),np__2)) ) ) ) ) )).

fof(t137_scmpds_6,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_4(B)
            & v3_scmpds_5(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( v1_int_1(E)
                     => ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),E)))
                       => k2_scmpds_2(k9_scmpds_4(k10_scmpds_6(C,E,B),A),D) = k2_scmpds_2(k9_scmpds_4(B,A),D) ) ) ) ) ) ) )).

fof(t138_scmpds_6,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) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( v1_int_1(E)
                     => ( ~ r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),E)))
                       => k2_scmpds_2(k9_scmpds_4(k10_scmpds_6(C,E,B),A),D) = k2_scmpds_2(A,D) ) ) ) ) ) ) )).

fof(dt_k1_scmpds_6,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ( v1_ami_3(k1_scmpds_6(A),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k1_scmpds_6(A))
        & m1_ami_1(k1_scmpds_6(A),k1_tarski(k4_numbers),k1_scmpds_2) ) ) )).

fof(dt_k2_scmpds_6,axiom,(
    ! [A,B,C,D] :
      ( ( m1_scmpds_2(A)
        & v1_int_1(B)
        & 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)
        & v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(D)
        & m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ( v1_ami_3(k2_scmpds_6(A,B,C,D),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k2_scmpds_6(A,B,C,D))
        & m1_ami_1(k2_scmpds_6(A,B,C,D),k1_tarski(k4_numbers),k1_scmpds_2) ) ) )).

fof(dt_k3_scmpds_6,axiom,(
    ! [A,B,C,D] :
      ( ( m1_scmpds_2(A)
        & v1_int_1(B)
        & 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)
        & v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(D)
        & m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ( v1_ami_3(k3_scmpds_6(A,B,C,D),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k3_scmpds_6(A,B,C,D))
        & m1_ami_1(k3_scmpds_6(A,B,C,D),k1_tarski(k4_numbers),k1_scmpds_2) ) ) )).

fof(dt_k4_scmpds_6,axiom,(
    ! [A,B,C,D] :
      ( ( m1_scmpds_2(A)
        & v1_int_1(B)
        & 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)
        & v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(D)
        & m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ( v1_ami_3(k4_scmpds_6(A,B,C,D),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k4_scmpds_6(A,B,C,D))
        & m1_ami_1(k4_scmpds_6(A,B,C,D),k1_tarski(k4_numbers),k1_scmpds_2) ) ) )).

fof(dt_k5_scmpds_6,axiom,(
    ! [A,B,C] :
      ( ( m1_scmpds_2(A)
        & v1_int_1(B)
        & 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) )
     => ( v1_ami_3(k5_scmpds_6(A,B,C),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k5_scmpds_6(A,B,C))
        & m1_ami_1(k5_scmpds_6(A,B,C),k1_tarski(k4_numbers),k1_scmpds_2) ) ) )).

fof(dt_k6_scmpds_6,axiom,(
    ! [A,B,C] :
      ( ( m1_scmpds_2(A)
        & v1_int_1(B)
        & 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) )
     => ( v1_ami_3(k6_scmpds_6(A,B,C),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k6_scmpds_6(A,B,C))
        & m1_ami_1(k6_scmpds_6(A,B,C),k1_tarski(k4_numbers),k1_scmpds_2) ) ) )).

fof(dt_k7_scmpds_6,axiom,(
    ! [A,B,C] :
      ( ( m1_scmpds_2(A)
        & v1_int_1(B)
        & 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) )
     => ( v1_ami_3(k7_scmpds_6(A,B,C),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k7_scmpds_6(A,B,C))
        & m1_ami_1(k7_scmpds_6(A,B,C),k1_tarski(k4_numbers),k1_scmpds_2) ) ) )).

fof(dt_k8_scmpds_6,axiom,(
    ! [A,B,C] :
      ( ( m1_scmpds_2(A)
        & v1_int_1(B)
        & 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) )
     => ( v1_ami_3(k8_scmpds_6(A,B,C),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k8_scmpds_6(A,B,C))
        & m1_ami_1(k8_scmpds_6(A,B,C),k1_tarski(k4_numbers),k1_scmpds_2) ) ) )).

fof(dt_k9_scmpds_6,axiom,(
    ! [A,B,C] :
      ( ( m1_scmpds_2(A)
        & v1_int_1(B)
        & 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) )
     => ( v1_ami_3(k9_scmpds_6(A,B,C),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k9_scmpds_6(A,B,C))
        & m1_ami_1(k9_scmpds_6(A,B,C),k1_tarski(k4_numbers),k1_scmpds_2) ) ) )).

fof(dt_k10_scmpds_6,axiom,(
    ! [A,B,C] :
      ( ( m1_scmpds_2(A)
        & v1_int_1(B)
        & 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) )
     => ( v1_ami_3(k10_scmpds_6(A,B,C),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k10_scmpds_6(A,B,C))
        & m1_ami_1(k10_scmpds_6(A,B,C),k1_tarski(k4_numbers),k1_scmpds_2) ) ) )).
%------------------------------------------------------------------------------