SET007 Axioms: SET007+78.ax


%------------------------------------------------------------------------------
% File     : SET007+78 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Variables in Formulae of the First Order Language
% 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    : qc_lang3 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  110 (  18 unit)
%            Number of atoms       :  600 ( 211 equality)
%            Maximal formula depth :   27 (   6 average)
%            Number of connectives :  520 (  30 ~  ;   0  |; 196  &)
%                                         (  18 <=>; 276 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   23 (   1 propositional; 0-3 arity)
%            Number of functors    :  111 (  35 constant; 0-4 arity)
%            Number of variables   :  225 (   0 singleton; 208 !;  17 ?)
%            Maximal term depth    :    5 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(t1_qc_lang3,axiom,(
    $true )).

fof(t2_qc_lang3,axiom,(
    $true )).

fof(t3_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_qc_lang1)
     => m2_subset_1(A,k5_qc_lang1,k7_qc_lang1(k6_qc_lang1(A))) ) )).

fof(d1_qc_lang3,axiom,(
    $true )).

fof(t4_qc_lang3,axiom,(
    $true )).

fof(t5_qc_lang3,axiom,(
    $true )).

fof(t6_qc_lang3,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k1_qc_lang1)
     => k22_qc_lang1(A) = k1_qc_lang3(A,k2_qc_lang1) ) )).

fof(t7_qc_lang3,axiom,(
    k24_qc_lang1(k11_qc_lang1) = k1_xboole_0 )).

fof(t8_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v2_qc_lang1(A)
       => k24_qc_lang1(A) = k22_qc_lang1(k16_qc_lang1(A)) ) ) )).

fof(t9_qc_lang3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A))
         => ! [C] :
              ( m1_qc_lang1(C,A)
             => k24_qc_lang1(k9_qc_lang1(B,C)) = k22_qc_lang1(C) ) ) ) )).

fof(t10_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v3_qc_lang1(A)
       => k24_qc_lang1(A) = k24_qc_lang1(k17_qc_lang1(A)) ) ) )).

fof(t11_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => k24_qc_lang1(k12_qc_lang1(A)) = k24_qc_lang1(A) ) )).

fof(t12_qc_lang3,axiom,(
    k24_qc_lang1(k1_qc_lang2) = k1_xboole_0 )).

fof(t13_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v4_qc_lang1(A)
       => k24_qc_lang1(A) = k4_subset_1(k2_qc_lang1,k24_qc_lang1(k18_qc_lang1(A)),k24_qc_lang1(k19_qc_lang1(A))) ) ) )).

fof(t14_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => k24_qc_lang1(k13_qc_lang1(A,B)) = k4_subset_1(k2_qc_lang1,k24_qc_lang1(A),k24_qc_lang1(B)) ) ) )).

fof(t15_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v5_qc_lang1(A)
       => k24_qc_lang1(A) = k6_subset_1(k2_qc_lang1,k24_qc_lang1(k21_qc_lang1(A)),k23_qc_lang1(k20_qc_lang1(A))) ) ) )).

fof(t16_qc_lang3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => k24_qc_lang1(k14_qc_lang1(A,B)) = k6_subset_1(k2_qc_lang1,k24_qc_lang1(B),k23_qc_lang1(A)) ) ) )).

fof(t17_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v1_qc_lang2(A)
       => k24_qc_lang1(A) = k4_subset_1(k2_qc_lang1,k24_qc_lang1(k10_qc_lang2(A)),k24_qc_lang1(k11_qc_lang2(A))) ) ) )).

fof(t18_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => k24_qc_lang1(k3_qc_lang2(A,B)) = k4_subset_1(k2_qc_lang1,k24_qc_lang1(A),k24_qc_lang1(B)) ) ) )).

fof(t19_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v2_qc_lang2(A)
       => k24_qc_lang1(A) = k4_subset_1(k2_qc_lang1,k24_qc_lang1(k12_qc_lang2(A)),k24_qc_lang1(k11_qc_lang2(A))) ) ) )).

fof(t20_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => k24_qc_lang1(k2_qc_lang2(A,B)) = k4_subset_1(k2_qc_lang1,k24_qc_lang1(A),k24_qc_lang1(B)) ) ) )).

fof(t21_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v3_qc_lang2(A)
       => k24_qc_lang1(A) = k4_subset_1(k2_qc_lang1,k24_qc_lang1(k13_qc_lang2(A)),k24_qc_lang1(k14_qc_lang2(A))) ) ) )).

fof(t22_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => k24_qc_lang1(k4_qc_lang2(A,B)) = k4_subset_1(k2_qc_lang1,k24_qc_lang1(A),k24_qc_lang1(B)) ) ) )).

fof(t23_qc_lang3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => k24_qc_lang1(k5_qc_lang2(A,B)) = k6_subset_1(k2_qc_lang1,k24_qc_lang1(B),k23_qc_lang1(A)) ) ) )).

fof(t24_qc_lang3,axiom,
    ( v6_qc_lang1(k11_qc_lang1)
    & v6_qc_lang1(k1_qc_lang2) )).

fof(t25_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v6_qc_lang1(A)
      <=> v6_qc_lang1(k12_qc_lang1(A)) ) ) )).

fof(t26_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ( ( v6_qc_lang1(A)
              & v6_qc_lang1(B) )
          <=> v6_qc_lang1(k13_qc_lang1(A,B)) ) ) ) )).

fof(t27_qc_lang3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ( v6_qc_lang1(k14_qc_lang1(A,B))
          <=> r1_tarski(k24_qc_lang1(B),k23_qc_lang1(A)) ) ) ) )).

fof(t28_qc_lang3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ( v6_qc_lang1(B)
           => v6_qc_lang1(k14_qc_lang1(A,B)) ) ) ) )).

fof(t29_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ( ( v6_qc_lang1(A)
              & v6_qc_lang1(B) )
          <=> v6_qc_lang1(k3_qc_lang2(A,B)) ) ) ) )).

fof(t30_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ( ( v6_qc_lang1(A)
              & v6_qc_lang1(B) )
          <=> v6_qc_lang1(k2_qc_lang2(A,B)) ) ) ) )).

fof(t31_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ( ( v6_qc_lang1(A)
              & v6_qc_lang1(B) )
          <=> v6_qc_lang1(k4_qc_lang2(A,B)) ) ) ) )).

fof(t32_qc_lang3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ( v6_qc_lang1(k5_qc_lang2(A,B))
          <=> r1_tarski(k24_qc_lang1(B),k23_qc_lang1(A)) ) ) ) )).

fof(t33_qc_lang3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ( v6_qc_lang1(B)
           => v6_qc_lang1(k5_qc_lang2(A,B)) ) ) ) )).

fof(d3_qc_lang3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k2_qc_lang3(A) = k4_tarski(np__4,A) ) )).

fof(t34_qc_lang3,axiom,(
    $true )).

fof(t35_qc_lang3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( k2_qc_lang3(A) = k2_qc_lang3(B)
           => A = B ) ) ) )).

fof(t36_qc_lang3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ? [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
          & k2_qc_lang3(B) = A ) ) )).

fof(d4_qc_lang3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k3_qc_lang3(A) = k4_tarski(np__6,A) ) )).

fof(t37_qc_lang3,axiom,(
    $true )).

fof(t38_qc_lang3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( k3_qc_lang3(A) = k3_qc_lang3(B)
           => A = B ) ) ) )).

fof(t39_qc_lang3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k4_qc_lang1)
     => ? [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
          & k3_qc_lang3(B) = A ) ) )).

fof(t40_qc_lang3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k3_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k4_qc_lang1)
         => A != B ) ) )).

fof(t41_qc_lang3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k3_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => A != B ) ) )).

fof(t42_qc_lang3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k4_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => A != B ) ) )).

fof(d5_qc_lang3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_qc_lang1)) )
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(A))
             => ( C = k4_qc_lang3(A,B)
              <=> ? [D] :
                    ( v1_funct_1(D)
                    & v1_funct_2(D,k8_qc_lang1,k1_zfmisc_1(A))
                    & m2_relset_1(D,k8_qc_lang1,k1_zfmisc_1(A))
                    & C = k8_funct_2(k8_qc_lang1,k1_zfmisc_1(A),D,B)
                    & ! [E] :
                        ( m1_subset_1(E,k8_qc_lang1)
                       => ! [F] :
                            ( m1_subset_1(F,k1_zfmisc_1(A))
                           => ! [G] :
                                ( m1_subset_1(G,k1_zfmisc_1(A))
                               => ( ( E = k11_qc_lang1
                                   => k8_funct_2(k8_qc_lang1,k1_zfmisc_1(A),D,E) = k1_subset_1(A) )
                                  & ( v2_qc_lang1(E)
                                   => k8_funct_2(k8_qc_lang1,k1_zfmisc_1(A),D,E) = k1_qc_lang3(k16_qc_lang1(E),A) )
                                  & ( ( v3_qc_lang1(E)
                                      & F = k8_funct_2(k8_qc_lang1,k1_zfmisc_1(A),D,k17_qc_lang1(E)) )
                                   => k8_funct_2(k8_qc_lang1,k1_zfmisc_1(A),D,E) = F )
                                  & ( ( v4_qc_lang1(E)
                                      & F = k8_funct_2(k8_qc_lang1,k1_zfmisc_1(A),D,k18_qc_lang1(E))
                                      & G = k8_funct_2(k8_qc_lang1,k1_zfmisc_1(A),D,k19_qc_lang1(E)) )
                                   => k8_funct_2(k8_qc_lang1,k1_zfmisc_1(A),D,E) = k4_subset_1(A,F,G) )
                                  & ( ( v5_qc_lang1(E)
                                      & F = k8_funct_2(k8_qc_lang1,k1_zfmisc_1(A),D,k21_qc_lang1(E)) )
                                   => k8_funct_2(k8_qc_lang1,k1_zfmisc_1(A),D,E) = F ) ) ) ) ) ) ) ) ) ) )).

fof(t43_qc_lang3,axiom,(
    $true )).

fof(t44_qc_lang3,axiom,(
    $true )).

fof(t45_qc_lang3,axiom,(
    $true )).

fof(t46_qc_lang3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_qc_lang1)) )
     => k4_qc_lang3(A,k11_qc_lang1) = k1_xboole_0 ) )).

fof(t49_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_qc_lang1)) )
         => ( v3_qc_lang1(A)
           => k4_qc_lang3(B,A) = k4_qc_lang3(B,k17_qc_lang1(A)) ) ) ) )).

fof(t50_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_qc_lang1)) )
         => k4_qc_lang3(B,k12_qc_lang1(A)) = k4_qc_lang3(B,A) ) ) )).

fof(t51_qc_lang3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_qc_lang1)) )
     => k4_qc_lang3(A,k1_qc_lang2) = k1_xboole_0 ) )).

fof(t52_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_qc_lang1)) )
         => ( v4_qc_lang1(A)
           => k4_qc_lang3(B,A) = k4_subset_1(B,k4_qc_lang3(B,k18_qc_lang1(A)),k4_qc_lang3(B,k19_qc_lang1(A))) ) ) ) )).

fof(t53_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(k1_qc_lang1)) )
             => k4_qc_lang3(C,k13_qc_lang1(A,B)) = k4_subset_1(C,k4_qc_lang3(C,A),k4_qc_lang3(C,B)) ) ) ) )).

fof(t54_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_qc_lang1)) )
         => ( v5_qc_lang1(A)
           => k4_qc_lang3(B,A) = k4_qc_lang3(B,k21_qc_lang1(A)) ) ) ) )).

fof(t55_qc_lang3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(k1_qc_lang1)) )
             => k4_qc_lang3(C,k14_qc_lang1(A,B)) = k4_qc_lang3(C,B) ) ) ) )).

fof(t56_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_qc_lang1)) )
         => ( v1_qc_lang2(A)
           => k4_qc_lang3(B,A) = k4_subset_1(B,k4_qc_lang3(B,k10_qc_lang2(A)),k4_qc_lang3(B,k11_qc_lang2(A))) ) ) ) )).

fof(t57_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(k1_qc_lang1)) )
             => k4_qc_lang3(C,k3_qc_lang2(A,B)) = k4_subset_1(C,k4_qc_lang3(C,A),k4_qc_lang3(C,B)) ) ) ) )).

fof(t58_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_qc_lang1)) )
         => ( v2_qc_lang2(A)
           => k4_qc_lang3(B,A) = k4_subset_1(B,k4_qc_lang3(B,k12_qc_lang2(A)),k4_qc_lang3(B,k11_qc_lang2(A))) ) ) ) )).

fof(t59_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(k1_qc_lang1)) )
             => k4_qc_lang3(C,k2_qc_lang2(A,B)) = k4_subset_1(C,k4_qc_lang3(C,A),k4_qc_lang3(C,B)) ) ) ) )).

fof(t60_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_qc_lang1)) )
         => ( v3_qc_lang2(A)
           => k4_qc_lang3(B,A) = k4_subset_1(B,k4_qc_lang3(B,k13_qc_lang2(A)),k4_qc_lang3(B,k14_qc_lang2(A))) ) ) ) )).

fof(t61_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(k1_qc_lang1)) )
             => k4_qc_lang3(C,k4_qc_lang2(A,B)) = k4_subset_1(C,k4_qc_lang3(C,A),k4_qc_lang3(C,B)) ) ) ) )).

fof(t62_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_qc_lang1)) )
         => ( v4_qc_lang2(A)
           => k4_qc_lang3(B,A) = k4_qc_lang3(B,k17_qc_lang1(k21_qc_lang1(k17_qc_lang1(A)))) ) ) ) )).

fof(t63_qc_lang3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(k1_qc_lang1)) )
             => k4_qc_lang3(C,k5_qc_lang2(A,B)) = k4_qc_lang3(C,B) ) ) ) )).

fof(d6_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => k5_qc_lang3(A) = k4_qc_lang3(k4_qc_lang1,A) ) )).

fof(t64_qc_lang3,axiom,(
    $true )).

fof(t65_qc_lang3,axiom,(
    k5_qc_lang3(k11_qc_lang1) = k1_xboole_0 )).

fof(t67_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => k5_qc_lang3(k12_qc_lang1(A)) = k5_qc_lang3(A) ) )).

fof(t68_qc_lang3,axiom,(
    k5_qc_lang3(k1_qc_lang2) = k1_xboole_0 )).

fof(t69_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => k5_qc_lang3(k13_qc_lang1(A,B)) = k4_subset_1(k4_qc_lang1,k5_qc_lang3(A),k5_qc_lang3(B)) ) ) )).

fof(t70_qc_lang3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => k5_qc_lang3(k14_qc_lang1(A,B)) = k5_qc_lang3(B) ) ) )).

fof(t71_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => k5_qc_lang3(k3_qc_lang2(A,B)) = k4_subset_1(k4_qc_lang1,k5_qc_lang3(A),k5_qc_lang3(B)) ) ) )).

fof(t72_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => k5_qc_lang3(k2_qc_lang2(A,B)) = k4_subset_1(k4_qc_lang1,k5_qc_lang3(A),k5_qc_lang3(B)) ) ) )).

fof(t73_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => k5_qc_lang3(k4_qc_lang2(A,B)) = k4_subset_1(k4_qc_lang1,k5_qc_lang3(A),k5_qc_lang3(B)) ) ) )).

fof(t74_qc_lang3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => k5_qc_lang3(k5_qc_lang2(A,B)) = k5_qc_lang3(B) ) ) )).

fof(d7_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => k6_qc_lang3(A) = k4_qc_lang3(k3_qc_lang1,A) ) )).

fof(t75_qc_lang3,axiom,(
    $true )).

fof(t76_qc_lang3,axiom,(
    k6_qc_lang3(k11_qc_lang1) = k1_xboole_0 )).

fof(t78_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => k6_qc_lang3(k12_qc_lang1(A)) = k6_qc_lang3(A) ) )).

fof(t79_qc_lang3,axiom,(
    k6_qc_lang3(k1_qc_lang2) = k1_xboole_0 )).

fof(t80_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => k6_qc_lang3(k13_qc_lang1(A,B)) = k4_subset_1(k3_qc_lang1,k6_qc_lang3(A),k6_qc_lang3(B)) ) ) )).

fof(t81_qc_lang3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => k6_qc_lang3(k14_qc_lang1(A,B)) = k6_qc_lang3(B) ) ) )).

fof(t82_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => k6_qc_lang3(k3_qc_lang2(A,B)) = k4_subset_1(k3_qc_lang1,k6_qc_lang3(A),k6_qc_lang3(B)) ) ) )).

fof(t83_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => k6_qc_lang3(k2_qc_lang2(A,B)) = k4_subset_1(k3_qc_lang1,k6_qc_lang3(A),k6_qc_lang3(B)) ) ) )).

fof(t84_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => k6_qc_lang3(k4_qc_lang2(A,B)) = k4_subset_1(k3_qc_lang1,k6_qc_lang3(A),k6_qc_lang3(B)) ) ) )).

fof(t85_qc_lang3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => k6_qc_lang3(k5_qc_lang2(A,B)) = k6_qc_lang3(B) ) ) )).

fof(s1_qc_lang3,axiom,
    ( ( ! [A] :
          ( m1_subset_1(A,k8_qc_lang1)
         => ! [B] :
              ( m1_subset_1(B,f1_s1_qc_lang3)
             => ! [C] :
                  ( m1_subset_1(C,f1_s1_qc_lang3)
                 => ( ( A = k11_qc_lang1
                     => k8_funct_2(k8_qc_lang1,f1_s1_qc_lang3,f2_s1_qc_lang3,A) = f4_s1_qc_lang3 )
                    & ( v2_qc_lang1(A)
                     => k8_funct_2(k8_qc_lang1,f1_s1_qc_lang3,f2_s1_qc_lang3,A) = f5_s1_qc_lang3(A) )
                    & ( ( v3_qc_lang1(A)
                        & B = k8_funct_2(k8_qc_lang1,f1_s1_qc_lang3,f2_s1_qc_lang3,k17_qc_lang1(A)) )
                     => k8_funct_2(k8_qc_lang1,f1_s1_qc_lang3,f2_s1_qc_lang3,A) = f6_s1_qc_lang3(B) )
                    & ( ( v4_qc_lang1(A)
                        & B = k8_funct_2(k8_qc_lang1,f1_s1_qc_lang3,f2_s1_qc_lang3,k18_qc_lang1(A))
                        & C = k8_funct_2(k8_qc_lang1,f1_s1_qc_lang3,f2_s1_qc_lang3,k19_qc_lang1(A)) )
                     => k8_funct_2(k8_qc_lang1,f1_s1_qc_lang3,f2_s1_qc_lang3,A) = f7_s1_qc_lang3(B,C) )
                    & ( ( v5_qc_lang1(A)
                        & B = k8_funct_2(k8_qc_lang1,f1_s1_qc_lang3,f2_s1_qc_lang3,k21_qc_lang1(A)) )
                     => k8_funct_2(k8_qc_lang1,f1_s1_qc_lang3,f2_s1_qc_lang3,A) = f8_s1_qc_lang3(A,B) ) ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,k8_qc_lang1)
         => ! [B] :
              ( m1_subset_1(B,f1_s1_qc_lang3)
             => ! [C] :
                  ( m1_subset_1(C,f1_s1_qc_lang3)
                 => ( ( A = k11_qc_lang1
                     => k8_funct_2(k8_qc_lang1,f1_s1_qc_lang3,f3_s1_qc_lang3,A) = f4_s1_qc_lang3 )
                    & ( v2_qc_lang1(A)
                     => k8_funct_2(k8_qc_lang1,f1_s1_qc_lang3,f3_s1_qc_lang3,A) = f5_s1_qc_lang3(A) )
                    & ( ( v3_qc_lang1(A)
                        & B = k8_funct_2(k8_qc_lang1,f1_s1_qc_lang3,f3_s1_qc_lang3,k17_qc_lang1(A)) )
                     => k8_funct_2(k8_qc_lang1,f1_s1_qc_lang3,f3_s1_qc_lang3,A) = f6_s1_qc_lang3(B) )
                    & ( ( v4_qc_lang1(A)
                        & B = k8_funct_2(k8_qc_lang1,f1_s1_qc_lang3,f3_s1_qc_lang3,k18_qc_lang1(A))
                        & C = k8_funct_2(k8_qc_lang1,f1_s1_qc_lang3,f3_s1_qc_lang3,k19_qc_lang1(A)) )
                     => k8_funct_2(k8_qc_lang1,f1_s1_qc_lang3,f3_s1_qc_lang3,A) = f7_s1_qc_lang3(B,C) )
                    & ( ( v5_qc_lang1(A)
                        & B = k8_funct_2(k8_qc_lang1,f1_s1_qc_lang3,f3_s1_qc_lang3,k21_qc_lang1(A)) )
                     => k8_funct_2(k8_qc_lang1,f1_s1_qc_lang3,f3_s1_qc_lang3,A) = f8_s1_qc_lang3(A,B) ) ) ) ) ) )
   => f2_s1_qc_lang3 = f3_s1_qc_lang3 )).

fof(s2_qc_lang3,axiom,
    ( ? [A] :
        ( m1_subset_1(A,f1_s2_qc_lang3)
        & ? [B] :
            ( v1_funct_1(B)
            & v1_funct_2(B,k8_qc_lang1,f1_s2_qc_lang3)
            & m2_relset_1(B,k8_qc_lang1,f1_s2_qc_lang3)
            & A = k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,B,f3_s2_qc_lang3)
            & ! [C] :
                ( m1_subset_1(C,k8_qc_lang1)
               => ! [D] :
                    ( m1_subset_1(D,f1_s2_qc_lang3)
                   => ! [E] :
                        ( m1_subset_1(E,f1_s2_qc_lang3)
                       => ( ( C = k11_qc_lang1
                           => k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,B,C) = f2_s2_qc_lang3 )
                          & ( v2_qc_lang1(C)
                           => k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,B,C) = f4_s2_qc_lang3(C) )
                          & ( ( v3_qc_lang1(C)
                              & D = k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,B,k17_qc_lang1(C)) )
                           => k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,B,C) = f5_s2_qc_lang3(D) )
                          & ( ( v4_qc_lang1(C)
                              & D = k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,B,k18_qc_lang1(C))
                              & E = k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,B,k19_qc_lang1(C)) )
                           => k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,B,C) = f6_s2_qc_lang3(D,E) )
                          & ( ( v5_qc_lang1(C)
                              & D = k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,B,k21_qc_lang1(C)) )
                           => k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,B,C) = f7_s2_qc_lang3(C,D) ) ) ) ) ) ) )
    & ! [A] :
        ( m1_subset_1(A,f1_s2_qc_lang3)
       => ! [B] :
            ( m1_subset_1(B,f1_s2_qc_lang3)
           => ~ ( ? [C] :
                    ( v1_funct_1(C)
                    & v1_funct_2(C,k8_qc_lang1,f1_s2_qc_lang3)
                    & m2_relset_1(C,k8_qc_lang1,f1_s2_qc_lang3)
                    & A = k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,C,f3_s2_qc_lang3)
                    & ! [D] :
                        ( m1_subset_1(D,k8_qc_lang1)
                       => ! [E] :
                            ( m1_subset_1(E,f1_s2_qc_lang3)
                           => ! [F] :
                                ( m1_subset_1(F,f1_s2_qc_lang3)
                               => ( ( D = k11_qc_lang1
                                   => k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,C,D) = f2_s2_qc_lang3 )
                                  & ( v2_qc_lang1(D)
                                   => k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,C,D) = f4_s2_qc_lang3(D) )
                                  & ( ( v3_qc_lang1(D)
                                      & E = k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,C,k17_qc_lang1(D)) )
                                   => k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,C,D) = f5_s2_qc_lang3(E) )
                                  & ( ( v4_qc_lang1(D)
                                      & E = k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,C,k18_qc_lang1(D))
                                      & F = k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,C,k19_qc_lang1(D)) )
                                   => k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,C,D) = f6_s2_qc_lang3(E,F) )
                                  & ( ( v5_qc_lang1(D)
                                      & E = k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,C,k21_qc_lang1(D)) )
                                   => k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,C,D) = f7_s2_qc_lang3(D,E) ) ) ) ) ) )
                & ? [C] :
                    ( v1_funct_1(C)
                    & v1_funct_2(C,k8_qc_lang1,f1_s2_qc_lang3)
                    & m2_relset_1(C,k8_qc_lang1,f1_s2_qc_lang3)
                    & B = k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,C,f3_s2_qc_lang3)
                    & ! [D] :
                        ( m1_subset_1(D,k8_qc_lang1)
                       => ! [E] :
                            ( m1_subset_1(E,f1_s2_qc_lang3)
                           => ! [F] :
                                ( m1_subset_1(F,f1_s2_qc_lang3)
                               => ( ( D = k11_qc_lang1
                                   => k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,C,D) = f2_s2_qc_lang3 )
                                  & ( v2_qc_lang1(D)
                                   => k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,C,D) = f4_s2_qc_lang3(D) )
                                  & ( ( v3_qc_lang1(D)
                                      & E = k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,C,k17_qc_lang1(D)) )
                                   => k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,C,D) = f5_s2_qc_lang3(E) )
                                  & ( ( v4_qc_lang1(D)
                                      & E = k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,C,k18_qc_lang1(D))
                                      & F = k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,C,k19_qc_lang1(D)) )
                                   => k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,C,D) = f6_s2_qc_lang3(E,F) )
                                  & ( ( v5_qc_lang1(D)
                                      & E = k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,C,k21_qc_lang1(D)) )
                                   => k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,C,D) = f7_s2_qc_lang3(D,E) ) ) ) ) ) )
                & A != B ) ) ) )).

fof(s3_qc_lang3,axiom,
    ( ! [A] :
        ( m1_subset_1(A,k8_qc_lang1)
       => ! [B] :
            ( m1_subset_1(B,f1_s3_qc_lang3)
           => ( B = f2_s3_qc_lang3(A)
            <=> ? [C] :
                  ( v1_funct_1(C)
                  & v1_funct_2(C,k8_qc_lang1,f1_s3_qc_lang3)
                  & m2_relset_1(C,k8_qc_lang1,f1_s3_qc_lang3)
                  & B = k8_funct_2(k8_qc_lang1,f1_s3_qc_lang3,C,A)
                  & ! [D] :
                      ( m1_subset_1(D,k8_qc_lang1)
                     => ! [E] :
                          ( m1_subset_1(E,f1_s3_qc_lang3)
                         => ! [F] :
                              ( m1_subset_1(F,f1_s3_qc_lang3)
                             => ( ( D = k11_qc_lang1
                                 => k8_funct_2(k8_qc_lang1,f1_s3_qc_lang3,C,D) = f3_s3_qc_lang3 )
                                & ( v2_qc_lang1(D)
                                 => k8_funct_2(k8_qc_lang1,f1_s3_qc_lang3,C,D) = f4_s3_qc_lang3(D) )
                                & ( ( v3_qc_lang1(D)
                                    & E = k8_funct_2(k8_qc_lang1,f1_s3_qc_lang3,C,k17_qc_lang1(D)) )
                                 => k8_funct_2(k8_qc_lang1,f1_s3_qc_lang3,C,D) = f5_s3_qc_lang3(E) )
                                & ( ( v4_qc_lang1(D)
                                    & E = k8_funct_2(k8_qc_lang1,f1_s3_qc_lang3,C,k18_qc_lang1(D))
                                    & F = k8_funct_2(k8_qc_lang1,f1_s3_qc_lang3,C,k19_qc_lang1(D)) )
                                 => k8_funct_2(k8_qc_lang1,f1_s3_qc_lang3,C,D) = f6_s3_qc_lang3(E,F) )
                                & ( ( v5_qc_lang1(D)
                                    & E = k8_funct_2(k8_qc_lang1,f1_s3_qc_lang3,C,k21_qc_lang1(D)) )
                                 => k8_funct_2(k8_qc_lang1,f1_s3_qc_lang3,C,D) = f7_s3_qc_lang3(D,E) ) ) ) ) ) ) ) ) )
   => f2_s3_qc_lang3(k11_qc_lang1) = f3_s3_qc_lang3 )).

fof(s4_qc_lang3,axiom,
    ( ( ! [A] :
          ( m1_subset_1(A,k8_qc_lang1)
         => ! [B] :
              ( m1_subset_1(B,f1_s4_qc_lang3)
             => ( B = f3_s4_qc_lang3(A)
              <=> ? [C] :
                    ( v1_funct_1(C)
                    & v1_funct_2(C,k8_qc_lang1,f1_s4_qc_lang3)
                    & m2_relset_1(C,k8_qc_lang1,f1_s4_qc_lang3)
                    & B = k8_funct_2(k8_qc_lang1,f1_s4_qc_lang3,C,A)
                    & ! [D] :
                        ( m1_subset_1(D,k8_qc_lang1)
                       => ! [E] :
                            ( m1_subset_1(E,f1_s4_qc_lang3)
                           => ! [F] :
                                ( m1_subset_1(F,f1_s4_qc_lang3)
                               => ( ( D = k11_qc_lang1
                                   => k8_funct_2(k8_qc_lang1,f1_s4_qc_lang3,C,D) = f2_s4_qc_lang3 )
                                  & ( v2_qc_lang1(D)
                                   => k8_funct_2(k8_qc_lang1,f1_s4_qc_lang3,C,D) = f5_s4_qc_lang3(D) )
                                  & ( ( v3_qc_lang1(D)
                                      & E = k8_funct_2(k8_qc_lang1,f1_s4_qc_lang3,C,k17_qc_lang1(D)) )
                                   => k8_funct_2(k8_qc_lang1,f1_s4_qc_lang3,C,D) = f6_s4_qc_lang3(E) )
                                  & ( ( v4_qc_lang1(D)
                                      & E = k8_funct_2(k8_qc_lang1,f1_s4_qc_lang3,C,k18_qc_lang1(D))
                                      & F = k8_funct_2(k8_qc_lang1,f1_s4_qc_lang3,C,k19_qc_lang1(D)) )
                                   => k8_funct_2(k8_qc_lang1,f1_s4_qc_lang3,C,D) = f7_s4_qc_lang3(E,F) )
                                  & ( ( v5_qc_lang1(D)
                                      & E = k8_funct_2(k8_qc_lang1,f1_s4_qc_lang3,C,k21_qc_lang1(D)) )
                                   => k8_funct_2(k8_qc_lang1,f1_s4_qc_lang3,C,D) = f8_s4_qc_lang3(D,E) ) ) ) ) ) ) ) ) )
      & v2_qc_lang1(f4_s4_qc_lang3) )
   => f3_s4_qc_lang3(f4_s4_qc_lang3) = f5_s4_qc_lang3(f4_s4_qc_lang3) )).

fof(s5_qc_lang3,axiom,
    ( ( ! [A] :
          ( m1_subset_1(A,k8_qc_lang1)
         => ! [B] :
              ( m1_subset_1(B,f1_s5_qc_lang3)
             => ( B = f8_s5_qc_lang3(A)
              <=> ? [C] :
                    ( v1_funct_1(C)
                    & v1_funct_2(C,k8_qc_lang1,f1_s5_qc_lang3)
                    & m2_relset_1(C,k8_qc_lang1,f1_s5_qc_lang3)
                    & B = k8_funct_2(k8_qc_lang1,f1_s5_qc_lang3,C,A)
                    & ! [D] :
                        ( m1_subset_1(D,k8_qc_lang1)
                       => ! [E] :
                            ( m1_subset_1(E,f1_s5_qc_lang3)
                           => ! [F] :
                                ( m1_subset_1(F,f1_s5_qc_lang3)
                               => ( ( D = k11_qc_lang1
                                   => k8_funct_2(k8_qc_lang1,f1_s5_qc_lang3,C,D) = f2_s5_qc_lang3 )
                                  & ( v2_qc_lang1(D)
                                   => k8_funct_2(k8_qc_lang1,f1_s5_qc_lang3,C,D) = f4_s5_qc_lang3(D) )
                                  & ( ( v3_qc_lang1(D)
                                      & E = k8_funct_2(k8_qc_lang1,f1_s5_qc_lang3,C,k17_qc_lang1(D)) )
                                   => k8_funct_2(k8_qc_lang1,f1_s5_qc_lang3,C,D) = f5_s5_qc_lang3(E) )
                                  & ( ( v4_qc_lang1(D)
                                      & E = k8_funct_2(k8_qc_lang1,f1_s5_qc_lang3,C,k18_qc_lang1(D))
                                      & F = k8_funct_2(k8_qc_lang1,f1_s5_qc_lang3,C,k19_qc_lang1(D)) )
                                   => k8_funct_2(k8_qc_lang1,f1_s5_qc_lang3,C,D) = f6_s5_qc_lang3(E,F) )
                                  & ( ( v5_qc_lang1(D)
                                      & E = k8_funct_2(k8_qc_lang1,f1_s5_qc_lang3,C,k21_qc_lang1(D)) )
                                   => k8_funct_2(k8_qc_lang1,f1_s5_qc_lang3,C,D) = f7_s5_qc_lang3(D,E) ) ) ) ) ) ) ) ) )
      & v3_qc_lang1(f3_s5_qc_lang3) )
   => f8_s5_qc_lang3(f3_s5_qc_lang3) = f5_s5_qc_lang3(f8_s5_qc_lang3(k17_qc_lang1(f3_s5_qc_lang3))) )).

fof(s6_qc_lang3,axiom,
    ( ( ! [A] :
          ( m1_subset_1(A,k8_qc_lang1)
         => ! [B] :
              ( m1_subset_1(B,f1_s6_qc_lang3)
             => ( B = f7_s6_qc_lang3(A)
              <=> ? [C] :
                    ( v1_funct_1(C)
                    & v1_funct_2(C,k8_qc_lang1,f1_s6_qc_lang3)
                    & m2_relset_1(C,k8_qc_lang1,f1_s6_qc_lang3)
                    & B = k8_funct_2(k8_qc_lang1,f1_s6_qc_lang3,C,A)
                    & ! [D] :
                        ( m1_subset_1(D,k8_qc_lang1)
                       => ! [E] :
                            ( m1_subset_1(E,f1_s6_qc_lang3)
                           => ! [F] :
                                ( m1_subset_1(F,f1_s6_qc_lang3)
                               => ( ( D = k11_qc_lang1
                                   => k8_funct_2(k8_qc_lang1,f1_s6_qc_lang3,C,D) = f2_s6_qc_lang3 )
                                  & ( v2_qc_lang1(D)
                                   => k8_funct_2(k8_qc_lang1,f1_s6_qc_lang3,C,D) = f3_s6_qc_lang3(D) )
                                  & ( ( v3_qc_lang1(D)
                                      & E = k8_funct_2(k8_qc_lang1,f1_s6_qc_lang3,C,k17_qc_lang1(D)) )
                                   => k8_funct_2(k8_qc_lang1,f1_s6_qc_lang3,C,D) = f4_s6_qc_lang3(E) )
                                  & ( ( v4_qc_lang1(D)
                                      & E = k8_funct_2(k8_qc_lang1,f1_s6_qc_lang3,C,k18_qc_lang1(D))
                                      & F = k8_funct_2(k8_qc_lang1,f1_s6_qc_lang3,C,k19_qc_lang1(D)) )
                                   => k8_funct_2(k8_qc_lang1,f1_s6_qc_lang3,C,D) = f5_s6_qc_lang3(E,F) )
                                  & ( ( v5_qc_lang1(D)
                                      & E = k8_funct_2(k8_qc_lang1,f1_s6_qc_lang3,C,k21_qc_lang1(D)) )
                                   => k8_funct_2(k8_qc_lang1,f1_s6_qc_lang3,C,D) = f6_s6_qc_lang3(D,E) ) ) ) ) ) ) ) ) )
      & v4_qc_lang1(f8_s6_qc_lang3) )
   => ! [A] :
        ( m1_subset_1(A,f1_s6_qc_lang3)
       => ! [B] :
            ( m1_subset_1(B,f1_s6_qc_lang3)
           => ( ( A = f7_s6_qc_lang3(k18_qc_lang1(f8_s6_qc_lang3))
                & B = f7_s6_qc_lang3(k19_qc_lang1(f8_s6_qc_lang3)) )
             => f7_s6_qc_lang3(f8_s6_qc_lang3) = f5_s6_qc_lang3(A,B) ) ) ) )).

fof(s7_qc_lang3,axiom,
    ( ( ! [A] :
          ( m1_subset_1(A,k8_qc_lang1)
         => ! [B] :
              ( m1_subset_1(B,f1_s7_qc_lang3)
             => ( B = f8_s7_qc_lang3(A)
              <=> ? [C] :
                    ( v1_funct_1(C)
                    & v1_funct_2(C,k8_qc_lang1,f1_s7_qc_lang3)
                    & m2_relset_1(C,k8_qc_lang1,f1_s7_qc_lang3)
                    & B = k8_funct_2(k8_qc_lang1,f1_s7_qc_lang3,C,A)
                    & ! [D] :
                        ( m1_subset_1(D,k8_qc_lang1)
                       => ! [E] :
                            ( m1_subset_1(E,f1_s7_qc_lang3)
                           => ! [F] :
                                ( m1_subset_1(F,f1_s7_qc_lang3)
                               => ( ( D = k11_qc_lang1
                                   => k8_funct_2(k8_qc_lang1,f1_s7_qc_lang3,C,D) = f2_s7_qc_lang3 )
                                  & ( v2_qc_lang1(D)
                                   => k8_funct_2(k8_qc_lang1,f1_s7_qc_lang3,C,D) = f4_s7_qc_lang3(D) )
                                  & ( ( v3_qc_lang1(D)
                                      & E = k8_funct_2(k8_qc_lang1,f1_s7_qc_lang3,C,k17_qc_lang1(D)) )
                                   => k8_funct_2(k8_qc_lang1,f1_s7_qc_lang3,C,D) = f5_s7_qc_lang3(E) )
                                  & ( ( v4_qc_lang1(D)
                                      & E = k8_funct_2(k8_qc_lang1,f1_s7_qc_lang3,C,k18_qc_lang1(D))
                                      & F = k8_funct_2(k8_qc_lang1,f1_s7_qc_lang3,C,k19_qc_lang1(D)) )
                                   => k8_funct_2(k8_qc_lang1,f1_s7_qc_lang3,C,D) = f6_s7_qc_lang3(E,F) )
                                  & ( ( v5_qc_lang1(D)
                                      & E = k8_funct_2(k8_qc_lang1,f1_s7_qc_lang3,C,k21_qc_lang1(D)) )
                                   => k8_funct_2(k8_qc_lang1,f1_s7_qc_lang3,C,D) = f7_s7_qc_lang3(D,E) ) ) ) ) ) ) ) ) )
      & v5_qc_lang1(f3_s7_qc_lang3) )
   => f8_s7_qc_lang3(f3_s7_qc_lang3) = f7_s7_qc_lang3(f3_s7_qc_lang3,f8_s7_qc_lang3(k21_qc_lang1(f3_s7_qc_lang3))) )).

fof(dt_k1_qc_lang3,axiom,(
    ! [A,B] :
      ( ( m1_finseq_1(A,k1_qc_lang1)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(k1_qc_lang1)) )
     => m1_subset_1(k1_qc_lang3(A,B),k1_zfmisc_1(B)) ) )).

fof(dt_k2_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => m2_subset_1(k2_qc_lang3(A),k1_qc_lang1,k2_qc_lang1) ) )).

fof(dt_k3_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => m2_subset_1(k3_qc_lang3(A),k1_qc_lang1,k4_qc_lang1) ) )).

fof(dt_k4_qc_lang3,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_qc_lang1))
        & m1_subset_1(B,k8_qc_lang1) )
     => m1_subset_1(k4_qc_lang3(A,B),k1_zfmisc_1(A)) ) )).

fof(dt_k5_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => m1_subset_1(k5_qc_lang3(A),k1_zfmisc_1(k4_qc_lang1)) ) )).

fof(dt_k6_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => m1_subset_1(k6_qc_lang3(A),k1_zfmisc_1(k3_qc_lang1)) ) )).

fof(d2_qc_lang3,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k1_qc_lang1)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_qc_lang1)) )
         => k1_qc_lang3(A,B) = a_2_0_qc_lang3(A,B) ) ) )).

fof(t47_qc_lang3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_qc_lang1)) )
         => ( v2_qc_lang1(A)
           => ( k4_qc_lang3(B,A) = k1_qc_lang3(k16_qc_lang1(A),B)
              & k4_qc_lang3(B,A) = a_2_1_qc_lang3(A,B) ) ) ) ) )).

fof(t48_qc_lang3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_qc_lang1)) )
         => ! [C] :
              ( m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(A))
             => ! [D] :
                  ( m1_qc_lang1(D,A)
                 => ( k4_qc_lang3(B,k9_qc_lang1(C,D)) = k1_qc_lang3(D,B)
                    & k4_qc_lang3(B,k9_qc_lang1(C,D)) = a_3_0_qc_lang3(A,B,D) ) ) ) ) ) )).

fof(t66_qc_lang3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A))
         => ! [C] :
              ( m1_qc_lang1(C,A)
             => k5_qc_lang3(k9_qc_lang1(B,C)) = a_2_2_qc_lang3(A,C) ) ) ) )).

fof(t77_qc_lang3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A))
         => ! [C] :
              ( m1_qc_lang1(C,A)
             => k6_qc_lang3(k9_qc_lang1(B,C)) = a_2_3_qc_lang3(A,C) ) ) ) )).

fof(fraenkel_a_2_0_qc_lang3,axiom,(
    ! [A,B,C] :
      ( ( m2_finseq_1(B,k1_qc_lang1)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(k1_qc_lang1)) )
     => ( r2_hidden(A,a_2_0_qc_lang3(B,C))
      <=> ? [D] :
            ( m2_subset_1(D,k1_numbers,k5_numbers)
            & A = k1_funct_1(B,D)
            & r1_xreal_0(np__1,D)
            & r1_xreal_0(D,k3_finseq_1(B))
            & r2_hidden(k1_funct_1(B,D),C) ) ) ) )).

fof(fraenkel_a_2_1_qc_lang3,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(B,k8_qc_lang1)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(k1_qc_lang1)) )
     => ( r2_hidden(A,a_2_1_qc_lang3(B,C))
      <=> ? [D] :
            ( m2_subset_1(D,k1_numbers,k5_numbers)
            & A = k1_funct_1(k16_qc_lang1(B),D)
            & r1_xreal_0(np__1,D)
            & r1_xreal_0(D,k3_finseq_1(k16_qc_lang1(B)))
            & r2_hidden(k1_funct_1(k16_qc_lang1(B),D),C) ) ) ) )).

fof(fraenkel_a_3_0_qc_lang3,axiom,(
    ! [A,B,C,D] :
      ( ( m2_subset_1(B,k1_numbers,k5_numbers)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(k1_qc_lang1))
        & m1_qc_lang1(D,B) )
     => ( r2_hidden(A,a_3_0_qc_lang3(B,C,D))
      <=> ? [E] :
            ( m2_subset_1(E,k1_numbers,k5_numbers)
            & A = k1_funct_1(D,E)
            & r1_xreal_0(np__1,E)
            & r1_xreal_0(E,k3_finseq_1(D))
            & r2_hidden(k1_funct_1(D,E),C) ) ) ) )).

fof(fraenkel_a_2_2_qc_lang3,axiom,(
    ! [A,B,C] :
      ( ( m2_subset_1(B,k1_numbers,k5_numbers)
        & m1_qc_lang1(C,B) )
     => ( r2_hidden(A,a_2_2_qc_lang3(B,C))
      <=> ? [D] :
            ( m2_subset_1(D,k1_numbers,k5_numbers)
            & A = k1_funct_1(C,D)
            & r1_xreal_0(np__1,D)
            & r1_xreal_0(D,k3_finseq_1(C))
            & r2_hidden(k1_funct_1(C,D),k4_qc_lang1) ) ) ) )).

fof(fraenkel_a_2_3_qc_lang3,axiom,(
    ! [A,B,C] :
      ( ( m2_subset_1(B,k1_numbers,k5_numbers)
        & m1_qc_lang1(C,B) )
     => ( r2_hidden(A,a_2_3_qc_lang3(B,C))
      <=> ? [D] :
            ( m2_subset_1(D,k1_numbers,k5_numbers)
            & A = k1_funct_1(C,D)
            & r1_xreal_0(np__1,D)
            & r1_xreal_0(D,k3_finseq_1(C))
            & r2_hidden(k1_funct_1(C,D),k3_qc_lang1) ) ) ) )).
%------------------------------------------------------------------------------