SET007 Axioms: SET007+578.ax


%------------------------------------------------------------------------------
% File     : SET007+578 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Predicate Calculus for Boolean Valued Functions. Part I
% 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    : bvfunc_3 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   41 (   0 unit)
%            Number of atoms       :  258 (   5 equality)
%            Maximal formula depth :   13 (  12 average)
%            Number of connectives :  258 (  41 ~  ;   0  |;   0  &)
%                                         (   0 <=>; 217 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    7 (   0 propositional; 1-4 arity)
%            Number of functors    :   11 (   1 constant; 0-4 arity)
%            Number of variables   :  215 (   0 singleton; 215 !;   0 ?)
%            Maximal term depth    :    7 (   2 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_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k14_bvfunc_1(A,C,D),k14_bvfunc_1(A,k6_bvfunc_2(A,C,B,E),k7_bvfunc_2(A,D,B,E))) ) ) ) ) ) )).

fof(t2_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k6_valuat_1(A,k6_bvfunc_2(A,C,B,E),k6_bvfunc_2(A,D,B,E)),k6_valuat_1(A,C,D)) ) ) ) ) ) )).

fof(t3_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k6_valuat_1(A,C,D),k6_valuat_1(A,k7_bvfunc_2(A,C,B,E),k7_bvfunc_2(A,D,B,E))) ) ) ) ) ) )).

fof(t4_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => k5_valuat_1(A,k6_valuat_1(A,k6_bvfunc_2(A,C,B,E),k6_bvfunc_2(A,D,B,E))) = k8_bvfunc_1(A,k7_bvfunc_2(A,k5_valuat_1(A,C),B,E),k7_bvfunc_2(A,k5_valuat_1(A,D),B,E)) ) ) ) ) ) )).

fof(t5_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => k5_valuat_1(A,k6_valuat_1(A,k7_bvfunc_2(A,C,B,E),k7_bvfunc_2(A,D,B,E))) = k8_bvfunc_1(A,k6_bvfunc_2(A,k5_valuat_1(A,C),B,E),k6_bvfunc_2(A,k5_valuat_1(A,D),B,E)) ) ) ) ) ) )).

fof(t6_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k8_bvfunc_1(A,k6_bvfunc_2(A,C,B,E),k6_bvfunc_2(A,D,B,E)),k8_bvfunc_1(A,C,D)) ) ) ) ) ) )).

fof(t7_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k8_bvfunc_1(A,C,D),k8_bvfunc_1(A,k7_bvfunc_2(A,C,B,E),k7_bvfunc_2(A,D,B,E))) ) ) ) ) ) )).

fof(t8_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k9_bvfunc_1(A,C,D),k8_bvfunc_1(A,k5_valuat_1(A,k9_bvfunc_1(A,k7_bvfunc_2(A,k5_valuat_1(A,C),B,E),k7_bvfunc_2(A,D,B,E))),k5_valuat_1(A,k9_bvfunc_1(A,k7_bvfunc_2(A,C,B,E),k7_bvfunc_2(A,k5_valuat_1(A,D),B,E))))) ) ) ) ) ) )).

fof(t9_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k6_bvfunc_2(A,k8_bvfunc_1(A,C,D),B,E),k8_bvfunc_1(A,k6_bvfunc_2(A,C,B,E),k7_bvfunc_2(A,D,B,E))) ) ) ) ) ) )).

fof(t10_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k6_bvfunc_2(A,k8_bvfunc_1(A,C,D),B,E),k8_bvfunc_1(A,k7_bvfunc_2(A,C,B,E),k6_bvfunc_2(A,D,B,E))) ) ) ) ) ) )).

fof(t11_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k6_bvfunc_2(A,k8_bvfunc_1(A,C,D),B,E),k8_bvfunc_1(A,k7_bvfunc_2(A,C,B,E),k7_bvfunc_2(A,D,B,E))) ) ) ) ) ) )).

fof(t12_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k6_valuat_1(A,k7_bvfunc_2(A,C,B,E),k6_bvfunc_2(A,D,B,E)),k7_bvfunc_2(A,k6_valuat_1(A,C,D),B,E)) ) ) ) ) ) )).

fof(t13_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k6_valuat_1(A,k6_bvfunc_2(A,C,B,E),k7_bvfunc_2(A,D,B,E)),k7_bvfunc_2(A,k6_valuat_1(A,C,D),B,E)) ) ) ) ) ) )).

fof(t14_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k6_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,E),k14_bvfunc_1(A,k6_bvfunc_2(A,C,B,E),k7_bvfunc_2(A,D,B,E))) ) ) ) ) ) )).

fof(t15_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k6_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,E),k14_bvfunc_1(A,k7_bvfunc_2(A,C,B,E),k7_bvfunc_2(A,D,B,E))) ) ) ) ) ) )).

fof(t16_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k14_bvfunc_1(A,k7_bvfunc_2(A,C,B,E),k6_bvfunc_2(A,D,B,E)),k6_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,E)) ) ) ) ) ) )).

fof(t17_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k14_bvfunc_1(A,C,D),k14_bvfunc_1(A,C,k7_bvfunc_2(A,D,B,E))) ) ) ) ) ) )).

fof(t18_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k14_bvfunc_1(A,C,D),k14_bvfunc_1(A,k6_bvfunc_2(A,C,B,E),D)) ) ) ) ) ) )).

fof(t19_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k7_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,E),k14_bvfunc_1(A,k6_bvfunc_2(A,C,B,E),k7_bvfunc_2(A,D,B,E))) ) ) ) ) ) )).

fof(t20_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k6_bvfunc_2(A,C,B,E),k14_bvfunc_1(A,k7_bvfunc_2(A,D,B,E),k7_bvfunc_2(A,k6_valuat_1(A,C,D),B,E))) ) ) ) ) ) )).

fof(t21_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( r3_bvfunc_2(A,C,B,E)
                       => r1_bvfunc_1(A,k7_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,E),k14_bvfunc_1(A,C,k7_bvfunc_2(A,D,B,E))) ) ) ) ) ) ) )).

fof(t22_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( r3_bvfunc_2(A,C,B,E)
                       => r1_bvfunc_1(A,k7_bvfunc_2(A,k14_bvfunc_1(A,D,C),B,E),k14_bvfunc_1(A,k6_bvfunc_2(A,D,B,E),C)) ) ) ) ) ) ) )).

fof(t23_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => k14_bvfunc_1(A,k6_bvfunc_2(A,C,B,E),k7_bvfunc_2(A,D,B,E)) = k7_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,E) ) ) ) ) ) )).

fof(t24_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k14_bvfunc_1(A,k6_bvfunc_2(A,C,B,E),k6_bvfunc_2(A,D,B,E)),k14_bvfunc_1(A,k6_bvfunc_2(A,C,B,E),k7_bvfunc_2(A,D,B,E))) ) ) ) ) ) )).

fof(t25_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k14_bvfunc_1(A,k7_bvfunc_2(A,C,B,E),k7_bvfunc_2(A,D,B,E)),k14_bvfunc_1(A,k6_bvfunc_2(A,C,B,E),k7_bvfunc_2(A,D,B,E))) ) ) ) ) ) )).

fof(t26_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => k6_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,E) = k6_bvfunc_2(A,k8_bvfunc_1(A,k5_valuat_1(A,C),D),B,E) ) ) ) ) ) )).

fof(t27_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => k6_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,E) = k5_valuat_1(A,k7_bvfunc_2(A,k6_valuat_1(A,C,k5_valuat_1(A,D)),B,E)) ) ) ) ) ) )).

fof(t28_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k7_bvfunc_2(A,C,B,E),k5_valuat_1(A,k6_valuat_1(A,k6_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,E),k6_bvfunc_2(A,k14_bvfunc_1(A,C,k5_valuat_1(A,D)),B,E)))) ) ) ) ) ) )).

fof(t29_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k7_bvfunc_2(A,C,B,E),k5_valuat_1(A,k6_valuat_1(A,k5_valuat_1(A,k7_bvfunc_2(A,k6_valuat_1(A,C,D),B,E)),k5_valuat_1(A,k7_bvfunc_2(A,k6_valuat_1(A,C,k5_valuat_1(A,D)),B,E))))) ) ) ) ) ) )).

fof(t30_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k6_valuat_1(A,k7_bvfunc_2(A,C,B,E),k6_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,E)),k7_bvfunc_2(A,k6_valuat_1(A,C,D),B,E)) ) ) ) ) ) )).

fof(t31_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k6_valuat_1(A,k7_bvfunc_2(A,C,B,E),k5_valuat_1(A,k7_bvfunc_2(A,k6_valuat_1(A,C,D),B,E))),k5_valuat_1(A,k6_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,E))) ) ) ) ) ) )).

fof(t32_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                     => ! [F] :
                          ( m1_eqrel_1(F,A)
                         => r1_bvfunc_1(A,k6_valuat_1(A,k6_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,F),k6_bvfunc_2(A,k14_bvfunc_1(A,D,E),B,F)),k6_bvfunc_2(A,k14_bvfunc_1(A,C,E),B,F)) ) ) ) ) ) ) )).

fof(t33_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                     => ! [F] :
                          ( m1_eqrel_1(F,A)
                         => r1_bvfunc_1(A,k6_valuat_1(A,k6_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,F),k7_bvfunc_2(A,k6_valuat_1(A,E,C),B,F)),k7_bvfunc_2(A,k6_valuat_1(A,E,D),B,F)) ) ) ) ) ) ) )).

fof(t34_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                     => ! [F] :
                          ( m1_eqrel_1(F,A)
                         => r1_bvfunc_1(A,k6_valuat_1(A,k6_bvfunc_2(A,k14_bvfunc_1(A,C,k5_valuat_1(A,D)),B,F),k6_bvfunc_2(A,k14_bvfunc_1(A,E,D),B,F)),k6_bvfunc_2(A,k14_bvfunc_1(A,E,k5_valuat_1(A,C)),B,F)) ) ) ) ) ) ) )).

fof(t35_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                     => ! [F] :
                          ( m1_eqrel_1(F,A)
                         => r1_bvfunc_1(A,k6_valuat_1(A,k6_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,F),k6_bvfunc_2(A,k14_bvfunc_1(A,E,k5_valuat_1(A,D)),B,F)),k6_bvfunc_2(A,k14_bvfunc_1(A,E,k5_valuat_1(A,C)),B,F)) ) ) ) ) ) ) )).

fof(t36_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                     => ! [F] :
                          ( m1_eqrel_1(F,A)
                         => r1_bvfunc_1(A,k6_valuat_1(A,k6_bvfunc_2(A,k14_bvfunc_1(A,C,k5_valuat_1(A,D)),B,F),k7_bvfunc_2(A,k6_valuat_1(A,E,D),B,F)),k7_bvfunc_2(A,k6_valuat_1(A,E,k5_valuat_1(A,C)),B,F)) ) ) ) ) ) ) )).

fof(t37_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                     => ! [F] :
                          ( m1_eqrel_1(F,A)
                         => r1_bvfunc_1(A,k6_valuat_1(A,k6_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,F),k7_bvfunc_2(A,k6_valuat_1(A,E,k5_valuat_1(A,D)),B,F)),k7_bvfunc_2(A,k6_valuat_1(A,E,k5_valuat_1(A,C)),B,F)) ) ) ) ) ) ) )).

fof(t38_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                     => ! [F] :
                          ( m1_eqrel_1(F,A)
                         => r1_bvfunc_1(A,k6_valuat_1(A,k6_valuat_1(A,k7_bvfunc_2(A,C,B,F),k6_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,F)),k6_bvfunc_2(A,k14_bvfunc_1(A,C,E),B,F)),k7_bvfunc_2(A,k6_valuat_1(A,E,D),B,F)) ) ) ) ) ) ) )).

fof(t39_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                     => ! [F] :
                          ( m1_eqrel_1(F,A)
                         => r1_bvfunc_1(A,k6_valuat_1(A,k6_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,F),k6_bvfunc_2(A,k14_bvfunc_1(A,D,k5_valuat_1(A,E)),B,F)),k6_bvfunc_2(A,k14_bvfunc_1(A,E,k5_valuat_1(A,C)),B,F)) ) ) ) ) ) ) )).

fof(t40_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                     => ! [F] :
                          ( m1_eqrel_1(F,A)
                         => r1_bvfunc_1(A,k6_valuat_1(A,k6_valuat_1(A,k7_bvfunc_2(A,C,B,F),k6_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,F)),k6_bvfunc_2(A,k14_bvfunc_1(A,D,E),B,F)),k7_bvfunc_2(A,k6_valuat_1(A,E,C),B,F)) ) ) ) ) ) ) )).

fof(t41_bvfunc_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                     => ! [F] :
                          ( m1_eqrel_1(F,A)
                         => r1_bvfunc_1(A,k6_valuat_1(A,k6_valuat_1(A,k7_bvfunc_2(A,C,B,F),k6_bvfunc_2(A,k14_bvfunc_1(A,D,k5_valuat_1(A,C)),B,F)),k6_bvfunc_2(A,k14_bvfunc_1(A,C,E),B,F)),k7_bvfunc_2(A,k6_valuat_1(A,E,k5_valuat_1(A,D)),B,F)) ) ) ) ) ) ) )).
%------------------------------------------------------------------------------