SET007 Axioms: SET007+77.ax


%------------------------------------------------------------------------------
% File     : SET007+77 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Connectives and Subformulae of the First Order Language
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : qc_lang2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  160 (  27 unit)
%            Number of atoms       :  673 ( 148 equality)
%            Maximal formula depth :   28 (   6 average)
%            Number of connectives :  547 (  34 ~  ;   6  |; 127  &)
%                                         (  24 <=>; 356 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   22 (   1 propositional; 0-3 arity)
%            Number of functors    :   43 (   9 constant; 0-7 arity)
%            Number of variables   :  336 (   0 singleton; 325 !;  11 ?)
%            Maximal term depth    :    5 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(t1_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ( k12_qc_lang1(A) = k12_qc_lang1(B)
           => A = B ) ) ) )).

fof(t2_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => k17_qc_lang1(k12_qc_lang1(A)) = A ) )).

fof(t3_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ! [C] :
              ( m1_subset_1(C,k8_qc_lang1)
             => ! [D] :
                  ( m1_subset_1(D,k8_qc_lang1)
                 => ( k13_qc_lang1(A,B) = k13_qc_lang1(C,D)
                   => ( A = C
                      & B = D ) ) ) ) ) ) )).

fof(t4_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v4_qc_lang1(A)
       => A = k13_qc_lang1(k18_qc_lang1(A),k19_qc_lang1(A)) ) ) )).

fof(t5_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ( k18_qc_lang1(k13_qc_lang1(A,B)) = A
            & k19_qc_lang1(k13_qc_lang1(A,B)) = B ) ) ) )).

fof(t6_qc_lang2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( m1_subset_1(C,k8_qc_lang1)
             => ! [D] :
                  ( m1_subset_1(D,k8_qc_lang1)
                 => ( k14_qc_lang1(A,C) = k14_qc_lang1(B,D)
                   => ( A = B
                      & C = D ) ) ) ) ) ) )).

fof(t7_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v5_qc_lang1(A)
       => A = k14_qc_lang1(k20_qc_lang1(A),k21_qc_lang1(A)) ) ) )).

fof(t8_qc_lang2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ( k20_qc_lang1(k14_qc_lang1(A,B)) = A
            & k21_qc_lang1(k14_qc_lang1(A,B)) = B ) ) ) )).

fof(d1_qc_lang2,axiom,(
    k1_qc_lang2 = k12_qc_lang1(k11_qc_lang1) )).

fof(d2_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => k2_qc_lang2(A,B) = k12_qc_lang1(k13_qc_lang1(A,k12_qc_lang1(B))) ) ) )).

fof(d3_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => k3_qc_lang2(A,B) = k12_qc_lang1(k13_qc_lang1(k12_qc_lang1(A),k12_qc_lang1(B))) ) ) )).

fof(d4_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => k4_qc_lang2(A,B) = k13_qc_lang1(k2_qc_lang2(A,B),k2_qc_lang2(B,A)) ) ) )).

fof(d5_qc_lang2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => k5_qc_lang2(A,B) = k12_qc_lang1(k14_qc_lang1(A,k12_qc_lang1(B))) ) ) )).

fof(t9_qc_lang2,axiom,(
    $true )).

fof(t10_qc_lang2,axiom,(
    $true )).

fof(t11_qc_lang2,axiom,(
    $true )).

fof(t12_qc_lang2,axiom,(
    $true )).

fof(t13_qc_lang2,axiom,
    ( v3_qc_lang1(k1_qc_lang2)
    & k17_qc_lang1(k1_qc_lang2) = k11_qc_lang1 )).

fof(t14_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => k3_qc_lang2(A,B) = k2_qc_lang2(k12_qc_lang1(A),B) ) ) )).

fof(t15_qc_lang2,axiom,(
    $true )).

fof(t16_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ! [C] :
              ( m1_subset_1(C,k8_qc_lang1)
             => ! [D] :
                  ( m1_subset_1(D,k8_qc_lang1)
                 => ( k3_qc_lang2(A,B) = k3_qc_lang2(C,D)
                   => ( A = C
                      & B = D ) ) ) ) ) ) )).

fof(t17_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ! [C] :
              ( m1_subset_1(C,k8_qc_lang1)
             => ! [D] :
                  ( m1_subset_1(D,k8_qc_lang1)
                 => ( k2_qc_lang2(A,B) = k2_qc_lang2(C,D)
                   => ( A = C
                      & B = D ) ) ) ) ) ) )).

fof(t18_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ! [C] :
              ( m1_subset_1(C,k8_qc_lang1)
             => ! [D] :
                  ( m1_subset_1(D,k8_qc_lang1)
                 => ( k4_qc_lang2(A,B) = k4_qc_lang2(C,D)
                   => ( A = C
                      & B = D ) ) ) ) ) ) )).

fof(t19_qc_lang2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( m1_subset_1(C,k8_qc_lang1)
             => ! [D] :
                  ( m1_subset_1(D,k8_qc_lang1)
                 => ( k5_qc_lang2(A,C) = k5_qc_lang2(B,D)
                   => ( A = B
                      & C = D ) ) ) ) ) ) )).

fof(d6_qc_lang2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( m1_subset_1(C,k8_qc_lang1)
             => k6_qc_lang2(A,B,C) = k14_qc_lang1(A,k14_qc_lang1(B,C)) ) ) ) )).

fof(d7_qc_lang2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( m1_subset_1(C,k8_qc_lang1)
             => k7_qc_lang2(A,B,C) = k5_qc_lang2(A,k5_qc_lang2(B,C)) ) ) ) )).

fof(t20_qc_lang2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( m1_subset_1(C,k8_qc_lang1)
             => ( k6_qc_lang2(A,B,C) = k14_qc_lang1(A,k14_qc_lang1(B,C))
                & k7_qc_lang2(A,B,C) = k5_qc_lang2(A,k5_qc_lang2(B,C)) ) ) ) ) )).

fof(t21_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [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)
                 => ! [E] :
                      ( m2_subset_1(E,k1_qc_lang1,k2_qc_lang1)
                     => ! [F] :
                          ( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
                         => ( k6_qc_lang2(C,E,A) = k6_qc_lang2(D,F,B)
                           => ( C = D
                              & E = F
                              & A = B ) ) ) ) ) ) ) ) )).

fof(t22_qc_lang2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ! [D] :
                  ( m1_subset_1(D,k8_qc_lang1)
                 => ! [E] :
                      ( m1_subset_1(E,k8_qc_lang1)
                     => ( k6_qc_lang2(A,B,D) = k14_qc_lang1(C,E)
                       => ( A = C
                          & k14_qc_lang1(B,D) = E ) ) ) ) ) ) ) )).

fof(t23_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [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)
                 => ! [E] :
                      ( m2_subset_1(E,k1_qc_lang1,k2_qc_lang1)
                     => ! [F] :
                          ( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
                         => ( k7_qc_lang2(C,E,A) = k7_qc_lang2(D,F,B)
                           => ( C = D
                              & E = F
                              & A = B ) ) ) ) ) ) ) ) )).

fof(t24_qc_lang2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ! [D] :
                  ( m1_subset_1(D,k8_qc_lang1)
                 => ! [E] :
                      ( m1_subset_1(E,k8_qc_lang1)
                     => ( k7_qc_lang2(A,B,D) = k5_qc_lang2(C,E)
                       => ( A = C
                          & k5_qc_lang2(B,D) = E ) ) ) ) ) ) ) )).

fof(t25_qc_lang2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( m1_subset_1(C,k8_qc_lang1)
             => ( v5_qc_lang1(k6_qc_lang2(A,B,C))
                & k20_qc_lang1(k6_qc_lang2(A,B,C)) = A
                & k21_qc_lang1(k6_qc_lang2(A,B,C)) = k14_qc_lang1(B,C) ) ) ) ) )).

fof(d8_qc_lang2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ! [D] :
                  ( m1_subset_1(D,k8_qc_lang1)
                 => k8_qc_lang2(A,B,C,D) = k14_qc_lang1(A,k6_qc_lang2(B,C,D)) ) ) ) ) )).

fof(d9_qc_lang2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ! [D] :
                  ( m1_subset_1(D,k8_qc_lang1)
                 => k9_qc_lang2(A,B,C,D) = k5_qc_lang2(A,k7_qc_lang2(B,C,D)) ) ) ) ) )).

fof(t26_qc_lang2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ! [D] :
                  ( m1_subset_1(D,k8_qc_lang1)
                 => ( k8_qc_lang2(A,B,C,D) = k14_qc_lang1(A,k6_qc_lang2(B,C,D))
                    & k9_qc_lang2(A,B,C,D) = k5_qc_lang2(A,k7_qc_lang2(B,C,D)) ) ) ) ) ) )).

fof(t27_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [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)
                 => ! [E] :
                      ( m2_subset_1(E,k1_qc_lang1,k2_qc_lang1)
                     => ! [F] :
                          ( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
                         => ! [G] :
                              ( m2_subset_1(G,k1_qc_lang1,k2_qc_lang1)
                             => ! [H] :
                                  ( m2_subset_1(H,k1_qc_lang1,k2_qc_lang1)
                                 => ( k8_qc_lang2(C,E,G,A) = k8_qc_lang2(D,F,H,B)
                                   => ( C = D
                                      & E = F
                                      & G = H
                                      & A = B ) ) ) ) ) ) ) ) ) ) )).

fof(t28_qc_lang2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ! [D] :
                  ( m1_subset_1(D,k8_qc_lang1)
                 => ! [E] :
                      ( m1_subset_1(E,k8_qc_lang1)
                     => ! [F] :
                          ( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
                         => ( k8_qc_lang2(A,B,C,D) = k14_qc_lang1(F,E)
                           => ( A = F
                              & k6_qc_lang2(B,C,D) = E ) ) ) ) ) ) ) ) )).

fof(t29_qc_lang2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ! [D] :
                  ( m1_subset_1(D,k8_qc_lang1)
                 => ! [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)
                             => ( k8_qc_lang2(A,B,C,D) = k6_qc_lang2(F,G,E)
                               => ( A = F
                                  & B = G
                                  & k14_qc_lang1(C,D) = E ) ) ) ) ) ) ) ) ) )).

fof(t30_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [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)
                 => ! [E] :
                      ( m2_subset_1(E,k1_qc_lang1,k2_qc_lang1)
                     => ! [F] :
                          ( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
                         => ! [G] :
                              ( m2_subset_1(G,k1_qc_lang1,k2_qc_lang1)
                             => ! [H] :
                                  ( m2_subset_1(H,k1_qc_lang1,k2_qc_lang1)
                                 => ( k9_qc_lang2(C,E,G,A) = k9_qc_lang2(D,F,H,B)
                                   => ( C = D
                                      & E = F
                                      & G = H
                                      & A = B ) ) ) ) ) ) ) ) ) ) )).

fof(t31_qc_lang2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ! [D] :
                  ( m1_subset_1(D,k8_qc_lang1)
                 => ! [E] :
                      ( m1_subset_1(E,k8_qc_lang1)
                     => ! [F] :
                          ( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
                         => ( k9_qc_lang2(A,B,C,D) = k5_qc_lang2(F,E)
                           => ( A = F
                              & k7_qc_lang2(B,C,D) = E ) ) ) ) ) ) ) ) )).

fof(t32_qc_lang2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ! [D] :
                  ( m1_subset_1(D,k8_qc_lang1)
                 => ! [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)
                             => ( k9_qc_lang2(A,B,C,D) = k7_qc_lang2(F,G,E)
                               => ( A = F
                                  & B = G
                                  & k5_qc_lang2(C,D) = E ) ) ) ) ) ) ) ) ) )).

fof(t33_qc_lang2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ! [D] :
                  ( m1_subset_1(D,k8_qc_lang1)
                 => ( v5_qc_lang1(k8_qc_lang2(A,B,C,D))
                    & k20_qc_lang1(k8_qc_lang2(A,B,C,D)) = A
                    & k21_qc_lang1(k8_qc_lang2(A,B,C,D)) = k6_qc_lang2(B,C,D) ) ) ) ) ) )).

fof(d10_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v1_qc_lang2(A)
      <=> ? [B] :
            ( m1_subset_1(B,k8_qc_lang1)
            & ? [C] :
                ( m1_subset_1(C,k8_qc_lang1)
                & A = k3_qc_lang2(B,C) ) ) ) ) )).

fof(d11_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v2_qc_lang2(A)
      <=> ? [B] :
            ( m1_subset_1(B,k8_qc_lang1)
            & ? [C] :
                ( m1_subset_1(C,k8_qc_lang1)
                & A = k2_qc_lang2(B,C) ) ) ) ) )).

fof(d12_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v3_qc_lang2(A)
      <=> ? [B] :
            ( m1_subset_1(B,k8_qc_lang1)
            & ? [C] :
                ( m1_subset_1(C,k8_qc_lang1)
                & A = k4_qc_lang2(B,C) ) ) ) ) )).

fof(d13_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v4_qc_lang2(A)
      <=> ? [B] :
            ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
            & ? [C] :
                ( m1_subset_1(C,k8_qc_lang1)
                & A = k5_qc_lang2(B,C) ) ) ) ) )).

fof(t34_qc_lang2,axiom,(
    $true )).

fof(t35_qc_lang2,axiom,(
    $true )).

fof(t36_qc_lang2,axiom,(
    $true )).

fof(t37_qc_lang2,axiom,(
    $true )).

fof(t38_qc_lang2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ! [D] :
                  ( m1_subset_1(D,k8_qc_lang1)
                 => ( v4_qc_lang2(k7_qc_lang2(A,B,D))
                    & v4_qc_lang2(k9_qc_lang2(A,B,C,D)) ) ) ) ) ) )).

fof(d14_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => k10_qc_lang2(A) = k17_qc_lang1(k18_qc_lang1(k17_qc_lang1(A))) ) )).

fof(d15_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => k11_qc_lang2(A) = k17_qc_lang1(k19_qc_lang1(k17_qc_lang1(A))) ) )).

fof(d16_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => k12_qc_lang2(A) = k18_qc_lang1(k17_qc_lang1(A)) ) )).

fof(d17_qc_lang2,axiom,(
    $true )).

fof(d18_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => k13_qc_lang2(A) = k12_qc_lang2(k18_qc_lang1(A)) ) )).

fof(d19_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => k14_qc_lang2(A) = k11_qc_lang2(k18_qc_lang1(A)) ) )).

fof(t39_qc_lang2,axiom,(
    $true )).

fof(t40_qc_lang2,axiom,(
    $true )).

fof(t41_qc_lang2,axiom,(
    $true )).

fof(t42_qc_lang2,axiom,(
    $true )).

fof(t43_qc_lang2,axiom,(
    $true )).

fof(t44_qc_lang2,axiom,(
    $true )).

fof(t45_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ( k10_qc_lang2(k3_qc_lang2(A,B)) = A
            & k11_qc_lang2(k3_qc_lang2(A,B)) = B
            & k17_qc_lang1(k3_qc_lang2(A,B)) = k13_qc_lang1(k12_qc_lang1(A),k12_qc_lang1(B)) ) ) ) )).

fof(t46_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ( k12_qc_lang2(k2_qc_lang2(A,B)) = A
            & k11_qc_lang2(k2_qc_lang2(A,B)) = B
            & k17_qc_lang1(k2_qc_lang2(A,B)) = k13_qc_lang1(A,k12_qc_lang1(B)) ) ) ) )).

fof(t47_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ( k13_qc_lang2(k4_qc_lang2(A,B)) = A
            & k14_qc_lang2(k4_qc_lang2(A,B)) = B
            & k18_qc_lang1(k4_qc_lang2(A,B)) = k2_qc_lang2(A,B)
            & k19_qc_lang1(k4_qc_lang2(A,B)) = k2_qc_lang2(B,A) ) ) ) )).

fof(t48_qc_lang2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => k17_qc_lang1(k5_qc_lang2(A,B)) = k14_qc_lang1(A,k12_qc_lang1(B)) ) ) )).

fof(t49_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v1_qc_lang2(A)
       => ( v2_qc_lang2(A)
          & v3_qc_lang1(A)
          & v4_qc_lang1(k17_qc_lang1(A))
          & v3_qc_lang1(k18_qc_lang1(k17_qc_lang1(A)))
          & v3_qc_lang1(k19_qc_lang1(k17_qc_lang1(A))) ) ) ) )).

fof(t50_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v2_qc_lang2(A)
       => ( v3_qc_lang1(A)
          & v4_qc_lang1(k17_qc_lang1(A))
          & v3_qc_lang1(k19_qc_lang1(k17_qc_lang1(A))) ) ) ) )).

fof(t51_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v3_qc_lang2(A)
       => ( v4_qc_lang1(A)
          & v2_qc_lang2(k18_qc_lang1(A))
          & v2_qc_lang2(k19_qc_lang1(A)) ) ) ) )).

fof(t52_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v4_qc_lang2(A)
       => ( v3_qc_lang1(A)
          & v5_qc_lang1(k17_qc_lang1(A))
          & v3_qc_lang1(k21_qc_lang1(k17_qc_lang1(A))) ) ) ) )).

fof(t53_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v1_qc_lang2(A)
       => A = k3_qc_lang2(k10_qc_lang2(A),k11_qc_lang2(A)) ) ) )).

fof(t54_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v2_qc_lang2(A)
       => A = k2_qc_lang2(k12_qc_lang2(A),k11_qc_lang2(A)) ) ) )).

fof(t55_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v3_qc_lang2(A)
       => A = k4_qc_lang2(k13_qc_lang2(A),k14_qc_lang2(A)) ) ) )).

fof(t56_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v4_qc_lang2(A)
       => A = k5_qc_lang2(k20_qc_lang1(k17_qc_lang1(A)),k17_qc_lang1(k21_qc_lang1(k17_qc_lang1(A)))) ) ) )).

fof(d20_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ( r1_qc_lang2(A,B)
          <=> ~ ( B != k12_qc_lang1(A)
                & ! [C] :
                    ( m1_subset_1(C,k8_qc_lang1)
                   => ( B != k13_qc_lang1(A,C)
                      & B != k13_qc_lang1(C,A) ) )
                & ! [C] :
                    ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
                   => B != k14_qc_lang1(C,A) ) ) ) ) ) )).

fof(t57_qc_lang2,axiom,(
    $true )).

fof(t58_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ~ r1_qc_lang2(A,k11_qc_lang1) ) )).

fof(t59_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(B))
             => ! [D] :
                  ( m1_qc_lang1(D,B)
                 => ~ r1_qc_lang2(A,k9_qc_lang1(C,D)) ) ) ) ) )).

fof(t60_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ( r1_qc_lang2(A,k12_qc_lang1(B))
          <=> A = B ) ) ) )).

fof(t61_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ( r1_qc_lang2(A,k1_qc_lang2)
      <=> A = k11_qc_lang1 ) ) )).

fof(t62_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ! [C] :
              ( m1_subset_1(C,k8_qc_lang1)
             => ( r1_qc_lang2(A,k13_qc_lang1(B,C))
              <=> ( A = B
                  | A = C ) ) ) ) ) )).

fof(t63_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( r1_qc_lang2(A,k14_qc_lang1(C,B))
              <=> A = B ) ) ) ) )).

fof(t64_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ~ ( v2_qc_lang1(A)
              & r1_qc_lang2(B,A) ) ) ) )).

fof(t65_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ( v3_qc_lang1(A)
           => ( r1_qc_lang2(B,A)
            <=> B = k17_qc_lang1(A) ) ) ) ) )).

fof(t66_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ( v4_qc_lang1(A)
           => ( r1_qc_lang2(B,A)
            <=> ( B = k18_qc_lang1(A)
                | B = k19_qc_lang1(A) ) ) ) ) ) )).

fof(t67_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ( v5_qc_lang1(A)
           => ( r1_qc_lang2(B,A)
            <=> B = k21_qc_lang1(A) ) ) ) ) )).

fof(d21_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ( r2_qc_lang2(A,B)
          <=> ? [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
                & ? [D] :
                    ( v1_relat_1(D)
                    & v1_funct_1(D)
                    & v1_finseq_1(D)
                    & r1_xreal_0(np__1,C)
                    & k3_finseq_1(D) = C
                    & k1_funct_1(D,np__1) = A
                    & k1_funct_1(D,C) = B
                    & ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => ~ ( r1_xreal_0(np__1,E)
                            & ~ r1_xreal_0(C,E)
                            & ! [F] :
                                ( m1_subset_1(F,k8_qc_lang1)
                               => ! [G] :
                                    ( m1_subset_1(G,k8_qc_lang1)
                                   => ~ ( k1_funct_1(D,E) = F
                                        & k1_funct_1(D,k1_nat_1(E,np__1)) = G
                                        & r1_qc_lang2(F,G) ) ) ) ) ) ) ) ) ) ) )).

fof(d22_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ( r3_qc_lang2(A,B)
          <=> ( r2_qc_lang2(A,B)
              & A != B ) ) ) ) )).

fof(t68_qc_lang2,axiom,(
    $true )).

fof(t69_qc_lang2,axiom,(
    $true )).

fof(t70_qc_lang2,axiom,(
    $true )).

fof(t71_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ~ ( r1_qc_lang2(A,B)
              & r1_xreal_0(k3_finseq_1(k10_qc_lang1(B)),k3_finseq_1(k10_qc_lang1(A))) ) ) ) )).

fof(t72_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ( r1_qc_lang2(A,B)
           => r2_qc_lang2(A,B) ) ) ) )).

fof(t73_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ( r1_qc_lang2(A,B)
           => r3_qc_lang2(A,B) ) ) ) )).

fof(t74_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ~ ( r3_qc_lang2(A,B)
              & r1_xreal_0(k3_finseq_1(k10_qc_lang1(B)),k3_finseq_1(k10_qc_lang1(A))) ) ) ) )).

fof(t75_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ~ ( r3_qc_lang2(A,B)
              & ! [C] :
                  ( m1_subset_1(C,k8_qc_lang1)
                 => ~ r1_qc_lang2(C,B) ) ) ) ) )).

fof(t76_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ! [C] :
              ( m1_subset_1(C,k8_qc_lang1)
             => ( ( r3_qc_lang2(A,B)
                  & r3_qc_lang2(B,C) )
               => r3_qc_lang2(A,C) ) ) ) ) )).

fof(t77_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ! [C] :
              ( m1_subset_1(C,k8_qc_lang1)
             => ( ( r2_qc_lang2(A,B)
                  & r2_qc_lang2(B,C) )
               => r2_qc_lang2(A,C) ) ) ) ) )).

fof(t78_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ( ( r2_qc_lang2(A,B)
              & r2_qc_lang2(B,A) )
           => A = B ) ) ) )).

fof(t79_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ~ ( r3_qc_lang2(A,B)
              & r2_qc_lang2(B,A) ) ) ) )).

fof(t80_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ~ ( r3_qc_lang2(A,B)
              & r3_qc_lang2(B,A) ) ) ) )).

fof(t81_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ~ ( r2_qc_lang2(A,B)
              & r1_qc_lang2(B,A) ) ) ) )).

fof(t82_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ~ ( r3_qc_lang2(A,B)
              & r1_qc_lang2(B,A) ) ) ) )).

fof(t83_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ! [C] :
              ( m1_subset_1(C,k8_qc_lang1)
             => ( ~ ( ~ ( r3_qc_lang2(A,B)
                        & r2_qc_lang2(B,C) )
                    & ~ ( r2_qc_lang2(A,B)
                        & r3_qc_lang2(B,C) )
                    & ~ ( r2_qc_lang2(A,B)
                        & r1_qc_lang2(B,C) )
                    & ~ ( r1_qc_lang2(A,B)
                        & r2_qc_lang2(B,C) )
                    & ~ ( r3_qc_lang2(A,B)
                        & r1_qc_lang2(B,C) )
                    & ~ ( r1_qc_lang2(A,B)
                        & r3_qc_lang2(B,C) ) )
               => r3_qc_lang2(A,C) ) ) ) ) )).

fof(t84_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ~ r3_qc_lang2(A,k11_qc_lang1) ) )).

fof(t85_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(B))
             => ! [D] :
                  ( m1_qc_lang1(D,B)
                 => ~ r3_qc_lang2(A,k9_qc_lang1(C,D)) ) ) ) ) )).

fof(t86_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ( r2_qc_lang2(A,B)
          <=> r3_qc_lang2(A,k12_qc_lang1(B)) ) ) ) )).

fof(t87_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ( r2_qc_lang2(k12_qc_lang1(A),B)
           => r3_qc_lang2(A,B) ) ) ) )).

fof(t88_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ( r3_qc_lang2(A,k1_qc_lang2)
      <=> r2_qc_lang2(A,k11_qc_lang1) ) ) )).

fof(t89_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ! [C] :
              ( m1_subset_1(C,k8_qc_lang1)
             => ( ( r2_qc_lang2(A,B)
                  | r2_qc_lang2(A,C) )
              <=> r3_qc_lang2(A,k13_qc_lang1(B,C)) ) ) ) ) )).

fof(t90_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ! [C] :
              ( m1_subset_1(C,k8_qc_lang1)
             => ( r2_qc_lang2(k13_qc_lang1(A,B),C)
               => ( r3_qc_lang2(A,C)
                  & r3_qc_lang2(B,C) ) ) ) ) ) )).

fof(t91_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( r2_qc_lang2(A,B)
              <=> r3_qc_lang2(A,k14_qc_lang1(C,B)) ) ) ) ) )).

fof(t92_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ! [C] :
              ( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
             => ( r2_qc_lang2(k14_qc_lang1(C,A),B)
               => r3_qc_lang2(A,B) ) ) ) ) )).

fof(t93_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ( r3_qc_lang2(k13_qc_lang1(A,k12_qc_lang1(B)),k2_qc_lang2(A,B))
            & r3_qc_lang2(A,k2_qc_lang2(A,B))
            & r3_qc_lang2(k12_qc_lang1(B),k2_qc_lang2(A,B))
            & r3_qc_lang2(B,k2_qc_lang2(A,B)) ) ) ) )).

fof(t94_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ( r3_qc_lang2(k13_qc_lang1(k12_qc_lang1(A),k12_qc_lang1(B)),k3_qc_lang2(A,B))
            & r3_qc_lang2(k12_qc_lang1(A),k3_qc_lang2(A,B))
            & r3_qc_lang2(k12_qc_lang1(B),k3_qc_lang2(A,B))
            & r3_qc_lang2(A,k3_qc_lang2(A,B))
            & r3_qc_lang2(B,k3_qc_lang2(A,B)) ) ) ) )).

fof(t95_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ~ ( v2_qc_lang1(A)
              & r3_qc_lang2(B,A) ) ) ) )).

fof(t96_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v3_qc_lang1(A)
       => r3_qc_lang2(k17_qc_lang1(A),A) ) ) )).

fof(t97_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v4_qc_lang1(A)
       => ( r3_qc_lang2(k18_qc_lang1(A),A)
          & r3_qc_lang2(k19_qc_lang1(A),A) ) ) ) )).

fof(t98_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v5_qc_lang1(A)
       => r3_qc_lang2(k21_qc_lang1(A),A) ) ) )).

fof(t99_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ( r2_qc_lang2(A,k11_qc_lang1)
      <=> A = k11_qc_lang1 ) ) )).

fof(t100_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(B))
             => ! [D] :
                  ( m1_qc_lang1(D,B)
                 => ( r2_qc_lang2(A,k9_qc_lang1(C,D))
                  <=> A = k9_qc_lang1(C,D) ) ) ) ) ) )).

fof(t101_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ( r2_qc_lang2(A,k1_qc_lang2)
      <=> ( A = k1_qc_lang2
          | A = k11_qc_lang1 ) ) ) )).

fof(d23_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( B = k15_qc_lang2(A)
        <=> ! [C] :
              ( r2_hidden(C,B)
            <=> ? [D] :
                  ( m1_subset_1(D,k8_qc_lang1)
                  & D = C
                  & r2_qc_lang2(D,A) ) ) ) ) )).

fof(t102_qc_lang2,axiom,(
    $true )).

fof(t103_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ( r2_hidden(A,k15_qc_lang2(B))
           => r2_qc_lang2(A,B) ) ) ) )).

fof(t104_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ( r2_qc_lang2(A,B)
           => r1_tarski(k15_qc_lang2(A),k15_qc_lang2(B)) ) ) ) )).

fof(t105_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ( r2_hidden(A,k15_qc_lang2(B))
           => r1_tarski(k15_qc_lang2(A),k15_qc_lang2(B)) ) ) ) )).

fof(t106_qc_lang2,axiom,(
    $true )).

fof(t107_qc_lang2,axiom,(
    k15_qc_lang2(k11_qc_lang1) = k1_tarski(k11_qc_lang1) )).

fof(t108_qc_lang2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A))
         => ! [C] :
              ( m1_qc_lang1(C,A)
             => k15_qc_lang2(k9_qc_lang1(B,C)) = k1_tarski(k9_qc_lang1(B,C)) ) ) ) )).

fof(t109_qc_lang2,axiom,(
    k15_qc_lang2(k1_qc_lang2) = k2_tarski(k11_qc_lang1,k1_qc_lang2) )).

fof(t110_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => k15_qc_lang2(k12_qc_lang1(A)) = k2_xboole_0(k15_qc_lang2(A),k1_tarski(k12_qc_lang1(A))) ) )).

fof(t111_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => k15_qc_lang2(k13_qc_lang1(A,B)) = k2_xboole_0(k2_xboole_0(k15_qc_lang2(A),k15_qc_lang2(B)),k1_tarski(k13_qc_lang1(A,B))) ) ) )).

fof(t112_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
         => k15_qc_lang2(k14_qc_lang1(B,A)) = k2_xboole_0(k15_qc_lang2(A),k1_tarski(k14_qc_lang1(B,A))) ) ) )).

fof(t113_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => k15_qc_lang2(k2_qc_lang2(A,B)) = k2_xboole_0(k2_xboole_0(k15_qc_lang2(A),k15_qc_lang2(B)),k1_enumset1(k12_qc_lang1(B),k13_qc_lang1(A,k12_qc_lang1(B)),k2_qc_lang2(A,B))) ) ) )).

fof(t114_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => k15_qc_lang2(k3_qc_lang2(A,B)) = k2_xboole_0(k2_xboole_0(k15_qc_lang2(A),k15_qc_lang2(B)),k2_enumset1(k12_qc_lang1(B),k12_qc_lang1(A),k13_qc_lang1(k12_qc_lang1(A),k12_qc_lang1(B)),k3_qc_lang2(A,B))) ) ) )).

fof(t115_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => k15_qc_lang2(k4_qc_lang2(A,B)) = k2_xboole_0(k2_xboole_0(k15_qc_lang2(A),k15_qc_lang2(B)),k5_enumset1(k12_qc_lang1(B),k13_qc_lang1(A,k12_qc_lang1(B)),k2_qc_lang2(A,B),k12_qc_lang1(A),k13_qc_lang1(B,k12_qc_lang1(A)),k2_qc_lang2(B,A),k4_qc_lang2(A,B))) ) ) )).

fof(t116_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ( ( A = k11_qc_lang1
          | v2_qc_lang1(A) )
      <=> k15_qc_lang2(A) = k1_tarski(A) ) ) )).

fof(t117_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v3_qc_lang1(A)
       => k15_qc_lang2(A) = k2_xboole_0(k15_qc_lang2(k17_qc_lang1(A)),k1_tarski(A)) ) ) )).

fof(t118_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v4_qc_lang1(A)
       => k15_qc_lang2(A) = k2_xboole_0(k2_xboole_0(k15_qc_lang2(k18_qc_lang1(A)),k15_qc_lang2(k19_qc_lang1(A))),k1_tarski(A)) ) ) )).

fof(t119_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ( v5_qc_lang1(A)
       => k15_qc_lang2(A) = k2_xboole_0(k15_qc_lang2(k21_qc_lang1(A)),k1_tarski(A)) ) ) )).

fof(t120_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => ! [B] :
          ( m1_subset_1(B,k8_qc_lang1)
         => ! [C] :
              ( m1_subset_1(C,k8_qc_lang1)
             => ( r2_hidden(B,k15_qc_lang2(C))
               => ( ( ~ r1_qc_lang2(A,B)
                    & ~ r3_qc_lang2(A,B)
                    & ~ r2_qc_lang2(A,B) )
                  | r2_hidden(A,k15_qc_lang2(C)) ) ) ) ) ) )).

fof(reflexivity_r2_qc_lang2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k8_qc_lang1)
        & m1_subset_1(B,k8_qc_lang1) )
     => r2_qc_lang2(A,A) ) )).

fof(irreflexivity_r3_qc_lang2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k8_qc_lang1)
        & m1_subset_1(B,k8_qc_lang1) )
     => ~ r3_qc_lang2(A,A) ) )).

fof(dt_k1_qc_lang2,axiom,(
    m1_subset_1(k1_qc_lang2,k8_qc_lang1) )).

fof(dt_k2_qc_lang2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k8_qc_lang1)
        & m1_subset_1(B,k8_qc_lang1) )
     => m1_subset_1(k2_qc_lang2(A,B),k8_qc_lang1) ) )).

fof(dt_k3_qc_lang2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k8_qc_lang1)
        & m1_subset_1(B,k8_qc_lang1) )
     => m1_subset_1(k3_qc_lang2(A,B),k8_qc_lang1) ) )).

fof(dt_k4_qc_lang2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k8_qc_lang1)
        & m1_subset_1(B,k8_qc_lang1) )
     => m1_subset_1(k4_qc_lang2(A,B),k8_qc_lang1) ) )).

fof(dt_k5_qc_lang2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k2_qc_lang1)
        & m1_subset_1(B,k8_qc_lang1) )
     => m1_subset_1(k5_qc_lang2(A,B),k8_qc_lang1) ) )).

fof(dt_k6_qc_lang2,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k2_qc_lang1)
        & m1_subset_1(B,k2_qc_lang1)
        & m1_subset_1(C,k8_qc_lang1) )
     => m1_subset_1(k6_qc_lang2(A,B,C),k8_qc_lang1) ) )).

fof(dt_k7_qc_lang2,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k2_qc_lang1)
        & m1_subset_1(B,k2_qc_lang1)
        & m1_subset_1(C,k8_qc_lang1) )
     => m1_subset_1(k7_qc_lang2(A,B,C),k8_qc_lang1) ) )).

fof(dt_k8_qc_lang2,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(A,k2_qc_lang1)
        & m1_subset_1(B,k2_qc_lang1)
        & m1_subset_1(C,k2_qc_lang1)
        & m1_subset_1(D,k8_qc_lang1) )
     => m1_subset_1(k8_qc_lang2(A,B,C,D),k8_qc_lang1) ) )).

fof(dt_k9_qc_lang2,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(A,k2_qc_lang1)
        & m1_subset_1(B,k2_qc_lang1)
        & m1_subset_1(C,k2_qc_lang1)
        & m1_subset_1(D,k8_qc_lang1) )
     => m1_subset_1(k9_qc_lang2(A,B,C,D),k8_qc_lang1) ) )).

fof(dt_k10_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => m1_subset_1(k10_qc_lang2(A),k8_qc_lang1) ) )).

fof(dt_k11_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => m1_subset_1(k11_qc_lang2(A),k8_qc_lang1) ) )).

fof(dt_k12_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => m1_subset_1(k12_qc_lang2(A),k8_qc_lang1) ) )).

fof(dt_k13_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => m1_subset_1(k13_qc_lang2(A),k8_qc_lang1) ) )).

fof(dt_k14_qc_lang2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k8_qc_lang1)
     => m1_subset_1(k14_qc_lang2(A),k8_qc_lang1) ) )).

fof(dt_k15_qc_lang2,axiom,(
    $true )).
%------------------------------------------------------------------------------