SET007 Axioms: SET007+860.ax


%------------------------------------------------------------------------------
% File     : SET007+860 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Coincidence Lemma and Substitution Lemma
% 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    : sublemma [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  132 (   7 unit)
%            Number of atoms       :  962 ( 113 equality)
%            Maximal formula depth :   25 (  10 average)
%            Number of connectives :  913 (  83 ~  ;   1  |; 194  &)
%                                         (  43 <=>; 592 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   26 (   1 propositional; 0-4 arity)
%            Number of functors    :   82 (  12 constant; 0-6 arity)
%            Number of variables   :  532 (   0 singleton; 529 !;   3 ?)
%            Maximal term depth    :   10 (   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(rc1_sublemma,axiom,(
    ? [A] :
      ( m1_subset_1(A,k2_zfmisc_1(k16_substut1,k2_qc_lang1))
      & v1_sublemma(A) ) )).

fof(t1_sublemma,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ! [E] :
                      ( ( v1_relat_1(E)
                        & v1_funct_1(E) )
                     => ( ( r1_tarski(k1_relat_1(D),k1_relat_1(C))
                          & r1_tarski(k1_relat_1(E),k1_relat_1(C)) )
                       => k1_funct_4(k1_funct_4(A,B),C) = k1_funct_4(k1_funct_4(k1_funct_4(A,D),k1_funct_4(B,E)),C) ) ) ) ) ) ) )).

fof(t2_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r2_hidden(A,k1_relat_1(B))
           => k1_funct_4(k7_relat_1(B,k4_xboole_0(k1_relat_1(B),k6_domain_1(k2_qc_lang1,A))),k3_cqc_lang(A,k1_funct_1(B,A))) = B ) ) ) )).

fof(d1_sublemma,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,k2_qc_lang1,A,k2_valuat_1(A))
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k2_qc_lang1,A) )
             => k1_sublemma(A,B,C) = k1_funct_4(B,C) ) ) ) )).

fof(d2_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k16_substut1,k38_substut1)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_fraenkel(C,k2_qc_lang1,B,k2_valuat_1(B))
             => k3_sublemma(A,B,C) = k7_relset_1(k2_qc_lang1,k2_qc_lang1,k2_qc_lang1,B,k2_substut1(k19_substut1(A)),C) ) ) ) )).

fof(t3_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k16_substut1,k38_substut1)
     => ( v2_substut1(A)
       => k39_substut1(A) = k9_cqc_lang ) ) )).

fof(d3_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k16_substut1,k38_substut1)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_fraenkel(C,k2_qc_lang1,B,k2_valuat_1(B))
             => ! [D] :
                  ( m1_valuat_1(D,B)
                 => ( r1_sublemma(A,B,C,D)
                  <=> r1_valuat_1(B,k2_sublemma(A),D,C) ) ) ) ) ) )).

fof(t4_sublemma,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_valuat_1(B,A)
         => ! [C] :
              ( m2_subset_1(C,k16_substut1,k38_substut1)
             => ( v2_substut1(C)
               => ! [D] :
                    ( m2_fraenkel(D,k2_qc_lang1,A,k2_valuat_1(A))
                   => ( r1_valuat_1(A,k39_substut1(C),B,D)
                    <=> r1_sublemma(C,A,k1_sublemma(A,D,k3_sublemma(C,A,D)),B) ) ) ) ) ) ) )).

fof(t5_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v1_cqc_lang(C,A)
                & m1_qc_lang1(C,A) )
             => ( r2_hidden(B,k4_relset_1(k5_numbers,k1_qc_lang1,C))
               => m2_subset_1(k1_funct_1(C,B),k1_qc_lang1,k2_qc_lang1) ) ) ) ) )).

fof(t6_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k16_substut1,k38_substut1)
     => ( v4_substut1(A)
       => k39_substut1(A) = k9_qc_lang1(k15_qc_lang1(k2_sublemma(A)),k3_substut1(k26_substut1(A),k19_substut1(A))) ) ) )).

fof(t7_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A))
         => ! [C] :
              ( m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(A))
             => ! [D] :
                  ( ( v1_cqc_lang(D,A)
                    & m1_qc_lang1(D,A) )
                 => ! [E] :
                      ( ( v1_cqc_lang(E,A)
                        & m1_qc_lang1(E,A) )
                     => ! [F] :
                          ( m1_subset_1(F,k1_substut1)
                         => ! [G] :
                              ( m1_subset_1(G,k1_substut1)
                             => ( k26_substut1(k17_substut1(B,D,F)) = k26_substut1(k17_substut1(C,E,G))
                               => D = E ) ) ) ) ) ) ) ) )).

fof(t8_sublemma,axiom,(
    $true )).

fof(t9_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A))
         => ! [C] :
              ( ( v1_cqc_lang(C,A)
                & m1_qc_lang1(C,A) )
             => ! [D] :
                  ( m1_subset_1(D,k1_substut1)
                 => k39_substut1(k4_sublemma(A,B,C,D)) = k9_qc_lang1(B,k3_substut1(C,D)) ) ) ) ) )).

fof(t10_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A))
         => ! [C] :
              ( ( v1_cqc_lang(C,A)
                & m1_qc_lang1(C,A) )
             => ! [D] :
                  ( m1_subset_1(D,k1_substut1)
                 => m2_subset_1(k9_qc_lang1(B,k3_substut1(C,D)),k8_qc_lang1,k7_cqc_lang) ) ) ) ) )).

fof(t11_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_cqc_lang(B,A)
            & m1_qc_lang1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_substut1)
             => ( v1_cqc_lang(k3_substut1(B,C),A)
                & m1_qc_lang1(k3_substut1(B,C),A) ) ) ) ) )).

fof(t12_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_fraenkel(C,k2_qc_lang1,B,k2_valuat_1(B))
             => ! [D] :
                  ( m2_subset_1(D,k16_substut1,k38_substut1)
                 => ( ~ r2_hidden(A,k1_relat_1(k19_substut1(D)))
                   => k8_funct_2(k2_qc_lang1,B,k1_sublemma(B,C,k3_sublemma(D,B,C)),A) = k8_funct_2(k2_qc_lang1,B,C,A) ) ) ) ) ) )).

fof(t13_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_fraenkel(C,k2_qc_lang1,B,k2_valuat_1(B))
             => ! [D] :
                  ( m2_subset_1(D,k16_substut1,k38_substut1)
                 => ( r2_hidden(A,k1_relat_1(k19_substut1(D)))
                   => k8_funct_2(k2_qc_lang1,B,k1_sublemma(B,C,k3_sublemma(D,B,C)),A) = k1_funct_1(k3_sublemma(D,B,C),A) ) ) ) ) ) )).

fof(t14_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_fraenkel(C,k2_qc_lang1,B,k2_valuat_1(B))
             => ! [D] :
                  ( m2_subset_1(D,k5_qc_lang1,k7_qc_lang1(A))
                 => ! [E] :
                      ( ( v1_cqc_lang(E,A)
                        & m1_qc_lang1(E,A) )
                     => ! [F] :
                          ( m1_subset_1(F,k1_substut1)
                         => k8_valuat_1(B,A,E,k1_sublemma(B,C,k3_sublemma(k4_sublemma(A,D,E,F),B,C))) = k8_valuat_1(B,A,k5_sublemma(A,E,F),C) ) ) ) ) ) ) )).

fof(t15_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A))
         => ! [C] :
              ( ( v1_cqc_lang(C,A)
                & m1_qc_lang1(C,A) )
             => ! [D] :
                  ( m1_subset_1(D,k1_substut1)
                 => k2_sublemma(k4_sublemma(A,B,C,D)) = k8_cqc_lang(A,B,C) ) ) ) ) )).

fof(t16_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_valuat_1(C,B)
             => ! [D] :
                  ( m2_subset_1(D,k5_qc_lang1,k7_qc_lang1(A))
                 => ! [E] :
                      ( ( v1_cqc_lang(E,A)
                        & m1_qc_lang1(E,A) )
                     => ! [F] :
                          ( m1_subset_1(F,k1_substut1)
                         => ! [G] :
                              ( m2_fraenkel(G,k2_qc_lang1,B,k2_valuat_1(B))
                             => ( r1_valuat_1(B,k39_substut1(k4_sublemma(A,D,E,F)),C,G)
                              <=> r1_sublemma(k4_sublemma(A,D,E,F),B,k1_sublemma(B,G,k3_sublemma(k4_sublemma(A,D,E,F),B,G)),C) ) ) ) ) ) ) ) ) )).

fof(t17_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k16_substut1,k38_substut1)
     => ( k18_substut1(k20_substut1(A)) = k10_cqc_lang(k2_sublemma(A))
        & k19_substut1(k20_substut1(A)) = k19_substut1(A) ) ) )).

fof(t18_sublemma,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_valuat_1(B,A)
         => ! [C] :
              ( m2_fraenkel(C,k2_qc_lang1,A,k2_valuat_1(A))
             => ! [D] :
                  ( m2_subset_1(D,k16_substut1,k38_substut1)
                 => ( ~ r1_sublemma(D,A,k1_sublemma(A,C,k3_sublemma(D,A,C)),B)
                  <=> r1_sublemma(k6_sublemma(D),A,k1_sublemma(A,C,k3_sublemma(D,A,C)),B) ) ) ) ) ) )).

fof(t19_sublemma,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,k2_qc_lang1,A,k2_valuat_1(A))
         => ! [C] :
              ( m2_subset_1(C,k16_substut1,k38_substut1)
             => k3_sublemma(C,A,B) = k3_sublemma(k6_sublemma(C),A,B) ) ) ) )).

fof(t20_sublemma,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_valuat_1(B,A)
         => ! [C] :
              ( m2_subset_1(C,k16_substut1,k38_substut1)
             => ( ! [D] :
                    ( m2_fraenkel(D,k2_qc_lang1,A,k2_valuat_1(A))
                   => ( r1_valuat_1(A,k39_substut1(C),B,D)
                    <=> r1_sublemma(C,A,k1_sublemma(A,D,k3_sublemma(C,A,D)),B) ) )
               => ! [D] :
                    ( m2_fraenkel(D,k2_qc_lang1,A,k2_valuat_1(A))
                   => ( r1_valuat_1(A,k39_substut1(k6_sublemma(C)),B,D)
                    <=> r1_sublemma(k6_sublemma(C),A,k1_sublemma(A,D,k3_sublemma(k6_sublemma(C),A,D)),B) ) ) ) ) ) ) )).

fof(d4_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k16_substut1,k38_substut1)
     => ! [B] :
          ( m2_subset_1(B,k16_substut1,k38_substut1)
         => ( k19_substut1(A) = k19_substut1(B)
           => k7_sublemma(A,B) = k21_substut1(A,B) ) ) ) )).

fof(t21_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k16_substut1,k38_substut1)
     => ! [B] :
          ( m2_subset_1(B,k16_substut1,k38_substut1)
         => ( k19_substut1(A) = k19_substut1(B)
           => ( k2_sublemma(k7_sublemma(A,B)) = k11_cqc_lang(k2_sublemma(A),k2_sublemma(B))
              & k19_substut1(k7_sublemma(A,B)) = k19_substut1(A) ) ) ) ) )).

fof(t22_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k16_substut1,k38_substut1)
     => ! [B] :
          ( m2_subset_1(B,k16_substut1,k38_substut1)
         => ( k19_substut1(A) = k19_substut1(B)
           => k19_substut1(k7_sublemma(A,B)) = k19_substut1(A) ) ) ) )).

fof(t23_sublemma,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,k2_qc_lang1,A,k2_valuat_1(A))
         => ! [C] :
              ( m2_subset_1(C,k16_substut1,k38_substut1)
             => ! [D] :
                  ( m2_subset_1(D,k16_substut1,k38_substut1)
                 => ( k19_substut1(C) = k19_substut1(D)
                   => ( k3_sublemma(C,A,B) = k3_sublemma(k7_sublemma(C,D),A,B)
                      & k3_sublemma(D,A,B) = k3_sublemma(k7_sublemma(C,D),A,B) ) ) ) ) ) ) )).

fof(t24_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k16_substut1,k38_substut1)
     => ! [B] :
          ( m2_subset_1(B,k16_substut1,k38_substut1)
         => ( k19_substut1(A) = k19_substut1(B)
           => k39_substut1(k7_sublemma(A,B)) = k11_cqc_lang(k39_substut1(A),k39_substut1(B)) ) ) ) )).

fof(t25_sublemma,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_valuat_1(B,A)
         => ! [C] :
              ( m2_fraenkel(C,k2_qc_lang1,A,k2_valuat_1(A))
             => ! [D] :
                  ( m2_subset_1(D,k16_substut1,k38_substut1)
                 => ! [E] :
                      ( m2_subset_1(E,k16_substut1,k38_substut1)
                     => ( k19_substut1(D) = k19_substut1(E)
                       => ( ( r1_sublemma(D,A,k1_sublemma(A,C,k3_sublemma(D,A,C)),B)
                            & r1_sublemma(E,A,k1_sublemma(A,C,k3_sublemma(E,A,C)),B) )
                        <=> r1_sublemma(k7_sublemma(D,E),A,k1_sublemma(A,C,k3_sublemma(k7_sublemma(D,E),A,C)),B) ) ) ) ) ) ) ) )).

fof(t26_sublemma,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_valuat_1(B,A)
         => ! [C] :
              ( m2_subset_1(C,k16_substut1,k38_substut1)
             => ! [D] :
                  ( m2_subset_1(D,k16_substut1,k38_substut1)
                 => ( ( k19_substut1(C) = k19_substut1(D)
                      & ! [E] :
                          ( m2_fraenkel(E,k2_qc_lang1,A,k2_valuat_1(A))
                         => ( r1_valuat_1(A,k39_substut1(C),B,E)
                          <=> r1_sublemma(C,A,k1_sublemma(A,E,k3_sublemma(C,A,E)),B) ) )
                      & ! [E] :
                          ( m2_fraenkel(E,k2_qc_lang1,A,k2_valuat_1(A))
                         => ( r1_valuat_1(A,k39_substut1(D),B,E)
                          <=> r1_sublemma(D,A,k1_sublemma(A,E,k3_sublemma(D,A,E)),B) ) ) )
                   => ! [E] :
                        ( m2_fraenkel(E,k2_qc_lang1,A,k2_valuat_1(A))
                       => ( r1_valuat_1(A,k39_substut1(k7_sublemma(C,D)),B,E)
                        <=> r1_sublemma(k7_sublemma(C,D),A,k1_sublemma(A,E,k3_sublemma(k7_sublemma(C,D),A,E)),B) ) ) ) ) ) ) ) )).

fof(t27_sublemma,axiom,(
    ! [A] :
      ( m1_subset_1(A,k2_zfmisc_1(k16_substut1,k2_qc_lang1))
     => ! [B] :
          ( m1_substut1(B,A)
         => ( v3_substut1(A)
           => ( k18_substut1(k24_substut1(A,B)) = k14_qc_lang1(k23_substut1(A),k18_substut1(k22_substut1(A)))
              & k19_substut1(k24_substut1(A,B)) = B ) ) ) ) )).

fof(d5_sublemma,axiom,(
    ! [A] :
      ( m1_subset_1(A,k2_zfmisc_1(k16_substut1,k2_qc_lang1))
     => ( v1_sublemma(A)
      <=> r2_hidden(k22_substut1(A),k38_substut1) ) ) )).

fof(d6_sublemma,axiom,(
    ! [A] :
      ( ( v1_sublemma(A)
        & m1_subset_1(A,k2_zfmisc_1(k16_substut1,k2_qc_lang1)) )
     => ! [B] :
          ( m1_substut1(B,A)
         => ( v3_substut1(A)
           => k10_sublemma(A,B) = k24_substut1(A,B) ) ) ) )).

fof(t28_sublemma,axiom,(
    ! [A] :
      ( ( v1_sublemma(A)
        & m1_subset_1(A,k2_zfmisc_1(k16_substut1,k2_qc_lang1)) )
     => ! [B] :
          ( m1_substut1(B,A)
         => ( v3_substut1(A)
           => v7_substut1(k10_sublemma(A,B)) ) ) ) )).

fof(d7_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k16_substut1,k38_substut1)
     => ( v7_substut1(A)
       => k11_sublemma(A) = k31_substut1(A) ) ) )).

fof(d8_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k16_substut1,k38_substut1)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ( ( v7_substut1(A)
              & B = k39_substut1(k11_sublemma(A)) )
           => k12_sublemma(A,B) = k36_substut1(A,B) ) ) ) )).

fof(t29_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k16_substut1,k38_substut1)
     => ( v7_substut1(A)
       => k39_substut1(A) = k12_sublemma(A,k39_substut1(k11_sublemma(A))) ) ) )).

fof(t30_sublemma,axiom,(
    ! [A] :
      ( ( v1_sublemma(A)
        & m1_subset_1(A,k2_zfmisc_1(k16_substut1,k2_qc_lang1)) )
     => ! [B] :
          ( m1_substut1(B,A)
         => ( v3_substut1(A)
           => k11_sublemma(k10_sublemma(A,B)) = k9_sublemma(A) ) ) ) )).

fof(t31_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k16_substut1,k38_substut1)
         => ! [C] :
              ( m1_substut1(C,k8_sublemma(B,A))
             => ( v3_substut1(k8_sublemma(B,A))
               => ( k11_sublemma(k10_sublemma(k8_sublemma(B,A),C)) = B
                  & k12_sublemma(k10_sublemma(k8_sublemma(B,A),C),k39_substut1(k11_sublemma(k10_sublemma(k8_sublemma(B,A),C)))) = k12_sublemma(k10_sublemma(k8_sublemma(B,A),C),k39_substut1(B)) ) ) ) ) ) )).

fof(t32_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k16_substut1,k38_substut1)
         => ! [C] :
              ( m1_substut1(C,k8_sublemma(B,A))
             => ( v3_substut1(k8_sublemma(B,A))
               => k12_sublemma(k10_sublemma(k8_sublemma(B,A),C),k39_substut1(B)) = k15_cqc_lang(k35_substut1(k32_substut1(k10_sublemma(k8_sublemma(B,A),C))),k39_substut1(B)) ) ) ) ) )).

fof(t33_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_fraenkel(C,k2_qc_lang1,B,k2_valuat_1(B))
             => ! [D] :
                  ( m2_subset_1(D,k16_substut1,k38_substut1)
                 => ( r2_hidden(A,k1_relat_1(k19_substut1(D)))
                   => k1_funct_1(C,k1_funct_1(k2_substut1(k19_substut1(D)),A)) = k8_funct_2(k2_qc_lang1,B,k1_sublemma(B,C,k3_sublemma(D,B,C)),A) ) ) ) ) ) )).

fof(t34_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k16_substut1,k38_substut1)
         => ( r2_hidden(A,k4_relset_1(k2_qc_lang1,k2_qc_lang1,k2_substut1(k19_substut1(B))))
           => m2_subset_1(k1_funct_1(k2_substut1(k19_substut1(B)),A),k1_qc_lang1,k2_qc_lang1) ) ) ) )).

fof(t35_sublemma,axiom,(
    r1_tarski(k2_zfmisc_1(k8_qc_lang1,k1_substut1),k1_relat_1(k15_substut1)) )).

fof(t36_sublemma,axiom,(
    ! [A] :
      ( ( v1_sublemma(A)
        & m1_subset_1(A,k2_zfmisc_1(k16_substut1,k2_qc_lang1)) )
     => ! [B] :
          ( m1_substut1(B,A)
         => ! [C] :
              ( m1_subset_1(C,k2_zfmisc_1(k16_substut1,k2_qc_lang1))
             => ! [D] :
                  ( m1_substut1(D,C)
                 => ( ( v3_substut1(A)
                      & v3_substut1(C)
                      & k24_substut1(A,B) = k24_substut1(C,D) )
                   => ( k23_substut1(A) = k23_substut1(C)
                      & B = D ) ) ) ) ) ) )).

fof(t37_sublemma,axiom,(
    ! [A] :
      ( ( v1_sublemma(A)
        & m1_subset_1(A,k2_zfmisc_1(k16_substut1,k2_qc_lang1)) )
     => ! [B] :
          ( m1_substut1(B,A)
         => ! [C] :
              ( m1_subset_1(C,k2_zfmisc_1(k16_substut1,k2_qc_lang1))
             => ! [D] :
                  ( m1_substut1(D,C)
                 => ( ( v3_substut1(A)
                      & v3_substut1(C)
                      & k10_sublemma(A,B) = k24_substut1(C,D) )
                   => ( k23_substut1(A) = k23_substut1(C)
                      & B = D ) ) ) ) ) ) )).

fof(t38_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k16_substut1,k38_substut1)
         => ! [C] :
              ( m1_substut1(C,k8_sublemma(B,A))
             => ( v3_substut1(k8_sublemma(B,A))
               => k30_substut1(k10_sublemma(k8_sublemma(B,A),C)) = A ) ) ) ) )).

fof(t39_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k16_substut1,k38_substut1)
         => ! [C] :
              ( m1_substut1(C,k8_sublemma(B,A))
             => ( ( v3_substut1(k8_sublemma(B,A))
                  & r2_hidden(A,k2_relat_1(k7_substut1(A,k15_cqc_lang(A,k2_sublemma(B)),C))) )
               => ( ~ r2_hidden(k35_substut1(k32_substut1(k10_sublemma(k8_sublemma(B,A),C))),k2_relat_1(k7_substut1(A,k15_cqc_lang(A,k2_sublemma(B)),C)))
                  & ~ r2_hidden(k35_substut1(k32_substut1(k10_sublemma(k8_sublemma(B,A),C))),k9_substut1(k2_sublemma(B))) ) ) ) ) ) )).

fof(t40_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k16_substut1,k38_substut1)
         => ! [C] :
              ( m1_substut1(C,k8_sublemma(B,A))
             => ~ ( v3_substut1(k8_sublemma(B,A))
                  & ~ r2_hidden(A,k2_relat_1(k7_substut1(A,k15_cqc_lang(A,k2_sublemma(B)),C)))
                  & r2_hidden(k35_substut1(k32_substut1(k10_sublemma(k8_sublemma(B,A),C))),k2_relat_1(k7_substut1(A,k15_cqc_lang(A,k2_sublemma(B)),C))) ) ) ) ) )).

fof(t41_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k16_substut1,k38_substut1)
         => ! [C] :
              ( m1_substut1(C,k8_sublemma(B,A))
             => ~ ( v3_substut1(k8_sublemma(B,A))
                  & r2_hidden(k35_substut1(k32_substut1(k10_sublemma(k8_sublemma(B,A),C))),k2_relat_1(k7_substut1(A,k15_cqc_lang(A,k2_sublemma(B)),C))) ) ) ) ) )).

fof(t42_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k16_substut1,k38_substut1)
         => ! [C] :
              ( m1_substut1(C,k8_sublemma(B,A))
             => ( v3_substut1(k8_sublemma(B,A))
               => k19_substut1(B) = k14_substut1(A,k2_sublemma(B),k7_substut1(A,k15_cqc_lang(A,k2_sublemma(B)),C)) ) ) ) ) )).

fof(t43_sublemma,axiom,(
    r1_tarski(k24_qc_lang1(k9_cqc_lang),k9_substut1(k9_cqc_lang)) )).

fof(t44_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A))
         => ! [C] :
              ( ( v1_cqc_lang(C,A)
                & m1_qc_lang1(C,A) )
             => r1_tarski(k24_qc_lang1(k8_cqc_lang(A,B,C)),k9_substut1(k8_cqc_lang(A,B,C))) ) ) ) )).

fof(t45_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ( r1_tarski(k24_qc_lang1(A),k9_substut1(A))
       => r1_tarski(k24_qc_lang1(k10_cqc_lang(A)),k9_substut1(k10_cqc_lang(A))) ) ) )).

fof(t46_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ( ( r1_tarski(k24_qc_lang1(A),k9_substut1(A))
              & r1_tarski(k24_qc_lang1(B),k9_substut1(B)) )
           => r1_tarski(k24_qc_lang1(k11_cqc_lang(A,B)),k9_substut1(k11_cqc_lang(A,B))) ) ) ) )).

fof(t47_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ( r1_tarski(k24_qc_lang1(A),k9_substut1(A))
           => r1_tarski(k24_qc_lang1(k15_cqc_lang(B,A)),k9_substut1(k15_cqc_lang(B,A))) ) ) ) )).

fof(t48_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => r1_tarski(k24_qc_lang1(A),k9_substut1(A)) ) )).

fof(d9_sublemma,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => k13_sublemma(A,B,C) = k3_cqc_lang(C,B) ) ) ) )).

fof(t49_sublemma,axiom,(
    ! [A,B] :
      ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
     => ! [C] :
          ( ~ v1_xboole_0(C)
         => ! [D] :
              ( m2_fraenkel(D,k2_qc_lang1,C,k2_valuat_1(C))
             => ! [E] :
                  ( m1_subset_1(E,C)
                 => ( B != A
                   => k1_funct_1(k1_sublemma(C,D,k13_sublemma(C,E,B)),A) = k1_funct_1(D,A) ) ) ) ) ) )).

fof(t50_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m2_fraenkel(D,k2_qc_lang1,C,k2_valuat_1(C))
                 => ! [E] :
                      ( m1_subset_1(E,C)
                     => ( A = B
                       => k8_funct_2(k2_qc_lang1,C,k1_sublemma(C,D,k13_sublemma(C,E,A)),B) = E ) ) ) ) ) ) )).

fof(t51_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_valuat_1(D,C)
                 => ! [E] :
                      ( m2_fraenkel(E,k2_qc_lang1,C,k2_valuat_1(C))
                     => ( r1_valuat_1(C,k15_cqc_lang(B,A),D,E)
                      <=> ! [F] :
                            ( m1_subset_1(F,C)
                           => r1_valuat_1(C,A,D,k1_sublemma(C,E,k13_sublemma(C,F,B))) ) ) ) ) ) ) ) )).

fof(d10_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k16_substut1,k38_substut1)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( m1_substut1(C,k8_sublemma(A,B))
             => ! [D] :
                  ( ~ v1_xboole_0(D)
                 => ! [E] :
                      ( m2_fraenkel(E,k2_qc_lang1,D,k2_valuat_1(D))
                     => k14_sublemma(A,B,C,D,E) = k7_relset_1(k2_qc_lang1,k2_qc_lang1,k2_qc_lang1,D,k2_substut1(k7_substut1(B,k15_cqc_lang(B,k2_sublemma(A)),C)),E) ) ) ) ) ) )).

fof(t52_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k16_substut1,k38_substut1)
         => ! [C] :
              ( m1_substut1(C,k8_sublemma(B,A))
             => ( ( v3_substut1(k8_sublemma(B,A))
                  & r2_hidden(A,k2_relat_1(k7_substut1(A,k15_cqc_lang(A,k2_sublemma(B)),C))) )
               => k35_substut1(k32_substut1(k10_sublemma(k8_sublemma(B,A),C))) = k2_qc_lang3(k13_substut1(k7_substut1(A,k15_cqc_lang(A,k2_sublemma(B)),C),k2_sublemma(B))) ) ) ) ) )).

fof(t53_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k16_substut1,k38_substut1)
         => ! [C] :
              ( m1_substut1(C,k8_sublemma(B,A))
             => ( v3_substut1(k8_sublemma(B,A))
               => ( r2_hidden(A,k2_relat_1(k7_substut1(A,k15_cqc_lang(A,k2_sublemma(B)),C)))
                  | k35_substut1(k32_substut1(k10_sublemma(k8_sublemma(B,A),C))) = A ) ) ) ) ) )).

fof(t54_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_fraenkel(C,k2_qc_lang1,B,k2_valuat_1(B))
             => ! [D] :
                  ( m2_subset_1(D,k16_substut1,k38_substut1)
                 => ! [E] :
                      ( m1_substut1(E,k8_sublemma(D,A))
                     => ( v3_substut1(k8_sublemma(D,A))
                       => ! [F] :
                            ( m1_subset_1(F,B)
                           => ( k3_sublemma(D,B,k1_sublemma(B,C,k13_sublemma(B,F,k35_substut1(k32_substut1(k10_sublemma(k8_sublemma(D,A),E)))))) = k15_sublemma(B,k14_sublemma(D,A,E,B,k1_sublemma(B,C,k13_sublemma(B,F,k35_substut1(k32_substut1(k10_sublemma(k8_sublemma(D,A),E)))))),k13_sublemma(B,F,A))
                              & r1_xboole_0(k1_relat_1(k7_substut1(A,k15_cqc_lang(A,k2_sublemma(D)),E)),k6_domain_1(k2_qc_lang1,A)) ) ) ) ) ) ) ) ) )).

fof(t55_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_valuat_1(C,B)
             => ! [D] :
                  ( m2_fraenkel(D,k2_qc_lang1,B,k2_valuat_1(B))
                 => ! [E] :
                      ( m2_subset_1(E,k16_substut1,k38_substut1)
                     => ! [F] :
                          ( m1_substut1(F,k8_sublemma(E,A))
                         => ( v3_substut1(k8_sublemma(E,A))
                           => ( ! [G] :
                                  ( m1_subset_1(G,B)
                                 => r1_sublemma(E,B,k1_sublemma(B,k1_sublemma(B,D,k13_sublemma(B,G,k35_substut1(k32_substut1(k10_sublemma(k8_sublemma(E,A),F))))),k3_sublemma(E,B,k1_sublemma(B,D,k13_sublemma(B,G,k35_substut1(k32_substut1(k10_sublemma(k8_sublemma(E,A),F))))))),C) )
                            <=> ! [G] :
                                  ( m1_subset_1(G,B)
                                 => r1_sublemma(E,B,k1_sublemma(B,k1_sublemma(B,D,k13_sublemma(B,G,k35_substut1(k32_substut1(k10_sublemma(k8_sublemma(E,A),F))))),k15_sublemma(B,k14_sublemma(E,A,F,B,k1_sublemma(B,D,k13_sublemma(B,G,k35_substut1(k32_substut1(k10_sublemma(k8_sublemma(E,A),F)))))),k13_sublemma(B,G,A))),C) ) ) ) ) ) ) ) ) ) )).

fof(t56_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_fraenkel(C,k2_qc_lang1,B,k2_valuat_1(B))
             => ! [D] :
                  ( m2_subset_1(D,k16_substut1,k38_substut1)
                 => ! [E] :
                      ( m1_substut1(E,k8_sublemma(D,A))
                     => ( v3_substut1(k8_sublemma(D,A))
                       => ! [F] :
                            ( m1_subset_1(F,B)
                           => k14_sublemma(D,A,E,B,k1_sublemma(B,C,k13_sublemma(B,F,k35_substut1(k32_substut1(k10_sublemma(k8_sublemma(D,A),E)))))) = k14_sublemma(D,A,E,B,C) ) ) ) ) ) ) ) )).

fof(t57_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_valuat_1(C,B)
             => ! [D] :
                  ( m2_fraenkel(D,k2_qc_lang1,B,k2_valuat_1(B))
                 => ! [E] :
                      ( m2_subset_1(E,k16_substut1,k38_substut1)
                     => ! [F] :
                          ( m1_substut1(F,k8_sublemma(E,A))
                         => ( v3_substut1(k8_sublemma(E,A))
                           => ( ! [G] :
                                  ( m1_subset_1(G,B)
                                 => r1_sublemma(E,B,k1_sublemma(B,k1_sublemma(B,D,k13_sublemma(B,G,k35_substut1(k32_substut1(k10_sublemma(k8_sublemma(E,A),F))))),k15_sublemma(B,k14_sublemma(E,A,F,B,k1_sublemma(B,D,k13_sublemma(B,G,k35_substut1(k32_substut1(k10_sublemma(k8_sublemma(E,A),F)))))),k13_sublemma(B,G,A))),C) )
                            <=> ! [G] :
                                  ( m1_subset_1(G,B)
                                 => r1_sublemma(E,B,k1_sublemma(B,k1_sublemma(B,D,k13_sublemma(B,G,k35_substut1(k32_substut1(k10_sublemma(k8_sublemma(E,A),F))))),k15_sublemma(B,k14_sublemma(E,A,F,B,D),k13_sublemma(B,G,A))),C) ) ) ) ) ) ) ) ) ) )).

fof(t58_sublemma,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k1_qc_lang1)
     => ( r1_tarski(k5_relset_1(k5_numbers,k1_qc_lang1,A),k2_qc_lang1)
       => k22_qc_lang1(A) = k5_relset_1(k5_numbers,k1_qc_lang1,A) ) ) )).

fof(t59_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_fraenkel(C,k2_qc_lang1,B,k2_valuat_1(B))
             => ! [D] :
                  ( m1_subset_1(D,B)
                 => ( k4_relset_1(k2_qc_lang1,B,C) = k2_qc_lang1
                    & k4_relset_1(k2_qc_lang1,B,k13_sublemma(B,D,A)) = k6_domain_1(k2_qc_lang1,A) ) ) ) ) ) )).

fof(t60_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_fraenkel(C,k2_qc_lang1,B,k2_valuat_1(B))
             => ! [D] :
                  ( ( v1_cqc_lang(D,A)
                    & m1_qc_lang1(D,A) )
                 => k8_valuat_1(B,A,D,C) = k7_relset_1(k5_numbers,k1_qc_lang1,k2_qc_lang1,B,D,k8_relset_1(k2_qc_lang1,B,C,k22_qc_lang1(D))) ) ) ) ) )).

fof(t61_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_valuat_1(C,B)
             => ! [D] :
                  ( m2_subset_1(D,k5_qc_lang1,k7_qc_lang1(A))
                 => ! [E] :
                      ( ( v1_cqc_lang(E,A)
                        & m1_qc_lang1(E,A) )
                     => ! [F] :
                          ( m2_fraenkel(F,k2_qc_lang1,B,k2_valuat_1(B))
                         => ! [G] :
                              ( m2_fraenkel(G,k2_qc_lang1,B,k2_valuat_1(B))
                             => ( k8_relset_1(k2_qc_lang1,B,F,k24_qc_lang1(k8_cqc_lang(A,D,E))) = k8_relset_1(k2_qc_lang1,B,G,k24_qc_lang1(k8_cqc_lang(A,D,E)))
                               => ( r1_valuat_1(B,k8_cqc_lang(A,D,E),C,F)
                                <=> r1_valuat_1(B,k8_cqc_lang(A,D,E),C,G) ) ) ) ) ) ) ) ) ) )).

fof(t62_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_valuat_1(C,B)
             => ( ! [D] :
                    ( m2_fraenkel(D,k2_qc_lang1,B,k2_valuat_1(B))
                   => ! [E] :
                        ( m2_fraenkel(E,k2_qc_lang1,B,k2_valuat_1(B))
                       => ( k8_relset_1(k2_qc_lang1,B,D,k24_qc_lang1(A)) = k8_relset_1(k2_qc_lang1,B,E,k24_qc_lang1(A))
                         => ( r1_valuat_1(B,A,C,D)
                          <=> r1_valuat_1(B,A,C,E) ) ) ) )
               => ! [D] :
                    ( m2_fraenkel(D,k2_qc_lang1,B,k2_valuat_1(B))
                   => ! [E] :
                        ( m2_fraenkel(E,k2_qc_lang1,B,k2_valuat_1(B))
                       => ( k8_relset_1(k2_qc_lang1,B,D,k24_qc_lang1(k10_cqc_lang(A))) = k8_relset_1(k2_qc_lang1,B,E,k24_qc_lang1(k10_cqc_lang(A)))
                         => ( r1_valuat_1(B,k10_cqc_lang(A),C,D)
                          <=> r1_valuat_1(B,k10_cqc_lang(A),C,E) ) ) ) ) ) ) ) ) )).

fof(t63_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_valuat_1(D,C)
                 => ( ( ! [E] :
                          ( m2_fraenkel(E,k2_qc_lang1,C,k2_valuat_1(C))
                         => ! [F] :
                              ( m2_fraenkel(F,k2_qc_lang1,C,k2_valuat_1(C))
                             => ( k8_relset_1(k2_qc_lang1,C,E,k24_qc_lang1(A)) = k8_relset_1(k2_qc_lang1,C,F,k24_qc_lang1(A))
                               => ( r1_valuat_1(C,A,D,E)
                                <=> r1_valuat_1(C,A,D,F) ) ) ) )
                      & ! [E] :
                          ( m2_fraenkel(E,k2_qc_lang1,C,k2_valuat_1(C))
                         => ! [F] :
                              ( m2_fraenkel(F,k2_qc_lang1,C,k2_valuat_1(C))
                             => ( k8_relset_1(k2_qc_lang1,C,E,k24_qc_lang1(B)) = k8_relset_1(k2_qc_lang1,C,F,k24_qc_lang1(B))
                               => ( r1_valuat_1(C,B,D,E)
                                <=> r1_valuat_1(C,B,D,F) ) ) ) ) )
                   => ! [E] :
                        ( m2_fraenkel(E,k2_qc_lang1,C,k2_valuat_1(C))
                       => ! [F] :
                            ( m2_fraenkel(F,k2_qc_lang1,C,k2_valuat_1(C))
                           => ( k8_relset_1(k2_qc_lang1,C,E,k24_qc_lang1(k11_cqc_lang(A,B))) = k8_relset_1(k2_qc_lang1,C,F,k24_qc_lang1(k11_cqc_lang(A,B)))
                             => ( r1_valuat_1(C,k11_cqc_lang(A,B),D,E)
                              <=> r1_valuat_1(C,k11_cqc_lang(A,B),D,F) ) ) ) ) ) ) ) ) ) )).

fof(t64_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_fraenkel(C,k2_qc_lang1,B,k2_valuat_1(B))
             => ! [D] :
                  ( m1_subset_1(D,B)
                 => ! [E] :
                      ( r1_tarski(E,k2_qc_lang1)
                     => ( k4_relset_1(k2_qc_lang1,B,k8_relset_1(k2_qc_lang1,B,C,E)) = k4_relset_1(k2_qc_lang1,B,k8_relset_1(k2_qc_lang1,B,k1_sublemma(B,C,k13_sublemma(B,D,A)),E))
                        & k4_relset_1(k2_qc_lang1,B,k8_relset_1(k2_qc_lang1,B,C,E)) = E ) ) ) ) ) ) )).

fof(t65_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m2_fraenkel(D,k2_qc_lang1,C,k2_valuat_1(C))
                 => ! [E] :
                      ( m2_fraenkel(E,k2_qc_lang1,C,k2_valuat_1(C))
                     => ! [F] :
                          ( m1_subset_1(F,C)
                         => ( k8_relset_1(k2_qc_lang1,C,D,k24_qc_lang1(A)) = k8_relset_1(k2_qc_lang1,C,E,k24_qc_lang1(A))
                           => k8_relset_1(k2_qc_lang1,C,k1_sublemma(C,D,k13_sublemma(C,F,B)),k24_qc_lang1(A)) = k8_relset_1(k2_qc_lang1,C,k1_sublemma(C,E,k13_sublemma(C,F,B)),k24_qc_lang1(A)) ) ) ) ) ) ) ) )).

fof(t66_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => r1_tarski(k24_qc_lang1(A),k4_subset_1(k2_qc_lang1,k24_qc_lang1(k15_cqc_lang(B,A)),k6_domain_1(k2_qc_lang1,B))) ) ) )).

fof(t67_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m2_fraenkel(D,k2_qc_lang1,C,k2_valuat_1(C))
                 => ! [E] :
                      ( m2_fraenkel(E,k2_qc_lang1,C,k2_valuat_1(C))
                     => ! [F] :
                          ( m1_subset_1(F,C)
                         => ( k8_relset_1(k2_qc_lang1,C,D,k6_subset_1(k2_qc_lang1,k24_qc_lang1(A),k6_domain_1(k2_qc_lang1,B))) = k8_relset_1(k2_qc_lang1,C,E,k6_subset_1(k2_qc_lang1,k24_qc_lang1(A),k6_domain_1(k2_qc_lang1,B)))
                           => k8_relset_1(k2_qc_lang1,C,k1_sublemma(C,D,k13_sublemma(C,F,B)),k24_qc_lang1(A)) = k8_relset_1(k2_qc_lang1,C,k1_sublemma(C,E,k13_sublemma(C,F,B)),k24_qc_lang1(A)) ) ) ) ) ) ) ) )).

fof(t68_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_valuat_1(D,C)
                 => ( ! [E] :
                        ( m2_fraenkel(E,k2_qc_lang1,C,k2_valuat_1(C))
                       => ! [F] :
                            ( m2_fraenkel(F,k2_qc_lang1,C,k2_valuat_1(C))
                           => ( k8_relset_1(k2_qc_lang1,C,E,k24_qc_lang1(A)) = k8_relset_1(k2_qc_lang1,C,F,k24_qc_lang1(A))
                             => ( r1_valuat_1(C,A,D,E)
                              <=> r1_valuat_1(C,A,D,F) ) ) ) )
                   => ! [E] :
                        ( m2_fraenkel(E,k2_qc_lang1,C,k2_valuat_1(C))
                       => ! [F] :
                            ( m2_fraenkel(F,k2_qc_lang1,C,k2_valuat_1(C))
                           => ( k8_relset_1(k2_qc_lang1,C,E,k24_qc_lang1(k15_cqc_lang(B,A))) = k8_relset_1(k2_qc_lang1,C,F,k24_qc_lang1(k15_cqc_lang(B,A)))
                             => ( r1_valuat_1(C,k15_cqc_lang(B,A),D,E)
                              <=> r1_valuat_1(C,k15_cqc_lang(B,A),D,F) ) ) ) ) ) ) ) ) ) )).

fof(t69_sublemma,axiom,(
    $true )).

fof(t70_sublemma,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_valuat_1(B,A)
         => ! [C] :
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ! [D] :
                  ( m2_fraenkel(D,k2_qc_lang1,A,k2_valuat_1(A))
                 => ! [E] :
                      ( m2_fraenkel(E,k2_qc_lang1,A,k2_valuat_1(A))
                     => ( k8_relset_1(k2_qc_lang1,A,D,k24_qc_lang1(C)) = k8_relset_1(k2_qc_lang1,A,E,k24_qc_lang1(C))
                       => ( r1_valuat_1(A,C,B,D)
                        <=> r1_valuat_1(A,C,B,E) ) ) ) ) ) ) ) )).

fof(t71_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_fraenkel(C,k2_qc_lang1,B,k2_valuat_1(B))
             => ! [D] :
                  ( m2_subset_1(D,k16_substut1,k38_substut1)
                 => ! [E] :
                      ( m1_substut1(E,k8_sublemma(D,A))
                     => ! [F] :
                          ( m1_subset_1(F,B)
                         => ( v3_substut1(k8_sublemma(D,A))
                           => k8_relset_1(k2_qc_lang1,B,k1_sublemma(B,k1_sublemma(B,C,k13_sublemma(B,F,k35_substut1(k32_substut1(k10_sublemma(k8_sublemma(D,A),E))))),k15_sublemma(B,k14_sublemma(D,A,E,B,C),k13_sublemma(B,F,A))),k24_qc_lang1(k2_sublemma(D))) = k8_relset_1(k2_qc_lang1,B,k1_sublemma(B,C,k15_sublemma(B,k14_sublemma(D,A,E,B,C),k13_sublemma(B,F,A))),k24_qc_lang1(k2_sublemma(D))) ) ) ) ) ) ) ) )).

fof(t72_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_valuat_1(C,B)
             => ! [D] :
                  ( m2_fraenkel(D,k2_qc_lang1,B,k2_valuat_1(B))
                 => ! [E] :
                      ( m2_subset_1(E,k16_substut1,k38_substut1)
                     => ! [F] :
                          ( m1_substut1(F,k8_sublemma(E,A))
                         => ( v3_substut1(k8_sublemma(E,A))
                           => ( ! [G] :
                                  ( m1_subset_1(G,B)
                                 => r1_sublemma(E,B,k1_sublemma(B,k1_sublemma(B,D,k13_sublemma(B,G,k35_substut1(k32_substut1(k10_sublemma(k8_sublemma(E,A),F))))),k15_sublemma(B,k14_sublemma(E,A,F,B,D),k13_sublemma(B,G,A))),C) )
                            <=> ! [G] :
                                  ( m1_subset_1(G,B)
                                 => r1_sublemma(E,B,k1_sublemma(B,D,k15_sublemma(B,k14_sublemma(E,A,F,B,D),k13_sublemma(B,G,A))),C) ) ) ) ) ) ) ) ) ) )).

fof(t73_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_fraenkel(C,k2_qc_lang1,B,k2_valuat_1(B))
             => ! [D] :
                  ( m2_subset_1(D,k16_substut1,k38_substut1)
                 => ! [E] :
                      ( m1_substut1(E,k8_sublemma(D,A))
                     => k4_relset_1(k2_qc_lang1,B,k14_sublemma(D,A,E,B,C)) = k1_relat_1(k7_substut1(A,k15_cqc_lang(A,k2_sublemma(D)),E)) ) ) ) ) ) )).

fof(t74_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_fraenkel(C,k2_qc_lang1,B,k2_valuat_1(B))
             => ! [D] :
                  ( m2_subset_1(D,k16_substut1,k38_substut1)
                 => ! [E] :
                      ( m1_substut1(E,k8_sublemma(D,A))
                     => ! [F] :
                          ( m1_subset_1(F,B)
                         => ( v3_substut1(k8_sublemma(D,A))
                           => k1_sublemma(B,C,k15_sublemma(B,k14_sublemma(D,A,E,B,C),k13_sublemma(B,F,A))) = k1_sublemma(B,k1_sublemma(B,C,k14_sublemma(D,A,E,B,C)),k13_sublemma(B,F,A)) ) ) ) ) ) ) ) )).

fof(t75_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_valuat_1(C,B)
             => ! [D] :
                  ( m2_fraenkel(D,k2_qc_lang1,B,k2_valuat_1(B))
                 => ! [E] :
                      ( m2_subset_1(E,k16_substut1,k38_substut1)
                     => ! [F] :
                          ( m1_substut1(F,k8_sublemma(E,A))
                         => ( v3_substut1(k8_sublemma(E,A))
                           => ( ! [G] :
                                  ( m1_subset_1(G,B)
                                 => r1_sublemma(E,B,k1_sublemma(B,D,k15_sublemma(B,k14_sublemma(E,A,F,B,D),k13_sublemma(B,G,A))),C) )
                            <=> ! [G] :
                                  ( m1_subset_1(G,B)
                                 => r1_sublemma(E,B,k1_sublemma(B,k1_sublemma(B,D,k14_sublemma(E,A,F,B,D)),k13_sublemma(B,G,A)),C) ) ) ) ) ) ) ) ) ) )).

fof(t76_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_valuat_1(C,B)
             => ! [D] :
                  ( m2_fraenkel(D,k2_qc_lang1,B,k2_valuat_1(B))
                 => ! [E] :
                      ( m2_subset_1(E,k16_substut1,k38_substut1)
                     => ! [F] :
                          ( m1_substut1(F,k8_sublemma(E,A))
                         => ( ! [G] :
                                ( m1_subset_1(G,B)
                               => r1_sublemma(E,B,k1_sublemma(B,k1_sublemma(B,D,k14_sublemma(E,A,F,B,D)),k13_sublemma(B,G,A)),C) )
                          <=> ! [G] :
                                ( m1_subset_1(G,B)
                               => r1_valuat_1(B,k2_sublemma(E),C,k1_sublemma(B,k1_sublemma(B,D,k14_sublemma(E,A,F,B,D)),k13_sublemma(B,G,A))) ) ) ) ) ) ) ) ) )).

fof(t77_sublemma,axiom,(
    $true )).

fof(t78_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_cqc_lang(C,A)
                & m1_qc_lang1(C,A) )
             => ! [D] :
                  ( m2_fraenkel(D,k2_qc_lang1,B,k2_valuat_1(B))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & m2_relset_1(E,k2_qc_lang1,B) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & m2_relset_1(F,k2_qc_lang1,B) )
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & m2_relset_1(G,k2_qc_lang1,B) )
                             => ( ( ! [H] :
                                      ( m2_subset_1(H,k1_qc_lang1,k2_qc_lang1)
                                     => ~ ( r2_hidden(H,k4_relset_1(k2_qc_lang1,B,F))
                                          & r2_hidden(H,k22_qc_lang1(C)) ) )
                                  & ! [H] :
                                      ( m2_subset_1(H,k1_qc_lang1,k2_qc_lang1)
                                     => ( r2_hidden(H,k4_relset_1(k2_qc_lang1,B,G))
                                       => k1_funct_1(G,H) = k8_funct_2(k2_qc_lang1,B,D,H) ) )
                                  & r1_xboole_0(k4_relset_1(k2_qc_lang1,B,E),k4_relset_1(k2_qc_lang1,B,G)) )
                               => k8_valuat_1(B,A,C,k1_sublemma(B,D,E)) = k8_valuat_1(B,A,C,k1_sublemma(B,D,k15_sublemma(B,k15_sublemma(B,E,F),G))) ) ) ) ) ) ) ) ) )).

fof(t79_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_valuat_1(C,B)
             => ! [D] :
                  ( m2_subset_1(D,k5_qc_lang1,k7_qc_lang1(A))
                 => ! [E] :
                      ( ( v1_cqc_lang(E,A)
                        & m1_qc_lang1(E,A) )
                     => ! [F] :
                          ( m2_fraenkel(F,k2_qc_lang1,B,k2_valuat_1(B))
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & m2_relset_1(G,k2_qc_lang1,B) )
                             => ! [H] :
                                  ( ( v1_funct_1(H)
                                    & m2_relset_1(H,k2_qc_lang1,B) )
                                 => ! [I] :
                                      ( ( v1_funct_1(I)
                                        & m2_relset_1(I,k2_qc_lang1,B) )
                                     => ( ( ! [J] :
                                              ( m2_subset_1(J,k1_qc_lang1,k2_qc_lang1)
                                             => ~ ( r2_hidden(J,k4_relset_1(k2_qc_lang1,B,H))
                                                  & r2_hidden(J,k24_qc_lang1(k8_cqc_lang(A,D,E))) ) )
                                          & ! [J] :
                                              ( m2_subset_1(J,k1_qc_lang1,k2_qc_lang1)
                                             => ( r2_hidden(J,k4_relset_1(k2_qc_lang1,B,I))
                                               => k1_funct_1(I,J) = k8_funct_2(k2_qc_lang1,B,F,J) ) )
                                          & r1_xboole_0(k4_relset_1(k2_qc_lang1,B,G),k4_relset_1(k2_qc_lang1,B,I)) )
                                       => ( r1_valuat_1(B,k8_cqc_lang(A,D,E),C,k1_sublemma(B,F,G))
                                        <=> r1_valuat_1(B,k8_cqc_lang(A,D,E),C,k1_sublemma(B,F,k15_sublemma(B,k15_sublemma(B,G,H),I))) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t80_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_valuat_1(C,B)
             => ( ! [D] :
                    ( m2_fraenkel(D,k2_qc_lang1,B,k2_valuat_1(B))
                   => ! [E] :
                        ( ( v1_funct_1(E)
                          & m2_relset_1(E,k2_qc_lang1,B) )
                       => ! [F] :
                            ( ( v1_funct_1(F)
                              & m2_relset_1(F,k2_qc_lang1,B) )
                           => ! [G] :
                                ( ( v1_funct_1(G)
                                  & m2_relset_1(G,k2_qc_lang1,B) )
                               => ( ( ! [H] :
                                        ( m2_subset_1(H,k1_qc_lang1,k2_qc_lang1)
                                       => ~ ( r2_hidden(H,k4_relset_1(k2_qc_lang1,B,F))
                                            & r2_hidden(H,k24_qc_lang1(A)) ) )
                                    & ! [H] :
                                        ( m2_subset_1(H,k1_qc_lang1,k2_qc_lang1)
                                       => ( r2_hidden(H,k4_relset_1(k2_qc_lang1,B,G))
                                         => k1_funct_1(G,H) = k8_funct_2(k2_qc_lang1,B,D,H) ) )
                                    & r1_xboole_0(k4_relset_1(k2_qc_lang1,B,E),k4_relset_1(k2_qc_lang1,B,G)) )
                                 => ( r1_valuat_1(B,A,C,k1_sublemma(B,D,E))
                                  <=> r1_valuat_1(B,A,C,k1_sublemma(B,D,k15_sublemma(B,k15_sublemma(B,E,F),G))) ) ) ) ) ) )
               => ! [D] :
                    ( m2_fraenkel(D,k2_qc_lang1,B,k2_valuat_1(B))
                   => ! [E] :
                        ( ( v1_funct_1(E)
                          & m2_relset_1(E,k2_qc_lang1,B) )
                       => ! [F] :
                            ( ( v1_funct_1(F)
                              & m2_relset_1(F,k2_qc_lang1,B) )
                           => ! [G] :
                                ( ( v1_funct_1(G)
                                  & m2_relset_1(G,k2_qc_lang1,B) )
                               => ( ( ! [H] :
                                        ( m2_subset_1(H,k1_qc_lang1,k2_qc_lang1)
                                       => ~ ( r2_hidden(H,k4_relset_1(k2_qc_lang1,B,F))
                                            & r2_hidden(H,k24_qc_lang1(k10_cqc_lang(A))) ) )
                                    & ! [H] :
                                        ( m2_subset_1(H,k1_qc_lang1,k2_qc_lang1)
                                       => ( r2_hidden(H,k4_relset_1(k2_qc_lang1,B,G))
                                         => k1_funct_1(G,H) = k8_funct_2(k2_qc_lang1,B,D,H) ) )
                                    & r1_xboole_0(k4_relset_1(k2_qc_lang1,B,E),k4_relset_1(k2_qc_lang1,B,G)) )
                                 => ( r1_valuat_1(B,k10_cqc_lang(A),C,k1_sublemma(B,D,E))
                                  <=> r1_valuat_1(B,k10_cqc_lang(A),C,k1_sublemma(B,D,k15_sublemma(B,k15_sublemma(B,E,F),G))) ) ) ) ) ) ) ) ) ) ) )).

fof(t81_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_valuat_1(D,C)
                 => ( ( ! [E] :
                          ( m2_fraenkel(E,k2_qc_lang1,C,k2_valuat_1(C))
                         => ! [F] :
                              ( ( v1_funct_1(F)
                                & m2_relset_1(F,k2_qc_lang1,C) )
                             => ! [G] :
                                  ( ( v1_funct_1(G)
                                    & m2_relset_1(G,k2_qc_lang1,C) )
                                 => ! [H] :
                                      ( ( v1_funct_1(H)
                                        & m2_relset_1(H,k2_qc_lang1,C) )
                                     => ( ( ! [I] :
                                              ( m2_subset_1(I,k1_qc_lang1,k2_qc_lang1)
                                             => ~ ( r2_hidden(I,k4_relset_1(k2_qc_lang1,C,G))
                                                  & r2_hidden(I,k24_qc_lang1(A)) ) )
                                          & ! [I] :
                                              ( m2_subset_1(I,k1_qc_lang1,k2_qc_lang1)
                                             => ( r2_hidden(I,k4_relset_1(k2_qc_lang1,C,H))
                                               => k1_funct_1(H,I) = k8_funct_2(k2_qc_lang1,C,E,I) ) )
                                          & r1_xboole_0(k4_relset_1(k2_qc_lang1,C,F),k4_relset_1(k2_qc_lang1,C,H)) )
                                       => ( r1_valuat_1(C,A,D,k1_sublemma(C,E,F))
                                        <=> r1_valuat_1(C,A,D,k1_sublemma(C,E,k15_sublemma(C,k15_sublemma(C,F,G),H))) ) ) ) ) ) )
                      & ! [E] :
                          ( m2_fraenkel(E,k2_qc_lang1,C,k2_valuat_1(C))
                         => ! [F] :
                              ( ( v1_funct_1(F)
                                & m2_relset_1(F,k2_qc_lang1,C) )
                             => ! [G] :
                                  ( ( v1_funct_1(G)
                                    & m2_relset_1(G,k2_qc_lang1,C) )
                                 => ! [H] :
                                      ( ( v1_funct_1(H)
                                        & m2_relset_1(H,k2_qc_lang1,C) )
                                     => ( ( ! [I] :
                                              ( m2_subset_1(I,k1_qc_lang1,k2_qc_lang1)
                                             => ~ ( r2_hidden(I,k4_relset_1(k2_qc_lang1,C,G))
                                                  & r2_hidden(I,k24_qc_lang1(B)) ) )
                                          & ! [I] :
                                              ( m2_subset_1(I,k1_qc_lang1,k2_qc_lang1)
                                             => ( r2_hidden(I,k4_relset_1(k2_qc_lang1,C,H))
                                               => k1_funct_1(H,I) = k8_funct_2(k2_qc_lang1,C,E,I) ) )
                                          & r1_xboole_0(k4_relset_1(k2_qc_lang1,C,F),k4_relset_1(k2_qc_lang1,C,H)) )
                                       => ( r1_valuat_1(C,B,D,k1_sublemma(C,E,F))
                                        <=> r1_valuat_1(C,B,D,k1_sublemma(C,E,k15_sublemma(C,k15_sublemma(C,F,G),H))) ) ) ) ) ) ) )
                   => ! [E] :
                        ( m2_fraenkel(E,k2_qc_lang1,C,k2_valuat_1(C))
                       => ! [F] :
                            ( ( v1_funct_1(F)
                              & m2_relset_1(F,k2_qc_lang1,C) )
                           => ! [G] :
                                ( ( v1_funct_1(G)
                                  & m2_relset_1(G,k2_qc_lang1,C) )
                               => ! [H] :
                                    ( ( v1_funct_1(H)
                                      & m2_relset_1(H,k2_qc_lang1,C) )
                                   => ( ( ! [I] :
                                            ( m2_subset_1(I,k1_qc_lang1,k2_qc_lang1)
                                           => ~ ( r2_hidden(I,k4_relset_1(k2_qc_lang1,C,G))
                                                & r2_hidden(I,k24_qc_lang1(k11_cqc_lang(A,B))) ) )
                                        & ! [I] :
                                            ( m2_subset_1(I,k1_qc_lang1,k2_qc_lang1)
                                           => ( r2_hidden(I,k4_relset_1(k2_qc_lang1,C,H))
                                             => k1_funct_1(H,I) = k8_funct_2(k2_qc_lang1,C,E,I) ) )
                                        & r1_xboole_0(k4_relset_1(k2_qc_lang1,C,F),k4_relset_1(k2_qc_lang1,C,H)) )
                                     => ( r1_valuat_1(C,k11_cqc_lang(A,B),D,k1_sublemma(C,E,F))
                                      <=> r1_valuat_1(C,k11_cqc_lang(A,B),D,k1_sublemma(C,E,k15_sublemma(C,k15_sublemma(C,F,G),H))) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t82_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,k2_qc_lang1,C) )
                 => ( ! [E] :
                        ( m2_subset_1(E,k1_qc_lang1,k2_qc_lang1)
                       => ~ ( r2_hidden(E,k4_relset_1(k2_qc_lang1,C,D))
                            & r2_hidden(E,k24_qc_lang1(k15_cqc_lang(B,A))) ) )
                   => ! [E] :
                        ( m2_subset_1(E,k1_qc_lang1,k2_qc_lang1)
                       => ~ ( r2_hidden(E,k6_subset_1(k2_qc_lang1,k4_relset_1(k2_qc_lang1,C,D),k6_domain_1(k2_qc_lang1,B)))
                            & r2_hidden(E,k24_qc_lang1(A)) ) ) ) ) ) ) ) )).

fof(t83_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_fraenkel(C,k2_qc_lang1,B,k2_valuat_1(B))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,k2_qc_lang1,B) )
                 => ! [E] :
                      ( ( v1_relat_1(E)
                        & v1_funct_1(E) )
                     => ( ( ! [F] :
                              ( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
                             => ( r2_hidden(F,k1_relat_1(E))
                               => k1_funct_1(E,F) = k8_funct_2(k2_qc_lang1,B,C,F) ) )
                          & r1_xboole_0(k4_relset_1(k2_qc_lang1,B,D),k1_relat_1(E)) )
                       => ! [F] :
                            ( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
                           => ( r2_hidden(F,k4_xboole_0(k1_relat_1(E),k6_domain_1(k2_qc_lang1,A)))
                             => k1_funct_1(k7_relat_1(E,k4_xboole_0(k1_relat_1(E),k6_domain_1(k2_qc_lang1,A))),F) = k8_funct_2(k2_qc_lang1,B,k1_sublemma(B,C,D),F) ) ) ) ) ) ) ) ) )).

fof(t84_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_valuat_1(D,C)
                 => ( ! [E] :
                        ( m2_fraenkel(E,k2_qc_lang1,C,k2_valuat_1(C))
                       => ! [F] :
                            ( ( v1_funct_1(F)
                              & m2_relset_1(F,k2_qc_lang1,C) )
                           => ! [G] :
                                ( ( v1_funct_1(G)
                                  & m2_relset_1(G,k2_qc_lang1,C) )
                               => ! [H] :
                                    ( ( v1_funct_1(H)
                                      & m2_relset_1(H,k2_qc_lang1,C) )
                                   => ( ( ! [I] :
                                            ( m2_subset_1(I,k1_qc_lang1,k2_qc_lang1)
                                           => ~ ( r2_hidden(I,k4_relset_1(k2_qc_lang1,C,G))
                                                & r2_hidden(I,k24_qc_lang1(A)) ) )
                                        & ! [I] :
                                            ( m2_subset_1(I,k1_qc_lang1,k2_qc_lang1)
                                           => ( r2_hidden(I,k4_relset_1(k2_qc_lang1,C,H))
                                             => k1_funct_1(H,I) = k8_funct_2(k2_qc_lang1,C,E,I) ) )
                                        & r1_xboole_0(k4_relset_1(k2_qc_lang1,C,F),k4_relset_1(k2_qc_lang1,C,H)) )
                                     => ( r1_valuat_1(C,A,D,k1_sublemma(C,E,F))
                                      <=> r1_valuat_1(C,A,D,k1_sublemma(C,E,k15_sublemma(C,k15_sublemma(C,F,G),H))) ) ) ) ) ) )
                   => ! [E] :
                        ( m2_fraenkel(E,k2_qc_lang1,C,k2_valuat_1(C))
                       => ! [F] :
                            ( ( v1_funct_1(F)
                              & m2_relset_1(F,k2_qc_lang1,C) )
                           => ! [G] :
                                ( ( v1_funct_1(G)
                                  & m2_relset_1(G,k2_qc_lang1,C) )
                               => ! [H] :
                                    ( ( v1_funct_1(H)
                                      & m2_relset_1(H,k2_qc_lang1,C) )
                                   => ( ( ! [I] :
                                            ( m2_subset_1(I,k1_qc_lang1,k2_qc_lang1)
                                           => ~ ( r2_hidden(I,k4_relset_1(k2_qc_lang1,C,G))
                                                & r2_hidden(I,k24_qc_lang1(k15_cqc_lang(B,A))) ) )
                                        & ! [I] :
                                            ( m2_subset_1(I,k1_qc_lang1,k2_qc_lang1)
                                           => ( r2_hidden(I,k4_relset_1(k2_qc_lang1,C,H))
                                             => k1_funct_1(H,I) = k8_funct_2(k2_qc_lang1,C,E,I) ) )
                                        & r1_xboole_0(k4_relset_1(k2_qc_lang1,C,F),k4_relset_1(k2_qc_lang1,C,H)) )
                                     => ( r1_valuat_1(C,k15_cqc_lang(B,A),D,k1_sublemma(C,E,F))
                                      <=> r1_valuat_1(C,k15_cqc_lang(B,A),D,k1_sublemma(C,E,k15_sublemma(C,k15_sublemma(C,F,G),H))) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t85_sublemma,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_valuat_1(B,A)
         => ! [C] :
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ! [D] :
                  ( m2_fraenkel(D,k2_qc_lang1,A,k2_valuat_1(A))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & m2_relset_1(E,k2_qc_lang1,A) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & m2_relset_1(F,k2_qc_lang1,A) )
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & m2_relset_1(G,k2_qc_lang1,A) )
                             => ( ( ! [H] :
                                      ( m2_subset_1(H,k1_qc_lang1,k2_qc_lang1)
                                     => ~ ( r2_hidden(H,k4_relset_1(k2_qc_lang1,A,F))
                                          & r2_hidden(H,k24_qc_lang1(C)) ) )
                                  & ! [H] :
                                      ( m2_subset_1(H,k1_qc_lang1,k2_qc_lang1)
                                     => ( r2_hidden(H,k4_relset_1(k2_qc_lang1,A,G))
                                       => k1_funct_1(G,H) = k8_funct_2(k2_qc_lang1,A,D,H) ) )
                                  & r1_xboole_0(k4_relset_1(k2_qc_lang1,A,E),k4_relset_1(k2_qc_lang1,A,G)) )
                               => ( r1_valuat_1(A,C,B,k1_sublemma(A,D,E))
                                <=> r1_valuat_1(A,C,B,k1_sublemma(A,D,k15_sublemma(A,k15_sublemma(A,E,F),G))) ) ) ) ) ) ) ) ) ) )).

fof(d11_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( B = k16_sublemma(A)
        <=> ! [C] :
              ( r2_hidden(C,B)
            <=> ? [D] :
                  ( m2_subset_1(D,k1_qc_lang1,k2_qc_lang1)
                  & D = C
                  & ~ r2_hidden(D,k24_qc_lang1(A)) ) ) ) ) )).

fof(d12_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m1_subset_1(B,k1_substut1)
         => ! [C] :
              ( C = k17_sublemma(A,B)
            <=> ! [D] :
                  ( r2_hidden(D,C)
                <=> ? [E] :
                      ( m2_subset_1(E,k1_qc_lang1,k2_qc_lang1)
                      & E = D
                      & r2_hidden(E,k24_qc_lang1(A))
                      & E = k1_funct_1(k2_substut1(B),E) ) ) ) ) ) )).

fof(t86_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m1_subset_1(B,k1_substut1)
         => r1_xboole_0(k4_relset_1(k2_qc_lang1,k2_qc_lang1,k8_relset_1(k2_qc_lang1,k2_qc_lang1,k2_substut1(B),k16_sublemma(A))),k4_relset_1(k2_qc_lang1,k2_qc_lang1,k8_relset_1(k2_qc_lang1,k2_qc_lang1,k2_substut1(B),k17_sublemma(A,B)))) ) ) )).

fof(t87_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( m1_subset_1(C,k1_substut1)
             => k2_substut1(k7_substut1(B,k15_cqc_lang(B,A),C)) = k3_relset_1(k2_qc_lang1,k2_qc_lang1,k2_substut1(C),k15_sublemma(k2_qc_lang1,k8_relset_1(k2_qc_lang1,k2_qc_lang1,k2_substut1(C),k16_sublemma(k15_cqc_lang(B,A))),k8_relset_1(k2_qc_lang1,k2_qc_lang1,k2_substut1(C),k17_sublemma(k15_cqc_lang(B,A),C)))) ) ) ) )).

fof(t88_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( m1_subset_1(C,k1_substut1)
             => r1_xboole_0(k4_relset_1(k2_qc_lang1,k2_qc_lang1,k2_substut1(k7_substut1(B,A,C))),k4_subset_1(k2_qc_lang1,k4_relset_1(k2_qc_lang1,k2_qc_lang1,k8_relset_1(k2_qc_lang1,k2_qc_lang1,k2_substut1(C),k16_sublemma(A))),k4_relset_1(k2_qc_lang1,k2_qc_lang1,k8_relset_1(k2_qc_lang1,k2_qc_lang1,k2_substut1(C),k17_sublemma(A,C))))) ) ) ) )).

fof(t89_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k16_substut1,k38_substut1)
         => ! [C] :
              ( m1_substut1(C,k8_sublemma(B,A))
             => ( v3_substut1(k8_sublemma(B,A))
               => k2_substut1(k19_substut1(k10_sublemma(k8_sublemma(B,A),C))) = k15_sublemma(k2_qc_lang1,k15_sublemma(k2_qc_lang1,k2_substut1(k7_substut1(A,k15_cqc_lang(A,k2_sublemma(B)),C)),k8_relset_1(k2_qc_lang1,k2_qc_lang1,k2_substut1(C),k16_sublemma(k15_cqc_lang(A,k2_sublemma(B))))),k8_relset_1(k2_qc_lang1,k2_qc_lang1,k2_substut1(C),k17_sublemma(k15_cqc_lang(A,k2_sublemma(B)),C))) ) ) ) ) )).

fof(t90_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_fraenkel(C,k2_qc_lang1,B,k2_valuat_1(B))
             => ! [D] :
                  ( m2_subset_1(D,k16_substut1,k38_substut1)
                 => ! [E] :
                      ( m1_substut1(E,k8_sublemma(D,A))
                     => ~ ( v3_substut1(k8_sublemma(D,A))
                          & ! [F] :
                              ( ( v1_funct_1(F)
                                & m2_relset_1(F,k2_qc_lang1,B) )
                             => ! [G] :
                                  ( ( v1_funct_1(G)
                                    & m2_relset_1(G,k2_qc_lang1,B) )
                                 => ~ ( ! [H] :
                                          ( m2_subset_1(H,k1_qc_lang1,k2_qc_lang1)
                                         => ~ ( r2_hidden(H,k4_relset_1(k2_qc_lang1,B,F))
                                              & r2_hidden(H,k24_qc_lang1(k15_cqc_lang(A,k2_sublemma(D)))) ) )
                                      & ! [H] :
                                          ( m2_subset_1(H,k1_qc_lang1,k2_qc_lang1)
                                         => ( r2_hidden(H,k4_relset_1(k2_qc_lang1,B,G))
                                           => k1_funct_1(G,H) = k8_funct_2(k2_qc_lang1,B,C,H) ) )
                                      & r1_xboole_0(k4_relset_1(k2_qc_lang1,B,k14_sublemma(D,A,E,B,C)),k4_relset_1(k2_qc_lang1,B,G))
                                      & k1_sublemma(B,C,k3_sublemma(k10_sublemma(k8_sublemma(D,A),E),B,C)) = k1_sublemma(B,C,k15_sublemma(B,k15_sublemma(B,k14_sublemma(D,A,E,B,C),F),G)) ) ) ) ) ) ) ) ) ) )).

fof(t91_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_valuat_1(C,B)
             => ! [D] :
                  ( m2_subset_1(D,k16_substut1,k38_substut1)
                 => ! [E] :
                      ( m1_substut1(E,k8_sublemma(D,A))
                     => ( v3_substut1(k8_sublemma(D,A))
                       => ! [F] :
                            ( m2_fraenkel(F,k2_qc_lang1,B,k2_valuat_1(B))
                           => ( r1_valuat_1(B,k15_cqc_lang(A,k2_sublemma(D)),C,k1_sublemma(B,F,k14_sublemma(D,A,E,B,F)))
                            <=> r1_sublemma(k10_sublemma(k8_sublemma(D,A),E),B,k1_sublemma(B,F,k3_sublemma(k10_sublemma(k8_sublemma(D,A),E),B,F)),C) ) ) ) ) ) ) ) ) )).

fof(t92_sublemma,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_valuat_1(C,B)
             => ! [D] :
                  ( m2_subset_1(D,k16_substut1,k38_substut1)
                 => ! [E] :
                      ( m1_substut1(E,k8_sublemma(D,A))
                     => ( ( v3_substut1(k8_sublemma(D,A))
                          & ! [F] :
                              ( m2_fraenkel(F,k2_qc_lang1,B,k2_valuat_1(B))
                             => ( r1_valuat_1(B,k39_substut1(D),C,F)
                              <=> r1_sublemma(D,B,k1_sublemma(B,F,k3_sublemma(D,B,F)),C) ) ) )
                       => ! [F] :
                            ( m2_fraenkel(F,k2_qc_lang1,B,k2_valuat_1(B))
                           => ( r1_valuat_1(B,k39_substut1(k10_sublemma(k8_sublemma(D,A),E)),C,F)
                            <=> r1_sublemma(k10_sublemma(k8_sublemma(D,A),E),B,k1_sublemma(B,F,k3_sublemma(k10_sublemma(k8_sublemma(D,A),E),B,F)),C) ) ) ) ) ) ) ) ) )).

fof(t93_sublemma,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_valuat_1(B,A)
         => ! [C] :
              ( m2_subset_1(C,k16_substut1,k38_substut1)
             => ! [D] :
                  ( m2_fraenkel(D,k2_qc_lang1,A,k2_valuat_1(A))
                 => ( r1_valuat_1(A,k39_substut1(C),B,D)
                  <=> r1_sublemma(C,A,k1_sublemma(A,D,k3_sublemma(C,A,D)),B) ) ) ) ) ) )).

fof(s1_sublemma,axiom,
    ( ! [A] :
        ( m2_subset_1(A,k16_substut1,k38_substut1)
       => ! [B] :
            ( m2_subset_1(B,k16_substut1,k38_substut1)
           => ! [C] :
                ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
               => ! [D] :
                    ( m1_substut1(D,k8_sublemma(A,C))
                   => ! [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))
                               => ! [H] :
                                    ( m1_subset_1(H,k1_substut1)
                                   => ( p1_s1_sublemma(k4_sublemma(E,G,F,H))
                                      & ( v2_substut1(A)
                                       => p1_s1_sublemma(A) )
                                      & ( p1_s1_sublemma(A)
                                       => p1_s1_sublemma(k6_sublemma(A)) )
                                      & ( ( k19_substut1(A) = k19_substut1(B)
                                          & p1_s1_sublemma(A)
                                          & p1_s1_sublemma(B) )
                                       => p1_s1_sublemma(k7_sublemma(A,B)) )
                                      & ( ( v3_substut1(k8_sublemma(A,C))
                                          & p1_s1_sublemma(A) )
                                       => p1_s1_sublemma(k10_sublemma(k8_sublemma(A,C),D)) ) ) ) ) ) ) ) ) ) )
   => ! [A] :
        ( m2_subset_1(A,k16_substut1,k38_substut1)
       => p1_s1_sublemma(A) ) )).

fof(dt_k1_sublemma,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k2_valuat_1(A))
        & v1_funct_1(C)
        & m1_relset_1(C,k2_qc_lang1,A) )
     => m2_fraenkel(k1_sublemma(A,B,C),k2_qc_lang1,A,k2_valuat_1(A)) ) )).

fof(dt_k2_sublemma,axiom,(
    ! [A] :
      ( m1_subset_1(A,k38_substut1)
     => m2_subset_1(k2_sublemma(A),k8_qc_lang1,k7_cqc_lang) ) )).

fof(redefinition_k2_sublemma,axiom,(
    ! [A] :
      ( m1_subset_1(A,k38_substut1)
     => k2_sublemma(A) = k1_mcart_1(A) ) )).

fof(dt_k3_sublemma,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k38_substut1)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,k2_valuat_1(B)) )
     => ( v1_funct_1(k3_sublemma(A,B,C))
        & m2_relset_1(k3_sublemma(A,B,C),k2_qc_lang1,B) ) ) )).

fof(dt_k4_sublemma,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k7_qc_lang1(A))
        & v1_cqc_lang(C,A)
        & m1_qc_lang1(C,A)
        & m1_subset_1(D,k1_substut1) )
     => m2_subset_1(k4_sublemma(A,B,C,D),k16_substut1,k38_substut1) ) )).

fof(redefinition_k4_sublemma,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k7_qc_lang1(A))
        & v1_cqc_lang(C,A)
        & m1_qc_lang1(C,A)
        & m1_subset_1(D,k1_substut1) )
     => k4_sublemma(A,B,C,D) = k17_substut1(B,C,D) ) )).

fof(dt_k5_sublemma,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k5_numbers)
        & v1_cqc_lang(B,A)
        & m1_qc_lang1(B,A)
        & m1_subset_1(C,k1_substut1) )
     => ( v1_cqc_lang(k5_sublemma(A,B,C),A)
        & m1_qc_lang1(k5_sublemma(A,B,C),A) ) ) )).

fof(redefinition_k5_sublemma,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k5_numbers)
        & v1_cqc_lang(B,A)
        & m1_qc_lang1(B,A)
        & m1_subset_1(C,k1_substut1) )
     => k5_sublemma(A,B,C) = k3_substut1(B,C) ) )).

fof(dt_k6_sublemma,axiom,(
    ! [A] :
      ( m1_subset_1(A,k38_substut1)
     => m2_subset_1(k6_sublemma(A),k16_substut1,k38_substut1) ) )).

fof(redefinition_k6_sublemma,axiom,(
    ! [A] :
      ( m1_subset_1(A,k38_substut1)
     => k6_sublemma(A) = k20_substut1(A) ) )).

fof(dt_k7_sublemma,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k38_substut1)
        & m1_subset_1(B,k38_substut1) )
     => m2_subset_1(k7_sublemma(A,B),k16_substut1,k38_substut1) ) )).

fof(dt_k8_sublemma,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k38_substut1)
        & m1_subset_1(B,k2_qc_lang1) )
     => ( v1_sublemma(k8_sublemma(A,B))
        & m1_subset_1(k8_sublemma(A,B),k2_zfmisc_1(k16_substut1,k2_qc_lang1)) ) ) )).

fof(redefinition_k8_sublemma,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k38_substut1)
        & m1_subset_1(B,k2_qc_lang1) )
     => k8_sublemma(A,B) = k4_tarski(A,B) ) )).

fof(dt_k9_sublemma,axiom,(
    ! [A] :
      ( ( v1_sublemma(A)
        & m1_subset_1(A,k2_zfmisc_1(k16_substut1,k2_qc_lang1)) )
     => m2_subset_1(k9_sublemma(A),k16_substut1,k38_substut1) ) )).

fof(redefinition_k9_sublemma,axiom,(
    ! [A] :
      ( ( v1_sublemma(A)
        & m1_subset_1(A,k2_zfmisc_1(k16_substut1,k2_qc_lang1)) )
     => k9_sublemma(A) = k1_mcart_1(A) ) )).

fof(dt_k10_sublemma,axiom,(
    ! [A,B] :
      ( ( v1_sublemma(A)
        & m1_subset_1(A,k2_zfmisc_1(k16_substut1,k2_qc_lang1))
        & m1_substut1(B,A) )
     => m2_subset_1(k10_sublemma(A,B),k16_substut1,k38_substut1) ) )).

fof(dt_k11_sublemma,axiom,(
    ! [A] :
      ( m1_subset_1(A,k38_substut1)
     => m2_subset_1(k11_sublemma(A),k16_substut1,k38_substut1) ) )).

fof(dt_k12_sublemma,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k38_substut1)
        & m1_subset_1(B,k7_cqc_lang) )
     => m2_subset_1(k12_sublemma(A,B),k8_qc_lang1,k7_cqc_lang) ) )).

fof(dt_k13_sublemma,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,k2_qc_lang1) )
     => ( v1_funct_1(k13_sublemma(A,B,C))
        & m2_relset_1(k13_sublemma(A,B,C),k2_qc_lang1,A) ) ) )).

fof(dt_k14_sublemma,axiom,(
    ! [A,B,C,D,E] :
      ( ( m1_subset_1(A,k38_substut1)
        & m1_subset_1(B,k2_qc_lang1)
        & m1_substut1(C,k8_sublemma(A,B))
        & ~ v1_xboole_0(D)
        & m1_subset_1(E,k2_valuat_1(D)) )
     => ( v1_funct_1(k14_sublemma(A,B,C,D,E))
        & m2_relset_1(k14_sublemma(A,B,C,D,E),k2_qc_lang1,D) ) ) )).

fof(dt_k15_sublemma,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & m1_relset_1(B,k2_qc_lang1,A)
        & v1_funct_1(C)
        & m1_relset_1(C,k2_qc_lang1,A) )
     => ( v1_funct_1(k15_sublemma(A,B,C))
        & m2_relset_1(k15_sublemma(A,B,C),k2_qc_lang1,A) ) ) )).

fof(idempotence_k15_sublemma,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & m1_relset_1(B,k2_qc_lang1,A)
        & v1_funct_1(C)
        & m1_relset_1(C,k2_qc_lang1,A) )
     => k15_sublemma(A,B,B) = B ) )).

fof(redefinition_k15_sublemma,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & m1_relset_1(B,k2_qc_lang1,A)
        & v1_funct_1(C)
        & m1_relset_1(C,k2_qc_lang1,A) )
     => k15_sublemma(A,B,C) = k1_funct_4(B,C) ) )).

fof(dt_k16_sublemma,axiom,(
    $true )).

fof(dt_k17_sublemma,axiom,(
    $true )).
%------------------------------------------------------------------------------