SET007 Axioms: SET007+79.ax


%------------------------------------------------------------------------------
% File     : SET007+79 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : A Classical 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    : cqc_lang [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   93 (  23 unit)
%            Number of atoms       :  502 ( 144 equality)
%            Maximal formula depth :   30 (   7 average)
%            Number of connectives :  422 (  13 ~  ;   1  |; 181  &)
%                                         (  18 <=>; 209 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   23 (   1 propositional; 0-3 arity)
%            Number of functors    :  126 (  42 constant; 0-5 arity)
%            Number of variables   :  251 (   0 singleton; 236 !;  15 ?)
%            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(fc1_cqc_lang,axiom,(
    ! [A,B] :
      ( v1_relat_1(k3_cqc_lang(A,B))
      & v1_funct_1(k3_cqc_lang(A,B)) ) )).

fof(fc2_cqc_lang,axiom,(
    ~ v1_xboole_0(k7_cqc_lang) )).

fof(rc1_cqc_lang,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => ? [B] :
          ( m1_qc_lang1(B,A)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v1_finseq_1(B)
          & v1_cqc_lang(B,A) ) ) )).

fof(d1_cqc_lang,axiom,(
    ! [A,B,C,D] :
      ( ( A = B
       => k1_cqc_lang(A,B,C,D) = C )
      & ( A != B
       => k1_cqc_lang(A,B,C,D) = D ) ) )).

fof(d2_cqc_lang,axiom,(
    ! [A,B] : k3_cqc_lang(A,B) = k2_funcop_1(k1_tarski(A),B) )).

fof(t1_cqc_lang,axiom,(
    $true )).

fof(t2_cqc_lang,axiom,(
    $true )).

fof(t3_cqc_lang,axiom,(
    $true )).

fof(t4_cqc_lang,axiom,(
    $true )).

fof(t5_cqc_lang,axiom,(
    ! [A,B] :
      ( k1_relat_1(k3_cqc_lang(A,B)) = k1_tarski(A)
      & k2_relat_1(k3_cqc_lang(A,B)) = k1_tarski(B) ) )).

fof(t6_cqc_lang,axiom,(
    ! [A,B] : k1_funct_1(k3_cqc_lang(A,B),A) = B )).

fof(t7_cqc_lang,axiom,(
    ! [A] :
      ( r2_hidden(A,k1_qc_lang1)
    <=> ~ ( ~ r2_hidden(A,k3_qc_lang1)
          & ~ r2_hidden(A,k4_qc_lang1)
          & ~ r2_hidden(A,k2_qc_lang1) ) ) )).

fof(d3_cqc_lang,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k1_qc_lang1)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k4_qc_lang1,k1_qc_lang1) )
         => ! [C] :
              ( m2_finseq_1(C,k1_qc_lang1)
             => ( C = k4_cqc_lang(A,B)
              <=> ( k3_finseq_1(C) = k3_finseq_1(A)
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( ( r1_xreal_0(np__1,D)
                          & r1_xreal_0(D,k3_finseq_1(A)) )
                       => ( ( r2_hidden(k1_funct_1(A,D),k1_relat_1(B))
                           => k1_funct_1(C,D) = k1_funct_1(B,k1_funct_1(A,D)) )
                          & ( ~ r2_hidden(k1_funct_1(A,D),k1_relat_1(B))
                           => k1_funct_1(C,D) = k1_funct_1(A,D) ) ) ) ) ) ) ) ) ) )).

fof(t8_cqc_lang,axiom,(
    $true )).

fof(t9_cqc_lang,axiom,(
    $true )).

fof(t10_cqc_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k4_qc_lang1)
         => ( v1_funct_1(k3_cqc_lang(B,A))
            & m2_relset_1(k3_cqc_lang(B,A),k4_qc_lang1,k1_qc_lang1) ) ) ) )).

fof(t11_cqc_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k4_qc_lang1)
             => ! [D] :
                  ( m2_finseq_1(D,k1_qc_lang1)
                 => ! [E] :
                      ( m2_finseq_1(E,k1_qc_lang1)
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & m2_relset_1(F,k4_qc_lang1,k1_qc_lang1) )
                         => ( ( F = k6_cqc_lang(C,B)
                              & D = k4_cqc_lang(E,F)
                              & r1_xreal_0(np__1,A)
                              & r1_xreal_0(A,k3_finseq_1(E)) )
                           => ( ( k1_funct_1(E,A) = C
                               => k1_funct_1(D,A) = B )
                              & ( k1_funct_1(E,A) != C
                               => k1_funct_1(D,A) = k1_funct_1(E,A) ) ) ) ) ) ) ) ) ) )).

fof(t12_cqc_lang,axiom,(
    $true )).

fof(t13_cqc_lang,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
      <=> ( k6_qc_lang3(A) = k1_xboole_0
          & k5_qc_lang3(A) = k1_xboole_0 ) ) ) )).

fof(d5_cqc_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_qc_lang1(B,A)
         => ( v1_cqc_lang(B,A)
          <=> r1_tarski(k2_relat_1(B),k2_qc_lang1) ) ) ) )).

fof(t14_cqc_lang,axiom,(
    $true )).

fof(t16_cqc_lang,axiom,(
    m2_subset_1(k11_qc_lang1,k8_qc_lang1,k7_cqc_lang) )).

fof(t18_cqc_lang,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ( m2_subset_1(k12_qc_lang1(A),k8_qc_lang1,k7_cqc_lang)
      <=> m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) ) ) )).

fof(t19_cqc_lang,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ( m2_subset_1(k13_qc_lang1(A,B),k8_qc_lang1,k7_cqc_lang)
          <=> ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
              & m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) ) ) ) ) )).

fof(t20_cqc_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => m2_subset_1(k2_qc_lang2(A,B),k8_qc_lang1,k7_cqc_lang) ) ) )).

fof(t21_cqc_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => m2_subset_1(k3_qc_lang2(A,B),k8_qc_lang1,k7_cqc_lang) ) ) )).

fof(t22_cqc_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => m2_subset_1(k4_qc_lang2(A,B),k8_qc_lang1,k7_cqc_lang) ) ) )).

fof(t23_cqc_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ( m2_subset_1(k14_qc_lang1(A,B),k8_qc_lang1,k7_cqc_lang)
          <=> m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) ) ) ) )).

fof(t24_cqc_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => m2_subset_1(k5_qc_lang2(A,B),k8_qc_lang1,k7_cqc_lang) ) ) )).

fof(d6_cqc_lang,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( m1_subset_1(C,k8_qc_lang1)
             => ( C = k17_cqc_lang(A,B)
              <=> ? [D] :
                    ( v1_funct_1(D)
                    & v1_funct_2(D,k8_qc_lang1,k8_qc_lang1)
                    & m2_relset_1(D,k8_qc_lang1,k8_qc_lang1)
                    & C = k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,A)
                    & ! [E] :
                        ( m1_subset_1(E,k8_qc_lang1)
                       => ( k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,k9_cqc_lang) = k9_cqc_lang
                          & ( v2_qc_lang1(E)
                           => k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,E) = k9_qc_lang1(k15_qc_lang1(E),k4_cqc_lang(k16_qc_lang1(E),k6_cqc_lang(k3_qc_lang3(np__0),B))) )
                          & ( v3_qc_lang1(E)
                           => k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,E) = k12_qc_lang1(k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,k17_qc_lang1(E))) )
                          & ( v4_qc_lang1(E)
                           => k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,E) = k13_qc_lang1(k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,k18_qc_lang1(E)),k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,k19_qc_lang1(E))) )
                          & ( v5_qc_lang1(E)
                           => k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,E) = k2_cqc_lang(k8_qc_lang1,k20_qc_lang1(E),B,E,k14_qc_lang1(k20_qc_lang1(E),k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,k21_qc_lang1(E)))) ) ) ) ) ) ) ) ) )).

fof(t25_cqc_lang,axiom,(
    $true )).

fof(t26_cqc_lang,axiom,(
    $true )).

fof(t27_cqc_lang,axiom,(
    $true )).

fof(t28_cqc_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => k17_cqc_lang(k9_cqc_lang,A) = k9_cqc_lang ) )).

fof(t29_cqc_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ( v2_qc_lang1(B)
           => k17_cqc_lang(B,A) = k9_qc_lang1(k15_qc_lang1(B),k4_cqc_lang(k16_qc_lang1(B),k6_cqc_lang(k3_qc_lang3(np__0),A))) ) ) ) )).

fof(t30_cqc_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(A))
             => ! [D] :
                  ( m1_qc_lang1(D,A)
                 => k17_cqc_lang(k9_qc_lang1(C,D),B) = k9_qc_lang1(C,k5_cqc_lang(A,D,k6_cqc_lang(k3_qc_lang3(np__0),B))) ) ) ) ) )).

fof(t31_cqc_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ( v3_qc_lang1(B)
           => k17_cqc_lang(B,A) = k12_qc_lang1(k17_cqc_lang(k17_qc_lang1(B),A)) ) ) ) )).

fof(t32_cqc_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => k17_cqc_lang(k12_qc_lang1(B),A) = k12_qc_lang1(k17_cqc_lang(B,A)) ) ) )).

fof(t33_cqc_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ( v4_qc_lang1(B)
           => k17_cqc_lang(B,A) = k13_qc_lang1(k17_cqc_lang(k18_qc_lang1(B),A),k17_cqc_lang(k19_qc_lang1(B),A)) ) ) ) )).

fof(t34_cqc_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ! [C] :
              ( m1_subset_1(C,k8_qc_lang1)
             => k17_cqc_lang(k13_qc_lang1(B,C),A) = k13_qc_lang1(k17_cqc_lang(B,A),k17_cqc_lang(C,A)) ) ) ) )).

fof(t35_cqc_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ( ( v5_qc_lang1(B)
              & k20_qc_lang1(B) = A )
           => k17_cqc_lang(B,A) = B ) ) ) )).

fof(t36_cqc_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ( v5_qc_lang1(B)
           => ( k20_qc_lang1(B) = A
              | k17_cqc_lang(B,A) = k14_qc_lang1(k20_qc_lang1(B),k17_cqc_lang(k21_qc_lang1(B),A)) ) ) ) ) )).

fof(t37_cqc_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => k17_cqc_lang(k14_qc_lang1(A,B),A) = k14_qc_lang1(A,B) ) ) )).

fof(t38_cqc_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( m1_subset_1(C,k8_qc_lang1)
             => ( A != B
               => k17_cqc_lang(k14_qc_lang1(A,C),B) = k14_qc_lang1(A,k17_cqc_lang(C,B)) ) ) ) ) )).

fof(t39_cqc_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ( k5_qc_lang3(B) = k1_xboole_0
           => k17_cqc_lang(B,A) = B ) ) ) )).

fof(t40_cqc_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => k17_cqc_lang(B,A) = B ) ) )).

fof(t41_cqc_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => k6_qc_lang3(k17_cqc_lang(B,A)) = k6_qc_lang3(B) ) ) )).

fof(t42_cqc_lang,axiom,(
    ! [A,B,C] : k9_funct_2(A,B,C) = k3_cqc_lang(k4_tarski(A,B),C) )).

fof(t43_cqc_lang,axiom,(
    ! [A,B,C] : k1_binop_1(k9_funct_2(A,B,C),A,B) = C )).

fof(s1_cqc_lang,axiom,
    ( ! [A] :
        ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
       => ! [B] :
            ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
           => ! [C] :
                ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ! [E] :
                        ( ( v1_cqc_lang(E,D)
                          & m1_qc_lang1(E,D) )
                       => ! [F] :
                            ( m2_subset_1(F,k5_qc_lang1,k7_qc_lang1(D))
                           => ( p1_s1_cqc_lang(k9_cqc_lang)
                              & p1_s1_cqc_lang(k8_cqc_lang(D,F,E))
                              & ( p1_s1_cqc_lang(A)
                               => p1_s1_cqc_lang(k10_cqc_lang(A)) )
                              & ( ( p1_s1_cqc_lang(A)
                                  & p1_s1_cqc_lang(B) )
                               => p1_s1_cqc_lang(k11_cqc_lang(A,B)) )
                              & ( p1_s1_cqc_lang(A)
                               => p1_s1_cqc_lang(k15_cqc_lang(C,A)) ) ) ) ) ) ) ) )
   => ! [A] :
        ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
       => p1_s1_cqc_lang(A) ) )).

fof(s2_cqc_lang,axiom,(
    ? [A] :
      ( v1_funct_1(A)
      & v1_funct_2(A,k7_cqc_lang,f1_s2_cqc_lang)
      & m2_relset_1(A,k7_cqc_lang,f1_s2_cqc_lang)
      & k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k9_cqc_lang) = f2_s2_cqc_lang
      & ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ! [D] :
                  ( m2_subset_1(D,k1_qc_lang1,k2_qc_lang1)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( ( v1_cqc_lang(F,E)
                            & m1_qc_lang1(F,E) )
                         => ! [G] :
                              ( m2_subset_1(G,k5_qc_lang1,k7_qc_lang1(E))
                             => ( k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k8_cqc_lang(E,G,F)) = f3_s2_cqc_lang(E,G,F)
                                & k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k10_cqc_lang(B)) = f4_s2_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,B))
                                & k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k11_cqc_lang(B,C)) = f5_s2_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,B),k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,C))
                                & k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k15_cqc_lang(D,B)) = f6_s2_cqc_lang(D,k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,B)) ) ) ) ) ) ) ) ) )).

fof(s3_cqc_lang,axiom,
    ( ( k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,k9_cqc_lang) = f4_s3_cqc_lang
      & ! [A] :
          ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
         => ! [B] :
              ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
             => ! [C] :
                  ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
                 => ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ! [E] :
                          ( ( v1_cqc_lang(E,D)
                            & m1_qc_lang1(E,D) )
                         => ! [F] :
                              ( m2_subset_1(F,k5_qc_lang1,k7_qc_lang1(D))
                             => ( k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,k8_cqc_lang(D,F,E)) = f5_s3_cqc_lang(D,F,E)
                                & k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,k10_cqc_lang(A)) = f6_s3_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,A))
                                & k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,k11_cqc_lang(A,B)) = f7_s3_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,A),k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,B))
                                & k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,k15_cqc_lang(C,A)) = f8_s3_cqc_lang(C,k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,A)) ) ) ) ) ) ) )
      & k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,k9_cqc_lang) = f4_s3_cqc_lang
      & ! [A] :
          ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
         => ! [B] :
              ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
             => ! [C] :
                  ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
                 => ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ! [E] :
                          ( ( v1_cqc_lang(E,D)
                            & m1_qc_lang1(E,D) )
                         => ! [F] :
                              ( m2_subset_1(F,k5_qc_lang1,k7_qc_lang1(D))
                             => ( k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,k8_cqc_lang(D,F,E)) = f5_s3_cqc_lang(D,F,E)
                                & k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,k10_cqc_lang(A)) = f6_s3_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,A))
                                & k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,k11_cqc_lang(A,B)) = f7_s3_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,A),k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,B))
                                & k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,k15_cqc_lang(C,A)) = f8_s3_cqc_lang(C,k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,A)) ) ) ) ) ) ) ) )
   => f2_s3_cqc_lang = f3_s3_cqc_lang )).

fof(s4_cqc_lang,axiom,
    ( ? [A] :
        ( m1_subset_1(A,f1_s4_cqc_lang)
        & ? [B] :
            ( v1_funct_1(B)
            & v1_funct_2(B,k7_cqc_lang,f1_s4_cqc_lang)
            & m2_relset_1(B,k7_cqc_lang,f1_s4_cqc_lang)
            & A = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,f2_s4_cqc_lang)
            & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,k9_cqc_lang) = f3_s4_cqc_lang
            & ! [C] :
                ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
               => ! [D] :
                    ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                   => ! [E] :
                        ( m2_subset_1(E,k1_qc_lang1,k2_qc_lang1)
                       => ! [F] :
                            ( m2_subset_1(F,k1_numbers,k5_numbers)
                           => ! [G] :
                                ( ( v1_cqc_lang(G,F)
                                  & m1_qc_lang1(G,F) )
                               => ! [H] :
                                    ( m2_subset_1(H,k5_qc_lang1,k7_qc_lang1(F))
                                   => ( k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,k8_cqc_lang(F,H,G)) = f4_s4_cqc_lang(F,H,G)
                                      & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,k10_cqc_lang(C)) = f5_s4_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,C))
                                      & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,k11_cqc_lang(C,D)) = f6_s4_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,C),k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,D))
                                      & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,k15_cqc_lang(E,C)) = f7_s4_cqc_lang(E,k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,C)) ) ) ) ) ) ) ) ) )
    & ! [A] :
        ( m1_subset_1(A,f1_s4_cqc_lang)
       => ! [B] :
            ( m1_subset_1(B,f1_s4_cqc_lang)
           => ~ ( ? [C] :
                    ( v1_funct_1(C)
                    & v1_funct_2(C,k7_cqc_lang,f1_s4_cqc_lang)
                    & m2_relset_1(C,k7_cqc_lang,f1_s4_cqc_lang)
                    & A = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,f2_s4_cqc_lang)
                    & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k9_cqc_lang) = f3_s4_cqc_lang
                    & ! [D] :
                        ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                       => ! [E] :
                            ( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
                           => ! [F] :
                                ( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
                               => ! [G] :
                                    ( m2_subset_1(G,k1_numbers,k5_numbers)
                                   => ! [H] :
                                        ( ( v1_cqc_lang(H,G)
                                          & m1_qc_lang1(H,G) )
                                       => ! [I] :
                                            ( m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G))
                                           => ( k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s4_cqc_lang(G,I,H)
                                              & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k10_cqc_lang(D)) = f5_s4_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D))
                                              & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k11_cqc_lang(D,E)) = f6_s4_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,E))
                                              & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k15_cqc_lang(F,D)) = f7_s4_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D)) ) ) ) ) ) ) ) )
                & ? [C] :
                    ( v1_funct_1(C)
                    & v1_funct_2(C,k7_cqc_lang,f1_s4_cqc_lang)
                    & m2_relset_1(C,k7_cqc_lang,f1_s4_cqc_lang)
                    & B = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,f2_s4_cqc_lang)
                    & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k9_cqc_lang) = f3_s4_cqc_lang
                    & ! [D] :
                        ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                       => ! [E] :
                            ( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
                           => ! [F] :
                                ( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
                               => ! [G] :
                                    ( m2_subset_1(G,k1_numbers,k5_numbers)
                                   => ! [H] :
                                        ( ( v1_cqc_lang(H,G)
                                          & m1_qc_lang1(H,G) )
                                       => ! [I] :
                                            ( m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G))
                                           => ( k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s4_cqc_lang(G,I,H)
                                              & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k10_cqc_lang(D)) = f5_s4_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D))
                                              & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k11_cqc_lang(D,E)) = f6_s4_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,E))
                                              & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k15_cqc_lang(F,D)) = f7_s4_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D)) ) ) ) ) ) ) ) )
                & A != B ) ) ) )).

fof(s5_cqc_lang,axiom,
    ( ! [A] :
        ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
       => ! [B] :
            ( m1_subset_1(B,f1_s5_cqc_lang)
           => ( B = f2_s5_cqc_lang(A)
            <=> ? [C] :
                  ( v1_funct_1(C)
                  & v1_funct_2(C,k7_cqc_lang,f1_s5_cqc_lang)
                  & m2_relset_1(C,k7_cqc_lang,f1_s5_cqc_lang)
                  & B = k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,A)
                  & k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,k9_cqc_lang) = f3_s5_cqc_lang
                  & ! [D] :
                      ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                     => ! [E] :
                          ( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
                         => ! [F] :
                              ( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
                             => ! [G] :
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ! [H] :
                                      ( ( v1_cqc_lang(H,G)
                                        & m1_qc_lang1(H,G) )
                                     => ! [I] :
                                          ( m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G))
                                         => ( k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s5_cqc_lang(G,I,H)
                                            & k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,k10_cqc_lang(D)) = f5_s5_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,D))
                                            & k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,k11_cqc_lang(D,E)) = f6_s5_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,E))
                                            & k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,k15_cqc_lang(F,D)) = f7_s5_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,D)) ) ) ) ) ) ) ) ) ) ) )
   => f2_s5_cqc_lang(k9_cqc_lang) = f3_s5_cqc_lang )).

fof(s6_cqc_lang,axiom,
    ( ! [A] :
        ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
       => ! [B] :
            ( m1_subset_1(B,f1_s6_cqc_lang)
           => ( B = f3_s6_cqc_lang(A)
            <=> ? [C] :
                  ( v1_funct_1(C)
                  & v1_funct_2(C,k7_cqc_lang,f1_s6_cqc_lang)
                  & m2_relset_1(C,k7_cqc_lang,f1_s6_cqc_lang)
                  & B = k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,A)
                  & k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k9_cqc_lang) = f2_s6_cqc_lang
                  & ! [D] :
                      ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                     => ! [E] :
                          ( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
                         => ! [F] :
                              ( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
                             => ! [G] :
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ! [H] :
                                      ( ( v1_cqc_lang(H,G)
                                        & m1_qc_lang1(H,G) )
                                     => ! [I] :
                                          ( m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G))
                                         => ( k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s6_cqc_lang(G,I,H)
                                            & k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k10_cqc_lang(D)) = f8_s6_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,D))
                                            & k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k11_cqc_lang(D,E)) = f9_s6_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,E))
                                            & k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k15_cqc_lang(F,D)) = f10_s6_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,D)) ) ) ) ) ) ) ) ) ) ) )
   => f3_s6_cqc_lang(k8_cqc_lang(f5_s6_cqc_lang,f6_s6_cqc_lang,f7_s6_cqc_lang)) = f4_s6_cqc_lang(f5_s6_cqc_lang,f6_s6_cqc_lang,f7_s6_cqc_lang) )).

fof(s7_cqc_lang,axiom,
    ( ! [A] :
        ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
       => ! [B] :
            ( m1_subset_1(B,f1_s7_cqc_lang)
           => ( B = f2_s7_cqc_lang(A)
            <=> ? [C] :
                  ( v1_funct_1(C)
                  & v1_funct_2(C,k7_cqc_lang,f1_s7_cqc_lang)
                  & m2_relset_1(C,k7_cqc_lang,f1_s7_cqc_lang)
                  & B = k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,A)
                  & k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k9_cqc_lang) = f3_s7_cqc_lang
                  & ! [D] :
                      ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                     => ! [E] :
                          ( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
                         => ! [F] :
                              ( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
                             => ! [G] :
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ! [H] :
                                      ( ( v1_cqc_lang(H,G)
                                        & m1_qc_lang1(H,G) )
                                     => ! [I] :
                                          ( m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G))
                                         => ( k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s7_cqc_lang(G,I,H)
                                            & k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k10_cqc_lang(D)) = f5_s7_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,D))
                                            & k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k11_cqc_lang(D,E)) = f7_s7_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,E))
                                            & k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k15_cqc_lang(F,D)) = f8_s7_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,D)) ) ) ) ) ) ) ) ) ) ) )
   => f2_s7_cqc_lang(k10_cqc_lang(f6_s7_cqc_lang)) = f5_s7_cqc_lang(f2_s7_cqc_lang(f6_s7_cqc_lang)) )).

fof(s8_cqc_lang,axiom,
    ( ! [A] :
        ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
       => ! [B] :
            ( m1_subset_1(B,f1_s8_cqc_lang)
           => ( B = f2_s8_cqc_lang(A)
            <=> ? [C] :
                  ( v1_funct_1(C)
                  & v1_funct_2(C,k7_cqc_lang,f1_s8_cqc_lang)
                  & m2_relset_1(C,k7_cqc_lang,f1_s8_cqc_lang)
                  & B = k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,A)
                  & k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k9_cqc_lang) = f3_s8_cqc_lang
                  & ! [D] :
                      ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                     => ! [E] :
                          ( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
                         => ! [F] :
                              ( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
                             => ! [G] :
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ! [H] :
                                      ( ( v1_cqc_lang(H,G)
                                        & m1_qc_lang1(H,G) )
                                     => ! [I] :
                                          ( m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G))
                                         => ( k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s8_cqc_lang(G,I,H)
                                            & k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k10_cqc_lang(D)) = f5_s8_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,D))
                                            & k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k11_cqc_lang(D,E)) = f6_s8_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,E))
                                            & k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k15_cqc_lang(F,D)) = f9_s8_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,D)) ) ) ) ) ) ) ) ) ) ) )
   => f2_s8_cqc_lang(k11_cqc_lang(f7_s8_cqc_lang,f8_s8_cqc_lang)) = f6_s8_cqc_lang(f2_s8_cqc_lang(f7_s8_cqc_lang),f2_s8_cqc_lang(f8_s8_cqc_lang)) )).

fof(s9_cqc_lang,axiom,
    ( ! [A] :
        ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
       => ! [B] :
            ( m1_subset_1(B,f1_s9_cqc_lang)
           => ( B = f2_s9_cqc_lang(A)
            <=> ? [C] :
                  ( v1_funct_1(C)
                  & v1_funct_2(C,k7_cqc_lang,f1_s9_cqc_lang)
                  & m2_relset_1(C,k7_cqc_lang,f1_s9_cqc_lang)
                  & B = k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,A)
                  & k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k9_cqc_lang) = f3_s9_cqc_lang
                  & ! [D] :
                      ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                     => ! [E] :
                          ( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
                         => ! [F] :
                              ( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
                             => ! [G] :
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ! [H] :
                                      ( ( v1_cqc_lang(H,G)
                                        & m1_qc_lang1(H,G) )
                                     => ! [I] :
                                          ( m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G))
                                         => ( k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s9_cqc_lang(G,I,H)
                                            & k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k10_cqc_lang(D)) = f5_s9_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,D))
                                            & k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k11_cqc_lang(D,E)) = f6_s9_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,E))
                                            & k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k15_cqc_lang(F,D)) = f7_s9_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,D)) ) ) ) ) ) ) ) ) ) ) )
   => f2_s9_cqc_lang(k15_cqc_lang(f8_s9_cqc_lang,f9_s9_cqc_lang)) = f7_s9_cqc_lang(f8_s9_cqc_lang,f2_s9_cqc_lang(f9_s9_cqc_lang)) )).

fof(dt_k1_cqc_lang,axiom,(
    $true )).

fof(dt_k2_cqc_lang,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(D,A)
        & m1_subset_1(E,A) )
     => m1_subset_1(k2_cqc_lang(A,B,C,D,E),A) ) )).

fof(redefinition_k2_cqc_lang,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(D,A)
        & m1_subset_1(E,A) )
     => k2_cqc_lang(A,B,C,D,E) = k1_cqc_lang(B,C,D,E) ) )).

fof(dt_k3_cqc_lang,axiom,(
    $true )).

fof(dt_k4_cqc_lang,axiom,(
    ! [A,B] :
      ( ( m1_finseq_1(A,k1_qc_lang1)
        & v1_funct_1(B)
        & m1_relset_1(B,k4_qc_lang1,k1_qc_lang1) )
     => m2_finseq_1(k4_cqc_lang(A,B),k1_qc_lang1) ) )).

fof(dt_k5_cqc_lang,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_qc_lang1(B,A)
        & v1_funct_1(C)
        & m1_relset_1(C,k4_qc_lang1,k1_qc_lang1) )
     => m1_qc_lang1(k5_cqc_lang(A,B,C),A) ) )).

fof(redefinition_k5_cqc_lang,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_qc_lang1(B,A)
        & v1_funct_1(C)
        & m1_relset_1(C,k4_qc_lang1,k1_qc_lang1) )
     => k5_cqc_lang(A,B,C) = k4_cqc_lang(B,C) ) )).

fof(dt_k6_cqc_lang,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k4_qc_lang1)
        & m1_subset_1(B,k2_qc_lang1) )
     => ( v1_funct_1(k6_cqc_lang(A,B))
        & m2_relset_1(k6_cqc_lang(A,B),k4_qc_lang1,k1_qc_lang1) ) ) )).

fof(redefinition_k6_cqc_lang,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k4_qc_lang1)
        & m1_subset_1(B,k2_qc_lang1) )
     => k6_cqc_lang(A,B) = k3_cqc_lang(A,B) ) )).

fof(dt_k7_cqc_lang,axiom,(
    m1_subset_1(k7_cqc_lang,k1_zfmisc_1(k8_qc_lang1)) )).

fof(dt_k8_cqc_lang,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k7_qc_lang1(A))
        & v1_cqc_lang(C,A)
        & m1_qc_lang1(C,A) )
     => m2_subset_1(k8_cqc_lang(A,B,C),k8_qc_lang1,k7_cqc_lang) ) )).

fof(redefinition_k8_cqc_lang,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k7_qc_lang1(A))
        & v1_cqc_lang(C,A)
        & m1_qc_lang1(C,A) )
     => k8_cqc_lang(A,B,C) = k9_qc_lang1(B,C) ) )).

fof(dt_k9_cqc_lang,axiom,(
    m2_subset_1(k9_cqc_lang,k8_qc_lang1,k7_cqc_lang) )).

fof(redefinition_k9_cqc_lang,axiom,(
    k9_cqc_lang = k11_qc_lang1 )).

fof(dt_k10_cqc_lang,axiom,(
    ! [A] :
      ( m1_subset_1(A,k7_cqc_lang)
     => m2_subset_1(k10_cqc_lang(A),k8_qc_lang1,k7_cqc_lang) ) )).

fof(redefinition_k10_cqc_lang,axiom,(
    ! [A] :
      ( m1_subset_1(A,k7_cqc_lang)
     => k10_cqc_lang(A) = k12_qc_lang1(A) ) )).

fof(dt_k11_cqc_lang,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k7_cqc_lang)
        & m1_subset_1(B,k7_cqc_lang) )
     => m2_subset_1(k11_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang) ) )).

fof(redefinition_k11_cqc_lang,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k7_cqc_lang)
        & m1_subset_1(B,k7_cqc_lang) )
     => k11_cqc_lang(A,B) = k13_qc_lang1(A,B) ) )).

fof(dt_k12_cqc_lang,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k7_cqc_lang)
        & m1_subset_1(B,k7_cqc_lang) )
     => m2_subset_1(k12_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang) ) )).

fof(redefinition_k12_cqc_lang,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k7_cqc_lang)
        & m1_subset_1(B,k7_cqc_lang) )
     => k12_cqc_lang(A,B) = k2_qc_lang2(A,B) ) )).

fof(dt_k13_cqc_lang,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k7_cqc_lang)
        & m1_subset_1(B,k7_cqc_lang) )
     => m2_subset_1(k13_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang) ) )).

fof(redefinition_k13_cqc_lang,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k7_cqc_lang)
        & m1_subset_1(B,k7_cqc_lang) )
     => k13_cqc_lang(A,B) = k3_qc_lang2(A,B) ) )).

fof(dt_k14_cqc_lang,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k7_cqc_lang)
        & m1_subset_1(B,k7_cqc_lang) )
     => m2_subset_1(k14_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang) ) )).

fof(redefinition_k14_cqc_lang,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k7_cqc_lang)
        & m1_subset_1(B,k7_cqc_lang) )
     => k14_cqc_lang(A,B) = k4_qc_lang2(A,B) ) )).

fof(dt_k15_cqc_lang,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k2_qc_lang1)
        & m1_subset_1(B,k7_cqc_lang) )
     => m2_subset_1(k15_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang) ) )).

fof(redefinition_k15_cqc_lang,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k2_qc_lang1)
        & m1_subset_1(B,k7_cqc_lang) )
     => k15_cqc_lang(A,B) = k14_qc_lang1(A,B) ) )).

fof(dt_k16_cqc_lang,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k2_qc_lang1)
        & m1_subset_1(B,k7_cqc_lang) )
     => m2_subset_1(k16_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang) ) )).

fof(redefinition_k16_cqc_lang,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k2_qc_lang1)
        & m1_subset_1(B,k7_cqc_lang) )
     => k16_cqc_lang(A,B) = k5_qc_lang2(A,B) ) )).

fof(dt_k17_cqc_lang,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k8_qc_lang1)
        & m1_subset_1(B,k2_qc_lang1) )
     => m1_subset_1(k17_cqc_lang(A,B),k8_qc_lang1) ) )).

fof(d4_cqc_lang,axiom,(
    k7_cqc_lang = a_0_0_cqc_lang )).

fof(t15_cqc_lang,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_qc_lang1(B,A)
         => ( ( v1_cqc_lang(B,A)
              & m1_qc_lang1(B,A) )
          <=> ( a_2_0_cqc_lang(A,B) = k1_xboole_0
              & a_2_1_cqc_lang(A,B) = k1_xboole_0 ) ) ) ) )).

fof(t17_cqc_lang,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)
             => ( m2_subset_1(k9_qc_lang1(B,C),k8_qc_lang1,k7_cqc_lang)
              <=> ( a_2_0_cqc_lang(A,C) = k1_xboole_0
                  & a_2_1_cqc_lang(A,C) = k1_xboole_0 ) ) ) ) ) )).

fof(fraenkel_a_0_0_cqc_lang,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_0_cqc_lang)
    <=> ? [B] :
          ( m1_subset_1(B,k8_qc_lang1)
          & A = B
          & k6_qc_lang3(B) = k1_xboole_0
          & k5_qc_lang3(B) = k1_xboole_0 ) ) )).

fof(fraenkel_a_2_0_cqc_lang,axiom,(
    ! [A,B,C] :
      ( ( m2_subset_1(B,k1_numbers,k5_numbers)
        & m1_qc_lang1(C,B) )
     => ( r2_hidden(A,a_2_0_cqc_lang(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_1_cqc_lang,axiom,(
    ! [A,B,C] :
      ( ( m2_subset_1(B,k1_numbers,k5_numbers)
        & m1_qc_lang1(C,B) )
     => ( r2_hidden(A,a_2_1_cqc_lang(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) ) ) ) )).
%------------------------------------------------------------------------------