SET007 Axioms: SET007+478.ax


%------------------------------------------------------------------------------
% File     : SET007+478 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Conditional Branch Macro Instructions of SCMFSA. Part I
% 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    : scmfsa8a [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   77 (   3 unit)
%            Number of atoms       :  506 (  64 equality)
%            Maximal formula depth :   14 (   7 average)
%            Number of connectives :  439 (  10 ~  ;   0  |; 222  &)
%                                         (   4 <=>; 203 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   31 (   1 propositional; 0-3 arity)
%            Number of functors    :   56 (   9 constant; 0-4 arity)
%            Number of variables   :  167 (   0 singleton; 165 !;   2 ?)
%            Maximal term depth    :   10 (   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_scmfsa8a,axiom,(
    ! [A,B] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_subset_1(B,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) )
     => ( v1_relat_1(k1_scmfsa8a(A,B))
        & v1_funct_1(k1_scmfsa8a(A,B))
        & v1_finset_1(k1_scmfsa8a(A,B))
        & v1_ami_3(k1_scmfsa8a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v2_scmfsa7b(k1_scmfsa8a(A,B)) ) ) )).

fof(fc2_scmfsa8a,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ( v1_relat_1(k1_scmfsa6a(A))
        & v1_funct_1(k1_scmfsa6a(A))
        & v1_finset_1(k1_scmfsa6a(A))
        & v1_ami_3(k1_scmfsa6a(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v2_scmfsa7b(k1_scmfsa6a(A)) ) ) )).

fof(fc3_scmfsa8a,axiom,(
    ! [A,B] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa7b(A)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_subset_1(B,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) )
     => ( v1_relat_1(k1_scmfsa8a(A,B))
        & v1_funct_1(k1_scmfsa8a(A,B))
        & v1_finset_1(k1_scmfsa8a(A,B))
        & v1_ami_3(k1_scmfsa8a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa7b(k1_scmfsa8a(A,B))
        & v2_scmfsa7b(k1_scmfsa8a(A,B)) ) ) )).

fof(fc4_scmfsa8a,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(A)
        & v1_scmfsa7b(A)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ( v1_relat_1(k1_scmfsa6a(A))
        & v1_funct_1(k1_scmfsa6a(A))
        & v1_finset_1(k1_scmfsa6a(A))
        & v1_ami_3(k1_scmfsa6a(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(k1_scmfsa6a(A))
        & v1_scmfsa7b(k1_scmfsa6a(A))
        & v2_scmfsa7b(k1_scmfsa6a(A)) ) ) )).

fof(fc5_scmfsa8a,axiom,(
    ! [A,B] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(A)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_subset_1(B,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) )
     => ( v1_relat_1(k1_scmfsa8a(A,B))
        & v1_funct_1(k1_scmfsa8a(A,B))
        & v1_finset_1(k1_scmfsa8a(A,B))
        & v1_ami_3(k1_scmfsa8a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(k1_scmfsa8a(A,B))
        & v2_scmfsa7b(k1_scmfsa8a(A,B)) ) ) )).

fof(fc6_scmfsa8a,axiom,(
    ! [A,B] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(A)
        & v1_scmfsa7b(A)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(B)
        & v1_scmfsa7b(B)
        & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ( v1_relat_1(k4_scmfsa6a(A,B))
        & v1_funct_1(k4_scmfsa6a(A,B))
        & v1_finset_1(k4_scmfsa6a(A,B))
        & v1_ami_3(k4_scmfsa6a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(k4_scmfsa6a(A,B))
        & v1_scmfsa7b(k4_scmfsa6a(A,B)) ) ) )).

fof(rc1_scmfsa8a,axiom,(
    ? [A] :
      ( m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
      & v1_scmfsa_4(A)
      & v1_scmfsa8a(A) ) )).

fof(t1_scmfsa8a,axiom,(
    $true )).

fof(t2_scmfsa8a,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( r1_xboole_0(k1_relat_1(B),C)
             => k7_relat_1(k1_funct_4(A,B),C) = k7_relat_1(A,C) ) ) ) )).

fof(t3_scmfsa8a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => k1_relat_1(k7_relat_1(A,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) = u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) )).

fof(t4_scmfsa8a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ( v9_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
       => ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ( r1_xreal_0(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A),B)
             => k8_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A),B)) = k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ) ) )).

fof(t5_scmfsa8a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ( v9_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
       => ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ( r1_xreal_0(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A),B)
             => k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A),B)) = k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A),k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A))) ) ) ) ) )).

fof(t6_scmfsa8a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
         => ( r1_funct_7(A,B,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
          <=> ( k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) = k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B)
              & k7_relat_1(A,k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(B,k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) )).

fof(t7_scmfsa8a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6b(B,A)) = k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k12_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(B)))) ) ) )).

fof(t8_scmfsa8a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa6c(A),k3_scmfsa6a(B)) = k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(B)) ) ) )).

fof(t9_scmfsa8a,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(A)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( m1_struct_0(B,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
         => r1_tarski(A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B))) ) ) )).

fof(t10_scmfsa8a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( m1_struct_0(B,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
         => k7_relat_1(A,k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B)),k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2)) ) ) )).

fof(t11_scmfsa8a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ! [C] :
              ( m1_struct_0(C,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
             => k7_relat_1(A,k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C))),k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2)) ) ) ) )).

fof(t12_scmfsa8a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( m1_struct_0(B,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
         => r1_xboole_0(k1_relat_1(k7_relat_1(A,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))),k1_relat_1(k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B))) ) ) )).

fof(t13_scmfsa8a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(B)) = k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa6c(A),k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0)))) ) ) )).

fof(t14_scmfsa8a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ! [D] :
                  ( m1_struct_0(D,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
                 => r1_funct_7(k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,D))),k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,D))),u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ) ) ) ) )).

fof(t15_scmfsa8a,axiom,(
    k1_relat_1(k5_scmfsa_4) = k1_struct_0(k1_scmfsa_2,k5_scmfsa_2(np__0)) )).

fof(t16_scmfsa8a,axiom,
    ( r2_hidden(k5_scmfsa_2(np__0),k1_relat_1(k5_scmfsa_4))
    & k1_funct_1(k5_scmfsa_4,k5_scmfsa_2(np__0)) = k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )).

fof(t17_scmfsa8a,axiom,(
    k4_card_1(k5_scmfsa_4) = np__1 )).

fof(d1_scmfsa8a,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( m1_struct_0(B,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
         => k1_scmfsa8a(A,B) = k5_relat_1(A,k1_funct_4(k6_relat_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k3_cqc_lang(k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_scmfsa_2(B)))) ) ) )).

fof(t18_scmfsa8a,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => k1_scmfsa6a(A) = k1_scmfsa8a(A,k5_scmfsa_2(k4_card_1(A))) ) )).

fof(t19_scmfsa8a,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( m1_struct_0(B,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
         => k1_relat_1(k1_scmfsa8a(A,B)) = k1_relat_1(A) ) ) )).

fof(t20_scmfsa8a,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( m1_struct_0(B,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
         => k1_scmfsa8a(A,B) = k1_funct_4(A,k5_relat_1(A,k3_cqc_lang(k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_scmfsa_2(B)))) ) ) )).

fof(t21_scmfsa8a,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( m1_struct_0(B,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
         => ! [C] :
              ( r2_hidden(C,k1_relat_1(A))
             => ( ( k1_funct_1(A,C) = k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                 => k1_funct_1(k1_scmfsa8a(A,B),C) = k13_scmfsa_2(B) )
                & ( k1_funct_1(A,C) != k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                 => k1_funct_1(k1_scmfsa8a(A,B),C) = k1_funct_1(A,C) ) ) ) ) ) )).

fof(t22_scmfsa8a,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( r3_scmfsa7b(A,B)
               => r3_scmfsa7b(k4_scmfsa_4(A,C),B) ) ) ) ) )).

fof(t23_scmfsa8a,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m1_scmfsa_2(C)
             => ( r4_scmfsa7b(A,C)
               => r4_scmfsa7b(k6_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa_5(A,B)),C) ) ) ) ) )).

fof(t24_scmfsa8a,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa7b(A)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => v1_scmfsa7b(k6_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa_5(A,B))) ) ) )).

fof(t25_scmfsa8a,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ! [C] :
              ( m1_scmfsa_2(C)
             => ( ( r4_scmfsa7b(A,C)
                  & r4_scmfsa7b(B,C) )
               => r4_scmfsa7b(k1_scmfsa_4(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,B),C) ) ) ) ) )).

fof(t26_scmfsa8a,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa7b(A)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa7b(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => v1_scmfsa7b(k1_scmfsa_4(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,B)) ) ) )).

fof(t27_scmfsa8a,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( m1_struct_0(B,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
         => ! [C] :
              ( m1_scmfsa_2(C)
             => ( r4_scmfsa7b(A,C)
               => r4_scmfsa7b(k1_scmfsa8a(A,B),C) ) ) ) ) )).

fof(d2_scmfsa8a,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
     => k2_scmfsa8a(A) = k14_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0),k13_scmfsa_2(A)) ) )).

fof(d3_scmfsa8a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ( r1_scmfsa8a(A,B)
          <=> ? [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
                & k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),C)) = k5_scmfsa_2(k4_card_1(k6_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B)))
                & ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( ~ r1_xreal_0(C,D)
                     => r2_hidden(k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),D)),k1_relat_1(B)) ) ) ) ) ) ) )).

fof(d4_scmfsa8a,axiom,(
    ! [A] :
      ( ( v1_scmfsa_4(A)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ( v1_scmfsa8a(A)
      <=> ! [B] :
            ( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
           => r1_scmfsa8a(B,A) ) ) ) )).

fof(d5_scmfsa8a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ( r1_scmfsa8a(A,B)
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ( C = k3_scmfsa8a(A,B)
                <=> ( k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),C)) = k5_scmfsa_2(k4_card_1(k6_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B)))
                    & ! [D] :
                        ( m2_subset_1(D,k1_numbers,k5_numbers)
                       => ( ~ r2_hidden(k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),D)),k1_relat_1(B))
                         => r1_xreal_0(C,D) ) ) ) ) ) ) ) ) )).

fof(t28_scmfsa8a,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(A)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ! [C] :
              ( r2_hidden(C,k1_relat_1(A))
             => k1_funct_1(k4_scmfsa6a(A,B),C) = k1_funct_1(k1_scmfsa6a(A),C) ) ) ) )).

fof(t29_scmfsa8a,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
     => k4_card_1(k2_scmfsa8a(A)) = np__1 ) )).

fof(t30_scmfsa8a,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( r2_hidden(B,k1_relat_1(A))
         => ( ( k1_funct_1(A,B) = k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
             => k1_funct_1(k1_scmfsa6a(A),B) = k13_scmfsa_2(k5_scmfsa_2(k4_card_1(A))) )
            & ( k1_funct_1(A,B) != k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
             => k1_funct_1(k1_scmfsa6a(A),B) = k1_funct_1(A,B) ) ) ) ) )).

fof(t31_scmfsa8a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ( r1_scmfsa8a(A,B)
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ( ~ r1_xreal_0(k3_scmfsa8a(A,B),C)
                 => ( r2_hidden(k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),C)),k1_relat_1(B))
                    & k8_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),C)) != k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ) ) ) ) )).

fof(t32_scmfsa8a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ( r1_scmfsa8a(A,B)
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( r1_xreal_0(D,k3_scmfsa8a(A,B))
                     => r1_funct_7(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),D),k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa6a(B,C),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),D),u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ) ) ) ) ) ) )).

fof(t33_scmfsa8a,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( m1_struct_0(B,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
         => k4_card_1(k1_scmfsa8a(A,B)) = k4_card_1(A) ) ) )).

fof(t34_scmfsa8a,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(A)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => k4_card_1(k1_scmfsa6a(A)) = k4_card_1(A) ) )).

fof(t35_scmfsa8a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ( ( r5_scmfsa7b(B,A)
              & r6_scmfsa7b(B,A) )
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ( r1_xreal_0(C,k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))))
                 => ( r1_funct_7(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),C),k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa6a(B),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),C),u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
                    & k8_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa6a(B),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),C)) != k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ) ) ) ) )).

fof(t36_scmfsa8a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ( ( r5_scmfsa7b(B,A)
              & r6_scmfsa7b(B,A) )
           => ( k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa6a(B),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),np__1))) = k5_scmfsa_2(k4_card_1(B))
              & k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0)))))),k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa6a(B),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),np__1)),k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) )).

fof(t37_scmfsa8a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ( ( r5_scmfsa7b(B,A)
              & r6_scmfsa7b(B,A) )
           => r1_scmfsa8a(A,k1_scmfsa6a(B)) ) ) ) )).

fof(t38_scmfsa8a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ( ( r5_scmfsa7b(B,A)
              & r6_scmfsa7b(B,A) )
           => k3_scmfsa8a(A,k1_scmfsa6a(B)) = k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),np__1) ) ) ) )).

fof(t39_scmfsa8a,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( m1_struct_0(B,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
         => ( v2_scmfsa7b(A)
           => k1_scmfsa8a(A,B) = A ) ) ) )).

fof(t40_scmfsa8a,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(A)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ( v2_scmfsa7b(A)
       => k1_scmfsa6a(A) = A ) ) )).

fof(t41_scmfsa8a,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(A)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => k4_scmfsa6a(k1_scmfsa6a(A),B) = k4_scmfsa6a(A,B) ) ) )).

fof(t42_scmfsa8a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ( ( r5_scmfsa7b(B,A)
                  & r6_scmfsa7b(B,A) )
               => ( ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( r1_xreal_0(D,k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))))
                       => ( k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa6a(B),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),D)) = k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa6a(B,C),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),D))
                          & k8_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa6a(B),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),D)) = k8_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa6a(B,C),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),D)) ) ) )
                  & k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa6a(B),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),np__1)),k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa6a(B,C),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),np__1)),k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2))
                  & k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa6a(B),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),np__1))) = k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa6a(B,C),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),np__1))) ) ) ) ) ) )).

fof(t43_scmfsa8a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ( ( r5_scmfsa7b(B,k1_scmfsa6c(A))
                  & r6_scmfsa7b(B,k1_scmfsa6c(A)) )
               => ( ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( r1_xreal_0(D,k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(B))))
                       => ( k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(k1_scmfsa6a(B)))),D)) = k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(k4_scmfsa6a(B,C)))),D))
                          & k8_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(k1_scmfsa6a(B)))),D)) = k8_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(k4_scmfsa6a(B,C)))),D)) ) ) )
                  & k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(k1_scmfsa6a(B)))),k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(B))),np__1)),k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(k4_scmfsa6a(B,C)))),k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(B))),np__1)),k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2))
                  & k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(k1_scmfsa6a(B)))),k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(B))),np__1))) = k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(k4_scmfsa6a(B,C)))),k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(B))),np__1))) ) ) ) ) ) )).

fof(t44_scmfsa8a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ( ( r5_scmfsa7b(B,k1_scmfsa6c(A))
              & r6_scmfsa7b(B,k1_scmfsa6c(A)) )
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ( r1_xreal_0(C,k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(B))))
                 => ( r1_funct_7(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(B))),C),k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(k1_scmfsa6a(B)))),C),u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
                    & k8_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(k1_scmfsa6a(B)))),C)) != k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ) ) ) ) )).

fof(t45_scmfsa8a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ( ( r5_scmfsa7b(B,k1_scmfsa6c(A))
              & r6_scmfsa7b(B,k1_scmfsa6c(A)) )
           => ( k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(k1_scmfsa6a(B)))),k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(B))),np__1))) = k5_scmfsa_2(k4_card_1(B))
              & k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(B))),k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(B)))),k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(k1_scmfsa6a(B)))),k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(B))),np__1)),k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) )).

fof(t46_scmfsa8a,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(A)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
         => ( ( r5_scmfsa7b(A,B)
              & r6_scmfsa7b(A,B) )
           => ( r5_scmfsa7b(k4_scmfsa6a(A,k5_scmfsa_4),B)
              & r6_scmfsa7b(k4_scmfsa6a(A,k5_scmfsa_4),B) ) ) ) ) )).

fof(t47_scmfsa8a,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
     => ( r2_hidden(k5_scmfsa_2(np__0),k1_relat_1(k2_scmfsa8a(A)))
        & k1_funct_1(k2_scmfsa8a(A),k5_scmfsa_2(np__0)) = k13_scmfsa_2(A) ) ) )).

fof(t48_scmfsa8a,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v8_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( ( v1_ami_3(C,A,B)
                & m1_ami_1(C,A,B) )
             => ! [D] :
                  ( r2_hidden(D,k1_relat_1(C))
                 => m2_subset_1(k1_funct_1(C,D),k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B)) ) ) ) ) )).

fof(t49_scmfsa8a,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B,C] :
          ( m2_subset_1(C,k1_numbers,k5_numbers)
         => ( r2_hidden(B,k1_relat_1(k6_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa_5(A,C))))
           => k1_funct_1(k6_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa_5(A,C)),B) = k1_funct_1(k1_scmfsa_5(A,C),B) ) ) ) )).

fof(t50_scmfsa8a,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => k6_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa_5(k1_scmfsa6a(A),B)) = k1_scmfsa8a(k6_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa_5(A,B)),k5_scmfsa_2(k1_nat_1(k4_card_1(A),B))) ) ) )).

fof(t51_scmfsa8a,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ! [C] :
              ( m1_struct_0(C,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
             => k1_scmfsa8a(k1_scmfsa_4(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,B),C) = k1_scmfsa_4(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa8a(A,C),k1_scmfsa8a(B,C)) ) ) ) )).

fof(t52_scmfsa8a,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(A)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => k1_scmfsa6a(k4_scmfsa6a(A,B)) = k4_scmfsa6a(A,k1_scmfsa6a(B)) ) ) )).

fof(t53_scmfsa8a,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(A)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
         => ( ( r5_scmfsa7b(A,k1_scmfsa6c(B))
              & r6_scmfsa7b(A,k1_scmfsa6c(B)) )
           => k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k3_scmfsa6a(k4_scmfsa6a(A,k5_scmfsa_4)))),k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k3_scmfsa6a(A))),np__1))) = k5_scmfsa_2(k4_card_1(A)) ) ) ) )).

fof(t54_scmfsa8a,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(A)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
         => ( ( r5_scmfsa7b(A,k1_scmfsa6c(B))
              & r6_scmfsa7b(A,k1_scmfsa6c(B)) )
           => k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k3_scmfsa6a(A))),k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k3_scmfsa6a(A)))),k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k3_scmfsa6a(k4_scmfsa6a(A,k5_scmfsa_4)))),k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k3_scmfsa6a(A))),np__1)),k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2)) ) ) ) )).

fof(t55_scmfsa8a,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(A)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
         => ( ( r5_scmfsa7b(A,k1_scmfsa6c(B))
              & r6_scmfsa7b(A,k1_scmfsa6c(B)) )
           => v9_ami_1(k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k3_scmfsa6a(k4_scmfsa6a(A,k5_scmfsa_4))),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ) )).

fof(t56_scmfsa8a,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(A)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
         => ( ( r5_scmfsa7b(A,k1_scmfsa6c(B))
              & r6_scmfsa7b(A,k1_scmfsa6c(B)) )
           => k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k3_scmfsa6a(k4_scmfsa6a(A,k5_scmfsa_4)))) = k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k3_scmfsa6a(A))),np__1) ) ) ) )).

fof(t57_scmfsa8a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ( ( r5_scmfsa7b(B,k1_scmfsa6c(A))
              & r6_scmfsa7b(B,k1_scmfsa6c(A)) )
           => k3_scmfsa6b(k4_scmfsa6a(B,k5_scmfsa_4),A) = k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6b(B,A),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(k4_card_1(B)))) ) ) ) )).

fof(t58_scmfsa8a,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(A)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
             => ( ( r5_scmfsa7b(A,C)
                  & r6_scmfsa7b(A,C) )
               => ( r5_scmfsa7b(k4_scmfsa6a(k4_scmfsa6a(k4_scmfsa6a(A,k2_scmfsa8a(k5_scmfsa_2(k1_nat_1(k4_card_1(B),np__1)))),B),k5_scmfsa_4),C)
                  & r6_scmfsa7b(k4_scmfsa6a(k4_scmfsa6a(k4_scmfsa6a(A,k2_scmfsa8a(k5_scmfsa_2(k1_nat_1(k4_card_1(B),np__1)))),B),k5_scmfsa_4),C) ) ) ) ) ) )).

fof(t59_scmfsa8a,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(A)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
             => ( ( r5_scmfsa7b(A,C)
                  & r6_scmfsa7b(A,C) )
               => v9_ami_1(k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa6a(k4_scmfsa6a(k4_scmfsa6a(A,k2_scmfsa8a(k5_scmfsa_2(k1_nat_1(k4_card_1(B),np__1)))),B),k5_scmfsa_4),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0)))),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ) ) )).

fof(t60_scmfsa8a,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(A)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
             => ( ( r5_scmfsa7b(A,k1_scmfsa6c(C))
                  & r6_scmfsa7b(A,k1_scmfsa6c(C)) )
               => v9_ami_1(k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k3_scmfsa6a(k4_scmfsa6a(k4_scmfsa6a(k4_scmfsa6a(A,k2_scmfsa8a(k5_scmfsa_2(k1_nat_1(k4_card_1(B),np__1)))),B),k5_scmfsa_4))),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ) ) )).

fof(t61_scmfsa8a,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(A)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
             => ( ( r5_scmfsa7b(A,k1_scmfsa6c(C))
                  & r6_scmfsa7b(A,k1_scmfsa6c(C)) )
               => k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6b(k4_scmfsa6a(k4_scmfsa6a(k4_scmfsa6a(A,k2_scmfsa8a(k5_scmfsa_2(k1_nat_1(k4_card_1(B),np__1)))),B),k5_scmfsa_4),C)) = k5_scmfsa_2(k1_nat_1(k1_nat_1(k4_card_1(A),k4_card_1(B)),np__1)) ) ) ) ) )).

fof(t62_scmfsa8a,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(A)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
             => ( ( r5_scmfsa7b(A,k1_scmfsa6c(C))
                  & r6_scmfsa7b(A,k1_scmfsa6c(C)) )
               => k3_scmfsa6b(k4_scmfsa6a(k4_scmfsa6a(k4_scmfsa6a(A,k2_scmfsa8a(k5_scmfsa_2(k1_nat_1(k4_card_1(B),np__1)))),B),k5_scmfsa_4),C) = k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6b(A,C),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(k1_nat_1(k1_nat_1(k4_card_1(A),k4_card_1(B)),np__1)))) ) ) ) ) )).

fof(dt_k1_scmfsa8a,axiom,(
    ! [A,B] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_subset_1(B,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) )
     => ( v1_ami_3(k1_scmfsa8a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_ami_1(k1_scmfsa8a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) )).

fof(dt_k2_scmfsa8a,axiom,(
    ! [A] :
      ( m1_subset_1(A,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
     => ( v1_ami_3(k2_scmfsa8a(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(k2_scmfsa8a(A))
        & v1_scmfsa7b(k2_scmfsa8a(A))
        & v2_scmfsa7b(k2_scmfsa8a(A))
        & m1_ami_1(k2_scmfsa8a(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) )).

fof(dt_k3_scmfsa8a,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
        & v1_scmfsa_4(B)
        & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => m2_subset_1(k3_scmfsa8a(A,B),k1_numbers,k5_numbers) ) )).
%------------------------------------------------------------------------------