SET007 Axioms: SET007+621.ax


%------------------------------------------------------------------------------
% File     : SET007+621 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Predicate Calculus for Boolean Valued Functions. Part V
% 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    : bvfunc13 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   62 (   5 unit)
%            Number of atoms       :  386 (   7 equality)
%            Maximal formula depth :   12 (  11 average)
%            Number of connectives :  381 (  57 ~  ;   0  |;   0  &)
%                                         (   0 <=>; 324 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    8 (   1 propositional; 0-4 arity)
%            Number of functors    :    7 (   1 constant; 0-4 arity)
%            Number of variables   :  285 (   0 singleton; 285 !;   0 ?)
%            Maximal term depth    :    4 (   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_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => r1_bvfunc_1(A,k6_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,D)),C,E),k5_valuat_1(A,k6_bvfunc_2(A,k6_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) ) )).

fof(t2_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k6_bvfunc_2(A,k6_bvfunc_2(A,k5_valuat_1(A,B),C,D),C,E),k5_valuat_1(A,k6_bvfunc_2(A,k6_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) )).

fof(t3_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k6_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,D)),C,E),k5_valuat_1(A,k6_bvfunc_2(A,k6_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) )).

fof(t4_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => r1_bvfunc_1(A,k6_bvfunc_2(A,k7_bvfunc_2(A,k5_valuat_1(A,B),C,D),C,E),k5_valuat_1(A,k6_bvfunc_2(A,k6_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) ) )).

fof(t5_bvfunc13,axiom,(
    $true )).

fof(t6_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => r1_bvfunc_1(A,k7_bvfunc_2(A,k6_bvfunc_2(A,k5_valuat_1(A,B),C,D),C,E),k5_valuat_1(A,k6_bvfunc_2(A,k6_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) ) )).

fof(t7_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => r1_bvfunc_1(A,k7_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,D)),C,E),k5_valuat_1(A,k6_bvfunc_2(A,k6_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) ) )).

fof(t8_bvfunc13,axiom,(
    $true )).

fof(t9_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => r1_bvfunc_1(A,k5_valuat_1(A,k6_bvfunc_2(A,k7_bvfunc_2(A,B,C,D),C,E)),k5_valuat_1(A,k7_bvfunc_2(A,k6_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) ) )).

fof(t10_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => r1_bvfunc_1(A,k5_valuat_1(A,k7_bvfunc_2(A,k7_bvfunc_2(A,B,C,D),C,E)),k5_valuat_1(A,k7_bvfunc_2(A,k6_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) ) )).

fof(t11_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k5_valuat_1(A,k7_bvfunc_2(A,k7_bvfunc_2(A,B,C,D),C,E)),k5_valuat_1(A,k6_bvfunc_2(A,k7_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) )).

fof(t12_bvfunc13,axiom,(
    $true )).

fof(t13_bvfunc13,axiom,(
    $true )).

fof(t14_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => r1_bvfunc_1(A,k5_valuat_1(A,k7_bvfunc_2(A,k6_bvfunc_2(A,B,C,D),C,E)),k5_valuat_1(A,k6_bvfunc_2(A,k6_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) ) )).

fof(t15_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => r1_bvfunc_1(A,k5_valuat_1(A,k6_bvfunc_2(A,k7_bvfunc_2(A,B,C,D),C,E)),k5_valuat_1(A,k6_bvfunc_2(A,k6_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) ) )).

fof(t16_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k5_valuat_1(A,k7_bvfunc_2(A,k7_bvfunc_2(A,B,C,D),C,E)),k5_valuat_1(A,k6_bvfunc_2(A,k6_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) )).

fof(t17_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => r1_bvfunc_1(A,k5_valuat_1(A,k7_bvfunc_2(A,k6_bvfunc_2(A,B,C,D),C,E)),k7_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) ) )).

fof(t18_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => r1_bvfunc_1(A,k5_valuat_1(A,k6_bvfunc_2(A,k7_bvfunc_2(A,B,C,D),C,E)),k7_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) ) )).

fof(t19_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k5_valuat_1(A,k7_bvfunc_2(A,k7_bvfunc_2(A,B,C,D),C,E)),k7_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) )).

fof(t20_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => r1_bvfunc_1(A,k5_valuat_1(A,k6_bvfunc_2(A,k7_bvfunc_2(A,B,C,D),C,E)),k6_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) ) )).

fof(t21_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => r1_bvfunc_1(A,k5_valuat_1(A,k7_bvfunc_2(A,k7_bvfunc_2(A,B,C,D),C,E)),k6_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) ) )).

fof(t22_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k5_valuat_1(A,k7_bvfunc_2(A,k7_bvfunc_2(A,B,C,D),C,E)),k7_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) )).

fof(t23_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => k5_valuat_1(A,k7_bvfunc_2(A,k7_bvfunc_2(A,B,C,D),C,E)) = k6_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,E)),C,D) ) ) ) ) ) ) )).

fof(t24_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => r1_bvfunc_1(A,k5_valuat_1(A,k6_bvfunc_2(A,k7_bvfunc_2(A,B,C,D),C,E)),k7_bvfunc_2(A,k7_bvfunc_2(A,k5_valuat_1(A,B),C,E),C,D)) ) ) ) ) ) ) )).

fof(t25_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k5_valuat_1(A,k7_bvfunc_2(A,k7_bvfunc_2(A,B,C,D),C,E)),k7_bvfunc_2(A,k7_bvfunc_2(A,k5_valuat_1(A,B),C,E),C,D)) ) ) ) ) ) )).

fof(t26_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => r1_bvfunc_1(A,k5_valuat_1(A,k6_bvfunc_2(A,k7_bvfunc_2(A,B,C,D),C,E)),k6_bvfunc_2(A,k7_bvfunc_2(A,k5_valuat_1(A,B),C,E),C,D)) ) ) ) ) ) ) )).

fof(t27_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => r1_bvfunc_1(A,k5_valuat_1(A,k7_bvfunc_2(A,k7_bvfunc_2(A,B,C,D),C,E)),k6_bvfunc_2(A,k7_bvfunc_2(A,k5_valuat_1(A,B),C,E),C,D)) ) ) ) ) ) ) )).

fof(t28_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k5_valuat_1(A,k7_bvfunc_2(A,k7_bvfunc_2(A,B,C,D),C,E)),k7_bvfunc_2(A,k6_bvfunc_2(A,k5_valuat_1(A,B),C,E),C,D)) ) ) ) ) ) )).

fof(t29_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => k5_valuat_1(A,k7_bvfunc_2(A,k7_bvfunc_2(A,B,C,D),C,E)) = k6_bvfunc_2(A,k6_bvfunc_2(A,k5_valuat_1(A,B),C,E),C,D) ) ) ) ) ) ) )).

fof(t30_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => r1_bvfunc_1(A,k7_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,D)),C,E),k5_valuat_1(A,k7_bvfunc_2(A,k6_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) ) )).

fof(t31_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k6_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,D)),C,E),k5_valuat_1(A,k7_bvfunc_2(A,k6_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) )).

fof(t32_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k6_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,D)),C,E),k5_valuat_1(A,k6_bvfunc_2(A,k7_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) )).

fof(t33_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => k6_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,D)),C,E) = k5_valuat_1(A,k7_bvfunc_2(A,k7_bvfunc_2(A,B,C,E),C,D)) ) ) ) ) ) ) )).

fof(t34_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => k7_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,D)),C,E) = k7_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,E)),C,D) ) ) ) ) ) ) )).

fof(t35_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => r1_bvfunc_1(A,k6_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,D)),C,E),k7_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) ) )).

fof(t36_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => r1_bvfunc_1(A,k7_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,D)),C,E),k7_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) ) )).

fof(t37_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k6_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,D)),C,E),k7_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) )).

fof(t38_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => r1_bvfunc_1(A,k7_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,D)),C,E),k6_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) ) )).

fof(t39_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => r1_bvfunc_1(A,k6_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,D)),C,E),k6_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) ) )).

fof(t40_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k6_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,D)),C,E),k7_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) )).

fof(t41_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => k6_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,D)),C,E) = k6_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,E)),C,D) ) ) ) ) ) ) )).

fof(t42_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => r1_bvfunc_1(A,k7_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,D)),C,E),k7_bvfunc_2(A,k7_bvfunc_2(A,k5_valuat_1(A,B),C,E),C,D)) ) ) ) ) ) ) )).

fof(t43_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k6_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,D)),C,E),k7_bvfunc_2(A,k7_bvfunc_2(A,k5_valuat_1(A,B),C,E),C,D)) ) ) ) ) ) )).

fof(t44_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => r1_bvfunc_1(A,k7_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,D)),C,E),k6_bvfunc_2(A,k7_bvfunc_2(A,k5_valuat_1(A,B),C,E),C,D)) ) ) ) ) ) ) )).

fof(t45_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => r1_bvfunc_1(A,k6_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,D)),C,E),k6_bvfunc_2(A,k7_bvfunc_2(A,k5_valuat_1(A,B),C,E),C,D)) ) ) ) ) ) ) )).

fof(t46_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k6_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,D)),C,E),k7_bvfunc_2(A,k6_bvfunc_2(A,k5_valuat_1(A,B),C,E),C,D)) ) ) ) ) ) )).

fof(t47_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => k6_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,D)),C,E) = k6_bvfunc_2(A,k6_bvfunc_2(A,k5_valuat_1(A,B),C,E),C,D) ) ) ) ) ) ) )).

fof(t48_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => r1_bvfunc_1(A,k7_bvfunc_2(A,k6_bvfunc_2(A,k5_valuat_1(A,B),C,D),C,E),k5_valuat_1(A,k7_bvfunc_2(A,k6_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) ) )).

fof(t49_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => r1_bvfunc_1(A,k6_bvfunc_2(A,k6_bvfunc_2(A,k5_valuat_1(A,B),C,D),C,E),k5_valuat_1(A,k7_bvfunc_2(A,k6_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) ) )).

fof(t50_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k6_bvfunc_2(A,k6_bvfunc_2(A,k5_valuat_1(A,B),C,D),C,E),k5_valuat_1(A,k6_bvfunc_2(A,k7_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) )).

fof(t51_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => r1_bvfunc_1(A,k6_bvfunc_2(A,k6_bvfunc_2(A,k5_valuat_1(A,B),C,D),C,E),k5_valuat_1(A,k7_bvfunc_2(A,k7_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) ) )).

fof(t52_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => r1_bvfunc_1(A,k7_bvfunc_2(A,k7_bvfunc_2(A,k5_valuat_1(A,B),C,D),C,E),k7_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) ) )).

fof(t53_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => r1_bvfunc_1(A,k6_bvfunc_2(A,k7_bvfunc_2(A,k5_valuat_1(A,B),C,D),C,E),k7_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) ) )).

fof(t54_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => r1_bvfunc_1(A,k7_bvfunc_2(A,k6_bvfunc_2(A,k5_valuat_1(A,B),C,D),C,E),k7_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) ) )).

fof(t55_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k6_bvfunc_2(A,k6_bvfunc_2(A,k5_valuat_1(A,B),C,D),C,E),k7_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) )).

fof(t56_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => r1_bvfunc_1(A,k7_bvfunc_2(A,k6_bvfunc_2(A,k5_valuat_1(A,B),C,D),C,E),k6_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) ) )).

fof(t57_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => r1_bvfunc_1(A,k6_bvfunc_2(A,k6_bvfunc_2(A,k5_valuat_1(A,B),C,D),C,E),k6_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) ) )).

fof(t58_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k6_bvfunc_2(A,k6_bvfunc_2(A,k5_valuat_1(A,B),C,D),C,E),k7_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) )).

fof(t59_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => k6_bvfunc_2(A,k6_bvfunc_2(A,k5_valuat_1(A,B),C,D),C,E) = k6_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,E)),C,D) ) ) ) ) ) ) )).

fof(t60_bvfunc13,axiom,(
    $true )).

fof(t61_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k6_bvfunc_2(A,k7_bvfunc_2(A,k5_valuat_1(A,B),C,D),C,E),k7_bvfunc_2(A,k7_bvfunc_2(A,k5_valuat_1(A,B),C,E),C,D)) ) ) ) ) ) )).

fof(t62_bvfunc13,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => r1_bvfunc_1(A,k7_bvfunc_2(A,k6_bvfunc_2(A,k5_valuat_1(A,B),C,D),C,E),k7_bvfunc_2(A,k7_bvfunc_2(A,k5_valuat_1(A,B),C,E),C,D)) ) ) ) ) ) ) )).
%------------------------------------------------------------------------------