SET007 Axioms: SET007+593.ax


%------------------------------------------------------------------------------
% File     : SET007+593 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Propositional 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_5 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   41 (   1 unit)
%            Number of atoms       :  209 (  69 equality)
%            Maximal formula depth :   13 (   8 average)
%            Number of connectives :  208 (  40 ~  ;   0  |;  11  &)
%                                         (   2 <=>; 155 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    4 (   1 propositional; 0-4 arity)
%            Number of functors    :    7 (   1 constant; 0-3 arity)
%            Number of variables   :  139 (   0 singleton; 139 !;   0 ?)
%            Maximal term depth    :    5 (   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_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ( ( B = k19_bvfunc_1(A)
                  & C = k19_bvfunc_1(A) )
              <=> k6_valuat_1(A,B,C) = k19_bvfunc_1(A) ) ) ) ) )).

fof(t2_bvfunc_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ( ( B = k19_bvfunc_1(A)
                  & k14_bvfunc_1(A,B,C) = k19_bvfunc_1(A) )
               => C = k19_bvfunc_1(A) ) ) ) ) )).

fof(t3_bvfunc_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ( B = k19_bvfunc_1(A)
               => k8_bvfunc_1(A,B,C) = k19_bvfunc_1(A) ) ) ) ) )).

fof(t4_bvfunc_5,axiom,(
    $true )).

fof(t5_bvfunc_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ( C = k19_bvfunc_1(A)
               => k14_bvfunc_1(A,B,C) = k19_bvfunc_1(A) ) ) ) ) )).

fof(t6_bvfunc_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ( k5_valuat_1(A,B) = k19_bvfunc_1(A)
               => k14_bvfunc_1(A,B,C) = k19_bvfunc_1(A) ) ) ) ) )).

fof(t7_bvfunc_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => k5_valuat_1(A,k6_valuat_1(A,B,k5_valuat_1(A,B))) = k19_bvfunc_1(A) ) ) )).

fof(t8_bvfunc_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => k14_bvfunc_1(A,B,B) = k19_bvfunc_1(A) ) ) )).

fof(t9_bvfunc_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ( k14_bvfunc_1(A,B,C) = k19_bvfunc_1(A)
              <=> k14_bvfunc_1(A,k5_valuat_1(A,C),k5_valuat_1(A,B)) = k19_bvfunc_1(A) ) ) ) ) )).

fof(t10_bvfunc_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ( ( k14_bvfunc_1(A,B,C) = k19_bvfunc_1(A)
                      & k14_bvfunc_1(A,C,D) = k19_bvfunc_1(A) )
                   => k14_bvfunc_1(A,B,D) = k19_bvfunc_1(A) ) ) ) ) ) )).

fof(t11_bvfunc_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ( ( k14_bvfunc_1(A,B,C) = k19_bvfunc_1(A)
                  & k14_bvfunc_1(A,B,k5_valuat_1(A,C)) = k19_bvfunc_1(A) )
               => k5_valuat_1(A,B) = k19_bvfunc_1(A) ) ) ) ) )).

fof(t12_bvfunc_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => k14_bvfunc_1(A,k14_bvfunc_1(A,k5_valuat_1(A,B),B),B) = k19_bvfunc_1(A) ) ) )).

fof(t13_bvfunc_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => k14_bvfunc_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,k5_valuat_1(A,k6_valuat_1(A,C,D)),k5_valuat_1(A,k6_valuat_1(A,B,D)))) = k19_bvfunc_1(A) ) ) ) ) )).

fof(t14_bvfunc_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => k14_bvfunc_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,k14_bvfunc_1(A,C,D),k14_bvfunc_1(A,B,D))) = k19_bvfunc_1(A) ) ) ) ) )).

fof(t15_bvfunc_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ( k14_bvfunc_1(A,B,C) = k19_bvfunc_1(A)
                   => k14_bvfunc_1(A,k14_bvfunc_1(A,C,D),k14_bvfunc_1(A,B,D)) = k19_bvfunc_1(A) ) ) ) ) ) )).

fof(t16_bvfunc_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => k14_bvfunc_1(A,C,k14_bvfunc_1(A,B,C)) = k19_bvfunc_1(A) ) ) ) )).

fof(t17_bvfunc_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => k14_bvfunc_1(A,k14_bvfunc_1(A,k14_bvfunc_1(A,B,C),D),k14_bvfunc_1(A,C,D)) = k19_bvfunc_1(A) ) ) ) ) )).

fof(t18_bvfunc_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => k14_bvfunc_1(A,C,k14_bvfunc_1(A,k14_bvfunc_1(A,C,B),B)) = k19_bvfunc_1(A) ) ) ) )).

fof(t19_bvfunc_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => k14_bvfunc_1(A,k14_bvfunc_1(A,D,k14_bvfunc_1(A,C,B)),k14_bvfunc_1(A,C,k14_bvfunc_1(A,D,B))) = k19_bvfunc_1(A) ) ) ) ) )).

fof(t20_bvfunc_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => k14_bvfunc_1(A,k14_bvfunc_1(A,C,D),k14_bvfunc_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,B,D))) = k19_bvfunc_1(A) ) ) ) ) )).

fof(t21_bvfunc_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => k14_bvfunc_1(A,k14_bvfunc_1(A,C,k14_bvfunc_1(A,C,D)),k14_bvfunc_1(A,C,D)) = k19_bvfunc_1(A) ) ) ) ) )).

fof(t22_bvfunc_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => k14_bvfunc_1(A,k14_bvfunc_1(A,B,k14_bvfunc_1(A,C,D)),k14_bvfunc_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,B,D))) = k19_bvfunc_1(A) ) ) ) ) )).

fof(t23_bvfunc_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ( B = k19_bvfunc_1(A)
               => k14_bvfunc_1(A,k14_bvfunc_1(A,B,C),C) = k19_bvfunc_1(A) ) ) ) ) )).

fof(t24_bvfunc_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ( k14_bvfunc_1(A,D,k14_bvfunc_1(A,C,B)) = k19_bvfunc_1(A)
                   => k14_bvfunc_1(A,C,k14_bvfunc_1(A,D,B)) = k19_bvfunc_1(A) ) ) ) ) ) )).

fof(t25_bvfunc_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ( ( k14_bvfunc_1(A,D,k14_bvfunc_1(A,C,B)) = k19_bvfunc_1(A)
                      & C = k19_bvfunc_1(A) )
                   => k14_bvfunc_1(A,D,B) = k19_bvfunc_1(A) ) ) ) ) ) )).

fof(t26_bvfunc_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ( ( k14_bvfunc_1(A,D,k14_bvfunc_1(A,C,B)) = k19_bvfunc_1(A)
                      & C = k19_bvfunc_1(A)
                      & D = k19_bvfunc_1(A) )
                   => B = k19_bvfunc_1(A) ) ) ) ) ) )).

fof(t27_bvfunc_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ( k14_bvfunc_1(A,B,k14_bvfunc_1(A,B,C)) = k19_bvfunc_1(A)
               => k14_bvfunc_1(A,B,C) = k19_bvfunc_1(A) ) ) ) ) )).

fof(t28_bvfunc_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ( k14_bvfunc_1(A,B,k14_bvfunc_1(A,C,D)) = k19_bvfunc_1(A)
                   => k14_bvfunc_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,B,D)) = k19_bvfunc_1(A) ) ) ) ) ) )).

fof(t29_bvfunc_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ( ( k14_bvfunc_1(A,B,k14_bvfunc_1(A,C,D)) = k19_bvfunc_1(A)
                      & k14_bvfunc_1(A,B,C) = k19_bvfunc_1(A) )
                   => k14_bvfunc_1(A,B,D) = k19_bvfunc_1(A) ) ) ) ) ) )).

fof(t30_bvfunc_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ( ( k14_bvfunc_1(A,B,k14_bvfunc_1(A,C,D)) = k19_bvfunc_1(A)
                      & k14_bvfunc_1(A,B,C) = k19_bvfunc_1(A)
                      & B = k19_bvfunc_1(A) )
                   => D = k19_bvfunc_1(A) ) ) ) ) ) )).

fof(t31_bvfunc_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [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))
                     => ( ( k14_bvfunc_1(A,B,k14_bvfunc_1(A,C,D)) = k19_bvfunc_1(A)
                          & k14_bvfunc_1(A,B,k14_bvfunc_1(A,D,E)) = k19_bvfunc_1(A) )
                       => k14_bvfunc_1(A,B,k14_bvfunc_1(A,C,E)) = k19_bvfunc_1(A) ) ) ) ) ) ) )).

fof(t32_bvfunc_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => k14_bvfunc_1(A,k14_bvfunc_1(A,k5_valuat_1(A,B),k5_valuat_1(A,C)),k14_bvfunc_1(A,C,B)) = k19_bvfunc_1(A) ) ) ) )).

fof(t33_bvfunc_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => k14_bvfunc_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,k5_valuat_1(A,C),k5_valuat_1(A,B))) = k19_bvfunc_1(A) ) ) ) )).

fof(t34_bvfunc_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => k14_bvfunc_1(A,k14_bvfunc_1(A,B,k5_valuat_1(A,C)),k14_bvfunc_1(A,C,k5_valuat_1(A,B))) = k19_bvfunc_1(A) ) ) ) )).

fof(t35_bvfunc_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => k14_bvfunc_1(A,k14_bvfunc_1(A,k5_valuat_1(A,B),C),k14_bvfunc_1(A,k5_valuat_1(A,C),B)) = k19_bvfunc_1(A) ) ) ) )).

fof(t36_bvfunc_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => k14_bvfunc_1(A,k14_bvfunc_1(A,B,k5_valuat_1(A,B)),k5_valuat_1(A,B)) = k19_bvfunc_1(A) ) ) )).

fof(t37_bvfunc_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => k14_bvfunc_1(A,k5_valuat_1(A,B),k14_bvfunc_1(A,B,C)) = k19_bvfunc_1(A) ) ) ) )).

fof(t38_bvfunc_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => k5_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,B,C),D)) = k8_bvfunc_1(A,k8_bvfunc_1(A,k5_valuat_1(A,B),k5_valuat_1(A,C)),k5_valuat_1(A,D)) ) ) ) ) )).

fof(t39_bvfunc_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => k5_valuat_1(A,k8_bvfunc_1(A,k8_bvfunc_1(A,B,C),D)) = k6_valuat_1(A,k6_valuat_1(A,k5_valuat_1(A,B),k5_valuat_1(A,C)),k5_valuat_1(A,D)) ) ) ) ) )).

fof(t40_bvfunc_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [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))
                     => k8_bvfunc_1(A,B,k6_valuat_1(A,k6_valuat_1(A,C,D),E)) = k6_valuat_1(A,k6_valuat_1(A,k8_bvfunc_1(A,B,C),k8_bvfunc_1(A,B,D)),k8_bvfunc_1(A,B,E)) ) ) ) ) ) )).

fof(t41_bvfunc_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [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))
                     => k6_valuat_1(A,B,k8_bvfunc_1(A,k8_bvfunc_1(A,C,D),E)) = k8_bvfunc_1(A,k8_bvfunc_1(A,k6_valuat_1(A,B,C),k6_valuat_1(A,B,D)),k6_valuat_1(A,B,E)) ) ) ) ) ) )).
%------------------------------------------------------------------------------