SET007 Axioms: SET007+101.ax


%------------------------------------------------------------------------------
% File     : SET007+101 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : A First-Order Predicate Calculus
% Version  : [Urb08] axioms.
% English  : Axiomatics, the Consequence Operation and a Concept of Proof

% 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_the1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  127 (  40 unit)
%            Number of atoms       :  570 ( 112 equality)
%            Maximal formula depth :   32 (   6 average)
%            Number of connectives :  541 (  98 ~  ;  10  |; 190  &)
%                                         (  24 <=>; 219 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   17 (   1 propositional; 0-3 arity)
%            Number of functors    :   45 (  21 constant; 0-3 arity)
%            Number of variables   :  219 (   0 singleton; 191 !;  28 ?)
%            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_the1,axiom,(
    ~ v1_xboole_0(k2_cqc_the1) )).

fof(t1_cqc_the1,axiom,(
    $true )).

fof(t2_cqc_the1,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ~ ( r1_xreal_0(A,np__1)
          & A != np__0
          & A != np__1 ) ) )).

fof(t3_cqc_the1,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ~ ( r1_xreal_0(A,np__2)
          & A != np__0
          & A != np__1
          & A != np__2 ) ) )).

fof(t4_cqc_the1,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ~ ( r1_xreal_0(A,np__3)
          & A != np__0
          & A != np__1
          & A != np__2
          & A != np__3 ) ) )).

fof(t5_cqc_the1,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ~ ( r1_xreal_0(A,np__4)
          & A != np__0
          & A != np__1
          & A != np__2
          & A != np__3
          & A != np__4 ) ) )).

fof(t6_cqc_the1,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ~ ( r1_xreal_0(A,np__5)
          & A != np__0
          & A != np__1
          & A != np__2
          & A != np__3
          & A != np__4
          & A != np__5 ) ) )).

fof(t7_cqc_the1,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ~ ( r1_xreal_0(A,np__6)
          & A != np__0
          & A != np__1
          & A != np__2
          & A != np__3
          & A != np__4
          & A != np__5
          & A != np__6 ) ) )).

fof(t8_cqc_the1,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ~ ( r1_xreal_0(A,np__7)
          & A != np__0
          & A != np__1
          & A != np__2
          & A != np__3
          & A != np__4
          & A != np__5
          & A != np__6
          & A != np__7 ) ) )).

fof(t9_cqc_the1,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ~ ( r1_xreal_0(A,np__8)
          & A != np__0
          & A != np__1
          & A != np__2
          & A != np__3
          & A != np__4
          & A != np__5
          & A != np__6
          & A != np__7
          & A != np__8 ) ) )).

fof(t10_cqc_the1,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ~ ( r1_xreal_0(A,np__9)
          & A != np__0
          & A != np__1
          & A != np__2
          & A != np__3
          & A != np__4
          & A != np__5
          & A != np__6
          & A != np__7
          & A != np__8
          & A != np__9 ) ) )).

fof(t13_cqc_the1,axiom,(
    ! [A,B,C] :
      ~ ( v1_finset_1(A)
        & r1_tarski(A,k2_zfmisc_1(B,C))
        & ! [D,E] :
            ~ ( v1_finset_1(D)
              & r1_tarski(D,B)
              & v1_finset_1(E)
              & r1_tarski(E,C)
              & r1_tarski(A,k2_zfmisc_1(D,E)) ) ) )).

fof(t14_cqc_the1,axiom,(
    ! [A,B,C] :
      ~ ( v1_finset_1(A)
        & v1_finset_1(B)
        & r1_tarski(A,k2_zfmisc_1(C,B))
        & ! [D] :
            ~ ( v1_finset_1(D)
              & r1_tarski(D,C)
              & r1_tarski(A,k2_zfmisc_1(D,B)) ) ) )).

fof(d1_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ( v1_cqc_the1(A)
      <=> ( r2_hidden(k9_cqc_lang,A)
          & ! [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,k8_qc_lang1,k7_cqc_lang)
                     => ! [E] :
                          ( m1_subset_1(E,k8_qc_lang1)
                         => ! [F] :
                              ( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
                             => ! [G] :
                                  ( m2_subset_1(G,k1_qc_lang1,k2_qc_lang1)
                                 => ( r2_hidden(k12_cqc_lang(k12_cqc_lang(k10_cqc_lang(B),B),B),A)
                                    & r2_hidden(k12_cqc_lang(B,k12_cqc_lang(k10_cqc_lang(B),C)),A)
                                    & r2_hidden(k12_cqc_lang(k12_cqc_lang(B,C),k12_cqc_lang(k10_cqc_lang(k11_cqc_lang(C,D)),k10_cqc_lang(k11_cqc_lang(B,D)))),A)
                                    & r2_hidden(k12_cqc_lang(k11_cqc_lang(B,C),k11_cqc_lang(C,B)),A)
                                    & ( ( r2_hidden(B,A)
                                        & r2_hidden(k12_cqc_lang(B,C),A) )
                                     => r2_hidden(C,A) )
                                    & r2_hidden(k12_cqc_lang(k15_cqc_lang(F,B),B),A)
                                    & ( r2_hidden(k12_cqc_lang(B,C),A)
                                     => ( r2_hidden(F,k24_qc_lang1(B))
                                        | r2_hidden(k12_cqc_lang(B,k15_cqc_lang(F,C)),A) ) )
                                    & ( ( r2_hidden(k17_cqc_lang(E,F),k7_cqc_lang)
                                        & r2_hidden(k17_cqc_lang(E,G),k7_cqc_lang)
                                        & r2_hidden(k17_cqc_lang(E,F),A) )
                                     => ( r2_hidden(F,k24_qc_lang1(E))
                                        | r2_hidden(k17_cqc_lang(E,G),A) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t15_cqc_the1,axiom,(
    $true )).

fof(t16_cqc_the1,axiom,(
    $true )).

fof(t17_cqc_the1,axiom,(
    $true )).

fof(t18_cqc_the1,axiom,(
    $true )).

fof(t19_cqc_the1,axiom,(
    $true )).

fof(t20_cqc_the1,axiom,(
    $true )).

fof(t21_cqc_the1,axiom,(
    $true )).

fof(t22_cqc_the1,axiom,(
    $true )).

fof(t23_cqc_the1,axiom,(
    $true )).

fof(t24_cqc_the1,axiom,(
    $true )).

fof(t25_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
         => ( ( v1_cqc_the1(A)
              & v1_cqc_the1(B) )
           => v1_cqc_the1(k5_subset_1(k7_cqc_lang,A,B)) ) ) ) )).

fof(d2_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
         => ( B = k1_cqc_the1(A)
          <=> ! [C] :
                ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
               => ( r2_hidden(C,B)
                <=> ! [D] :
                      ( m1_subset_1(D,k1_zfmisc_1(k7_cqc_lang))
                     => ( ( v1_cqc_the1(D)
                          & r1_tarski(A,D) )
                       => r2_hidden(C,D) ) ) ) ) ) ) ) )).

fof(t26_cqc_the1,axiom,(
    $true )).

fof(t27_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => r2_hidden(k9_cqc_lang,k1_cqc_the1(A)) ) )).

fof(t28_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => r2_hidden(k12_cqc_lang(k12_cqc_lang(k10_cqc_lang(B),B),B),k1_cqc_the1(A)) ) ) )).

fof(t29_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => r2_hidden(k12_cqc_lang(B,k12_cqc_lang(k10_cqc_lang(B),C)),k1_cqc_the1(A)) ) ) ) )).

fof(t30_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_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,k8_qc_lang1,k7_cqc_lang)
                 => r2_hidden(k12_cqc_lang(k12_cqc_lang(B,C),k12_cqc_lang(k10_cqc_lang(k11_cqc_lang(C,D)),k10_cqc_lang(k11_cqc_lang(B,D)))),k1_cqc_the1(A)) ) ) ) ) )).

fof(t31_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => r2_hidden(k12_cqc_lang(k11_cqc_lang(B,C),k11_cqc_lang(C,B)),k1_cqc_the1(A)) ) ) ) )).

fof(t32_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ( ( r2_hidden(B,k1_cqc_the1(A))
                  & r2_hidden(k12_cqc_lang(B,C),k1_cqc_the1(A)) )
               => r2_hidden(C,k1_cqc_the1(A)) ) ) ) ) )).

fof(t33_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(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)
             => r2_hidden(k12_cqc_lang(k15_cqc_lang(C,B),B),k1_cqc_the1(A)) ) ) ) )).

fof(t34_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_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)
                 => ( r2_hidden(k12_cqc_lang(B,C),k1_cqc_the1(A))
                   => ( r2_hidden(D,k24_qc_lang1(B))
                      | r2_hidden(k12_cqc_lang(B,k15_cqc_lang(D,C)),k1_cqc_the1(A)) ) ) ) ) ) ) )).

fof(t35_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ! [D] :
                  ( m2_subset_1(D,k1_qc_lang1,k2_qc_lang1)
                 => ( ( r2_hidden(k17_cqc_lang(B,C),k7_cqc_lang)
                      & r2_hidden(k17_cqc_lang(B,D),k7_cqc_lang)
                      & r2_hidden(k17_cqc_lang(B,C),k1_cqc_the1(A)) )
                   => ( r2_hidden(C,k24_qc_lang1(B))
                      | r2_hidden(k17_cqc_lang(B,D),k1_cqc_the1(A)) ) ) ) ) ) ) )).

fof(t36_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => v1_cqc_the1(k1_cqc_the1(A)) ) )).

fof(t37_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
         => ( ( v1_cqc_the1(A)
              & r1_tarski(B,A) )
           => r1_tarski(k1_cqc_the1(B),A) ) ) ) )).

fof(t38_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => r1_tarski(A,k1_cqc_the1(A)) ) )).

fof(t39_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
         => ( r1_tarski(A,B)
           => r1_tarski(k1_cqc_the1(A),k1_cqc_the1(B)) ) ) ) )).

fof(t40_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => k1_cqc_the1(k1_cqc_the1(A)) = k1_cqc_the1(A) ) )).

fof(t41_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ( v1_cqc_the1(A)
      <=> k1_cqc_the1(A) = A ) ) )).

fof(t42_cqc_the1,axiom,(
    $true )).

fof(t43_cqc_the1,axiom,
    ( r2_hidden(np__0,k2_cqc_the1)
    & r2_hidden(np__1,k2_cqc_the1)
    & r2_hidden(np__2,k2_cqc_the1)
    & r2_hidden(np__3,k2_cqc_the1)
    & r2_hidden(np__4,k2_cqc_the1)
    & r2_hidden(np__5,k2_cqc_the1)
    & r2_hidden(np__6,k2_cqc_the1)
    & r2_hidden(np__7,k2_cqc_the1)
    & r2_hidden(np__8,k2_cqc_the1)
    & r2_hidden(np__9,k2_cqc_the1) )).

fof(t44_cqc_the1,axiom,(
    v1_finset_1(k2_cqc_the1) )).

fof(t45_cqc_the1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_finseq_1(B,k2_zfmisc_1(k7_cqc_lang,k2_cqc_the1))
         => ~ ( r1_xreal_0(np__1,A)
              & r1_xreal_0(A,k3_finseq_1(B))
              & k2_mcart_1(k1_funct_1(B,A)) != np__0
              & k2_mcart_1(k1_funct_1(B,A)) != np__1
              & k2_mcart_1(k1_funct_1(B,A)) != np__2
              & k2_mcart_1(k1_funct_1(B,A)) != np__3
              & k2_mcart_1(k1_funct_1(B,A)) != np__4
              & k2_mcart_1(k1_funct_1(B,A)) != np__5
              & k2_mcart_1(k1_funct_1(B,A)) != np__6
              & k2_mcart_1(k1_funct_1(B,A)) != np__7
              & k2_mcart_1(k1_funct_1(B,A)) != np__8
              & k2_mcart_1(k1_funct_1(B,A)) != np__9 ) ) ) )).

fof(d4_cqc_the1,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k2_zfmisc_1(k7_cqc_lang,k2_cqc_the1))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k7_cqc_lang))
             => ( ( k2_mcart_1(k1_funct_1(A,B)) = np__0
                 => ( r1_cqc_the1(A,B,C)
                  <=> r2_hidden(k1_mcart_1(k1_funct_1(A,B)),C) ) )
                & ( k2_mcart_1(k1_funct_1(A,B)) = np__1
                 => ( r1_cqc_the1(A,B,C)
                  <=> k1_mcart_1(k1_funct_1(A,B)) = k9_cqc_lang ) )
                & ( k2_mcart_1(k1_funct_1(A,B)) = np__2
                 => ( r1_cqc_the1(A,B,C)
                  <=> ? [D] :
                        ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                        & k1_mcart_1(k1_funct_1(A,B)) = k12_cqc_lang(k12_cqc_lang(k10_cqc_lang(D),D),D) ) ) )
                & ( k2_mcart_1(k1_funct_1(A,B)) = np__3
                 => ( r1_cqc_the1(A,B,C)
                  <=> ? [D] :
                        ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                        & ? [E] :
                            ( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
                            & k1_mcart_1(k1_funct_1(A,B)) = k12_cqc_lang(D,k12_cqc_lang(k10_cqc_lang(D),E)) ) ) ) )
                & ( k2_mcart_1(k1_funct_1(A,B)) = np__4
                 => ( r1_cqc_the1(A,B,C)
                  <=> ? [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,k8_qc_lang1,k7_cqc_lang)
                                & k1_mcart_1(k1_funct_1(A,B)) = k12_cqc_lang(k12_cqc_lang(D,E),k12_cqc_lang(k10_cqc_lang(k11_cqc_lang(E,F)),k10_cqc_lang(k11_cqc_lang(D,F)))) ) ) ) ) )
                & ( k2_mcart_1(k1_funct_1(A,B)) = np__5
                 => ( r1_cqc_the1(A,B,C)
                  <=> ? [D] :
                        ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                        & ? [E] :
                            ( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
                            & k1_mcart_1(k1_funct_1(A,B)) = k12_cqc_lang(k11_cqc_lang(D,E),k11_cqc_lang(E,D)) ) ) ) )
                & ( k2_mcart_1(k1_funct_1(A,B)) = np__6
                 => ( r1_cqc_the1(A,B,C)
                  <=> ? [D] :
                        ( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
                        & ? [E] :
                            ( m2_subset_1(E,k1_qc_lang1,k2_qc_lang1)
                            & k1_mcart_1(k1_funct_1(A,B)) = k12_cqc_lang(k15_cqc_lang(E,D),D) ) ) ) )
                & ( k2_mcart_1(k1_funct_1(A,B)) = np__7
                 => ( r1_cqc_the1(A,B,C)
                  <=> ? [D] :
                        ( m2_subset_1(D,k1_numbers,k5_numbers)
                        & ? [E] :
                            ( m2_subset_1(E,k1_numbers,k5_numbers)
                            & ? [F] :
                                ( m2_subset_1(F,k8_qc_lang1,k7_cqc_lang)
                                & ? [G] :
                                    ( m2_subset_1(G,k8_qc_lang1,k7_cqc_lang)
                                    & r1_xreal_0(np__1,D)
                                    & ~ r1_xreal_0(B,D)
                                    & r1_xreal_0(np__1,E)
                                    & ~ r1_xreal_0(D,E)
                                    & F = k1_mcart_1(k1_funct_1(A,E))
                                    & G = k1_mcart_1(k1_funct_1(A,B))
                                    & k1_mcart_1(k1_funct_1(A,D)) = k12_cqc_lang(F,G) ) ) ) ) ) )
                & ( k2_mcart_1(k1_funct_1(A,B)) = np__8
                 => ( r1_cqc_the1(A,B,C)
                  <=> ? [D] :
                        ( m2_subset_1(D,k1_numbers,k5_numbers)
                        & ? [E] :
                            ( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
                            & ? [F] :
                                ( m2_subset_1(F,k8_qc_lang1,k7_cqc_lang)
                                & ? [G] :
                                    ( m2_subset_1(G,k1_qc_lang1,k2_qc_lang1)
                                    & r1_xreal_0(np__1,D)
                                    & ~ r1_xreal_0(B,D)
                                    & k1_mcart_1(k1_funct_1(A,D)) = k12_cqc_lang(E,F)
                                    & ~ r2_hidden(G,k24_qc_lang1(E))
                                    & k1_mcart_1(k1_funct_1(A,B)) = k12_cqc_lang(E,k15_cqc_lang(G,F)) ) ) ) ) ) )
                & ( k2_mcart_1(k1_funct_1(A,B)) = np__9
                 => ( r1_cqc_the1(A,B,C)
                  <=> ? [D] :
                        ( m2_subset_1(D,k1_numbers,k5_numbers)
                        & ? [E] :
                            ( m2_subset_1(E,k1_qc_lang1,k2_qc_lang1)
                            & ? [F] :
                                ( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
                                & ? [G] :
                                    ( m1_subset_1(G,k8_qc_lang1)
                                    & r1_xreal_0(np__1,D)
                                    & ~ r1_xreal_0(B,D)
                                    & r2_hidden(k17_cqc_lang(G,E),k7_cqc_lang)
                                    & r2_hidden(k17_cqc_lang(G,F),k7_cqc_lang)
                                    & ~ r2_hidden(E,k24_qc_lang1(G))
                                    & k17_cqc_lang(G,E) = k1_mcart_1(k1_funct_1(A,D))
                                    & k17_cqc_lang(G,F) = k1_mcart_1(k1_funct_1(A,B)) ) ) ) ) ) ) ) ) ) ) )).

fof(d5_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] :
          ( m2_finseq_1(B,k2_zfmisc_1(k7_cqc_lang,k2_cqc_the1))
         => ( r2_cqc_the1(A,B)
          <=> ( B != k1_xboole_0
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( ( r1_xreal_0(np__1,C)
                      & r1_xreal_0(C,k3_finseq_1(B)) )
                   => r1_cqc_the1(B,C,A) ) ) ) ) ) ) )).

fof(t46_cqc_the1,axiom,(
    $true )).

fof(t47_cqc_the1,axiom,(
    $true )).

fof(t48_cqc_the1,axiom,(
    $true )).

fof(t49_cqc_the1,axiom,(
    $true )).

fof(t50_cqc_the1,axiom,(
    $true )).

fof(t51_cqc_the1,axiom,(
    $true )).

fof(t52_cqc_the1,axiom,(
    $true )).

fof(t53_cqc_the1,axiom,(
    $true )).

fof(t54_cqc_the1,axiom,(
    $true )).

fof(t55_cqc_the1,axiom,(
    $true )).

fof(t56_cqc_the1,axiom,(
    $true )).

fof(t57_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] :
          ( m2_finseq_1(B,k2_zfmisc_1(k7_cqc_lang,k2_cqc_the1))
         => ~ ( r2_cqc_the1(A,B)
              & k2_relat_1(B) = k1_xboole_0 ) ) ) )).

fof(t58_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] :
          ( m2_finseq_1(B,k2_zfmisc_1(k7_cqc_lang,k2_cqc_the1))
         => ( r2_cqc_the1(A,B)
           => r1_xreal_0(np__1,k3_finseq_1(B)) ) ) ) )).

fof(t59_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] :
          ( m2_finseq_1(B,k2_zfmisc_1(k7_cqc_lang,k2_cqc_the1))
         => ~ ( r2_cqc_the1(A,B)
              & k2_mcart_1(k1_funct_1(B,np__1)) != np__0
              & k2_mcart_1(k1_funct_1(B,np__1)) != np__1
              & k2_mcart_1(k1_funct_1(B,np__1)) != np__2
              & k2_mcart_1(k1_funct_1(B,np__1)) != np__3
              & k2_mcart_1(k1_funct_1(B,np__1)) != np__4
              & k2_mcart_1(k1_funct_1(B,np__1)) != np__5
              & k2_mcart_1(k1_funct_1(B,np__1)) != np__6 ) ) ) )).

fof(t60_cqc_the1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
         => ! [C] :
              ( m2_finseq_1(C,k2_zfmisc_1(k7_cqc_lang,k2_cqc_the1))
             => ! [D] :
                  ( m2_finseq_1(D,k2_zfmisc_1(k7_cqc_lang,k2_cqc_the1))
                 => ( ( r1_xreal_0(np__1,A)
                      & r1_xreal_0(A,k3_finseq_1(C)) )
                   => ( r1_cqc_the1(C,A,B)
                    <=> r1_cqc_the1(k8_finseq_1(k2_zfmisc_1(k7_cqc_lang,k2_cqc_the1),C,D),A,B) ) ) ) ) ) ) )).

fof(t61_cqc_the1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
         => ! [C] :
              ( m2_finseq_1(C,k2_zfmisc_1(k7_cqc_lang,k2_cqc_the1))
             => ! [D] :
                  ( m2_finseq_1(D,k2_zfmisc_1(k7_cqc_lang,k2_cqc_the1))
                 => ( ( r1_xreal_0(np__1,A)
                      & r1_xreal_0(A,k3_finseq_1(C))
                      & r1_cqc_the1(C,A,B) )
                   => r1_cqc_the1(k8_finseq_1(k2_zfmisc_1(k7_cqc_lang,k2_cqc_the1),D,C),k1_nat_1(A,k3_finseq_1(D)),B) ) ) ) ) ) )).

fof(t62_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] :
          ( m2_finseq_1(B,k2_zfmisc_1(k7_cqc_lang,k2_cqc_the1))
         => ! [C] :
              ( m2_finseq_1(C,k2_zfmisc_1(k7_cqc_lang,k2_cqc_the1))
             => ( ( r2_cqc_the1(A,B)
                  & r2_cqc_the1(A,C) )
               => r2_cqc_the1(A,k8_finseq_1(k2_zfmisc_1(k7_cqc_lang,k2_cqc_the1),B,C)) ) ) ) ) )).

fof(t63_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
         => ! [C] :
              ( m2_finseq_1(C,k2_zfmisc_1(k7_cqc_lang,k2_cqc_the1))
             => ( ( r2_cqc_the1(A,C)
                  & r1_tarski(A,B) )
               => r2_cqc_the1(B,C) ) ) ) ) )).

fof(t64_cqc_the1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
         => ! [C] :
              ( m2_finseq_1(C,k2_zfmisc_1(k7_cqc_lang,k2_cqc_the1))
             => ( ( r2_cqc_the1(B,C)
                  & r1_xreal_0(np__1,A)
                  & r1_xreal_0(A,k3_finseq_1(C)) )
               => r2_hidden(k1_mcart_1(k1_funct_1(C,A)),k1_cqc_the1(B)) ) ) ) ) )).

fof(d6_cqc_the1,axiom,(
    ! [A] :
      ( m2_finseq_1(A,k2_zfmisc_1(k7_cqc_lang,k2_cqc_the1))
     => ( A != k1_xboole_0
       => k3_cqc_the1(A) = k1_mcart_1(k1_funct_1(A,k3_finseq_1(A))) ) ) )).

fof(t65_cqc_the1,axiom,(
    $true )).

fof(t66_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] :
          ( m2_finseq_1(B,k2_zfmisc_1(k7_cqc_lang,k2_cqc_the1))
         => ( r2_cqc_the1(A,B)
           => r2_hidden(k3_cqc_the1(B),k1_cqc_the1(A)) ) ) ) )).

fof(t70_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ( r2_hidden(B,k1_cqc_the1(A))
          <=> ? [C] :
                ( m2_finseq_1(C,k2_zfmisc_1(k7_cqc_lang,k2_cqc_the1))
                & r2_cqc_the1(A,C)
                & k3_cqc_the1(C) = B ) ) ) ) )).

fof(t71_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ~ ( r2_hidden(B,k1_cqc_the1(A))
              & ! [C] :
                  ( m1_subset_1(C,k1_zfmisc_1(k7_cqc_lang))
                 => ~ ( r1_tarski(C,A)
                      & v1_finset_1(C)
                      & r2_hidden(B,k1_cqc_the1(C)) ) ) ) ) ) )).

fof(d7_cqc_the1,axiom,(
    $true )).

fof(d8_cqc_the1,axiom,(
    k4_cqc_the1 = k1_cqc_the1(k1_subset_1(k7_cqc_lang)) )).

fof(t72_cqc_the1,axiom,(
    $true )).

fof(t73_cqc_the1,axiom,(
    $true )).

fof(t74_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ( v1_cqc_the1(A)
       => r1_tarski(k4_cqc_the1,A) ) ) )).

fof(t75_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => r1_tarski(k4_cqc_the1,k1_cqc_the1(A)) ) )).

fof(t76_cqc_the1,axiom,(
    v1_cqc_the1(k4_cqc_the1) )).

fof(t77_cqc_the1,axiom,(
    r2_hidden(k9_cqc_lang,k4_cqc_the1) )).

fof(t78_cqc_the1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => r2_hidden(k12_cqc_lang(k12_cqc_lang(k10_cqc_lang(A),A),A),k4_cqc_the1) ) )).

fof(t79_cqc_the1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => r2_hidden(k12_cqc_lang(A,k12_cqc_lang(k10_cqc_lang(A),B)),k4_cqc_the1) ) ) )).

fof(t80_cqc_the1,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,k8_qc_lang1,k7_cqc_lang)
             => r2_hidden(k12_cqc_lang(k12_cqc_lang(A,B),k12_cqc_lang(k10_cqc_lang(k11_cqc_lang(B,C)),k10_cqc_lang(k11_cqc_lang(A,C)))),k4_cqc_the1) ) ) ) )).

fof(t81_cqc_the1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => r2_hidden(k12_cqc_lang(k11_cqc_lang(A,B),k11_cqc_lang(B,A)),k4_cqc_the1) ) ) )).

fof(t82_cqc_the1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ( ( r2_hidden(A,k4_cqc_the1)
              & r2_hidden(k12_cqc_lang(A,B),k4_cqc_the1) )
           => r2_hidden(B,k4_cqc_the1) ) ) ) )).

fof(t83_cqc_the1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => r2_hidden(k12_cqc_lang(k15_cqc_lang(B,A),A),k4_cqc_the1) ) ) )).

fof(t84_cqc_the1,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)
             => ( r2_hidden(k12_cqc_lang(A,B),k4_cqc_the1)
               => ( r2_hidden(C,k24_qc_lang1(A))
                  | r2_hidden(k12_cqc_lang(A,k15_cqc_lang(C,B)),k4_cqc_the1) ) ) ) ) ) )).

fof(t85_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( ( r2_hidden(k17_cqc_lang(A,B),k7_cqc_lang)
                  & r2_hidden(k17_cqc_lang(A,C),k7_cqc_lang)
                  & r2_hidden(k17_cqc_lang(A,B),k4_cqc_the1) )
               => ( r2_hidden(B,k24_qc_lang1(A))
                  | r2_hidden(k17_cqc_lang(A,C),k4_cqc_the1) ) ) ) ) ) )).

fof(d9_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ( r3_cqc_the1(A,B)
          <=> r2_hidden(B,k1_cqc_the1(A)) ) ) ) )).

fof(t86_cqc_the1,axiom,(
    $true )).

fof(t87_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => r3_cqc_the1(A,k9_cqc_lang) ) )).

fof(t88_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => r3_cqc_the1(A,k12_cqc_lang(k12_cqc_lang(k10_cqc_lang(B),B),B)) ) ) )).

fof(t89_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => r3_cqc_the1(A,k12_cqc_lang(B,k12_cqc_lang(k10_cqc_lang(B),C))) ) ) ) )).

fof(t90_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_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,k8_qc_lang1,k7_cqc_lang)
                 => r3_cqc_the1(A,k12_cqc_lang(k12_cqc_lang(B,C),k12_cqc_lang(k10_cqc_lang(k11_cqc_lang(C,D)),k10_cqc_lang(k11_cqc_lang(B,D))))) ) ) ) ) )).

fof(t91_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => r3_cqc_the1(A,k12_cqc_lang(k11_cqc_lang(B,C),k11_cqc_lang(C,B))) ) ) ) )).

fof(t92_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ! [C] :
              ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
             => ( ( r3_cqc_the1(A,B)
                  & r3_cqc_the1(A,k12_cqc_lang(B,C)) )
               => r3_cqc_the1(A,C) ) ) ) ) )).

fof(t93_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(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)
             => r3_cqc_the1(A,k12_cqc_lang(k15_cqc_lang(C,B),B)) ) ) ) )).

fof(t94_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_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)
                 => ( r3_cqc_the1(A,k12_cqc_lang(B,C))
                   => ( r2_hidden(D,k24_qc_lang1(B))
                      | r3_cqc_the1(A,k12_cqc_lang(B,k15_cqc_lang(D,C))) ) ) ) ) ) ) )).

fof(t95_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ! [D] :
                  ( m2_subset_1(D,k1_qc_lang1,k2_qc_lang1)
                 => ( ( r2_hidden(k17_cqc_lang(B,C),k7_cqc_lang)
                      & r2_hidden(k17_cqc_lang(B,D),k7_cqc_lang)
                      & r3_cqc_the1(A,k17_cqc_lang(B,C)) )
                   => ( r2_hidden(C,k24_qc_lang1(B))
                      | r3_cqc_the1(A,k17_cqc_lang(B,D)) ) ) ) ) ) ) )).

fof(d10_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v2_cqc_the1(A)
      <=> r3_cqc_the1(k1_subset_1(k7_cqc_lang),A) ) ) )).

fof(d11_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v2_cqc_the1(A)
      <=> r2_hidden(A,k4_cqc_the1) ) ) )).

fof(t96_cqc_the1,axiom,(
    $true )).

fof(t97_cqc_the1,axiom,(
    $true )).

fof(t98_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ( v2_cqc_the1(B)
           => r3_cqc_the1(A,B) ) ) ) )).

fof(t99_cqc_the1,axiom,(
    v2_cqc_the1(k9_cqc_lang) )).

fof(t100_cqc_the1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => v2_cqc_the1(k12_cqc_lang(k12_cqc_lang(k10_cqc_lang(A),A),A)) ) )).

fof(t101_cqc_the1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => v2_cqc_the1(k12_cqc_lang(A,k12_cqc_lang(k10_cqc_lang(A),B))) ) ) )).

fof(t102_cqc_the1,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,k8_qc_lang1,k7_cqc_lang)
             => v2_cqc_the1(k12_cqc_lang(k12_cqc_lang(A,B),k12_cqc_lang(k10_cqc_lang(k11_cqc_lang(B,C)),k10_cqc_lang(k11_cqc_lang(A,C))))) ) ) ) )).

fof(t103_cqc_the1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => v2_cqc_the1(k12_cqc_lang(k11_cqc_lang(A,B),k11_cqc_lang(B,A))) ) ) )).

fof(t104_cqc_the1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
         => ( ( v2_cqc_the1(A)
              & v2_cqc_the1(k12_cqc_lang(A,B)) )
           => v2_cqc_the1(B) ) ) ) )).

fof(t105_cqc_the1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(B,A),A)) ) ) )).

fof(t106_cqc_the1,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)
             => ( v2_cqc_the1(k12_cqc_lang(A,B))
               => ( r2_hidden(C,k24_qc_lang1(A))
                  | v2_cqc_the1(k12_cqc_lang(A,k15_cqc_lang(C,B))) ) ) ) ) ) )).

fof(t107_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( ( r2_hidden(k17_cqc_lang(A,B),k7_cqc_lang)
                  & r2_hidden(k17_cqc_lang(A,C),k7_cqc_lang)
                  & v2_cqc_the1(k17_cqc_lang(A,B)) )
               => ( r2_hidden(B,k24_qc_lang1(A))
                  | v2_cqc_the1(k17_cqc_lang(A,C)) ) ) ) ) ) )).

fof(dt_k1_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => m1_subset_1(k1_cqc_the1(A),k1_zfmisc_1(k7_cqc_lang)) ) )).

fof(dt_k2_cqc_the1,axiom,(
    $true )).

fof(dt_k3_cqc_the1,axiom,(
    ! [A] :
      ( m1_finseq_1(A,k2_zfmisc_1(k7_cqc_lang,k2_cqc_the1))
     => m2_subset_1(k3_cqc_the1(A),k8_qc_lang1,k7_cqc_lang) ) )).

fof(dt_k4_cqc_the1,axiom,(
    m1_subset_1(k4_cqc_the1,k1_zfmisc_1(k7_cqc_lang)) )).

fof(t11_cqc_the1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => a_1_0_cqc_the1(A) = k2_xboole_0(a_1_1_cqc_the1(A),k1_tarski(k1_nat_1(A,np__1))) ) )).

fof(t12_cqc_the1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => v1_finset_1(a_1_1_cqc_the1(A)) ) )).

fof(d3_cqc_the1,axiom,(
    k2_cqc_the1 = a_0_0_cqc_the1 )).

fof(t67_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => r1_tarski(A,a_1_2_cqc_the1(A)) ) )).

fof(t68_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
         => ( A = a_1_2_cqc_the1(B)
           => v1_cqc_the1(A) ) ) ) )).

fof(t69_cqc_the1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
     => a_1_2_cqc_the1(A) = k1_cqc_the1(A) ) )).

fof(fraenkel_a_1_0_cqc_the1,axiom,(
    ! [A,B] :
      ( m2_subset_1(B,k1_numbers,k5_numbers)
     => ( r2_hidden(A,a_1_0_cqc_the1(B))
      <=> ? [C] :
            ( m2_subset_1(C,k1_numbers,k5_numbers)
            & A = C
            & r1_xreal_0(C,k1_nat_1(B,np__1)) ) ) ) )).

fof(fraenkel_a_1_1_cqc_the1,axiom,(
    ! [A,B] :
      ( m2_subset_1(B,k1_numbers,k5_numbers)
     => ( r2_hidden(A,a_1_1_cqc_the1(B))
      <=> ? [C] :
            ( m2_subset_1(C,k1_numbers,k5_numbers)
            & A = C
            & r1_xreal_0(C,B) ) ) ) )).

fof(fraenkel_a_0_0_cqc_the1,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_0_cqc_the1)
    <=> ? [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
          & A = B
          & r1_xreal_0(B,np__9) ) ) )).

fof(fraenkel_a_1_2_cqc_the1,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
     => ( r2_hidden(A,a_1_2_cqc_the1(B))
      <=> ? [C] :
            ( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
            & A = C
            & ? [D] :
                ( m2_finseq_1(D,k2_zfmisc_1(k7_cqc_lang,k2_cqc_the1))
                & r2_cqc_the1(B,D)
                & k3_cqc_the1(D) = C ) ) ) ) )).
%------------------------------------------------------------------------------